chapter 4 power loss minimization by the placement of dg in the distribution...
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CHAPTER 4
POWER LOSS MINIMIZATION BY THE PLACEMENT OF DG
IN THE DISTRIBUTION SYSTEMS
4.1 INTRODUCTION
The power loss in the distribution system is significantly higher because
of lower voltage and hence high current, compared to that in a high voltage
transmission system, which in turn, causes an increase in the cost of power and poor
voltage profile along the distribution feeder. The total loss in the distribution system
is composed of two parts : real power loss and reactive power loss. The real power
loss due to the active component of current required by the load and reactive power
loss due to reactive component of current required to compensate the reactive power
requirement of network component and hence to control of the system voltage.
Among these losses, the active power loss is much more important due to the low
operating voltage of the distribution system and higher current. Moreover, in the
distribution system the resistance value is large compared to the reactance value.
There are many methods used for loss reduction like,
Feeder reconfiguration
Capacitor placement
Conductor grading
DG placement
All these methods are involved with passive elements except DG
placement. Both DG unit placement and capacitor reduce power loss and improve
the voltage profile significantly, but the placement of DG reduces the loss almost
double that of the capacitor.
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4.2 PROBLEM FORMULATION
The objective of the present optimization problem is to minimize the
network power loss,
21
1.
bN
b bb
Min f I R (4.1)
Where,
Nb - Total number of branches in the given radial distribution system
b - Branch number
Ib - Current in branch b
Rb - Resistance of branch b
PDG min < PDG < PDG max
Vi min < Vi < Vi max
The optimal location and size of DG found by VSI, PSI, LSF and GA has
been used to minimize the total real power loss of the radial distribution system.
4.3 TYPES OF DG MODELS
DG units can be classified into three major types based on their terminal
characteristics in terms of real and reactive power delivering capability as follows,
Type 1 DG : Supplying real power only
Ex. Photovoltaic cell
Type 2 DG : Supplying both real and reactive power
Ex. Variable speed Wind Turbine Generator
The reactive power injected by DG is given by,
QDG = PDG * tan
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Type 3 DG : Supplying the real power, but consuming
proportionately reactive power.
Ex. Fixed speed wind turbine generator
The reactive power consumed by DG is given by,
QDG = - (0.5 + 0.04 * P2DG )
4.4 LOAD MODELING
A balanced load that can be represented either as constant power,
constant current or constant impedance load. The definition of these load model is
given below,
4.4.1 Constant impedance load model (constant Z)
A static load model where the power varies with the square of the
voltage magnitude. It is also referred to as a constant admittance load model.
4.4.2 Constant current load model (constant I)
A static load model where the power varies directly with voltage
magnitude.
4.4.3 Constant power load model (constant P)
A static load model where the power does not vary with changes in
voltage magnitude. It is also known as a constant MVA load model.
The general expression of load is given below,
21 2 3( ) [ ( ) ( ) ]nP m P a a V m a V m (4.2)
21 2 3( ) [ ( ) ( ) ]nQ m Q b b V m b V m (4.3)
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Where,
Pn , Qn - Nominal real and reactive power respectively.
V(m) – Voltage at node m.
a1, a2, a3, b1, b2, b3 are constant.
For Constant power load (CP)
a1=b1=1 and ai=bi=0 for i= 2, 3.
For Constant current load (CI)
a2=b2=1 and ai=bi=0 for i= 1, 3.
For Constant impedance load (CZ)
a3=b3=1 and ai=bi=0 for i= 1, 2.
4.5 PERFORMANCE ENHANCEMENT OF DISTRIBUTION
SYSTEM WITH THE PLACEMENT OF DG
In this work, the performance index is formulated taking into account of
important indices such as real power loss index, reactive power loss index and
voltage regulation index. The definition of these indices is given below
4.5.1 Real Power Loss Index
The Real Power Loss Index (RPLI) is defined as the ratio between real
power loss with and without DG. The lower value this index shows that the effect
DG on loss reduction is more compared to without DG.
Re
RealpowerlosswithDGRPLI
alpowerlosswithoutDG (4.4)
Where,
RPLI < 1 DG has reduced Real Power losses,
RPLI = 1 DG has no impact on Real Power losses,
RPLI > 1 DG has caused more Real Power losses.
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4.5.2 Reactive Power Loss Index
The Reactive Power Loss Index (QPLI) is defined as the ratio between
reactive power loss with and without DG. The lower value this index shows that the
effect DG on loss reduction is more compared to without DG.
