# The Optimization Of Power Generation Engineering Essay

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Over the past two decades, considerable advances have been made in the optimization of power generation and major transmission networks. Only recently, much attention has been paid for systematic planning and to optimize the performance of distribution networks with an objective to reduce losses and provide good quality supply to the consumers.

This thesis presents the analysis of voltage regulating devices and conductor grading in radial distribution networks using fuzzy logic for reduction of losses and improvement of bus voltages. The various investigations carried out are selection of optimal branch conductors for radial distribution systems, optimal locations with size of capacitors, optimal locations of voltage regulators with their tap settings and optimal locations with size of distributed generators. In all these studies, load flow solution is required and hence it is necessary to use a simple and efficient load flow method.

In Chapter 2, a simple method of load flow technique for solving balanced radial distribution systems has been presented. The proposed method involves only the solution of a simple algebraic equation of receiving end bus voltages and no trigonometric functions are involved as in the conventional load flow technique. In addition, to identify the structure of the radial distribution system, the concept of data structure is employed. This method can handle system data with any random bus and line numbering scheme except the slack bus being numbered as 1. This method involves construction of a Bus Incidence Matrix (BIM) which is then processed to reflect the structure of the RDS. The proposed method has been tested on several radial distribution systems and results are presented and analyzed.

In Chapter 3, the above load flow technique has been extended for solving 3 phase unbalanced radial distribution systems. The proposed method involves modeling of 3 phase network elements such as transformers, transmission lines and loads to obtain the solution. The load flow solution method makes use of conventional symmetrical component representation for analysis. The proposed method has been tested on 25 and 37 bus three phase unbalanced radial distribution systems and results are presented and compared with the results obtained using existing method [127].

In Chapter 4, a method for optimal branch conductor selection of radial distribution systems using fuzzy logic has been presented. The problem is posed as an optimization problem with an objective to minimize the overall cost of annual energy losses and annual depreciation on the cost of conductors. The conductor, which is determined by this method, will satisfy the maximum current carrying capacity and simultaneously maintain acceptable voltages at all buses. The effectiveness of the proposed method is demonstrated through different examples. In addition, the proposed algorithm can determine the number of years up to which the optimal conductor selected will be suitable considering a constant annual growth rate on the system load without violating the constraints on voltage and current carrying capacity of the conductor.

The losses at distribution level contribute a major portion of power system losses. Appropriate size of shunt capacitors can reduce substantial amount of this loss and can improve the voltage profile of the feeder. By reducing the peak power and energy losses the total system cost is ultimately minimized. To achieve these objectives, in Chapter 5, a method is proposed to select optimal locations using fuzzy logic and size of capacitor by an analytical method. The efficacy of the proposed method has been demonstrated with four different radial distribution systems. It is observed from the results obtained using the proposed method there is a higher percentage of loss reduction and a better voltage profile compared to the results obtained using an existing method [36].

It is a common practice to employ voltage regulators at suitable locations to maintain the voltage profile in the distribution systems. A fuzzy expert system has been employed for identification of optimal location of voltage regulator and its tap setting is determined by an analytical method with an objective to maximize the net savings. Also, an analytical method named as Back Tracking Algorithm has been proposed to identify suitable location and tap position of voltage regulators. Both the methods are tested with different examples of radial distribution systems and the results are presented in Chapter 6. The results obtained by the proposed method using fuzzy logic determine the optimal location of voltage regulators directly whereas the other existing methods [59, 113] employ sequential or recursive algorithms to determine optimal locations of voltage regulators.

The present trend in planning distribution systems is to employ distributed generators preferably at high load density buses. Fuzzy logic approach is employed to obtain optimal location of DG and its size by an analytical method to minimize losses and improve voltage regulation in radial distribution systems. The proposed method has been tested with different radial distribution systems and the results are presented in Chapter 7. From the results obtained using the proposed method it is observed that even with a lower size DG there is a higher percentage of loss reduction and a better voltage profile compared to the results obtained using existing methods [97, 130].

