Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network

Electrical Power and Energy Systems 74 (2016) 348–373

Contents lists available at ScienceDirect

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

Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine for optimal allocation of DG in radial distribution network Sharmistha Sharma 1, Subhadeep Bhattacharjee 2, Aniruddha Bhattacharya ⇑ National Institute of Technology-Agartala, Tripura 799046, India

a r t i c l e

i n f o

Article history: Received 28 September 2014 Received in revised form 19 June 2015 Accepted 21 July 2015

Keywords: Distributed generations Power losses Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine (QOSIMBO-Q) Voltage profile Voltage stability

a b s t r a c t Optimal allocation of Distributed Generations (DGs) is one of the major problems of distribution utilities. Optimum locations and sizes of DG sources have profoundly created impact on system losses, voltage profile, and voltage stability of a distribution network. In this paper Quasi-Oppositional Swine Influenza Model Based Optimization with Quarantine (QOSIMBO-Q) has been applied to solve a multi-objective function for optimal allocation and sizing of DGs in distribution systems. The objective is to minimize network power losses, achieve better voltage regulation and improve the voltage stability within the frame-work of the system operation and security constraints in radial distribution systems. The limitation of SIMBO-Q algorithm is that it takes large number of iterations to obtain optimum solution in large scale real systems. To overcome this limitation and to improve computational efficiency, quasi-opposition based learning (QOBL) concept is introduced in basic SIMBO-Q algorithm. The proposed QOSIMBO-Q algorithm has been applied to 33-bus and 69-bus radial distribution systems and results are compared with other evolutionary techniques like Genetic Algorithm (GA), Particle Swarm Optimization (PSO), combined GA/PSO, Teaching Learning Based Optimization (TLBO) and Quasi-Oppositional Teaching Learning Based Optimization (QOTLBO). Numerical studies represent the effectiveness and out-performance of the proposed QOSIMBO-Q algorithm. Ó 2015 Elsevier Ltd. All rights reserved.

Introduction Electric utilities are continuously planning the expansion of their existing electrical networks to meet the increasing load growth. The traditional solution is the construction of new substation or the expansion of those already exists. However, these companies began to evaluate new alternatives of expanding their capacities when government started to simulate the addition of new power sources to the system [1–3]. An alternative way to satisfy the increasing demand is to use Distributed Generation (DG) system. Distributed Generation can be defined as small scale generation which is located onsite or close to the load centre and is interconnected to the distribution network. Some advantages of DG are grid reinforcement, power loss reduction, increasing efficiency, eliminating the upgrades of power system, reliability, improving voltage profile and load factors and hence power ⇑ Corresponding author. Tel.: +91 9474188660. E-mail addresses: [email protected] (S. Sharma), [email protected] (S. Bhattacharjee), bhatta.aniruddha@ gmail.com (A. Bhattacharya). 1 Tel.: +91 9402158783. 2 Tel.: +91 9436582874. http://dx.doi.org/10.1016/j.ijepes.2015.07.034 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.

quality, reducing transmission and distribution costs, saving the fossil fuel, decreasing in electricity price, reduction in emissions of green-house gases and also sound pollutions. Presently a number of DG technologies available in the market and few are still under research and development stage. Different DG technologies are reciprocating engines, combustion gas turbines, micro turbines, fuel cells, photovoltaic system, wind turbines, small hydro-electric plant, etc. One of the important aspects of DG research study is related to its proper placement at strategic points of power systems to minimize the losses of power system, improving the voltage profile, reliability, maximizing DG capacity, cost minimization, etc. Selection of the best places for installation of DG units and their preferable sizes is possible by using an appropriate optimization method which can provide the best solution for a given distribution network [3]. Many researchers proposed different methods such as analytical methods as well as deterministic and heuristic methods to solve optimal DG placement and sizing problem. Authors Frauk Ugranli and Engin Karatepe [4] proposed a power flow algorithm based on Newton–Raphson method to consider the impact of multiple DG units on power losses and voltage profile in respect of point of

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

common coupling (PCC), DG size and power factor of DG. Elnashar et al. [5] presented a visual optimization approach for determining the optimal placement and sizing of the DG through the choice of the appropriate weight factors of the parameters like losses, voltage profile and short circuit level. Ghosh et al. [6] suggested a simple conventional iterative search technique based on Newton–Raphson load flow method study for optimal sizing and placement of DG by optimizing both cost and loss simultaneously. Singh and Goswami [7] presented a new methodology based on nodal pricing for optimally allocating DG for profit maximization, loss reduction and voltage improvement including voltage rise phenomenon. Gozel and Hocaoglu [8] proposed an analytical method based on loss sensitivity factor for optimal size and location of DG in radial systems to minimize the power losses. The proposed method was based on equivalent current injection that uses the bus-injection to branch current (BIBC) and branch-current to bus-voltage (BCBV) matrices developed on the basis of the topological structure of the distribution systems. Acharya et al. [9] presented an analytical approach which is based on the exact loss formula to calculate the optimal size and location of DG for minimizing the total power losses in primary distribution systems. Authors of [10–12] also applied analytical methods for solving DG sizing and placement problems. Kazemi and Sadeghi [13] presented a load flow based algorithm for DG allocation in radial systems for voltage profile improvement and loss minimization. Moradi et al. [14] presented a Genetic Algorithm (GA) based evolutionary technique for optimum placement and sizing of four different types of DG and the objective was to minimize real power loss within security and operational constraints. Aliabadi et al. [15] proposed a combination of GA and optimum power flow (OPF) technique for optimum placement and sizing of DG units in a given distribution system to minimize the cost of active and reactive power generation. Gomez-Gonzalez et al. [16] applied a new discrete Particle Swarm Optimization (PSO) and OPF technique to achieve optimal location and size of DG system in a distribution system. Moradi and Abedini [17] proposed a combined GA/PSO technique for finding optimal location and sizing of DG to minimize the losses, to increase the voltage stability and to improve the voltage regulation index within the framework of the system operation and security constraints in radial distribution systems. Sultana and Roy [18] presented a quasi-oppositional teaching learning based optimization (QOTLBO) to find optimal location of DG units to minimize power loss and voltage deviation, and to improve the voltage stability index of radial distribution network. Moradi et al. [19] presented a multi-objective Pareto Frontier Differential Evolution (PFDE) algorithm to determine optimal location and size of multiple DG sources for loss minimization, voltage profile and voltage stability improvement of 33 bus and 69 bus radial distribution systems. Esmaili et al. [20] applied dynamic programming search method for locating and sizing of DGs in distribution network to enhance voltage stability and to reduce network losses simultaneously by maintaining voltage security limits. Ishak et al. [21] determined optimal DG location and size through a novel maximum power stability index (MPSI) with PSO to improve power system stability and to reduce system active power losses. Aman et al. [22] presented a new approach based on maximization of system loadability to determine optimum placement and sizing of multi-DG using Hybrid PSO (HPSO) algorithm. The aim was to minimize system loss, maximize system loadability and to improve voltage quality. Devi and Geethanjali [23] proposed Modified Bacterial Foraging Optimization (MBFO) algorithm for optimal allocation of DG to reduce the total power loss and to improve the voltage profile of radial distribution systems. In [24] Attia El-Fergany presented Backtracking Search Optimization Algorithm (BSOA) to determine optimal allocation of multi-type DG in radial distribution network to reduce the network real power loss and to enhance the voltage profile. Mohandas et al. [25] presented Chaotic

349

Artificial Bee Colony (CABC) algorithm for optimal allocation of real power DG units for enhancing the voltage stability of radial distribution system using multi-objective performance index (MOPI). In [26,27], authors applied ant colony optimization and dynamic programming approach for solving DG sizing and placement problems. In this paper a new population based optimization technique known as Quasi-Oppositional Swine Influenza Model based Optimization with Quarantine (QOSIMBO-Q) has been applied to solve the optimal allocation problem of DG in radial distribution systems. Swine Influenza Model based Optimization (SIMBO) was developed by Pattnaik et al. [28] and it is mimicked from Sus ceptible-Infectious-Recovered (SIR) models of swine flu. The developments of SIMBO follow through treatment (SIMBO-T), vaccination (SIMBO-V) and quarantine (SIMBO-Q) based on probability. The SIMBO variants are used to solve complex multimodal problems with fast convergence and also delivering good quality of optima. SIMBO algorithms do not require more computational effort to achieve the optimum value. The algorithm converges rapidly due to the presence of vaccination/quarantine and treatment loops. The major advantages of SIMBO variants are their easy implementation and better accuracy to reach to the optimum solution. Exploration and exploitation ability of SIMBO is much improved compared to many previously developed optimization techniques. It has been observed that the performance of SIMBO-Q is quite satisfactory compared to many other optimization techniques like GA, PSO, combined GA/PSO, TLBO and QOTLBO. However for applying SIMBO-Q algorithm in large scale real system, large number of iterations may be required to obtain optimum solution. As a result the convergence rate becomes slower for large scale optimization problem. Therefore to improve the solution quality and to accelerate the convergence speed quasi-opposition based learning (QOBL) concept has been incorporated to basic SIMBO-Q algorithm. In this paper the authors have proposed Quasi-Oppositional Swine Influenza Model based Optimization with Quarantine (QOSIMBO-Q) to evaluate optimum location and size of multiple DG to minimize active power loss, to improve voltage profile and voltage stability of 33 bus and 69 bus radial distribution networks. To show the effectiveness and superiority, the results obtained with QOSIMBO-Q algorithm is compared with many other popular optimization techniques. The paper is structured as follows: Section ‘‘Problem formulation’’ of the paper provides a brief description and mathematical formulation of power loss minimization, voltage profile improvement and voltage stability improvement problems for optimal placement and sizing of DG. Section ‘‘Optimal placement and sizing of DG using QOSIMBO-Q algorithm’’ describes optimal placement and sizing of DG using QOSIMBO-Q algorithm. Simulation results and discussion are presented in Section ‘‘Simulation results and discussion’’. The conclusion is drawn in Section ‘‘Conclusion’’. Problem formulation Proposed methodology in this paper aims to find optimum placement and size of DGs in a given radial distribution system by minimizing the power losses, maximizing the voltage stability and improving voltage profile in a radial distribution network. The full formulation of the DG optimization problem is organized in the following sections. Case 1: Active power loss minimization The objective function to minimize real power loss of the distribution system is given by:

f 1 ¼ MinðP RPL Þ

ð1Þ

350

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

where P RPL is the real power loss of nn -bus distribution system and is expressed as:

PRPL ¼

N X I2ni Rni

ð2Þ

i¼1

where f 1 is the objective function value for active power loss minimization in p.u.; i is the branch number that fed bus ni ; ni is the receiving bus number; mi is the bus number that sending power to bus ni ; N is the total number of branches in the given radial distribution system ðN ¼ nn  1Þ; Ini is the branch current of the radial system shown in Fig.1 and is obtained from:

Ini ¼

V mi  V ni Rni þ jX ni

ð3Þ

Fig. 1. A representative branch of a radial distribution system.

(0,1). Initially, w = 0 was set, and increments were made in steps of 0.05 up to 1. Case 5: Active power loss minimization and voltage stability index improvement

where V mi is the voltage of bus mi ; V ni is the voltage of bus ni ; Rni is the resistance of branch i; X ni is the reactance of branch i.

Objective function for active power loss minimization and voltage stability index improvement is given by:

Case 2: Voltage profile improvement

f ¼ Minðw  f 1 þ ð1  wÞ  f 3 Þ

The objective function to improve voltage profile is expressed as:

0 f 2 ¼ Min@

nn X

!2 ! V ni  V rated

ð4Þ

ð9Þ

where f 1 is the objective function for active power loss minimization; f 3 is the objective function for voltage stability index improvement; Case 6: Voltage profile and voltage stability index improvement

ni¼1

where V ni is the voltage of bus ni ; V rated is the rated voltage (1 p.u.).

Objective function for voltage profile and voltage stability index improvement is given by:

Case 3: Voltage stability index improvement

f ¼ Minðw  f 2 þ ð1  wÞ  f 3 Þ

where f 2 is the objective function for voltage profile improvement; f 3 is the objective function for voltage stability index improvement;

Objective function for improving voltage stability index is,

 f 3 ¼ Min

 1 ; ðSIðni ÞÞ

ni ¼ 2; 3; . . . ; nn

ð5Þ

where the voltage stability index of node ni is given by:

ð6Þ

where V mi is the voltage of bus mi ; Pni ðni Þ is total real power load fed through bus ni ; Q ni ðni Þ is total reactive power load fed through bus ni ; Rni is the resistance of branch i; X ni is the reactance of branch i; P ni and Q ni of any bus ni are obtained from:

Pni ðni Þ  jQ ni ðni Þ ¼ V ni Ini

Case 7: Active power loss minimization, voltage profile and voltage stability index improvement Objective function for active power loss minimization, voltage profile and voltage stability index improvement is given by:

SIðni Þ ¼ jV mi j4  4½Pni ðni ÞRni þ Q ni ðni ÞX ni jV mi j2  4½Pni ðni ÞX ni  Q ni ðni ÞRni 2

ð10Þ

ð7Þ

where Ini is the branch current of the radial system shown in Fig.1 and is obtained from Eq. (3); V ni is the voltage of bus ni ; When DG is connected to a distribution network, the index of voltage stability limit of that network changes. The stability index which can be evaluated at all nodes of a radial distribution system was presented by Chakravorty and Das [29] and the equations used to formulate this index are presented in [30], to solve the load flow for radial distribution systems. For stable operation of radial distribution systems, SIðni Þ > 0 for ni ¼ 2; 3; . . . ; nn , there exists a feasible solution.

f ¼ Minðw1  f 1 þ w2  f 2 þ w3  f 3 Þ

ð11Þ

where f 1 is the objective function for active power loss minimization; f 2 is the objective function for voltage profile improvement; f 3 is the objective function for voltage stability index improvement; w1 ; w2 ; w3 are the weighting factors whose value varies uniformly between (0,1) such that w1 þ w2 þ w3 ¼ 1. Constraints The constraints used for solving optimum placement and sizing problem of DG in radial distribution network, are: Load balance constraint For each bus, the following equations should be satisfied:

Pgni  Pdni  V ni

N X

V nj Y nj cosðdni  dnj  hnj Þ ¼ 0

ð12Þ

j¼1

Case 4: Active power loss minimization and voltage profile improvement

Q gni  Q dni  V ni

Objective function for active power loss minimization and voltage profile improvement is given by:

f ¼ Minðw  f 1 þ ð1  wÞ  f 2 Þ

ð8Þ

where f 1 is the objective function for active power loss minimization; f 2 is the objective function for voltage profile improvement; w is the weighting factor whose value varies uniformly between

N X V nj Y nj sinðdni  dnj  hnj Þ ¼ 0

ð13Þ

j¼1

where ni ¼ 1; 2; . . . ; nn ; P gni is active power output of the generator at bus ni ; Q gni is reactive power output of the generator at bus ni ; Pdni is active power demand at bus ni ; Q dni is reactive power demand at bus ni ; V ni is voltage of bus ni ; dni is phase angle of voltage at bus ni ; N ¼ ðnn  1Þ is total number of branches in the given radial distribution system (RDS); nn is total number of buses in the given RDS.

