Optimal placement and sizing of distributed generators and shunt capacitors for power loss minimization in radial distribution networks using hybrid heuristic search optimization technique

Electrical Power and Energy Systems 78 (2016) 299–319

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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes

Optimal placement and sizing of distributed generators and shunt capacitors for power loss minimization in radial distribution networks using hybrid heuristic search optimization technique K. Muthukumar ⇑, S. Jayalalitha SASTRA University, Tirumalaisamudram, Thanjavur, Tamil Nadu, India

a r t i c l e

i n f o

Article history: Received 3 December 2014 Received in revised form 17 September 2015 Accepted 7 November 2015

Keywords: Harmony Search Algorithm (HSA) Particle Artificial Bee Colony Algorithm (PABC) Distributed Generator (DG) Radial Distribution Network (RDN) Loss Sensitivity Factor (LSF) Voltage Stability Index (VSI)

a b s t r a c t This paper attempts to minimize power losses in radial distribution networks and facilitates an enhancement in bus voltage profile by determining optimal locations, optimally sized distributed generators and shunt capacitors by hybrid Harmony Search Algorithm approach. To overcome the drawback of premature and slow convergence of Harmony Search Algorithm (HSA) over multi model fitness landscape, the Particle Artificial Bee Colony algorithm (PABC) is utilized to enhance the harmony memory vector. In the first approach, the formulation echoes the determination of loss sensitivity factor to decide the sensitive nodes and thereafter decides on the optimal rating through the use of hybrid Algorithm. The second approach encircles the role of hybrid Algorithm to search for both the optimal candidate nodes and sizing of compensating devices by significant increase in loss reduction with the former approach. The procedure travels to examine the robustness of the proposed hybrid approach on 33 and 119 node test systems and the result outcomes are compared with the other techniques existing in the literature. The simulation results reveal the efficiency of the proposed hybrid algorithm in obtaining optimal solution for simultaneous placement of distributed generators and shunt capacitors in distribution networks. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction The power generation capacities around the world are to be expanded at dizzying speed to meet out the increased load demand and thereby to avoid power blackouts which have significant economic impact on developing countries. Moreover the location of electricity generation is spatially isolated from the consumer load. This poses huge challenge in electricity transportation over long distance which leads to more power loss. Solution of above said problems to some extent is achieved by the installation of shunt capacitors and Distributed Generators (DG) close to the load center in the power system network. Industrialized and emerging countries are opening up for investment in renewable energy based distributed energy sources due to fast decline in fossil fuel resources as well as to reduce the emission. Installation of such sources has several advantages such as deferment in construction of new transmission and distribution lines, curtailment in power loss along with improved bus voltage profile, power quality enhancement and improved system reliability. Prior ⇑ Corresponding author. Tel.: +91 99424 08096. E-mail addresses: [email protected] [email protected] (S. Jayalalitha). http://dx.doi.org/10.1016/j.ijepes.2015.11.019 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

(K.

Muthukumar),

to placing these devices in the distribution network, there is a pre requisite to explore their effect in the system parameters like change in bus voltage profile, direction of power flows and associated power loss, harmonic distortion and system voltage stability and reliability. An appropriate planning methodology must be carried out for incorporating shunt capacitors and DG units into the distribution network to get the constructive benefits. The installation of these units at non-appropriate places with improper sizing leads to negative consequences such as increase in power loss, Poor system reliability and voltage instability state of the power system network. Heuristic optimization algorithms are capable of producing the best solution for the placement and sizing problem of DG units and shunt capacitors in distribution networks when compared with conventional optimization techniques. Newly developed evolutionary algorithms namely teaching learning based optimization technique to locate the apt position with appropriate rating of capacitors in RDN to minimize the power loss and energy cost has been addressed in [1]. Artificial bee colony approach has been utilized to get the optimum sizing of static capacitors and loss sensitivity factors are utilized to find the potential nodes for capacitor installation has been addressed in [2]. HSA based approach for

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K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319

Nomenclature Piþ1 Q iþ1 Ri;iþ1 X i;iþ1 Pi;iþ1 Q i;iþ1 PLiþ1 Q Liþ1

real power flows out of node i + 1 reactive power flows out of node i + 1 resistance of line between nodes i and i + 1 reactance of line between nodes i and i + 1 active power flows out of node i to node i + 1 reactive power flows out of node i to node i + 1 real power load demand at node i + 1 reactive power load demand at node i + 1 active power multiplier which is equal to zero if there is no active power injection source or equal to 1 if any active power injection source (DG unit) is present. reactive power multiplier which is set to zero if there is no reactive power injection or set to 1 if any reactive power injection sources (Type-III DG unit) are present. reactive power multiplier which is set to zero if there is no reactive power injection or set to 1 if any reactive power injection (by the shunt capacitor) sources are present. real power injection by the DG unit at node i + 1

aPDG aqDG aqcp

PlossT PDGCP lossði;iþ1Þ PDGCP lossT
sys

V
i
spec

V
min
spec

V


max PDG max PDG min DG p: f i DG p: f min DG p:f max

total power loss in the RDN without DG’s and shunt capacitors real power loss in the branch connected between nodes i and i + 1 with DG’s and shunt capacitors total power loss in the RDN with DG units and shunt capacitors nominal bus voltage magnitude of ith bus of the RDN the specified lower bound of bus voltage of the RDN the specified upper bound of bus voltage of the RDN maximum size of DG unit in kilowatts minimum size of DG unit in kilowatts operating power factor of ith DG unit minimum operating power factor of DG unit maximum operating power factor of DG unit

Q DG iþ1

reactive power injection by the DG unit at node i + 1

Piþ1eff

total effective reactive power supplied beyond node i +1 total effective active power supplied beyond node i + 1

Q Ciþ1

reactive power injection by the shunt capacitor at node i+1 total number of nodes in the RDN total number of branches in the RDN total number of load buses in the RDN total number of capacitors to be installed in RDN current flows between the nodes i and i + 1 allowable maximum permissible current of the branch i +1 real part of the branch current flows between the nodes i and i + 1 reactive part of the branch current between the nodes i and i + 1

QcL

sum of total kVAR demand of the RDN

PDG iþ1

n nb nl nc Ii;iþ1 Ii;iþ1

max




IPði;iþ1Þ



Iqði;iþ1Þ


capacitor allocation and rating in unbalanced and balanced radial networks was proposed in [3–5]. Hybrid approach of fuzzy and GA for capacitor allocation with varying load conditions has been introduced in [6]. Integration of evolutionary algorithm like differential Evolution and pattern search approach for shunt capacitor allocation to realize maximum savings has been developed in [7]. The impact of DG integration in the distribution network which leads to abrupt changes in system operational characteristics has been addressed in [8–10]. Differential Evolution Technique used to determine the optimal DG sizing and its location with power loss minimization as objective has been addressed in [11]. For optimum DG allocation and sizing, a novel power stability index was proposed in [12] to locate the most sensitive buses in the radial distribution network. An analytical approach was presented in [13] for optimum sizing and sitting of DG and shunt capacitor simultaneously to achieve power loss reduction. A hybrid approach using imperialist competitive algorithm and GA for the placement of DG units and shunt capacitor has been addressed in [14]. The weak nodes in radial distribution network was identified by computing Voltage Stability Index (VSI) in [15,16]. Analytical approach and modeling aspects of different types of DG units integration in distribution system has been addressed in [17]. DG planning in distribution networks with different load models has been addressed in [18]. Various heuristic algorithms have been adopted by the researchers to solve complex optimization problems. Few modifications or improvisation of the algorithms by hybridizing the existing algorithms are necessary in order to balance and accelerate the

Q iþ1eff

Q cj

kVAR injection by the jth shunt capacitor

PDG i

Size of ith DG unit in kilowatts

Q DG i

Size of ith DG units in kilovolt amperes reactive

Plossi;iþ1

Power loss associated with the branch between the nodes i and i + 1 power factor Single Capacitor Placement Multiple Capacitor Placement

p.f SCP MCP

exploration and exploitation ability of heuristic optimization algorithms for searching optimal solutions in multi model fitness landscape. The present work is aimed to develop a fast and novel hybrid heuristic optimization technique by integrating harmony search algorithm with PSO embedded artificial bee colony (HSA–PABC) to find the optimal location and sizing of DG units and shunt capacitors for power loss minimization and to enhance bus voltage profile in radial distribution network at three different load levels subject to certain operating constraints. In hybrid HSA–PABC approach, the exploration ability of HSA and the exploitation ability of PABC are integrated to synthesize the strength of both algorithms to evaluate the DG units and shunt capacitors location and sizing in the RDN. Simulation results reveals that the proposed hybrid HSA–PABC algorithm is capable of obtaining optimum solution with less computational time, with improved convergence characteristics than classical HSA. In this article, different test scenarios are considered with an aim to quantify the benefits for distribution networks with the placement of shunt capacitors and DG units with real power injection (Type-I DG units) as well as real and reactive power injection capability (Type-III DG units). Simulation work carried on 33 node and 119 node radial distribution systems and the effectiveness of the proposed hybrid algorithm is validated with the classical HSA and the existing algorithms present in the literature. This article is organized as follows: Formulation of objective function of the problem and its associated constraints is described

K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319

in Section ‘Problem formulation’. Overview of classical HSA and the methodology of proposed hybrid algorithm is presented in Section ‘Hybrid HSA–PABC algorithm techniques’. Application of proposed hybrid approach for power loss reduction is discussed in Section ‘Application of proposed approach for power loss reduction’. Numerical results and discussion are presented in Section ‘Numerical results and discussions’.

