# Extraction of Transmission Parameters for Siting and Sizing of Distributed Energy Sources in Distribution Network

Authors: Shilpa Kalambe; Ganga Agnihotri
Journal: Journal of Energy
 (2013)

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## Abstract

This paper introduces a novel method for sitting and sizing the grid connected distributed generator (DG) for installation in distribution system at any input load condition, which is based on two port transmission equations, named as modified transmission parameters (MTP) method by considering the loss minimization as a constraint. If properly organized, with the help of various transmission parameters optimal DG allocation with minimum transmission losses, contribution of DG as well as the main supply source to each load, type of DG required to handle the existing power flow scenario, and operating power factor at which DG should operate can be easily investigated. Apart from this the author has also investigated the worst location for DG installation and referred to it as Consecutive Bus. The method has been tested on two test distribution systems with varying sizes and intricacy and the results have been compared with the two established methods reported earlier. Relative study presented has shown that the proposed method leads existing methods in terms of its simplicity, computational time, and handling less number of variables.


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## Body

## 1. Introduction

It is universally acknowledged that distributed generator (DG) is perched to become a key element in our future energy generation. DGs are generally defined as the generating plants serving a customer on-site or providing support to a distribution network, connected to the grid at distribution-level voltages [1]. The main reasons for continuous growth in incursion of DG are the environmental concerns, insufficiency of energy sources, constraints on building new transmission and distribution lines, technological advances in small generators, power electronics, and energy storage devices for transient backup, but it was also observed that improper siting or sizing of DG can counter effect the system [2]. Apart from providing the solution to most of the power network problems they are adding new problems as well, such as their grid connection, pricing, change in protection scheme, and limits on the number of DG connections in the weak grids, and also the addition of DGs may increase real power flow back to grid causing voltage rise or increase reactive power flow into feeder causing voltage to fall. Thus it is clear that DGs come with lots of benefits as well as challenges that is why the problem of DG planning has recently received much attention by power system researchers so as to garner maximum benefit from this upcoming power generation technology without violating the existing power system infrastructure. In [2] Willis has applied a 2/3 rule for capacitor placement for loss reduction thereafter in [3] by giving a very simple “Zero Point Analysis” applied the 2/3 rule for DG placement in radial distribution network. His analysis has proved to be undemanding and easy to apply but the approach may not be functional in case of variable load conditions. In [4] Mao and Miu proposed switch placement schemes to improve the system reliability by DG placement in distribution network. In [5] Atwa et al. have given an effective probabilistic-based planning technique for determining the optimal fuel mix of different types of renewable DG units in order to minimize the annual energy losses in the distribution system. Considering total power penetration from DG units, Kim et al. [6] and Gandomkar et al. [7] employed the Hereford Ranch algorithm to minimize system losses. Acharya et al. [8] have used an Exact Loss Formula to calculate losses and to find out the optimal location of DG in distribution system in a very effective manner and then Hung et al. [9, 10] have continued the work with the same formulation and applied the method for multiple DG allocation. In most of the methods [6–13] reported earlier either new complicated equation or existing loss calculation equations such as Exact Loss Formula and Marginal Loss Coefficients have been implemented which in turn necessitate, calculation of many other complicated subcoefficients requisite in the equations. Many methods of loss minimization may also require cumbersome iterative steps; thus, all those methods gratuitously make the loss calculation process prolonged, but in the proposed method we directly utilize the transmission equations and convert them into power form to get both types of losses in the distribution system. In spite of calculating the losses encountered in the system we can also avail the value of the capacity of DG, its operating power factor, and the type of the DG from the same equation without any extra calculations. Thus the allure of method lies in its simplicity.The proposed method has been tested on two test distribution systems (IEEE 16-Bus [14] as well as IEEE 33-Bus [15] Radial Distribution Test Systems) with varying complexity and validated by comparing results with Improved Analytical method suggested by Hung et al. and Exhaustive Load Flow method [9]. The result shows that the proposed method requires less computational equations thereby fast for obtaining an optimal solution with greater accuracy as verified by the Exhaustive Load Flow and IA methods; hence, it is well suited for on-line execution in an energy control centre.The rest of the paper is organized as follows. Section2 explains proposed methodology. Section 3 presents algorithm of the proposed method. Section 4 presents results and analysis of IEEE 16-Bus [14] and 33-Bus [15] Test Radial Distribution Systems and the analysis of results. Section 5 outlines conclusions.