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

351

Y nj is the admittance magnitude of branch j; hnj is the admittance angle of branch j.

Optimal placement and sizing of DG using QOSIMBO-Q algorithm

Voltage limits Voltage at each bus must be kept within its maximum and minimum standard values i.e.

The optimal placement and sizing problems of DG are formulated as a multi-objective constrained optimization problem. This paper uses Quasi-Opposition based Swine Influenza Model Based Optimization with Quarantine (QOSIMBO-Q) for solving optimal placement and sizing problem DG in radial distribution system.

max V min ni 6 V ni 6 V ni

ð14Þ

where V ni is the voltage of bus ni ; V min is the minimum voltage at ni bus ni ; V max is the maximum voltage at bus ni . ni DG generation limits As DG capacity is inherently limited by the energy resources at any given location, it is necessary to maintain capacity between the maximum and the minimum levels. max Pmin gni 6 P gni 6 P gni

ð15Þ

where Pgni is active power output of the DG at bus ni ; Pmin gni is minimum active power of DG at bus ni ; Pmax gni is maximum active power of DG at bus ni ; The amount of reactive power delivered by DG is given by: 1

Q gni ¼ Pgni  tanðcos ðpower factorÞÞ

ð16Þ

The apparent power from DG is given by:

Sgni ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P2gni þ Q 2gni

ð17Þ

DG capacity constraint Sum of the total generation from DG is limited by maximum penetration level of DG. Capacity constraint of DG generating power at unity power factor is given by: NDG X Pgi 6 ðDpf  P load Þ

ð18Þ

Swine Influenza Model Based Optimization with Quarantine (SIMBO-Q) SIMBO-Q performs the optimization through quarantine and treatment loop [28]. In this optimization technique initially all suspected individuals are identified according to the current health of individual and then they undergo for the swine flu test. After swine flu test, the confirmed case is quarantined or isolated from population. Then treatment is given to all individuals depending upon their current health. Basic steps of SIMBO-Q algorithm are given below and these steps continue until all generations are over. Step 1: Evaluate health [28] In this step, initially the health of all individuals is evaluated which depends upon the given fitness function. Then the suspected patients of swine flu are sampled for confirmation of the diagnosis. Step 2: Swine flu test [28] This test is done to confirm the suspected patients with swine flu virus. If current health of individual is greater than dynamic threshold (D_Threshold) then it is suspected, otherwise it is recovered case. D_Threshold depends on the health of best 50% population (Sr), l, rand and primary symptoms as given in Eq. (22). Before calculation of D_Threshold value, all the individuals are sorted in order of ascending current health [28]. D Threshold ¼ ½SumðCurrent healthð1 : SrÞ=SrÞ  l  rand  PrimaryðDayÞ ð22Þ

i¼1

If DG is generating both active and reactive power, then Eq. (18) can be modified as: NDG X Sgi 6 ðDpf  Sload Þ

ð19Þ

i¼1

where N DG is the number of DG in the system; Dpf is the maximum penetration limit as a percentage of peak load of the system; P load is the total active power load of the system; Sload is the total apparent power load of the system. Thermal limit Final thermal limit of distribution lines for the network must not be exceeded:

  ; jSni j 6 Smax ni

i ¼ 1; . . . ; N

ð20Þ Smax ni

where Sni is the apparent power at bus ni ; is maximum apparent power at bus ni ; i is the branch number that fed bus ni ; N is the total number of branches in the given RDS. Line current limit constraint Line current of each branch must be less than or equal to maximum current carrying capacity of that branch.

Ini;nj 6 Imax ni;nj Imax ni;nj

ð21Þ

where is the maximum current carrying capacity of the distribution line connected between bus ni and nj ; Ini;nj is the current flowing through the branch connected between bus ni and nj .

where l is the probability of vaccination; PrimaryðDayÞ is the primary symptoms of swine flu caused due to fever, cough, fatigue and headache, nausea and vomiting and diarrhea during each day. It is expressed as:

  TD PrimaryðDayÞ ¼ ðFe  Co  fathead  NV  DaiÞ  exp  Day

ð23Þ

where Fe, fever; Co, cough; fathead, fatigue and headache; NV, nausea and vomiting; Dai, diarrhea; TD, total number of days or generations; Day, current generation or iteration; The first term in Eq. (23) is the total influence of primary symptom and second term increases the primary symptom per day as the number of day’s increases. Step 3: Quarantine [28] Quarantine is enforced isolation or restriction of free movement imposed to prevent the spread of contagious disease. The confirmed cases of swine flu are isolated or quarantined from the population so that they would not affect the health of other individual in population [28]. The quarantined individual is swapped with best individual in population. The rand is multiplied with best individual population i.e. Pandemic State (PS) to achieve diversity in the population. If probability of quarantined (b) is less than rand and current health of individual is greater than D_Threshold, then individual is quarantined otherwise it is part of population [28]. In order to isolate less number of individual from the population, the probability of quarantine (b) is kept high. The steps are:

352

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

soft computing includes quasi-oppositional BBO (QOBBO) [36], quasi-oppositional DE (QODE) [37], quasi-oppositional TLBO (QOTLBO) [18,38]. Opposite number may be defined as the mirror point of the solution from the center of search point. If x be any real number between [a; b] in a one-dimensional search space, then its opposite number xo is defined as

for k = 1:TI if rand > b if current_health(k) > D_Threshold S(k) = PS ⁄ rand end end end

xo ¼ a þ b  x where TI is total number of individuals in population; S is the state or position of individual; PS is pandemic (global) best state amongst all individuals. Step 4: Treatment [28] Generally treatment is based on signs and symptoms of any disease and it is often a trial and error process. In SIMBO-Q the percentage of antiviral drugs depend on primary and secondary symptom as well as current health and pandemic health [28]. The dose given to the individual and the corresponding change in individual state are given by Eqs. (24) and (25).

Doseðm þ 1Þ ¼ DoseðmÞ  Md þ PrimaryðDayÞ  rand  ð1  Current healthðmÞ=rand  PHÞ þ R0ðDayÞ  rand  ðCurrent healthðmÞ  PHÞ Sðm þ 1Þ ¼ SðmÞ  Ms þ Doseðm þ 1Þ

For d-dimensional search space, the opposite point may be defined as:

xoi ¼ ai þ bi  xi ;

xi 2 ½a; b;

i ¼ 1; 2; . . . ; d

ð24Þ ð25Þ

ð26Þ

S is the state or position of individual; PH is the fitness value corresponding to pandemic (global) best state amongst all individuals; Md is momentum factor of dose and is used to restrict the dose of individual; Ms is the momentum factor of state and is used to restrict the state of individual; The treatment given to individuals in the population depends upon the probability of recovery (a), which is kept very low to recover most of the individuals. Quasi-opposition based learning To improve computational efficiency of different optimization techniques and to accelerate the convergence rate Oppositionbased learning (OBL) was developed by Tizhoosh [31]. OBL improves the candidate solution by considering current population and its opposite population at the same time. The inventors of OBL claims that an opposite candidate solution has a better chance to be closer to the global optimum solution than a random candidate solution. Thus, by comparing a number to its opposite, a smaller search space is needed to converge to the right solution. Many researchers have successfully implemented this technique into different soft computing techniques [32–34]. Simon et al. [35] proved that a quasi-opposite number is usually closer than a random number to the solution. It has also been proven that a quasi-opposite number is usually closer than an opposite number to the solution. The improved computational efficiency of quasi-opposition based learning concept (QOBL) has motivated the present authors to incorporate this concept in basic SIMBO-Q algorithm to improve the quality of solution and convergence rate. The idea of QOBL technique is used in population initialization and generation jumping. This QOSIMBO-Q approach applied in this paper has not been used so far to determine optimal size and location of DG in radial distribution system. Some application of QOBL technique in the field of

ð28Þ

If x be any real number between [a; b], then its quasi-opposite number xqo is defined as:

xqo ¼ randðc; xo Þ

ð29Þ

where c is the center of the interval [a; b] and can be calculated as ða þ bÞ=2 and randðc; xo Þ is a random number uniformly distributed between c and xo . The quasi-opposite point for d-dimensional search space is given by: o xqo i ¼ randðc i ; xi Þ

where Dose is the anti-virual drugs given to swine flu patient as a curative strategy; PrimaryðDayÞ is the primary symptom of swine flu per day which is calculated by using Eq. (23); R0ðDayÞ is the secondary symptom caused per day which is expressed as:

R0ðDayÞ ¼ 1  expðPrimaryðDayÞÞ

ð27Þ

ð30Þ

i where ci ¼ ai þb ; xi 2 ½a; b; i ¼ 1; 2; . . . ; d 2

QOSIMBO-Q algorithm for optimum placement and sizing of DG Different steps for applying this algorithm for optimum placement and sizing of DG in radial distribution system are given below: Step (1) Read the system data, constraints, total number of individuals in population (TI) and maximum number of days or iterations (TD). Step (2) Initialize the SIMBO-Q parameters i.e. Fe; Co; fathead; NV; Dai; a; b; l. Step (3) Generate an initial population or state matrix S with random location and size of DG. Step (4) Run the load flow and check the constraints limits used in the problem. Step (5) If constraints limits are satisfied, then go to the next step, otherwise again generate the initial population matrix and repeat the step 4. Step (6) Generate quasi-oppositional state matrix (QOS) using Eq. (30). Step (7) Set the initial ‘‘dose’’ given to individual randomly between 0 to 1. Step (8) Evaluate the fitness function value of each individual in terms of objective function values for initial state matrix ðSÞ and quasi-oppositional state matrix (QOS). Step (9) Select np (population or state size) fittest individuals from initial state matrix S and quasi-oppositional state matrix QOS. Step (10) Calculate the initial value of minimum fitness function value i.e. pandemic_health (PH) and the corresponding state i.e. pandemic_state (PS) from the newly generated population or state matrix. Step (11) Evaluate the current health of each individual which is equal to fitness function of each individual. Step (12) Sort individual in order of ascending health and determine the dynamic threshold value, primary and secondary symptom values of swine flu using Eqs. (22), (23) and (26).

353

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Step (13) Update the dose given to individual and state of individual depending on the values of probability of recovery, a and probability of quarantined, b. Step (14) Check the limits of position and size of DG of the newly generated state matrix and run the load flow and check the constraints limits. Step (15) If constraints limits are satisfied, then go to the next step, otherwise go to step 13 again and update the dose and state values of individual using its old value. r Step (16) Select a new parameter ‘jumping rate’ ðj Þ within [0,1]. Generate quasi-oppositional state matrix (QOS) from the newly generated state matrix as per the following steps: if rand (0,1) < jr for i = 1: np for j = 1: nd

  a þb xqo ¼ rand j 2 j ; aj þ bj  xi;j i;j

where np is the population or state matrix size; nd is the number of control variable. Step (17) Evaluate the fitness function value of each individual for newly generated state matrix ðSÞ and quasi-oppositional state matrix (QOS). Step (18) Select np fittest individuals from the newly generated state and the quasi-oppositional state and update the values of PS and PH and also calculate the best solution corresponding to the minimum fitness function value. Step (19) For single objective optimization, if the maximum number of iterations is reached, terminate the iterative process, else repeat steps 11 to 18. For multi-objective optimization problems, if the current iteration is greater than or equal to the maximum iteration, keep the result in an array (known as the Pareto-optimal set) and stop; otherwise, repeat steps 11 to 18. Step (20) In case of the bi-objective problem, as per Eqs. (8)– (10), increment the value of w in steps of 0.05 and repeat the steps starting from step 3 to step 19. Repeat this process until the value of w reaches 1. For tri-objective optimization using three weighting factors w1 ; w2 ; w3 (as per Eq. (11)), increment the value of the weighting factors in steps of 0.1 starting from 0 to 1 so that sum of w1 ; w2 ; w3 is 1 and each time repeat the steps starting from step 3 to step 19. Step (21) Best compromise solution—the algorithm described above generates the non-dominated set of solutions known as the Pareto-optimal solutions. In the proposed method, for solving multi-objective optimization problems, fuzzy based mechanism and fitness sharing are employed to choose the best compromise solution from the pareto-front. For selecting an operating point from the obtained set of Pareto-optimal solutions, the fuzzy logic theory is applied to each objective function to obtain a fuzzy membership function lfi as follows: max

fi

max fi

lfi ¼

8 > <0

 fi min

 fi

li 6 0 li 0\li \1 > : 1 li P 1

min

tion FDMk is calculated as:

2

PNobj

3

lkfi 5 FDM ¼ 4PM PN obj k k¼1 i¼1 lfi k

i¼1

ð33Þ

where M is the number of non-dominated solutions, and Nobj is the number of objective functions. The best non-dominated solution can be found when Eq. (33) is maximum, where the normalized sum of membership function values for all objectives is highest. After completing the process, the best solution of the optimization problem is found.

