electrical power.pdf

8/13/2019 Electrical power.pdf

http://slidepdf.com/reader/full/electrical-powerpdf 1/22

CHAPTER 1

INTRODUCTION

1.1 Electrical Power Distribution System

In order to remain competitive, it is becoming more and more

important for a power distribution planner to be able to meet efficiently

the demands of Electrical Load Distribution System (ELDS) [1-3] having

Radial and Weakly-meshed Delivery Networks (RWDNs). It is necessary

to develop efficient techniques for the analysis of load-flow of these

networks.

Since the use of digital-computers, many algorithms were developed

for solving the Distribution Power Flow. These algorithms are found to be

robust to obtain the solution for transmission system, but are unsuitable

for Radial and Weakly-meshed Delivery Networks (RWDNs). This difficulty

is attributed to following reasons: RWDNs with the wide range of R/X

ratio; Multi-phase and Unbalanced System with data inclusion like

linedata, busdata, -section tap-changing transformer. Then the

included data may not be certain i.e. uncertain data has to be considered

for the analysis. To tackle these challenges efficient algorithms are

proposed to analyse RWDNs. Further, the analysis is extended to find

Reliability Range Indices (RRIs) for RDN with Data Uncertainties (DU).



2

The Distribution or Delivery Load-Flow analysis should contain:

Ordered input data ordered output data

Radial to Weakly-meshed circuits on loading

Voltage magnitude and Phase angle

Change in nodal voltages due to ‗Data Uncertainties‘

Reliability Range Indices (RRIs)

Flow of Power injection and losses and load demands

Voltage variation for different possible components like: -section

or co-generator ; tap-changing transformer

To solve the problems of distribution system the basic load-flow

analysis must be robust and time efficient. This doctoral work proposes

distribution power flow algorithms to find efficient solution for Radial and

Weakly-meshed Load Delivery Network.

The methods discussed in [4-7] fall into the category of

ill-conditioned Load Delivery System (LDS) for the high R/X ratio data

reported in[8]. The generic Newton-Raphson (NR) and Fast Decoupled

Load Flow algorithms diverge for majority of the LDS studied. The basic

types of networks in LDS for load-flow studies are:



3

1.1.1 Radial Delivery Network

In this type of Radial Delivery Network (RDN) each node is connected

to the substation via at least one path shown in Fig. 1.1. To index the

node-element relation data from main feeder to laterals and sub-laterals

a special technique is needed.

Fig.1.1 Single phase Node-27 RDN with open tie-switches.

1.1.2 Weakly-meshed Delivery Network

In Distribution System some loops are formed by closing normally

open-tie-switches. The RDN can be extracted from a Weakly-meshed

Delivery Network (WDN), even if few loops exist. WDNs with loops, are



4

converted into RDN presented by Horia Andrei [9]. Sometimes

distribution feeder serving high-density load areas contain few loops

created by closing normally open tie switches A, B and C as shown in

Fig. 1.2.

Fig.1.2 Single phase WDN with closed tie-lines at A, B and C.

In WDN, there is a set of simultaneous equations that should be

solved, but its order is relatively small. It is equal to the number of loops

in the network (or close points) which is much smaller than number of

nodes. In case of WDN, to read and index the input data from the main

feeder to the laterals and sub-laterals is still complex as compared to the

RDN. Since 1988 very few techniques have been developed to obtain

WDN Power Flow solution.



5

In a Radial-Weakly meshed Delivery Networks (RWDNs)‘ as the

number of nodes and elements increases the complexity of network also

increases. The present thesis analyzes ‗power flow methods for balanced

and unbalanced networks using standard input data as mentioned in the

references [8, 17, 27, 33]. Efficient algorithms are proposed to solve

power flow problems for RWDNs.

In this Chapter, section 1.2 gives review of the literature for the

RWDNs load flow studies and then the plan of organization of thesis is

laid out in section 1.3.

1.2 Literature survey

This section gives a brief review of the literature in the area of data

assigning, algorithm design and load flow analysis.