## 2. Proposed Methodology

Consider a system withG1,G2,…,Gm number of generator buses and L1,L2,…,Ln remaining load buses. For a given system the two port transmission equations are given by
(1)V1=AV2-BI2,I1=CV2-DI2.
We can write the above equations as
(2)[VG]=[A][VL]-[B][IL],(3)[IG]=[C][VL]-[D][IL],
where VG, IG are source voltages and currents and VL, IL load voltages and currents. From the above equation we can get the relation between load voltage to source voltage at no load or light load condition,
(4)VLVG=[A]-1.
But the value of [A] in terms of Z-parameters is
(5)[A]=[Z11Z21].
So,
(6)[A]-1=[Z11Z21]-1=[Z21][Z11]-1=[ZLG][ZGG]-1[ZGG] and [ZLG] are corresponding partitioned portions of network Zbus matrix. The above relation will give the factor by which the source voltage may be reduced due to transmission losses due to impedance encountered in the path from respective source to load destination, so we can define this factor as Impedance Loss Factor (ILF) having dimension L×G.Thus,(7)ILF≤1.The columns of ILF matrix correspond to the generator bus numbers and its rows correspond to the load bus numbers. Higher the value of this factor lower will be the loss occurred across the path between respective generator and the load bus to which it will feed the power. Thus this matrix can directly give the proportion of power which should be supplied by each source present in the system to individual load so as to accomplish the total demand with maximum efficiency.


### 2.1. Optimal Loss

By rearranging (2) we will get
(8)[VL]=[A]-1[VG]+[A]-1[B][IL].
But,
(9)[A]-1=[ZLG][ZGG]-1
and for simplicity we use the value of [A]-1[B] in terms of Ybus matrix.So,(10)[A]-1[B]=[YLL]-1.
So that the final form of equation will be
(11)[VL]=[ZLG][ZGG]-1[VG]+[YLL]-1[IL],
where [YLL]L×L-1 = Corresponding partitioned portion of Ybus matrix, [VL]L×1 = Column matrix of load voltages, [VG]G×1 = Column matrix of generator voltages, and [IL]L×1 = Column matrix of load currents.Now premultiplying the above matrix by diagonal matrix[IL] of load currents with dimension L×L we get
(12)[IL][VL]=[IL][ZLG][ZGG]-1[VG]+[IL][YLL]-1[IL];
that is,
(13)[IL]L×L[VL]L×1=[IL]L×L[A]L×G-1[VG]G×1+[IL]L×L[YLL]L×L-1[IL]L×1.It will give the power consumed in load which can also be obtained by subtraction of total transmission power losses from the total power supplied by generators; thus, we can say(14)PowerconsumedinLoad=[PLoad]L×1=[IL][VL],(15)Powersuppliedfromgenerators=[PG]L×1=[IL][A]-1[VG],(16)Transmissionpowerlosses=[PLoss]L×1=[IL][YLL]-1[IL].Thus we can use the term of transmission power losses given by (16) to calculate the total power losses encountered for different structures of power system. In this paper the author has used this equation to calculate the power losses in the distribution system for different locations of DG placement apart from this without any separate calculations; the same equation has been also used to calculate the capacity, operating power factor, and type of DG which should be included in the power system to achieve minimum losses.