Simulation results and discussion

end end end

li ¼

max

where f i and f i are the maximum and minimum values of the ith objective function respectively. For each non-dominated solution k, the normalized membership func-

ð31Þ

ð32Þ

The proposed SIMBO-Q and QOSIMBO-Q algorithms for optimum placement and sizing of DG have been implemented using MATLAB software and executed on a personal computer with core i3, 2.53 GHz processor with 3 GB RAM. The proposed algorithms have been tested on standard 33 bus and 69 bus radial distribution systems and the test results are presented and discussed in this section. The rating of maximum active power generation of distributed generation sources is taken as 1.5 MW and power factors of DG are considered as unity and 0.95 (lagging) respectively. Maximum apparent power flow limit is taken as Smax ¼ 5 MVA, as mentioned in [19]. The optimization has ni been performed using SIMBO-Q and QOSIMBO-Q algorithms. During simulation, the values of parameters used in SIMBO-Q and QOSIMBO-Q algorithms are Fe = 0.4, Co = 0.4, fathead = 0.2, NV = 0.2, Dai = 0.2, a ¼ 0:2, b ¼ 0:5, l ¼ 0:8, Md = rand and r Ms = rand and j ¼ 0:3. Description of the test systems 33-bus radial distribution system In this case study a radial distribution system with the total load of 3.72 MW, 2.3 MVAR, 33 bus and 32 branches is used to show the effectiveness and validity of the proposed QOSIMBO-Q and SIMBO-Q algorithms. Fig. 2 shows the single line diagram of the test system and the line data and load data are taken from [39]. Maximum line current limit of 33 bus system is taken from [22]. The real power loss in the system is 210.98 kW and the reactive power loss is 143 kVAR when calculated using the Backward-Forward Sweep method of load flow [40]. The details discussions on the case studies are presented in Section ‘‘Test system 1: Optimal location and size of DG in 33 bus system’’. 69-bus radial distribution system In this case study a 69 bus radial distribution system with the total load of 3.80 MW, 2.69 MVAR has been used to show the performance of QOSIMBO-Q and SIMBO-Q algorithm in large scale distribution system. Fig. 3 shows the single line diagram of the test system and the line data and load data are taken from [29]. Maximum line current limit of 69 bus system is taken from [22]. Before installation of DG, the real and reactive power losses in the system are found to be 224.7 kW and 102.13 kVAR, when calculated using the Backward-Forward Sweep method of load flow [40]. The details discussions on the case studies are presented in Section ‘‘Test system 2: Optimal location and size of DG in 69 bus system’’.

354

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Fig. 2. Single line diagram of 33 bus radial distribution system.

Test system 1: Optimal location and size of DG in 33 bus system In this paper performance analysis of seven different case studies has been made on the basis of the DG location and size. The aim is to minimize active power loss, to improve voltage profile and to increase voltage stability. In ‘Case 1’ DG locations and sizes have been found to minimize active power loss of the system. In ‘Case 2’, aim is to improve voltage profile of the system. In ‘Case 3’ improvement of voltage stability index has been considered. In ‘Case 4’ DG sizes and locations have been found to minimize loss and to improve voltage profile simultaneously, while ‘Case 5’ aims to minimize loss and to improve voltage stability index. In ‘Case 6’ improvement of both voltage profile and voltage stability index have been considered. In ‘Case 7’ a tri-objective optimization has been performed to minimize active power loss, to improve voltage profile and voltage stability index. Table 1 shows the objective function values before installation of DG. Details of the results obtained for optimal location and size of DG in 33 bus system for different case studies are presented below: Optimal location and size of DG operating at unity and 0.95 lagging power factors in 33 bus system without DG penetration limit In this case study performance analysis has been made for seven different case studies for two types of DG, where DG sources are operating at unity and 0.95 lagging power factors respectively without considering any penetration limit of DG. Here optimum allocation of DG operating at unity power factor in 33 bus system has been determined by considering apparent power flow limit (thermal limit) constraint instead of current limit constraint, whereas for DG operating at 0.95 lagging power factor, optimum allocation has been determined by considering current limit constraint. Case 1: Active power loss minimization: The simulation results for optimal allocation of DG operating at unity power factor show that for Case 1 the active power loss reduces to 0.0728 MW with QOSIMBO-Q algorithm, while active power loss of 0.0736 MW, 0.0755 MW and 0.0741 MW are obtained by SIMBO-Q, TLBO and QOTLBO algorithms as shown in Table 2. Here the simulation results for Case 1 show

better result with QOSIMBO-Q algorithm compared to other algorithms. It is also observed that QOSIMBO-Q algorithm reduces system active power loss by 65.48% (compared to base case), while voltage profile and voltage stability index are improved by 88.72% and 31.97% respectively. The convergence characteristics of power loss obtained by SIMBO-Q and QOSIMBO-Q algorithms for optimal allocation of DG operating at unity power factor in 33-bus radial distribution system are shown in Fig. 4. It is observed from the convergence graphs that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. The simulation results with DG operating at 0.95 lagging power factor for Case 1 show that without any penetration limit the active power loss reduces to 0.0285 MW by QOSIMBO-Q algorithm which is better than that obtained by SIMBO-Q algorithm, which is shown in Table 2. From the convergence graphs shown in Fig. 5 it is observed that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. Case 2: Voltage profile improvement: For optimal allocation of DG operating at unity power factor, the objective function for Case 2 are 0.0004 p.u., 0.00085 p.u., 0.0010 p.u. and 0.00086 p.u. with QOSIMBO-Q, SIMBO-Q, TLBO and QOTLBO algorithms as shown in Table 3. Here the objective function value obtained by QOSIMBO-Q algorithm is better than those obtained by other algorithms. In this case study the objective function value reduces by 99.70% (compared to base case), while system active power loss is reduced by 48.03% and voltage stability index is improved by 46.43% with QOSIMBO-Q algorithm. Fig. 6 shows the convergence characteristics of voltage deviation obtained by SIMBO-Q and QOSIMBO-Q algorithms for 33-bus radial distribution system. Graphs show that less number of iterations is required with QOSIMBO-Q algorithm compared to the SIMBO-Q algorithm. The objective function for Case 2 with DG operating at 0.95 lagging power factor attains a value of 0.00023 p.u. by QOSIMBO-Q algorithm, which is much better

355

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Fig. 3. Single line diagram of 69 bus radial distribution system.

Table 1 Performance analysis of 33-bus and 69-bus system before DG installation. Test system

Condition

Active power loss in MW

Voltage deviation in p.u.

Voltage stability index1

Voltage stability index

33 bus system 69 bus system

Without DG Without DG

0.2109 0.2249

0.1338 0.0993

1.4988 1.4635

0.6672 0.6833

than the value obtained by SIMBO-Q algorithm as shown in Table 3. The convergence graphs shown in Fig. 7 show that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm.

Case 3: Voltage stability index improvement: Optimal allocation of DG operating at unity power factor for voltage stability index improvement reduces objective function values to 1.0233, 1.0346, 1.0412 and 1.0397 by QOSIMBO-Q, SIMBO-Q, TLBO and QOTLBO algorithms as shown in Table 4. Here the objective function value obtained by QOSIMBO-Q algorithm is better than those obtained by other algorithms. In this case, QOSIMBO-Q algorithm reduces objective function value by 31.73% (compared to base case), while system loss is reduced by 41.92% and voltage profile is improved by 99.63%. Fig. 8 shows the convergence characteristics of voltage stability index1 obtained by SIMBO-Q and

Table 2 Simulation results for loss minimization of 33-bus system (case 1) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no. DG size

Active power loss in Voltage deviation in Voltage stability MW p.u. index1

Voltage stability index

MW

MVAR

MVA

0.8246,1.0311, 0.8862 0.8808,1.0592, 1.0714 0.7613,0.8657, 1.1070 1.0906,1.0542, 0.8016

–

–

–

–

–

–

–

–

0.7638,1.0415, 1.1352 0.7708,1.0965, 1.0655

–

–

–

–

13, 24, 30 24, 30, 13

0.9185,1.1088, 1.2001 1.1073,1.2384, 0.8317

0.3019,0.3644, 0.3945 0.3640,0.4070, 0.2734

0.9668, 1.1672, 1.2633 1.1656, 1.3036, 0.8755

Loss of 33 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0290 0.00098 1.0367 0.9646 13, 24, 30 OSIMBO-Q 0.0285 0.0021 1.0493 0.9530 30, 13, 24

0.8875,1.0853, 1.3092 1.2398,0.8303, 1.1239

0.2917,0.3567, 0.4303 0.4075,0.2729, 0.3694

0.9342, 1.1424, 1.3781 1.3051,0.8740, 1.1831

Loss of 33 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.0755 0.0222 1.1954 0.8365 QOTLBO [18] SIMBO-Q

0.0741

0.0160

1.1552

0.8656

0.0736

0.0156

1.1343

0.8816

QOSIMBO- 0.0728 Q

0.0151

1.1357

0.8805

10, 31 12, 29 14, 30 24, 13

24, 24, 25, 30,

Loss of 33 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0734 0.0151 1.1444 0.8738 14, 24, 29 QOSIMBO- 0.0728 0.0151 1.1358 0.8804 14, 24, Q 30 Loss of 33 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0289 0.0014 1.0500 0.9524 QOSIMBO- 0.0285 Q

0.0021

1.0498

0.9526

356

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Active power loss (MW)

0.077

Loss without DG penetration limit using QOSIMBO-Q Loss without DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using QOSIMBO-Q

0.076

0.075

0.074

0.073

0.072

50

100

150

200

250

300

Iteration no. Fig. 4. Convergence characteristics of active power loss of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f.

QOSIMBO-Q algorithms for 33-bus radial distribution systems. Graphs show that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. The objective function for Case 3 with DG operating at 0.95 lagging power factor attains a value of 1.0213 with QOSIMBO-Q algorithm, which is closer to that obtained by SIMBO-Q algorithm, as shown in Table 4. The convergence graphs shown in Fig. 9 show that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 4: Loss minimization and voltage profile improvement: Fig. 10 shows the pareto-optimal front obtained by QOSIMBO-Q and SIMBO-Q algorithm for Case 4 with DG operating at unity power factor without any penetration limit. From Table 5 it is observed that the active power loss and voltage deviation are reduced to 0.0811 MW and 0.0041 p.u. by QOSIMBO-Q algorithm. These show slightly better results compared to those obtained by SIMBO-Q algorithm. Also the results show that with QOSIMBO-Q algorithm system loss decreases by 61.55% (0.0811 MW) and voltage profile improves by 96.94% (0.0041 p.u.) compared to their base case values. From Table 5 it is also observed that with DG operating at 0.95 lagging power factor, the active power loss and voltage deviation obtained by QOSIMBO-Q algorithm are 0.0306 MW and 0.00036 p.u. respectively. Though in this case loss increases by 2% with QOSIMBO-Q algorithm, but voltage deviation reduces by a large percentage of value 20% compared to SIMBO-Q algorithm.

Active power loss (MW)

0.05

Loss without DG penetration limit using SIMBO-Q Loss without DG penetration limit using QOSIMBO-Q Loss with 100% DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using QOSIMBO-Q

0.045

0.04

0.035

0.03

0.025

50

100

150

200

250

300

Iteration no. Fig. 5. Convergence characteristics of active power loss of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

Case 5: Loss minimization and voltage stability index improvement: The pareto-optimal front obtained by QOSIMBO-Q and SIMBO-Q algorithm for Case 5 with DG operating at unity power factor is shown in Fig. 11. Table 5 also shows that the active power loss and voltage stability index1 are reduced to 0.0840 MW and 1.0602 respectively with QOSIMBO-Q algorithm, which show improved result than those obtained by SIMBO-Q algorithm (0.0861 MW and 1.0733). In this bi-objective optimization, system loss decreases by 60.17% and voltage stability index improves by 41.37% (0.9432) compared to their base case values with QOSIMBO-Q algorithm. Table 5 also shows that for DG operating at 0.95 lagging power factor, the active power loss and voltage stability index1 are 0.0324 MW and 1.0232 respectively with QOSIMBO-Q algorithm. Though in this case voltage stability index1 increases 0.039% with QOSIMBO-Q algorithm, however loss reduces by 9.5% compared to SIMBO-Q algorithm. Case 6: Voltage profile and voltage stability index improvement: Fig. 12 shows the pareto-optimal front obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 6 with DG operating at unity power factor. From Table 5 it is also observed that the best compromise solution obtained by QOSIMBO-Q algorithm (with DG operating at unity power factor) for voltage profile and voltage stability index improvement are 0.00038 p.u. and 1.0234 which are better than those obtained by SIMBO-Q algorithm. It is clear from the results that voltage profile improves by 99.68% and voltage stability index improves by 46.46% (0.9772) compared to their base case values with QOSIMBO-Q algorithm. From Table 5 it is also observed that for DG operating at 0.95 lagging power factor the voltage deviation and voltage stability index1 are 0.00053 p.u. and 1.0224 with QOSIMBO-Q algorithm. In this case, voltage stability index1 increases slightly by 0.01% with QOSIMBO-Q algorithm, but voltage deviation improves by 19.7% compared to SIMBO-Q algorithm. Case 7: Loss minimization, voltage profile and voltage stability index improvement: In Case 7 a multi-objective optimization has been performed to minimize loss and to improve voltage profile and voltage stability index to verify the effectiveness of SIMBO-Q and QOSIMBO-Q algorithms. The pareto-optimal front graph for loss minimization, voltage profile and voltage stability index improvement of 33 bus system with QOSIMBO-Q algorithm is shown in Fig. 13. The individual objective functions in case of multi-objective optimization, show slight increment of their values from their respective single objective values. In case of single objective optimization, value of main objective function is much better compared to that of multi-objective optimization, but the values of other functions are inferior to that of multi-objective case. Therefore, to achieve simultaneous improved performance of all the objectives, multi-objective optimization has been applied here for simultaneous improvements of both or all three objectives. Table 6 shows the comparison between the results obtained for Case 7 using QOSIMBO-Q and SIMBO-Q algorithms for 33 bus system with those obtained using GA [17], PSO [17], GA/PSO [17], TLBO [18] and QOTLBO [18] methods. It is found that active power loss obtained

357

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 3 Simulation results for voltage profile improvement of 33-bus system (case 2) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no.

