bus voltage ranking and voltage stability enhancement for
TRANSCRIPT
Department of Electrical and Computer Engineering
Bus Voltage Ranking and Voltage Stability Enhancement
for Unbalanced Multiphase Networks
Parachai Juanuwattanakul
This thesis is presented for the Degree of
Doctor of Philosophy
of
Curtin University
February 2012
Declaration
To the best of my knowledge and belief this thesis contains no material previously
published by any other person except where due acknowledgment has been made.
This thesis contains no material which has been accepted for the award of any other
degree or diploma in any university.
Signature: β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.
Date: β¦β¦β¦β¦β¦β¦β¦β¦β¦...
ABSTRACT
Voltage instabilities and subsequent system collapses are considered as growing
concerns in modern multiphase distribution networks as they are progressively
forced to operate closer to their stability limits due to many factors such as increasing
load level, lack of reactive power sources, high installation of single-phase shunt
capacitors and reverse action of voltage control devices. System operators must be
able to quickly identify trouble spots and take corrective steps to avoid critical
voltage collapses. To achieve this, suitable indices must be defined to assess system
security and take corrective control actions when predefined thresholds are reached.
In this regard, the identification and ranking of weak buses in a power system is an
important research area.
The existing conventional bus voltage ranking indices are only defined for single-
phase and balanced three-phase networks. This thesis proposes a new bus voltage
ranking index (VRI) to identify the weakest single-, two- and three-phase buses of
multiphase distribution networks. Then, applications of the proposed bus ranking
index will be tested for enhancing the voltage stability of unbalanced multiphase
distribution networks.
In the first part of this thesis, the definition of conventional voltage ranking indices
are modified and generalized to also include unbalanced and multiphase networks
using symmetrical components. For the first time, the method of symmetrical
components is applied to the three-phase voltages computed from three-phase power
flow. The new index is defined as the ratio of the (fundamental) positive-sequence
voltage at the point of voltage collapse to the positive-sequence voltage at the base-
load source. The former voltage level is determined by increasing the active power
of all loads while keeping power factor constant until the point of voltage collapse is
reached.
In the second part of this thesis, the new VRI is validated through the calculation of
grid losses and PV curves based on positive-sequence voltage. Extensive simulations
of the IEEE 13 and 34 node test feeders are performed using the DIgSILENT
PowerFactory to further validate and compare the performance of the new VRI with
three well-known conventional ranking indices.
In the third part of the thesis, the new VRI is used to identify the weakest three-phase
buses in unbalanced three-phase distribution networks. Then, the index is utilized to
place compensation devices at the weakest buses of the modified unbalanced three-
phase 13 node test feeder to improve voltage stability and increase the maximum
loading factor (MLF) under unbalanced three-phase operating conditions.
In the fourth part of the thesis, static analyses are carried out to demonstrate
applications of the proposed VRI in increasing MLF and improving voltage stability
of multiphase networks under unbalanced loading and/or network conditions. Then,
dynamic simulations are performed to further validate the accuracy of the proposed
VRI and improving voltage stability under dynamic operating conditions.
In the fifth part of the thesis, an online application of the proposed bus ranking is
introduced to identify the weakest buses in multiphase smart grids with plug-in
electric vehicle (PEV) charging stations.
Finally, the proposed voltage ranking and stability enhancement approach are
utilized to improve the performance of multiphase distribution networks by proper
placement and sizing of distributed generator (DG) units such as doubly-fed
induction generators (DFIGs) and single-phase capacitors. An iterative algorithm is
proposed for the placement and sizing of DG units and single-phase capacitors in
multiphase networks to reduce grid losses and increase MLF while keeping all bus
voltages within acceptable limits. The approach consists of utilizing the positive-
sequence voltage ratio Vcollapse/Vbase-load to identify the weakest three-phase and
single-phase buses for the installation of DG units and shunt capacitors, respectively.
DG penetration levels are increased (e.g., 40%) by evaluating their impacts on
voltage profile, grid losses, and voltage stability margin while considering the
voltage limits at all buses. The impacts of DIFG on voltage profile, active power
loss, MLF and voltage unbalance factor are highlighted.
DEDICATION
To my parents, Mamie and Papa, as well as my brother and sister for their endless
support and love.
ACKNOWLEDGMENT
I would like to express my special thanks to my supervisor, Associate Professor
Mohammad A.S. Masoum, for his invaluable advice, guidance and support all
throughout my PhD studies. I am also greatly thankful to my co-supervisor,
Professor Syed M. Islam for his assistance during the course of my study. Finally,
financial support from Sripatum University is gratefully acknowledged. Last but not
least, I wish to express my love and gratitude to my family and friends for their
endless support and love.
TABLE OF CONTENTS
Abstract ................................................................................................................... ii
Table of Contents ................................................................................................... vi
Chapter 1. Introduction .......................................................................................... 1
1.1 Statement of the problem ........................................................................... 1
1.2 Literature review ...................................................................................... 2
1.2.1 Bus ranking approaches for balanced networks .................................. 2
1.2.2 Existing bus ranking approaches for unbalanced networks ................. 7
1.2.3 Voltage stability enhancement by connecting compensation devices
considering grid losses and MLFβ¦β¦β¦β¦β¦β¦β¦β¦.. ............................... 7
1.3 Research objectives .................................................................................. 10
1.4 Thesis structure ....................................................................................... 11
1.5 List of publications .................................................................................. 12
Chapter 2. Proposed bus voltage ranking index (VRI) for multiphase
distribution networks ............................................................................................ 14
2.1 Introduction ............................................................................................. 14
2.2 Conventional VRI for balanced networks ................................................. 14
2.3 Derivation of proposed VRI for balanced networks .................................. 16
2.4 Proposed VRI for unbalanced multiphase distribution networks ............... 17
2.5 Derivation of proposed VRI for unbalanced multiphase networks ............. 18
2.6 Conclusions ........................................................................................... 20
Chapter 3. Validation of the proposed VRI ........................................................ 22
3.1 Introduction ............................................................................................. 22
3.2 Validation of proposed VRI using grid loss calculationsβ¦β¦β¦................ 22
3.3 Validation of proposed VRI using PV curves β¦β¦β¦.. ............................. 23
3.4 Validation of proposed VRI using voltage sensitivity indices..β¦.. ............ 23
3.4.1 Bus ranking based on sensitivity of voltage to reactive power
(V/Q)β¦β¦β¦β¦β¦β¦β¦β¦. .................................................................... 24
3.4.2 Bus ranking based on sensitivity of voltage to active power
(V/P)β¦β¦β¦β¦β¦β¦β¦β¦. ..................................................................... 24
3.5 Detailed simulation of IEEE multiphase 13 node test feeder to validate
proposed VRIβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .................. 24
3.5.1 Identification of the weakest buses using proposed VRI for the IEEE
multiphase 13 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦26
3.5.1.1 Bus ranking without/with a voltage regulator (Cases 1 and
2)β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦..β¦β¦.β¦β¦β¦.β¦27
3.5.1.2 Bus ranking with DG at the most suitable bus
(Case 5 )β¦β¦β¦β¦β¦β¦β¦β¦β¦...β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦...28
3.5.1.3 Bus ranking with DG and SVC (Case 6) .β¦β¦β¦β¦.β¦β¦β¦.30
3.5.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 13 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦..30
3.5.2.1 Grid losses with one DG Unit for the IEEE multiphase 13
node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦.β¦β¦β¦30
3.5.2.2 Grid losses with two DG Units for the IEEE multiphase 13
node test feeder β¦β¦β¦β¦β¦β¦β¦..β¦...β¦β¦β¦β¦β¦β¦β¦.β¦.β¦β¦..32
3.5.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 13 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦32
3.5.4 Comparison of proposed VRI with other bus ranking
approaches for the IEEE multiphase 13 node test feeder .....................β¦...34
3.6 Detailed simulation of IEEE multiphase 34 node test feeder to validate
proposed VRIβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ .......... 37
3.6.1 Identification of the weakest buses using proposed VRI for the IEEE
multiphase unbalanced 34 node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.39
3.6.1.1 Bus ranking without/with a voltage regulator
(Cases 8 and 9) .β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦40
3.6.1.2 Bus ranking with an induction generator DG unit at the
most suitable bus (Case 10)β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦40
3.6.1.3 Bus ranking with a 200kW DFIG wind turbine DG unit at
the most suitable bus (Case 11)β¦β¦β¦β¦β¦β¦.β¦β¦...β¦β¦β¦β¦.β¦.41
3.6.1.4 Bus ranking with a 2.4 MW DFIG wind turbine DG unit
(Case 12) β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦...β¦...β¦β¦.β¦β¦β¦β¦β¦β¦.45
3.6.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 34 node test feeder ........................................................ 46
3.6.2.1 Grid losses with one DG Unit for the IEEE multiphase 34
node test feeder .β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦46
3.6.2.2 Grid losses with two DG Units for the IEEE multiphase 34
node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦..47
3.6.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 34 node test feeder .................................................................. 47
3.6.4 Comparison of proposed VRI with other bus ranking
approaches for the IEEE multiphase 34 node test feeder............................48
3.7 Conclusions ........................................................................................... 51
Chapter 4. Validation and application of proposed VRI in improving voltage
stability of unbalanced three-phase networks...................................................... 52
4.1 Introduction ........................................................................................... 52
4.2 Detailed simulation of of modified IEEE unbalanced three-phase 13
node test feeder to validate proposed VRIβ¦β¦β¦. .................................... 52
4.2.1 Identification of weakest three-phase buses using the proposed VRI
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦ 54
4.2.1.1 Bus ranking without/with a voltage regulator ........β¦β¦β¦β¦54
4.2.1.2 Bus ranking with DG at the most suitable bus .............β¦β¦..55
4.2.1.3 Bus ranking with DG and SVCβ¦β¦β¦β¦β¦β¦β¦..β¦β¦β¦.....56
4.2.2 Validation of proposed VRI based on grid loss calculations β¦..........58
4.2.2.1 Grid losses with one DG unitβ¦β¦β¦β¦β¦β¦..........β¦β¦β¦β¦58
4.2.2.2 Grid losses with two DG unitsβ¦β¦β¦β¦β¦β¦..............β¦β¦..59
4.2.3 Validation of proposed VRI based on PV curvesβ¦β¦β¦β¦β¦.......... . 59
4.3 Application of proposed VRI in improving MLF of the modified
unbalanced three-phase 13 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. ... 61
4.3.1 Enhancement of MLF by optimal sizing of one DG Unitβ¦β¦........... 62
4.3.2 Improving MLF by placement and sizing of compensation devices
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦. ... 63
4.4 Conclusions ........................................................................................... 64
Chapter 5. Application of proposed VRI in improving voltage stability of
multiphase networks ............................................................................................. 65
5.1 Introduction ........................................................................................... 65
5.2 Application of proposed VRI in improving static voltage stability of the
IEEE 13 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. ...................... 65
5.2.1 Enhancement of MLF by optimal sizing of one compensation device
in of the IEEE 13 node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ ..................... 67
5.2.2 Improving MLF by placement and sizing of compensation devices in
the IEEE 13 node test feeder ........................................................................68
5.3 Application of proposed VRI in improving static voltage stability of the
IEEE 34 node test feederβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦. ........................... 69
5.3.1 Enhancement of MLF by optimal sizing of one compensation device
in the IEEE 34 node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦71
5.4 Application of Proposed VRI in improving dynamic voltage stability of
the IEEE 13 node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. ................ 73
5.5 Application of Proposed VRI in improving dynamic voltage stability of
the IEEE 34 node test feeder β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. ................ 77
5.6 Conclusions ........................................................................................... 80
Chapter 6. Online bus voltage ranking in unbalanced multiphase smart grid
with plug-in electric vehicle (PEV) charging stations .......................................... 82
6.1 Introduction ......................................................................................... 82
6.2 The modified IEEE 13 node test system with PEV charging stations ........ 83
6.3 Simulation results .................................................................................. 84
6.4 Online placement of SVC units to improve the performance of the
modified IEEE 13 node test system with PEV charging stations
β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. ............................................................. 92
6.5 Conclusions ......................................................................................... 95
Chapter 7. Increasing DG penetration in multiphase distribution networks
considering grid losses, MLF and bus voltage limits ........................................... 96
7.1 Introduction ......................................................................................... 96
7.2 Impacts of DG placement on voltage profile, grid loss, and
MLFβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. ...... 97
7.2.1 Impact of DG on voltage profiles ..................................................... 97
7.2.2 Impact of DG on grid losses ............................................................. 97
7.2.3 Impact of DG on MLF ..................................................................... 97
7.2.4 Impact of DG on voltage unbalance factor ....................................... 98
7.3 Proposed algorithm for DG placementβ¦β¦β¦β¦β¦. .................................. 98
7.4 Simulation results .............................................................................. 100
7.4.1 Bus voltage ranking based on proposed VRI index ........................ 100
7.4.2 Placement and sizing of DG units to improve voltage profile, grid loss,
and MLFβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦ 100
7.4.3 Placement and sizing of single-phase capacitor banks to further
improve voltage profile, grid loss, and MLFβ¦β¦β¦β¦β¦β¦β¦β¦β¦β¦β¦.. 104
7.4.4 Summary and analysis of simulation results ................................... 106
7.5 Conclusions ......................................................................................... 107
Chapter 8. Conclusions ....................................................................................... 109
8.1 Contributions ..................................................................................... 111
8.2 Future works ..................................................................................... 111
References ........................................................................................................... 112
Appendix A β The IEEE 13 node and 34 node test systems .............................. 118
Appendix B β Simulation parameters ............................................................... 138
Appendix C β DIgSILENT PowerFactory [32] ................................................. 140
Appendix D β Paper published in Elixir journal .............................................. 141
TABLE OF FIGURES
Figure β2-1 Equivalent circuit of a two bus balanced network. --------------------------14
Figure β2-2 PV curve based on positive-sequence voltages.------------------------------17
Figure β2-3 An unbalanced multiphase distribution system; network configuration
consisting of four nodes with single-, two-, and three-phase sections. ---------- 19
Figure β2-4 The equivalent unbalanced three-phase four-wire network for the
unbalanced multiphase distribution system of Fig. 2-3.---------------------------- 19
Figure β3-1 The IEEE multiphase 13 node test feeder.------------------------------------25
Figure β3-2 Bus ranking for Case 1 (without any voltage regulators). ----------------- 27
Figure β3-3 Bus ranking for Case 2 (with a voltage regulator). ------------------------- 27
Figure β3-4 Bus ranking for Case 5 (with one DG at bus 675). ------------------------- 29
Figure 3-5 Bus ranking for Case 6 (with one DG and one SVC at bus 675). --------30
Figure β3-6 Reactive and active power losses associated with DG connections at
different buses of Figure 3-1 (Case 2).----------------------------------------------- 31
Figure β3-7 Reactive and active power losses associated with the first DG installed at
bus 675 and the second DG connected at different buses of Figure 3-1 (Case 5).-
------------------------------------------------------------- ------------------------------- 32
Figure β3-8 PV curves of positive-sequence voltage at each three-phase bus for
Case 2.------------------------------------------------------------------------------------- 33
Figure β3-9 PV curves of positive-sequence voltage at each two-phase bus for
Case 2.------------------------------------------------------------------------------------- 33
Figure β3-10 PV curves of positive-sequence voltage at each single-phase bus for
Case 2.------------------------------------------------------------------------------------- 34
Figure β3-11 PV curves of positive-sequence voltage at each bus for Case 6.--------- 34
Figure β3-12 PV curves of positive-sequence voltages at buses 634 and 675 for the
modified IEEE 13 node network (Figure 3-1) with only unbalanced three-phase
networks/loads.-------------------------------------------------------------------------- 37
Figure β3-13 The IEEE multiphase 34 node test feeder. ----------------------------------38
Figure β3-14 Bus ranking for Case 8 (without any voltage regulators). ---------------- 40
Figure β3-15 Bus ranking for Case 9 (with a voltage regulator). ------------------------ 40
Figure β3-16 Bus ranking for Case 10 (with a DG type induction generator at bus
890).--------------------------------------------------------------------------------------- 40
Figure β3-17 Bus ranking for Case 11 (with a DFIG wind turbine DG unit at bus
890).------------------------------------------------------------------------------------- -- 41
Figure 3-18 Bus ranking for Case 12 (with DFIG wind turbines at bus 890). --------46
Figure β3-19 Active power loss associated with DG connections at different buses of
Figure 3-1 (Case 9).--------------------------------------------------------------------- 47
Figure β3-20 Active power loss associated with the first DG installed at bus 890 and
the second DG connected at different buses of Figure 3-13 (Case 10).-------------
--------------------------------------------------------------------------------------------- 47
Figure β3-21 PV curves of positive-sequence voltage at each three-phase bus for Case
9.------------------------------------------------------------------------------------------- 49
Figure β3-22 PV curves of positive-sequence voltage at each single-phase bus for
Case 9.-------------------------------------------------------------------------------------49
Figure β3-23 PV curves of positive-sequence voltage at each bus for Case 12.-----------
--------------------------------------------------------------------------------------------- 50
Figure 4-1 The modified unbalanced three-phase 13 node test feeder.---------------- 53
Figure β4-2 Bus ranking for Case 1 (without any voltage regulators). ----------------- 55
Figure β4-3 Bus ranking for Case 2 (with a voltage regulator). ------------------------- 55
Figure β4-4 Bus ranking for Case 3 (with one DG at bus 675). ------------------------- 55
Figure 4-5 Bus ranking for Case 4 (with one DG and one SVC at bus 675). ---------57
Figure 4-6 Reactive and active power losses associated with DG connections at
different buses of Figure 4-1 (Case 2).----------------------------------------------- 59
Figure β4-7 Reactive and active power losses associated with the first DG installed at
bus 675 and the second DG connected at different buses of Figure 4-1 (Case 3).-
------------------------------------------------------------- ------------------------------- 59
Figure β4-8 PV curves of positive-sequence voltage at each three-phase bus for
Case 2.------------------------------------------------------------------------------------- 60
Figure β4-9 PV curves of positive-sequence voltage at each bus for Case 4.-----------61
Figure β4-10 MLF as a function of the number of DG units placed at the weakest node
(bus 675).------------------------------------------------ -------------------------------- 63
Figure β4-11 Simulation results for placement and sizing of DG units in the modified
unbalanced three-phase 13 node feeder (Figure 4-1).-------------------- ---------- 63
Figure 5-1 MLF (for the IEEE 13 node test feeder) as a function of shunt capacitor
size at the weakest single-phase node (bus 611).------------------------------------ 68
Figure β5-2 MLF (for the IEEE 13 node test feeder) as a function of the number of
DG units placed at the weakest three-phase node (bus 675).---------------------- 68
Figure β5-3 Simulation results for placement and sizing of DG units in the unbalanced
IEEE 13 node test feeder (Figure 3-1).----------------------------------------------- 69
Figure β5-4 MLF (for the IEEE 13 node test feeder) as a function of shunt capacitor
size at the weakest single-phase node (bus 684).-------------------- --------------- 72
Figure β5-5 MLF (for the IEEE 13 node test feeder) as a function of the number of
DG units (DFIG wind turbines) placed at the weakest three-phase node (bus
890).--------------------------------------------------------------------------------------- 73
Figure β5-6 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 2 (Table 5-1).---------------------------------------------------- 74
Figure β5-7 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 5 (Table 5-1).---------------------------------------------------- 75
Figure β5-8 Voltage profiles of bus 675 under switch operation of Case 5 (Table 5-1).-
--------------------------------------------------------------------------------------------- 75
Figure β5-9 Active and reactive power of DG at bus 675 under switch operation of
Case 5 (Table 5-1).---------------------------------------------------------------------- 76
Figure β5-10 Active and reactive power of DG installed at bus 675 (of the IEEE 13
node test feeder)with/without SVC after switch closed at time 0.67s.------------- 76
Figure β5-11 Comparison of VRI values for dynamic operating conditions in the IEEE
13 node test feeder.------------------------------------------------------ --------------- 77
Figure β5-12 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 9 (Table 5-2).---------------------------------------------------- 78
Figure β5-13 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 10 (Table 5-2).-------------------------------------------------- 78
Figure β5-14 Voltage profiles of bus 890 under circuit breaker operation of Case 10
(Table 5-2).------------------------------------------------------------------------------- 79
Figure β5-15 Active and reactive power of DG at bus 890 under circuit breaker
operation of Case 10 (Table 5-2).----------------------------------------------------- 79
Figure β5-16 Active and reactive power of DG installed at bus 890 (of the IEEE 34
node test feeder) with/without SVC after circuit breaker closed at time 0.54s.----
--------------------------------------------------------------------------------------------- 80
Figure β5-17 Comparison of VRI values for dynamic operating conditions in the IEEE
34 node test feeder.---------------------------------------------------------------------- 80
Figure β6-1 The unbalanced multiphase 13 node test feeder with PEV charging
stations at bus 634 or bus 680.--------------------------------------------------------- 84
Figure β6-2 Daily load curves associated with Figure 6-1 for linear loads [45]. ------ 86
Figure β6-3 Daily load curves associated with Figure 6-1 for PEV charging stations
[36].---------------------------------------------------------------------------------------- 86
Figure β6-4 Simulation results for Case 1: the 24 hour voltage profile of buses 634,
675 and 680.------------------------------------------------------------------------------ 87
Figure β6-5 Simulation results for Case 2: the 24 hour voltage profile of buses 634,
675 and 680.------------------------------------------------------------------------------ 87
Figure β6-6 Simulation results for Case 3: the 24 hour voltage profile of buses 634,
675 and 680.------------------------------------------------------------------------------ 88
Figure β6-7 Simulation results for Case 4: the 24 hour voltage profile of buses 634,
675 and 680.----------------------------------------------------------------------------- 88
Figure β6-8 Simulation results for Case 5 with online placement of two SVC units:
the 24 hour voltage profile of buses 634, 675 and 680.---------------------------- 93
Figure β7-1 The proposed algorithm for the placement and sizing of DG units and
single-phase capacitors in multiphase networks.------------------------------------ 99
Figure β7-2 Simulation results for the first DG placement (stage one, iteration one);
voltage ranking index with no DFIG installation (base-case load).------------- 101
Figure β7-3 Simulation results for the first DG placement (stage one, iteration one);
loading factor and active power loss with different DG penetrations at bus 890.-
-------------------------------------------------------------------------------------------- 101
Figure β7-4 Voltage profile with 40% DG penetration at bus 890. --------------------101
Figure β7-5 Simulation results for the first DG placement (stage one, iteration one);
voltage profile with 30% DFIG penetration at bus 890.-------------------------- 102
Figure β7-6 Simulation results for the second DG placement (stage one, iteration two);
voltage ranking index with 30% DFIG units installed at bus 890.-------------- 103
Figure β7-7 Simulation results for the second DG placement (stage one, iteration two);
loading factor and active power loss with 30% DFIG penetration at bus 890 and
different DFIG penetration at bus 852.---------------------------------------------- 103
Figure β7-8 Simulation results for the second DG placement (stage one, iteration two);
voltage profile with 30% DFIG penetration at bus 890 and 30% DFIG
penetration at bus 852.---------------------------------------------------------------- 104
Figure β7-9 Simulation results for the third DG placement (stage one, iteration three)
showing voltage ranking index with 30% DFIG units installed at bus 890 and
30% DFIG at bus 852.----------------------------------------------------------------- 105
Figure β7-10 Simulation results for the single-phase capacitor placement (stage two,
iteration one); voltage ranking index with 30% DG units installed at bus 890,
30% DG at bus 852, and single-phase shunt capacitor 0.273MVAr at bus 822.---
-------------------------------------------------------------------------------------------- 105
Figure β7-11 Simulation results for the single-phase capacitor placement (stage two,
iteration one); voltage profile with 30% DG penetration at bus 890, 30% DG
penetration at bus 852, and single-phase 0.273MVAr shunt capacitor at bus
822.---------------------------------------------------------------------------------------106
Figure β7-12 Comparison of %VUF at different iterations of the proposed algorithm
(Figure 7-1).-----------------------------------------------------------------------------107
LIST OF TABLES
Table β3-1 Simulated case studies for the IEEE multiphase 13 node test feeder (Fig. 3-
1).------------------------------------------------------------ ----------------------------- 26
Table β3-2 Bus ranking for cases 1 and 2 based on the proposed VRI.----------------- 28
Table β3-3 Bus ranking for case 5 based on the proposed VRI.--------------------------29
Table β3-4 Bus ranking for case 6 based on the proposed VRI.--------------------------31
Table β3-5 Bus ranking results for the IEEE 13 node network with only unbalanced
three-phase networks/loads.------------------------------------------------------------ 36
Table β3-6 Bus ranking results for the IEEE 13 node test feeder (Fig. 3-1) with only
unbalanced three-phase networks/loads.------------------------------------------ --- 36
Table β3-7 Maximum loading factors with SVC.------------------------------------------ 37
Table β3-8 Simulated case studies for the IEEE 34 node test feeder (Fig. 3-13).------ 39
Table β3-9 Bus ranking for cases 8 and 9 based on the proposed VRI.----------------- 42
Table β3-10 Bus ranking for case 10 based on the proposed VRI. ----------------------43
Table β3-11 Bus ranking for case 11 based on the proposed VRI. ----------------------44
Table β3-12 Bus ranking for case 12 based on the proposed VRI.----------------------- 45
Table β3-13 Bus ranking results for the multiphase IEEE 34 node network. ---------- 50
Table β4-1 Simulated case studies for the modified unbalanced three-phase 13 node
test feeder (Fig. 4-1). ------------------------------------ ------------------------------ 54
Table β4-2 Bus ranking for cases 1 and 2 based on the proposed VRI.----------------- 56
Table β4-3 Bus ranking for case 3 based on the proposed VRI. -------------------------57
Table β4-4 Bus ranking for case 4 based on the proposed VRI. -------------------------58
Table β4-5 Simulation results of the modified unbalanced three-phase 13 node test
feeder (Fig. 4-1, Table 4-1): comparison of MLF without/with regulator, DG
and SVC.---------------------------------------------------------------------------------- 62
Table β5-1 Simulation results of the IEEE 13 node test feeder (Fig. 3-1, Table 3-1):
comparison of MLF without/with regulator, single-phase shunt capacitor, DG
and SVC. -------------------------------------------------------- ------------------------ 66
Table β5-2 Simulation results of the IEEE 34 node test feeder (Fig. 3-13, Table 3-1):
comparison of MLF without/with regulator, DG types IG and DFIG. ---------- 70
Table β5-3 Simulation results of the IEEE 34 node test feeder (Fig. 3-1): comparison
of MLF with single-phase shunt capacitor placed at different buses. ------------71
Table β5-4 MLF (for the IEEE 34 node test feeder) as a function of the number of DG
units (IGs) placed at the weakest three-phase node (bus 890). -------------- ----- 72
Table β6-1 Case 2 - Bus voltage ranking indices over 24 hours with four PEV
charging stations at bus 634.----------------------------------------------------------- 89
Table β6-2 Case 3 - Bus voltage ranking index for the multiphase system of Figure 6-1
with four PEV charging stations at bus 680.----------------------------------------- 90
Table β6-3 Case 4 - Bus voltage ranking index for the multiphase system of Figure 6-1
with four PEV charging stations at bus 680 and two PEV charging stations at
bus 634.---------------------------------------------------------------------------------- - 91
Table β6-4 Case 5 with online placement of two SVC units - Bus voltage ranking
index for the multiphase system of Figure 6-1.-------------------------------------- 94
Table β7-1 Detailed solution for DFIG and capacitor placement and sizing in the IEEE
multiphase 34 node test feeder (Figure 3-13) using the proposed algorithm of
Figure 6-1.-------------------------------------------------------------------------------108
List of abbreviations
ALR Active power loss reduction
CPF Continuation power flow
CS Charging station
DG Distributed generator
DFIG Doubly-fed induction generator
DVCI Dynamic voltage collapse index
IG Induction generator
MLF Maximum Loading Factor
PEV Plug-in electric vehicle
RLR Reactive power losses reduction
SVC Static VAR compensators
TPSI Transfer power stability index
VCPI Voltage collapse predictor indicator
VR Voltage regulator
VRI Voltage ranking index
VUF Voltage unbalance factor
List of symbols
Vectors and parameters
B, R, X, Y, Z Susceptance, resistance, reactance, admittance and impedance.