### 2.2. Optimal DG Capacity

From (15) corresponding optimal DG capacity at that optimal location can be obtained. Here Impedance Loss Factor (ILF) plays an important role in giving the approximate value of capacity, operating power factor, and type of DG which should be installed at an optimal location obtained for the given system. ILF gives the loss which may be faced by the generator while feeding particular load from any concerned location. As ILF matrix is independent of the load connected to any bus, it will give the proportion of power at any input load condition. Thus if the generators are scheduled as per the value of loss encountered while supplying the load, the minimum loss can be achieved. So the power which should be contributed by the individual generator to meet each load can be obtained as given below:(17)[PG]=Powersuppliedfromeachgenerator=[IL][A]-1[VG]=[IL][ILF][VG]=L1L2⋮LnG1supply[IL1ILFL1G1VG1IL2ILFL2G1VG1⋮ILnILFLnG1VG1++++G2supplyIL1ILFL1G2VG2IL2ILFL2G2VG2⋮ILnILFLnG2VG2++++⋯⋯⋯⋱⋯++++GmsupplyIL1ILFL1GmVGmIL2ILFL2GmVGm⋮ILnILFLnGmVGm]L×1.From the matrix given above the power contributed by the generators placed at any particular location can be obtained which is actually similar to theT-index value explained in [13]. Here each row of matrix gives the summation of power supplied to Lth row load bus by all generators in that system and each individual term of the equation formed at every row is the desirable contribution of generator of respective column. So if we connect a new DG at any load bus in the system, then power contribution from all existing generators will change as some of the power will now be shared by newly installed DG. The previously connected load will now be assumed as the local load for that bus which will be supplied by the newly installed DG. Therefore by ignoring the local load of that bus we can now assume that a new DG is installed by replacing any load bus there by increasing the total number of generators by one, reducing the load buses by one and thus now the dimension of matrix [PG] given by (17) will be (L-1)×1. Thus the restructured matrix will be(18)[PG]=L1L2⋮Ln-1G1supply[IL1ILFL1G1VG1IL2ILFL2G1VG1⋮ILn-1ILFLn-1G1VG1++++G2supplyIL1ILFL1G2VG2IL2ILFL2G2VG2⋮ILn-1ILFLn-1G2VG2++++⋯⋯⋯⋱⋯++++GnsupplyIL1ILFL1GnVGmIL2ILFL2GnVGm⋮ILFLn-1GnVGm++++DGsupplyIL1ILFL1DGVDGIL2ILFL2DGVDG⋮ILn-1ILFLn-1DGVDG](L-1)×1.Thus the desired contribution of the DG is the summation of terms of power contribution of DG to each load and the local load at that bus, which will give the required capacity of DG which should be installed at that location(19)Thatis,DGcapacity=IL1ILFL1DGVDG+IL2ILFL2DGVDG+⋯+ILn-1ILFLn-1DGVDG=∑i=1n(ILi×ILFLiDG×VDG+LocalLoadi),
where n = Total number of load buses.The capacity which we obtain will be a complex quantity giving both real as well as reactive power capacity of the DG. The capacity of the DG to be installed can also be used for calculation of power factor as explained in the next section.


### 2.3. Optimal Power Factor

Operating power factor of the DG to be installed can be obtained by using the equation(20)PFDG=PDGPDG2+QDG2,
where PDG and QDG can be obtained from the complex capacity value of DG obtained from (18).


### 2.4. Type of the DG

DG can be classified into four major types [9] based on their terminal characteristics in terms of real and reactive power delivering capability as follows.(1)
Type I:  DG capable of injecting active power only, for example, photovoltaic, fuel cells, and so forth.(2)
Type II: DG capable of injecting reactive power only, for example, synchronous compensators such as gas turbines.(3)
Type III: DG capable of injecting both active and reactive power, for example, DG units that are based on synchronous machines and so forth.(4)
Type IV: DG capable of injecting active power but consuming reactive power, for example, induction generators that are used in wind farms and so forth.So, if practically we will analyze the information given in [9] we should actually consider the Type-II DG as nothing but a capacitor, FACTS devices, and so forth, and Type-III DG may be like synchronous generator which can inject both active and reactive power based on its inverter control, but in this paper we are not dealing with the way by which DG can be controlled to give its output, but we have assumed only the output of the DGs mentioned above.From the complex equation (19) obtained for calculating the capacity of DG to be installed we can also predict the type of DG.As per the proposed method the DG to be installed will be of the following types.Type I:
if the value of reactive power will be zero, operating power factor will be unity.Type II:
if value of active power will be zero, operating power factor will be zero.Type III:
if value of reactive power will be positive,0<PFDG<0 and the sign will be positive.Type IV:
if value of reactive power will be negative,0<PFDG<0 and the sign will be negative.The proposed method suggests the optimal DG location, optimal DG capacity as well as power factor thereafter predicting the type of DG which should be installed at that location to achieve minimum losses. But if practically this is not possible, then with the available DG unit we can interconnect any other DG of other type, so as to achieve the required DG output in terms of reactive power output, power factor, and so forth.