Active power Voltage deviation Voltage stability Voltage stability loss in MW in p.u. index1 index

DG size MW

MVAR

MVA

1.1320,1.1980, 1.0081 1.0744,1.2000, 1.2000 1.0998,1.1702, 1.2743 1.4933,1.4361, 1.4343

– – – –

– – – –

Voltage deviation of 33 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.1138 0.00075 1.0711 0.9336 7, 31, 13 1.0608,1.4418, 1.0558 – QOSIMBO-Q 0.1116 0.00066 1.0685 0.9359 7, 13, 31 1.4903,0.9580, 1.2714 –

– –

Voltage deviation of 33 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.1265 0.0010 1.0750 0.9302 14, 29, 30 QOTLBO [18] 0.1154 0.00086 1.0725 0.9324 14, 27, 33 SIMBO-Q 0.1265 0.00085 1.0716 0.9332 13, 29, 28 QOSIMBO-Q 0.1096 0.0004 1.0236 0.9769 31, 12, 24

Voltage deviation of 33 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0322 0.00026 1.0240 0.9766 13, 30, 24 0.9377,1.5000, 1.0775 0.3082,0.4930, 0.3541 0.9871, 1.5789, 1.1342 QOSIMBO-Q 0.0324 0.00023 .0235 0.9770 30, 13, 24 1.5000,0.8982, 1.2935 0.4930,0.2952, 0.4252 1.5789, 0.9455, 1.3616 Voltage deviation of 33 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0332 0.00032 1.0236 0.9769 30, 12, 24 1.4221,1.0906, 1.1286 0.4674,0.3585, 0.3710 1.4969, 1.1480, 1.1880 QOSIMBO-Q 0.0323 0.00023 1.0236 0.9769 3, 24, 30 0.9144,1.2287, 1.5000 0.3005,0.4039, 0.4930 0.9625,1.2934, 1.5789

16

x 10

-4

Voltage deviation without DG penetration limit using QOSIMBO-Q Voltage deviation without DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit using QOSIMBO-Q

12 10 8 6

x 10

-3

Voltage deviation without DG penetration limit using SIMBO-Q Voltage deviation without DG penetration limit using QOSIMBO-Q Voltage deviation with 100% DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit usingQOSIMBO-Q

1.8

Voltage deviation (p.u.)

Voltage deviation (p.u.)

14

2

1.6 1.4 1.2 1 0.8 0.6

4 0.4

50

100

150

200

250

300

Iteration no.

0.2

50

100

150

200

250

300

Iteration no. Fig. 6. Convergence characteristics of voltage deviation of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f

without DG is 0.2109 MW. However, considering multi-objective formulation, after DG installation, the active power loss obtained using QOSIMBO-Q algorithm is 0.0971 MW, which is better than the losses obtained by SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO algorithms. The reduction of loss using QOSIMBO-Q algorithm is 53.96% whereas with SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO methods, the loss reduction are 53.44%, 50.97%, 49.6%, 50.07%, 40.87% and 50.97% respectively compared to the base case (without DG). Similarly, voltage deviation achieved by QOSIMBO-Q, SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO methods are 0.00088 p.u., 0.00081 p.u., 0.0124 p.u., 0.0407 p.u., 0.0335 p.u., 0.0011 p.u. and 0.0011 p.u. respectively. The value of voltage stability index attained by QOSIMBO-Q, SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO methods are 0.9631 p.u., 0.9643 p.u. 0.9508 p.u., 0.9490 p.u., 0.9256 p.u., 0.9503 p.u. and 0.9530 p.u. respectively. From the results, it is observed that for Case 7 though the objective function value for voltage profile and voltage stability index improvement slightly increases than that obtained with SIMBO-Q algorithm, but system loss has reduced by 2.24% with QOSIMBO-Q algorithm. Also from the Table 6 it is observed that the simulation time taken per iteration by QOSIMBO-Q algorithm is 0.0444 s which is less compared to other algorithms.

Fig. 7. Convergence characteristics of voltage deviation of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

Table 6 also shows the results obtained for Case 7 using QOSIMBO-Q and SIMBO-Q algorithms for 33 bus system with DG operating at 0.95 lagging power factor. It is found that the active power loss, voltage deviation and voltage stability index values obtained using QOSIMBO-Q algorithm are 0.0354 MW, 0.00036 p.u. and 0.9778 p.u. respectively, which show improved results than those obtained with SIMBO-Q algorithm. Also from the Table 6 it is observed that the simulation time taken per iteration by QOSIMBO-Q algorithm is 0.0472 s, which is less compared to other algorithms. So, overall performance improvement of 33 bus radial distribution system is better with QOSIMBO-Q algorithm compared to other techniques for minimization of active power loss, maximization of the voltage stability index and improvement of voltage profile by optimal placement and sizing of DG operating at unity and 0.95 lagging power factors without any penetration limit.

Optimal location and size of DG operating at unity and 0.95 lagging power factors in 33 bus system with maximum 100% DG penetration limit constraint and current limit constraint From the earlier case studies it is observed that without any penetration limit total installed capacity of DG may be greater than total load demand of the system. So to limit the DG installed

358

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 4 Simulation results for voltage stability index improvement of 33-bus system (case 3) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no.

DG size

Active power Voltage deviation Voltage stability Voltage stability loss in MW in p.u. index1 index

MW

MVAR

MVA

– – – –

– – – –

Voltage stability index1 of 33 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.1376 0.0031 1.0337 0.9674 16, 25, 33 1.4866,0.6873, 1.4995 – QOSIMBO-Q 0.1080 0.00066 1.0292 0.9716 12, 25, 31 1.5000,0.7199, 1.5000 –

– –

Voltage stability index1 of 33 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.1327 0.0023 1.0412 0.9604 8, 12, 31 1.1993,1.1996, 1.1992 QOTLBO [18] 0.1049 0.0016 1.0397 0.9618 6, 11, 29 1.1998,1.2000, 1.1983 SIMBO-Q 0.1460 0.0036 1.0346 0.9666 18, 24, 32 1.4270,1.0761, 1.4623 QOSIMBO-Q 0.1225 0.0005 1.0233 0.9772 12, 33, 24 1.5000,1.5000, 1.5000

Voltage stability index1 of 33 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0520 0.0027 1.0213 0.9791 24, 9, 30 1.5000,1.5000, 1.5000 0.4930,0.4930, 0.4930 1.5789, 1.5789, 1.5789 QOSIMBO-Q 0.0520 0.0027 1.0213 0.9791 24, 9, 30 1.5000,1.5000, 1.5000 0.4930,0.4930, 0.4930 1.5789, 1.5789, 1.5789 Voltage stability index1 of 33 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% penetration limit SIMBO-Q 0.0414 0.0016 1.0235 0.9770 24, 10, 31 1.1494,1.5000, 1.0648 0.3778,0.4930, 0.3500 1.2099, 1.5789, 1.1208 QOSIMBO-Q 0.0338 0.0003 1.0234 0.9771 29, 24, 13 1.5000,1.2706, 0.9485 0.4930,0.4176, 0.3117 1.5789, 1.3375, 0.9984

1.1

1.07

(1/Voltage stability index) without DG penetration limit using QOSIMBO-Q (1/Voltage stability index) without DG penetration limit using SIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using SIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using QOSIMBO-Q

1.09

1 / Voltage stability index

1 / Voltage stability index

1.08

1.06 1.05 1.04 1.03

1.08

(1/Voltage stability index) with 100% DG penetration limit using SIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using QOSIMBO-Q (1/Voltage stability index) without DG penetration limit using QOSIMBO-Q (1/Voltage stability index) without DG penetration limit using SIMBO-Q

1.07 1.06 1.05 1.04 1.03

1.02

50

100

150

200

250

1.02

300

50

100

Iteration no.

capacity within the load demand of the system, penetration limit constraint of DG has been included in these case studies. Here DG allocation has been determined by considering DG sources operating at unity and 0.95 lagging power factors respectively with maximum 100% DG penetration limit. Also branch current limit constraint has been included in this case study instead of maximum apparent power limit of each branch. Case 1: Active power loss minimization: The simulation results for Case 1 show that for DG operating at unity and 0.95 lagging power factors with maximum 100% DG penetration limit, the active power losses reduce to 0.0728 MW and 0.0285 MW respectively by QOSIMBO-Q algorithm, which are better than the losses obtained by SIMBO-Q, TLBO and QOTLBO algorithms, as shown in Table 2. The convergence characteristics for Case 1 with DG operating at unity and 0.95 lagging power factors obtained by SIMBO-Q and QOSIMBO-Q algorithms are shown in Figs. 4 and 5. The characteristics show that QOSIMBO-Q algorithm converges in less number of iterations compared to that obtained by SIMBO-Q algorithm. Case 2: Voltage profile improvement: The objective function values obtained by QOSIMBO-Q algorithm for voltage profile improvement with DG operating at unity and 0.95 lagging power factors are

200

250

300

Fig. 9. Convergence characteristics of voltage stability index1 of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

0.016 QOSIMBO-Q SIMBO-Q

0.014

Voltage deviation (p.u.)

Fig. 8. Convergence characteristics of voltage stability index1 of 33 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f.

150

Iteration no.

0.012 0.01 X : 0.0812 Y : 0.0040

X : 0.0811 Y : 0.0041

0.008 0.006 0.004 0.002 0

0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11

0.115

Active power loss (MW) Fig. 10. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 considering DG operating at unity p.f. without any penetration limit in 33 bus system.

0.00066 p.u. and 0.00023 p.u. respectively, which show better results than that obtained with SIMBO-Q, TLBO and QOTLBO algorithms, as shown in Table 3. The convergence characteristics of voltage deviation obtained by SIMBO-Q and QOSIMBO-Q algorithms with both types of DG are shown in Figs. 6 and 7. It is observed from the convergence graphs that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm.

359

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 5 Performance analysis of SIMBO-Q and QOSIMBO-Q algorithms for the 33-bus system after DG installation for different bi-objective cases. Case study

Method

Objective function value

Bus no.

Active power loss Voltage deviation Voltage stability in MW in p.u. index1

Voltage stability index

DG size MW

MVAR MVA

Bi-objective optimization of 33 bus system with DG operating at unity p.f. (without any penetration level) Case 4: Loss minimization and voltage profile improvement

Case 5: Loss minimization and voltage stability index improvement

SIMBO-Q

0.0812

0.0040

–

–

QOSIMBO-Q 0.0811

0.0041

–

–

SIMBO-Q

0.0861

–

1.0733

0.9317

QOSIMBO-Q 0.0840

–

1.0602

0.9432

–

0.00043

1.0233

0.9772

QOSIMBO-Q –

0.00038

1.0234

0.9771

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

Bi-objective optimization of 33 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit Case 4: Loss minimization and voltage profile SIMBO-Q 0.0925 0.0022 – improvement

Case 5: Loss minimization and voltage stability index improvement

QOSIMBO-Q 0.0889

0.0022

–

–

SIMBO-Q

0.1055

–

1.0321

0.9689

QOSIMBO-Q 0.1040

–

1.0323

0.9687

–

0.00071

1.0301

0.9708

QOSIMBO-Q –

0.00066

1.0292

0.9716

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

Bi-objective optimization of 33 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) Case 4: Loss minimization and voltage profile SIMBO-Q 0.0300 0.00045 – improvement

Case 5: Loss minimization and voltage stability index improvement

–

–

QOSIMBO-Q 0.0306

0.00036

–

–

SIMBO-Q

0.0358

–

1.0228

0.9777

QOSIMBO-Q 0.0324

–

1.0232

0.9773

–

0.00066

1.0223

0.9782

QOSIMBO-Q –

0.00053

1.0224

0.9781

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

Bi-objective optimization of 33 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit Case 4: Loss minimization and voltage profile SIMBO-Q 0.0322 0.0003 – – improvement

Case 5: Loss minimization and voltage stability

QOSIMBO-Q 0.0311

0.0003

–

–

SIMBO-Q

–

1.0234

0.9771

0.0328

30 13 24 30 13 24

1.3331 – 1.0632 1.1687 1.3331 – 1.0632 1.1687

–

31 5 13 24 13 30

1.0229 – 1.4225 0.9370 1.0823 – 1.0148 1.5000

–

31 24 12 12 24 31

1.5000 – 1.5000 1.5000 1.4494 – 1.5000 1.5000

–

31 26 14 24 30 12

0.9137 – 1.4491 0.9029 1.0223 – 1.3735 1.3232

–

12 31 25 12 31 25

1.4605 – 1.4956 0.6912 1.4356 – 1.4881 0.7956

–

25 33 12 12 25 31

0.7160 – 1.5000 1.5000 1.5000 – 0.7199 1.5000

–

13 24 30 24 30 13

0.9195 1.1860 1.3611 1.3053 1.3719 0.9177

0.3022 0.3898 0.4474 0.4290 0.4509 0.3016

0.9679 1.2484 1.4327 1.3740 1.4441 0.9660

24 12 30 30 24 13

1.4957 1.1924 1.2492 1.3964 1.5000 0.8902

0.4916 0.3919 0.4106 0.4590 0.4930 0.2926

1.5744 1.2552 1.3149 1.4699 1.5789 0.9371

10 24 29 24 29

1.1405 1.5000 1.5000 1.5000 1.5000

0.3749 0.4930 0.4930 0.4930 0.4930

1.2005 1.5789 1.5789 1.5789 1.5789

30 13 24 24 30 13

1.5000 0.8813 1.3048 1.2339 1.4637 0.8828

0.4930 0.2897 0.4289 0.4056 0.4811 0.2902

1.5789 0.9277 1.3735 1.2988 1.5407 0.9293

30

1.5000 0.4930 1.5789

–

–

–

–

–

–

(continued on next page)

360

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 5 (continued) Case study

Method

Objective function value

Bus no.

Active power loss Voltage deviation Voltage stability in MW in p.u. index1

Voltage stability index

index improvement QOSIMBO-Q 0.0319

–

1.0235

0.9770

–

0.0003

1.0235

0.9770

QOSIMBO-Q –

0.0003

1.0234

0.9771

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

1 / Voltage stability index

1.18 QOSIMBO-Q SIMBO-Q

1.16 1.14 X : 0.0840 Y : 1.0602

1.12

X : 0.0861 Y : 1.0733

1.1 1.08 1.06 1.04 1.02 0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

Active power loss (MW) Fig. 11. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 considering DG operating at unity p.f. without any penetration limit in 33 bus system.

Case 3: Voltage stability index improvement: For DG operating at unity and 0.95 lagging power factors with maximum 100% penetration limit, the objective function values for Case 3 are 1.0292 and 1.0234 respectively with QOSIMBO-Q algorithm. These are better than those obtained with SIMBO-Q, TLBO and QOTLBO algorithms as mentioned in Table 4. The convergence characteristics of voltage stability index1 obtained by SIMBO-Q and QOSIMBO-Q algorithms with both types of DG are shown in Figs. 8 and 9. It is observed that QOSIMBO-Q algorithm converges faster compared to the SIMBO-Q algorithm.