P, Q, S, V Real power, reactive power, complex power and voltage.
Phase angle.
πΌ Phase angle of the load impedance.
π½ Phase angle of the Thevenin impedance.
Subscripts
Base-load Base-load condition.
Collapse The point of voltage collapse.
i, j,k,m,N Bus number.
No-load No-load condition.
Thev Thevenin.
Superscripts
+ Positive-sequence.
* Complex conjugate operator.
init Initial operating state
limit Voltage stability limit
1
Chapter 1. Introduction
1.1 STATEMENT OF THE PROBLEM
Modern distribution networks are being operated closer to their voltage stability
limits due to many factors such as increasing load levels [1], lack of reactive power
sources [2], high installation of single-phase shunt capacitors [3] and reverse action
of voltage control devices [4]. Under these stressed operating conditions, voltage
instability and voltage collapse may occur if suitable monitoring and control
measures are not engaged.
The analyses of voltage stability are divided in two categories depending on the type
of disturbance; static approaches based on the power flow calculation and dynamic
approaches based on time-domain simulation. Static analyses are simple and fast
solutions widely used to identify the weakest buses and determine voltage stability
margins for small disturbances. However, dynamic analyses for large disturbances
should also be performed and compared to verify the results of static approaches [5]-
[7].
Unbalanced operation of distribution networks significantly decreases the voltage
stability margins. Analyses of unbalanced networks indicate that there is at least one
phase with clockwise rotation (e.g., as the load levels increase on the PV curves, the
voltage magnitudes decrease) and much lower voltage level than the other two
phases [9]. This considerably complicates the voltage stability analysis of unbalanced
and multiphase networks. Therefore, it is very complicated to rank the buses and
identify the weakest bus under different voltage level and phase-voltage stability
margins unless these conditions are somehow merged to simplify the procedure.
This thesis proposes a new voltage ranking index (VRI) based on the (fundamental)
positive- sequence voltage ratio of Vcollapse/Vbase-load to identify the weakest single-,
two- and three-phase buses in unbalanced and multiphase distribution networks. The
proposed VRI is compared with three conventional indices and validated by grid loss
2
calculations and PV curves. Further validations of the new index are presented
through extensive simulations of the IEEE unbalanced multiphase 13 node and 34
node test feeders without/with voltage regulators, single-phase shunt capacitors,
distribution generations (DGs) and static VAR compensators (SVCs). Finally,
simulations are performed to demonstrate the application of the new VRI in
increasing maximum loading factor (MLF) and improving voltage stability under
static and dynamic operating conditions.
1.2 LITERATURE REVIEW
In this section, a comprehensive literature review is carried out to (1) examine
different existing approaches to rank the buses for balanced networks, (2) study the
sensitivity method proposed to rank the buses for unbalanced networks, (3)
investigate voltage stability enhancement by connecting compensation devices
considering grid losses and MLF.
1.2.1 Bus ranking approaches for balanced networks
In balanced networks, there are several techniques based on static approaches to
identify the weakest bus. The current bus ranking approaches include:
Modal analysis [5-6], [9-10], [14]- In this method the eigenvalues and
eigenvectors of the reduced Jacobian matrix are first calculated. The
magnitudes of the eigenvalues are then used to provide a relative proximity of
the system to voltage instability. Positive eigenvalues represent voltage
stability of system and the smaller the magnitude, the closer the relevant
modal voltage is to being unstable. Finally, the weakest bus of the system is
determined by computing the eigenvector for different buses in the system.
The node with the highest eigenvector is identified as the weakest bus of the
system. This method is very useful as it provides a relative proximity of the
system to voltage instability, as well as the key contributing factors to
instability such as the weakest buses and branches. However, the approach is
based on the assumption that the active power is kept constant and can only
be applied to balanced systems. When the system is under stressed, both
dV/dQ and dV/dP are important parameters to determine the stability of the
3
system. Therefore, this method can be invalid when the system is under stress
conditions.
Sensitivity analysis [6], [14]- This method is based on the relative sensitivity
of voltage magnitude with respect to the reactive power. Load flow
calculations are utilized to compute the relationship between voltage changes
and reactive power changes at different buses (dV/dQ). The magnitude of the
sensitivity index becomes large when the system is close to MLF. Therefore,
the weakest bus is classified as the one with the maximum value of the
voltage sensitivity index. However, according to reference [14] the
magnitudes of the sensitivities for different system conditions may not
accurately provide a direct measure of the relative degree of stability.
The V/V0 index [10-11]- This conventional and well-known index is based on
the ratio of the voltage magnitude at certain load obtained from load flow
study to the voltage magnitude at an identical state but with all the loads set
to zero. This index allows immediate detection of the weakest bus and
corrective action can be taken to prevent the voltage instability. In this
proposal, both the magnitude and phase of bus voltage will be applied to
modify this index and extend its application to multiphase networks using
symmetrical components.
Bus voltage change index [12]- A bus voltage change index is defined for
each load bus as:
ππΆπ =ππ
ππππ‘ βπππππππ‘
πππππππ‘ (1-1)
where ππππππ‘ and ππ
πππππ‘ are the voltage magnitudes at bus i at the initial
operating state and at the voltage stability limit, respectively. The order of the
bus ranking can be sorted based on this index. The largest bus voltage change
index will correspond to the weakest bus.
L index [10]- This index calculates the distance between the present state of
the system and the stability limit. L-index describes the stability of the
complete system as it varies from 0 to 1 corresponding to no load and voltage
4
collapse conditions, respectively. Buses with highest index values are
identified as the weakest buses in the system.
Reactive power margin [48]- Reactive power margin of load buses is
determined as a margin between the voltage axis and the lowest MVAr point
of the Q-V curve. This index indicates how further the loading on a particular
bus can be increased before its loading limit is exhausted and voltage collapse
takes place. Reference [11] proves that reactive power margin is a suitable
index to identify the weakest bus irrespective of the load pattern in a
distribution system.
PV curve [6], [10-11], [14]- PV curve is generated by calculating a series of
power flow calculations. With a load increasing, its voltage magnitude will
become lower until reaching a point of voltage collapse. This curve can be
utilized to determine voltage stability margins. The margin between the
voltage collapse point and the current operating point can be used as an index
for bus ranking. The weakest bus is identified as the bus with the lowest
voltage stability margin.
QV curve [6], [10-11]- This curve is also generated by calculating a series of
power flow. With the help of QV curve, it is possible for the operators to
know the maximum reactive power that can be compensated before reaching
minimum voltage limit. The MVAr distance from the operating point to the
bottom of the QV curve is called the reactive power margin. QV curve can be
used as an index for voltage stability limit. The bus, which has the lowest
margin of reactive power, is the weakest bus in the system.
Integrated bus voltage change index with reactive power margin [13]- This
method combines the bus voltage change index with the reactive power
margin index. The bus with largest value of the two indices is identified as
the weak buses.
For dynamic analyses of balanced networks, the following indices can be used to
predict and indicate voltage collapse:
5
Voltage collapse prediction index (VCPI) [14]- The voltage magnitude and
voltage angle information of the participating buses in the system and the
network admittance matrix are required to calculate this index and predict
voltage collapse. The technique relies on basic power flow equations to
compute voltage phasors and the network admittance matrix and calculate the
VCPI index at every participating bus. The voltage collapse prediction index
at bus k is obtained as:
ππΆππΌπ =
1 β
πππ
πππππ=1
πβ π
π
π =1π β π
ππ
ππ
(1-2)
where N is the number of participating buses; j, k, and m are positive integer
numbers; πππ is the admittance between buses k and m;πππ is the admittance
between buses k and j; ππ is the voltage phasor at bus m; and ππ is the
voltage phasor at bus k.
The VCPI index varies from 0 to 1. The values of this index determine the
proximity to voltage collapse at a bus. The buses with VCPI index values of 0
are stable while a bus with an index value of 1 is experiencing a voltage
collapse.
Power transfer stability index (PTSI) [15]- The PTSI is calculated at every
bus by using information of the load apparent power, Thevenin voltage,
Thevenin impedances and phase angles of the load. The PTSI requires
voltage phasor information of the participating buses in a system and network
admittance matrix:
ππππΌ = 2ππΏπππππ£ (1+cos (π½βπΌ))
πΈππππ£2 (1-3)
where ππΏ is the load apparent power, πππππ£ is the Thevenin impedance,
πΈππππ£ is the Thevenin voltage, πΌ is the phase angle of the load impedance,
and π½ is the phase angle of the Thevenin impedance.
6
The value of PTSI will vary between 0 and 1. When PTSI value reaches 1, it
indicates that a voltage collapse has occurred. Compared to VCPI, PTSI is
more sensitive in detecting dynamic voltage collapse because its value will be
very near to unity during a collapse condition. Therefore, the PTSI index can
be considered to be a more accurate indicator compared to the VCPI for
voltage collapse prediction.
Dynamic voltage collapse index (DVCI) [16]- The DVCI is implemented by
measuring power and voltage at the sending end:
π·ππΆπΌ =ππ
2 β π ππ ππ + πππ ππ + π ππ2 +πππ
2 (ππ2+ππ
2 )
2(πππ ππ β π ππ ππ )2 (1-4)
where ππ is the magnitude of voltage at sending bus i, π ππ is the resistance
between buses i and j, πππ is the reactance between buses i and j, ππ is the
active power flowing at receiving bus j, and ππ is the reactive power flowing
at receiving bus j.
When the power-flow equations are solvable, this index is greater than or
equal to 1.0. The index equals 1.0 when the system is reaching the maximum
loading level. On loading the feeder more than its capacity, the index assumes
a value less than 1.0.
The bus ranking problem becomes very complicated under unbalanced and
multiphase operating conditions and has not been addressed in the literature. None of
the above-mentioned indices for dynamic analysis and prediction of voltage collapse
identifies the weakest bus of the system. In term of static voltage stability analysis,
all above-mentioned bus ranking indices are only capable of identifying the weakest
buses of balanced systems and do not apply to unbalanced and multiphase networks.
Therefore, there is much need and interest to define a reliable bus ranking index for
unbalanced and multiphase networks that may be used for static and dynamic
analyses. In this proposal, definition of the V/V0 index will be modified by including
both the voltage magnitude and the voltage phase information and its application will
be extended to unbalanced and multiphase networks using symmetrical components.
7
1.2.2 Existing bus ranking approaches for unbalanced networks
Many three-phase continuation power flow (CPF) methods have been used to
analyze voltage stability margins of unbalanced distribution networks [8, 17-19]. The
usual approach is to run three-phase power flow and generate PV curves by
increasing the active power at selected loads. Reference [18] shows that PV curves of
phases βbβ and βcβ at bus 675 in the IEEE 13 node test feeder (Fig. 3-1) have counter-
clockwise rotations while phase βaβ has a clockwise rotation. In addition, the PV
curves for the unbalanced networks and/or unbalanced loads have shown different
voltage stability margins on each phase. Reference [19] applies the voltage
sensitivities index V/P associated with the maximum loading factor (MLF) to
perform stability analysis on unbalanced three-phase networks. However, according
to reference [14] and [20], the magnitudes of the voltage sensitivity indices (V/P)
do not provide a correct measure of voltage stability for unbalanced three-phase
networks. In addition, references [10-11] state that bus voltage ranking allows
immediate detection of weakest bus. However, in the literature, bus voltage ranking
index is only defined for balanced three-phase networks. Therefore, it is essential to
define a new VRI that also includes unbalanced three-phase and multiphase
networks.
1.2.3 Voltage stability enhancement by connecting compensation devices
considering grid losses and MLF
An important application of bus ranking in distribution networks is for voltage
stability enhancement. The purpose of bus ranking is to determine which node is the
weakest bus for connecting DG and/or reactive power compensation devices. DGs
can be allocated at the first bus reaching the voltage limit to improve voltage profile
and reduce grid losses [21]. In addition, the best location for reactive power
compensation to improve voltage stability margins is the weakest bus in the network
[9]. Hence, it might also be sufficient and reasonable to enhance voltage stability
margins in unbalanced multiphase distribution networks by connecting DG and/or
reactive power compensation devices at the weakest single-, two- and three-phase
buses [3]. The present integration of Distributed Generation (DG) units in power
systems has many advantages, but also challenges the performance of the old
8
networks. One of these challenges is to investigate the location and the penetration
level of DG units which can easily be absorbed in the system without major
structural changes while keeping all bus voltage levels within permissible limits. Due
to the high penetration of DG, voltage instability problems have become important
issues in power systems. Most studies confirm that 10-15% penetration of DG can be
absorbed in the electricity network [22]. It is well-known that high penetration levels
of DG (e.g., 40%) may have significant impacts on voltage profile, grid loss, and
voltage stability margin [29-30]. These impacts may appear either positively or
negatively, depending on the type of distribution networks, nature of distributed
generation sources and load characteristics. It seems reasonable to expect that the
connection of DG to the utility grid might improve the voltage profile and will
enhance the voltage stability of a distribution system while reducing active and
reactive losses [23]. Even though DG has a variety of benefits, it also imposes some
problems and limitations. These problems become highly significant as the
penetration level of DG increases and its impact will become worse. This will
eventually require voltage stability analysis to ensure a proper and reliable operation
of the power system with large amounts of DG [6]. When the power system becomes
stressed (e.g., as a result of increasing load), voltage instability can easily occur. This
type of voltage instability mostly occurs at the weakest bus [24]. Therefore, both the
location and the penetration level of DG become a challenging task for system
planning and operation. Several methods to place DG units have been reported in the
literature including:
Voltage sensitivity analysis [19]- The voltage sensitivities can be considered
as an indicator of voltage instability. In principle, the larger the voltage
sensitivity is, the lower the maximum loading factor will be. Therefore, the
best locations to install compensation devices for voltage stability
enhancement are the buses with the highest voltage sensitivity values.
Continuation of power flow for determination of the most sensitive bus to
voltage collapse [19], [25-26]- This method is based on the analysis of
power-flow continuation and determination of most sensitive buses based on
ππ/ππ at the point of voltage collapse. After that, the compensation devices
9
with certain capacity will be placed at the most sensitive buses with the
highest on ππ/ππ values.
Voltage stability index (VSI) [27], [49]- The locations of DG units will be
identified by means of the voltage stability index of buses. The computation
of voltage stability index of all the buses in the system is defined as:
πππΌπ = ππ4 β 4 πππ ππ + πππππ )ππ
2 β 4 πππππ β πππ ππ 2 (1-5)
where ππ is the magnitude of voltage at bus i, π ππ is the resistance between
buses i and j, πππ is the reactance between buses i and j, ππ is the active power
flowing at bus j, and ππ is the reactive power flowing at bus j.
Clearly, the most appropriate locations for DG placement and voltage
stability enhancement are the buses with the minimum VSI values.
Optimization approaches [27-28]- In [27], optimization approaches based on
genetic algorithms (GAs) are used to determine the size of compensation
devices placed at the weakest bus as identified by VSI index to minimise the
network power loss and maximise the voltage regulation in a given network.
According to [28], optimum placement of DG units with reactive power
capability can enhance voltage stability and maximize voltage stability
margin in the entire power network.
Voltage profile and loss calculations [29-30]- In [29], a system unbalanced
voltage variance index which is more reasonable and more accurate than the
system average voltage index is proposed for considering voltage profiles
and grid losses in order to find the optimal location of DG. The buses with
the lowest voltage profile and active power loss were selected for placing
compensation devices. According to [30], the voltage profile and loss studies
confirmed that DG unit could provide a significant improvement to the
voltage profile of the system. These studies also revealed the significance of
properly locating and sizing DG units. They also demonstrated that increasing
DG power output does not necessarily correlate to an improved voltage
profile.
10
References [28, 31] show that the proper sizing and location of DG can significantly
influence the voltage profile and should be well planned to maintain the node
voltages within the permissible limits. Detailed analyses of unbalanced networks
based on continuation three-phase power flow show that the three PV curves on each
phase of the unbalanced networks are different [18-19]. Therefore, to determine the
voltage stability margins, the method of symmetrical components has been employed
in this thesis to merge the three PV curves to one PV curve based on positive-
sequence voltage. Furthermore, in order to extend and generalize the conventional
definition of bus voltage ranking index for multiphase networks, symmetrical
components are also applied to the three-phase voltages computed from three-phase
power flow [3].
1.3 RESEARCH OBJECTIVES
The main objective of this research is to develop a new ranking index for unbalanced
multiphase distribution networks and to propose a new algorithm for the placement
and sizing of DG units and single-phase capacitors in multiphase networks in order
to reduce grid losses and increase MLF while keeping all bus voltages within
acceptable limits. In particular, the new index must identify the weakest single-
phase, two-phase and three-phase buses suitable for reactive power compensation
and voltage stability enhancement. Therefore, the main objectives of this thesis can
be summarized as follows:
1- Define a new bus ranking index for balanced and unbalanced multiphase
networks. This new index will help researchers to identify the weakest bus
for voltage stability enhancement.
2- Validate the proposed bus ranking index and confirm its accuracy using grid
losses calculations and PV curves based on positive-sequence voltage.
3- Validate the accuracy of the proposed bus ranking index in dynamic system
conditions.
4- Application of the proposed bus ranking index to improve and increase MLF
by placing single-phase shunt capacitor, DG and FACTS devices.
11
5- Propose an iterative algorithm to improve the performance of multiphase
distribution networks by proper placement and sizing of DG units and single-
phase capacitors.
1.4 THESIS STRUCTURE
This thesis consists of seven chapters. Chapter 1 discusses bus ranking and voltage
stability enhancement approaches. Chapter 2 presents the conventional bus ranking
approach for balanced networks and proposes new bus ranking approaches to
identify the weakest buses of balanced and unbalanced networks. The method of
symmetrical component has been applied to three-phase voltages resulting from
three-phase power flow. These indices will be compared and applied to different
situations in later chapters through extensive simulations.
Chapter 3 compares the performance and accuracy of the conventional and the new
ranking indices with the well-known voltage sensitivity ratios V/P and V/Q
defined for balanced and unbalanced three-phase distribution networks. Grid loss
calculations, PV curves based on positive-sequence voltage and voltage sensitivity
methods are compared through simulation studies.
In Chapter 4, the proposed VRI is applied to the modified unbalanced three-phase 13
node test feeder to improve voltage stability and increase MLF under unbalanced
three-phase conditions.
In Chapter 5, an application of proposed VRI for improving voltage stability margins
is utilized to improve MLF in multiphase distribution networks. It is revealed that the
proposed VRI can fulfill both the static and dynamic voltage stability criteria.
In Chapter 6, a bus ranking approach for online applications is proposed to identify
the weakest buses during the 24 hour period in order to study and compensate the
detrimental impacts of PEV charging stations on voltage profiles and voltage
stability of smart grid. Simulations results show that the proposed online bus ranking
approach can be used to control and improve the detrimental impacts of large PEV
charging stations.
12
Chapter 7 presents an iterative algorithm for the placement and sizing of DG units
and single-phase capacitors in multiphase networks to reduced grid losses, increase
MLF while keeping all bus voltage within acceptable limits. Simulation results
including locations and the maximum penetration levels of DG units (DFIGs) as well
as the locations and sizes of single-phase capacitors are presented for the IEEE
multiphase 34-node test feeder.
Finally, conclusions and suggestions for future research are presented in Chapter 7.
1.5 LIST OF PUBLICATIONS
The main content of the thesis is based on the following published/submitted articles:
Journal articles:
J1. P. Juanuwattanakul and M.A.S Masoum βBus Voltage Ranking for
Unbalanced Three-phase Distribution Networks and Voltage Stability
Enhancement,β Elixir on electrical engineering, pp. 5976-5981, Dec 2011.
J2. P. Juanuwattanakul and M.A.S Masoum βBus Voltage Ranking
Index for Multiphase Distribution Networks,β Submitted to IET Science,
Measurement & Technology (Manuscript ID SMT-2011-0063).
J3. P. Juanuwattanakul and M.A.S Masoum βIncreasing DG
Penetration in Multiphase Distribution Networks Considering Grid Losses,
Maximum Loading Factor and Bus Voltage Limits,β Submitted to IET
Generation, Transmission & Distribution (Manuscript ID GTD-2011-0841).
Conference papers:
C1. P. Juanuawattanakul and M.A.S Masoum βVoltage Stability
Enhancement for Unbalanced Multiphase Distribution Networks,β in the
proceedings of IEEE PES General Meeting 2011, Detroit, USA, July 2011.