## 2.1. Optimal Loss

By rearranging (2) we will get
(8)[VL]=[A]-1[VG]+[A]-1[B][IL].
But,
(9)[A]-1=[ZLG][ZGG]-1
and for simplicity we use the value of [A]-1[B] in terms of Ybus matrix.So,(10)[A]-1[B]=[YLL]-1.
So that the final form of equation will be
(11)[VL]=[ZLG][ZGG]-1[VG]+[YLL]-1[IL],
where [YLL]L×L-1 = Corresponding partitioned portion of Ybus matrix, [VL]L×1 = Column matrix of load voltages, [VG]G×1 = Column matrix of generator voltages, and [IL]L×1 = Column matrix of load currents.Now premultiplying the above matrix by diagonal matrix[IL] of load currents with dimension L×L we get
(12)[IL][VL]=[IL][ZLG][ZGG]-1[VG]+[IL][YLL]-1[IL];
that is,
(13)[IL]L×L[VL]L×1=[IL]L×L[A]L×G-1[VG]G×1+[IL]L×L[YLL]L×L-1[IL]L×1.It will give the power consumed in load which can also be obtained by subtraction of total transmission power losses from the total power supplied by generators; thus, we can say(14)PowerconsumedinLoad=[PLoad]L×1=[IL][VL],(15)Powersuppliedfromgenerators=[PG]L×1=[IL][A]-1[VG],(16)Transmissionpowerlosses=[PLoss]L×1=[IL][YLL]-1[IL].Thus we can use the term of transmission power losses given by (16) to calculate the total power losses encountered for different structures of power system. In this paper the author has used this equation to calculate the power losses in the distribution system for different locations of DG placement apart from this without any separate calculations; the same equation has been also used to calculate the capacity, operating power factor, and type of DG which should be included in the power system to achieve minimum losses.


## 2.2. Optimal DG Capacity

From (15) corresponding optimal DG capacity at that optimal location can be obtained. Here Impedance Loss Factor (ILF) plays an important role in giving the approximate value of capacity, operating power factor, and type of DG which should be installed at an optimal location obtained for the given system. ILF gives the loss which may be faced by the generator while feeding particular load from any concerned location. As ILF matrix is independent of the load connected to any bus, it will give the proportion of power at any input load condition. Thus if the generators are scheduled as per the value of loss encountered while supplying the load, the minimum loss can be achieved. So the power which should be contributed by the individual generator to meet each load can be obtained as given below:(17)[PG]=Powersuppliedfromeachgenerator=[IL][A]-1[VG]=[IL][ILF][VG]=L1L2⋮LnG1supply[IL1ILFL1G1VG1IL2ILFL2G1VG1⋮ILnILFLnG1VG1++++G2supplyIL1ILFL1G2VG2IL2ILFL2G2VG2⋮ILnILFLnG2VG2++++⋯⋯⋯⋱⋯++++GmsupplyIL1ILFL1GmVGmIL2ILFL2GmVGm⋮ILnILFLnGmVGm]L×1.From the matrix given above the power contributed by the generators placed at any particular location can be obtained which is actually similar to theT-index value explained in [13]. Here each row of matrix gives the summation of power supplied to Lth row load bus by all generators in that system and each individual term of the equation formed at every row is the desirable contribution of generator of respective column. So if we connect a new DG at any load bus in the system, then power contribution from all existing generators will change as some of the power will now be shared by newly installed DG. The previously connected load will now be assumed as the local load for that bus which will be supplied by the newly installed DG. Therefore by ignoring the local load of that bus we can now assume that a new DG is installed by replacing any load bus there by increasing the total number of generators by one, reducing the load buses by one and thus now the dimension of matrix [PG] given by (17) will be (L-1)×1. Thus the restructured matrix will be(18)[PG]=L1L2⋮Ln-1G1supply[IL1ILFL1G1VG1IL2ILFL2G1VG1⋮ILn-1ILFLn-1G1VG1++++G2supplyIL1ILFL1G2VG2IL2ILFL2G2VG2⋮ILn-1ILFLn-1G2VG2++++⋯⋯⋯⋱⋯++++GnsupplyIL1ILFL1GnVGmIL2ILFL2GnVGm⋮ILFLn-1GnVGm++++DGsupplyIL1ILFL1DGVDGIL2ILFL2DGVDG⋮ILn-1ILFLn-1DGVDG](L-1)×1.Thus the desired contribution of the DG is the summation of terms of power contribution of DG to each load and the local load at that bus, which will give the required capacity of DG which should be installed at that location(19)Thatis,DGcapacity=IL1ILFL1DGVDG+IL2ILFL2DGVDG+⋯+ILn-1ILFLn-1DGVDG=∑i=1n(ILi×ILFLiDG×VDG+LocalLoadi),
where n = Total number of load buses.The capacity which we obtain will be a complex quantity giving both real as well as reactive power capacity of the DG. The capacity of the DG to be installed can also be used for calculation of power factor as explained in the next section.