DG size MW

MVAR MVA

24 13 24 30 13

1.2980 0.9171 1.3057 1.4614 0.9107

0.4266 0.3015 0.4292 0.4803 0.2993

1.3663 0.9654 1.3744 1.5383 0.9586

24 30 13 30 24 13

1.2760 1.5000 0.9331 1.5000 1.2722 0.9430

0.4194 0.4930 0.3067 0.4930 0.4182 0.3100

1.3432 1.5789 0.9822 1.5789 1.3392 0.9926

Case 4: Loss minimization and voltage profile improvement: From Table 5 it is observed that by applying QOSIMBO-Q algorithm, the active power loss and voltage deviation are reduced to 0.0889 MW, 0.0022 p.u. with DG operating at unity power factor and 0.0311 MW, 0.0003 p.u. with DG operating at 0.95 lagging power factor, which show improved results than the results obtained with SIMBO-Q algorithm. Figs. 14 and 15 show the pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 4 with both types of DG. Case 5: Loss minimization and voltage stability index improvement: Table 5 also shows that for DG operating at unity power factor, the active power loss and voltage stability index1 reduces to 0.1040 MW and 1.0323 respectively with QOSIMBO-Q algorithm. Though in this case voltage stability index1 increases by 0.019% with QOSIMBO-Q algorithm, but loss reduces by 1.42% compared to SIMBO-Q algorithm. So the overall performance is better with QOSIMBO-Q algorithm. Fig. 16 shows the pareto-optimal front obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 5. For DG operating at 0.95 lagging power factor, the active power loss and voltage stability index1 are reduced to 0.0319 MW and 1.0235 respectively with QOSIMBO-Q algorithm, which show better results than those

QOSIMBO-Q SIMBO-Q

X : 0.00043 Y : 1.0233

1.025

1 / Voltage stability index

1 / Voltage stability index

1.026

X : 0.00038 Y : 1.0234

1.024 1.023 1.022

1.15

1.1

X : 0.0971 (f1) Y : 0.00088 (f2) Z : 1.0383 (f3)

1.05

1 0.02

0.015

1.021

0.01

3.8

4

4.2

4.4

4.6

4.8

5

5.2

Voltage deviation (p.u.)

5.4

5.6

5.8 -4 x 10

Fig. 12. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 considering DG operating at unity p.f. without any penetration limit in 33 bus system.

0.005

Voltage deviation (p.u.)

0

0.08

0.09

0.1

0.11

0.12

0.13

Active power loss (MW)

Fig. 13. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at unity p.f. without any penetration limit in 33 bus system.

361

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 6 Performance analysis of SIMBO-Q and QOSIMBO-Q algorithms for the 33-bus system after DG installation, with three objective optimization (case 7). Method

Objective function value Active power loss in MW

Voltage deviation in p.u.

Bus no. Voltage stability index1

Voltage stability index

Three-objective optimization for 33 bus system with DG operating at unity p.f. (without any penetration level) GA/PSO [17] 0.1034 0.0124 1.0517 0.9508 32 16 11

DG size

Simulation time per iteration (sec.)

MW

MVAR

MVA

1.2000 0.8630 0.9250

–

–

NA

GA [17]

0.1063

0.0407

1.0537

0.9490

11 29 30

1.5000 0.4228 1.0714

–

–

NA

PSO [17]

0.1053

0.0335

1.0804

0.9256

13 32 8

0.9816 0.8297 1.1768

–

–

NA

TLBO [18]

0.1247

0.0011

1.0523

0.9503

12 28 30

1.1826 1.1913 1.1863

–

–

0.1263

QOTLBO [18]

0.1034

0.0011

1.0493

0.9530

13 26 30

1.0834 1.1876 1.1992

–

–

0.1255

SIMBO-Q

0.0982

0.00081

1.0370

0.9643

30 12 24

1.5000 1.3482 1.3805

–

–

0.0526

QOSIMBO-Q

0.0971

0.00088

1.0383

0.9631

24 30 12

1.3043 1.5000 1.3465

–

–

0.0444

–

–

0.0518

–

–

0.0435

0.4583 0.3562 0.4930

1.4676 1.1408 1.5789

0.0554

0.4930 0.3482 0.4644

1.5789 1.1151 1.4873

0.0472

Three-objective optimization for 33 bus system with DG operating at 0.95 lagging p.f. and maximum 100% DG penetration limit SIMBO-Q 0.0324 0.0003 1.0234 0.9771 30 1.4429 0.4742 13 0.9429 0.3099 24 1.3271 0.4362

1.5188 0.9925 1.3969

0.0547

1.4940 1.4661 0.9453

0.0464

Three-objective optimization for 33 bus system with DG operating at unity p.f. and maximum 100% DG penetration SIMBO-Q 0.1043 0.0011 1.0400 0.9615 13 24 31

limit 1.4000 0.9198 1.4000

QOSIMBO-Q

1.4368 0.8262 1.4433

0.1019

0.00088

1.0342

0.9669

12 25 31

Three-objective optimization for 33 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0356 0.00038 1.0227 0.9778 30 1.3942 12 1.0838 24 1.5000 QOSIMBO-Q

QOSIMBO-Q

0.0354

0.0317

0.00036

0.0003

1.0227

1.0235

obtained by SIMBO-Q algorithm as shown in Table 5. Fig. 17 shows the pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 5. Case 6: Voltage profile and voltage stability index improvement: From Table 5 it is also observed that, the voltage deviation and voltage stability index1 values reduce to 0.00066 p.u., 1.0292 with DG operating at unity power factor and 0.0003 p.u., 1.0234 with DG operating at 0.95 lagging power factor as obtained by QOSIMBO-Q algorithm, which show improved performances than those obtained by SIMBO-Q algorithm. The pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 6 with both types of DG are shown in Figs. 18 and 19. Case 7: Loss minimization, voltage profile and voltage stability index improvement:

0.9778

0.9770

24 12 30

30 24 13

1.5000 1.0593 1.4129

1.4193 1.3928 0.8980

0.4665 0.4578 0.2952

In Case 7 a multi-objective optimization has been performed to minimize loss and to improve voltage profile and voltage stability index of 33 bus system, to verify the effectiveness of SIMBO-Q and QOSIMBO-Q algorithms. Table 6 shows the results obtained for Case 7 using QOSIMBO-Q and SIMBO-Q algorithms for DG operating at unity and 0.95 lagging power factors with maximum 100% penetration limit. From Table 6 it is observed that, the active power loss, voltage deviation and voltage stability index values obtained using QOSIMBO-Q algorithm are 0.1019 MW, 0.00088 p.u. and 0.9669 p.u. respectively with DG operating at unity power factor and 0.0317 MW, 0.0003 p.u. and 0.9770 p.u. respectively with DG operating at 0.95 lagging power factor. Table 6 shows that the results obtained by QOSIMBO-Q

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

algorithm for Case 7 with both types of DG are better than the results obtained by SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO algorithms. Table 6 also depicts that the simulation time taken per iteration by QOSIMBO-Q algorithm are 0.0435 s and 0.0464 s respectively with both types of DG, those are also less compared to other algorithms. The pareto-optimal graphs for Case 7 with QOSIMBO-Q algorithm are shown in Figs. 20 and 21. So, overall performance improvement of 33 bus radial distribution system is better with QOSIMBO-Q algorithm compared to other techniques for minimization of active power loss, maximization of the voltage stability index and improvement of voltage profile by optimal placement and sizing of DG operating at unity and 0.95 lagging power factors with maximum 100% DG penetration limit constraint.

5

x 10

-3

SIMBO-Q QOSIMBO-Q

4.5

Voltage deviation (p.u.)

362

4 3.5

X : 0.0925 Y : 0.0022

X : 0.0889 Y : 0.0022

3 2.5 2 1.5 1 0.5 0.085

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

Active power loss (MW) Fig. 14. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 with DG operating at unity p.f. and maximum 100% penetration limit in 33 bus system.

Test system 2: Optimal location and size of DG in 69 bus system

Case 1: Active power loss minimization: The simulation results for optimal allocation of DG operating at unity power factor show that for Case 1, the active power losses of 69 bus system reduce to 0.0710 MW, 0.0714 MW, 0.0724 MW and 0.0716 MW with QOSIMBO-Q, SIMBO-Q, TLBO and QOTLBO algorithms as shown in Table 7. So, the simulation results for Case 1 show better result with QOSIMBO-Q algorithm compared to other algorithms. It is also observed that QOSIMBO-Q algorithm reduces system active power loss by 68.43% (compared to base case), while voltage profile and voltage stability index are improved by 92.85% and 31.48% respectively. The convergence characteristics of power loss obtained by SIMBO-Q and QOSIMBO-Q algorithms for 69-bus radial distribution systems are shown in Fig. 22. It is observed from the convergence graphs that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. The simulation results for optimal allocation of DG operating at 0.95 lagging power factor show that for Case 1 without any penetration limit the active power loss reduces to 0.0229 MW with QOSIMBO-Q algorithm, which is better than the loss obtained by SIMBO-Q algorithm, as shown in Table 7. The convergence graphs shown in Fig. 23 depict that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 2: Voltage profile improvement: Table 8 shows that the objective function values for voltage profile improvement of 69 bus system with DG operating at unity power factor are 0.000197 p.u., 0.000208 p.u., 0.0003 p.u. and 0.00022 p.u. by QOSIMBO-Q, SIMBO-Q, TLBO and QOTLBO algorithms. Here the objective function value obtained by QOSIMBO-Q algorithm is better than those obtained by other algorithms. In this case study the objective function value reduces by 99.80% (compared to base case),

8

x 10

-4

Voltage deviation (p.u.)

SIMBO-Q QOSIMBO-Q

7 X : 0.0311 Y : 0.0003

6

X : 0.0322 Y : 0.0003

5 4 3 2 0.03

0.032

0.034

0.036

0.038

0.04

0.042

0.044

Active power loss (MW) Fig. 15. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 33 bus system.

1.15 SIMBO-Q QOSIMBO-Q

1 / Voltage stability index

Optimal location and size of DG operating at unity and 0.95 lagging power factors in 69 bus system without DG penetration limit In this case study optimum allocation of DG operating at unity power factor has been determined by considering apparent power flow limit (thermal limit) constraint instead of current limit constraint, whereas for DG operating at 0.95 lagging power factor, optimum allocation has been determined by considering current limit constraint.

X : 0.1040 Y : 1.0323

1.1

X : 0.1055 Y : 1.0321

1.05

1 0.09

0.1

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

Active power loss (MW)

Fig. 16. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 with DG operating at unity p.f. and maximum 100% penetration limit in 33 bus system.

while system active power loss is reduced by 58.92% and voltage stability index is improved by 42.99% with QOSIMBO-Q algorithm. Fig. 24 shows the convergence characteristics of voltage deviation obtained by SIMBO-Q and QOSIMBO-Q algorithms. Graphs show that less number of iterations is required with QOSIMBO-Q algorithm compared to the SIMBO-Q algorithm. The objective function value for voltage profile improvement of 69 bus system obtained by QOSIMBO-Q algorithm with DG operating at 0.95 lagging power factor is 0.00026 p.u., which is better than that obtained by SIMBO-Q algorithm as shown in Table 8. From the

363

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 1.045

1 / Voltage stability index

1 / Voltage stability index

SIMBO-Q QOSIMBO-Q

1.04

1.035

X : 0.0319 Y : 1.0235 X : 0.0328 Y : 1.0234

1.03

1.1 1.08

X : 0.1019 Y : 0.00088 Z : 1.0342

1.06 1.04 1.02 3.5

3

1.025 x 10

1.02 0.03

0.035

0.04

0.045

0.05

Fig. 17. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 33 bus system.

1 / Voltage stability index

SIMBO-Q QOSIMBO-Q

1.07 1.06 X : 0.00066 Y : 1.0292

1.05 X : 0.00071 Y : 1.0301

1.04

1

0.5

0.09

0.11

0.1

0.12

1.0235 1.0234 8 -4

4

Voltage deviation (p.u.) 1.5

2

2.5

3

3.5 x 10

Voltage deviation (p.u.)

-3

0.15

X : 0.0317 Y : 0.0003 Z : 1.0235

1.0236

6

1

0.14

Active power loss (MW)

1.0237

x 10

1.02

0.13

1.0238

1.03

1.01 0.5

1.5

Fig. 20. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at unity p.f. with maximum 100% DG penetration limit in 33 bus system.

1 / Voltage stability index

1.08

2

Voltage deviation (p.u.)

0.055

Active power loss (MW)

2.5

-3

2

0.03

0.032

0.034

0.036

0.038

0.04

0.042

Active power loss (MW)

Fig. 21. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at 0.95 lagging p.f. with maximum 100% DG penetration limit in 33 bus system.

Fig. 18. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 with DG operating at unity p.f. and maximum 100% penetration limit in 33 bus system.

1.045

1 / Voltage stability index

SIMBO-Q QOSIMBO-Q

1.04

1.035 X : 0.0003 Y : 1.0235

X : 0.0003 Y : 1.0234

1.03

1.025

1.02

2

2.5

3

3.5

4

Voltage deviation (p.u.)