In LDS load-flow algorithms are differed based on types of network

structures like:

Radial Delivery Network (RDN)

Weakly-meshed Delivery Network (WDN)

1.2.1 Previous power-flow algorithms for RDN

In recent past load flow algorithms for RDN ‗ are evaluated in A.G.

Bhutad et al [10]. The first category consists of different version of

Newton-Raphson (NR) based methods [11-14], the second category based



6

on Gauss-Seidel (GS) algorithms are [15-19]. Usually the second category

algorithms are found to be more efficient, when compared to the first

one. The proposed RDN power flow algorithms are compared with the

algorithms of second category.

The below mentioned conclusions of A.G. Bhutad et al [10] are

motivated to improve the solution for RDN and further extended to solve

for WDN.

It expresses difficulty with the algorithms like : Network-Topology (NT)

[17]; Implicit Z-bus [15] and modified GS [16], since the whole

matrices needs to be updated ___ Forward-Backward (FB) [25, 27] and

Ladder Network (LN) theory [18, 19, 24] are more flexible, even if input

data and system data gets modified.

In NT, FB substitution and LN theory algorithms, Net Execution

Time (NET) is of descending order i.e., 3.1250 secs, 2.9220 secs and

2.7340 secs, respectively, on P-IV computer with 1.6 GHz frequency

and 128 MB RAM.

Discussions on RDN power-flow algorithms:

The implicit Z-bus T.H.Chen et al [15] based on principle of

superposition, only one type of source is considered at a time for ‗ the

calculation of bus voltages. Initially, all the bus voltages are assumed to

be equal to the swing bus voltage. In the next step, since the current

injections and bus voltages are dependent on each other, these



7

quantities are required to be determined iteratively. The ‗ swing bus‘ is

short-circuited while calculating the component of bus voltages due to

the current injections. This algorithm is based on the complete

factorization of bus admittance matrix [Ybus] which leads to take more

NET to find the direct power flow solution.

The disadvantage of [15] was overcome by J.H. Teng [16] with merge

of Implicit Z-bus algorithm and the Gauss-Seidal (GS) algorithms to

obtain improve the computational efficiency. In [15, 16] complete or

fractional factorization of [Ybus] is necessary to solve power-flow problem.

But J.H Teng of [17] does not require such factorization for both the

balanced and unbalanced networks, whereas disadvantage of [17] is

extraction of partial topographical information about the network. Using

partial information this method develops matrices [Bus Injection to

Branch Current] and [Branch Current to Bus Voltage] i.e. [BCBV] and

[BIBC] and which leads to less flexibility to modify the system data and

also it takes more computation time to solve these special matrices.

LN theory [18, 19], traces the network to and fro from its load to the

source ends to find power flow solution. The performance of conventional

power routines and shunts/pi-sections are studied in [20-22]. S.Ghosh

and D.Das [23] formulated FB based power flow equations to find voltage

during Forward Sweep, and element current using little complex

technique i.e. nodes beyond the element at backward sweep.



8

The steps of LN based methods [18-19, 24]:

(i) Backward-Sweep (BS): The current in each element is obtained by

tracing in the backward direction using KCL

( ) ( )

( ) ( )

( ) ( )

main ia La ap

main ib Lb bp

p M main i

c Lc cp

I i I

I i I

I i I

where I a (m ), I b (m ) and I c (m ) are the element currents of line section m , and

i La, i Lb and i Lc are the equivalent node-currents

(ii) Forward-Sweep (FS): Using the element-currents calculated in the

BS, the values of voltages are calculated by using KVL during FS.

LN theory is very much similar to the FB. Though the basic idea of

both the algorithms is same, there are differences in the steps of

implementation. In the LN theory, the ‗optimal __ ordering‘ of nodes is

done as shown in Fig.1.3. In the BS, the node voltages are assumed to be

equal to some initial value in the first – iteration.