## 2.3. Optimal Power Factor

Operating power factor of the DG to be installed can be obtained by using the equation(20)PFDG=PDGPDG2+QDG2,
where PDG and QDG can be obtained from the complex capacity value of DG obtained from (18).


## 2.4. Type of the DG

DG can be classified into four major types [9] based on their terminal characteristics in terms of real and reactive power delivering capability as follows.(1)
Type I:  DG capable of injecting active power only, for example, photovoltaic, fuel cells, and so forth.(2)
Type II: DG capable of injecting reactive power only, for example, synchronous compensators such as gas turbines.(3)
Type III: DG capable of injecting both active and reactive power, for example, DG units that are based on synchronous machines and so forth.(4)
Type IV: DG capable of injecting active power but consuming reactive power, for example, induction generators that are used in wind farms and so forth.So, if practically we will analyze the information given in [9] we should actually consider the Type-II DG as nothing but a capacitor, FACTS devices, and so forth, and Type-III DG may be like synchronous generator which can inject both active and reactive power based on its inverter control, but in this paper we are not dealing with the way by which DG can be controlled to give its output, but we have assumed only the output of the DGs mentioned above.From the complex equation (19) obtained for calculating the capacity of DG to be installed we can also predict the type of DG.As per the proposed method the DG to be installed will be of the following types.Type I:
if the value of reactive power will be zero, operating power factor will be unity.Type II:
if value of active power will be zero, operating power factor will be zero.Type III:
if value of reactive power will be positive,0<PFDG<0 and the sign will be positive.Type IV:
if value of reactive power will be negative,0<PFDG<0 and the sign will be negative.The proposed method suggests the optimal DG location, optimal DG capacity as well as power factor thereafter predicting the type of DG which should be installed at that location to achieve minimum losses. But if practically this is not possible, then with the available DG unit we can interconnect any other DG of other type, so as to achieve the required DG output in terms of reactive power output, power factor, and so forth.


## 3. Algorithm for Proposed Method

For finding the optimal location, optimal capacity at that location, operating power factor, and type of the DG to be installed, following algorithm should be followed.(1)
For the given test system without DG run the load flow and find out the voltage at each bus as well as calculate the total losses.(2)
Select next bus as a DG location and consider the remaining buses (except original generator sources and the load bus on which DG is installed) as load buses.(3)
Now run the load flow for the case with DG installed at new position and find out the voltage at each bus.(4)
By using equation (16), calculate the active as well as reactive power losses.(5)
Now select all the next buses individually as DG location and repeat the steps from 2 to 4.(6)
Rank the buses in ascending order as per the amount of losses encountered at that location.(7)
Consider the top ranking bus as the best location for DG installation.(8)
Then calculate the optimal capacity of DG to be installed at optimal location from (19).(9)
By using the complex power capacity of DG obtained in the above step calculate the operating power factor of the DG as per (20).(10)
Then from the values of active as well as reactive power capacities obtained in step (8) and the calculated operating power factor from step (9) suggest the type of DG which should be installed on the candidate location obtained in step (7).Figure1 shows the flowchart for the proposed algorithm.Figure 1
Flowchart for obtaining optimal location, optimal size at that location, operating power factor, and type of the new DG to be installed in the existing system to minimize the losses by MTP method.