4.5

5

5.5

x 10

-4

Fig. 19. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 33 bus system.

convergence characteristics shown in Fig. 25, it is observed that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 3: Voltage stability index improvement: For DG operating at unity power factor without any penetration limit, the objective function values for voltage stability index improvement are 1.0234, 1.0235, 1.0244 and 1.0235 by QOSIMBO-Q, SIMBO-Q, TLBO and QOTLBO algorithms, as shown in Table 9. Here the objective function value obtained by QOSIMBO-Q algorithm is better than those obtained by other algorithms. In this case, QOSIMBO-Q algorithm reduces objective

function value by 30.07% (compared to base case), while system loss is reduced by 52.47% and voltage profile is improved by 98.89%. Fig. 26 shows the convergence characteristics for Case 3 obtained by SIMBO-Q and QOSIMBO-Q algorithms for 69-bus radial distribution systems. Graphs show that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. For DG operating at 0.95 lagging power factor without any penetration limit, the objective function value for voltage stability index improvement is 1.0232 by QOSIMBO-Q algorithm, which is similar to that obtained by SIMBO-Q algorithm as shown in Table 9. From the convergence characteristics shown in Fig. 27, it is observed that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 4: Loss minimization and voltage profile improvement: Fig. 28 shows the pareto-optimal front for Case 4 obtained by QOSIMBO-Q and SIMBO-Q algorithm for DG operating at unity power factor without any penetration limit. From Table 10 it is observed that the active power loss and voltage deviation are reduced to 0.0733 MW, 0.002 p.u. by QOSIMBO-Q algorithm and 0.0743 MW, 0.002 p.u. by SIMBO-Q algorithm. Here QOSIMBO-Q algorithm gives much better results than those obtained by SIMBO-Q algorithms. Also with QOSIMBO-Q algorithm system loss decreases by 67.41% and voltage profile improves by 97.99% compared to their base case values. From Table 10 it is also observed that for DG operating at 0.95 lagging power factor without any penetration limit, the active power loss and voltage deviation are

364

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 7 Simulation results for loss minimization of 69-bus system (case 1) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no. DG size

Active power loss in Voltage deviation in Voltage stability MW p.u. index1

Voltage stability index

MW

MVAR

MVA

0.5919,0.8188, 0.9003 0.5334,1.1986, 0.5672 1.5000,0.4285, 0.4863 0.8314,0.4538, 1.5000

–

–

–

–

–

–

–

–

1.5000,0.6189, 0.5297 0.8336,0.4511, 1.5000

–

–

–

–

18, 64, 61 17, 64, 61

0.5863,0.5378, 1.4321 0.5838,0.4148, 1.5000

0.1927,0.1768, 0.4707 0.1919,0.1363, 0.4930

0.6172, 0.5661, 1.5075 0.6145, 0.4366, 1.5789

Loss of 69 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0231 0.00075 1.0281 0.9727 64, 19, 61 QOSIMBO-Q 0.0228 0.00069 1.0266 0.9741 64, 17, 61

0.4220,0.5656, 1.5000 0.4272,0.5828, 1.5000

0.1387,0.1859, 0.4930 0.1404,0.1916, 0.4930

0.4442, 0.5954, 1.5789 0.4497,0.6135, 1.5789

Loss of 69 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.0724 0.0063 1.0908 0.9167 QOTLBO [18] 0.0716

0.0062

1.0874

0.9196

SIMBO-Q

0.0714

0.0082

1.1231

0.8904

QOSIMBO-Q

0.0710

0.0071

1.1131

0.8984

15, 61, 63 18, 61, 63 61, 17, 67 9, 17, 61

Loss of 69 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0713 0.0071 1.1168 0.8954 61, 9, 17 QOSIMBO-Q 0.0710 0.0071 1.1131 0.8984 9, 18, 61 Loss of 69 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0231 0.00055 1.0252 0.9754 QOSIMBO-Q

0.0229

0.00073

1.0269

0.9738

0.045

Loss without DG penetration limit using QOSIMBO-Q Loss without DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using QOSIMBO-Q

0.08

Active power loss (MW)

Active power loss (MW)

0.082

0.078 0.076 0.074 0.072 0.07

50

100

150

200

250

300

Iteration no.

Loss with 100% DG penetration limit using SIMBO-Q Loss with 100% DG penetration limit using QOSIMBO-Q Loss without DG penetration limit using SIMBO-Q Loss without DG penetration limit using QOSIMBO-Q

0.04

0.035

0.03

0.025

0.02

50

100

150

200

250

300

Iteration no.

Fig. 22. Convergence characteristics of active power loss of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f.

Fig. 23. Convergence characteristics of active power loss of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

reduced to 0.0246 MW and 0.0002 p.u. respectively by QOSIMBO-Q algorithm, which show improved results than those obtained by SIMBO-Q algorithm. Case 5: Loss minimization and voltage stability index improvement: Fig. 29 shows the pareto-optimal front for Case 5 obtained by QOSIMBO-Q and SIMBO-Q algorithms for DG operating at unity power factor without any penetration limit. Table 10 also shows that the best compromise solutions obtained by QOSIMBO-Q algorithm for loss minimization and voltage stability index improvement are 0.0741 MW and 1.0386 respectively which show improved result than those obtained by SIMBO-Q algorithm (0.0754 MW and 1.0386). In this bi-objective optimization, system loss decreases by 67.05% and voltage stability index improves by 40.91% (0.9628) compared to their base case values with QOSIMBO-Q algorithm. Table 10 also shows that for DG operating at 0.95 lagging power factor without any penetration limit,

the active power loss and voltage stability index1 reduced to 0.0230 MW and 1.0234 respectively by QOSIMBO-Q algorithm, which show better results than those obtained by SIMBO-Q algorithm. Case 6: Voltage profile and voltage stability index improvement: Fig. 30 shows the pareto-optimal front for Case 6 obtained by QOSIMBO-Q and SIMBO-Q algorithm for DG operating at unity power factor without any penetration limit. From Table 10 it is also observed that the best compromise solutions obtained for voltage profile and voltage stability index improvement with QOSIMBO-Q algorithm are 0.0005 p.u. and 1.0235, which are better than the results obtained by SIMBO-Q algorithm (0.0008 p.u. and 1.0235). It is clear from the results that voltage profile improves by 99.5% and voltage stability index improves by 42.99% (0.9770) compared to their base case values with QOSIMBO-Q algorithm. With DG operating at 0.95 lagging power factor, Table 10 shows that the values of voltage deviation and voltage

365

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 8 Simulation results for voltage profile improvement of 69-bus system (case 2) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no. DG size

Active power loss in Voltage deviation in Voltage stability MW p.u. index1

Voltage stability index

MW

MVAR

MVA

0.9762,1.1388, 1.1635 1.1764,1.1177, 1.1962 1.5000,0.8224, 1.1716 1.5000,0.8737, 1.1443

–

–

–

–

–

–

–

–

–

–

–

–

0.9508,0.9838, 0.9621 0.5120,1.5000, 1.2881

0.3125,0.3233, 0.3162 0.1683,0.4930, 0.4234

1.0008,1.0356, 1.0127 0.5389,1.5789, 1.3559

Voltage deviation of 69 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0297 0.00026 1.0234 0.9771 62, 59, 1.1212,1.0020, 13 0.9531 QOSIMBO-Q 0.0314 0.00022 1.0233 0.9772 63, 56, 1.5000,1.2600, 17 0.4871

0.3685,0.3293, 0.3133 0.4930,0.4142, 0.1601

1.1802,1.0547, 1.0033 1.5789,1.3263, 0.5127

Voltage deviation of 69 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.0901 0.0003 1.0735 0.9315 QOTLBO [18] 0.0907

0.00022

1.0873

0.9197

SIMBO-Q

0.0908

0.000208

1.0235

0.9770

QOSIMBO-Q

0.0924

0.000197

1.0235

0.9770

14, 64 13, 62 63, 13 63, 57

59, 60, 59, 14,

Voltage deviation of 69 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0926 0.000201 1.0235 0.9770 63, 14, 1.5000,0.9011, 57 1.1320 QOSIMBO-Q 0.0926 0.000198 1.0235 0.9770 14, 57, 0.8777,1.1559, 63 1.4914 Voltage deviation of 69 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0278 0.00028 1.0234 0.9771 13, 62, 63 QOSIMBO-Q 0.0370 0.00026 1.0233 0.9772 18, 64, 55

x 10

-3

3.5

Voltage deviation without DG penetration limit using QOSIMBO-Q Voltage deviation without DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit using QOSIMBO-Q

3

x 10

-3

Voltage deviation with 100% DG penetration limit using SIMBO-Q Voltage deviation with 100% DG penetration limit using QOSIMBO-Q Voltage deviation without DG penetration limit using QOSIMBO-Q Voltage deviation without DG penetration limit using SIMBO-Q

3

Voltage deviation (p.u.)

Voltage deviation (p.u.)

3.5

2.5 2 1.5 1 0.5

2.5 2 1.5 1 0.5

0

50

100

150

200

250

300

Iteration no.

0

50

100

150

200

250

300

Iteration no. Fig. 24. Convergence characteristics of voltage deviation of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f.

stability index1 are 0.0002 p.u. and 1.0235 using QOSIMBO-Q algorithm, which show improved results than those obtained by SIMBO-Q algorithm. Case 7: Loss minimization, voltage profile and voltage stability index improvement: The pareto-optimal front graph for DG operating at unity power factor without any penetration limit for Case 7 with QOSIMBO-Q algorithm is shown in Fig. 31. In Table 11 the values of objective function obtained for Case 7 for 69 bus system using QOSIMBO-Q and SIMBO-Q algorithms have been compared with those obtained using GA [17], PSO [17] and GA/PSO [17], TLBO [18] and QOTLBO [18] algorithms. It is found that active power loss obtained without DG is 0.2249 MW. However, considering multi-objective formulation, after DG installation, the active power loss obtained using QOSIMBO-Q, SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO algorithms are 0.0797 MW, 0.0800 MW, 0.0811 MW, 0.0890 MW, 0.0832 MW, 0.0822 MW, and 0.0806 MW respectively. The reduction of loss using QOSIMBO-Q algorithm is 64.56% whereas with

Fig. 25. Convergence characteristics of voltage deviation of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO algorithms, the loss reduction obtained are 64.43%, 63.94%, 60.43%, 63%, 63.45% and 64.16% respectively compared to the base case (without DG). So loss reduction is more with QOSIMBO-Q algorithm than other algorithms. Similarly, voltage deviation achieved by QOSIMBO-Q, SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO methods are 0.0007 p.u., 0.0007 p.u., 0.0031 p.u., 0.0012 p.u., 0.0049 p.u., 0.0008 p.u. and 0.0007 p.u. respectively. The value of voltage stability index attained by QOSIMBO-Q, SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO methods are 0.9768 p.u., 0.9770 p.u., 0.9768 p.u., 0.9705 p.u., 0.9676 p.u., 0.9745 p.u. and 0.9769 p.u. respectively. From the results it is observed that for Case 7 though the objective function value for voltage stability index improvement (1.0237) slightly increases by 0.02% than that obtained with SIMBO-Q algorithm (1.0235), but system loss reduces by 0.38% with QOSIMBO-Q algorithm. The objective function

366

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 9 simulation results for voltage stability index improvement of 69-bus system (case 3) using SIMBO-Q and QOSIMBO-Q algorithm. Method

Objective function value

Bus no. DG size

Active power loss in Voltage deviation in Voltage stability MW p.u. index1

Voltage stability index

MW

MVAR

MVA

0.7026,1.1716, 1.1630 1.1931,1.1967, 1.1914 1.3841,1.5000, 1.0555 1.5000,1.5000, 1.5000

–

–

–

–

–

–

–

–

–

–

–

–

Voltage stability index1 of 69 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0501 0.0020 1.0232 0.9773 61, 53, 1.5000,1.5000, 66 1.5000 QOSIMBO-Q 0.0461 0.0017 1.0232 0.9773 62, 8, 11 1.5000,1.5000, 1.5000

0.4930,0.4930, 0.4930 0.4930,0.4930, 0.4930

1.5789,1.5789, 1.5789 1.5789,1.5789, 1.5789

Voltage stability index1 of 69 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% penetration limit SIMBO-Q 0.0352 0.00089 1.0233 0.9772 12, 61, 1.1859,1.5000, 55 1.1118 QOSIMBO-Q 0.0352 0.00086 1.0233 0.9772 12, 61, 1.1517,1.5000, 55 1.1482

0.3898,0.4930, 0.3654 0.3785,0.4930, 0.3774

1.2483,1.5789, 1.1703 1.2123,1.5789, 1.2086

Voltage stability index1 of 69 bus system with DG operating at unity p.f. (without any penetration level) TLBO [18] 0.0889 0.0009 1.0244 0.9762 27, 61 QOTLBO [18] 0.1105 0.0072 1.0235 0.9770 22, 62 SIMBO-Q 0.1420 0.0147 1.0235 0.9770 21, 64 QOSIMBO-Q 0.1069 0.0011 1.0234 0.9771 12, 63

60, 61, 63, 56,

Voltage stability index1 of 69 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit SIMBO-Q 0.0916 0.00049 1.0235 0.9770 12, 58, 1.5000,0.8000, 61 1.5000 QOSIMBO-Q 0.0917 0.00049 1.0235 0.9770 58, 12, 0.8465,1.5000, 61 1.4534

(1/Voltage stability index) without DG penetration limit using SIMBO-Q (1/Voltage stability index) without DG penetration limit using QOSIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using SIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using QOSIMBO-Q

1.0235

1.0234

50

100

150

200

250

1.14

1 / Voltage stability index

1 / Voltage stability index

1.0236

(1/Voltage stability index) with 100% DG penetration limit using SIMBO-Q (1/Voltage stability index) with 100% DG penetration limit using QOSIMBO-Q (1/Voltage stability index) without DG penetration limit using SIMBO-Q (1/Voltage stability index) without DG penetration limit using QOSIMBO-Q

1.12 1.1 1.08 1.06 1.04 1.02

300

50

100

Iteration no.

value for voltage profile improvement remains same in both the cases. Table 11 also shows that the simulation time required per iteration with QOSIMBO-Q algorithm is 0.0486 s which is less compared to other algorithms. Table 11 also shows that for DG operating at 0.95 lagging power factor without any penetration limit, the active power loss, voltage deviation and voltage stability index values obtained using QOSIMBO-Q algorithm are 0.0263 MW, 0.0002 p.u. and 0.9771 p.u. respectively, which show improved results than those obtained by SIMBO-Q algorithm. The simulation time required per iteration with QOSIMBO-Q algorithm is 0.0514 s, which is less compared to other algorithms as shown in Table 11. So, overall performance improvement of 69 bus radial distribution network is better with QOSIMBO-Q algorithm compared to other techniques for minimization of active power loss, maximization of the voltage

200

250

300

Fig. 27. Convergence characteristics of voltage stability index1 of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at 0.95 lagging p.f.

0.012

Voltage deviation (p.u.)

Fig. 26. Convergence characteristics of voltage stability index1 of 69 bus system obtained by SIMBO-Q and QOSIMBO-Q algorithms considering DG operating at unity p.f.

150

Iteration no.

QOSIMBO-Q SIMBO-Q

0.01 X : 0.0733 Y : 0.002

0.008 0.006

X : 0.0743 Y : 0.002

0.004 0.002 0

0.075

0.08

0.085

0.09

0.095

0.1

Active power loss (MW) Fig. 28. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 considering DG operating at unity p.f. without any penetration limit in 69 bus system.

stability index and improvement of voltage profile by optimal placement and sizing of both types of DG without any penetration limit.