C2. P. Juanuawattanakul and M.A.S Masoum, βAnalysis and
Comparison of Bus Ranking Indices for Balanced and Unbalanced Three-Phase
Distribution Networks,β in the proceedings of AUPEC 2011, Brisbane,
Australia, September 2011.
13
C3. P. Juanuawattanakul, M.A.S Masoum, and Pual. S. Moses βVoltage
Analysis for Placement of DG in Unbalanced Distribution Networks,β in the
proceedings of EPQU 2011, Lisbon, Portugal, October 2011.
C4. P. Juanuawattanakul and M.A.S Masoum, βIdentification of the
weakest buses in Unbalanced Multiphase Smart Grids with Plug-In Electrical
Vehicle Charging Stations,β in the proceeding of ISGT 2011, Perth, Australia,
November 2011.
C5. P. Juanuawattanakul, M.A.S Masoum, C. Niyomsak, and M.
Mohseni βVoltage Analysis for Placement of DG in Multiphase Distribution
Networks,β Accepted for presentation and publication, IEEE PES General
Meeting 2012, San Diego, USA, July 22-26, 2012.
14
Chapter 2. Proposed bus voltage ranking index (VRI)
for multiphase distribution networks
2.1 INTRODUCTION
In balanced networks, all conventional methods mentioned in chapter 1 can be used
to identify the weakest bus. However, in unbalanced three-phase networks, the only
existing method available is based on voltage sensitivities index V/P associated
with MLF to perform bus ranking on unbalanced three-phase networks. However,
this method does not provide a correct measure of voltage stability under unbalanced
three-phase networks [14], [20]. Furthermore, the conventional voltage bus ranking
index as shown in equation (2-1) is only defined for balanced three-phase networks.
Therefore, the rationale is toward defining a new VRI that can be applied to
unbalanced three-phase and multiphase networks. The development of such an index
constitutes the main focus of this chapter.
2.2 CONVENTIONAL VRI FOR BALANCED NETWORKS
This section starts with the definition and derivation of the conventional voltage
ranking index (VRI=V/Vo) using the two bus balanced network of Figure 2-1 and
continues to extend its definition to multiphase networks using symmetrical
components [3].
Rij+jXij
i j
ViΓi VjΓj
Pi+jQi
Figure 2-1 Equivalent circuit of a two bus balanced network.
The conventional VRI is only defined for single-phase and balanced three-phase
networks [9-10]:
15
ππ πΌπππππ£πππ‘πππππ =
π
π0=
ππ ,πππ π βππππ
ππ ,ππ βππππ (2-1)
where j is the bus number, ππ ,πππ π βππππ and ππ ,ππβππππ are the bus voltages for the
base-load and no-load operating conditions, respectively.
Balanced three-phase load flow can be used to compute ππ ,πππ π βππππ by setting the
complex power at bus j to zero:
ππ = π πΏ, π = ππ β πππ = ππ β πΏπ β
ππβ πΏπβππ β πΏπ
π ππ +π πππ = 0 (2-2)
where ππβ πΏπ and ππ β πΏπ are the voltages at buses i and j, respectively. Separating real
and imaginary parts of (2-2):
π πππ ππ = 0
πΌπππ ππ = 0 β
πππππ πΏππ , ππ = πππ ππ + ππ πππ = ππππ πππ πΏππ β ππ 2
πππππ πΏππ , ππ = πππππ β ππ π ππ = ππππ π πππΏππ (2-3)
where πΏππ = πΏπ β πΏπ . The voltage ππ is computed by squaring and adding the real and
imaginary parts of (2-3):
ππ4 + 2 πππ ππ + ππ πππ β 0.5ππ
2 ππ2 + ππ
2 + ππ2 π ππ
2 + πππ2 = 0 (2-4)
There are four solutions to (2-4),
ππ = Β± 1
2 βπ Β± π2 β 4π (2-5)
where π = β ππ2 β 2πππ ππ β 2ππ πππ and π = ππ
2 + ππ2 π ππ
2 + πππ2 . However,
βπ is always positive because the term (β2πππ ππ β 2ππ πππ ) is small as compared
to (ππ2) and also (4π) is small as compared to (π2); therefore, the unique positive
and stable solution of (2-5) is
ππ = ππ ,πππ ππ βππππ = + 1
2 βπ + π2 β 4π (2-6)
Substituting (2-6) in (2-1) results in
ππ πΌπππππ£πππ‘πππππ =
π
π0=
0.5ππ2βππ π ππ βππ πππ +π΄
ππ (2-7)
16
where A = 0.25 ππ2 β 2πππ ππ β 2ππ πππ
2β ππ
2 + ππ2 π ππ
2 + πππ2
The conventional VRI (2-7) is based on the ratio of the voltage magnitude at the
base-load (obtained from power flow calculation) to the voltage magnitude at an
identical state but with all loads set to zero. This index works well under balanced
operating conditions. For unbalanced conditions, the conventional VRI will be
modified and extended to unbalanced networks using symmetrical components.
2.3 DERIVATION OF PROPOSED VRI FOR BALANCED NETWORKS
The proposed VRI for balanced networks is defined as:
ππ πΌπππππππππ =
ππ ,πππππππ π
ππ ,πππ π βππππ
(2-8)
To compute the proposed VRI for balanced three-phase networks; the bus voltage at
the point of voltage collapse (ππ ,πππππππ π ) is computed based on the Newton-Raphson
load flow by forcing (2-3) to zero. The Jacobian corresponding to (2-3) is defined as
follows:
π½ = βππππ π πππΏππ ππππ πππ πΏππ β 2ππ
ππππ πππ πΏππ πππ πππΏππ (2-9)
At the collapse point, the Jacobian matrix is singular, therefore:
πππ‘ π½ = 0 β ππ πππ πΏππ
ππ= 0.5 β ππ ,πππππππ π =
0.5ππ
πππ πΏππ (2-10)
Substituting (2-6) and (2-10) in (2-8) results in
ππ πΌπππππππππ =
ππ ,πππππππ π
ππ ,πππ π βππππ
=0.5ππ
πππ πΏππ 0.5ππ2βπππ ππ βππ πππ +π΄
(2-11)
Note that
ππ πΌπππππππππ =
πππ πΏππ
0.5 ππ πΌπ
ππππ£πππ‘πππππ (2-12)
17
Therefore, compared to the conventional index (2-1), the proposed index (2-12) is
sensitive to both voltage magnitude (e.g., π/π0) and voltage phase angle (πΏππ ). The
phase angle is computed as:
πΏππ = π‘ππβ1 πππππ βππ π ππ
ππ π ππ +ππ πππ + ππ 2 (2-13)
2.4 PROPOSED VRI FOR UNBALANCED MULTIPHASE
DISTRIBUTION NETWORKS
To extend and generalize the definition of VRI for unbalanced three-phase and
multiphase networks, symmetrical components are applied to the three-phase
voltages resulting from three-phase power flow calculations. The new index is
defined as the ratio of the positive-sequence voltage at the point of voltage collapse
to the positive-sequence voltage at the base-load.
ππ πΌπunbalanced & ππ’ππ‘ππ πππ π
=ππ ,πππππππ π
+
ππ ,πππ π βππππ+ (2-14)
where ππ ,πππππππ π+ and ππ ,πππ π βππππ
+ are the positive-sequence bus voltages at the point
of voltage collapse and the base case load, respectively. The positive-sequence
voltage at the point of voltage collapse is determined by increasing the active power
of all loads while keeping the power factor constant until the point of voltage
collapse is reached as demonstrated in Figure 2-2.
Posit
ive S
eque
nce
Volta
ge (V
+ )
Active Power (P)
Collapse
Base-load
Figure 2-2 PV curve based on positive-sequence voltages.
18
This new index can be used to reveal the weakest buses of single-phase and
(un)balanced three-phase networks, as well as the weakest single-, two- and three-
phase buses of multiphase networks with unbalanced loads and/or line
configurations.
Symmetrical components can also be applied to the conventional VRI (2-1) to extend
its application to online identification of the weakest buses in unbalanced multiphase
distribution networks, as it is fast to detect the weakest bus. Therefore, the
conventional VRI for online application is defined as:
ππ πΌπonline =
ππ ,πππ π βππππ+
ππ ,ππ βππππ+ (2-15)
However, VRI for online application (2-15) in balanced networks is less sensitive
than the proposed VRI (2-14) with the factor of 2
πππ πΏππ (see (2-12)).
2.5 DERIVATION OF PROPOSED VRI FOR UNBALANCED
MULTIPHASE NETWORKS
For unbalanced three-phase networks, equation (2-14) can be easily applied to
unbalanced three-phase networks using symmetrical components. Derivation of the
symmetrical components based on (2-14) to multiphase networks is not straight
forward and can be performed as follows:
The multiphase network (Figure 2-3) can be represented by an equivalent
unbalanced four line three-phase network (Figure 2-4) using dummy nodes and
lines. This is done to hypothetically complete the missing phases and missing
lines of the unbalanced multiphase network [17]. The line parameters in Figure 2-
4 can be obtained by Carson's Equation:
19
i j
a
k l
aaijZ
b
c
n
a
b
c
n
c
n
c
n
bbijZ
ccijZ bc
ijZ
caijZ
nnijZ
banijZ
bnijZ
cnijZ
abijZ bb
jkZ
ccjkZ
nnjkZ nn
klZ
ccklZ
bcjkZ
cnjkZ cn
klZ
bnjkZ
Figure 2-3 An unbalanced multiphase distribution system; network configuration
consisting of four nodes with single-, two-, and three-phase sections.
πππ
ππ πππππ πππ
ππ πππππ
πππππ πππ
ππ πππππ πππ
ππ
πππππ πππ
ππ πππππ πππ
ππ
πππππ πππ
ππ πππππ πππ
ππ
(2-16)
i j
aaaijZ
b
c
n
a
b
c
n
bbijZ
ccijZ bc
ijZ
caijZ
nnijZ
anijZ
bnijZ
cnijZ
abijZ
Figure 2-4 The equivalent unbalanced three-phase four-wire network for the unbalanced
multiphase distribution system of Fig. 2-3.
Applying Kronβs reduction, the effects of the neutral or ground wire are still
included in this model:
ππππππ =
πππππβπ πππ
ππβπ πππππβπ
πππππβπ πππ
ππβπ πππππβπ
πππππβπ πππ
ππβπ πππππβπ
(2-17)
20
For any missing phases, the corresponding rows and columns in (2-17) will
contain zero entries.
For the equivalent unbalanced three-phase network (Figure 2-4), the relationship
between bus voltages and branch currents can be expressed as:
πππ
πππ
πππ
=
πππ
πππ
πππ
+
πππππβπ πππ
ππβπ πππππβπ
πππππβπ πππ
ππβπ πππππβπ
πππππβπ πππ
ππβπ πππππβπ
πΌπππ
πΌπππ
πΌπππ
(2-18)
Finally, symmetrical components are applied to the equivalent unbalanced three-
phase voltages resulting from three-phase power flow.
ππ
π0
πππ1
πππ2
=1
3 1 1 11 π2 π1 π π2
πππ
πππ
πππ
(2-19)
Therefore, to extend the application of the proposed VRI index (2-8) to
multiphase networks, we take the following steps: i) draw the equivalent
unbalanced four line three-phase network (Figure 2-4) using dummy nodes and
lines, ii) use symmetrical components to find the equivalent positive-sequence
components (2-19) of the multiphase systems, (iii) compute the new VRI index
for multiphase networks:
ππ πΌπππ’ππ‘ππ πππ π
=πΈππ’ππ£πππππ‘ ππ ,πππππππ π
+
πΈππ’ππ£πππππ‘ ππ ,πππ π βππππ+ =
0.5ππ
πππ πΏππ 0.5ππ2βπππ ππ βππ πππ +π΄
(2-20)
2.6 CONCLUSIONS
A new idea is presented in this chapter that applies the method of symmetrical
components to the conventional bus ranking problem to extend its definition and
applications to both unbalanced three-phase and (un)balanced multiphase networks.
Main conclusions regarding the proposed bus ranking indices are as follows:
The new VRI can be utilized to identify the weakest single-phase, two-phase, and
three-phase bus under multiphase operating conditions.
Compared to the conventional bus ranking definition, the proposed bus ranking
index is sensitive to both voltage magnitudes and voltage phase angles.
21
In subsequent chapters, the new VRI will be compared to other bus ranking
methods and then applied to different power system configurations. The ability of
the new VRI to assist in voltage stability improvement by identifying appropriate
DG locations and sizes will also be investigated.
22
Chapter 3. Validation of the proposed VRI
3.1 INTRODUCTION
In Chapter 2, a new bus voltage ranking index (2-14) is defined as the ratio of the
positive-sequence voltage at the point of voltage collapse to the positive-sequence
voltage at the base-load. This new index can be used to reveal the weakest buses of
single-phase and (un)balanced three-phase networks, as well as the weakest single-,
two- and three-phase buses of multiphase networks with unbalanced loads and/or line
configurations.
In this chapter, the performance and accuracy of the conventional and the new bus
ranking indices are validated using grid loss calculations, PV curves and the well-
known voltage sensitivity approaches V/P and V/Q for balanced and unbalanced
three-phase distribution networks. Validations of the proposed VRI based on the
above mentioned four approaches are performed through detailed simulations of the
IEEE 13 node and IEEE 34 node test feeders under balanced and unbalanced
operating conditions using the DIgSILENT PowerFactory software package [32]. In
addition, applications of the generalized index of V/V0 to improve voltage stability of
unbalanced networks are also demonstrated.
3.2 VALIDATION OF PROPOSED VRI USING GRID LOSSES
CALCULATIONS
In order to validate the proposed VRI, grid losses associated with the placement of a
DG unit at different buses (e.g., all possible locations of DG) are computed and
compared with the losses without a DG unit. The active power losses reduction
(ALR) and the reactive power losses reduction (RLR) associated with the application
of one DG unit are calculated from:
23
%100,
loss
DGVRlossloss
PPPALR (3-1)
%100,
loss
DGVRlossloss
QQQ
RLR (3-2)
where lossP and lossQ are the total active and reactive power losses without voltage
regulator or DG unit, respectively. DGVRlossP , and DGVR
lossQ , are the total active and
reactive power losses with voltage regulator or DG unit, respectively.
The weakest bus of the system after the placement of a DG unit will be the bus with
the lowest ALR and RLR values. Validation of the proposed ranking approach can
be performed by comparing the weakest buses identified by grid losses (according to
ALR and RLR values) and by (2-14).
3.3 VALIDATION OF PROPOSED VRI USING PV CURVES
To further validate the proposed VRI, a continuation three-phase power flow is
utilized to plot the PV curves for unbalanced three-phase distribution networks. The
method of symmetrical components will then be applied to merge the three
individual PV curves into one based on positive-sequence voltage. Finally, the
maximum loading factor (MLF) will be determined using the PV curves based on
positive-sequence voltage. MLF is defined as the ratio of the maximum system load
(at the voltage collapse point) to the base load:
loadbase
collapse
PP
MLF (3-3)
The bus that has the lowest voltage stability margin or lowest MLF factor will be
considered as the weakest bus of the system. Therefore, further validation of the
proposed ranking approach can be performed by comparing the weakest buses
identified by PV curves and by index (2-14).
24
3.4 VALIDATION OF PROPOSED VRI USING VOLTAGE
SENSITIVITY INDICES
The next approach to validate the proposed VRI is through voltage sensitivity
analysis. This will be done using the sensitivities of voltage magnitude to reactive
and active powers at each bus.
3.4.1 Bus ranking based on sensitivity of voltage to reactive power (V/Q)
The sensitivity of voltage to reactive power injection (V/Q) at each bus is first
calculated. Then, the weakest bus is identified as the one with the maximum value of
the voltage sensitivity index [6]. Validation of the proposed ranking approach can be
performed by comparing the weakest buses according to the sensitivity index V/Q
and the proposed index of (2-14).
3.4.2 Bus ranking based on sensitivity of voltage to active power (V/P)
Reference [19] utilized the voltage sensitivities (V/P) along with the PV curves as
an indicator of voltage instability. In general, the higher the voltage sensitivity is, the
lower MLF will be. Therefore, the bus with the highest voltage sensitivity index
value (V/P) at the maximum loading factor point can be considered as the weakest
bus. Therefore, validation of the proposed ranking approach can also be performed
by comparing the weakest buses identified by V/P and (2-14).
3.5 DETAILED SIMULATION OF IEEE MULTIPHASE 13 NODE
TEST FEEDER TO VALIDATE PROPOSED VRI
In this section, detailed simulations of the IEEE multiphase 13 node test feeder
(Figure 3-1) is performed to: (1) find the weakest buses of the feeder (without/with
shunt capacitors, voltage regulators, DGs and SVCs) based on the proposed VRI, (2)
validate the identified weakest buses through grid losses calculations, PV curves and
voltage sensitivity indices (ππ/ππ and ππ/ππ). The IEEE multiphase 13 node test
feeder is simulated using DIgSILENT PowerFactory software [32]. The system data,
simulation parameters and general information on DIgSILENT PowerFactory
software are presented in Appendixes A1-A2 [33], B and C, respectively. This
25
multiphase unbalanced feeder consists of three-phase (buses 650, RG60, 632, 634,
634, 671, 692 and 675), two-phase (buses 645, 646 and 684) and single-phase (buses
611 and 652) sections with overhead lines, two underground lines (through buses
684, 652 and 692, 675), unbalanced spot loads (Y-PQ, D-PQ, Y-I, D-I, Y-Z, D-Z),
distributed loads (Y-PQ) between buses 632 and 671, a single-phase shunt capacitor
(at buses 611), a three-phase shunt capacitor (at buses 675), and an in-line
transformer (between buses 633 and 634). There is also a three-phase voltage
regulator connected between buses 650 and RG60.
646 645 632 633 634
650
692 675611 684
652
671
680
RG604.16 kV
0.48 kV4.16 kV
Switch
Two-phase
Single-phaseThree-phase
115 kV
Figure 3-1 The IEEE multiphase 13 node test feeder.
Simulations are performed on the IEEE multiphase 13 node test feeder (Figure 3-1)
for the following seven cases (Table 3-1):
Case 1: without any voltage regulators and fixed transformer tap ratio set to 1.0.
Case 2: with a voltage regulator and variable transformer tap ratio.
Case 3: similar to Case 2 with the addition of a single-phase shunt capacitor
(0.1MVar) connected at the weakest node (bus 611, identified by the proposed VRI
index).
Case 4: similar to Case 2 with the addition of a single-phase shunt capacitor
(0.1MVar) at bus 652.
Case 5: similar to Case 2 with a DG (Appendix B, Table B1) injecting 358 kW
active power (e.g., 10% of the total load) installed at the weakest three-phase node
(bus 675, identified by the proposed VRI index).
26
Case 6: similar to Case 2 with one DG (358 kW) and one SVC (0.36 MVAr, acting
as an unbalanced voltage controller) installed at the weakest three-phase node (bus
675, identified by the proposed VRI index).
Case 7: similar to Case 6 with the DG and SVC installed at bus 680.
TABLE 3-1 SIMULATED CASE STUDIES FOR THE IEEE MULTIPHASE 13 NODE TEST FEEDER (FIG. 3-1).
Case
number
System operating condition of the IEEE multiphase 13
node test feeder
Simulation results
1 No voltage regulators, transformer tap ratio set to
1.0
Fig. 3-2, Table 3-2
(column 1)
2 A voltage regulator, variable transformer tap ratio Figs. 3-3, 3-8, 3-9
and 3-10, Table 3-2
(column 2)
3 Case 2 with a single-phase shunt capacitor at the
weakest single-phase bus (bus 611)
Table 4-1
4 Case 2 with a single-phase shunt capacitor at bus
652
Table 4-1
5 Case 2 with a DG at the weakest three-phase bus
(bus 675)
Fig. 3-4, Table 3-3
6 Case 2 with a DG and a SVC at the weakest three-
phase bus (bus 675)
Figs. 3-5 and 3-11,
Table 3-4
7 Case 6 with the DG and SVC installed at bus 680 Table 4-1
3.5.1 Identification of the weakest buses using the proposed VRI for the
IEEE multiphase 13 node test feeder
The proposed VRI (2-14) will be utilized to locate the weakest single-phase and
three-phase buses for the placement of single-phase shunt capacitors and three-phase
DGs with SVC to enhance voltage stability. At each compensation level, the
27
proposed index (2-14) is calculated and the bus ranking is updated since the system
configuration is changed.
3.5.1.1 Bus ranking without/with a voltage regulator (Cases 1 and 2)
Figures 3-2 and 3-3 (and Table 3-2, columns 2-3) show the bus rankings for Cases 1
and 2 based on (2-14) without and with a voltage regulator, respectively. According
to these figures, the voltage regulator has no effect on the order of bus ranking.
0
0.2
0.4
0.6
0.8
1
1.2
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest bus (single-phase)Weakest bus (three-phase)
Weakest bus (two-phase)
Figure 3-2 Bus ranking for Case 1 (without any voltage regulators).
Note that the four nodes with the lowest positive-sequence voltage ratios (2-14) are
buses 611, 684, 652 and 675. Therefore, the best single-phase node for the capacitor
connection is bus 611, while the most appropriate location for the installation of
three-phase DG and SVC compensators is bus 675 since nodes 611, 684 and 652 are
single-phase, two-phase and single-phase buses, respectively.
0
0.2
0.4
0.6
0.8
1
1.2
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest bus (single-phase)Weakest bus (three-phase)
Weakest bus (two-phase)
Figure 3-3 Bus ranking for Case 2 (with a voltage regulator).
28
3.5.1.2 Bus ranking with DG at the most suitable bus (Case 5)
It is well-known that DG devices (e.g., induction generators) should be connected at
the most suitable three-phase buses (e.g., weakest buses with the lowest VRI values)
to improve the voltage stability. Simulation results of Figure 3-4 and Table 3-3
indicate that the application of one DG (an induction generator) at bus 675 does not
change the order of VRI values and therefore has no impact on the order of bus
ranking.
TABLE 3-2 BUS RANKING FOR CASES 1 AND 2 BASED ON THE PROPOSED VRI.
Bus number Case 1 Case 2
RG60 0.98593 1.04609
632 0.88131 0.90252
633 0.87531 0.89467
634 0.80824 0.80699
645 0.88264 0.91523
646 0.88035 0.91147
671 0.80418 0.79744
680 0.80418 0.79744
684 0.70594** 0.64939**
611 0.62933* 0.55389*
652 0.77406 0.73490
692 0.80418 0.79744
675 0.79423*** 0.78377***
*) The weakest single-phase bus.
**) The weakest two-phase bus.
***) The weakest three-phase bus.
29
0
0.2
0.4
0.6
0.8
1
1.2
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest bus (single-phase)Weakest bus (three-phase)
Weakest bus (two-phase)
Figure 3-4 Bus ranking for Case 5 (with one DG at bus 675).
TABLE 3-3 BUS RANKING FOR CASE 5 BASED ON THE PROPOSED VRI.
Bus number Case 5
RG60 1.04587
632 0.90546
633 0.89770
634 0.81110
645 0.91791
646 0.91415
671 0.80186
680 0.80186
684 0.66207**
611 0.57571*
652 0.73902
692 0.80186
675 0.78862***
*) The weakest single-phase bus.
**) The weakest two-phase bus.
***) The weakest three-phase bus.
30
3.5.1.3 Bus ranking with DG and SVC (Case 6)
One DG and one SVC are connected at bus 675 (e.g., the three-phase node with the
lowest VRI) and the proposed index (2-14) is recalculated. As a result, the order of
the weakest nodes are changed to buses 611, 684, 634, 652, 671 (or 692), and 680 as
shown in Figure 3-5 and Table 3-4. This means the next suitable bus for connecting
additional DG and SVC units is bus 634. However, this bus has a different voltage
level (0.46 kV) compared to other buses (4.16 kV) and therefore, bus 671 (or 692)
will be selected to properly compare grid losses.
0
0.2
0.4
0.6
0.8
1
1.2
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest bus (single-phase)Weakest bus (three-phase) Weakest bus (two-phase)
Figure 3-5 Bus ranking for Case 6 (with one DG and one SVC at bus 675).
3.5.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 13 node test feeder
Grid losses associated with the placement of DG units at each node (e.g., all possible
locations of DG) are computed and compared with the losses generated with the DG
unit connected at the weakest bus as identified by the proposed VRI.