## 4. Results and Analysis

In this paper two test systems are summarized, namely, the IEEE 16-Bus Test Radial Distribution System [14] with a load of 28.7 MW and 5.9 MVAR and IEEE 33-Bus Test Radial Distribution System [15] with a load of 3.7 MW and 2.3 MVAR. Comparison of the proposed algorithm is made against two DG allocation methods, one based on Exact Loss Formula [8–10] known as Improved Analytical (IA) method [9] and the other is Exhaustive Load Flow (ELF) method. Table 1 and Figure 2 show comparative analysis of three methods of DG allocation by considering loss minimization as a constraint for 16-bus system. Similarly Table 2 and Figure 5 show comparative analysis of three methods for the 33-bus system. In MTP method we can calculate optimal loss, size, and operating power factor by using a single equation but in other two methods for active and reactive loss as well as for power calculations separate equations are required apart from this solution demands iterative approach which makes the methods lengthy.Table 1
Comparative analysis of three methods of loss calculations for 16-bus system.
Bus numbers
Calculated loss at different DG location
Bus numbers
Calculated real loss at different DG location
Location of DG
MTP(Kw + Kvar)
ELF(Kw)
IA(Kw)
Priority list of buses
MTP(Kw)
ELF(Kw)
IA(Kw)
W/O DG
515.4 + 607.7i
511.43
511.43
Bus 9
163.4
164.01
166.31
Bus 4
350.1 + 418.2i
450.33
450.7
Bus 12
249
196.84
200.93
Bus 5
298.4 + 336.5i
456.57
456.86
Bus 11
264.6
270.99
283.55
Bus 6
359.5 + 427.9i
450.21
450.44
Bus 8
290.4
228.57
233.17
Bus 7
356.5 + 423.2i
455.05
455.32
Bus 5
298.4
456.57
456.86
Bus 8
290.4 + 380.6i
228.57
233.17
Bus 10
341.3
335.61
350.77
Bus 9
163.4 + 212.7i
164.01
166.31
Bus 4
350.1
450.33
450.7
Bus 10
341.3 + 418.9i
335.61
350.77
Bus 14
351.1
491.93
493.16
Bus 11
264.6 + 296.7i
270.99
283.55
Bus 7
356.5
455.05
455.32
Bus 12
249.0 + 304.3i
196.84
200.93
Bus 6
359.5
450.21
450.44
Bus 13
368.5 + 452.4i
483.53
483.7
Bus 13
368.5
483.53
483.7
Bus 14
351.1 + 429.0i
491.93
493.16
Bus 15
378.1
477.74
477.86
Bus 15
378.1 + 445.1i
477.74
477.86
Bus 16
379.8
478.01
478.13
Bus 16
379.8 + 458.6i
478.01
478.13
W/O DG
515.4
511.43
511.43Table 2
Comparative analysis of three methods of loss calculations for 33-bus system.
Bus numbers
Calculated loss at different DG location
Bus numbers
Calculated loss at different DG location
Location of DG
Modified transmission parameters method
ELF
IA
Priority list of buses as per losses
Modified transmission parameters method
ELF
IA
W/O DG
212.5 + 142i
211.2
211
Bus 6
68.1 + 50.1i
68.2
74.89
Bus 2
197.4 + 133.9i
197.4
198.79
Bus 26
70.9 + 55.4i
69.48
76.18
Bus 3
144.7 + 107.0i
141.05
146.78
Bus 7
73.1 + 59.2i
69.89
76.81
Bus 4
126.0 + 97.5i
122.15
129
Bus 27
72.1 + 55.9i
71.04
77.7
Bus 5
108.1 + 88.4i
104.33
111.64
Bus 29
72.2 + 55.7i
72.93
78.18
Bus 6
68.1 + 50.1i
68.2
74.89
Bus 28
72.5 + 55.0i
73.22
79.27
Bus 7
73.1 + 59.2i
69.89
76.81
Bus 30
72.8 + 58.4i
73.64
78.52
Bus 8
80.6 + 59.0i
82.91
89.33
Bus 8
80.6 + 59.0i
82.91
89.33
Bus 9
92.0 + 65.0i
88.89
95.03
Bus 31
81.4 + 60.3i
83.9
89.12
Bus 10
98.4 + 68.2i
93.15
98.85
Bus 32
85.4 + 63.9i
87.64
92.92
Bus 11
99.5 + 68.4i
93.95
99.58
Bus 9
92.0 + 65.0i
88.89
95.03
Bus 12
101.6 + 68.9i
95.68
101.2
Bus 33
92.2 + 71.8i
92.9
98.44
Bus 13
109.2 + 74.2i
102.1
107.32
Bus 10
98.4 + 68.2i
93.15
98.85
Bus 14
111.6 + 76.8i
104.39
109.54
Bus 11
99.5 + 68.4i
93.95
99.58
Bus 15
115.9 + 80.0i
107.88
113.1
Bus 12
101.6 + 68.9i
95.68
101.2
Bus 16
120.8 + 82.8i
112.31
117.64
Bus 13
109.2 + 74.2i
102.1
107.32
Bus 17
129.3 + 91.4i
119.65
125.19
Bus 5
108.1 + 88.4i
104.33
111.64
Bus 18
133.3 + 93.5i
123.73
129.39
Bus 14
111.6 + 76.8i
104.39
109.54
Bus 19
204.1 + 138.0i
204.63
205.25
Bus 15
115.9 + 80.0i
107.88
113.1
Bus 20
206.8 + 138.4i
207.9
208.08
Bus 16
120.8 + 82.8i
112.31
117.64
Bus 21
206.9 + 138.5i
208.06
208.21
Bus 17
129.3 + 91.4i
119.65
125.19
Bus 22
207.3 + 138.7i
208.5
208.63
Bus 4
126.0 + 97.5i
122.15
129
Bus 23
157.8 + 114.7i
154.92
159.31
Bus 18
133.3 + 93.5i
123.73
129.39
Bus 24
164.0 + 116.6i
161.67
164.81
Bus 3
144.7 + 107.0i
141.05
146.78
Bus 25
171.3 + 120.0i
169.38
171.94
Bus 23
157.8 + 114.7i
154.92
159.31
Bus 26
70.9 + 55.4i
69.48
76.18
Bus 24
164.0 + 116.6i
161.67
164.81
Bus 27
72.1 + 55.9i
71.04
77.7