Piþ1 ¼ P i;iþ1  Ri;iþ1

P2i;iþ1

" Q iþ1 ¼ Q i;iþ1  X i;iþ1

þ

Q 2i;iþ1 2

!

jV i j

P2i;iþ1 þ Q 2i;iþ1 jV i j2

#  P Liþ1 þ aPDG P DG iþ1

ð1Þ

!

# C  Q Liþ1 þ aqDG Q DG iþ1 þ aqcp Q iþ1

ð2Þ "

R2 þ X 2  

i;iþ1 i;iþ1 2 2 2 P þ Q j V iþ1 j ¼
V 2i
þ i;iþ1 i;iþ1 jV i j2    i ¼ 1; 2; . . . ; n 2 Ri;iþ1 Pi;iþ1 þ X i;iþ1 Q i;iþ1

ð3Þ

Current flows through the branch between the nodes i and i + 1 is computed as

Ii;iþ1

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u 2 2 uP i;iþ1 þ Q i;iþ1 ¼t 2 jV i j

ð4Þ

Power loss associated with the branch between the nodes i and i + 1 may be computed as

Plossi;iþ1 ¼ jIi;iþ1 j2 Ri;iþ1

PlossT

" # nb X ¼ Plossi;iþ1 i¼1

" # nb
X



IPði;iþ1Þ
2 Ri;iþ1 þ
Iqði;iþ1Þ
2 Ri;iþ1

ð6Þ

i¼1

Identification of sensitive nodes for simultaneous placement of distributed generators and shunt capacitors with optimum sizing in distribution network to realize the constructive benefits is a complex combinatorial optimization problem. The objective of this study is to obtain power loss minimization with the optimal placement and sizing of DG units and shunt capacitors at three different load levels while satisfying the operating constraints. The radial distribution networks include series impedances to represent the distribution lines, balanced power sinks and constant power loads to form a symmetrical network. The simplified recursive Eqs. (1)–(3) used to get the load flow solution in the RDN with DG units and shunt capacitors is shown in Fig. 1. The active and reactive power flows at the terminal node of i + 1th branch can be mathematically stated as,

"

The total system loss amounts to the summation of power losses related with the real and reactive part of branch current magnitude in all the branches of the RDN as indicated in Eq. (6).

PlossT ¼

Problem formulation

301

ð5Þ

Obf ¼ Minimize ðPlossT Þ

ð7Þ

This study aims to minimize the real power loss by reducing the real and reactive part of branch current by injecting real and reactive power with the aid of shunt capacitors and DG units of suitable ratings placed at appropriate locations. Power loss of a branch in RDN which lays between the nodes i and i + 1 after the placement of DG units and shunt capacitors is computed as, 20 6B PDGCP lossði;iþ1Þ ¼ 4@Ri;iþ1



 2 13 2  P i;iþ1  aPDG PDGiþ1 þ; Q i;iþ1  aqDG Q DGiþ1  aqcp Q Ciþ1 C7 A5 jV i j2 ð8Þ

Total power loss of RDN after compensation with DG units and shunt capacitors is computed as,

"

PDGCP lossT ¼

nb X PDGCP lossði;iþ1Þ

#

ð9Þ

i¼1

Constraints Active and reactive power balance constraints The two nonlinear recursive load flow Eqs. (1) and (2) associated with real and reactive power flow in all the branches of RDN serve as the equality constraints and the nominal bus voltage magnitude limit, thermal capacity limits of the radial feeder lines and maximum reactive power compensation limit by the shunt capacitors and DG units are considered as inequality constraints. RMS values of bus voltage limits At each node of radial distribution network, the bus voltage magnitudes should be maintained within the prescribed operating range is considered as the inequality constraint as specified in Eq. (10).


spec

sys

spec

V
6
V
6
V
max min i

ð10Þ

In this presence case, bus voltage taken as ±10% of the nominal system voltage which lies between,

Fig. 1. Single line diagram of RDN feeder with DG unit and shunt capacitor placed at an arbitary location.

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6 1:1 i ¼ 1; 2; . . . ; n 0:9 6
V sys i Thermal capacity limits of feeder lines The current flow through the each branch of the RDN should not exceed its maximum current flow limits of the feeder lines as in Eq. (11)

jIi;iþ1 j 6 jIi;iþ1

max j;

i ¼ 1; 2; . . . ; nb

ð11Þ

Reactive power injection limits of the shunt capacitors The total reactive power supplied by the shunt capacitors and DG units to be installed must be less than total reactive power demand of network to avoid over compensation. nc nl X X Q cj 6 1:0 QcL j¼1

ð12Þ

j¼1

The multiple integers of smallest size capacitors are taken into consideration along with the total kVAR supplied by the capacitors is taken as one of the constraint.

Q cj 6 KQ c ;

K ¼ 1; 2; . . . ; nc

ð13Þ

where K is an integer number and Qc is the smallest capacitor size taken into the consideration for the installation. Therefore for each location, K sizes {Qc, 2Qc, 3Qc,. . .KQc} are the available capacitors for installation in that location. DG unit sizing limit In this study, DG units are modeled as Type-I DG units (photovoltaic systems, micro turbines) supply real power with unity power factor and Type-III DG units [33] (controllable synchronous generator, biogas plants) deliver both active and reactive power at a pre-specified operating power factor of 0.85(leading) [19]. The kW range of DG rating is chosen as 10% to 80% of the total system real power demand. DG PDG 6 PDG min 6 P i max

ð14Þ

n X where PDG PDG min ¼ 0:1 i

and PDG Max ¼ 0:8

i¼2 DG

DG

p:f max P p:f i

n X PDG i i¼2

DG

P p:f min

ð15Þ

 1  ¼ PDG ðp:f Þ Q DG i tan cos i

ð16Þ DG

Consider a branch of RDN consisting of impedance (Z = R + jX) and a load of P + jQ connected between nodes s and r as shown in Fig. 2. The system stability index is improved when DG units and shunt capacitors are installed in the distribution system. The voltage stability of each node of the RDN is computed as in [15,16],

VSIðrÞ ¼ fjVsj4  4:0fPX  QRg2  4:0fPR þ QXgjVsj2 g

ð17Þ

For stable radial system with ‘‘n” number of buses, VSI(r) P 0, for r = 2, 3, . . ., n. Identification of vulnerable nodes using loss sensitivity factors for DG and shunt capacitor installation LSF is utilized to predict the sensitive nodes which are prone to more loss reduction when active and reactive power injected by the DG units and shunt capacitors is put in place [7]. Consider a distribution feeder branch between the node i and i + 1 as shown in Fig. 1. The active and reactive power loss between i and i + 1 node is given by jIi;iþ1 j2 Ri;iþ1; and it can be expressed as,

Pline

loss

¼

P 2iþ1;eff þ Q 2iþ1;eff jV iþ1 j2

!

ð18Þ

Ri;iþ1

Thus the real and reactive power loss sensitivity factors (PLSF and QLSF) are computed by taking the derivative of the power loss Eq. (18) with respect to real and reactive power injection as shown in the Eqs. (19) and (20).

PLSF ði; i þ 1Þ ¼

@Pline loss ¼ @Piþ1eff

@Pline loss QLSF ði; i þ 1Þ ¼ ¼ @Q iþ1eff

2Piþ1eff Ri;iþ1

! ð19Þ

jV iþ1 j2 2Q iþ1eff Ri;iþ1

!

jV iþ1 j2

ð20Þ

The PLSF and QLSF values are computed using Eqs. (19) and (20) at each node of the RDN from the base case load flow and arranged in descending order according to their sensitivity factors to form the priority list. The sensitivity factors of the RDN nodes indicate the change in real and reactive power loss in each node with respect to the injected active and reactive power by the DG units and shunt capacitors. The top most nodes with highest real power loss sensitivity w.r.t. real power injection (PLSF) is the potential node for DG unit placement and the node with highest real power loss sensitivity w.r.t. reactive power injection (QLSF) is the potential node for shunt capacitor installation [13].

DG

In the case of Type-I DG units; p:f max ¼ p:f min ¼ 1: Computation of VSI For stable operation of distribution system, the stability index values of each node should be near to unity [15]. The stability level of each node is computed to indicate the weak buses which are likelihood of voltage collapse.

Fig. 2. Branch of radial distribution system.