Re
ReactivepowerlosswithDGQPLI
activepowerlosswithoutDG (4.5)
QPLI < 1 DG has reduced Reactive Power losses,
QPLI = 1 DG has no impact on Reactive Power losses,
QPLI > 1 DG has caused more Reactive Power losses.
4.5.3 Voltage Regulation Index
The Voltage Regulation Index (VRI) gives the information about the
deviation of node voltage from the reference value (Vnom). The lower value this
index shows that lesser deviation of node voltage from the reference value
2
| |nbnom i
n nom
V VVRIV
(4.6)
Where,
nb - Number of buses
Vnom - nominal Voltage =1.0 p.u
Vi - Bus Voltage
4.5.4 Performance Index (PI)
To select the best DG model among all the DG models, a performance
index has been formulated. The minimum value this index shows the best DG model
among all DG types
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Objective function: Min PI = w1* RPLI +w2 * QPLI +w3 * VRI
w1 = 0.5; w2 = 0.3; w3 = 0.2
w1+w2+w3 =1
4.6 RESULT AND DISCUSSION
4.6.1 Analysis of load models for 33 bus and 69 bus RDS
Table 4.1 and Table 4.2 show that the analysis of different load models
for 33 bus and 69 bus radial distribution system. From the tables, it is proved that
constant impedance model reduces loss effectively for 33 bus RDS and 69 bus RDS.
In the present work, the constant power model has been used in which the P and Q
are independent of the voltage changes. Moreover the objective function is to
minimize power losses, so the constant power model is considered for modeling the
behavior of loads for the present analysis.
Table 4.1 Analysis of Load models – 33 bus Radial Distribution System
Load Model
Base Case
with DG
Optimal Location = 18
Optimal Size = 1.4 MW
Ploss
(kW)
Qloss
(kVAR)
Ploss
(kW)
Qloss
(kVAR)
Constant Power 223.8788 149.0574 213.9561 142.0609
Constant Current 193.1345 128.2945 184.7406 122.3879
Constant Impedance 166.6848 110.4666 151.4223 100.0054
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Table 4.2 Analysis of Load models – 69 bus Radial Distribution System
Load Model
Base Case with DG
Optimal Location = 61 Optimal Size = 1.3 MW
Ploss
(kW)
Qloss
(kVAR)
Ploss
(kW)
Qloss
(kVAR)
Constant Power 216.6168 98.0373 113.3205 54.3213
Constant Current 182.113 83.1569 98.4427 47.7024
Constant Impedance 154.7065 71.4546 87.6569 42.9967
4.6.2 Power loss reduction by the placement of multiple DGs in 33 bus
RDS and 69 bus RDS
Table 4.3 and Table 4.4 gives the information about power loss reduction
by the placement of multiple Type-I DGs on 33 bus RDS and 69 bus RDS. From the
tables it was understood that placement of more DGs reduces the power loss
effectively, but it increases cost factor of the system and in some cases it will
increase the power losses due to reverse power flow.
Figure 4.1 and Figure 4.2 shows the comparative analysis for voltage
profile improvement of 33 bus RDS and 69 bus RDS by the placement of multiple
DGs. The placement of multiple DGs on the 33 RDS improves the voltage profile of
system in the critical node (i.e node 18) and the last nodes (node 30 to 33). For 69
bus RDS improves the voltage profile of system in the critical node (i.e node 65).
But placement of multiple DGs on the increase cost function and hence in this
analysis maximum number of DGs is restricted as four DGs for 33 bus RDS and
three DGs for 69 bus RDS.