Fig 1.3 A simple nonlinear ladder network



9

Due to the voltage dependency of loads in Distribution System (DS),

various static load models are incorporated in the ‗ power flow‘ [29] to

obtain better and more accurate results, wherein convergence of the

algorithm is slow.

It is practical requirement to have effective power flow solution with

the inclusion of ‗system components‘ (pi-section, ground-wire, tap-

changing-transformer, co-generator etc..) FB based 3-power flow in

four-wire is reported by M.Rade Ciric et al [25] and A unified 3

transformer model is studied in [26].

Comprehensive models are considered including lines, switches,

transformer, shunts capacitors, co-generator and several types of loads

in Fast Decoupled Load Flow method by R.D.Zimmerman et al [27], but

does not read as per the test data of IEEE feeders [28]. In A. Golkar [29]

each network element loss is expressed in small size matrix form, which

plays a key role to obtain the solution only for RDN. In K.Prakash and

M.Sydulu [30] using this concept of primitive impedances of the lines,

only diagonal elements of the ‗ Distribution Load Flow‘ (DLF) matrix are

considered to find more direct solution than the method illustrated in

[17], the necessary information is stored in ‗ single dimension vectors‘ to

obtain the solution only for RDN. Whereas in [25, 29, 30] methods do not

deal with addition of system-components in the Delivery System.

Further, In LDS due to presence of uncertainties in input data (line,

bus, pi-section etc.), it is not economically advisable to employ



10

measuring devices everywhere along the laterals of RDN and WDN. The

reliable theoretical error analysis is expected to provide an accurate

range-solution for data uncertainty problem in load flow. For that,

‗Possibilistic and probabilistic‘ solutions are found using Fuzzy-

Techniques [31, 32] and Self-Validating (SV) tools (Interval Arithmetic

and Affine Arithmetic) [35, 37], respectively. These solutions are not

comparable because the underlying assumptions on the data are very

different i.e. one is qualitative; the other is quantitative, though random.

The load flow algorithms like Fuzzy-Model [31] and load estimation using

the Fuzzy set [32] are applied in ‗Fuzzy plus Interval Arithmetic‘ based

algorithm submitted by D.Das [33], but are applicable only for balanced

RDN. An iterative 3- RDN power flow method was solved by B. Das

[34] for uncertain input data using Interval Arithmetic(IA) given in [35].

Similarly, IA tool has been applied to RDN by A.Vaccaro and D.Villacci

[36] and the solutions are found superior over Monte Carlo simulation

and Stochastic load flow algorithm. IA allows for numerical computation

where in each quantity is represented by interval number without a

probability order. This leads to find strict closed bound solution.

Unfortunately, IA often yields an interval-solution that is much wider

than the exact range of the computed function. It means, IA utilizes the

data variation within relatively for small interval, to obtain feasible

solution. The IA algorithm saves the computation time, but with less



11

accuracy when compared to application of Affine Arithmetic (AA) [37]

tool.

Unlike IA, the quantity representation used by AA are first order

approximation, whose error is generally quadratic in the width of the

input intervals. Hence, when compared to IA higher asymptotic accuracy

of AA-Tool compensates for the increased cost of its operation. In this

thesis, IA and AA-tools have been used to formulate ‗ power flow

equations‘ and find solution for both the RDN and WDN with input

parameter uncertainties. The work also develops IA and AA tools based

power flow equations obtain the solution for networks with data

uncertainty in lines with pi-sections and tap-changing transformer.

Some applications in Reliability Indices (RI) using fuzzy arithmetic

and fuzzy logic have been suggested in [38-39] for RDN. These ‗ Fuzzy-Set‘

concepts are applied to find RDN performance evaluation accounting for

data uncertainties [40]. The reliability indices evaluation using IA is

reported by Claudio. M et al [41] for data uncertainty, which deals only

for RDN. Object-oriented based RDN and WDN load flow studies

presented by A.Losi and M.Russo [42], which leads to discussion in next

section.