Hybrid HSA–PABC algorithm techniques Overview of Harmony Search Algorithm (HSA) HSA was proposed by Geem et al. [20,21] based on the natural phenomena of music played on musical instruments. It mimics the behavior of a musical improvisation process aiming at composing the most harmonious melody. The HSA algorithm is formulated with fewer mathematical requirements that are easily adaptable by selecting proper parameters values within their limits. The Procedure is detailed below. Step 1: Parameter initialization Suitable value for Harmony Memory Size (HMS), Harmony Memory Consideration Rate (HMCR) and Pitch Adjusting Rate (PAR) are initialized to get better solution vector. Step 2: Harmony Memory Vector initialization In HMV, randomly generated solution vectors are used to form the HMS matrix.

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K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319

Step 3: Improvisation of Harmony Memory (HMV) The following three measures are adopted to develop the New Harmony vector value [20,21]. The first one is Memory Consideration followed by the Pitch Adjustment and the Random Selection stages. The variable values of HMV, x02 , x03 ; . . . ; x0N are selected randomly. The HMCR value is elected between 0 and 1, and it is the rate of selecting one value from the formerly stored values in the HMV. (1-HMCR) is the rate of randomly choosing each value for the variable from the specified range of values as, if (rand( ) < HMCR) n o xi xi 2 xi1 ; xi2 ; . . . ; xHMS 1 else xi xi 2 Xi end

rand ( ) is the uniform random number lies within 0,1 and ‘‘Xi” is the feasible range of values for each decision variable (x0i ). HSA will select the decision variable value from values stored in the HM with 85% probability, if HMCR value chosen as 0.85 or from the possible range lies between (100–85%) probability [22]. Each element from the memory consideration is to be pitch adjustment as, If (rand ( ) < PAR) xi0 = xi0 ± BW⁄rand( ) else xi0 =xi0

where, ‘‘BW” indicates a random distance bandwidth. Step 4: Updating Harmony Memory Vector (HMV) The improved harmony vector values and its corresponding best fitness values obtained in step 3 are included in HM by replacing the existing bad harmony vector. Step 5: Repeat step 3 and step 4 until the termination condition is reached In classical HS algorithm, HMCR, PAR and BW are considered as control parameters along with harmony memory improvisation strategies plays a vital role which determines the algorithm performance. The HSA algorithm is well suited for identifying a good solution within a reasonable time. But it has inefficient in local searching ability in numerical optimization applications [22]. The premature and slow convergence over multi model fitness landscape is the main draw back in classical HS algorithm. To enhance the original HS algorithm performance, various modifications were adopted such as dynamic adaptation of its parameters like (HMCR) Harmony Memory Consideration Rate and (PAR) Pitch Adjustment Rate [23]. To favor the exploration during the initial stages and exploitation in the final phase of the search process, the bandwidth is adjusted dynamically. The local search ability of HSA has been improved by hybridizing the HS algorithm with various optimization algorithms like sequential Quadratic program, [24–26]. Hybrid Harmony Search Algorithm (HSA–PABC) To overcome the above said drawbacks of classical HSA algorithm and to enhance the solution accuracy and the convergence rate of the classical HSA, the PSO embedded Artificial Bee Colony algorithm (PABC) is utilized in this work. The learning mechanism for the improvement of harmony vector in HSA is proposed in [27,28]. In the proposed HSA–PABC hybrid approach, the HSA plays as the main procedure for global search and PABC algorithm is utilized for local search to optimize harmony memory.

In classical ABC algorithm, the exploration and exploitation of the employed bees and onlooker bees carried out using the same formula i.e. using Eq. (24) which decides the performance of the ABC. The searching ability of the ABC as described using Eq. (24) is better interms of exploration but poor at exploitation. A hard constriction on the bee’s trajectories by greedy mechanism may result into premature convergence and sometimes traps into local optimal solution. The exploration and exploitation ability of ABC algorithm is balanced by embedding the PSO algorithm into the ABC which is called as PABC algorithm. The inertia weight and acceleration coefficients are introduced to modify the search process which combines local and global searching ability of the bees through cognitive and social knowledge. The modified and improved ABC algorithm (PABC) which make use of Eq. (21) to update the bees position and these capabilities results to mitigation of premature converge and stagnation problem of ABC algorithm and it leads to faster convergence speed and reasonable accurate solution than the classical ABC algorithm.

  h  i V jk ¼ x X jk þ C 1 /jk X best  X jk þ C 2 /jk X nk  X jk k

ð21Þ

where V jk is the new modified feasible solution on its previous solution X jk . The term ‘‘x” represent the inertia weight used to control the current position of bees with respect to previous position. The inertia weight is linearly decreased as recommended in [29] from 0.9 to 0.4 to promote global search initially and gradually towards the local search. C 1 and C 2 are nonnegative social weight constants, which has control over the position of the best and neighboring bees on the current one. In this study, the appropriate default values of C 1 and C 2 are chosen as 2.05 as recommended in [29]. X best indicates the preeminent food source among the population. X nk is the random neighbor value in the population and /jk is the random value within [0, 1]. The new values of the bee are determined based its current value, its neighboring value and the best bee in the population as in Eq. (21). The control parameters of PABC algorithm are the trial limit and Maximum cycle number (MCN). Trial limit prevents the solution trap in local optima. Thus it has few parameters to be tuned which reduce the number of trial and error procedure to decide the tuning parameter values. Algorithmic steps of PABC are lined below. Step 1: Initialize the parameters of ABC algorithms such as maximum cycle (MCN), scout bee limit. Step 2: Generate the initial population. Step 3: Initiate the employed bee phase to produce new populations in the neighborhood of solution obtained in step 2 using Eq. (21). After the evaluation of each candidate food source position, apply the greedy selection process between the solution obtained in step 2 and step 3 and compute the probability using Eq. (22).

fitnessj P j ¼ PHMS j¼1 fitnessj

ð22Þ

The fitness value of jth solution is considered as fitnessj. The fitness values of the each solution is calculated by using Eq. (23) as,

fitnessj ¼ ð1=ð1 þ PlossT Þ

ð23Þ

PlossT is computed by performing the load flow for each individual jth solution using Eq. (6) (continued on next page)

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K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319 Table 1 Control parameters setting of the Hybrid HSA–PABC algorithm & relevant data utilized in simulation.

Step 4: In the onlooker bee phase, generate new solutions based on the probability of the employed bee phase. The new food source location V new j;k in the neighborhood of food source X old j;k is determined by using Eq. (24)

V new j;k

n

 o old ¼ X old j;k þ u X j;k  X n;k

ð24Þ

where nЄ {1, 2, . . ., CS} and k Є {1, 2, . . ., D} are indices chosen randomly; D is the total number of optimization parameters (dimension of the problem); n – j; ‘u’ represents a random number generated within the range of [1, 1]. It should be noted that the estimated components of the candidate food position V j;k using Eq. (24) may violate the predefined limits. To tackle this problem, the resetting scheme is utilized in this work, which sets the violating components to the nearest boundary value, i.e,

V j;k ¼ X jmin ;

if V j;k 6 X jmin

V j;k ¼ X jmax ;

if V j;k P X jmax

kðnewÞ

In the first approach, the exercise travels to compute the LSF of the RDN to trace the most receptive nodes suitable for placing DG units and shunt capacitors using the Eqs. (19) and (20). The nodes are sorted in descending sequence of LSF to form a priority list. The nodes with higher value of LSF are cleaved to be higher priority candidate nodes for installation of DG units and shunt capacitors to achieve loss reduction. It thereafter resorts to the use of HSA– PABC algorithm for obtaining the optimality in the size of the DG units and shunt capacitors. Let the number of DG units and shunt capacitors to be installed is K at as many number of candidate nodes. The first and second part of solution vector has the DG unit and shunt capacitor sizes whose length is K and the corresponding potential nodes are selected from the priority list. Thus the solution vector HMV1 of length 2K for DG and shunt capacitor installation can be formulated as,

ð25Þ

In the proposed HSA–PABC hybrid approach, the HMV in the HS algorithm is considered as the initial food source and explored and exploited in three phases namely employed bee phase, onlooker bee phase and the scout bee phase of the PABC algorithm. Thus the populations in harmony memory vector of HS algorithm are intelligently improved through PABC algorithm during the optimization process to reach the optimal solution within the search space. The exploration ability of HSA and the exploitation ability of PABC are integrated to blend the strength of both algorithms to get the optimal solution of the proposed optimization problem. Finally improved harmony vector is generated as an outcome of self-adaptive HSA which is more efficient to get better solutions than the classical HSA variants [23]. The HSA–PABC is a

DGS11

B 2 HMV ¼ B @ DGS1 DGSHMS 1

20 0.5 0.9 0.4 2.05 0.9 100 10 0.9 to 1.1 p.u 50 kVAR

LSF based approach

Step 6: Repeat steps 3 to 5 until the optimal solution is obtained; or the stopping criterion is satisfied. i.e. total number of MCN is reached.