3.5.2.1 Grid losses with one DG unit for the IEEE multiphase 13 node test feeder
A three-phase induction generator is placed at different buses of the IEEE multiphase
13 node feeder (Figure 3-1) and system active and reactive losses are plotted in
Figure 3-6. This figure confirms that bus 675 (resulting in the lowest grid losses) is
the most suitable bus for DG placement, as was previously identified by the proposed
VRI (2-14).
31
TABLE 3-4 BUS RANKING FOR CASE 6 BASED ON THE PROPOSED VRI.
Bus number Case 6
RG60 1.05177
632 0.96139
633 0.94595
634 0.77360***
645 0.94095
646 0.93346
671 0.98381
680 0.98381
684 0.89518**
611 0.77550*
652 1.00702
692 0.98381
675 1.00000
*) The weakest single-phase bus.
**) The weakest two-phase bus.
***) The weakest three-phase bus.
Bus Number
Re
acti
ve P
ow
er
Lo
ss (
MV
Ar)
Ac
tive
Po
wer
Lo
ss (
MW
)
0.285
0.295
0.305
0.315
0.325
0.335
0.345
0.355
RG60 632 633 671 680 692 675
0.090
0.095
0.100
0.105
0.110
0.115
Active power loss
Reactive power loss0.120
0.125
Figure 3-6 Reactive and active power losses associated with DG connections at different buses of Figure 3-1 (Case 2).
32
3.5.2.2 Grid losses with two DG units for the IEEE multiphase 13 node test feeder
According to (2-14), with the addition of one DG (at bus 675, Figure 3-4), the most
suitable location for the connection of a second DG unit is still at bus 675. This is in
agreement with the grid loss plots of Figure 3-7 generated by connecting the first DG
at bus 675 and placing a second DG at different buses of the IEEE 13 node feeder.
These results further confirm the accuracy of the proposed bus ranking index.
3.5.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 13 node test feeder
The PV curves based on positive-sequence voltages are plotted and compared with
the PV curve generated when DG and SVC units are connected at the weakest bus.
Figures 3-8, 3-9, and 3-10 show the PV curves of positive-sequence voltages at each
three-, two- and single-phase bus for Case 2, respectively. According to these
figures, buses 675, 684 and 611 are the weakest three-, two- and single-bus as
previously recognized by (2-14).
After connecting a combination of DG and SVC units at bus 675, PV curves for Case
6 are regenerated and plotted in Figure 3-11. As expected and previously recognized
by the proposed VRI, the lowest stability margins occur at bus 634.
Re
acti
ve P
ow
er
Lo
ss (
MV
Ar)
Acti
ve
Po
wer
Lo
ss (
MW
)
0.250
0.260
0.270
0.280
0.290
0.300
0.310
Bus NumberRG60 632 633 671 680 692 675
0.084
0.088
0.092
0.096
0.100
Active power loss
Reactive power loss0.104
0.108
Figure 3-7 Reactive and active power losses associated with the first DG installed at bus 675 and the second DG connected at different buses of Figure 3-1 (Case 3).
33
114669466746654663466
1.2
1.1
1.0
0.9
0.8
0.7
Total Load of Selected Loads (kW)
Bus 675; the weakest three-phase bus
632671
633 634675
RG60680 692
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-8 PV curves of positive-sequence voltage at each three-phase bus for Case 2.
1146694667466
0.70
0.60
684645 646Total Load of S elected L oads (kW)
5466
Bus 684; the weakest two- phase bus
0.50
0.403466
Po
sit
ive
-Se
qu
en
ce
Vo
lta
ge
(p
.u.)
Figure 3-9 PV curves of positive-sequence voltage at each two-phase bus for Case 2.
34
11466946674665466
0.36
0.32
0.28
0.24
3466
0.20
0.16
611652Total Load of S elected L oads (kW)
Bus 611; the weakest single- phase bus
Po
sit
ive
-Se
qu
en
ce
Vo
lta
ge
(p
.u.)
Figure 3-10 PV curves of positive-sequence voltage at each single-phase bus for Case 2.
19466154661146674663466
1.2
1.1
1.0
0.9
0.8
0.7
Total Load of Selected Loads (kW)
Bus 634; the weakest three-phase bus
632671
633 634675
RG60680 692
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-11 PV curves of positive-sequence voltage at each bus for Case 6.
3.5.4 Comparison of proposed VRI with other bus ranking approaches for
the IEEE multiphase 13 node test feeder
Table 3-5 compares the performance of the proposed VRI (2-14) with three well-
known bus ranking indices; π/π0, ππ/ππ and ππ/ππ for the IEEE 13 node network
35
of Figure 3-1 under balanced three-phase, unbalanced three-phase and unbalanced
multiphase operating conditions.
Under balanced three-phase conditions (Table 3-5, column 2), all methods
identify the same weakest bus (e.g., node 634). However, the conventional
ranking approaches are not applicable to unbalanced three-phase and multiphase
systems and fail to identify the correct weakest buses.
Under unbalanced three-phase conditions (Table 3-5, column 3), the weakest bus
is node 675 as identified by the proposed VRI and confirmed by the calculated
PV curves (Figure 3-12) and grid losses (Table 3-6, columns 2-3). However,
based on the two voltage sensitivity methods (ππ/ππ and ππ/ππ), the weakest
bus is node 634 which is not correct. This is further confirmed by placing SVC
units at buses 634 and 675 and computing the corresponding maximum loading
factors as demonstrated in Table 3-7. Therefore, the magnitudes of the voltage
sensitivity methods do not provide a correct measure of voltage stability under
unbalanced three-phase networks.
For multiphase operation (Table 3-5, column 4), the weakest three-, two- and
single- phase buses are nodes 675, 684 and 611, respectively; as identified by the
proposed VRI (Figure 3-3) and confirmed by grid losses (Figure 3-6) and PV
curves PV curves (Figures 3-8 to 3-10). Therefore, the conventional indices
(π/π0, ππ/ππ and ππ/ππ) cannot properly identify the weakest buses of
multiphase networks.
36
TABLE 3-5 BUS RANKING RESULTS FOR THE IEEE 13 NODE NETWORK WITH ONLY UNBALANCED THREE-PHASE NETWORKS/LOADS.
Bus ranking approach
The weakest buses of the unbalanced IEEE 13 node test feeder
(Figure 3-1)
Balanced
three-phase *
Unbalanced three-
phase **
Unbalanced
multiphase***
Grid losses 634 675 (Table 3-6) 675(3p), see Figure 3-7
PV curves 634 675 (Figure 3-12) 611 (1p, Figure 3-10),
684 (2p, Figure 3-9),
675 (3p, Figure 3-8)
π/π0 (2-1)
[10-11]
634 N/A N/A
Index ππ/ππ [6] 634 634**** (Table 3-6) N/A
Index ππ/ππ [19] 634 634**** (Table 3-6) N/A
Proposed VRI (2-14) 634 675 (Table 3-6) 611(1p), 684 (2p),
675(3p), see Fig 3-3
*) Modified Figure 3-1 with only balanced networks/loads.
**) Modified Figure 3-1 with only unbalanced three-phase networks/loads.
***) 1p, 2p and 3p correspond to single-, two- and three-phase buses.
****) Calculated by positive sequence.
TABLE 3-6 BUS RANKING RESULTS FOR THE IEEE 13 NODE TEST FEEDER (FIG. 3-1) WITH ONLY UNBALANCED THREE-PHASE NETWORKS/LOADS.
Bus
number
Grid losses ππ/ππ
[p.u./MW]
ππ/ππ
[p.u./MVAr]
Proposed VRI
(2-14) P
[MW]
Q
[MVAr]
634 0.13555 0.47702 -0.26223 0.36904 0.61776
675 0.13448 0.47281 -0.23591 0.30041 0.60153
37
TABLE 3-7 MAXIMUM LOADING FACTORS WITH SVC.
MLF
Base-case 2.687
SVC at bus 634 3.282
SVC at bus 675 5.095
971684667216596647163466
Total Load of S elected L oads (kW)
675634
1.00
0.90
0.80
0.70
0.60
0.50
Bus 675
Bus 634
Po
sit
ive-S
eq
uen
ce V
olt
ag
e (
p.u
.)
Figure 3-12 PV curves of positive-sequence voltages at buses 634 and 675 for the
modified IEEE 13 node network (Figure 3-1) with only unbalanced three-phase
networks/loads.
3.6 DETAILED SIMULATION OF IEEE MULTIPHASE 34 NODE
TEST FEEDER TO VALIDATE PROPOSED VRI
In this section, detailed simulations of the IEEE multiphase unbalanced 34 node test
feeder (Figure 3-13) is performed to: (1) find the weakest buses of the feeder
(without/with voltage regulators, induction generator and DFIG wind turbine) based
on the proposed VRI (2-14), (2) validate the identified weakest buses through grid
losses calculations, PV curves and voltage sensitivity indices (ππ/ππ and ππ/ππ).
38
The system data for the IEEE multiphase 34 node test feeder is presented in
Appendixes A3 and A4 [33]. This unbalanced multiphase feeder consists of three-
phase and single-phase sections with unbalanced spot loads (Y-PQ, D-PQ, Y-I, D-I,
Y-Z, and D-Z), distributed loads (Y-PQ, Y-I, Y-Z, D-I, D-Z, and D-PQ), three-phase
shunt capacitors (at buses 844 and 848), and an in-line transformer (between buses
832 and 888).
There are also two automatic voltage regulators. Bus 800 is treated as a slack bus
with a voltage set point of 1.05 p.u. At a base-case load condition, the voltage at bus
890 is lower than the permissible voltage limit because the line between buses 888
and 890 is relatively long. However, other bus voltages are in the acceptable range of
0.95p.u. to 1.05p.u.
800
806 808 812 814
810
802 850818
824 826816
820
822
828 830 854 856
852
832888 890
838
862
840836860834
842
844
846
848
864
858
Single-phase (phase-a)
Single-phase (phase-b)
Single-phase (phase-b)
Figure 3-13 The IEEE multiphase 34 node test feeder.
Simulations are performed on the multiphase unbalanced IEEE 34 node test feeder
(Figure 3-13) for the following cases (Table 3-8):
Case 8: without a voltage regulator (fixed transformer tap ratio set to 1.0).
Case 9: with a voltage regulator (variable transformer tap ratio).
Case 10: Case 9 with a DG (three-phase induction generator) injecting 200 kW
active power (e.g., 10% of the total load) installed at the weakest three-phase node
(bus 890).
Case 11: Case 9 with one DG (200 kW DFIG wind turbine) installed at the weakest
three-phase node (bus 890).
39
Case 12: Case 9 with DGs (2.4 MW DFIG wind turbines) installed at the weakest
three-phase node (bus 890).
TABLE 3-8 SIMULATED CASE STUDIES FOR THE IEEE 34 NODE TEST FEEDER (FIG. 3-13).
Case
number
System operating condition of the IEEE 34 node
test feeder Simulation results
8 No voltage regulators, transformer tap ratio
set to 1.0
Fig. 3-14, Table 3-9
(column 1)
9 A voltage regulator, variable transformer tap
ratio
Figs. 3-15, 3-21 and 3-
22, Table 3-9
(column 2)
10 Case 9 with a DG (200 kW IG) at the
weakest three-phase node (bus 890)
Fig. 3-16, Table 3-10
11 Case 9 with a DG (200 kW DFIG wind
turbine) at the weakest three-phase node
(bus 890)
Fig. 3-17, Table 3-11
12 Case 9 with DGs (2.4 MW DFIG wind
turbines) at the weakest three-phase node
(bus 890)
Figs. 3-18 and 3-23,
Table 3-12
3.6.1 Identification of the weakest buses using the proposed VRI for the
IEEE multiphase unbalanced 34 node test feeder
In the following sections, the proposed VRI (2-14) will be utilized to locate the
weakest three-phase buses for the placement of three-phase induction generator and
DFIG wind turbine to enhance voltage stability. At each compensation level, the
proposed index (2-14) is calculated and the bus ranking is updated since the system
configuration is changed. To show the validity of the proposed bus ranking and the
effectiveness of the compensation devices (induction generator and DFIG wind
turbine), grid losses, PV curves (based on positive-sequence voltages) and voltage
stability margins are calculated and compared for the aforementioned cases.
40
3.6.1.1 Bus ranking without/with a voltage regulator (Cases 8 and 9)
Figures 3-14 (corresponding to columns 2 of Table 3-9) and 3-15 (corresponding to
column 3 of Table 3-9) show the bus rankings for Cases 8 and 9 based on (2-14)
without and with a voltage regulator, respectively. According to these figures, the
voltage regulator has no effect on the order of bus ranking.
0
0.2
0.4
0.6
0.8
1
1.2
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-14 Bus ranking for Case 8 (without any voltage regulators).
Note that the four nodes with the lowest positive-sequence voltage ratios (2-14) are
buses 890, 864, 822 and 888. Therefore, the most appropriate location for the
installation of a three-phase DG is bus 890 since nodes 864 and 822 are single-phase
buses and nodes 890 and 888 are three-phase buses.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-15 Bus ranking for Case 9 (with a voltage regulator).
3.6.1.2 Bus ranking with an induction generator DG unit at the most suitable bus (Case 10)
As mentioned before, installation of DG devices (e.g., induction generators) at the
most suitable three-phase buses (e.g., weakest buses with the lowest VRI values) can
improve the voltage stability. Simulation results of Figure 3-16 and Table 3-10
41
indicate that the application of one DG (an induction generator) at bus 890 does not
change the order of VRI values and therefore has no impact on the order of bus
ranking.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-16 Bus ranking for Case 10 (with a DG type induction generator at bus 890).
3.6.1.3 Bus ranking with a 200kW DFIG wind turbine DG unit at the most
suitable bus (Case 11)
One DFIG wind turbine DG unit is connected at bus 890 (e.g., the three-phase node
with the lowest VRI) and the proposed index (2-14) is recalculated. As a result, the
order of the weakest nodes are changed to buses 890, 864, 822, 888, and 620 as
shown in Figure 3-17 and Table 3-11. Simulation results indicate that the application
of one DG (200 kW DFIG wind turbine) at bus 890 does not change the order of VRI
values and therefore has no impact on the order of bus ranking.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 3-17 Bus ranking for Case 11 (with a DFIG wind turbine DG unit at bus 890).
42
TABLE 3-9 BUS RANKING FOR CASES 8 AND 9 BASED ON THE PROPOSED VRI.
Bus number Case 8 Case 9
800 1.00000 1.00000
802 0.99799 0.99573
806 0.99666 0.99290
808 0.97176 0.93948
810 (single-phase) 0.97495 0.94645
812 0.94172 0.87464
814 0.91684 0.82070
850 1.00154 0.83477
816 0.90944 0.83414
818 (single-phase) 0.88203 0.79616
820 (single-phase) 0.84634 0.71782
822 (single-phase) 0.84140 0.70916
824 0.89911 0.81571
826 (single-phase) 0.91036 0.84105
828 0.89828 0.81422
830 0.87777 0.77750
854 0.87725 0.77657
852 0.83959 0.70887
832 0.83322 0.74432
858 0.82963 0.73901
834 0.82548 0.73287
842 0.82538 0.73271
844 0.82488 0.73197
846 0.82442 0.73130
848 0.82437 0.73124
860 0.82491 0.73202
836 0.82455 0.73150
840 0.82452 0.73145
862 0.82454 0.73149
838 (single-phase) 0.83164 0.75167
864 (single-phase) 0.80473* 0.68868*
888 0.80342 0.69969
890 0.69640*** 0.54248 ***
856 (single-phase) 0.88758 0.80031
*) The weakest single-phase bus.
***) The weakest three-phase bus.
43
TABLE 3-10 BUS RANKING FOR CASE 10 BASED ON THE PROPOSED VRI.
Bus number Case 10
800 1.00000
802 0.99582
806 0.99305
808 0.94083
810 (single-phase) 0.94775
812 0.87803
814 0.82600
850 0.85138
816 0.85077
818 (single-phase) 0.79710
820 (single-phase) 0.73635
822 (single-phase) 0.72791
824 0.83300
826 (single-phase) 0.85770
828 0.83156
830 0.79632
854 0.79543
852 0.73097
832 0.77219
858 0.76691
834 0.76079
842 0.76063
844 0.75988
846 0.75920
848 0.75918
860 0.75996
836 0.75946
840 0.75941
862 0.75944
838 (single-phase) 0.77859
864 (single-phase) 0.71722*
888 0.73057
890 0.59503***
856 (single-phase) 0.81841
*) The weakest single-phase bus.
***) The weakest three-phase bus.
44
TABLE 3-11 BUS RANKING FOR CASE 11 BASED ON THE PROPOSED VRI.
Bus number Case 11
800 1.00000
802 0.99498
806 0.99498
808 0.99165
810 (single-phase) 0.92914
812 0.93821
814 0.85398
850 0.79201
816 0.82070
818 (single-phase) 0.74986
820 (single-phase) 0.66849
822 (single-phase) 0.65709
824 0.79889
826 (single-phase) 0.83131
828 0.79720
830 0.75550
854 0.75444
852 0.67831
832 0.71712
858 0.71062
834 0.70310
842 0.70291
844 0.70201
846 0.70117
848 0.70109
860 0.70204
836 0.70150
840 0.70134
862 0.70138
838 (single-phase) 0.72512
864 (single-phase) 0.64766*
888 0.67604
890 0.53690***
856 (single-phase) 0.78413
*) The weakest single-phase bus.
***) The weakest three-phase bus.
45
3.6.1.4 Bus ranking with a 2.4 MW DFIG wind turbine DG unit (Case 12)
A 2.4 MW DFIG wind turbine (Case 12) is connected at bus 890 (e.g., the three-
phase node with the lowest VRI) and the proposed index (2-14) is recalculated. As a
result, the order of the weakest three-phase nodes are changed to buses 852, 890 and
814 as shown in Figure 3-18 and Table 3-12. This means the next suitable bus for
connecting a compensation device is bus 852.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
800
802
806
808
810
812
814
850
816
818
820
822
824
826
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
838
864
888
890
856
Weakest bus (three-phase)
Bus Number
VR
I
Weakest bus (single-phase)Single-phase Three-phase
Figure 3-18 Bus ranking for Case 12 (with DFIG wind turbines at bus 890).
3.6.2 Validation of proposed VRI based on grid loss calculations for the
IEEE multiphase 34 node test feeder
Grid losses associated with the placement of DG units at each node (e.g., all possible
locations of DG) are computed and compared with the losses generated with the DG
unit connected at the weakest bus as identified by the proposed VRI.
3.6.2.1 Grid losses with one DG unit for the IEEE multiphase 34 node test feeder
A three-phase DFIG wind turbine is placed at different buses of the unbalanced IEEE
34 node feeder (Figure 3-13) and the system active power losses are plotted in Figure
3-19. This figure confirms that bus 890 (resulting in the lowest grid losses) is the
most suitable bus for DG placement, as was previously identified by the proposed
VRI (2-14).
46
TABLE 3-12 BUS RANKING FOR CASE 12 BASED ON THE PROPOSED VRI.
Bus number Case 12
800 1.00000
802 0.99298
806 0.98835
808 0.90360
810 (single-phase) 0.92369
812 0.80679
814 0.73076
850 0.85460
816 0.85357
818 (single-phase) 0.71349
820 (single-phase) 0.54996
822 (single-phase) 0.52667*
824 0.82593
826 (single-phase) 0.89795
828 0.82374
830 0.77118
854 0.76989
852 0.68017***
832 0.76769
858 0.75772
834 0.74618
842 0.74588
844 0.74448
846 0.74326
848 0.74314
860 0.74459
836 0.74364
840 0.74355
862 0.74362
838 (single-phase) 0.79897
864 (single-phase) 0.63886
888 0.73966
890 0.68601
856 (single-phase) 0.83478
*) The weakest single-phase bus.
***) The weakest three-phase bus.
47
0
0.05
0.10
0.15
0.20
0.25
0.30
800
802
806
808
812
814
850
816
824
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
888
890
Acti
ve
Po
wer
Lo
ss (
MW
)
Bus Number
Figure 3-19 Active power loss associated with DG connections at different buses of Figure 3-13 (Case 9).
3.6.2.2 Grid losses with two DG units for the IEEE multiphase 34 node test
feeder
According to (2-14), with the addition of one DG (at bus 890, Figure 3-16), the most
suitable location for the connection of a second DG unit is still at bus 890. This is in
agreement with the grid loss plots of Figure 3-20 generated by connecting the first
DG at bus 890 and placing a second DG at different buses of the IEEE 34 node
feeder. These results further confirm the accuracy of the proposed bus ranking index.
0
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
800
802
806
808
812
814
850
816
824
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
888
890
Acti
ve
Po
wer
Lo
ss (
MW
)
Bus Number
Figure 3-20 Active power loss associated with the first DG installed at bus 890 and the second DG connected at different buses of Figure 3-13 (Case 10).
3.6.3 Validation of proposed VRI based on PV curves for the IEEE
multiphase 34 node test feeder
Figure 3-21 shows the PV curves of positive-sequence voltages at each three-phase
bus for Case 9. According to this figure, bus 890 has the lowest stability margin.
48
Therefore, this is the weakest three-phase bus as previously recognized by (2-14).
The PV curves based on positive-sequence voltages of single-phase bus are plotted
as shown in Figure 3-22. As expected and previously recognized by the proposed
VRI, the weakest single-phase bus is bus 864.
After connecting a 2.4 MW DFIG wind turbine at bus 890, PV curves for Case 12
are regenerated and plotted in Figure 3-23. As expected and previously recognized
by the proposed VRI, the lowest stability margins occur at bus 852.
3.6.4 Comparison of proposed VRI with other bus ranking approaches for
the IEEE multiphase 34 node test feeder
Table 3-13 compares the performance of the proposed VRI (2-14) with three well-
known bus ranking indices; π/π0, ππ/ππ and ππ/ππ for the IEEE 34 node network
of Figure 3-13 under unbalanced multiphase operating conditions. For multiphase
operation (Table 3-13), the weakest three- and single- phase buses are nodes 890 and
864, respectively; as identified by the proposed VRI (Figure 3-15) and confirmed by
grid losses (Figure 3-19) and PV curves (Figures 3-21 and 3-22). Therefore, the
conventional indices (π/π0 , ππ/ππ and ππ/ππ) cannot properly identify the
weakest buses of multiphase networks.
49
4769376927691769
1.125
1.000
0.875
0.750
0.625
0.500
0.375
Total Load of Selected Loads (kW)
Bus 890; the weakest three-phase bus
848840
852846858
888 890
808812 814
850
816 824832830828
854
800
834842 844
860
836
802
862
806
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.
Figure 3-21 PV curves of positive-sequence voltage at each three-phase bus for Case 9.
Total Load of Selected Loads (kW)
)
4769376927691769
0.39
0.36
0.33
0.30
0.27
0.24
0.21
810 818 820 822826 856 864 838
Bus 864; the weakest single-phase bus
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.
Figure 3-22 PV curves of positive-sequence voltage at each single-phase bus for Case 9.
50
801967695519426930191769
1.40
1.20
1.00
0.80
0.60
Total Load of Selected Loads (kW)
Po
sit
ive-
S
eq
uen
ce
Vo
lta
ge
(p.u
.)
Bus 852; the weakest three-phase bus
848840
852846858
888 890
808812 814
850
816 824832830828
854
800
834842 844
860
836
802
862
806
Figure 3-23 PV curves of positive-sequence voltage at each bus for Case 12.
TABLE 3-13 BUS RANKING RESULTS FOR THE MULTIPHASE IEEE 34 NODE NETWORK.
Bus ranking approach The weakest buses of the multiphase IEEE 34 node test
feeder* (Figure 3-13)
Grid losses 890(3p), see Figure 3-19
PV curves 890 (3p, Figure 3-21), 864 (1p, Figure 3-22)
π/π0 (2-1) [10-11] N/A
Index ππ/ππ [6] N/A
Index ππ/ππ [19] N/A
Proposed VRI (2-14) 864(1p), 890(3p), see Figure 3-15
*) 1p and 3p correspond to the weakest single- and three-phase buses.