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Table 4.3 Power Loss Reduction by the placement of multiple DGs using GA 33 bus Radial Distribution System
Base Case (without DG)
Ploss (kW) = 223.88 Qloss (kVAR) = 149.05
Min.BusVoltage (p.u)=0.9134
Technique GA
No.of DGs Single DG Two DGs Three DGs Four DGs
Total Real Power Loss (kW)
201.6078 187.7812 178.2516 165.3235
Total Reactive Power Loss (kVAR)
133.829 125.4414 118.6868 109.9001
Location 32 32, 25 32, 25, 18 32, 25, 18, 8
DG size (MW) 2 2, 0.4 2, 0.4, 0.1 2, 0.4, 0.1,0.2
Min.Voltage (p.u) 0.9165 0.9182 0.9259 0.9302
Table 4.4 Power Loss Reduction by the placement of multiple DGs using GA - 69 bus Radial Distribution System
Base Case (without DG)
Ploss (kW) = 216.6168 Qloss (kVAR) = 98.0373
Min.Bus Voltage (p.u) = 0.9134
Technique GA
No.of DGs Single DG Two DGs Three DGs
Total RealPower Loss (kW) 113.3205 109.5748 106.2457
Total Reactive Power Loss (KVAR)
54.3213 52.711 51.1878
Location 61 61, 65 61, 65, 12
DG size (MW) 1.3 1.3, 0.3 1.3, 0.3, 0.2
Min.Voltage (p.u) 0.9601 0.9625 0.9637
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Figure 4.1 Comparative analysis of Voltage Profile Improvement by the placement of multiple DGs- 33 bus System
Figure 4.2 Comparative analysis of Voltage Profile Improvement by the placement of multiple DGs- 69 bus System
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4.6.3 Analysis of DG models for power loss reduction in 33 bus RDS and
69 bus RDS
Table 4.5 gives the comparative analysis of optimal placement of DG by
using VSI, PSI, LSF and GA with the consideration of different types of DG models
for 33 bus RDS. From Table 4.5, it is manifest that the maximum real power loss is
reduced to 14.517% and reactive power loss is reduced to 14.86% with the
placement of Type-2 DG at the location 32 as found out by GA.
Table 4.6 gives the comparative analysis of optimal placement of DG
using VSI, PSI, LSF and GA with the consideration of different types of DG models
for 69 bus RDS. From Table 4.6, it is proved that the maximum real power loss is
reduced to 67.608% and reactive power loss is reduced to 63.474% with the
placement of Type-2 DG at the location 61 as found out by GA. With reference to
the Table 4.5 and Table 4.6, it is evident that each index and GA gives the optimal
location depending upon the characteristic equation. The VSI gives more
importance to voltage stability instead of loss reduction. The PSI finds the weakest
link that leads to voltage collapse when the system load increases beyond the
margin. The loss sensitivity factor gives more importance to loss reduction instead
of voltage profile improvement. Each index gives a different location depending on
its own characteristic equation.
Figure 4.3 to Figure 4.8 gives the comparative analysis of voltage profile
improvement by the placement of Type-1, Type-2 and Type-3 DG on 33 bus RDS
and 69 bus RDS. From the Figures it is clear that among all types of DG, Placement
of type-2 DG is found by GA gives better performance on voltage profile
improvement due to the injection of both real and reactive power. The convergence
characteristics of GA for the placement of different type of DG in 33 bus RDS and
69 bus RDS is shown in figure 4.9 to 4.14. The detailed load flow solution by the
placement of Type-1, Type-2 and Type-3 on 33 bus RDS and 69 bus RDS is given
in Appendix-I.
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Table 4.5 Comparative Analysis of Power Loss Reduction using VSI, PSI, LSF and GA– 33 bus Radial Distribution System
Base Case
(without DG)
Ploss (kW) =223.88
Qloss (KVAR) = 149.05
Min. Bus Voltage (p.u) = 0.9134
Type of DG Type- I Type -2 Type -3
Technique VSI PSI LSF GA VSI PSI LSF GA VSI PSI LSF GA
Optimal Location 18 7 31 32 18 7 31 32 18 7 31 32
Optimal Size (MW) 1.3 2 1.7 2 1.3 2 1.7 2 1.3 2.6 1.6 2
Ploss (kW) 213.95 210.97 207.92 201.54 209.30 204.39 200.28 191.37 218.27 215.81 214.92 211.33