Bus 25
171.3 + 120.0i
169.38
171.94
Bus 28
72.5 + 55.0i
73.22
79.27
Bus 2
197.4 + 133.9i
197.4
198.79
Bus 29
72.2 + 55.7i
72.93
78.18
Bus 19
204.1 + 138.0i
204.63
205.25
Bus 30
72.8 + 58.4i
73.64
78.52
Bus 20
206.8 + 138.4i
207.9
208.08
Bus 31
81.4 + 60.3i
83.9
89.12
Bus 21
206.9 + 138.5i
208.06
208.21
Bus 32
85.4 + 63.9i
87.64
92.92
Bus 22
207.3 + 138.7i
208.5
208.63
Bus 33
92.2 + 71.8i
92.9
98.44
W/O DG
212.5 + 142i
211.2
211Figure 2
Comparative representation of loss calculation by three methods for 16-bus system.Comparative table gives total losses calculated by MTP method, but comparison of only real losses is made against available results of, other two methods.Figures2 and 5 can verify that proposed method gives the same results as that of ELF and IA methods but with much less computational equations as well as time. In 16-bus system the optimum location of DG to be installed is bus 9 where the total power losses are reduced to 163.4 kW, 212.7 kvar. The second best location is bus 12, where the power losses are 249.0 kw, 304.3 kvar. Similarly in 33-bus system the optimum location of DG to be installed is bus 6 where the total power losses are reduced to 68.2 kw, 53.8 kvar. The second best location is bus 26, where the power losses are 69.3 kw, 54.2 kvar and the successive priority list can be obtained in Tables 1 and 2. Figures 3 and 4 show both active and reactive power losses for 16-bus system which can be achieved if DG is installed at each bus location.Figure 3
Active power contribution by each source as well as DG in 16-bus system to achieve minimum losses.Figure 4
Reactive power contribution by each source as well as DG in 16-bus system to achieve minimum losses.Figure 5
Comparative representation of loss calculation by three methods for 33-bus system.For obtaining the optimal capacity, operating power factor, and type of the DG to be installed we can refer to Figures3 and 4 for 16-bus system and Figures 6 and 7 for 33-bus system. The results obtained from these figures are summarized in Table 3. From Table 3 it can be observed that all calculated parameters of the proposed method are identical to that of the IA and ELF methods except type and the operating power factor. In IA and ELF methods the type of the of the system was predetermined as the Type-I,  supplying real power only and as per the type of the system the power factor as well as size has been determined so these methods show the results of only active power loss minimization whereas in the proposed method the type of the system is not predetermined, but it is considered as the prediction factor which can be predicted as per the operating condition as well as requirement of the system which may be considered as the additional benefit of the method. Other two methods require the repetition of  complete calculations for other types of the DG and the obtained results may not satisfy completely the system conditions; that is, total loss minimization may not be achieved whereas  proposed method initiates its calculations as per the requirement of the system which is clear from the results shown in Table 3 where operating power factor of the 16-bus system is 0.88 which identifies requirement of the Type-III DG which can supply both real as well as reactive power so it could minimize both the losses, whereas in the other two methods the power factor is 0.98 which identifies Type-I DG which can supply only real power. In 33-bus system MTP method gives 0.81 as the operating power factor identifying Type-III DG, whereas the other two methods give 0.85 which contradicts the presence of Type-I DG.Table 3
Summarized results of both systems.
Test systems
Methods
Optimal location
Optimal size (MVA)
Operating power factor
Type
Base active loss, kw (W/O DG)
Reduced active loss (kw)
16-bus system
MTP
9
13.634
0.88
Type III
515.4
190.4
IA
9
13.0877
0.98
Type I
511.43
164.02
ELF
9
13.1551
0.98
Type I
511.43
164.01
33-bus system
MTP
6
3.2552
0.81
Type III
212.5
69
IA
6
3.0247
0.85
Type I
211.2
68.28
ELF
6
3.1034
0.85
Type I
211.2
68.2Figure 6
Active power Contribution by each source as well as DG in 33-bus system to achieve minimum losses.Figure 7
Reactive power contribution by each source as well as DG in 33-bus system to achieve minimum losses.


