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,

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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)


For Constant impedance load (CZ)


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



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



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 4.9 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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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


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



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

CHAPTER 4 POWER LOSS MINIMIZATION BY THE PLACEMENT OF DG IN THE DISTRIBUTION...

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