0

Typical value (s)

HMS (Harmony Memory Size) Pitch Adjustment Rate (PAR) HMCR (Harmony Memory Consideration Rate ) Minimum inertia weight ðW min Þ Positive acceleration coefficient (C 1 , C 2 Þ Maximum inertia weight ðW max Þ Maximum Cycle Number (MCN) Scout bee limit Bus voltage limits Step size of one fixed capacitor unit

Application of proposed approach for power loss reduction

  ¼ min X kj

h    i þ randð0; 1Þ ðmax X kj  min X kj

Parameters

1 2 3 4 5 6 7 8 9 10

an implementation point of view. The parameters selected for the hybrid HSA–PABC based algorithm for 33 and 119-node radial distribution networks are summarized in Table 1.

Greedy selection is adopted after the evaluation of each candidate food source position Step 5: Abandoned solution is eliminated by generating a new random solution using scout bee as in Eq. (25)

Xj

S. No

2

3

6 1 1 1 1 7 HMV1 ¼ 4DGS11 DGS12 . .. DGS1k ; kVAR1 kVAR2 .. . kVARk  Objk 5 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |ffl{zffl} DG Sizes 1

...

DGS1k

kVAR1

1

kVAR2

1

...

kVARk

1



DGS22

...

DGS2k

kVAR1

2

kVAR2

2

...

kVARk

2



. . . DGSHMS k

HMS

kVAR1

HMS

kVAR2

co-evolutionary algorithm runs in parallel to reach the optimal solution with short processing time. Besides, this hybrid algorithm is easy to implement and requires only the tuning of the following control parameters to achieve the optimal solution. The parameters influencing the hybrid algorithm performance are Harmony Memory Consideration Rate (HMCR), Pitch Adjustment Rate (PAR), Harmony Memory Size (HMS), Maximum Cycle Number (MCN) and Scout bee limit [27]. In the proposed hybrid approach, it is the fact that it has more parameters to be tuned. Conversely the proposed HSA–PABC can perform well even with the default values of its control parameters which make it good-looking from

1

Power loss 1

where DGS11 DGS12 . . . DGS1k and kVAR1 kVAR2 . . . kVARk are the DG units and shunt capacitors sizes to be installed at candidate nodes

DGS12 DGSHMS 2

Capacitor Sizes

HMS

. . . : kVARk

1

Objk

1

C 2 Objk C A HMS  Objk

identified based on LSF approach. The total harmony matrix is filled randomly with all other possible solution vectors and the corresponding HMV is shown as below. The HMV is arranged in descending order based on the objective function values computed against each solution vector in HM Proposed Hybrid Approach (HSA–PABC) However solution obtained based of LSF based locations for placing DG units and shunt capacitors may not be the optimal one. Since the computation of LSF depends on RDN topology and

K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319

305

Fig. 3. Flowchart of hybrid HSA–PABC algorithm for the proposed optimization problem.

its loading pattern. [30]. In second approach to overcome the above said difficulty, the HSA–PABC algorithm is utilized to determine the location and the optimality in the size of the shunt capacitors and DG units simultaneously. In order to minimize the computational time and search space for the identification of potential

2

buses for placing the DG units and shunt capacitors by the proposed hybrid optimization approach, top 25 to 30% of nodes from the LSF priority list are nominated [30]. Each set of the feasible solution of HMV indicates a potential solution of the problem for placing shunt capacitors and DG units which can be represented

3

6 1 1 1 1 7 HMV1 ¼ 4DGS11 DGS12 . . . DGS1k kVAR1 kVAR2 . . . kVARk Loc11 Loc12 . . . Loc1k  Objk 5 |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |ffl{zffl} DG Sizes

Capacitor Sizes

Locations

Power loss

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combined placement and sizing of DG units and shunt capacitors for the proposed test systems, the LSF and HSA–PABC based approaches are considered. In LSF based method, the sensitive

as,where the DGS11 DGS12 . . . DGS1k and KVAR11 KVAR12 . KVAR1k are the DG and shunt capacitors sizes to be installed at candidate nodes   Loc11 Loc12 . . . Loc1k

0

DGS11

B 2 HMV ¼ B @ DGS1 DGSHMS 1

which are identified by the nominated nodes

DGS12

...

DGS1k

kVAR1

1

kVAR2

1

...

kVARk

1

Loc11

Loc12

...

Loc1k



DGS22

...

DGS2k

kVAR1

2

kVAR2

2

...

kVARk

2

Loc21

Loc22

...

Loc2k



HMS

LocHMS 1

LocHMS 2

DGSHMS 2

. . . DGSHMS k

HMS

kVAR1

HMS

kVAR2

from priority list with the proposed hybrid HSA–PABC algorithm. The total harmony matrix is filled randomly with all other feasible solution vectors and the harmony matrix is formed shown as below, For the procedure outlined above, the objective function for each solution vector of HMV is obtained and new objective function values are updated if found better than the previous one. These cyclic steps are repeated until a termination criterion is satisfied. The primary focus owes to a systematic reduction in the power losses with the enhanced bus voltage profile and stability of the radial distribution network. Fig. 3 explains the flowchart of hybrid HSA–PABC algorithm utilized in the proposed optimal DG units and shunt capacitor sizing and sitting problem. The procedure estimates the bus voltages, line flows and line losses using Backward-Forward Sweep based load flow method [11] to investigate the impact of the capacitor placements in the RDN. Numerical results and discussions The application of hybrid HSA–PABC algorithm has not been explored in previous works for optimal DG units and shunt capacitor allocation problem in the distribution networks. This motivates to use hybrid approach of HSA and PABC algorithms to identify the location and sizing of DG units and shunt capacitors in the passage to articulate a higher region of power loss reduction with improved bus voltage profile. To study the impact of

. . . kVARk

. . . LocHMS k

1

Objk

1

C 2 Objk C A HMS  Objk

nodes for installation of DG units and shunt capacitors are selected based on LSF values arranged in descending order. The top nodes from the priority list ranked are selected as candidate potential nodes and the optimal sizing of DG units and shunt capacitors at selected nodes are obtained using HSA–PABC algorithm. In the proposed hybrid approach, the candidate nodes and optimal sizes of the compensating devices are found simultaneously using HSA–PABC algorithm to realize more loss reduction as compared with LSF based approach. To demonstrate the effectiveness of the proposed HSA–PABC algorithm, comparative analyses were made with the LSF based method. The strategy envisages examining the veracity of the hybrid optimization algorithm using 33 node and 119 node test systems on a Matlab7.7.0 platform. The test systems data are taken from [31,32]. To highlight the superiority of the proposed HSA–PABC approach, the following two test scenarios are taken into considered. Scenario I: Type-I DG units capable of injecting active power only (unity p.f) is installed at potential nodes with and without shunt capacitors. Scenario II: Type-III DG units capable of injecting .both real and reactive powers operating at 0.85 p.f (leading) is installed at potential nodes with and without shunt capacitors In each scenario, LSF and HSA–PABC based approaches are simulated on the test networks with constant power load model at 0.5 (light), 1.0 (nominal), 1.6 (peak) load level conditions. The

Fig. 4. Single line diagram of 33 node radial distribution system.

307

K. Muthukumar, S. Jayalalitha / Electrical Power and Energy Systems 78 (2016) 299–319

Real power loss sensivity

PLSF

QLSF

0.0402 0.0302 0.0202 0.0102 0.0002

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Node number Fig. 5. Real power loss sensitivity at various nodes of 33 node RDN.

Table 2 Simulation results of 33 node RDN for Scenario-I (Type-I DG & SCP) at 50% load levels. Test cases

Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

48.79

–

0.9540 (18)

Case-1 Single DG

LSF HYBRID

1240 (6) 1240 (6)

–

26.58 26.58

45.52 45.52

0.9714 (18) 0.9714 (18)

Case-2 Three DG

LSF HYBRID

650 (6), 384 (3), 464 (28) 514 (30), 550 (24), 388 (14)

–

23.93 17.64

50.95 63.84

0.9712 (18) 0.9842 (33)

Case-3 Single DG + SCP

LSF HYBRID

1245 (6) 1242 (6)

700 (28) 600 (30)

15.31 14.21

68.57 70.87

0.9778 (18) 0.9770 (18)

Table 3 Simulation results of 33 node RDN for Scenario-I (Type-I DG & SCP) at 100% load levels. Test cases

Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

211

–

0.9037 (18)

Case-1 Single DG

LSF HYBRID

2598 (6) 2598 (6)

–

111.03 111.03

47.38 47.38

0.9425 (18) 0.9425 (18)

Case-2 Three DG

LSF HYBRID

1369 (6), 791 (3), 820 (28) 1068 (30), 1073 (24), 755 (14)

–

99.79 72.81

52.70 65.49

0.9398 (18) 0.9684 (33)

Case-3 Single DG + SCP

LSF HYBRID

2543 (6) 2531 (6)

1400 (28) 1250 (30)

62.97 58.45

70.15 72.29

0.9549 (18) 0.9536 (18)

Table 4 Simulation results of 33 node RDN for Scenario-I (Type-I DG & SCP) at 160% load levels. Test cases

Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

603.48

–

0.8360 (18)

Case-1 Single DG

LSF HYBRID

4349 (6) 4349 (6)