Qloss (kVAR) 142.06 139.93 138.18 133.78 138.80 135.30 132.99 126.88 145.10 144.14 142.95 140.46
Min. Bus Voltage (p.u)
0.9178 0.9161 0.9151 0.9166 0.918 0.9169 0.9155 0.9175 0.9174 0.914 0.9144 0.9153
%Ploss reduction 4.435 5.765 7.127 9.978 6.509 8.704 10.54 14.517 2.5020 3.6037 3.9991 5.6018
%Qloss reduction 4.6897 6.1154 7.290 10.24 6.873 9.220 10.769 14.86 2.6483 3.288 4.0919 5.758
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Table 4.6 Comparative Analysis of Power Loss Reduction using VSI, PSI, LSF and GA – 69 bus Radial Distribution System
Base Case (without DG)
Ploss (kW) = 216.6168 Qloss (kVAR) = 98.0373
Min. Bus Voltage (p.u) = 0.9134
Type of DG Type- I Type -2 Type -3
Technique VSI PSI LSF GA VSI PSI LSF GA VSI PSI LSF GA
Optimal Location 65 61 65 61 65 61 65 61 65 61 65 61
Optimal Size (MW) 0.3 1.3 0.3 1.3 0.3 1.6 0.3 1.4 0.2 1.2 0.2 0.9
Ploss (kW) 210.99 113.34 210.99 113.32 207.48 70.93 207.48 70.16 214.39 162.05 214.39 160.96
Qloss (kVAR) 95.65 54.33 95.65 54.32 94.16 36.14 94.16 35.809 97.096 75.01 97.09 74.54
Min. Bus Voltage (p.u)
0.9143 0.9591 0.9143 0.9590 0.9145 0.9626 0.9145 0.971 0.9132 0.9376 0.9132 0.9416
%Ploss reduction 2.59375 47.672 2.5937 47.68 4.2148 67.252 4.2148 67.608 1.0236 25.18 1.0236 25.688
%Qloss reduction 2.42907 44.579 2.4290 44.589 3.9457 63.131 3.9459 63.474 0.9596 23.485 0.9596 23.958
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Figure 4.3 Comparative analysis of Voltage Profile Improvement-Type-1 DG-33 bus RDS
Figure 4.4 Comparative analysis of Voltage Profile Improvement-Type-2 DG- 33 bus RDS
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Figure 4.5 Comparative analysis of Voltage Profile Improvement-Type-3 DG-33 bus RDS
Figure 4.6 Comparative analysis of Voltage Profile Improvement-Type-1 DG- 69 bus RDS
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Figure 4.7 Comparative analysis of Voltage Profile Improvement-Type-2 DG- 69 bus RDS
Figure 4.8 Comparative analysis of Voltage Profile Improvement-Type-3 DG-69 bus RDS
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Figure 4.9 Convergence characteristics and best individual of GA for the placement of Type-I DG in 33 bus RDS
Figure 4.10 Convergence characteristics and best individual of GA for the placement of Type-2 DG in 33 bus RDS
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Figure 4.11 Convergence characteristics and best individual of GA for the placement of Type-3 DG in 33 bus RDS
Figure 4.12 Convergence characteristics and best individual of GA for the placement of Type-1 DG in 69 bus RDS
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Figure 4.13 Convergence characteristics and best individual of GA for the placement of Type-2 DG in 69 bus RDS
Figure 4.14 Convergence characteristics and best individual of GA for the placement of Type-3 DG in 69 bus RDS
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4.6.4 Performance Index for 33 bus RDS and 69 bus RDS
To get the multiple benefits from DG, the performance index has been
formulated. It is minimized using genetic algorithm and the results are given in the
Table 4.7 for 33 bus RDS. The performance index has been solved by genetic
algorithm and the optimal location has been found at 32nd bus for all types of DGs.
From Table 4.7, it is also concluded that among all types of DG, Type-2 DG gives a
better performance compared to other DGs and it has the minimized performance
index of 0.69206.
For 69 bus RDS, Type-2 DG gives a better performance on real power,
reactive power and voltage profile improvement. The minimized value of
performance index is found to be 0.2176 by placement of DG at location 61 with the
size of 1.4 MW shown in Table 4.8. Thus the performance index is used to select the
best DG model (Type-II) for loss reduction and voltage profile improvement of 33
bus and 69 bus RDS.