The conclusions of the above studies and scope of the future work are presented in Chapter 8. The system data for radial distribution systems employed in the analysis are presented in Appendices.

## LIST OF ABBREVIATIONS

RDS : Radial Distribution System

BIM : Bus Incidence Matrix

TCIM : Three-phase Current Injection Method

BIBC : Bus Injection to Branch Current

BCBV : Branch-Current to Bus-Voltage

URDS : Unbalanced Radial Distribution System

PLI : Power Loss Index

TPL : Total Active Power Loss

TQL : Total Reactive Power Loss

Lsf : Loss Factor

LF : Load Factor

CSI : Capacitor Suitability Index

NC : Number of Combinations

FES : Fuzzy Expert System

AVB : Automatic Voltage Booster

VR : Voltage Regulator

BAT : Back Tracking Algorithm

VRSI : Voltage Regulator Suitability Index

DPSO : Discrete Particle Swarm Optimization

DG : Distributed Generator

SQP : Sequential Quadratic programming

GA : Genetic Algorithm

DGSI : Distributed Generator Suitability Index

p.u. : per unit

b.no. : bus number

br.no. : branch number

c.no. : number of contours

D.no. : Data structure number

Eqn. : Equation

nbus : Total number of buses

## LIST OF SYMBOLS

i, j : Bus number

k : Branch number

ntype : number of types of conductor

Vi : Voltage at bus, i

Pi+1 : Total real power load of all buses beyond bus, i+1

plus real power load at bus, i+1 and plus the sum of the

real power losses of all the branches beyond bus, i+1

Qi+1 : Total reactive power load of all buses beyond bus, i+1

plus reactive power load at bus, i+1 and plus the sum of the reactive power losses of all the branches beyond bus, i+1