51
3.7 CONCLUSIONS
This chapter utilized the proposed new voltage ranking index (2-14) to identify the
weakest single-, two- and three-phase buses of unbalanced and multiphase
distribution networks. The validity of the new index is demonstrated for the IEEE
unbalanced multiphase 13 node and IEEE 34 node test feeders based on grid losses,
PV curves and voltage sensitivity analysis. Main conclusions are as follows:
The proposed ranking index can accurately identify the weakest single-, two- and
three-phase buses under different operating conditions without and with voltage
regulators, capacitors and DGs (without/with SVCs).
The performance and the accuracy of the proposed VRI for system operations
without/with single-phase capacitors, voltage regulators, DGs and SVCs have
been clearly validated through detailed simulations and analysis.
52
Chapter 4. Validation and application of proposed VRI
in improving voltage stability of unbalanced three-phase
networks
4.1 INTRODUCTION
In this chapter, a new bus positive-sequence voltage index of Vcollapse/Vbase-load is
introduced to identify the weakest three-phase buses in unbalanced three-phase
distribution networks. First, the proposed ranking index is validated based on grid
losses and PV curves without and with compensation devices. Then, the index is
utilized to place three-phase DG units without and with SVC devices at the weakest
buses of the modified IEEE unbalanced three-phase 13 node test feeder. Finally,
simulation results and extensive case studies without/with a voltage regulator, DGs
and SVCs are presented to show the application of the proposed approach in
improving voltage stability and increasing MLF under unbalanced three-phase
conditions.
4.2 DETAILED SIMULATION OF MODIFIED IEEE UNBALANCED
THREE-PHASE 13 NODE TEST FEEDER TO VALIDATE PROPOSED VRI
In this section, detailed simulations of the modified unbalanced three-phase 13 node
test feeder shown in Figure 4-1 is performed to: (1) find the weakest buses of the
feeder (without/with voltage regulators, DGs and SVCs) based on the proposed VRI,
(2) validate the identified weakest buses through grid losses calculations and PV
curves, (3) improve MLF of the networks using compensation devices.
The unbalanced three-phase 13 node test feeder (Figure 4-1) has been modified to
have unbalanced three-phase conditions. The feeder specifications and data are
presented in Appendixes A-5 and A-6.
53
Simulations are performed on the modified unbalanced three-phase 13 node test
feeder (Figure 4-1) for the following case studies:
Case 1: without a voltage regulator (fixed transformer tap ratio set to 1.0).
Case 2: with a voltage regulator (variable transformer tap ratio).
Case 3: Case 2 with a DG (three-phase induction generator) injecting 358 kW active
power (e.g., 10% of the total load) installed at the weakest three-phase node (bus
675).
Case 4: Case 2 with one DG (358 kW) and one SVC (0.36 MVar, acting as an
unbalanced voltage controller) installed at the weakest three-phase node (bus 675).
Case 5: similar to Case 4 with the DG and SVC installed at bus 680.
646 645 632 633 634
650
692 675611 684
652
671
680
RG604.16 kV
0.48 kV4.16 kV
Switch
Three-phase
Three-phaseThree-phase
115 kV
Figure 4-1 The modified unbalanced three-phase 13 node test feeder.
The proposed VRI (2-14) will be utilized to locate the weakest three-phase buses for
the placement of three-phase DGs with SVC to enhance voltage stability. At each
compensation level, the proposed index (2-14) is calculated and the bus ranking is
updated since the system configuration is changed. To show the validity of the
proposed bus ranking and the effectiveness of the compensation devices (DG and
SVC), grid losses, PV curves (based on positive-sequence voltages) and voltage
stability margins are calculated and compared for the aforementioned cases.
54
TABLE 4-1 SIMULATED CASE STUDIES FOR THE MODIFIED UNBALANCED THREE-PHASE 13 NODE TEST FEEDER (FIG. 4-1).
Case
number
System operating condition of the modified
unbalanced three-phase 13 node test feeder
Simulation results
1 No voltage regulators, transformer tap ratio set to 1.0 Fig. 4-2, Table 4-2
(column 1)
2 A voltage regulator, variable transformer tap ratio Figs. 4-3, 4-6 and 4-8,
Table 4-2
(column 2)
3 Case 2 with a DG at the weakest three-phase bus
(bus 675)
Figs. 4-4 and 4-7,
Table 4-3
4 Case 2 with a DG and a SVC at the weakest three-
phase bus (bus 675)
Figs. 4-5 and 4-9,
Table 4-4
5 Case 4 with the DG and SVC installed at bus 680 Table 4-5
4.2.1 Identification of weakest three-phase buses using the proposed VRI
The proposed VRI (2-14) will be utilized to locate the weakest three-phase buses for
the placement of DGs with/without SVC to enhance voltage stability. The proposed
VRI is applied to a practical scenario of improving the voltage stability of the
modified unbalanced three-phase 13 node test feeder (Figure 4-1).
4.2.1.1 Bus ranking without/with a voltage regulator
Figures 4-2 and 4-3 (and Table 4-2, columns 2-3) show the bus rankings for Cases 1
and 2 based on (2-14) without and with a voltage regulator, respectively. According
to these figures, the voltage regulator has no effect on the order of bus ranking.
Note that the four nodes with the lowest VRI are buses 675, 652, 611 and 684.
Therefore, the most appropriate location for the installation of three-phase DG and
SVC compensators is bus 675.
55
0.75
0.80
0.85
0.90
0.95
1.00
1.05
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest Bus
Figure 4-2 Bus ranking for Case 1 (without any voltage regulators).
0.75
0.80
0.85
0.90
0.95
1.00
1.05
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I Weakest Bus
Figure 4-3 Bus ranking for Case 2 (with a voltage regulator).
4.2.1.2 Bus ranking with DG at the most suitable bus
DG devices (e.g., induction generators) are to be connected at the weakest three-
phase buses (e.g., weakest buses with the lowest VRI values) to improve the voltage
stability. Simulation results of Figure 4-4 and Table 4-3 indicate that the application
of one DG (an induction generator) at bus 675 does not change the order of VRI
values and therefore has no impact on the order of bus ranking.
0.75
0.80
0.85
0.90
0.95
1.00
1.05
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I Weakest Bus
Figure 4-4 Bus ranking for Case 3 (with one DG at bus 675).
56
TABLE 4-2 BUS RANKING FOR CASES 1 AND 2 BASED ON THE PROPOSED VRI.
Bus number Case 1 Case 2
RG60 0.95790 1.00004
632 0.85406 0.91581
633 0.84810 0.91099
634 0.78130 0.85749
645 0.85087 0.91252
646 0.85000 0.91148
671 0.77672 0.85468
680 0.77672 0.85468
684 0.77610 0.85403
611 0.77562 0.85359
652 0.7756 0.85329
692 0.77672 0.85468
675 0.76663 0.84700
4.2.1.3 Bus ranking with DG and SVC
One DG and one SVC are connected at bus 675 (e.g., the node with the lowest VRI
value) and the proposed index (2-14) is recalculated (Figure 4-5 and Table 4-4). As a
result, the orders of the weakest nodes are changed to buses 634, 633, 646, 645, 632,
and 652. This means the next suitable bus for connecting additional DG and SVC
units is bus 634.
57
TABLE 4-3 BUS RANKING FOR CASE 3 BASED ON THE PROPOSED VRI.
Bus number Case 3
RG60 1.00005
632 0.91926
633 0.91460
634 0.86290
645 0.91604
646 0.91503
671 0.86000
680 0.86000
684 0.85937
611 0.85895
652 0.8586
692 0.86000
675 0.85272
0.75
0.80
0.85
0.90
0.95
1.00
1.05
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
VR
I
Weakest Bus
Figure 4-5 Bus ranking for Case 4 (with one DG and one SVC at bus 675).
58
TABLE 4-4 BUS RANKING FOR CASE 4 BASED ON THE PROPOSED VRI.
Bus number Case 4
RG60 1.00002
632 0.93408
633 0.91952
634 0.75705
645 0.9250
646 0.92233
671 0.98042
680 0.98042
684 0.97848
611 0.97755
652 0.97496
692 0.98042
675 1.00000
4.2.2 Validation of proposed VRI based on grid loss calculations
Grid losses associated with the placement of DG units at each node (e.g., all possible
locations of DG) are computed and compared with the losses generated with the DG
unit connected at the weakest bus as identified by the proposed VRI (2-14).
4.2.2.1 Grid losses with one DG unit
A three-phase induction generator is placed at different buses of the modified
unbalanced three-phase 13 node test feeder (Figure 4-1) and system active and
reactive losses are plotted in Figure 4-6. This figure confirms that bus 675 (resulting
in the lowest grid losses) is the most suitable bus for DG placement, as was
previously identified by the proposed VRI (2-14).
59
0.100
0.105
0.110
0.115
0.120
0.125
0.130
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
Ac
tiv
e P
ow
er
Lo
ss
(M
W)
0.345
0.365
0.385
0.405
0.425
0.445
0.465R
ea
ctiv
e P
ow
er L
os
s (M
VA
r)
Active power loss
Reactive power loss
Figure 4-6 Reactive and active power losses associated with DG connections at different buses of Figure 4-1 (Case 2).
4.2.2.2 Grid losses with two DG units
According to (2-14), with the addition of one DG (at bus 675, Figure 4-4), the most
suitable location for the connection of a second DG unit is still at bus 675. This is in
agreement with the grid loss plots of Figure 4-7 generated by connecting the first DG
at bus 675 and placing a second DG at different buses of the modified unbalanced
three-phase 13 node feeder. These results further confirm the accuracy of the
proposed bus ranking index.
0.088
0.092
0.096
0.100
0.104
0.108
0.112
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
Ac
tiv
e P
ow
er
Lo
ss
(M
W)
0.300
0.315
0.330
0.345
0.360
0.375
0.390
Re
ac
tive
Po
we
r Lo
ss
(MV
Ar)
Active power loss
Reactive power loss
Figure 4-7 Reactive and active power losses associated with the first DG installed at bus 675 and the second DG connected at different buses of Figure 4-1 (Case 3).
4.2.3 Validation of proposed VRI based on PV curves
The PV curves based on positive-sequence voltages are plotted and compared with
the PV curve generated when DG and SVC units are connected at the weakest bus.
Figure 4-8 shows the PV curves of positive-sequence voltages at each bus for Case 2.
60
According to this figure, bus 675 has the lowest stability margin. Therefore, this is
the weakest bus as previously recognized by (2-14).
After connecting a combination of DG and SVC units at bus 675, PV curves for
Case 6 are regenerated and plotted in Figure 4-9. As expected and previously
recognized by the proposed VRI, the lowest stability margins occur at bus 634. This
will further reveal the validity of the proposed voltage ranking index for unbalanced
three-phase networks.
846674666466546644663466
1.04
1.00
0.96
0.92
0.88
0.84
0.80
Po
sit
ive-S
eq
uen
ce V
olt
ag
e [
p.u
.]
Total Load of Selected Loads (kW)
Bus 675
646 680 611 634 675 652
Figure 4-8 PV curves of positive-sequence voltage at each three-phase bus for Case 2.
61
184661546612466946664663466
1.10
1.00
0.90
0.80
0.70
Total Load of Selected Loads (kW)646 680 611 634 675 652
Bus 634
Po
sit
ive-S
eq
uen
ce V
olt
ag
e [
p.u
.]
Figure 4-9 PV curves of positive-sequence voltage at each bus for Case 4.
4.3 APPLICATION OF PROPOSED VRI IN IMPROVING MLF OF
THE MODIFIED UNBALANCED THREE-PHASE 13 NODE TEST FEEDER
Application of the proposed bus ranking index for the placement of DGs
without/with SVCs at the weakest three-phase buses will improve the maximum
loading factors as demonstrated in Table 4-5. According to the tabulated results:
A comparison of the maximum loading factors for Cases 1 and 2 indicates that the
voltage stability margin is higher with a voltage regulator. Therefore, voltage
regulators can help to improve the voltage stability margins of unbalanced
distribution systems.
After connecting DG at bus 675 (Case 3), the voltage stability margin has slightly
decreased from 2.375 to 2.343.
There is a significant improvement in MLF when a combination of DG and SVC
units is placed at the weakest three-phase bus. For example, after connecting DG
and SVC (358 kW and 0.36 MVar) at buses 680 (Case 5) and 675 (Case 4) the
maximum loading factor is improved (from 2.375 with no compensation) to 4.390
and 4.967, respectively.
62
TABLE 4-5 SIMULATION RESULTS OF THE MODIFIED UNBALANCED THREE-PHASE 13 NODE TEST FEEDER (FIG. 4-1, TABLE 4-1): COMPARISON OF MLF WITHOUT/WITH REGULATOR, DG
AND SVC.
Case
number Description Order of bus ranking
(2-14) MLF*
1 No regulation 675, 652, 611, 684, 680 2.199
2 With regulation 675, 652, 611, 684, 680 2.375
3 DG at bus 675 675, 652, 611, 684, 680 2.343
4 Combination of DG
and SVC at bus 675
634, 633, 646, 645, 632 4.967
5 Combination of DG
and SVC at bus 680
634, 633, 646, 645, 675 4.390
*) Computed by increasing the active power of all loads until the power flow solution
becomes unstable.
4.3.1 Enhancement of MLF by optimal sizing of one DG Unit
The maximum loading factors of Table 4-5 are computed for DG compensation
values of 358 kW. These factors can be improved by proper sizing of the
compensation devices as shown in Figure 4-10.
Figure 4-10 shows the impact of increasing the number of DG units on MLF. Each
DG unit injects 358 kW of active power. According to this figure, MLF can be
improved from 4.967 (Case 4) to 5.223 if the level of DG compensation at the
weakest three-phase node (bus 675) is increased from 358 kW to 5.012 MW.
63
4.80
4.85
4.90
4.95
5.00
5.05
5.10
5.15
5.20
5.25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
The number of DG units
Lo
ad
ing
Facto
r
Figure 4-10 MLF as a function of the number of DG units placed at the weakest node
(bus 675).
4.3.2 Improving MLF by placement and sizing of compensation devices
A relatively simple procedure is used to properly place and size the compensation
devices to further improve MLF of the unbalanced distribution system. The approach
is to place one compensation unit (e.g., a 358 kW DG with SVC) at the weakest bus
and compute the corresponding MLF. The procedure is then repeated by relocating
the weakest bus (based on Eq. 2-14 with all previous units in service) and placing
more compensation devices.
With the above-mentioned approach for placement of DG (with a 0.36 MVAr SVC
used for voltage regulation) are shown in Figure 4-11. The selected size of the unit
DG is 358 kW. Based on Figure 4-11, MLF can be further improved to 6.119 with a
total DG of 716 kW (consisting of 358 kW and 358 kW units at buses 675 and 634,
respectively).
0
1
2
3
4
5
6
7
No DG DG at bus
675
DG at bus
675, 634
DG at bus
675, 634, 646
Lo
ad
ing
Fa
cto
r
Figure 4-11 Simulation results for placement and sizing of DG units in the modified
unbalanced three-phase 13 node feeder (Figure 4-1).
64
4.4 CONCLUSIONS
This chapter employed the new VRI of (2-14) to identify the weakest three-phase
buses of unbalanced three-phase distribution networks. The validity of the new index
is demonstrated for the modified unbalanced three-phase 13 node feeder based on
grid losses and PV curves. The proposed index is used to improve MLF by placing
DGs (without and with SVCs) at the weakest three-phase buses. Main conclusions
regarding the stability of unbalanced distribution networks are as follows:
Voltage regulators have positive impacts on voltage stability margins under
unbalanced three-phase conditions.
After connecting induction generator at bus 675 (Case 3), the voltage stability
margin has slightly decreased from 2.375 to 2.343. However, a combination of
DG and SVC devices at the weakest three-phase bus will considerably increase
MLF and significantly improve the voltage stability.
The order of bus ranking cannot be changed without reactive power compensation
devices. The order of bus ranking is changed when SVC with voltage controller is
installed at the weakest bus (bus 675) and at bus 680.
Both the new VRI and PV curves based on positive-sequence voltage can be
properly utilized to identify the weakest bus under unbalanced conditions.
Proper sizing of one compensation device (DG with SVC) at the weakest bus will
improve MLF.
65
Chapter 5. Application of proposed VRI in improving
voltage stability of multiphase networks
5.1 INTRODUCTION
Voltage stability enhancement has always been a main concern of the distribution
system operators who are unremittingly trying to optimize energy resources and
maximize the overall profits. As discusses in Chapters 3 and 4, the voltage stability
of a system can be improved by increasing the maximum loading factor (MLF)
defined in equation (3-3) as the ratio of the maximum system load (at the voltage
collapse point) to the base load. The proposed VRI of (2-14) can be used to properly
place shunt capacitors and DG units (without/with SVCs) at the weakest single-phase
and three-phase buses to increase MLF. In this chapter, the proposed VRI is applied
to a practical scenario of improving the voltage stability of the IEEE 13 node test
feeder (Figure 3-1) and the IEEE 34 node test feeder (Figure 3-13).
5.2 APPLICATION OF PROPOSED VRI IN IMPROVING STATIC
VOLTAGE STABILITY OF THE IEEE 13 NODE TEST FEEDER
Application of the proposed VRI for the placement of shunt capacitors and DGs
without/with SVCs at the weakest single-phase and three-phase buses will improve
MLF as demonstrated in Table 5-1. According to the tabulated results:
A comparison of the maximum loading factors for Cases 1 and 2 (Table 5-1)
indicates that the voltage stability margin is higher with a voltage regulator.
Therefore, voltage regulators can help to improve the voltage stability margins of
unbalanced distribution systems.
Application of the single-phase shunt capacitor at the weakest single-phase bus
will improve MLF as demonstrated in rows 3-4 (Table 5-1) where MLF is
increased from 3.155 (without a shunt capacitor) to 3.189 (with a shunt capacitor
66
placed at the weakest node; bus 611). However, the stability margin will decrease
if the weakest bus is not selected. For example, MLF is decreased to 3.127 if the
shunt capacitor is placed at bus 652 (Case 4, Table 5-1).
TABLE 5-1 SIMULATION RESULTS OF THE IEEE 13 NODE TEST FEEDER (FIG. 3-1, TABLE 3-1): COMPARISON OF MLF WITHOUT/WITH REGULATOR, SINGLE-PHASE SHUNT CAPACITOR,
DG AND SVC.
Case
Number
(Table 3-1)
Description Order of bus ranking (2-14)* MLF**
1 No regulation 611(1p), 684(2p), 652(1p),
675(3p), Figure 3-2
2.359
2 With regulation 611(1p), 684(2p), 652(1p),
675(3p), Figure 3-3
3.155
3 Shunt capacitor at
bus 611
611(1p), 684(2p), 652(1p),
675(3p)
3.189
4 Shunt capacitor at
bus 652
611(1p), 684(2p), 652(1p),
675(3p)
3.127
5 DG at bus 675 611(1p), 684(2p), 652(1p),
675(3p), Figure 3-4
3.158
6 Combination of
DG and SVC at bus
675
611(1p), 684(2p), 634(3P),
652(1p), 671(3p) or 692(3p),
Figure 3-5
5.415
7 Combination of
DG and SVC at bus
680
611(1p), 634(3p), 684(2P),
646(2p), 675(3p)
5.126
*) 1p, 2p and 3p correspond to single-phase, two-phase and three-phase buses,
respectively.
**) Computed according to (3-3) by increasing the active power of all loads while keeping
the power factor constant until the power flow solution diverges.
67
The reason is that the voltage at bus 652 is increased whereas the voltage at bus
611 is decreased. In addition, the phase voltage unbalance rate (defined as the
ratio of the max voltage deviation from the average phase voltage to average
phase voltage [34]) at bus 684 is 0.022526 which is higher than the base-case
value of 0.006294 due to the unbalanced multiphase loading at buses 611 (phase
c), 652 (phase a) and 684 (phase ac). On the other hand, the phase voltage
unbalance rate at bus 684 (with a shunt capacitor placed at bus 611) is decreased
to 0.000448 which is lower than the base-case value.
After connecting DG at bus 675 (Case 5, Table 5-1), the voltage stability margin
has slightly increased from 3.155 to 3.158.
There is a significant improvement in MLF when a combination of DG and SVC
units is placed at the weakest three-phase bus. For example, after connecting DG
and SVC (358 kW and 0.36 MVAr) at buses 680 (Case 7, Table 5-1) and 675
(Case 6, Table 5-1), MLF is improved (from 3.155 with no compensation) to
5.126 and 5.415, respectively.
5.2.1 Enhancement of MLF by optimal sizing of one compensation device in
the IEEE 13 node test feeder
The maximum loading factors of Table 5-1 are computed for fixed shunt capacitor
and DG compensation values of 0.1 MVAr and 358 kW, respectively. These factors
can be improved by optimal sizing of the compensation devices as shown in Figures
5-1 and 5-2. The approach is to place one compensation device at the weakest bus
and compute the corresponding MLF. The procedure is then repeated by increasing
the size of compensation devices until reaching the maximum possible loading
factor. Based on Figure 5-1, MLF can be improved from 3.189 (Case 3, Table 5-1) to
3.446 if the size of the shunt capacitor placed at the weakest single-phase node (bus
611) is increased from 0.1 MVAr to 2.8 MVAr.
Figure 5-2 shows the impact of increasing the number of DG units on MLF. Each
DG unit injects 358 kW of active power. According to this figure, MLF can be
improved from 5.415 (Case 6, Table 5-1) to 5.826 if the level of DG compensation at
the weakest three-phase node (bus 675) is increased from 358 kW to 3.938 MW.
68
Furthermore, MLF of Case 5 (Table 5-1) can also be improved from 3.158 to 3.159 if
the size of DG is increased from 358 kW to 716 kW.
0
0.5
1
1.5
2
2.5
3
3.5
4
0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5 2.7 2.9 3.1
Capacitor size (MVAr)
Lo
ad
ing
Facto
rs
Figure 5-1 MLF (for the IEEE 13 node test feeder) as a function of shunt
capacitor size at the weakest single-phase node (bus 611).
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
1
Lo
ad
ing
Fa
cto
r
2 3 4 5 6 7 8 9 10 11 12 13
The Number of DG Units
Figure 5-2 MLF (for the IEEE 13 node test feeder) as a function of the number of
DG units placed at the weakest three-phase node (bus 675).
5.2.2 Improving MLF by placement and sizing of compensation devices in
the IEEE 13 node test feeder
A relatively simple procedure is used to properly place and size the compensation
devices to further improve MLF of the unbalanced distribution system. The approach
is to place one compensation unit (e.g., a 0.1 MVAr capacitor or a 358 kW DG with
SVC) at the weakest bus and compute the corresponding MLF. The procedure is then
repeated by relocating the weakest bus (based on Eq. 2-14 with all previous units in
service) and placing more compensation devices.
With the above-mentioned approach for placement and sizing of single-phase shunt
capacitors (with a unit size of 0.1 MVAr), the weakest nodes will be buses 611 and
652. MLF of the IEEE 13 node test feeder will be increased from 3.155 (Case 2 of
69
Table 5-1, one capacitor unit at bus 611) to 3.623 with a total shunt capacitor size of
3.6 MVAr (consisting of 2.7 MVAr and 0.9 MVAr at buses 611 and 652,
respectively). The accuracy can be improved by selecting a smaller unit capacitor
size.
Simulation results for the placement and sizing of DG (with a 0.36 MVAr SVC used
for voltage regulation) are shown in Figure 5-3. The selected size of the unit DG is
358 kW. Based on Figure 5-3, MLF can be further improved to 6.758 with a total DG
of 716 kW (consisting of 358 kW and 358 kW units at buses 675 and 634,
respectively).
0
1
2
3
4
5
6
7
8
No DG DG at bus 675 DGs at buses
675, 634
DGs at buses
675, 634, 633
Lo
ad
ing
Fa
cto
r
Figure 5-3 Simulation results for placement and sizing of DG units in the IEEE 13 node
test feeder (Figure 3-1).
5.3 APPLICATION OF PROPOSED VRI IN IMPROVING STATIC
VOLTAGE STABILITY OF THE IEEE 34 NODE TEST FEEDER
Application of the proposed VRI for the placement of DGs at the weakest three-
phase buses will improve MLF as demonstrated in Table 5-2. According to the
tabulated results:
A comparison of the maximum loading factors for Cases 8 and 9 (Table 5-2)
indicates that the voltage stability margin is higher with voltage regulators.
Therefore, voltage regulators can help to improve the voltage stability margins of
unbalanced distribution systems.