Table 4.7 Performance Enhancement of Distribution System with the Placement of DG - 33 bus Radial Distribution System
Base Case (without DG)
Ploss (kW) =223.88 Qloss (kVAR) = 149.05
Min. Bus Voltage (p.u) = 0.9134 Type of DG Type- I Type -2 Type -3
Technique GA
Optimal Location 32 32 32
Optimal Size (MW) 2 1.89 2.12
ILP 0.9 0.8540 0.9440
ILQ 0.897 0.8510 0.9424
VRI 0.0541 0.0488 0.0511
PI 0.72992 0.69206 0.76494
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Table 4.8 Performance Enhancement of Distribution System with the Placement of DG–69 bus Radial Distribution System
Base Case (without DG)
Ploss (kW) = 216.6168 Qloss (kVAR) = 98.0373
Min. Bus Voltage (p.u) = 0.9134 Type of DG Type- I Type -2 Type -3
Technique GA
Optimal Location 61 61 61
Optimal Size (MW) 1.3 1.4 0.9
ILP 0.4879 0.3021 0.6929
ILQ 0.3456 0.2279 0.4743
VRI 0.0011 0.0009 0.0014
PI 0.3479 0.2176 0.489
4.7 SUMMARY
This chapter deals with the power loss minimization of radial distribution
system by the placement of multiple DGs and multi-type DG. The optimal location
and optimal size of DG using VSI, PSI and LSF has been analyzed. The genetic
algorithm based AI techniques has been used to find the optimal location and size of
DG. From the analysis, it is proved that Type-2 DG found by GA has been given
better performance on loss reduction and voltage profile improvement. From the
analysis, it is found that each index and GA gives different location based on the
characteristics equation of the index. In order to get multiple benefits from DG an
performance index has been formulated which extract important benefits of DG
such as real power loss reduction, reactive power loss reduction and voltage profile
improvement at the single location found by GA. Due to the rapid development of
industrial and commercial demand, the load growth on the feeder increases rapidly
day by day. To meet the incremental load, the feeder needs additional substation or
additional feeders. The effect of DG on the feeder to meet the incremental load is
discussed in next chapter.
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CHAPTER 5
PLACEMENT OF DISTRIBUTED GENERATION WITH THE
CONSIDERATION OF LOAD GROWTH
5.1 INTRODUCTION
Due to the rapid development of industrial and commercial loads, the
growth in feeder load has been increasing every year. The growth in feeder load may
be due to the addition of new loads to the feeder or due to the incremental addition
to the existing loads. Once the load exceeds the feeder capacity, it is limited by
either voltage regulation or thermal constraints. The feeder can accept the loads only
when the voltage constraint is satisfied.
Increase in load demand system experiences
Increase in power loss
Increase in load factor
Increase in cost of feeder energy loss
Increase in cost of supplied energy
Deviation in system voltage
To maintain the stability of system, additional feeders or substations has
been needed to meet the loads. But it is practically difficult due to the economic
constraints. Moreover the feeder has been designed on a long term basis and the
peak demand may exist only for a few hours. Due to these reasons, the placement of
DG can extend the life of the existing feeder for few years without need of
additional feeders or substations. This chapter deals about placement of different
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DG models on RDS to meet the incremental loads and a comparative analysis has
been made to enumerate the effect of different DG models on reducing cost of
feeder energy loss.
5.2 PROBLEM FORMULATION
The objective of this chapter is to reduce the cost of energy loss by the
placement of DG with the consideration of load growth. Different type of DG
models is used to validate the result. The cost of energy loss equation is derived by
considering the effect of load growth on real and reactive power demand, effect of
load growth on active power loss and effect of load growth on load factor of the
system [37].
5.2.1 Effect of load growth on active and reactive power demand
Real and reactive power load at any year k is given by,
PLOAD(k) = PLOAD(0)(1+g)k (5.1)
QLOAD(k) = QLOAD(0)(1+g)k (5.2)
g =annual load growth rate = 7.5%
PLOAD(0) = real power loads in the base year (0th year)
QLOAD(0) = reactive power loads in the base year (0th year)
PLOAD(k) = real power load in the year k
QLOAD(k) = reactive power load in the year k
33 bus Radial Distribution System (RDS)
The 33 bus RDS has the base real power load of 3.71 MW and maximum
load PLOAD (k=kmax) of 12.6858 MW. Then kmax is found using the Equation (5.1)
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12.6858= 3.71 * (1+0.075) kmax
kmax = 17 years (appx)
69 bus Radial Distribution System (RDS)
The 33 bus RDS has the base real power load of 3.8014 MW and
maximum load PLOAD (k=kmax) of 12.0914 MW. Then kmax is found using the
equation 5.1.
12.0914 = 3.8014 * (1+0.075) kmax
kmax = 15.999 =16 years (appx)
5.2.2 Determination of loss in terms of load growth
Real power loss at any year k is given by
PLoss(k) = PLoss(0)(1+ growth) k (5.3)
g =annual load growth rate = 7.5%; = a constant = 2.15
PLoss (0) = real power loss in the base year (0th year)
PLoss(k) = real power loss in the kth year
5.2.3 Effect of load growth on load factor of the system
The system experiences growth in load factor due to increase in load
diversity with load growth. The load factor at any year k is given as,
( ) ( )( )u u pLF k LF y k LF LF (5.4)
Where,
16( ) (0.5)k
y k
ultimate load factor = 0.26uLF
present load factor 0.55pLF