– –

300.55 300.55

50.19 50.19

0.9063 (18) 0.9063 (18)

Case-2 Three DG

LSF HYBRID

2221 (6), 1002 (3), 1474 (28) 1784 (30), 1702 (24), 1202 (14)

– –

270.39 194.17

55.19 67.82

0.9012 (18) 0.9494 (33)

Case-3 Single DG + SCP

LSF HYBRID

4186 (6) 4151 (6)

2300 (28) 2050 (30)

166.85 155.23

72.35 74.28

0.9272 (18) 0.9247 (18)

Table 5 Simulation results of 33 node RDN for Scenario-II (Type-III DG & SCP) at 50% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

48.79

–

0.9540 (18)

Case-1 Single DG

LSF HYBRID

1489.41 (6) 1489.41 (6)

– –

16.59 16.59

65.99 65.99

0.9788 (18) 0.9788 (18)

Case-2 Three DG

LSF HYBRID

711.7 (6),428.23 (3), 621.17 (28) 501.2 (12), 697.6 (30), 445.8 (25)

– –

12.06 3.95

75.28 91.90

0.9781 (18) 0.9944 (18)

Case-3 Single DG + SCP

LSF HYBRID

1365.8 (6) 1337.6 (6)

250 (28) 300 (30)

15.14 13.73

68.96 71.86

0.9790 (18) 0.9791 (18)

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Table 6 Simulation results of 33 node RDN for Scenario-II (Type-III DG & SCP) at 100% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

211

–

0.9037 (18)

Case-1 Single DG

LSF HYBRID

3011.76 (6) 3011.76 (6)

– –

68.29 68.29

67.63 67.63

0.9568 (18) 0.9568 (18)

Case-2 Three DG

LSF HYBRID

1328.2 (6), 850.58 (3), 1338.8 (28) 1014 (12), 1363.5 (30), 960 (25)

– –

49.76 15.91

76.42 92.46

0.9549 (18) 0.9889 (18)

Case-3 Single DG + SCP

LSF HYBRID

2792.9 (6) 2730.58 (6)

550 (28) 650 (30)

62.01 56.16

70.61 73.38

0.9582 (18) 0.9583 (18)

Table 7 Simulation results of 33 node RDN for Scenario-II (Type-III DG & SCP) at 160% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

603.48

–

0.8360 (18)

Case-1 Single DG

LSF HYBRID

5145.8 (6) 5145.8 (6)

– –

180.47 180.47

70.09 70.09

0.9334 (18) 0.9334 (18)

Case-2 Three DG

LSF HYBRID

2548.2 (6), 940 (3), 2022.3 (28) 1542.3 (12), 2287 (30), 1563.5 (25)

–

132.80 41.11

77.99 93.18

0.9285 (18) 0.9792 (18)

Case-3 Single DG + SCP

LSF HYBRID

4596.4 (6) 4482.3 (6)

900 (28) 1050 (30)

163.70 147.91

72.87 75.49

0.9327 (18) 0.9325 (18)

substation voltage and load power factors of test networks in both scenarios were considered as 1.0 p.u and lagging p.f respectively. For the above said two scenarios, the following three test cases are considered: Test case-1-placement of single DG unit. Test case-2-placement of multiple DG units. Test case-3-Placement of single DG unit with single capacitor and multiple shunt capacitors. 33 node radial distribution test system results To demonstrate the effectiveness of the proposed hybrid approach, it is applied on small scale distribution network. It is a balanced three phase radial network consists of 33 nodes with 32 segments with 12.66 kV as operating voltage level and total real and reactive power load demands of the system are 3720 kW and 2300 kVAR respectively. Before the placement of DG units and shunt capacitor, the total active and reactive power losses are 211 kW and 143.03 kVAR respectively. The test system data such as line and load data are obtained from [31]. The single line diagram of the 33 node test system is shown in Fig. 4. For LSF based approach, nodes with higher values of PLSF are considered for the placement of DG units and higher values of QLSF

are considered for shunt capacitors as depicted in Fig. 5. The nodes with higher values of PLSF i.e.. node 6 for single DG placement (Test case-1),node 6, 3 & 28 for three DG placement (Test case-2) are considered. Nodes with higher values of QLSF (node 6, 28,. . .) are considered for shunt capacitors. For simultaneous one DG and one capacitor placement (for test case-3), as node 6 is nominated for DG placement and second highest node i.e. node 28 from QLSF is chosen for capacitor placement. Scenario-I: In scenario-I, Type-I DG units capable of injecting active power only is installed at potential nodes with and without shunt capacitors. The LSF and HSA–PABC based approaches are simulated at different load levels with above said three test cases and the simulation results are presented in Tables 2–4. For test case-3 (Placement of single DG unit along with single capacitor) the loss reduction percentage by LSF and Hybrid approaches at light load (50%), nominal load (100%) and (160%) peak load conditions are {68.57, 70.87}, {70.15, 72.29} and {72.35, 74.28} respectively. Similar improved results were obtained with other two test cases (Test case-1 and Test case-2) with hybrid approach as compared with LSF approach all load levels. It can be concluded that for all the three test cases, the proposed

Bus Voltage Profile Base Case

Bus Voltage (p.u)

1

Single DG(Type I)

Three DG (Type-I)

Single DG (Type-I)+SCP

0.98 0.96 0.94 0.92 0.9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Fig. 6. Bus voltage profile of 33 node RDN for Scenario-I (Type-I DG units with SCP) at 100% load level (HSA–PABC approach).

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Bus Voltage Profile

Bus Voltage (p.u)

Base Case

Single DG(Type III)

Three DG (Type-III)

Single DG (Type-III)+SCP

1 0.98 0.96 0.94 0.92 0.9

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Fig. 7. Bus voltage profile of 33 node RDN for Scenario-II (Type-III DG units with SCP) at 100% load level (HSA–PABC approach).

Voltage Stability Index

VSI

Base Case 1 0.96 0.92 0.88 0.84 0.8 0.76 0.72 0.68 0.64 0.6

Single DG(Type I)

Three DG (Type-I)

Single DG (Type-I)+SCP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Fig. 8. VSI of 33 node RDN for Scenario-I (Type-I DG units with SCP) at 100% load level (HSA–PABC approach).

Voltage Stability Index

VSI

Base Case 1 0.96 0.92 0.88 0.84 0.8 0.76 0.72 0.68 0.64 0.6

Single DG(Type III)

Three DG (Type-III)

Single DG (Type-III)+SCP

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Bus Number Fig. 9. VSI of 33 node RDN for Scenario-II (Type-III DG units with SCP) at 100% load level (HSA–PABC approach).

Table 8 Comparison of simulation results of hybrid HSA–PABC based approach (Highlighted in bold) for Scenario-I at 100% load level (Test case-1-Type-I Single DG Placement) with other methods. Items

Ploss before compensation (kW) DG size (kW) (location) Ploss after compensation (kW) % loss reduction Vmin in p.u @(bus)

References

Proposed HSA–PABC

[44]

[36]

[36]

[36]

[42]

[38]

[41]

[40]

210.84 1857.5 (8) 118.12 43.98 0.9441

211.20 2601 (6) 111.1 47.39 NA

211.20 2601 (6) 111.1 47.39 NA

211.20 743 (18) 146.82 30.48 NA

211.20 2490 (6) 111.24 47.33 NA

210.84 2590 (6) 110.89 47.40 0.9468

210.97 2494.8 (6) 111.1462 47.31 0.9412

211 3150 (6) 115.29 45.36 NA

HSA–PABC approach with the simultaneous placement of single DG unit along with one shunt capacitor (Test case-3) with different load levels yields the higher percentage loss reduction as compared with other two cases (Test case-1 and Test case-2).

211 2598 (6) 111.03 47.38 0.9425 (18)

It can be inferred from the simulation results, due to improper choice of optimal locations by the LSF based approach yields less loss reduction percentage when compared with the HSA–PABC approach for all the test cases.