### 4.1. Consecutive Bus

Figures3, 4, 6, and 7 indicating the data of active and reactive power contribution of each generating source to the system from corresponding location show that if DG is placed at the bus which is just next to main sub-station may be referred as Consecutive Bus, then no power will be shared from the substation and the total power will be supplied by the DG alone. So the high capacity DG is required to supply the power if placed at Consecutive Bus despite of that very less amount of loss minimization could be achieved from this location. Apart from this while designing any DG parameter we consider the maximum demand condition and practically highly variable load conditions can be observed and during such a situation high reverse power flow from the DG may increase the losses to a huge amount which may even be more than the base condition, that is, the system without DG. So it can be suggested that the Consecutive Bus should never be considered for DG installation.In this paper in 16-bus system with a total load of 29.3 MVA and three substations handling approximately 10 MVA load each, buses number 4, 8, and 13 are the Consecutive Buses where the sizes of the DGs required are 14.375 MVA, 15.542 MVA, and 12.214 MVA each whereas in 33-bus system with a total load of 4.3566 MVA, bus number 2 is the Consecutive Bus at which the size required for the of DG is 4.6496 MVA. So here we can conclude that the Consecutive Bus may be considered as the worst location for DG installation.


## 4.1. Consecutive Bus

Figures3, 4, 6, and 7 indicating the data of active and reactive power contribution of each generating source to the system from corresponding location show that if DG is placed at the bus which is just next to main sub-station may be referred as Consecutive Bus, then no power will be shared from the substation and the total power will be supplied by the DG alone. So the high capacity DG is required to supply the power if placed at Consecutive Bus despite of that very less amount of loss minimization could be achieved from this location. Apart from this while designing any DG parameter we consider the maximum demand condition and practically highly variable load conditions can be observed and during such a situation high reverse power flow from the DG may increase the losses to a huge amount which may even be more than the base condition, that is, the system without DG. So it can be suggested that the Consecutive Bus should never be considered for DG installation.In this paper in 16-bus system with a total load of 29.3 MVA and three substations handling approximately 10 MVA load each, buses number 4, 8, and 13 are the Consecutive Buses where the sizes of the DGs required are 14.375 MVA, 15.542 MVA, and 12.214 MVA each whereas in 33-bus system with a total load of 4.3566 MVA, bus number 2 is the Consecutive Bus at which the size required for the of DG is 4.6496 MVA. So here we can conclude that the Consecutive Bus may be considered as the worst location for DG installation.


## 5. Conclusion

This paper presents a novel method, that is, modified transmission parameters method of extracting  the two port transmission equations for finding the optimal location, optimal size of that location, operating power factor, and the type of the DG to be installed in a primary distribution system to minimize the total losses of the system. The prominent feature of this method lies in its simplicity and ease of calculations as well as preciseness in achieving results. It avoids the time consuming and cumbersome iterative approach for handling the undemanding problem of designing the new DG to be installed in radial distribution system. Validity of the proposed method for designing DG to install in distribution system is tested and verified on two test distribution systems with varying sizes and complexity using already published Improved Analytical method and Exhaustive Load Flow solutions. Results show that locations, sizes, operating power factor, and type of distributed generators are decisive factors in minimizing total losses in the system and properly placed; pertinently chosen distributed generators can reduce losses appreciably. In this paper the worst location for DG allocation has been also located and referred as Consecutive Bus.



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*Source: 938958-2013-07-25.xml*