Rk : Resistance of branch k, k= 1, 2, â€¦..nbus -1

Xk : Reactance of branch k, k= 1, 2, â€¦..nbus -1

Ploss : Real Power Loss

Qloss : Reactive Power Loss

Î´i : Phase Angle of voltage Vi

Îµ : tolerance limit

count : iteration count, IC

Via, Vib, Vic : Voltages at ith bus in phases a, b, c respectively

Vja, Vjb, Vjc : Voltages at jth bus in phases a, b, c respectively

Vin, Vjn : Neutral voltage at ith bus and jth bus respectively

Iija, Iijb, Iijc : Currents in a branch connected between i and j buses in a,

b, c phases respectively

Iijn : Neutral current in a branch connected between i and j

buses

Zijaa, Zijbb, Zijcc : Self-impedances of three phase element connected between

buses i, j

Zijab, Zijbc, Zijca : Mutual impedances of three phase element connected

between buses i, j

Zijan, Zijbn, Zijcn : Impedance of each phase a, b, c and neutral n

respectively which are connected between buses i, j

Zijnn : Neutal impedance of element connected between

buses i, j

Zij00, Zij11, Zij22 : Self sequence impedances of three phase element

connected between buses i, j

Zij01, Zij12, Zij02 : Mutual impedance between three sequence networks 0, 1,

2 respectively of element connected between buses i, j

Vi0, Vi1, Vi2 : Sequence components of voltages at ith bus

Vj0, Vj1, Vj2 : Sequence components of voltages at jth bus

Iij0, Iij1, Iij2 : Sequence components of currents in a branch connected

between buses i and j

: load current per phase at ith bus

: Complex power per phase at ith bus

: Phase to neutral voltage at ith bus

: Phase to phase voltage at ith bus

: Leakage admittance of three phase transformer at bus, T

A, B, C, D, E, and F : Transformer dependent constants

: Per unit leakage admittance

Î±, Î² : Tappings on the primary and secondary sides of

transformer respectively

: Sequence current vector in kth branch

and : Sequence voltage vectors of ith and jth buses respectively

: Sequence impedance vector of kth branch

: Complex power loss in the branch, k connected between

buses i and j

and : Phase voltage at buses i and j respectively

: The current through branch k connected between buses i

and j

Kp : annual demand cost of power loss in `./kW

Ke : annual cost of energy loss in `./kWh

Î» : Interest and depreciation factor

A(ff) : Cross sectional area of ff type of conductor in mm2

cost(ff) : Cost of 'ff' type conductor in `./ mm2 /km

len(k) : Length of branch k in km

Imax(ff) : Maximum current carrying capacity of ff type

conductor

BNC+k : Vector B of NC+k combinations

: Satisfaction parameter value of combination Bk

: Maximum satisfaction parameter value

Î¼v(v(B)) : Membership function of voltage-deviation index

v(B) : Voltage-deviation index value for the combination B

BMIN and BMAX : Maximum and Minimum values of satisfaction

parameter for the combination, B

vMAX and vMIN : Maximum and Minimum values of Voltage-deviation

index

FMAX and FMIN : Maximum and Minimum values of objective function

NL : Number of time intervals

: Voltage-deviation index for the iith interval

BNV : Number of buses that violate the prescribed voltage

limits

ViLIM : Limit of ith bus voltage

PL, QL : Real and reactive power load at the Nth year

PL0 , QL0 : Real and reactive power load at base year (0th year)

N : Number of years

g : Annual load growth rate

F : Objective function/net saving function

Plr : Reduction in power losses

KI : Installation cost

Qc : Total size of capacitor

Nc : Total number of capacitors

Kc : Capital cost of each capacitor

ïs : Capacitor suitability index membership function

ïp and ïv : Membership functions of the power loss index and p.u.

voltage level respectively

Qeffective load,i : Total reactive load beyond ith bus plus reactive load at

ith bus

Qtotal : Total reactive load of the given distribution system

Qload[i] : Local reactive load at ith bus

Index[i] : Index value at ith bus

Ip[k] and Iq[k] : Real & imaginary component of current at kth branch.

KVR : Capital cost of each Voltage regulator

NVR : Number of voltage regulators

tap : Tap position of VR

Vrated : Rated voltage in p.u.