310

Table 9 Comparison of simulation results of hybrid HSA–PABC based approach (Highlighted in bold) for Scenario-I (Test case-2 and Test case-3) at 100% load level with other methods. Items

References (Test Case-2 Type-I Multiple DG)

(Test Case-3) (Type-I Single DG with SCP )

[34]

[34]

[34]

[35]

[36]

[37]

[36]

[38]

[36]

[44]

Proposed HSA– PABC

[39]

[40]

Proposed HSA– PABC

Ploss before compensation (kW)

210.9

210.9

210.9

210.9

211.2

210.9

211.2

210.84

211.2

210.84

211

211

211

211

DG size (kW) (location)

1500 (11)

981.6 (13)

1200 (32)

652.1 (14)

1667 (6)

2531.7 (6)

2531 (6)

198.4 (18)

1071.4 (30) –

1176.8 (8)

925 (11)

–

–

1067.2 (32) –

–

900 (12) 720 (31) –

736.1 (14) 890.4 (31) –

632 (13) 487 (28) 550 (31) –

2510.6 (6)

863 (16)

900 (13) 900 (30) 900 (24) –

1068 (30)

829.7 (32)

1112.4 (16) 487.4 (18)

900 (6)

422.8 (29)

720 (18) 810 (33) 900 (25) –

105.35

103.4

89.9

85.07

82.03

81.05

78

74.27

89.05

72.81

1225.8 (30) 58.45

1250 (30)

106.3

1457 (30) 59.7

58.45

49.6 0.9809 (25)

50.06 0.9808 (30)

50.99 0.9808 (25)

57.38 0.9705 (28)

59.72 NA

61.12 0.9676 (14)

61.62 NA

63 0.976

64.83 NA

57.76 0.9554

65.49 0.9684 (33)

71.71 NA

72.29 NA

72.29 0.9536 (18)

Ploss after compensation (kW) % loss reduction Vmin in p.u @ (bus)

755 (14) –

Table 10 Comparison of simulation results of hybrid HSA–PABC based approach (Highlighted in bold) for Scenario-II (Test Case-1, Test Case-2 and Test Case-3) at 100% load level with other methods. Items

References (Test Case-1) (Type-III Single DG)

(Test Case-2) (Type-III Multiple DG)

(Test Case-3) (Type-III Single DG with SCP )

[33]

[44]

[40]

[36]

Proposed HSA– PABC

[35]

[37]

[36]

[44]

Proposed HSA– PABC

[13]

[43]

Proposed HSA– PABC

Ploss before compensation (kW)

211

210.84

211

211.2

211

210.9

210.9

211.2

210.84

211

213.3

211

211

DG size (kVA) (location)

3024.7 (6)

2265.2 (8)

3020 (6)

3103 (6)

3011.7 (6)

784.98 (14)

1382.9 (6)

1059 (6)

1014 (12)

894.4 (18)

3027.9 (6)

2730.58 (6)

150.38 (18)

551.7 (18)

1280.02 (32)

1062.5 (30)

1059 (30) 741 (14)

811.62 (13) 566.19 (29) 940 (31)

960 (25) 0.82 1255.8 (30) 3027.4 58.45

0.85 650 (30)

72.29 NA

73.38 0.9583 (18)

1363.5 (30)

Operating p.f of DG Shunt capacitor size(kVAR)

0.85 –

0.82 –

0.82 –

0.85 –

0.85 –

0.866 –

0.866 –

0.85 –

0.92 –

0.85 –

0.85 800(33)

Total KVA supplied by the DG Ploss after compensation (kW) % loss reduction Vmin in p.u @ (bus)

3024.7 68.28

2265.2 82.78

3020 67.95

3103 68.2

3011.7 68.29

2215.3 37.85

2997.1 26.72

2859 23.05

2317.81 21.23

3337.5 15.91

894.4 89.72

67.63 NA

60.73 0.9549

67.79 NA

67.71 NA

67.63 0.9568 (18)

82.06 0.9802 (29)

87.33 0.9826 (25)

89.09 NA

85.93 0.9795

92.46 0.9889 (18)

57.94 0.9566 (30)

2730.58 (6) 56.16

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Shunt capacitor size(kVAR)

867.9 (30)

1073 (24)

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Fig. 10. Convergence plot of HSA and hybrid HSA–PABC approach for Scenario-I (Type-I Single DG with SCP) at nominal load level.

Fig. 11. Convergence plot of HSA and hybrid HSA–PABC approach for Scenario-II (Type-III Single DG with SCP) at nominal load level.

{72.87,75.49} respectively. It can be noticed that a significant higher percentage loss reduction is offered by the hybrid approach for all the three test cases at three different load levels over LSF based approach. As compared with test case-1 and test case-3 results, more loss reduction is realized in test case-2 (Placement of three DG units) with LSF and hybrid approaches at all load levels indicate the Type-III DG unit’s capability for injecting both real and reactive power. For instance, comparing the simulation results obtained by the hybrid approach for test case-2 with test case-1 and test case-3 results, the percentage loss reduction is 24.83 more than case-1 and 19.08 more than test case-3 at 100% load level. However, in economical point

0.1000

QLSF

PLSF

0.0800 0.0600 0.0400 0.0200

Node Numbers Fig. 12. Real power loss sensitivity at various nodes of 119 node RDN.

118

114

110

106

98

102

94

90

86

78

82

74

70

66

58

62

54

46

50

42

38

34

26

30

18

22

14

6

10

0.0000 2

Real Power Loss Sensivity

Scenario-II: The proposed scheme continuous to investigate the performance of the test system with the placement of Type-III DG units capable of injecting both real and reactive powers operating at 0.85 p.f (leading) is installed at potential nodes with and without shunt capacitors at different load levels such as light load (50%), nominal load (100%) and (160%) peak load conditions with LSF and Hybrid approaches and the simulation results presented in Tables 5–7. For test case-3(placement of single DG unit along with single capacitor), the loss reduction percentage by LSF and Hybrid approaches at 50%, 100% and 160% load levels are {68.96,71.86}, {70.61,73.38} and

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Fig. 13. Single line diagram of 119 node radial distribution system (Node numbers are reordered).

of view, installation of single DG unit (Type-III DG unit) along with single capacitor placement on the test system obtained with hybrid approach (Test case-3) is a viable solution than placing three Type-III DG units (Test case-2) on the test system even though less loss reduction is realized. Bus voltage profile of the test system is depicted in Figs. 6 and 7 for scenario-I and scenario-II of hybrid approach with all test cases at nominal load condition of the test system. For scenario-I, it can be realized that a significant improvement in bus voltage profile in test case-3 (Placement of single DG unit along with a shunt capacitor) as compared to base case and test case-1 results with the proposed hybrid approach. For scenario-II, it can be witnessed from Fig. 7 that the bus voltage profile is enhanced with Type-III DG units (Test case-2) indicates its real and reactive power injection capability. In addition, type-III DG units provide better voltage

profile enhancement as compared to Type-I DG units (refer Figs. 6 and 7 with Test case-2). The voltage stability index of the test system with scenario-I and scenario-II for all test cases are depicted in Figs. 8 and 9. Significant improvement in VSI is realized with the placement of single DG unit along with shunt capacitor in both scenarios (Test case-3). Comparative analysis of simulation results with other methods Simulation results of the proposed hybrid approach at nominal load condition for scenario-I (for test case-1-with the installation of single DG unit (Type-I) is shown in Table 8. The simulation results summarized in Table 8 comprehend the findings of the HSA–PABC based approach at nominal loading condition (for test case-1with the installation of single DG unit ) and validate the same with the obtained results in other references that stretch across [36,38,40–42,44] respectively.

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Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

297.15

–

0.9385 (78)

Case-1 Single DG

LSF HYBRID

1491 (70) 1461 (71)

– –

238.75 237.73

19.65 19.99

0.9548 (112) 0.9548 (112)

Case-2 Three DG

LSF HYBRID

1380 (70), 3282 (30), 2234 (64) 1461 (71), 1615 (47), 1576 (108)

– –

211.88 164.68

28.69 44.58

0.9548 (112) 0.9744 (55)

Case-3 Single DG + MCP

LSF

1477 (70)

191.75

35.47

0.9591 (112)

HYBRID

1302 (73)

1200 (30), 600 (64), 1900 (101) 900 (78), 1500 (31), 950 (68) 1500 (28), 1500 (34), 900 (70) 600 (86), 250 (85), 1150 (110)

153.56

48.32

0.9668 (112)

Table 12 Simulation results of 119 node RDN for Scenario-I (Type-I DG & MCP) at 75% load levels. Test cases

Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base Case

–

–

–

697.33

–

0.9049 (78)

Case-1 Single DG

LSF HYBRID

2260 (70) 2212 (71)

– –

554.85 552.48

20.43 20.77

0.9307 (112) 0.9307 (112)

Case-2 Three DG

LSF HYBRID

2092 (70), 4996 (30), 3397 (64) 2211 (71), 2443 (47), 2385 (108)

– –

492.28 373.72

29.40 46.40

0.9307 (112) 0.9612 (55)

Case-3 Single DG + MCP

LSF

2249 (70)

443.39

36.41

0.9372 (112)

HYBRID

2014 (73)

2100 (30), 1450 (64), 2800 (101), 1150 (78), 2150 (31), 1450 (68) 4100 (28), 2150 (34), 1350 (70) 700 (86), 450 (85), 1750 (110)

353.40

49.32

0.9496 (112)

Table 13 Simulation results of 119 node RDN for Scenario-I (Type-I DG & MCP) at 100% load levels. Test cases

Method

DG size in kW @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

1298.1

–

0.8688 (78)

Case-1 Single DG

LSF HYBRID

3050 (70) 3000 (71)

– –

1021.09 1016.77

21.33 21.67

0.9052 (112) 0.9052 (112)

Case-2 Three DG

LSF HYBRID

2800 (70), 6800 (30), 4700 (64) 2950 (71), 3250 (47), 3200 (108)

– –

904.38 677.74

30.33 47.78

0.9053(112) 0.9474 (55)

Case-3 Single DG + MCP

LSF

3050 (70)

810.12

37.59

0.9155 (112)