12

1.2.2 Previous power-flow algorithms for WDN

The RDN algorithm can not be directly applied to find WDN power

flow solution. In particular, the Newton-Raphson and Decoupled

algorithm in some circumstances, fail to converge for larger or ill-

conditioned systems. For WDN multi-post compensation technique is

proposed by W. F. Tinney [43] using triangular factorization. Then

‗ compensation-technique‘ based algorithms are reported in

D.Shirmohammadi et al [44] and A. Semlyen and G.H.Luo [45]. It was

found to be significantly more efficient than the NR ‗ power flow algorithm‘

while converging to the same solution. The essential advantages of [44]

over [45] are:

i) It uses real and reactive powers as flow variables rather than

complex-currents to simplify the treatment of P-V buses and

reduce the computational effort to half.

ii) It uses a Radial – labelling technique which also contributes to the

computational efficiency of the procedure.

iii) It compensates the open-loop by power-injection.

The compensation based techniques can be classified as Loop

Breaking Technique (LBT), where the accuracy is controlled by the

‗tolerance of voltage-mismatch‘ between the nodes of a break point. This

mismatch value must be small enough, or else error in the convergence

of solution increases. In these LBTs, it is also observed that there is no

direct mathematical relationship between the System-Status and



13

Control-Variable, which makes these LBTs difficult. In [44-45] the Loop

Break Point (LBP) Impedance matrix is developed without considering -

section and tap-changing transformer model.

Further, the compensation-based algorithm was extended to 3-

unbalanced system by C.S.Cheng et al [46]. The Phase Decoupled Load

Flow for RDN and WDN W.M.Lin and J.H Teng [47] is based on NR De-

coupling Technique. Here, the element – current based procedure uses a

constant Jacobian Matrix which needs factorization.

Y. Zhu and K. Tomsovic [48] presents an Adaptive Distributed Power

Flow Algorithm based on compensation-approach, which is useful for

system with Dispersed Generation. The comprehensive load delivery

system model includes 3- non-linear loads, lines, capacitors,

transformers, etc. In BT (Loop Breaking Technique) reported by

M.H.Haque [49] power-injections at the Loop Break (LB) point in the

equivalent RDN are computed through a reduced order node-impedance

matrix. The additional advantage of [49] over [44] the ‗shunt-load‘

admittances are incorporated in the calculation of injection-power at the

LBPs, but tap-changing transformer model is not considered in the

analysis. D. Rajičić, R.Ačkovski and R. Taleski [50] presented some

Voltage-Correction Power Flow, further the same authors of [50]

expressed two methods [51] based on i)element by element



14

computational admittance summation approach, which is of non-

iterative ii) extension of famous current summation method.

The Network Topology (NT) based Loop Making Technique (LMT)

J.H.Teng [52] solves both RDN and WDN, but it requires two special

matrices i.e. ‗ Branch Current to Bus Voltage‘ [BCBV] and ‗ Bus Injection

to Branch Current‘ [BIBC]; to obtain solution, which is similar to [BIBC]

and BCBV] of [17] discussed for ‗RDN. To solve these matrices to find

solution for WDN need both KVL and KCL. [52] also does not deal with

handling of issues when WDN elements are modeled as ‗ -section and

tap-changing transformer‘ .

In P.R.Bijwe and Viswanadha Raju [53] a Fuzzy Distribution Power

Flow combines the features of [52] and ‗Boundary Power Flow‘

A.Dimitrovski and K.Tomsovic [54] for WDN, which gives possibilistic

solution. The algorithm can handle simultaneous presence of several

uncertainties in input variables like: input-data; load-model coefficients;

load-forest and node-shunts.

Sometimes, it is necessary to find the Range Reliability Indices (RRIs)

for RDN, because network parameter may have uncertainties. Alok

Thapar et. al [55] compares the reliability of 2-different network

topologies-meshed and extended (radial), which differs in transmission

network topology, whereas the uncertainty in the input data is not



15

considered. The Reliability Indices performance for fixed data can seen in

[56]. Reliability assessment of the LDS is concerned with the systems

performance at the customer end, i.e., at the load points. For that

Distribution Engineers, especially are expected to achieve the highest

possible range reliability levels. The reliability for four industrial utility

configurations like: i) Basic RDN, ii) RDN with co-generation, iii) RDN

with two utility sources iv) RDN with dual utility sources and

cogeneration presented by Daniel J.Love [57], but this method does not

consider the possible uncertainty in the input data. IA based method

reported by J.Nahman and Dragoslav [58] finds voltage drops, energy

losses and reliability indices, which may differ from the actual value due

overestimation problem. This [58] deal only for constant data of RDN.