: Total capacity of distributed generators in kW

KDG : Capital cost of each Distributed Generator

IDG : Distributed generator current

ï„Pi : Reduction of power losses due to installation of DG

SDG : Size of DG

## LIST OF TABLES

## Table No. Description Page No.

2.1 The Bus Incidence Matrix of the 15 bus radial distribution system 31

2.2 Data Structure of all contours of 15 bus Radial Distribution System 33

2.3 Voltage profile of 15 bus radial distribution system 37

2.4 Line flows of 15 bus radial distribution system 38

2.5 Voltage profile of 33 bus radial distribution system 39

2.6 Line flows of 33 bus radial distribution system 40

2.7 Comparison of computational efficiency of proposed method with 41

other methods

2.8 Voltage profile of 69 bus radial distribution system 42

2.9 Line flows of 69 bus radial distribution system 44

2.10 Comparison of computational efficiency of proposed method with 45

other methods

3.1 Sub-matrices of for common step-down transformer connections 56

3.2 Sub-matrices of for common step-up transformer connections 56

3.3 Load flow result of 25 bus unbalanced radial distribution system 61

3.4 Summary of load flow result of 25 bus system 62

3.5 Load flow result of 37 bus unbalanced radial distribution system 64

3.6 Summary of load flow result of 37 bus unbalanced radial 65

distribution system

4.1 Voltage profile of 26 bus radial distribution system before and after 78

Conductor grading

4.2 Summary of results after conductor grading of 26 bus RDS 78

4.3 Modifications in the feeder conductor type after conductor grading 79

4.4 Total loads, losses and minimum voltage for 26 bus system before 80

conductor selection when considering the load growth

## 4.5 Total loads, losses and minimum voltage for 26 bus system after 80

## conductor selection when considering the load growth

4.6 Modifications in the feeder conductor type after conductor grading 81

for load Growth

4.7 Summary of results after conductor grading of 32 bus RDS 82

## 4.8 Total loads, losses and minimum voltage for 32 bus system before 83

## conductor selection when considering the load growth

## 4.9 Total loads, losses and minimum voltage for 32 bus system after 83

## conductor selection when considering the load growth

5.1 Decision matrix for determining suitable capacitor locations 91

5.2 Power Loss Index and voltage 93

5.3 Capacitor suitability indices of 15 bus system 93

5.4. Capacitor allocation and loss reduction of 15 bus RDS for 98

calculated size of capacitor

5.5 Capacitor allocation and loss reduction of 15 bus RDS for 98

standard size of capacitor

5.6 Voltage profile before and after compensation of 15 bus RDS 99

5.7 Line flows of 15 bus system 99

5.8 CSI and size of capacitor of 34 bus RDS 101

5.9 Capacitor allocation and loss reduction for 34 bus system 101

5.10 Comparison of results of 34 bus system with existing methods 102

5.11 CSI and size of capacitor for 33 bus system 103

5.12 Capacitor allocation and loss reduction for 33 bus system 104

5.13 CSI and size of capacitor for 69 bus system 105

5.14 Capacitor allocation and loss reduction for 69 bus system 105

6.1 Optimal bus numbers and tap setting of VR using Back Tracking 118

Algorithm for 15 bus system

6.2 VRSI and tap setting of voltage regulator using FES for 15 bus system 118

6.3 Voltage profile without and with Voltage Regulators 119

## 6.4 Comparison of Results of 15 bus RDS 119

6.5 Optimal bus numbers and tap setting of VR using Back Tracking 121

algorithm for 33 bus system

6.6 VRSI and tap setting of voltage regulator using FES for 33 bus system 121

## 6.7 Comparison of Results of 33 bus RDS 121

6.8 Comparison of results with the existing method 122

6.9 Optimal bus number and tap setting of VR using Back Tracking 124

algorithm for 69 bus system

6.10 VRSI and tap setting of voltage regulator using FES for 69 bus system 124

## 6.11 Comparison of Results of 69 bus RDS 124

6.12 Comparison of results with the existing method 125

7.1 Distributed Generator suitability index and size of Distributed 135

Generator of 15 bus RDS

7.2 Summary of results of 15 bus system RDS with and without 136

actual size of DG

7.3 Summary of results of 15 bus system RDS with and without 136

standard size of DG

7.4 Voltage profile before and after DG placement of 15 bus RDS 137

7.5 DGSI and size of Distributed Generator of 33 bus RDS 138

7.6 Summary of results of 33 bus system with and without DG 139

7.7 Comparison of test results of 33 bus system with existing method 139

7.8 DGSI and size of Distributed Generator of 69 bus RDS 141

7.9 Summary of results of 69 bus system with and without DG 141

7.10 Comparison of test results of 69 bus system with existing method 142