HYBRID

2650 (73)

2450 (30), 1400 (64), 4250 (101) 1700 (78), 3250 (31), 1950 (68) 4400 (28), 2900 (34), 1850 (70) 1200 (86), 500 (85), 2350 (110)

641.61

50.57

0.9317 (112)

Table 14 Simulation results of 119 node RDN for Scenario-II (Type-III DG & MCP) at 50% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

297.15

–

0.9385 (78)

Case-1 Single DG

LSF HYBRID

1762.35 (70) 1724.7 (71)

– –

216.31 215.03

27.20 27.63

0.9548 (112) 0.9548 (112)

Case-2 Three DG

LSF HYBRID

1605.8 (70), 4223.5 (30), 2703.5 (64) 1274.7 (71), 2123.5 (47), 1991.7 (108)

– –

173.74 92.36

41.53 68.92

0.9548 (112) 0.9804 (100)

Case-3 Single DG + MCP

LSF

1703.5 (70)

184.69

37.84

0.9592 (111)

HYBRID

1496.4 (73)

1150 (30), 650 (64), 1950 (101), 850 (78), 1550 (31), 50 (68) 2150 (28), 1450 (34), 150 (70) 600 (86), 250 (85), 1150 (110)

152.53

48.67

0.9668 (112)

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Table 15 Simulation results of 119 node RDN for Scenario-II (Type-III DG & MCP) at 75% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

697.33

–

0.9049 (78)

Case-1 Single DG

LSF HYBRID

2661 (70) 2602 (71)

– –

502.68 499.78

27.91 28.33

0.9307 (112) 0.9307 (112)

Case-2 Three DG

LSF HYBRID

2447 (70), 6431.7 (30), 4108 (64) 2602 (71), 3205.8 (47), 3001 (108)

– –

402.60 210.41

42.26 69.83

0.9307 (112) 0.9704 (100)

Case-3 Single DG + MCP

LSF

2570.58 (70)

426.96

38.77

0.9377 (111)

HYBRID

2270.6 (73)

1800 (30), 1000 (64), 3050 (101), 1250 (78), 2350 (31), 100 (68) 3250 (28), 2150 (34), 150 (70) 850 (86), 400 (85),1750 (110)

350.94

49.67

0.9496 (112)

Table 16 Simulation results of 119 node RDN for Scenario-II (Type-III DG & MCP) at 100% load levels. Test cases

Method

DG size in kVA @ (node)

Cap size in kVAR @ (node)

Real power loss (kW)

% loss reduction

Vmin (p.u) @ (node)

Base case

–

–

–

1298.1

–

0.8688 (78)

Case-1 Single DG

LSF HYBRID

3588 (70) 3470.6 (71)

– –

925.14 919.96

28.73 29.13

0.9053 (112) 0.9053 (111)

Case-2 Three DG

LSF HYBRID

3294 (70), 8705 (30), 5529 (64) 3470 (71), 4294 (47), 4000 (108)

– –

738.72 378.87

43.09 70.81

0.9053 (112) 0.9601 (99)

Single DG + MCP

LSF

3450.6 (70)

781.09

39.83

0.9155 (111)

HYBRID

3053 (73)

2450 (30), 1400 (64), 4250 (101), 1700 (78), 3200 (31), 100 (68) 4100 (28), 3100 (34), 250 (70) 1000 (86), 550 (85), 2300 (110)

639.34

50.75

0.9312 (112)

Bus Voltage Profile Base Case

Single DG(Type I)

Three DG (Type-I)

Single DG (Type-I)+MCP

Bus Voltage (p.u)

0.99 0.97 0.95 0.93 0.91 0.89 0.87 117

113

109

105

97

101

93

89

85

81

77

73

69

65

61

57

53

49

45

41

37

33

29

25

21

17

9

13

5

1

0.85

Bus Number Fig. 14. Bus voltage profile of 119 node RDN for Scenario-I (Type-I DG units with MCP) at 100% load level with HSA–PABC approach.

Bus Voltage Profile Base Case

Single DG(Type III)

Three DG (Type-III)

Single DG (Type-III)+MCP

Bus Voltage (p.u)

0.99 0.97 0.95 0.93 0.91 0.89 0.87 117

113

109

105

101

97

93

89

85

81

77

73

69

65

61

57

53

49

45

41

37

33

29

25

17

21

13

5

9

1

0.85

Bus Number Fig. 15. Bus voltage profile of 119 RDN for Scenario-II (Type-III DG unit with MCP) at 100% load level with HSA–PABC approach.

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Voltage Stability Index

117

109

113

105

97

101

93

89

81

85

73

Single DG (Type-I)+MCP

77

69

65

61

57

53

45

49

37

Three DG (Type-I)

41

33

25

29

21

17

9

Single DG(Type I)

13

5

1

VSI

Base Case 1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5

Bus Number Fig. 16. VSI of 119 node test system for Scenario-I (Type-I DG unit with MCP) at 100% load level with HSA–PABC Approach.

Voltage Stability Index Single DG(Type III)

Three DG (Type-III)

Single DG (Type-III)+MCP

117

113

109

101

105

97

93

89

85

81

77

73

69

65

61

57

53

49

45

41

37

33

29

25

21

17

13

9

5

1 0.95 0.9 0.85 0.8 0.75 0.7 0.65 0.6 0.55 0.5 1

VSI

Base Case

Bus Number Fig. 17. VSI of 119 node RDN for scenario-II (Type-III DG units with MCP) at 100% load level with HSA–PABC approach.

Table 17 Comparative analysis of 119 node RDN for Scenario-I (Type-I DG & MCP) at 100% load levels. Item

[37]

[37]

Proposed HSA–PABC

5 DG (kW) at unity p.f

7 DG (kW) at unity p.f

Test case-2 3 DG (kW) at unity p.f

Test case-3 1 DG (kW) at unity p.f with MCP (kVAR)

Ploss before compensation (kW)

1296.3

1296.3

DG size (kW) (location)

4535.3 (36) 1132.9 (56) 2131.8 (75) 4945.2 (103) 750.1 (116)

Ploss after compensation (kW) % loss reduction

858.8133 33.75

7467.3 (36) 710.9 (48) 3673.9 (56) 2824.6 (75) 2297.9 (88) 5080.3 (103) 460.6 (116) 900.1885 30.56

To illustrate the performance of the proposed hybrid approach, the simulation results summarized in Table 9 for scenario-I, for test case-2 (with the installation of three numbers of Type-I DG units) at nominal load conditions is compared with the results of the other references that includes [34–38,44] respectively. The proposed hybrid algorithm performance is validated further for the comparison of results obtained in test case-3 (with the installation of Type-I single DG unit along with single capacitor) with results presented in references [39,40]. Results of the proposed hybrid approach with scenario-II (TypeIII DG units) presented in Table 10 are compared with the solutions

1298.1

1298.1

2950 (71) 3250 (47) 3200 (108)

2650 (73)

677.74 47.78

641.61 50.57

4400 (28) 2900 (34) 1850 (70) 1200 (86) 500 (85) 2350 (110)

obtained with the other approaches reported in references [33,36,40,44] for test case-1(single DG unit placement), in references [35–37,44] for test case-2 (Multiple DG units installation) and reference [13,43] for test case-3 (installation of single DG units with a shunt capacitor). The comparative analysis of all the test cases considered, the proposed hybrid approach yields better solution than other methods proposed in the literature elicits the superiority of the proposed HSA–PABC based hybrid approach. It points out that the HSA–PABC algorithm spins around the objective function more closely than the other techniques. The solution accuracy reveals that the proposed HSA–PABC algorithm is proved to be one

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Table 18 Comparative analysis of 119 node RDN for Scenario-II (Type-III DG & MCP) at 100% load levels. Item

[37]

[37]

Proposed HSA–PABC

5 DGs (kVA) at 0.866 p.f

7 DGs (kVA) at 0.866 p.f

Test case-2 3 DGs (kVA) at 0.85 p.f

Test case-3 1 DG (kVA) at 0.85 p.f with MCP (kVAR)

Ploss before compensation (kW)

1296.3

1296.3

1298.1

1298.1

DG size (kW) (location)

5144.5 (36) 1713.7 (56) 3381.9 (75) 6827 (103) 1785.8 (116)

3470 (71) 4294 (47) 4000 (108)

3053 (73)

378.87 70.81

639.34 50.75

Ploss after compensation (kW) % loss reduction

684.0282 47.23

7056.5 2514.7 4979.5 3180.5 723.10 6160.5 586.14

(36) (48) (56) (75) (88) (103) (116)

638.9684 50.71

4100 (28) 3100 (34) 250 (70) 1000 (86) 550 (85) 2300 (110)

Fig. 18. Convergence plot of HSA–PABC approach for Scenario-I (Type-I Single DG with MCP) at 100% load level in 119 node RDN.