The Reliability Indices for RDN Claudio.M et. al [59] calculated using

IA by assigning bounds to some or all the input data like failure rate,

repair time, unavailability and observing the effects on the final interval

outcome that will contain all possible solutions due to the variations in

input parameters. An to AA J.Stolfi and L.H.de.Fifueiredo [37] and AA

division S. Miyajima and M.Kashiwagi [60], these models produces

confirmed enclosures for computed numbers, taking into account any

uncertainties in the input data as well as internal truncation and errors.



16

1.3 Proposed Power-Flow Algorithms: RDN and WDN

The power flow algorithms for both Radial and Weakly-meshed

Distribution Networks (RWDNs or RDN and WDN) with and without

system data uncertainties and reliability issues are:

Tellegen‘s-Theorem and Directed-Graphical information based power

flow algorithms are discussed in sections 1.3.1 to 1.3.2. for 1- RDN.

Concept of Duality based Power flow algorithms for 1- RDN and

WDN are presented in section 1.3.3.

Concept of Duality is extended to solve 3- RDN and WDN in section

1.3.4.

Interval Arithmetic based power flow algorithm for 1- Radial and

Weakly-meshed Distribution Networks with Data Uncertainties are

reported in section 1.3.5.

Affine Arithmetic based power flow algorithm for 1- Radial and

Weakly-meshed Delivery Networks with parameter uncertainties are

proposed in sections 1.3.6.

Interval and Affine Arithmetic based reliability range indices for 1-

radial networks with Data Uncertainties are computed in sections

1.3.7.

These algorithms are found to be efficient in solving the power flow

problems of RWDNs:



17

1.3.1 Tellegen‟s Theorem (TT) based Load Flow algorithm for 1-

Radial Delivery Network

A new power flow algorithm is proposed for 1- RDN based on

Tellegen‘s Theorem (TT). A set of iterative power flow equations are

developed to compute power and current during Backward and Forward

sweeps, respectively. The accurate value of injected current computation

from up stream to down stream RDN using TT and KVL leads to faster

convergence when compared to Network topology and Ladder theory

based methods [17, 24].

1.3.2 Directed-Graph based Power-Flow algorithm for 1- Radial

Delivery Network

The Directed-Graph (DG) based algorithm is developed to obtain

power-flow solution for single phase RDN. The Backward and Forward

sweep based algorithms [10] are improved using Directed-Paths in the

RDN. The number of nodes and elements in the paths are used to build

Node Load to Path Load [NLPL] information matrix. The NLPL matrix is

used to formulate power flow equations. The algorithm has been

successfully tested for different values of R/X IEEE 15 bus RDN in

comparison with [17, 24].



18

1.3.3 Concept of Duality based Power Flow Algorithm for 1- Radial

and Weakly meshed Delivery Networks

In this algorithm an attempt is made to apply the Concept of Duality

(CD) for both RDN and WDN. Here, the algorithm arranges the nodal

input data of both the networks into an incremental order, based on

Graphical information of the system. CD demonstrates that the network

‗ Forward-element voltage‘ information is the dual of ‗ Backward-nodal

current‘. The CD facilitates the use of either KVL or KCL in the ‗forward

or backward‘ step to develop power flow equations. In case of

conventional algorithms [17-19, 23-27, 44, 45, 52], it is necessary to use

KVL and KCL in the forward and backward steps, respectively. Unlike,

other existing algorithms CD can also be extended to deal the networks

with -section, co-generator and tap-changing transformer. This idea

helps to improve input data feeding to algorithm and display output with

lees computation time. The algorithm is implemented in MATLAB, for

IEEE 15-Node and 57 node network.