70
After connecting DG at bus 890 (Case 10, Table 5-2), the voltage stability margin
has slightly decreased from 2.518 to 2.411. However, after connecting DG at bus
890 (Case 11, Table 5-2), MLF is improved to 2.862.
There is a significant improvement in MLF when a DG unit (2.4 MW DFIG wind
turbines) is installed at the weakest three-phase node (bus 890). For example,
after connecting DG at buses 890 (Case 12, Table 5-2), MLF is improved (from
2.518 with no compensation) to 3.890.
TABLE 5-2 SIMULATION RESULTS OF THE IEEE 34 NODE TEST FEEDER (FIG. 3-13, TABLE 3-1): COMPARISON OF MLF WITHOUT/WITH REGULATOR, DG TYPES IG AND DFIG.
Case
Number
(Table 3-8)
System operating condition of the
IEEE 34 node test feeder MLF*
8 No voltage regulators, transformer tap ratio set to 1.0 1.895
9 Two voltage regulator, variable transformer tap ratio 2.518
10 Case 9 with a DG (200 kW IG, Appendix B, Table B2)
at the weakest three-phase node (bus 890)
2.411
11 Case 9 with a DG (200 kW DFIG wind turbine,
Appendix B, Table B3) at the weakest three-phase
node (bus 890)
2.862
12 Case 9 with DGs (2.4 MW DFIG wind turbines) at the
weakest three-phase node (bus 890)
3.890
*) Computed according to (3-3) by increasing the active power of all loads while keeping the
power factor constant until the power flow solution diverges.
Application of the proposed VRI for the placement of single-phase shunt capacitors
(0.1 MVAr) at the weakest single-phase buses will further improve MLF as
demonstrated in Table 5-3. According to the tabulated results:
Application of the single-phase shunt capacitor at the weakest single-phase bus
will improve MLF as demonstrated in Table 5-3 where MLF is increased from
2.518 (without a shunt capacitor) to 2.574 (with a shunt capacitor placed at the
71
weakest node; bus 864). However, the stability margin will decrease if the
weakest bus is not selected. For example, MLF is decreased to 2.502 if the shunt
capacitor is placed at bus 826 (Table 5-3).
TABLE 5-3 SIMULATION RESULTS OF THE IEEE 34 NODE TEST FEEDER
(FIG. 3-13): COMPARISON OF MLF WITH SINGLE-PHASE SHUNT CAPACITOR PLACED AT
DIFFERENT BUSES.
Bus number MLF*
810 2.522
818 2.554
820 2.546
822 2.526
826 2.502
838 2.502
864 2.574
856 2.530
*) Computed according to (3-3) by increasing the active power of all loads while
keeping the power factor constant until the power flow solution diverges.
5.3.1 Enhancement of MLF by optimal sizing of one compensation device in
the IEEE 34 node test feeder
The maximum loading factors of Table 5-3 are computed for fixed shunt capacitor
0.1 MVAr. These factors can be improved by optimal sizing of the compensation
devices as shown in Figures 5-4. The approach is to place one compensation device
at the weakest bus and compute the corresponding MLF. The procedure is then
repeated by increasing the size of compensation devices until reaching the maximum
possible loading factor. Based on Figure 5-4, MLF can be improved from 2.574
(Table 5-3) to 2.682 if the size of the shunt capacitor placed at the weakest single-
phase node (bus 864) is increased from 0.1 MVAr to 0.275 MVAr.
72
Table 5-4 shows the impact of increasing the number of DG units (IGs) on MLF.
Each DG unit injects 200 kW of active power. According to this table, MLF is
getting worse with the increasing in the number of DG units.
However, MLF of Case 11 (Table 5-2) continues to increase from the base-case if the
size of DG is increased as shown in Figure 5-5.
2.30
2.35
2.40
2.45
2.50
2.55
2.60
2.65
2.70
2.75
0.05 0.075 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.275 0.3
Capacitor size (MVAr)
Lo
ad
ing
Fac
tor
Figure 5-4 MLF (for the IEEE 34 node test feeder) as a function of shunt capacitor size
at the weakest single-phase node (bus 684).
TABLE 5-4 MLF (FOR THE IEEE 34 NODE TEST FEEDER) AS A FUNCTION OF THE NUMBER OF DG UNITS (IGS) PLACED AT THE WEAKEST THREE-PHASE NODE (BUS 890).
Number of DG unit MLF*
1 2.411
2 2.410
3 2.301
4 2.200
5 2.071
*) Computed according to (3-3) by increasing the active power of all loads while
keeping the power factor constant until the power flow solution becomes unstable.
73
0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
1 2 3 4 5 6 7 8 9 10
The number of DG units
Lo
ad
ing
Fac
tor
Figure 5-5 MLF (for the IEEE 34 node test feeder) as a function of the number of
DG units (DFIG wind turbines) placed at the weakest three-phase node (bus 890).
5.4 APPLICATION OF PROPOSED VRI IN IMPROVING DYNAMIC
VOLTAGE STABILITY OF THE IEEE 13 NODE TEST FEEDER
Dynamic simulations are performed to further validate the accuracy of the proposed
VRI. The IEEE 13 node test feeder (Figure 3-1) will be subjected to small and large
disturbances.
We will first consider a small disturbance caused by the operation of the voltage
regulator connected between buses 650 and RG60:
With a voltage regulator (Case 2, Table 5-1), the proposed VRI (2-14) is
calculated based on static (using power flow calculations) and dynamic (using
time-domain simulation) approaches and compared in Figure 5-6. Note that the
order of bus rankings based on the static and dynamic simulations are almost the
same. This confirms that the proposed VRI can be utilized in both static and
dynamic analyses.
With DG placed at bus 675 (Case 5, Table 5-1), the proposed VRI (2-14) is
applied to each bus at t=3sec. Although there is a clear distinction in the
calculated VRI values at some buses (Figure 5-7), the order of dynamic and static
bus voltage rankings are still the same. This confirms that the application of one
DG (type IG) has no significant impact and will not change the order of bus
ranking.
74
We now consider the impact of large disturbances caused by the operation of the
switch (Figure 3-1) connected between buses 671 and 692. Figure 5-8 shows the
voltage profiles of bus 675 at the static voltage collapse point (MLF=3.158) for Case
5 (Table 5-1) for two critical operating conditions corresponding to the switch being
opened at t=0.50sec and closed at t=0.66sec and t=0.67sec, respectively.
It can be seen that after the switch is closed at t=0.67sec, the voltage profile
cannot recover to its initial value (Figure 5-8). Furthermore, DG remains stable
after the switch is closed at t=0.66sec and becomes unstable if it is closed at
t=0.67sec (Figure 5-9).
However, with the placement of SVC at bus 675, DG becomes stable as shown in
Figure 5-10.
Figure 5-11 compares the calculated values of VRI for the above mentioned
critical operating conditions. Based on this figure, it is clear that VRI of the
critical case with the switched being closed at t=0.66sec can be used as an
indicator to identify the stability of the system.
0
0.2
0.4
0.6
0.8
1
1.2
Static Dynamic at time 200sec
VR
I
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
Figure 5-6 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 2 (Table 5-1).
75
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
0
0.2
0.4
0.6
0.8
1
1.2
VR
I
Static Dynamic at time 3sec
Figure 5-7 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 5 (Table 5-1).
2.97112.37691.78271.18850.5942 [sec]
1.0
0.8
0.6
0.4
SW closed at time 0.66sec
SW closed at time 0.67sec
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.)
675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
0
0.2
0.0
Figure 5-8 Voltage profiles of bus 675 under switch operation of Case 5 (Table 5-1).
76
2.97112.37691.78271.18850.5942 [sec]
0.80
0.40
0.00
-0.40
SW closed at time 0.66sec
SW closed at time 0.67sec
DG at bus 675: Total Active Power in MW
DG at bus 675: Total Reactive Power in MVArDG at bus 675: Total Reactive Power in MVArDG at bus 675: Total Active Power in MW
SW closed at time 0.66sec
SW closed at time 0.67sec
0
-0.80
-1.20
Acti
ve P
ow
er
[MW
] / R
eacti
ve
Po
wer
[MV
Ar]
Figure 5-9 Active and reactive power of DG at bus 675 under switch operation of Case
5 (Table 5-1).
2.97112.37691.78271.18850.5942 [sec]
0.80
0.40
0.00
-0.40
With SVC at bus 675
Without SVC
DG/SVC at bus 675: Total Active Power in MW
DG at bus 675: Total Reactive Power in MVAr
DG at bus 675: Total Active Power in MWDG/SVC at bus 675: Total Reactive Power in MVAr
Without SVC
With SVC at bus 675
0
-0.80
-1.20
Acti
ve P
ow
er
[MW
] / R
eacti
ve P
ow
er
[MV
Ar]
Figure 5-10 Active and reactive power of DG installed at bus 675 (of the IEEE 13 node
test feeder) with/without SVC after switch closed at time 0.67s.
77
0
0.2
0.4
0.6
0.8
1
1.2
RG60 632 633 634 645 646 671 680 684 611 652 692 675
Bus Number
(Stable) SW closed 0.66s (Unstable) SW closed 0.67s (Stable) SVC+ SW closed 0.67s
VR
I
Figure 5-11 Comparison of VRI values for dynamic operating conditions in the IEEE 13
node test feeder.
5.5 APPLICATION OF PROPOSED VRI IN IMPROVING DYNAMIC
VOLTAGE STABILITY OF THE IEEE 34 NODE TEST FEEDER
Dynamic simulations are performed to further validate the accuracy of the proposed
VRI. The IEEE 34 node test feeder (Figure 3-13) will be subjected to small and large
disturbances.
We will first consider a small disturbance caused by the operation of the two voltage
regulators connected between buses 814-RG10 and 852-RG11:
With two voltage regulators (Case 9, Table 5-2), the proposed VRI (2-14) is
calculated based on static (using power flow calculations) and dynamic (using
time-domain simulation) approaches and compared in Figure 5-12. Note that the
order of bus rankings based on the static and dynamic simulations are almost the
same. This confirms that the proposed VRI can be utilized in both static and
dynamic analysis.
With DG placed at bus 890 (Case 10, Table 5-2), the proposed VRI (2-14) is
applied to each bus at t=3sec. Although there is a clear distinction in the
calculated VRI values at some buses (Figure 5-12), the order of dynamic and
static bus voltage rankings are still the same. This confirms that the application of
one DG (type IG) has no significant impact and will not change the order of bus
ranking.
78
0
0.2
0.4
0.6
0.8
1.0
1.2
80
0
80
2
80
6
80
8
81
0
81
2
81
4
85
0
81
6
81
8
82
0
82
2
82
4
82
6
82
8
83
0
85
4
85
2
83
2
85
8
83
4
84
2
84
4
84
6
84
8
86
0
83
6
84
0
86
2
83
8
86
4
88
8
89
0
85
6
Bus Number
VR
IStatic Dynamic at time 400 sec
Figure 5-12 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 9 (Table 5-2).
0
0.2
0.4
0.6
0.8
1.0
1.2
800
802
806
808
810
812
814
850
816
818
820
822
824
826
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
838
864
888
890
856
Bus Number
VR
I
Static Dynamic at time 3 sec
Figure 5-13 Comparison of the proposed VRI (Eq. 2-14) based on static and dynamic
approaches for Case 10 (Table 5-2).
We now consider the impact of large disturbances caused by the operation of the
circuit breaker between buses 888 and 890 (Figure 3-13). Figure 5-14 shows the
voltage profiles of bus 890 at the static voltage collapse point (MLF=2.411) for Case
10 (Table 5-2) for two critical operating conditions corresponding to the circuit
breaker being opened at t=0.50sec and closed at t=0.53sec and t=0.54sec,
respectively.
It can be seen that after the switch is closed at t=0.54sec, the voltage profile
cannot recover to its initial value (Figure 5-14). Furthermore, DG remains stable
after the circuit breaker is closed at t=0.53sec and becomes unstable if it is closed
at t=0.54sec (Figure 5-15).
However, with the placement of SVC at bus 890, DG becomes stable as shown in
Figure 5-16.
79
Figure 5-17 compares the calculated values of VRI for the above mentioned
critical operating conditions. Based on this figure, it is clear that VRI of the
critical case with the circuit breaker being closed at t=0.53sec can be used as an
indicator to identify the stability of the system.
3.002.001.000.00 [sec]
0.60
0.50
0.40
0.30
0.20
0.10
CB closed at time 0.53sec
CB closed at time 0.54sec
Po
sit
ive
-
Se
qu
en
ce
Vo
lta
ge
(p.u
.)
675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Figure 5-14 Voltage profiles of bus 890 under circuit breaker operation of Case 10
(Table 5-2).
3.002.001.000.00 [sec]
0.250
0.125
0.000
-0.125
-0.250
-0.375
CB closed at time 0.53sec
CB closed at time 0.54sec
DG at bus 890: Total Active Power in MW
DG at bus 890: Total Reactive Power in MVArDG at bus 890: Total Reactive Power in MVArDG at bus 890: Total Active Power in MW
CB closed at time 0.53sec
CB closed at time 0.54sec
Ac
tiv
e P
ow
er
[MW
] /
Re
ac
tiv
e P
ow
er
[MV
Ar]
Figure 5-15 Active and reactive power of DG at bus 890 under circuit breaker operation
of Case 10 (Table 5-2).
80
3.002.001.000.00 [sec]
0.250
0.125
0.000
-0.125
-0.250
-0.375
With SVC at bus 890
Without SVC
DG at bus 890: Total Active Power in MW
DG at bus 890: Total Reactive Power in MvarDG at bus 890: Total Reactive Power in MvarDG at bus 890: Total Active Power in MW
With SVC at bus 890Without SVC
Ac
tiv
e P
ow
er
[MW
] / R
ea
cti
ve
Po
we
r [M
VA
r]
Figure 5-16 Active and reactive power of DG installed at bus 890 (of the IEEE 34
node test feeder) with/without SVC after circuit breaker closed at time 0.54s.
0
0.2
0.4
0.6
0.8
1.0
1.2
800
802
806
808
810
812
814
850
816
818
820
822
824
826
828
830
854
852
832
858
834
842
844
846
848
860
836
840
862
838
864
888
890
856
Bus Number
VR
I
(Stable) CB closed 0.53s (Unstable) CB closed 0.54s (Stable) SVC+CB closed 0.54s
Figure 5-17 Comparison of VRI values for dynamic operating conditions in the IEEE 34
node test feeder.
5.6 CONCLUSIONS
This chapter employed the new VRI of (2-14) to identify the weakest single-, two-
and three-phase buses of unbalanced and multiphase distribution networks for
voltage stability enhancement. Main conclusions are as follows:
Application of the proposed bus ranking index for the placement of shunt
capacitors and DGs without/with SVCs at the weakest single-phase and three-
phase buses will improve the maximum loading factors.
81
Installation of a single-phase shunt capacitor at the bus which is not the weakest
single-phase bus can reduced the overall loading factor.
The new index can be applied to both static and dynamic approaches. The
proposed index based on static approach can be used to determine which bus is
the weakest bus for the voltage stability enhancement whereas the proposed index
based on dynamic approach can be used as an indicator to identify the stability of
the system.
Time domain simulation is recommended in critical cases.
DG units with controllable reactive power such as a synchronous generator may
perform better than an induction generator in terms of voltage stability
enhancement.
The application of symmetrical components as employed in this thesis may
require values that are difficult to obtain without full three-phase measurements at
all levels of the system.
82
Chapter 6. Online bus voltage ranking in unbalanced
multiphase smart grids with plug-in electric vehicle
(PEV) charging stations
6.1 INTRODUCTION
Plug-in electric vehicles (PEVs) are expected to become popular in the near future as
alternatives to conventional fuel-based automobiles in order to reduce the emission to
the environment [35-40]. However with the random charging behaviors and
unpredictable penetration levels of PEVs in the residential feeders, voltage drop
issues and voltage stability problems are anticipated in the future smart grid
configurations [35-37, 41]. A possible solution will be to shift a portion of PEV
loading to the distribution networks by intelligently siting and sizing PEV charging
stations or PEV smart parks.
To promote and support the increasing penetration of PEVs entering into smart grid,
many counties are planning to increase the number of charging stations and/or smart
parks [39-40]. However, there are also important issues associated with increasing
the number of charging stations and smart parks in term of line overloading, bus
voltage regulations and stability problems. PEV charging stations can affect system
voltage profile, load flow and stability of the smart grid. Therefore, electric utilities
are very interested in investigating the possible impacts and drawbacks of PEV
charging demand on their distribution networks [38, 42].
In smart parks, PEV charging operation can be performed in charging mode and
discharging mode. To increase the effectiveness of smart parks, PEVs should be
charged from the grid during off-peak load hours (charging modes) and discharged to
the grid during the peak load hours (discharging mode). The electric utilities may
require load shedding if there is a high demand charging during the peak load hours
[38, 40]. In [41, 43], smart parks are placed at the lowest voltage lines under normal
83
operating conditions as reactive power and voltage supports to enhance voltage
stability in discharging modes. However, in charging modes, the system is less
stable. In addition, the bus which has the lowest voltage may not be the most suitable
location for connecting smart parks as reactive and voltage supports.
Identification of weakest buses through the bus ranking indices will play an
important role for the analysis and voltage stability enhancement of smart grids. The
purpose of bus ranking in smart grid is to determine which nodes are the weakest
buses during 24 hours for connecting compensation devices [44]. Furthermore, it can
provide insights for properly placing and sizing future PEV charging stations and
smart parks. It has been shown that the best location for reactive power
compensation to improve voltage stability margin is the weakest bus [3, 10].
In this chapter, symmetrical components are applied to the conventional bus voltage
ranking index V/Vo to extend its application to online (for example every one hour)
identification of the weakest buses of unbalanced multiphase smart grids during the
24 hours considering the impacts of charging stations. Simulations are performed and
compared using DIgSILENT PowerFactory software to identify the weakest three-
phase buses of the modified unbalanced multiphase 13 node test feeder without/with
PEV charging stations.
6.2 THE MODIFIED IEEE 13 NODE TEST SYSTEM WITH PEV
CHARGING STATIONS
For the analysis of this chapter, the IEEE unbalanced multiphase 13 node test feeder
of Figure 6-1 [33] is considered with four PEV charging stations connected at bus
634 or bus 680. The network has been simulated using DIgSILENT PowerFactory
software [32]. The system is identical to Figure 3-1 with exception of the PEV
charging stations. System data is available in the Appendixes A1 and A2.
For the dynamic analysis of this chapter, the daily P and Q load curves of Figure 6-2
are assumed and utilized for the linear loads [45]. For the PEV charging stations (at
buses 634 and 680), the daily load curve of Figure 6-3 with two peaks at 7am and
6pm is employed [36].
84
646 645 632 633 634
650
692 675611 684
652
671
680
RG604.16 kV
0. 48 kV4. 16 kV
Switch
Two- phase
Single-phaseThree- phase
115 kV
CS1
CS4CS3CS2
CS8
CS5
CS6
CS7
Case 2
Case 3
Figure 6-1 The modified unbalanced multiphase 13 node test feeder with PEV charging
stations at bus 634 or bus 680.
6.3 SIMULATION RESULTS
Simulations are performed for the modified IEEE unbalanced multiphase 13 node
test feeder of Figure 6-1 without and with PEV charging stations to investigate their
impacts on voltage profiles and bus voltage ranking indices. Simulation results are
presented for four case studies.
Case 1: No PEV charging stations.
The VRI index for an online application (2-15) is calculated and ranked to locate the
weakest three-phase buses of Figure 6-1 without any PEV charging stations. Figure
6-4 shows the impact of the dynamic daily load curves of Figures 6-2 and 6-3 on the
voltage profiles of selected nodes (buses 634, 675 and 680). According to this figure,
bus 634 has the lowest voltage profile. However the three-phase buses over 24 hours
which have the lowest bus voltage ranking indices are buses 675, 634, and 680.
Therefore, the three-phase weakest bus for Case 1 is bus 675.
85
Case 2: Four PEV charging stations at bus 634.
In the multiphase unbalanced system of Figure 6-1 four 0.2MW PEV charging
stations with the total peak charge level of 0.8MW are included at bus 634. The peak
charging (0.8MW) is about 25% of total load (3.46MW). Figure 6-5 shows the
impact of placing the PEV charging stations at bus 634 on the voltage profiles of
buses 634, 675 and 680. With the pattern charging of PEVs (Figure 6-3) at buses
634, the voltage levels at bus 634 is lower than other buses as shown in Figure 6-5.
Table 6-1 shows bus voltage ranking indices with PEV charging stations at bus 634
over 24 hours. According to this Table, the weakest three-phase bus has changed
from bus 675 (Case 1) to bus 634 as a result of PEV charging activities at bus 634.
Case 3: Four PEV charging stations at bus 680.
Case 2 is repeated, except the four 0.2MW PEV charging stations with the daily load
curves of Figure 6-3 located at bus 680. Figure 6-6 shows the impact of the charging
stations on voltage profiles with PEV charging stations at bus 680. Compared to
Case 2, the voltage profile is improved during 11am to 17pm. Table 6-2 shows the
bus voltage ranking indices with PEV charging stations at bus 680 over 24 hours.
According to this Table, the three lowest bus voltage ranking indices are associated
with buses 675, 680, and 634.
Case 4: Four PEV charging stations at bus 680 and two PEV charging stations at bus
634.
Case 3 is repeated with the addition of two 0.2MW PEV charging stations with the
daily load curves of Figure 6-3 located at bus 634. Figure 6-7 shows the impact of
the charging stations on voltage profiles with four PEV charging stations at bus 680
and two PEV charging stations at bus 634. Table 6-3 shows the bus voltage ranking
indices over 24 hours with PEV charging stations at bus 680. According to this
Table, the locations of the weakest bus have changed between buses 675 and 680.
For example, the weakest three-phase bus has changed to bus 680 at 7-9 a.m. and 6-9
p.m.
86
24.019.214.49.64.80.0
100
80
60
40
20
0
Time [Hour]
Per
cent
age
of P
eak
Load
[%]
P daily load curve
Q daily load curve
Figure 6-2 Daily load curves associated with Figure 6-1 for linear loads [45].
24.019.214.49.64.80.0
100
80
60
40
20
0
Time [Hour]
Per
cent
age
of P
eak
Load
[%]
P load curve
Figure 6-3 Daily load curves associated with Figure 6-1 for PEV charging stations [36].
87
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Figure 6-4 Simulation results for Case 1: the 24 hour voltage profile of buses 634, 675
and 680.
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Figure 6-5 Simulation results for Case 2: the 24 hour voltage profile of buses 634, 675
and 680.
88
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Time [Hour]
Figure 6-6 Simulation results for Case 3: the 24 hour voltage profile of buses 634, 675
and 680.
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Time [Hour]634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Figure 6-7 Simulation results for Case 4: the 24 hour voltage profile of buses 634, 675
and 680.
89
TABLE 6-1 CASE 2 - BUS VOLTAGE RANKING INDICES OVER 24 HOURS WITH FOUR PEV CHARGING STATIONS AT BUS 634.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.952573 0.976249 0.979515 634
1.00 0.903801 0.929840 0.933893 634
2.00 0.887627 0.913419 0.917316 634
3.00 0.877407 0.902948 0.906692 634
4.00 0.864649 0.889935 0.893688 634
5.00 0.859166 0.884163 0.887809 634
6.00 0.852665 0.878688 0.882301 634
7.00 0.830194 0.862575 0.866267 634
8.00 0.799218 0.841839 0.845514 634
9.00 0.766849 0.802819 0.807022 634
10.00 0.750888 0.775109 0.779623 634
11.00 0.735064 0.756605 0.761184 634
12.00 0.721301 0.741535 0.746147 634
13.00 0.716600 0.736621 0.741095 634
14.00 0.710610 0.730538 0.735009 634
15.00 0.708724 0.728681 0.733081 634
16.00 0.709924 0.730943 0.735222 634
17.00 0.705164 0.731868 0.736030 634
18.00 0.714965 0.748383 0.752134 634
19.00 0.718777 0.756636 0.76027 634
20.00 0.732496 0.766829 0.770428 634
21.00 0.755066 0.781949 0.785535 634
22.00 0.769885 0.794123 0.797730 634
23.00 0.781631 0.804035 0.807678 634
90
TABLE 6-2 CASE 3 - BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.979404 0.972515 0.974186 675
1.00 0.933280 0.925467 0.927765 675
2.00 0.916540 0.909093 0.911267 675
3.00 0.905937 0.898683 0.900723 675
4.00 0.892817 0.885717 0.88779 675
5.00 0.887124 0.880024 0.882001 675
6.00 0.881562 0.874371 0.876254 675
7.00 0.865036 0.856942 0.858496 675
8.00 0.843357 0.833764 0.834641 675
9.00 0.804699 0.795358 0.797155 675
10.00 0.777989 0.769874 0.772719 675
11.00 0.760107 0.752256 0.755335 675
12.00 0.745374 0.737803 0.741009 675
13.00 0.740763 0.733249 0.736329 675
14.00 0.734825 0.727404 0.730494 675
15.00 0.733023 0.725723 0.728745 675
16.00 0.735255 0.727916 0.730753 675
17.00 0.735924 0.727764 0.730107 675
18.00 0.751547 0.742872 0.744385 675
19.00 0.758997 0.749838 0.750951 675
20.00 0.768964 0.760327 0.761631 675
21.00 0.784309 0.776794 0.778571 675
22.00 0.796762 0.789638 0.791612 675
23.00 0.807028 0.800091 0.802215 675
91
TABLE 6-3 CASE 4 - BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680 AND TWO PEV CHARGING
STATIONS AT BUS 634.