367

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 10 Performance analysis of SIMBO-Q and QOSIMBO-Q algorithms for the 69-bus system after DG installation for different bi-objective cases. Case study

Method

Objective function value

Bus no.

Active power loss Voltage deviation Voltage stability in MW in p.u. index1 Bi-objective optimization of 69 bus system with DG operating at unity p.f. (without any penetration level) Case 4:Loss minimization and voltage profile SIMBO-Q 0.0743 0.002 – improvement

Case 5:Loss minimization and voltage stability index improvement

0.002

–

–

SIMBO-Q

0.0754

–

1.0386

0.9628

QOSIMBO-Q 0.0741

–

1.0386

0.9628

–

0.0008

1.0235

0.9770

QOSIMBO-Q –

0.0005

1.0235

0.9770

Bi-objective optimization of 69 bus system with DG operating at unity p.f. and with maximum 100% DG penetration limit Case 4: Loss minimization and voltage profile SIMBO-Q 0.0781 0.0010 – improvement

–

QOSIMBO-Q 0.0774

0.0010

–

–

SIMBO-Q

0.0805

–

1.0235

0.9770

QOSIMBO-Q 0.0797

–

1.0235

0.9770

–

0.00027

1.0235

0.9770

QOSIMBO-Q –

0.00025

1.0235

0.9770

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

Bi-objective optimization of 69 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) Case 4: Loss minimization and voltage profile SIMBO-Q 0.0272 0.0002 – improvement

Case 5: Loss minimization and voltage stability index improvement

–

QOSIMBO-Q 0.0733

Case 6:Voltage profile and voltage stability index SIMBO-Q improvement

Case 5: Loss minimization and voltage stability index improvement

Voltage stability index

–

QOSIMBO-Q 0.0246

0.0002

–

–

SIMBO-Q

0.0355

–

1.0233

0.9772

QOSIMBO-Q 0.0230

–

1.0234

0.9771

–

0.0008

1.0235

0.9770

QOSIMBO-Q –

0.0002

1.0235

0.9770

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

Bi-objective optimization of 69 bus system with DG operating at 0.95 lagging p.f. and with maximum 100% DG penetration limit Case 4: Loss minimization and voltage profile SIMBO-Q 0.0259 0.0002 – – improvement

Case 5: Loss minimization and voltage stability index improvement

QOSIMBO-Q 0.0246

0.0002

–

–

SIMBO-Q

–

1.0234

0.9771

0.0235

dg size MW

MVAR MVA

18 59 61 64 17 61

0.6479 – 0.5896 1.4976 0.4403 – 0.6805 1.5000

–

61 62 18 17 64 61

1.3381 – 0.7660 0.5621 0.6370 – 0.5198 1.5000

–

69 57 64 64 12 59

1.3630 – 1.3775 1.1985 1.0671 – 1.5000 1.2115

–

16 61 59 61 18 59

0.7693 – 1.4597 0.7233 1.5000 – 0.6987 0.7037

–

62 61 14 64 61 14

0.8110 – 1.3579 0.8435 0.6445 – 1.5000 0.8259

–

13 57 62 62 57 13

1.1231 – 1.1276 1.5000 1.4703 – 1.1272 1.1113

–

60 14 63 61 64 14

0.7235 0.8159 1.2795 1.5000 0.4466 0.8205

0.2378 0.2682 0.4206 0.4930 0.1468 0.2697

0.7616 0.8588 1.3468 1.5789 0.4701 0.8637

61 54 12 17 64 61

1.5000 1.5000 0.8999 0.6190 0.4516 1.5000

0.4930 0.4930 0.2958 0.2035 0.1484 0.4930

1.5789 1.5789 0.9473 0.6516 0.4754 1.5789

63 57 69 57 63 13

1.5000 0.9593 1.5000 1.0696 1.5000 1.1106

0.4930 0.3153 0.4930 0.3516 0.4930 0.3650

1.5789 1.0098 1.5789 1.1259 1.5789 1.1691

62 14 61 64 61 14

1.3615 0.7976 0.6549 0.4615 1.5000 0.8167

0.4475 0.2622 0.2153 0.1517 0.4930 0.2685

1.4332 0.8396 0.6894 0.4858 1.5789 0.8597

64 61 16

0.5304 0.1743 0.5583 1.5000 0.4930 1.5789 0.6090 0.2002 0.6411

–

–

–

–

–

–

(continued on next page)

368

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 10 (continued) Case study

Method

Objective function value

Bus no.

Active power loss Voltage deviation Voltage stability in MW in p.u. index1 QOSIMBO-Q 0.0233

Voltage stability index

dg size MW

MVAR MVA

–

1.0234

0.9771

16 64 61

0.6115 0.2010 0.6437 0.5530 0.1818 0.5821 1.4143 0.4649 1.4887

–

0.00028

1.0233

0.9772

QOSIMBO-Q –

0.00025

1.0233

0.9772

55 63 15 55 63 18

1.5000 1.5000 0.4772 1.5000 1.5000 0.4612

Case 6: Voltage profile and voltage stability index SIMBO-Q improvement

0.4930 0.4930 0.1569 0.4930 0.4930 0.1516

1.5789 1.5789 0.5023 1.5789 1.5789 0.4855

QOSIMBO-Q SIMBO-Q

1.12 1.1

X : 0.0741 Y : 1.0386

1 / Voltage stability index

1 / Voltage stability index

1.14

X : 0.0754 Y : 1.0386

1.08 1.06 1.04

1.15

1.1 X : 0.0797 Y : 0.0007 Z : 1.0237

1.05

1 8

6

1.02

0.075

0.08

0.085

0.09

0.095

0.1

0.105

0.11

Active power loss (MW)

1 / Voltage stability index

1.0237 QOSIMBO-Q SIMBO-Q X : 0.0008 Y : 1.0235

1.0236

X : 0.0005 Y : 1.0235

1.0235 1.0235 1.0235 1.0234 1.0233 1.0233

4

5

6

7

8

Voltage deviation (p.u.)

4 2

Voltage deviation (p.u.)

Fig. 29. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 considering DG operating at unity p.f. without any penetration limit in 69 bus system.

1.0236

x 10

-3

9

10

11

x 10

-4

Fig. 30. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 considering DG operating at unity p.f. without any penetration limit in 69 bus system.

Optimal location and size of DG operating at unity and 0.95 lagging power factors in 69 bus system with maximum 100% DG penetration limit constraint and current limit constraint In this case study, DG allocation has been determined by considering DG sources are operating at unity and 0.95 lagging power factors respectively with maximum 100% DG penetration limit. Also branch current limit constraint has been included here instead of maximum apparent power limit of each branch. Case 1: Active power loss minimization: The simulation results for optimum allocation of DG operating at unity and 0.95 lagging power factors for

0

0.08

0.09

0.1

0.11

0.12

Active power loss (MW)

Fig. 31. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at unity p.f. without any penetration limit in 69 bus system.

Case 1 show that the active power losses reduce to 0.0710 MW and 0.0228 MW respectively by QOSIMBO-Q algorithm, which show better results than those obtained by SIMBO-Q, TLBO and QOTLBO algorithms, as shown in Table 7. The convergence characteristics of Case 1 with both types of DG are shown in Figs. 22 and 23, which show that QOSIMBO-Q algorithm converges in less number of iterations compared to the SIMBO-Q algorithm. Case 2: Voltage profile improvement: For DG operating at unity and 0.95 lagging power factors, the objective function values obtained for voltage profile improvement are 0.000198 p.u. and 0.00022 p.u. with QOSIMBO-Q algorithm, which are comparatively better than those obtained with SIMBO-Q, TLBO and QOTLBO algorithms, as shown in Table 8. The convergence characteristics of Case 2 obtained by SIMBO-Q and QOSIMBO-Q algorithms with both types of DG are shown in Figs. 24 and 25. The convergence graphs show that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 3: Voltage stability index improvement: Table 9 shows that the objective function values for Case 3 with DG operating at unity and 0.95 lagging power factors are 1.0235 and 1.0233 respectively with QOSIMBO-Q algorithm, which are similar to the results obtained by SIMBO-Q algorithm, but better than the values obtained by TLBO and QOTLBO algorithms. Figs. 26 and 27 depict the convergence characteristics of Case 3 with both types of DG and it is observed from the figures

369

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 11 Performance analysis of SIMBO-Q and QOSIMBO-Q algorithms for the 69-bus system after DG installation, with three objective optimization (case 7). Method

Objective function value Active power loss in MW

Bus no.

Voltage deviation in p.u.

Voltage stability index1

DG size

Voltage stability index

Three-objective optimization for 69 bus system with DG operating at unity p.f. (without any penetration level) GA/PSO [17] 0.0811 0.0031 1.0237 0.9768 21 61 63

Simulation time per iteration (sec.)

MW

MVAR

MVA

0.9105 1.1926 0.8849

–

–

NA

GA [17]

0.0890

0.0012

1.0303

0.9705

21 62 64

0.9297 1.0752 0.9848

–

–

NA

PSO [17]

0.0832

0.0049

1.0335

0.9676

17 61 63

0.9925 1.1998 0.7956

–

–

NA

TLBO [18]

0.0822

0.0008

1.0262

0.9745

13 61 62

1.0134 0.9901 1.1601

–

–

0.1577

QOTLBO [18]

0.0806

0.0007

1.0236

0.9769

15 61 63

0.8114 1.1470 1.0022

–

–

0.1571

SIMBO-Q

0.0800

0.0007

1.0235

0.9770

15 62 61

0.7722 0.8232 1.3526

–

–

0.0554

QOSIMBO-Q

0.0797

0.0007

1.0237

0.9768

61 15 63

1.4385 07754 0.7235

–

–

0.0486

–

–

0.0545

–

–

0.0478

0.3425 0.4930 0.1579

1.0967 1.5789 0.5057

0.0585

0.4186 1.0407 1.5000

0.1376 0.3420 0.4930

0.4406 1.0955 1.5789

0.0514

Three-objective optimization for 69 bus system with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit SIMBO-Q 0.0309 0.0002 1.0233 0.9772 15 0.5380 62 1.5000 56 1.2817

0.1768 0.4930 0.4213

0.5663 1.5789 1.3492

0.0576

0.4930 0.2720 0.1755

1.5789 0.8712 0.5620

0.0507

Three-objective optimization for 69 bus system with DG operating at unity p.f. and maximum 100% DG penetration SIMBO-Q 0.0805 0.0007 1.0235 0.9770 61 15 62 QOSIMBO-Q

0.0798

0.0007

1.0235

0.9770

61 15 63

limit 1.3975 0.7803 0.7907 1.4986 0.7851 0.6623

Three-objective optimization for 69 bus system with DG operating at 0.95 lagging p.f. (without any penetration level) SIMBO-Q 0.0273 0.0002 1.0234 0.9771 13 1.0419 61 1.5000 60 0.4804 QOSIMBO-Q

0.0263

QOSIMBO-Q

4

x 10

0.0002

0.0257

1.0234

0.0002

1.0234

0.9771

61 14 60

4

SIMBO-Q QOSIMBO-Q

1.5000 0.8276 0.5339

X : 0.0774 Y : 0.0010

X : 0.0781 Y : 0.0010

2 1.5 1

x 10

-4

SIMBO-Q QOSIMBO-Q

Voltage deviation (p.u.)

3 2.5

64 13 61

-3

3.5

Voltage deviation (p.u.)

0.9771

3.5

X : 0.0246 Y : 0.0002 X : 0.0259 Y : 0.0002

3

2.5

2

0.5 0 0.075

0.08

0.085

0.09

0.095

0.1

0.105

Active power loss (MW) Fig. 32. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 with DG operating at unity p.f. and maximum 100% DG penetration limit in 69 bus system.

1.5 0.022

0.024

0.026

0.028

0.03

0.032

0.034

0.036

0.038

0.04

Active power loss (MW) Fig. 33. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 4 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 69 bus system.

370

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 1.0236

1.09

SIMBO-Q QOSIMBO-Q

SIMBO-Q QOSIMBO-Q

1 / Voltage stability index

1 / Voltage stability index

1.08 1.07 X : 0.0797 Y : 1.0235

1.06

X : 0.0805 Y : 1.0235

1.05 1.04 1.03

1.0236 1.0236 X : 0.00025 Y : 1.0233

1.0235 1.0235

X : 0.00028 Y : 1.0233

1.0234 1.0234 1.0233

1.02 1.0233 2.2

1.01 0.075

0.08

0.085

0.09

2.4

2.6

0.095

2.8

3

3.2

3.4

3.6 x 10

Voltage deviation (p.u.)

-4

Active power loss (MW)

SIMBO-Q QOSIMBO-Q

1.0248

1 / Voltage stability index

Fig. 37. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 69 bus system.

1 / Voltage stability index

Fig. 34. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 with DG operating at unity p.f. and maximum 100% DG penetration limit in 69 bus system.

1.0246 1.0244 X : 0.0233 Y : 1.0234

1.0242 1.024

X : 0.0235 Y : 1.0234

1.0238 1.0236

1.06 1.05 X : 0.0798 Y : 0.0007 Z : 1.0235

1.04 1.03 1.02 4 3

1.0234 x 10

2

-3

1

1.0232 1.023 0.02

Voltage deviation (p.u.) 0.022

0.024 0.026

0.028

0.03

0.032 0.034

0.036 0.038

0 0.072

0.074

0.076

0.078

0.08

0.082

0.084

Active power loss (MW)

0.04

Active power loss (MW) Fig. 35. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 5 with DG operating at 0.95 lagging p.f. and maximum 100% penetration limit in 69 bus system.

Fig. 38. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at unity p.f. with maximum 100% DG penetration limit in 69 bus system.

SIMBO-Q QOSIMBO-Q

1.028 1.027 1.026 X : 0.00025 Y : 1.0235

1.025

X : 0.00027 Y : 1.0235

1 / Voltage stability index

1 / Voltage stability index

1.03 1.029

X : 0.0257 Y : 0.0002 Z : 1.0234

1.0235 1.0234 1.0234 1.0233 1.0233 6 4

1.024 1.5

x 10

2

2.5

3

3.5

Voltage deviation (p.u.)