## IN APPENDICES

A.1 The line and load data of 15-bus radial distribution system 160

A.2 The line and load data of 33-bus radial distribution system 161

A.3 The line and load data of 69-bus radial distribution system 162

A.4 The line and load data of 34-bus radial distribution system 164

B.1 Line & load data of 25 bus unbalanced radial distribution system 166

B.2 Line & load data of IEEE 37-bus unbalanced radial distribution system 168

B.3 Phase impedance matrices of IEEE 37-bus unbalanced 168

radial distribution system

B.4 Phase admittance matrices of IEEE 37-bus unbalanced 169

radial distribution system

B.5 Transformer data of IEEE 37-bus unbalanced radial distribution system 169

C.1 Electrical properties of various conductors used for 11 kV distribution 170

systems

C.2 Line and load data of Practical 26 bus radial distribution system 171

C.3 Line and Load data of Practical 32 bus radial distribution 172

system

## LIST OF FIGURES

## Fig. No. Description Page No.

2.1 Electrical equivalent of a typical branch 1 25

2.2 Phasor diagram of a branch 1 connected between buses 1 and 2 25

2.3 Single line diagram of 15 bus radial distribution system 31

2.4 The general data structure of the system 32

2.5 Flow chart of the proposed method 36

2.6 Single line diagram of 33 bus radial distribution system 39

2.7 Single line diagram of 69 bus radial distribution system 42

3.1 Basic Building Block of Distribution System 50

3.2 Model of the three-phase four-wire distribution line 51

3.3 General Three-phase Transformer Model 54

3.4 Flow chart of the proposed method 60

3.5 Single line diagram of 25-Bus URDS 61

3.6 Single line diagram of IEEE 37-Bus URDS 63

4.1 Flow chart of optimal conductor selection 76

4.2 Single line diagram of practical 26 bus radial distribution system 77

4.3 Voltage (p.u.) of 26 bus RDS before and after conductor selection 79

4.4 Real power loss (kW) of 26 bus RDS before and after conductor 79

selection

4.5 Single line diagram of practical 32 bus radial distribution system 81

4.6 Voltage (p.u.) of 32 bus RDS before and after conductor selection 82

4.7 Real power loss (kW) of 32 bus RDS before and after conductor 82

selection

5.1 Power loss index membership function 90

5.2 Voltage membership function 90

5.3 Capacitor suitability index membership function 91

5.4 Flow chart of optimal capacitor placement using FES 96

5.5 Real Power loss at each branch of 15 bus RDS with and without 100

capacitor

5.6 Voltages at each bus of 15 bus RDS with and without capacitor 100

5.7 Single line diagram of 34 bus radial distribution system 101

5.8 Real power loss at each branch of 34 bus RDS with and without 102

capacitor

5.9 Voltages at each bus of 34 bus RDS with and without capacitor 103

5.10 Real power loss at each branch of 33 bus RDS with and without 104

capacitor

5.11 Voltages at each bus of 33 bus RDS with and without capacitor 104

5.12 Real power loss at each branch of 69 bus RDS with and without 106

capacitor

5.13 Voltages at each bus of 69 bus RDS with and without capacitor 106

6.1(a) The 19 bus RDS before shifting of Voltage regulators 112

## 6.1(b) The 19 bus RDS after shifting of Voltage regulators 113

6.2 Flow chart of optimal voltage regulator placement using 114

Back tracking algorithm

6.3 Flow chart of optimal voltage regulator placement using FES 117

6.4 Real power loss of 15 bus RDS with and without Voltage regulator 120

6.5 Voltage profile of 15 bus RDS with and without Voltage regulator 120

6.6 Real power loss of 33 bus RDS with and without Voltage regulator 123

6.7 Voltage profile of 33 bus RDS with and without Voltage regulator 123

6.8 Real power loss of 69 bus RDS with and without Voltage regulator 126

6.9 Voltage profile of 69 bus RDS with and without Voltage regulator 126

7.1 Flow chart of optimal distributed generator placement using FES 134

7.2 Voltage profile of 15 bus RDS with and without DG 137

7.3 Real power loss of 15 bus RDS with and without DG 138

7.4 Voltage profile of 33 bus RDS with and without DG 140

7.5 Real power loss of 33 bus RDS with and without DG 140

7.6 Voltage profile of 69 bus RDS with and without DG 142

7.7 Real power loss of 69 bus RDS with and without DG 142

## IN APPENDICES

A1 Single line diagram of 15 bus radial distribution system 160

A2 Single line diagram of 33 bus radial distribution system 161

A3 Single line diagram of 69 bus radial distribution system 162

A4 Single line diagram of 34 bus radial distribution system 164

B1 Single line diagram of 25 bus unbalanced radial distribution system 166

B2 Single line diagram of IEEE 37 bus unbalanced radial 167

distribution system

C1 Single line diagram of practical 26 bus radial distribution system 170

C2 Single line diagram of practical 32 bus radial distribution system 172