1.3.4 Concept of Duality based Power Flow Algorithm for 3- Radial

and Weakly meshed Delivery Networks

The Concept of Duality is extended to formulate the power flow

equations for unbalanced 3-phase networks. The method is tested on 8

bus data [15] with different range of R/X values and it is found that the



19

proposed algorithm is more efficient than algorithms discussed in [17-19,

23-27, 44, 45, 52].

1.3.5 Interval Arithmetic based Power Flow Algorithm for 1- Radial

and Weakly-meshed Networks with Data Uncertainties

‗ The proposed work predicts the interval load flow solution for both

RDN and WDN with input Data Uncertainties. In order to handle such

uncertainties, an Interval Arithmetic (IA) tool has been applied to obtain

interval load flow solution. This algorithm first arranges the uncertain

input data and then proceeds further to obtain solution by using an

established Concept of Duality based load flow algorithm of Section

1.3.3. The work also expresses an IA relation for the problems such as,

lines with sections and tap changing transformer. The proposed

algorithm is validated for RWDNs having 15, 27, and 4 bus using

MATLAB Ver. 7.0 .

1.3.6 Affine Arithmetic based Power Flow Algorithm for 1- „Radial

and Weakly meshed Delivery Networks with Data Uncertainties

AA based algorithm predicts load flow for both Radial and Weakly-

meshed distribution networks, consisting of uncertainties in input data.

Here, AA solution is compared with IA solution of Section 1.3.4. AA

based algorithm formulates power flow equations by using load flow



20

algorithm of Section 1.3.3. It also presents AA relations for simulation of

sections and lines with tap changing transformer. AA based algorithm

is solved for networks having 15 and 4 bus, using MATLAB and the

results are compared with the IA results of Section1.3.5.

1.3.7 Interval and Affine Arithmetic based Reliability Range Indices

for 1- Radial Delivery Network with Data Uncertainties

IA and AA tools are used to estimate Reliability Range Indices (RRI) for

RDN, with data uncertainties. This algorithm formulates IA and AA based

RRI equations and then proceeds to obtain the variation in the reliability

indices. As a case four feeder practical distribution network 11/33,

Saipeta, Dist.Kurnool, AP,India was under taken. The algorithm is

successfully evaluated using AA and IA tools and the results are

compared with results of non-interval solution.

Problem Statement

Investigate by developing and formulating new algorithms to solve

power flow problems efficiently and accurately for Radial and Weakly

meshed Delivery Networks (RWDNs or RDN and WDN).



21

1.4 Organization of the thesis:

CHAPTER 1: It describes the background and motivation for the thesis

and provides an overview of the research effort.

CHAPTER 2: presents a new and efficient RDN power flow algorithm

based on Tellegen‘s law to obtain fast and accurate power flow solution.

CHAPTER 3: proposes another algorithm based on Directed Graph

information and formulates ‗ Node-Load to Path-Load matrix‘ to efficient

solution for RDN.

CHAPTER 4: Identifying the duality in Forward and Backward sweeps of

power flow equations for RWDNs, the Concept of Duality is applied to

develop a novel algorithm to solve power flow problems.

CHAPTER 5: extends the application of ‗Concept of Duality‘ for

unbalanced 3-phase RDN and WDN.

CHAPTER 6: IA based algorithm predicts load flow solution for 1-

RWDNs with Data Uncertainties in lines with pi-sections and tap

changing transformer.



CHAPTER 7: Presents an Affine Arithmetic (AA) tool to predict accurate

range load flow solution for 1 RWDNs, the results of which are better

than results of IA based algorithm of Chapter 6.

CHAPTER 8: Applies both IA and AA tools to evaluate Reliability Range

Indices studied for RDN with Data Uncertainties.

CHAPTER 9: Summarizes the major contributions of this thesis and

suggestions for further work.

electrical power.pdf

Documents