of the efficient hybrid heuristic optimization techniques for solving complex optimization problems. Figs. 10 and 11 show the convergence characteristics of HSA and Hybrid HSA–PABC algorithm with scenario-I and scenario-II (Test case-3) at nominal load level. The parameters of the HSA utilized in the simulation of 33 node radial network are HMS = 20, HMCR = 0.9, PAR = 0.5, iter = 300. It can be clearly shown from the convergence plots that the hybrid HSA–PABC algorithm obtains the optimal solution with lesser iterations when compared with classical HSA. 119 node radial distribution test system results To show the applicability of the proposed hybrid approach in large scale distribution network, it is applied on 119 node radial distribution network. It is a balanced three phase radial network consists of 119 nodes with 11 kV as operating voltage level at 100 MVA base and total real and reactive power load demands of the system are 22709.7 kW and 17041.1 kVAR respectively. The initial real and reactive power loss before compensation are 1298.1 kW and 978.74 kVAR respectively. It observed that the minimum bus voltage magnitude of 0.8688 p.u occurs at node number 78 at nominal load condition. The test system data such as line and

load data are obtained from [32]. The node numbers of the test system is renumbered and the tie switches (normally open) are removed from the test system for the sake of clarity. For LSF based approach, nodes with higher values of PLSF (node 70, 30 and 64) are considered for DG placement and higher values of QLSF (node70, 30, 64, 101, 78, 31, 68) are considered for shunt capacitor placement as depicted in Fig. 12. The nodes with higher values of PLSF i.e.. node 70 for single DG placement (Test case-1), node 70, 30 & 64 for three DG placement (Test case-2) are considered. For simultaneous one DG and multiple capacitors placement (for test case-3), as node 70 is nominated for DG placement, the node selection for capacitor placement is from the second highest node 30 onwards from the QLSF.i.e.. node 30, 64, 101, 78, 31 and 68. The single line diagram of the 119 node test system is shown in Fig. 13. Scenario-I: In scenario-I, Type-I DG units capable of injecting active power only is installed at potential nodes with and without shunt capacitors. The three test cases are simulated at different load levels with LSF and HSA–PABC based approaches and the simulation results are summarized in Tables 11–13. For Test case-3, the loss reduction percentage by LSF and Hybrid approaches at 50%, 75% and 100% load levels are {35.47, 48.32}, {36.41, 49.32}

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Fig. 19. Convergence plot of HSA and hybrid HSA–PABC approach for Scenario-II (Type-III Single DG with MCP) at nominal load level in 119 node RDN.

Table 19 Comparison of HSA and HSA–PABC algorithms in minimizing fitness function in 33 and 119 node RDN. (Note: Statistical results of proposed algorithm is highlighted in bold.) Test system

Test case

DG Type

Method

33 node RDN

Case-3 Single DG + SCP

Type-I

HSA HSA–PABC HSA HSA–PABC

61.10 59.20 58.42 57.39

58.47 58.45 56.16 56.16

59.19 58.50 56.82 56.22

HSA HSA–PABC HSA HSA–PABC

683.01 652.06 667.16 640.15

644.71 641.61 643.93 639.34

658.58 643.37 654.44 639.74

Type-III 119 node RDN

Case-3 Single DG + MCP

Type-I Type-III

Worst fitness (Ploss in kW)

and {37.59, 50.57} respectively. Similar improved results were obtained with other two test cases with hybrid approach as compared with LSF approach all load levels. It can be witnessed that for all the three test cases at each load level, the proposed HSA–PABC approach with the simultaneous placement of single DG unit along with multiple shunt capacitors (Test case-3) yields higher percentage loss reduction as compared with installation of single and multiple number of Type-I DG units (Test case-1 and Test case-2) alone on the test system. The LSF based approach yields less loss reduction percentage when compared with the HSA–PABC approach for all the cases due to improper selection of optimal locations. Scenario-II: The proposed scheme continuous to investigate the performance of the test system with the placement of Type-III DG units capable of injecting both real and reactive powers operating at 0.85 power factor (leading) is placed at potential nodes with and without shunt capacitors at light load (50%), nominal load (75%) and (100%) peak load conditions by the LSF and Hybrid approaches and three test cases are simulated with LSF and HSA–PABC based approaches and the simulation results are summarized in Tables 14–16. For Test case-3, the loss reduction percentage by LSF and Hybrid approaches at 50%, 75% and 100% load levels are {37.84, 48.67}, {38.77, 49.67} and {39.83, 50.75} respectively. It can be noticed that a significant higher percentage loss reduction is offered in test case-2

Best fitness (Ploss in kW)

Mean fitness (Ploss in kW)

Std. deviation 0.676869 0.160896 0.634991 0.24894 1.252916e+004 3.135033e+003 8.135835e+003 1.55089e+002

Average run time (s) 1.5028 1.3233 1.7082 1.6741 210.19 122.02 219.11 111.00

(three DG units) with LSF and hybrid approaches at all load levels as compared with test case-1 and test case-3 results reflect the real and reactive power injecting capability of Type-III DG units. Figs. 14 and 15 depicts the bus voltage profile for scenario-I and scenario-II with hybrid approach for all test cases at nominal load condition of the test system. For scenario-I, it can be realized that a significant improvement in bus voltage profile in test case-3 (placement of single DG unit along with multiple shunt capacitor) as compared to base case and test case-1 results with the proposed hybrid approach. For scenario-II, it can be witnessed from Fig. 15 that the bus voltage profile is enhanced with Type-III DG units (test case-2) indicates its real and reactive power injection capability. In addition, type-III DG units provide better voltage profile enhancement as compared to Type-I DG units (refer Figs. 14 and 15 with test case-2). The voltage stability index of the test system with scenario-I and scenario-II for all test cases are depicted in Figs. 16 and 17. Significant improvement in VSI is realized with the placement of single DG unit along with multiple shunt capacitors in both scenarios (Test case-3). Comparative analysis of simulation results with other methods Simulation results of the proposed hybrid approach at nominal load condition for scenario-I (for test case-2-with the installation of multiple DG unit (Type-I) and for test case-3 with single DG units along with multiple shunt capacitors) is shown in Table 17 comprehend the findings of the HSA–PABC based approach at

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nominal loading condition and compared its results with LSFSA [37] approach. It is seen from Table 17 that the power loss obtained using proposed HSA–PABC approach with the installation of Type-I DG unit along with multiple shunt capacitors (Test case-2) is better than test case-3 results of the proposed approach as well as the results obtained with five DG unit and seven DG unit’s placement using LSFSA method [37]. Results of the proposed hybrid approach with scenario-II (Type-III DG units) presented in Table 18 are compared with the solutions obtained with LSFSA [37] approach for test case-2 (Multiple DG units installation) and test case-3 (installation of single DG units with multiple shunt capacitors). The comparative analysis reveals that the proposed hybrid approach spins around the objective function more closely than the other techniques proposed in the literature elicits the superiority of the proposed HSA–PABC based hybrid approach. The convergence plot of HSA and Hybrid HSA–PABC algorithms with scenario-I and scenario-II (Test case-3) at nominal load level are depicted in Figs. 18 and 19. The control parameters of the HS algorithm utilized in the simulation of 119 node radial network are HMS = 20, HMCR = 0.9, PAR = 0.5, iter = 1500. It can be clearly publicized from the convergence plots that the hybrid HSA–PABC algorithm obtains the optimal solution with lesser iterations when compared with classical HSA. The convergence ability of HSA and hybrid HSA–PABC algorithm is depicted in Table 19 with scenario-I and scenario-II (Test case-3) for both test systems. The best, worst, average, standard deviations and average run time are presented with 25 independent runs for each algorithm. It is statistically proved that the proposed Hybrid HSA–PABC algorithm has better performance interms of solution accuracy and fast convergence characteristics with lesser iterations to reach the optimal solution than classical HS algorithm.

Conclusion Simultaneous optimal sitting and sizing of distributed generators and shunt capacitors has been developed for RDN to accomplish the benefits of reduction in power loss along with enhancement in bus voltage profile. The main draw back in classical HS algorithm is premature and slow convergence over multi model fitness landscape. In this proposed optimization work, in order to overcome the above said drawbacks, harmony memory is considered as the pool of the elite solution and the PABC algorithm is utilized as the learning mechanism for harmony memory improvisation in order to enhance the solution accuracy and the rate of convergence of the HSA. A novel Hybrid approach of HSA–PABC algorithm has been utilized and leaves way for a realistic solution with a higher rate of probability. The methodology has been stratified through the combinatorial use of LSF and HSA–PABC to arrive at the appropriate location and size of the distributed generators and shunt capacitors. The performance analysis has been leveled to outweigh the merits of the search procedure in the process of arriving at the optimality in the rating and location of the compensating devices. The superiority of the proposed hybrid approach is demonstrated on 33 and 119 node radial distribution networks and the simulation results are presented. Simulation results reveals that the proposed hybrid HSA–PABC algorithm exhibited a higher capability in obtaining optimum solution with less computational time, with improved convergence characteristics than standard HSA. The close comparison of results with similar other approaches has been projected to acclaim the hybrid HSA–PABC approach shrewdness in the selection pursuit and persuade a new ambience for its use in practical distribution systems.

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