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.980186 0.969367 0.969430 675
1.00 0.931868 0.919640 0.920164 675
2.00 0.915040 0.903259 0.903690 675
3.00 0.904979 0.893448 0.893767 675
4.00 0.892726 0.881386 0.881763 675
5.00 0.888124 0.876815 0.877107 675
6.00 0.882623 0.871067 0.871200 675
7.00 0.861427 0.847999 0.847394 680
8.00 0.830174 0.813725 0.811798 680
9.00 0.792331 0.777062 0.776437 680
10.00 0.774322 0.761940 0.763098 675
11.00 0.762916 0.751094 0.752668 675
12.00 0.753490 0.742078 0.743883 675
13.00 0.752773 0.741401 0.743099 675
14.00 0.749586 0.738288 0.740013 675
15.00 0.749811 0.738618 0.740282 675
16.00 0.752786 0.741394 0.742800 675
17.00 0.749838 0.736729 0.737238 675
18.00 0.759273 0.744732 0.743968 680
19.00 0.760036 0.744424 0.742983 680
20.00 0.768626 0.754182 0.753168 680
21.00 0.787815 0.775682 0.775632 680
22.00 0.803453 0.792100 0.792427 675
23.00 0.816681 0.805766 0.806365 675
92
6.4 ONLINE PLACEMENT OF SVC UNITS TO IMPROVE THE
PERFORMANCE OF THE MODIFIED IEEE 13 NODE TEST SYSTEM WITH
PEV CHARGING STATIONS
This section introduces a new online approach to improve the performances of the
emerging smart grids with renewable energy resources and smart appliances. For
these systems, prediction and forecasting of the daily load curves may not be feasible
as the location, time and duration of the smart loads (such as PEVs and smart
appliances) are randomly changing during the 24 hour period. Therefore, the
conventional approaches of locating and sizing of compensation devices based on the
forecasted daily load curves are not accurate.
The proposed approach is to place compensation devices at the weakest buses,
perform online VRI ranking, and then switch these devices in (and out of) service
according to the lowest VRI values. The approach will be demonstrated for the
modified unbalanced multiphase 13 node test feeder of Figure 6-1 through the
following case study.
Case 5: Online placement of SVC units for Case 4.
Online VRI ranking of the modified unbalanced multiphase 13 node test feeder with
four PEV charging stations at bus 680 and two PEV charging stations or bus 634
(Case 4) indicates that the weakest bus changed between nodes 675 and 680 over the
24 hour period (Table 6-3). Therefore, compensation devices which are installed at
buses 675 and 680 will be switched on and off according to the time in Table 6-3.
Figure 6-8 shows the impact of online placement of two SVC units on voltage
profiles with four PEV charging stations at bus 680 and two PEV charging stations at
bus 634.
Compared to Case 4 (Figure 6-7), the voltage profiles at all buses are improved,
especially at buses 675 and 680. Table 6-4 shows the bus voltage ranking indices
after the online placement of SVC units installed at bus 675 and 680. According to
this Table, the weakest node (after online SVC placement) is changed from buses
675 and 680 to bus 634.
93
24.019.214.49.64.80.0
1.10
1.00
0.90
0.80
0.70
Pos
itive
-Seq
uenc
e V
olta
ge [p
.u.]
Time [Hour]634: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.675: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.680: Line-Ground Positive-Sequence Voltage, Magnitude in p.u.
Figure 6-8 Simulation results for Case 5 with online placement of two SVC units: the
24 hour voltage profile of buses 634, 675 and 680.
94
TABLE 6-4 CASE 5 BUS VOLTAGE RANKING INDEX FOR THE MULTIPHASE SYSTEM OF FIGURE 6-1 WITH FOUR PEV CHARGING STATIONS AT BUS 680 AND TWO PEV CHARGING
STATIONS AT BUS 634 AFTER ONLINE PLACEMENT OF TWO SVC UNITS
Time
VRI
(Eq. 2-15)
at Bus 634
VRI
(Eq. 2-15)
at Bus 675
VRI
(Eq. 2-15)
at Bus 680
Weakest bus
0.00 0.998229 1.007018 1.003504 634
1.00 0.901377 0.918712 0.919228 634 2.00 0.885086 0.902328 0.902751 634 3.00 0.875946 0.893086 0.893397 634 4.00 0.864844 0.881851 0.88222 634 5.00 0.861389 0.878238 0.878524 634 6.00 0.854892 0.872471 0.872597 634 7.00 0.823465 0.845201 0.844589 634 8.00 0.774945 0.80296 0.801047 634 9.00 0.744331 0.767646 0.767017 634 10.00 0.744796 0.760438 0.761584 634 11.00 0.741155 0.755132 0.756705 634 12.00 0.737111 0.750354 0.752172 634 13.00 0.739296 0.752539 0.754253 634 14.00 0.737999 0.751276 0.753022 634 15.00 0.739474 0.752874 0.754561 634 16.00 0.741581 0.755811 0.757236 634 17.00 0.729233 0.747394 0.747900 634 18.00 0.726917 0.749654 0.748874 634 19.00 0.718291 0.743732 0.742282 634 20.00 0.729811 0.752813 0.751791 634 21.00 0.760041 0.778158 0.778101 634 22.00 0.781170 0.797583 0.797903 634 23.00 0.798652 0.813863 0.814459 634
95
6.5 CONCLUSIONS
This chapter has extended the application of the conventional bus voltage ranking
index of V/Vo defined for balanced three-phase systems to online identification of
the weakest buses of the unbalanced multiphase smart grid over 24 hours considering
the impacts of PEV charging stations. Furthermore, the impacts of PEV charging
stations on voltage profiles and bus ranking indices have been investigated. The
approach is demonstrated on an unbalanced multiphase 13 node test feeder using
DIgSILENT PowerFactory software considering two locations for the PEV charging
stations. Main conclusions are:
PEV charging stations with relatively large power ratings can have detrimental
impacts of smart grid loading and voltage profiles over the 24 hour period.
As the smart grid loads (such as PEV chargers, smart appliances, charging
stations and smart parks) and renewable resources (such as rooftop PVs and
wind generators) have inherent discontinuous characteristics, the locations of
the weakest voltage buses will change over the 24 hour period. Therefore,
online dynamic bus ranking approaches are required in smart gird systems.
The proposed dynamic bus ranking approach of this chapter can be utilized to
identify the weakest buses over the 24 hour period.
To control and improve the detrimental impacts of large PEV charging
stations, they should be located at the strongest buses.
96
Chapter 7. Increasing DG penetration in multiphase
distribution networks considering grid losses, maximum
loading factor and bus voltage limits
7.1 INTRODUCTION
This chapter proposes a new algorithm to improve the performance of multiphase
distribution networks by properly locating DG units and single-phase capacitors in
the three-phase and single-phase sections and increasing their ratings. The approach
consists of utilizing the positive-sequence voltage ratio Vcollapse/Vbase-load (2-14) to
identify the weakest three-phase and single-phase buses for the installation of DG
units and shunt capacitors, respectively. DG penetration levels are increased by
evaluating their impacts on voltage profile, grid losses, and MLF while considering
the voltage limits at all buses. Detailed simulations are performed for the placement
and sizing of a doubly-fed induction generator (DFIG) and single-phase capacitors in
the IEEE multiphase 34 node test feeder using DIgSILENT PowerFactory software.
The impacts of DFIG on voltage profile, active power loss and voltage stability
margin are highlighted.
An iterative algorithm is proposed for the placement and sizing of DG units and
single-phase capacitors in multiphase networks to reduced grid losses and increase
MLF while keeping all bus voltage within acceptable limits. Simulation results
including locations and the maximum penetration levels of DG units as well as the
locations and sizes of single-phase capacitors are presented for the IEEE multiphase
34 node test feeder as shown in Figure 3-13.
97
7.2 IMPACTS OF DG PLACEMENT ON VOLTAGE PROFILE, GRID
LOSS, AND MLF
7.2.1 Impact of DG on voltage profiles
In balanced three-phase networks, voltage profiles are usually plotted using the rms
bus voltage values. For unbalanced networks, system unbalanced voltage variance
index [46] has been proposed for considering voltage profiles instead of using system
rms voltage [26, 30]. However, for multiphase networks, voltage magnitudes in some
phases are missing. Therefore, in this chapter, the voltage profiles of all phases will
be plotted in the range of 0.95-1.05p.u. (see Figures 7-5, 7-8 and 7-11).
7.2.2 Impact of DG on grid losses
Grid losses associated with the placement and the penetration level of a DG unit
(e.g., at the weakest bus) are computed and compared with the losses without any
compensation device. The active power loss reduction (ALR) (for example due to the
installation of DG units or compensation devices) is calculated by (3-1).
The DG penetration level is defined as
πππππ‘πππ‘πππ πΏππ£ππ =ππ·πΊ
πππππΓ 100% (7-1)
where ππ·πΊ and πππππ are the total active power of the DG units and system loads,
respectively.
7.2.3 Impact of DG on MLF
Using a continuation three-phase power flow, PV curves for multiphase distribution
networks will be plotted. The method of symmetrical components will then be
applied to merge the three individual PV curves into a single PV curve based on
positive-sequence voltage. Finally, the maximum loading factor (MLF) will be
determined using the single PV curve based on positive-sequence voltage [3]. MLF
is defined as the ratio of the maximum system load (at the voltage collapse point) to
the base load.
98
7.2.4 Impact of DG on voltage unbalance factor
The voltage unbalance factor (VUF) is defined as the ratio of negative-sequence
voltage component to positive-sequence voltage component [47]:
% πππΉ =negative βsequence voltage component
positive βsequence voltage componentΓ 100% (7-2)
7.3 PROPOSED ALGORITHM FOR DG PLACEMENT
The proposed iterative algorithm of Figure 7-1 is designed to increase the penetration
level of DG units in multiphase networks in order to reduce total active power loss
and enhance voltage stability margins considering voltage limits at all buses. In
addition, single-phase shunt capacitors are also utilized to further improve the
performance of the systems.
Stage one of the algorithm consists of an iterative procedure to properly place and
increase the penetration of DG units in multiphase system. DG units are located one
at a time and their corresponding sizes are increased until a voltage violation is
detected in the system. To find the best location and rate of the first DG, a small
DFIG is temporary placed at the weakest three-phase bus as identified by the
calculated VRI (2-14). The size of DFIG is then increase (to reduce total system loss
and increase MLF) until one of the bus voltages is increased above the permissible
level. The first iteration terminates by permanently connecting the first DG at BusDG
with PLDG. This procedure is repeated to place more DG units as long as no voltage
violations are noticed and there are improvements in the total system loss and MLF.
Stage two of the proposed algorithm is similar to stage one with the exception of
selecting the weakest single-phase buses (identified by VRI) and connecting single-
phase capacitor banks to the single-phase sections of the multiphase network.
99
run three-phase load flow, calculate ALR (Eq. 3-1) and MLF
yes
no
0.95Β£VbusΒ£1.05 ?
run three-phase power flow, calculate VRI (Eq. 2-14), and identify the weakest three-phase bus (exclude any buses with DG),
set BusDG=the weakest three-phase bus
S
tage one: placement and sizing of D
G units
initialize parameters, location of DG (BusDG=0) and penetration level of DG (PLDG=0)
start
increase PLDG
by 1% of PLoad
temporary placement of one DG unit at BusDG with PLDG
run three-phase load flow, calculate ALR (Eq. 3-1) and MLF
0.95Β£VbusΒ£1.05 ?
run three-phase power flow, calculate VRI (Eq. 2-14), and identify the weakest single-phase bus (exclude any buses with single-phase shunt
capacitor), Set BusCap=the weakest single-phase bus
initialize parameters, location of single-phase shunt capacitor (BusCap=0) and sizing of single-phase shunt capacitor (QCap=0)
temporary connection of a single-phase shunt capacitor at BusCap with QCap
connect DG at BusDG with PLDG
yes
noPLDGΒΉ0 ?
connect a single-phase shunt capacitor at BusCap with QCap
yesnoQCapΒΉ0 ?
Stage tw
o: placement and sizing of single-phase shunt capacitorsstop
increase QCap
by 1% of Qload
yes
no
Figure 7-1 The proposed algorithm for the placement and sizing of DG units and
single-phase capacitors in multiphase networks.
100
7.4 SIMULATION RESULTS
For the analysis of this chapter, the IEEE multiphase 34 node test feeder of Figure 3-
13 [33] is considered. The network has been simulated using DIgSILENT
PowerFactory software [32]. The system data are available in [33].
7.4.1 Bus voltage ranking based on proposed VRI index
Figure 7-2 shows the bus voltage ranking for the base-case load with two automatic
voltage regulators which regulate the voltages in the range of 0.95-1.05p.u. The
weakest three-phase and single-phase buses are 890 and 864, respectively.
7.4.2 Placement and sizing of DG units to improve voltage profile, grid loss, and MLF
Stage one of the proposed iterative algorithm (Figure 7-1) consists of the installation
of DFIG wind turbines.
Iteration One- A DFIG wind turbine with power factor control is installed at the
weakest three-phase bus (bus 890) through a 4.16kV/0.69kV transformer. The
size of DFIG output is gradually increased to determine its impacts on loading
factor, active power loss reduction, and voltage profile. Simulations results are
presented in Figure 7-3 indicating that active power loss is lowest (ALR =
62.31%) at a DG penetration level of 40% while the loading factor escalates as
the DG penetration increases. However, with 40% DG penetration at bus 890, as
identified by grid loss calculation, there will be a voltage violation (at bus 890, all
phases) for a DG penetration of 40% as shown in Figure 7-4. According to the
algorithm of Figure 7-1, with 30% DG penetration at bus 890, all the bus voltage
profiles are in the range of 0.95-1.05p.u. (Figure 7-5). Notice that the voltage
profile of phase c at bus 890 is 1.0499p.u., which is very close to the upper
voltage limit of 1.05p.u. Any further increase in the DG penetration level at this
bus beyond 30% will cause an overvoltage condition at bus 890. Therefore, the
maximum penetration of the first DFIG that can be installed at bus 890 is 30%
(600kW, 666.66kVA). Furthermore, the total active power loss is reduced from
0.2641MW to 0.1053MW and MLF is increased from 2.518 to 3.150. These
101
results indicate that voltage limits should be considered as a constraint for the
methods of DG placement.
0
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0.3
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0.7
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0.9
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89
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6
Weakest bus (single-phase)Weakest bus (three-phase)
Bus Number
VR
I
Single-phase Three-phase
Figure 7-2 Simulation results for the first DG placement (stage one, iteration one);
voltage ranking index with no DFIG installation (base-case load).
0.00
0.10
0.20
0.30
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
% DG Penetration
Lo
ad
ing
Facto
r
Acti
ve
Po
wer
Lo
ss (
MW
)
Loading FactorActive Power Loss
Figure 7-3 Simulation results for the first DG placement (stage one, iteration one);
loading factor and active power loss with different DG penetrations at bus 890.
1.085
1.058
1.031
1.004
0.977
0.950
808
810
812
814
850
816
818
824
820
822
826
858
832
852
830
828
854
856
800
864
888
890
834
842
844
846
848
860
836
840
802
862
838
806
Bus Number
Vo
lta
ge
Pro
file
[p
.u.]
Line-Ground Voltage, phase-aLine-Ground Voltage, phase-bLine-Ground Voltage, phase-c
Figure 7-4 Voltage profile with 40% DG penetration at bus 890.
102
808
810
812
814
850
816
818
824
820
822
826
858
832
852
830
828
854
856
800
864
888
890
834
842
844
846
848
860
836
840
802
862
838
806
1.050
1.030
1.010
0.990
0.970
0.950
Bus Number
Vo
lta
ge
Pro
file
[p
.u.]
Line-Ground Voltage, phase-aLine-Ground Voltage, phase-bLine-Ground Voltage, phase-c
Figure 7-5 Simulation results for the first DG placement (stage one, iteration one);
voltage profile with 30% DFIG penetration at bus 890.
Iteration Two- With 30% DFIG connected at bus 890, a similar procedure is
implemented in the second iteration to properly locate and size the second DFIG
and increase the penetration of DG units. According to Figure 7-6, the four
weakest buses are now 890, 852, 888, and 814. That is the weakest three-phase
bus is still bus 890. However, according to the results of the first iteration, the
DG penetration level is restricted at this bus due to a voltage violation at bus 890.
As a result, the most appropriate position for the second DFIG is bus 852. The
algorithm continues by increasing the size of DG while considering MLF, active
power loss (Figure 7-7) and voltage profiles (Figure 7-8). Iteration two is
terminated at a maximum DG penetration of 30% at bus 852. This will result in a
further active power loss reduction of 76.92% and MLF will be increased to
3.519.
103
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0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
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4
88
8
89
0
85
6
Weakest bus (three-phase)
Bus Number
VR
IWeakest bus (single-phase) Single-phase Three-phase
Figure 7-6 Simulation results for the second DG placement (stage one, iteration two);
voltage ranking index with 30% DFIG units installed at bus 890.
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
4.50
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0.00
0.10
0.20
0.30
Lo
ad
ing
Fa
cto
r
% DG Penetration
Ac
tiv
e P
ow
er
Lo
ss
(M
W)
Loading FactorActive Power Loss
Figure 7-7 Simulation results for the second DG placement (stage one, iteration two);
loading factor and active power loss with 30% DFIG penetration at bus 890 and different
DFIG penetration at bus 852.
Iteration Three- With the two DFIGs in service at buses 890 and 852, the four
weakest three-phase buses are buses 890, 814, 888, and 848 (Figure 7-9). As
there is already a DG unit in service at bus 890, the best location for the third
DFIG connection is bus 814. However, with only 1% penetration of DG at bus
814, there will be a voltage violation at bus 808 (e.g., phase c voltage is increased
to 1.050142p.u.). The first stage of the algorithm (Figure 7-1) will be terminated
as any further DFIG connection will result in a voltage violation. Therefore,
according to the results of iterations 1-3, the maximum DG penetration can be
safely increased to 60% (30% DFIG units installed at bus 890 and 30% DFIG at bus
852) without any voltage violations.
104
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8
81
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6
1.050
1.030
1.010
0.990
0.970
0.950
Bus Number
Vo
ltag
e P
rofi
le [
p.u
.]
Line-Ground Voltage, phase-aLine-Ground Voltage, phase-bLine-Ground Voltage, phase-c
Figure 7-8 Simulation results for the second DG placement (stage one, iteration two);
voltage profile with 30% DFIG penetration at bus 890 and 30% DFIG penetration at bus
852.
7.4.3 Placement and sizing of single-phase capacitor banks to further improve voltage profile, grid loss, and MLF
Stage two of the proposed algorithm (Figure 7-1) aims at further improvements in
voltage unbalanced factor (VUF), total power loss, MLF and voltage profiles through
the installation of capacitor banks in the single-phase sections of the multiphase
network.
Iteration One- The first capacitor bank is connected at the weakest single-phase
bus and its size is increased until a voltage violation is spotted. According to
Figure 7-9, the weakest single-phase location is bus 822 and the capacitor size
can be safely increased to 273kVAr while all bus voltage profiles are kept in the
range of 0.95-1.05p.u. (Figure 7-10). Note that any further increase of this
capacitor size beyond 273kVAr will cause an overvoltage condition at bus 802
(phase c). The inclusion of the two DFIGs (at busses 890 and 852) and a single-
phase capacitor (at bus 822) has increased the total active power loss from
0.0610MW to 0.0778MW while MLF is further increased to 3.575.
105
Iteration Two- The iterative procedure is repeated to install more single-phase
shunt capacitors. According to Figure 7-10, the four weakest single-phase
locations are buses 822, 820, 864 and 818. The next location for capacitor
placement is bus 820. However, installation of a 3kVAr (1% of Qload) single-
phase shunt capacitor at this bus 820 will cause an overvoltage condition at bus
802 (phase a) as shown in Figure 7-11. Therefore, the second stage of the
algorithm terminates with only one capacitor bank connected to bus 822.
0
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89
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6
Weakest bus (three-phase)
Bus Number
VR
I
Weakest bus (single-phase)Single-phase Three-phase
Figure 7-9 Simulation results for the third DG placement (stage one, iteration three)
showing voltage ranking index with 30% DFIG units installed at bus 890 and 30% DFIG at
bus 852.
0
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89
0
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6
Weakest bus (three-phase)
Bus Number
VR
I
Weakest bus (single-phase)Single-phase Three-phase
Figure 7-10 Simulation results for the single-phase capacitor placement (stage two,
iteration one); voltage ranking index with 30% DG units installed at bus 890, 30% DG at bus
852, and single-phase shunt capacitor 0.273MVAr at bus 822.
106
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1.050
1.030
1.010
0.990
0.970
0.950
Bus Number
Vo
ltag
e P
rofi
le [
p.u
.]
Line-Ground Voltage, phase-aLine-Ground Voltage, phase-bLine-Ground Voltage, phase-c
Figure 7-11 Simulation results for the single-phase capacitor placement (stage two,
iteration one); voltage profile with 30% DG penetration at bus 890, 30% DG penetration at
bus 852, and single-phase 0.273MVAr shunt capacitor at bus 822.
7.4.4 Summary and analysis of simulation results
Simulation results for increasing the penetration of DFIG and single-phase capacitors
in the IEEE multiphase 34 node test feeder of Figure 3-13 based on the proposed
algorithm (Figure 7-1) are summarized and compared in Table 7-1. The impacts of
DG and capacitor installations on the performance (total active power loss, MLF and
VUF) of the multiphase network are highlighted in rows 3-6 and 9-11 of Table 7-1,
respectively. With the proposed algorithm, a total DG penetration level of 60% (30%
DFIG units installed at bus 890 and 30% DFIG at bus 852) is achieved and a 0.273MVar
shunt capacitor is placed at bus 822 without any voltage violations which will
reduced the total active power loss to 0.0778MW and increased MLF to 3.575. In
addition, the percentage of VUF at the weakest three-phase bus has been
considerably improved from 2.99 to 0.36 as shown in Figure 7-12.
107
0.00
0.50
1.00
1.50
2.00
2.50
3.00
800 802 806 808 812 814 850 816 824 828 830 854 852 832 858 834 842 844 846 848 860 836 840 862 888 890
%VUF Base-case%VUF with 30% DG penetration at bus 890%VUF with 30% DG penetration at buses 890 and 852%VUF with 30% DG penetration at buses 890 and 852and single-phase shunt capacitor at bus 822
Vo
ltag
e U
nb
ala
nce
Facto
r [%
]
Bus Number
Figure 7-12 Comparison of %VUF at different iterations of the proposed algorithm
(Figure 7-1).
7.5 CONCLUSIONS
This chapter has extended the definition of the conventional bus voltage ranking
index (VRI) of V/Vo defined for balanced three-phase systems to identify the
weakest buses of the multiphase systems. The new VRI is utilized through a
proposed iterative procedure to increase the penetration levels of DG and single-
phase capacitors in order to improve the performance of the multiphase networks.
The proposed algorithm is relatively simple and can effectively reduce total active
power loss, increase MLF and decrease VUF while keeping all bus voltages within
the allowable lower and higher limits. Main conclusions are:
The proposed bus ranking approach based on the positive-sequence voltage
ratio Vcollapse/Vno-load can effectively identify the weakest three-phase and
single-phase buses for DG and shunt capacitors placements, respectively.
Analysis of simulation results indicates that the penetration level of DG is
limited by considering the bus voltage limits rather than grid losses and/or
MLF. Therefore, at high penetration levels of DG units, it is necessary to take
voltage limits into account.
Placements of shunt capacitors at the weakest single-phase buses will not only
increase MLF, but also further improve the unbalanced voltage factor.
108
TABLE 7-1 DETAILED SOLUTION FOR DFIG AND CAPACITOR PLACEMENT AND SIZING IN THE IEEE MULTIPHASE 34 NODE TEST FEEDER (FIGURE 3-13) USING THE PROPOSED
ALGORITHM OF FIGURE 7-1.
Stage one: Placement and sizing of DFIGs
Itera
tion
Weakest
three-
phase bus
Penetration
of DFIG [%]
Total
loss
[MW]
MLF VUF at
bus 890
[%]
Simulation
results
0 - - 0.2641 2.518 2.985199 Fig. 7-12
1 890 30 0.1053 3.150 0.492043 Figs. 7-2, 7-3,
7-12
2 852 30 0.0610 3.519 0.361299 Figs. 7-6, 7-7,
7-12
3 814 - - - - Fig. 7-9
Stage two: Placement and sizing of single-phase shunt capacitors
Itera
tion
Weakest
single-
phase bus
Capacitor
size [kVAr]
Total
loss
[MW]
MLF VUF at
bus 890
[%]
Simulation
results
0 - - 0.0610 3.519 0.361299 Fig. 7-12
1 822 273 0.0778 3.575 0.356531 Figs. 7-10 and
7-12
2 820 - - - - Fig. 7-11
Final Solution: 30% DFIG penetration at bus 890, 30% DFIG penetration at bus 852
and 273kVAr capacitor at bus 822.
109
Chapter 8. Conclusions
This thesis proposes a new bus voltage ranking index (VRI) and applies it to improve
the voltage stability of unbalanced three-phase and multiphase networks. After a
literature review conducted in Chapter 1, Chapter 2 proposed a new bus ranking
approach based on positive-sequence voltage of Vcollapse/Vbase-load for unbalanced and
multiphase networks (2-14) to identify the weakest single-phase, two-phase, and
three-phase buses. Another bus ranking approach is also introduced for online
applications such as the emerging smart grids.
Chapter 3 compares the performance and accuracy of the conventional and the
proposed VRI for multiphase networks. The new index is validated using the well-
known voltage sensitivity approaches ππ/ππ and ππ/ππ for balanced and
unbalanced three-phase distribution networks. Further validations are performed
through grid loss calculations and generation of PV curves based on positive-
sequence voltage and voltage sensitivity methods. Detailed simulation results for the
modified IEEE multiphase 13 node and 34 node test feeders show the validity and
accuracy of the new bus ranking approach. The main outcomes of this chapter are as
follows: (1) the proposed ranking index can accurately identify the weakest single-,
two- and three-phase buses under different operating conditions without and with
voltage regulators, capacitor banks and DG units (without/with SVCs); (2) the
conventional bus voltage ranking index and the two voltage sensitivity methods
(ππ/ππ and ππ/ππ) are able to accurately identify the weakest buses of balanced
networks. However, in unbalanced networks, the conventional VRI and the two
voltage sensitivity methods failed to detect the weakest bus.
Chapter 4 presents the application of the proposed VRI in improving the voltage
stability and increasing the MLF of unbalanced three-phase networks. Detailed
simulation results including five case studies are presented for the modified IEEE
unbalanced three-phase 13 node test feeder. Main conclusions are: (1) the proposed
ranking index can be properly utilized to identify the weakest bus under unbalanced
110
three-phase operating conditions; (2) the proposed VRI can be used as an index to
place compensation devices at the weakest buses of unbalanced three-phase networks
to enhance the voltage stability and improve MLF; (3) placement of compensation
devices at the weakest bus may change the location of the weakest bus.
In Chapter 5, the proposed VRI in utilized to improve the voltage stability margins
and MLF of multiphase distribution networks. Extensive simulation results are
carried on for the IEEE multiphase 13 and 34 node test feeders. It is revealed that the
proposed VRI can fulfill both the static and dynamic voltage stability criteria. Static
voltage stability improvements are achieved by using the proposed VRI to identify
the weakest single-, two- and three-phase buses of multiphase distribution networks,
while the proposed index based on dynamic approach at the critical time can be used
as an indicator to identify the stability of the system.
In Chapter 6, an online bus ranking approach is proposed to identify the weakest
buses over the 24 hour period considering active and reactive daily loads curves. The
approach is used to study and compensate the detrimental impacts of PEV charging
stations on voltage profiles and voltage stability of the distribution network.
Simulations results indicate that the location of the weakest buses can be changed
over 24 hours with PEV charging stations. Then, the switching strategy of
compensation devices connected at the weakest buses according to the lowest hourly
VRI values can perform better than the conventional installations of the
compensation devices in terms of voltage profiles.
In Chapter 7, the proposed VRI is utilized to improve the performance of multiphase
distribution networks by properly increasing the penetration levels and ratings of DG
units such as DFIGs and single-phase capacitors. Simulation results show that high
penetration levels of DG units can cause overvoltage problems. Consequently, at
high penetration levels of DGs, it is necessary to also take voltage limits into
account. Therefore, an iterative algorithm for the placement and sizing of DG units
and single-phase capacitors is introduced to reduced grid losses and increase MLF in
multiphase networks while keeping all bus voltages within acceptable limits. It is
shown that the new algorithm for the placement and sizing of three-phase DG units
and single-phase capacitors can effectively reduce total active power loss, increase
111
MLF and decrease VUF of multiphase distribution networks while keeping all bus
voltages levels within the permissible limits.
8.1 CONTRIBUTIONS
The main results of this thesis have been released in five conference papers and three
journal articles (two under review) as listed in Section 1.5. The primary contributions
are as follow.
1. The proposed bus voltage ranking index can be used to identify the weakest
single-, two- and three-phase buses in multiphase networks for voltage stability
enhancement.
2. The proposed index can be applied to both static and dynamic approaches. Static
voltage stability can be improved by using the proposed VRI to identify the
weakest single-, two- and three-phase buses of multiphase distribution networks,
while the proposed index based on dynamic approach at the critical time can be
used as an indicator to identify the stability of the system.
3. The proposed index is modified for online bus voltage ranking and voltage
stability improvement in distribution systems with dynamic loads to identify the
weakest buses over the 24 hour period considering active and reactive daily loads
curves.
4. A new iterative algorithm is proposed and tested for properly placing and
increasing the penetration levels of three-phase DG units and single-phase
capacitor banks in multiphase networks to reduced grid losses, increase MLF and
decrease VUF while keeping all bus voltages within acceptable limits.
8.2 FUTURE WORKS
The following areas are suggested for future research in continuation of this work.
1. Online bus voltage ranking and control of compensation devices for voltage
stability enhancement in the emerging smart grid configurations with renewable
energy resources and dynamic loads such as PEVs and smart appliances.
112
2. Online application of the proposed iterative algorithm for the placement and
sizing of DG units and single-phase capacitors in smart grids for dynamically
increasing the penetration levels of compensation devices.
113
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Every reasonable effort has been made to acknowledge the owners of copyright
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Appendix A - The IEEE 13 Node and 34 Node Test
Systems
A1-IEEE 13 Node Test Feeder Data
TABLE A1-1 OVERHEAD LINE CONFIGURATION DATA.
Configuration Phasing Phase Neutral Spacing
ACSR ACSR ID
601 B A C N 556,500 26/7 4/0 6/1 500
602 C A B N 4/0 6/1 4/0 6/1 500
603 C B N 1/0 1/0 505
604 A C N 1/0 1/0 505
605 C N 1/0 1/0 510
TABLE A1-2 UNDERGROUND LINE CONFIGURATION DATA.
Configuration Phasing Cable Neutral Space ID
606 A B C N 250,000 AA, CN None 515
607 A N 1/0 AA, TS 1/0 Cu 520
TABLE A1-3 TRANSFORMER DATA.
kVA kV-high kV-low R - % X - %
Substation 5,000 115 - D 4.16 Gr. Y 1 8
XFM -1 500 4.16 β Gr.W 0.48 β Gr.W 1.1 2
120
TABLE A1-4 LINE SEGMENT DATA.
Node A Node B Length(ft.) Configuration
632 645 500 603
632 633 500 602
633 634 0 XFM-1
645 646 300 603
650 632 2000 601
684 652 800 607
632 671 2000 601
671 684 300 604
671 680 1000 601
671 692 0 Switch
684 611 300 605
692 675 500 606
TABLE A1-5 CAPACITOR DATA.
Node Ph-A Ph-B Ph-C
kVAr kVAr kVAr
675 200 200 200
611 100
Total 200 200 300
121
TABLE A1-6 REGULATOR DATA.
Regulator ID 1
Line Segment 650 - 632
Location 50
Phases A - B -C
Connection 3-Ph,LG
Monitoring Phase A-B-C
Bandwidth 2.0 volts
PT Ratio 20
Primary CT Rating 700
Compensator Settings Ph-A Ph-B Ph-C
R - Setting 3 3 3
X - Setting 9 9 9
Voltage Level 122 122 122
TABLE A1-7 DISTRIBUTED LOAD DATA.
Node A Node B Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-3
Model kW kVAr kW kVAr kW kVAr
632 671 Y-PQ 17 10 66 38 117 68
122
TABLE A1-8 SPOT LOAD DATA.
Node Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-3
Model kW kVAr kW kVAr kW kVAr
634 Y-PQ 160 110 120 90 120 90
645 Y-PQ 0 0 170 125 0 0
646 D-Z 0 0 230 132 0 0
652 Y-Z 128 86 0 0 0 0
671 D-PQ 385 220 385 220 385 220
675 Y-PQ 485 190 68 60 290 212
692 D-I 0 0 0 0 170 151
611 Y-I 0 0 0 0 170 80
TOTAL 1158 606 973 627 1135 753
123
A2-IEEE 13 Node Test Feeder Impedance
For overhead line configuration, impedance matrix given below can be input directly
to DiGSILENT software. Except for underground line configuration data,
DiGSILENT requires in R0+jX0 and B0 format. Therefore, the phase impedance
matrix has to be converted to the sequence impedance matrix by the modified
Carsonβs equation (A-1) [50].
ππππ = π¨ βπ ππππ π¨ = πππ πππ πππ
πππ πππ πππ
πππ πππ πππ
(A-1)
where
π¨ = π π ππ ππ ππ π ππ
π¨ βπ =π
π π π ππ π ππ
π ππ π
For example, the phase impedance matrix of underground line configuration 606
connecting between buses 692 and 675 can be converted to the sequence impedance
matrix as shown in (A-2).
ππππ = π. ππππ + π. πππππ βπ. ππππ β π. πππππ βπ. ππππ + π. πππππ
βπ. ππππ + π. πππππ π. ππππ + π. πππππ βπ. ππππ + π. πππππβπ. ππππ β π. πππππ π. ππππ + π. πππππ π. ππππ + π. πππππ
(A-2)
Configuration 601:
Z (R +jX) in ohms per mile
0.3465 1.0179 0.1560 0.5017 0.1580 0.4236
0.3375 1.0478 0.1535 0.3849
0.3414 1.0348
B in micro Siemens per mile
6.2998 -1.9958 -1.2595
5.9597 -0.7417
5.6386
124
Configuration 602:
Z (R +jX) in ohms per mile
0.7526 1.1814 0.1580 0.4236 0.1560 0.5017
0.7475 1.1983 0.1535 0.3849
0.7436 1.2112
B in micro Siemens per mile
5.6990 -1.0817 -1.6905
5.1795 -0.6588
5.4246
Configuration 603:
Z (R +jX) in ohms per mile
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.3294 1.3471 0.2066 0.4591
1.3238 1.3569
B in micro Siemens per mile
0.0000 0.0000 0.0000
4.7097 -0.8999
4.6658
Configuration 604:
Z (R +jX) in ohms per mile
1.3238 1.3569 0.0000 0.0000 0.2066 0.4591
0.0000 0.0000 0.0000 0.0000
1.3294 1.3471
B in micro Siemens per mile
4.6658 0.0000 -0.8999
0.0000 0.0000
4.7097
125
Configuration 605:
Z (R +jX) in ohms per mile
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
1.3292 1.3475
B in micro Siemens per mile
0.0000 0.0000 0.0000
0.0000 0.0000
4.5193
Configuration 606:
Z (R +jX) in ohms per mile
0.7982 0.4463 0.3192 0.0328 0.2849 -0.0143
0.7891 0.4041 0.3192 0.0328
0.7982 0.4463
B in micro Siemens per mile
96.8897 0.0000 0.0000
96.8897 0.0000
96.8897
Configuration 607:
Z (R +jX) in ohms per mile
1.3425 0.5124 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000
B in micro Siemens per mile
88.9912 0.0000 0.0000
0.0000 0.0000
0.0000
126
A3-IEEE 34 Node Test Feeder Data
TABLE A3-1 LINE SEGMENT DATA.
Node A Node B Length(ft.) Configuration 800 802 2580 300 802 806 1730 300 806 808 32230 300 808 810 5804 303 808 812 37500 300 812 814 29730 300 814 850 10 301 816 818 1710 302 816 824 10210 301 818 820 48150 302 820 822 13740 302 824 826 3030 303 824 828 840 301 828 830 20440 301 830 854 520 301 832 858 4900 301 832 888 0 XFM-1 834 860 2020 301 834 842 280 301 836 840 860 301 836 862 280 301 842 844 1350 301 844 846 3640 301 846 848 530 301 850 816 310 301 852 832 10 301 854 856 23330 303 854 852 36830 301 858 864 1620 303 858 834 5830 301 860 836 2680 301 862 838 4860 304 888 890 10560 300
127
TABLE A3-2 OVERHEAD LINE CONFIGURATION.
Configuration Phasing Phase Neutral Spacing ID
ACSR ACSR
300 B A C N 1/0 1/0 500
301 B A C N #2 6/1 #2 6/1 500
302 A N #4 6/1 #4 6/1 510
303 B N #4 6/1 #4 6/1 510
304 B N #2 6/1 #2 6/1 510
TABLE A3-3 TRANSFORMER DATA.
kVA kV-high kV-low R [%] X [%]
Substation 2500 69 - D 24.9 -Gr. W 1 8
XFM -1 500 24.9 - Gr.W 4.16 - Gr. W 1.9 4.08
TABLE A3-4 SPOT LOADS.
Model kW kVAr kW kVAr kW kVAr
860 Y-PQ 20 16 20 16 20 16
840 Y-I 9 7 9 7 9 7
844 Y-Z 135 105 135 105 135 105
848 D-PQ 20 16 20 16 20 16
890 D-I 150 75 150 75 150 75
830 D-Z 10 5 10 5 25 10
Total 344 224 344 224 359 229
128
TABLE A3-5 SHUNT CAPACITORS.
Node Ph-A Ph-B Ph-C
kVAr kVAr kVAr
844 100 100 100
848 150 150 150
Total 250 250 250
129
TABLE A3-6 DISTRIBUTED LOADS.
Node Node Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-3
A B Model kW kVAr kW kVAr kW kVAr
802 806 Y-PQ 0 0 30 15 25 14
808 810 Y-I 0 0 16 8 0 0
818 820 Y-Z 34 17 0 0 0 0
820 822 Y-PQ 135 70 0 0 0 0
816 824 D-I 0 0 5 2 0 0
824 826 Y-I 0 0 40 20 0 0
824 828 Y-PQ 0 0 0 0 4 2
828 830 Y-PQ 7 3 0 0 0 0
854 856 Y-PQ 0 0 4 2 0 0
832 858 D-Z 7 3 2 1 6 3
858 864 Y-PQ 2 1 0 0 0 0
858 834 D-PQ 4 2 15 8 13 7
834 860 D-Z 16 8 20 10 110 55
860 836 D-PQ 30 15 10 6 42 22
836 840 D-I 18 9 22 11 0 0
862 838 Y-PQ 0 0 28 14 0 0
842 844 Y-PQ 9 5 0 0 0 0
844 846 Y-PQ 0 0 25 12 20 11
846 848 Y-PQ 0 0 23 11 0 0
Total 262 133 240 120 220 114
130
TABLE A3-7 REGULATOR DATA.
Regulator ID 1
Line Segment 814 - 850
Location 814
Phases A - B -C
Connection 3-Ph,LG
Monitoring Phase A-B-C
Bandwidth 2.0 volts
PT Ratio 120
Primary CT Rating 100
Compensator Settings Ph-A Ph-B Ph-C
R - Setting 2.7 2.7 2.7
X - Setting 1.6 1.6 1.6
Voltage Level 122 122 122
Regulator ID 2
Line Segment 852 - 832
Location 852
Phases A - B -C
Connection 3-Ph,LG
Monitoring Phase A-B-C
Bandwidth 2.0 volts
PT Ratio 120
Primary CT Rating 100
Compensator Settings Ph-A Ph-B Ph-C
R - Setting 2.5 2.5 2.5
X - Setting 1.5 1.5 1.5
Voltage Level 124 124 124
131
A4-IEEE 34 Node Test Feeder Impedance
Configuration 300
Z (R +jX) in ohms per mile
1.3368 1.3343 0.2101 0.5779 0.2130 0.5015
1.3238 1.3569 0.2066 0.4591
1.3294 1.3471
B in micro Siemens per mile
5.3350 -1.5313 -0.9943
5.0979 -0.6212
4.8880
Configuration 301
Z (R +jX) in ohms per mile
1.9300 1.4115 0.2327 0.6442 0.2359 0.5691
1.9157 1.4281 0.2288 0.5238
1.9219 1.4209
B in micro Siemens per mile
5.1207 -1.4364 -0.9402
4.9055 -0.5951
4.7154
Configuration 302
Z (R +jX) in ohms per mile
2.7995 1.4855 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000
0.0000 0.0000
B in micro Siemens per mile
4.2251 0.0000 0.0000
0.0000 0.0000
0.0000
132
Configuration 303
Z (R +jX) in ohms per mile
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
2.7995 1.4855 0.0000 0.0000
0.0000 0.0000
B in micro Siemens per mile
0.0000 0.0000 0.0000
4.2251 0.0000
0.0000
Configuration 304
Z (R +jX) in ohms per mile
0.0000 0.0000 0.0000 0.0000 0.0000 0.0000
1.9217 1.4212 0.0000 0.0000
0.0000 0.0000
B in micro Siemens per mile
0.0000 0.0000 0.0000
4.3637 0.0000
0.0000
133
A5- The Modified Unbalanced Three-Phase 13 Node Test Feeder Data
TABLE A5-1 OVERHEAD LINE CONFIGURATION DATA.
Configuration Phasing Phase Neutral Spacing
ACSR ACSR ID
601 B A C N 556,500 26/7 4/0 6/1 500
602 C A B N 4/0 6/1 4/0 6/1 500
TABLE A5-2 UNDERGROUND LINE CONFIGURATION DATA.
Configuration Phasing Cable Neutral Space ID
606 A B C N 250,000 AA, CN None 515
TABLE A5-3 TRANSFORMER DATA.
kVA kV-high kV-low R [%] X [%]
Substation 5,000 115 - D 4.16 Gr. Y 1 8
XFM -1 500 4.16 β Gr.W 0.48 β Gr.W 1.1 2
134
TABLE A5-4 LINE SEGMENT DATA.
Node A Node B Length(ft.) Configuration
632 645 500 602
632 633 500 602
633 634 0 XFM-1
645 646 300 602
650 632 2000 601
684 652 800 606
632 671 2000 601
671 684 300 601
671 680 1000 601
671 692 0 Switch
684 611 300 601
692 675 500 606
TABLE A5-5 CAPACITOR DATA.
Node Ph-A Ph-B Ph-C
kVAr kVAr kVAr
675 200 200 200
611 100
Total 200 200 300
135
TABLE A5-6 REGULATOR DATA.
Regulator ID 1
Line Segment 650 - 632
Location 50
Phases A - B -C
Connection 3-Ph,LG
Monitoring Phase A-B-C
Bandwidth 2.0 volts
PT Ratio 20
Primary CT Rating 700
Compensator Settings Ph-A Ph-B Ph-C
R - Setting 3 3 3
X - Setting 9 9 9
Voltage Level 122 122 122
TABLE A5-7 DISTRIBUTED LOAD DATA.
Node A Node B Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-3
Model kW kVAr kW kVAr kW kVAr
632 671 Y-PQ 17 10 66 38 117 68
136
TABLE A5-8 SPOT LOAD DATA.
Node Load Ph-1 Ph-1 Ph-2 Ph-2 Ph-3 Ph-3
Model kW kVAr kW kVAr kW kVAr
634 Y-PQ 160 110 120 90 120 90
645 Y-PQ 0 0 170 125 0 0
646 D-Z 0 0 230 132 0 0
652 Y-Z 128 86 0 0 0 0
671 D-PQ 385 220 385 220 385 220
675 Y-PQ 485 190 68 60 290 212
692 D-I 0 0 0 0 170 151
611 Y-I 0 0 0 0 170 80
TOTAL 1158 606 973 627 1135 753
137
A6- The Modified Unbalanced Three-Phase 13 Node Test Feeder Impedance
Configuration 601:
Z (R +jX) in ohms per mile
0.3465 1.0179 0.1560 0.5017 0.1580 0.4236
0.3375 1.0478 0.1535 0.3849
0.3414 1.0348
B in micro Siemens per mile
6.2998 -1.9958 -1.2595
5.9597 -0.7417
5.6386
Configuration 602:
Z (R +jX) in ohms per mile
0.7526 1.1814 0.1580 0.4236 0.1560 0.5017
0.7475 1.1983 0.1535 0.3849
0.7436 1.2112
B in micro Siemens per mile
5.6990 -1.0817 -1.6905
5.1795 -0.6588
5.4246
Configuration 606:
Z (R +jX) in ohms per mile
0.7982 0.4463 0.3192 0.0328 0.2849 -0.0143
0.7891 0.4041 0.3192 0.0328
0.7982 0.4463
B in micro Siemens per mile
96.8897 0.0000 0.0000
96.8897 0.0000
96.8897
138
Appendix B β Simulation parameters
TABLE B1 SIMULATION PARAMETERS FOR THE INDUCTION GENERATOR (400 KW).
Generator Parameters
Nominal voltage 4.16 kV
Power factor 0.9 lagging
Nominal apparent power 475 kVA
Rated mechanical power 400 kW
Nominal frequency 50 Hz
No of pole pairs 1
Connection D
TABLE B2 SIMULATION PARAMETERS FOR THE INDUCTION GENERATOR (200 KW).
Generator Parameters
Nominal voltage 0.69 kV
Power factor 0.92 lagging
Nominal apparent power 226.92 kVA
Rated mechanical power 200 kW
Nominal frequency 50 Hz
No of pole pairs 1
Connection Y
139
TABLE B3 SIMULATION PARAMETERS FOR THE DFIG WIND TURBINE.
Generator Parameters
Nominal voltage 0.69 kV
Power factor 0.92 lagging
Nominal apparent power 226.92 kVA
Rated mechanical power 200 kW
Nominal frequency 50 Hz
No of pole pairs 1
Connection Y
Efficiency at nominal operation 95.8 %
Nominal speed 2980 rpm
Zero-sequence resistance 0.01 p.u.
Zero-sequence reactance 0.1 p.u.
140
Appendix C βDIgSILENT PowerFactory [32]
DIgSILENT is a computer aided engineering tool for the analysis of industrial,
utility, and commercial electrical power systems. It has been designed as an
advanced integrated and interactive software package dedicated to electrical power
system and control analysis in order to achieve the main objectives of planning and
operation optimization. DIgSILENT was the world's first power system analysis
software with an integrated graphical one-line interface. That interactive one-line
diagram included drawing functions, editing capabilities and all relevant static and
dynamic calculation features. The accuracy and validity of the results obtained with
this package has been confirmed in a large number of implementations, by
organizations involved in planning and operation of power systems.
141
Appendix D β Elixir Journal: Bus Voltage Ranking for
Unbalanced Three-phase Distribution Networks and
Voltage Stability Enhancement
142
143
144
145
146
147