4

4.5 -4 x 10

Fig. 36. Pareto-optimal front obtained by SIMBO-Q and QOSIMBO-Q algorithms for Case 6 with DG operating at unity p.f. and maximum 100% DG penetration limit in 69 bus system.

that QOSIMBO-Q algorithm converges faster than SIMBO-Q algorithm. Case 4: Loss minimization and voltage profile improvement: From Table 10 it is observed that by applying QOSIMBO-Q algorithm, the active power loss and voltage deviation are reduced to 0.0774 MW, 0.0010 p.u. with DG operating at unity power factor and 0.0246 MW, 0.0002 p.u. with DG operating at 0.95 lagging power factor, which show improved results than those obtained by SIMBO-Q algorithm. Figs. 32 and 33

-4

2

Voltage deviation (p.u.)

0 0.024 0.026

0.028

0.03

0.032

0.034

0.036

0.038

Active power loss (MW)

Fig. 39. Pareto-optimal front obtained by QOSIMBO-Q algorithm for Case 7 considering DG operating at 0.95 lagging p.f. with maximum 100% DG penetration limit in 69 bus system.

Table 12 Effect of population size on minimum value of objective function for loss minimization of 33 bus system using QOSIMBO-Q algorithm (for 300 iterations). Population No. of hits to size optimum solution

Simulation time Overall Objective function (f ) per iteration (sec) Minimum Maximum Average

20 50 100 150

0.0105 0.0224 0.0408 0.0552

0 0 50 18

0.07920 0.07390 0.07280 0.07280

0.07920 0.07390 0.07280 0.07300

0.07920 0.07390 0.07280 0.07293

371

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373 Table 13 Influence of QOSIMBO-Q parameters on objective function value for loss minimization of 33 bus system for population size = 100 (after 50 trails). Probability of Vaccination (l)

Probability of Quarantine (b)

Jumping rate (Jr )

Probability of Recovery (a) 0.1

0.2

0.3

0.4

0.5

l = 0.5

b = 0.5

0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9

0.0733 0.0734 0.0735 0.0736 0.0737 0.0735 0.0737 0.0739 0.0741 0.0742 0.0740 0.0738 0.0740 0.0742 0.0743 0.0745 0.0747 0.0744 0.0746 0.0747

0.0733 0.0735 0.0733 0.0737 0.0738 0.0736 0.0738 0.0740 0.0742 0.0744 0.0739 0.0740 0.0738 0.0742 0.0744 0.0743 0.0745 0.0744 0.0746 0.0748

0.0740 0.0742 0.0741 0.0744 0.0743 0.0738 0.0740 0.0739 0.0741 0.0743 0.0742 0.0741 0.0744 0.0746 0.0745 0.0746 0.0748 0.0745 0.0749 0.0747

0.0738 0.0740 0.0739 0.0741 0.0742 0.0741 0.0742 0.0744 0.0743 0.0745 0.0745 0.0743 0.0742 0.0746 0.0745 0.0745 0.0744 0.0745 0.0746 0.0748

0.0735 0.0737 0.0739 0.0740 0.0742 0.0742 0.0744 0.0743 0.0746 0.0745 0.0738 0.0740 0.0742 0.0741 0.0744 0.0744 0.0746 0.0743 0.0748 0.0749

0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9

0.0732 0.0734 0.0733 0.0736 0.0738 0.0735 0.0738 0.0734 0.0736 0.0737 0.0735 0.0737 0.0736 0.0738 0.0740 0.0736 0.0735 0.0733 0.0737 0.0738

0.0733 0.0735 0.0736 0.0738 0.0737 0.0737 0.0740 0.0738 0.0739 0.0738 0.0737 0.0739 0.0740 0.0740 0.0742 0.0735 0.0737 0.0734 0.0736 0.0738

0.0737 0.0736 0.0739 0.0740 0.0742 0.0739 0.0741 0.0740 0.0739 0.0741 0.0740 0.0742 0.0741 0.0744 0.0743 0.0736 0.0738 0.0739 0.0740 0.0741

0.0735 0.0738 0.0736 0.0739 0.0741 0.0741 0.0742 0.0740 0.0742 0.0743 0.0738 0.0739 0.0740 0.0741 0.0742 0.0738 0.0740 0.0741 0.0743 0.0743

0.0734 0.0734 0.0734 0.0734 0.0734 0.0742 0.0743 0.0740 0.0742 0.0743 0.0736 0.0738 0.0737 0.0739 0.0741 0.0740 0.0738 0.0741 0.0742 0.0743

0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9

0.0730 0.0730 0.0731 0.0733 0.0735 0.0731 0.0732 0.0735 0.0734 0.0735 0.0731 0.0733 0.0735 0.0736 0.0734 0.0734 0.0735 0.0738 0.0739 0.0738

0.0731 0.0728 0.0730 0.0733 0.0734 0.0730 0.0732 0.0730 0.0734 0.0733 0.0733 0.0734 0.0731 0.0732 0.0735 0.0736 0.0739 0.0734 0.0741 0.0740

0.0731 0.0730 0.0732 0.0734 0.0736 0.0733 0.0732 0.0734 0.0733 0.0736 0.0734 0.0733 0.0736 0.0737 0.0737 0.0737 0.0735 0.0734 0.0739 0.0742

0.0733 0.0735 0.0737 0.0736 0.0737 0.0734 0.0736 0.0734 0.0735 0.0737 0.0737 0.0739 0.0740 0.0738 0.0739 0.0742 0.0740 0.0740 0.0745 0.0747

0.0733 0.0733 0.0734 0.0735 0.0734 0.0736 0.0737 0.0734 0.0735 0.0737 0.0740 0.0741 0.0739 0.0743 0.0742 0.0742 0.0744 0.0742 0.0743 0.0746

0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9

0.0732 0.0734 0.0732 0.0735 0.0737 0.0737 0.0736 0.0739 0.0741 0.0743

0.0734 0.0735 0.0737 0.0739 0.0737 0.0738 0.0736 0.0737 0.0742 0.0744

0.0736 0.0737 0.0734 0.0739 0.0740 0.0736 0.0739 0.0734 0.0738 0.0743

0.0735 0.0735 0.0737 0.0738 0.0741 0.0738 0.0740 0.0739 0.0742 0.0746

0.0737 0.0739 0.0741 0.0740 0.0743 0.0740 0.0744 0.0742 0.0745 0.0747

b = 0.6

b = 0.8

b = 0.9

l = 0.6

b = 0.5

b = 0.6

b = 0.8

b = 0.9

l = 0.8

b = 0.5

b = 0.6

b = 0.8

b = 0.9

l = 0.9

b = 0.5

b = 0.6

(continued on next page)

372

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

Table 13 (continued) Probability of Vaccination (l)

Probability of Quarantine (b)

Jumping rate (Jr )

b = 0.8

0.1 0.3 0.5 0.7 0.9 0.1 0.3 0.5 0.7 0.9

b = 0.9

show the pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 4 with both types of DG. Case 5: Loss minimization and voltage stability index improvement: Table 10 shows that by applying QOSIMBO-Q algorithm, the active power loss and voltage stability index1 are reduced to 0.0797 MW, 1.0235 with DG operating at unity power factor and 0.0233 MW, 1.0234 respectively with DG operating at 0.95 lagging power factor, which are better than the results obtained by SIMBO-Q algorithm. The pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 5 with both types of DG are shown in Figs. 34 and 35. Case 6: Voltage profile and voltage stability index improvement: From Table 10 it is observed that the values of voltage deviation and voltage stability index1 obtained by QOSIMBO-Q algorithm are 0.00025 p.u., 1.0235 with DG operating at unity power factor, and 0.00025 p.u., 1.0233 with DG operating at 0.95 lagging power factor, which show much improved results than those obtained by SIMBO-Q algorithm. Figs. 36 and 37 show the pareto-optimal front graphs obtained by QOSIMBO-Q and SIMBO-Q algorithms for Case 6 with both types of DG. Case 7: Loss minimization, voltage profile and voltage stability index improvement: Table 11 shows that for Case 7 the active power loss, voltage deviation and voltage stability index values obtained using QOSIMBO-Q algorithm are 0.0798 MW, 0.0007 p.u., 0.9770 p.u. respectively with DG operating at unity power factor and 0.0257 MW, 0.0002 p.u., 0.9771 p.u. respectively with DG operating at 0.95 lagging power factor. Table 11 also shows that the results obtained by QOSIMBO-Q algorithm for Case 7 with both types of DG are better than the results obtained by SIMBO-Q, GA/PSO, GA, PSO, TLBO and QOTLBO algorithms. Also from the Table 11 it is observed that the simulation time taken per iteration by QOSIMBO-Q algorithm are 0.0478 s and 0.0507 s with both types of DG, which are much less compared to other algorithms. The pareto-optimal front graphs obtained by QOSIMBO-Q algorithm for Case 7 with both types of DG are shown in Figs. 38 and 39. So, overall performance improvement of 69 bus radial distribution network is better with QOSIMBO-Q algorithm compared to other techniques for minimization of active power loss, improvement of voltage profile and voltage stability index with DG operating at unity and 0.95 lagging power factors with maximum 100% DG penetration limit constraint.

Probability of Recovery (a) 0.1

0.2

0.3

0.4

0.5

0.0739 0.0740 0.0740 0.0743 0.0744 0.0744 0.0745 0.0747 0.0745 0.0749

0.0742 0.0743 0.0741 0.0745 0.0747 0.0746 0.0744 0.0744 0.0748 0.0750

0.0744 0.0742 0.0744 0.0745 0.0748 0.0748 0.0749 0.0747 0.0750 0.0748

0.0743 0.0745 0.0747 0.0745 0.0748 0.0746 0.0745 0.0746 0.0748 0.0750

0.0745 0.0746 0.0745 0.0748 0.0750 0.0747 0.0749 0.0748 0.0748 0.0749

Therefore, it may be concluded that the proposed QOSIMBO-Q algorithm is more efficient compared to GA/PSO, GA, PSO, TLBO, QOTLBO and SIMBO-Q algorithms for minimization of active power loss, maximization of the voltage stability index and improvement of voltage profile of 33 bus and 69 bus radial distribution networks by optimal placement and sizing of DG. Effect of population size on QOSIMBO-Q algorithm Table 12 shows the performance of QOSIMBO-Q algorithm for different population sizes to determine optimal placement and size of DG operating at unity power factor for minimizing the active power losses in the 33 bus radial distribution network. From the results it is clear that change in population size affects the performance of the QOSIMBO-Q algorithm. Tests are carried out 50 times for each case with 300 iteration numbers. It is observed from the results that for population size 20 and 50, number of hits to optimum solution is zero, whereas for population size 100 and 150, numbers of hits to optimum solution are 50 and 18 respectively. So from Table 12 it is clear that with population size 100, the number of hits to optimum solution is more than other population sizes. Also the simulation time per iteration for population size 100 is quite less (0.0408 s). By considering all these factors, a population size of 100 is considered as the best population size in achieving optimum solution with less computational time for both single objective and multi-objective optimization case studies. Tuning of parameters for QOSIMBO-Q algorithm The following procedure has been adopted to calculate optimum values of different probability factors used in QOSIMBO-Q algorithm. These probability factors are probability of recovery (a), probability of quarantine (b), probability of vaccination (l) r and jumping rate (j ). The value of probability of recovery (a) is kept too small to recover most of the individuals. The probability of quarantine (b) is kept high so that less number of individual are isolated from the population. Similarly the probability of vaccination (l) is kept high so that less number of individual will r change their state directly. Jumping rate (j ) is chosen within (0,1). Different population sizes used in this paper are 20, 50, 100 and 150. For each population size the probability of recovery (a) is increased from 0.1 to 0.5 in steps of 0.1 and probability of quarantine (b) and probability of vaccination (l) are increased from 0.5 r to 0.9 in steps of 0.1 and jumping rate (j ) is varied from 0.1 to 0.9. Performance of QOSIMBO-Q algorithm for optimum placement and sizing of DG operating at unity power factor to minimize active power loss is evaluated for all the above mentioned combinations.

S. Sharma et al. / Electrical Power and Energy Systems 74 (2016) 348–373

50 independent trials have been made with 300 iterations per trail. Based on the minimum value of 50 trails, the objective function values obtained for optimal placement and sizing of DG for minimizing the active power losses of the 33 bus radial distribution network for different values of parameters, are shown in Table 13. However, to present all these results in a single table takes lots of space. Therefore the tuning results obtained with the best population size 100 are only shown in the Table 13. Results show that probability of recovery (a) 0.2, probability of quarantine (b) 0.5, r probability of vaccination (l) 0.8 and jumping rate (j ) 0.3 give the minimum active power loss of 0.0728 MW. So these parameter values are used for all the seven case studies performed in both the test systems reported in this paper. Conclusion In this paper QOSIMBO-Q algorithm has been applied to determine optimum location and size of DG in 33-bus and 69-bus radial distribution networks to minimize the active power loss, to increase the voltage stability and to improve the voltage regulation index of the network. Results obtained using the proposed QOSIMBO-Q algorithm have been compared with the results obtained by other evolutionary algorithms like GA, PSO, combined GA/PSO, TLBO, QOTLBO and SIMBO-Q. Analysis shows that QOSIMBO-Q algorithm is able to find the improved quality solutions for those systems, with superior computational efficiency. From the comparison of simulation results and convergence characteristics obtained with QOSIMBO-Q algorithm, it may be concluded that the algorithm exhibits a higher capability in finding optimum size and location of DG in radial distribution systems. References [1] Ackermann T, Andersson G, So’’der L. Distributed generation: a definition. Electric Power Syst Res 2001;57(3):195–204. [2] Abookazemi K, Hassan MY, Majid MS. A review on optimal placement of distribution generation sources. IEEE Int Conf Power Energy 2010;1:712–6. [3] Singh B, Verma KS, Singh D, Singh SN. A novel approach for optimal placement of distributed generation and FACTS controllers in power system: an overview and key issues. Int J Rev Comput 2011;7:29–54. ISSN: 2076-3328. [4] Ugranli F, Karatepe E. Convergence of rule of thumb sizing and allocating rules of distributed generation in meshed power networks. Renew Sustain Energy Rev 2012;16(1):582–90. [5] Einashar Mohab M, Shatshat Ramadan Ei, Salama Magdy MA. Optimum sitting and sizing of a large distributed generator in a mesh connected system. Electric Power Syst Res 2010;80(6). [6] Ghosh S, Ghosal SP, Ghosh S. Optimum sizing and placement of distributed generation in a network system. Electrical Power Energy Syst 2010;32(8):849–56. [7] Singh RK, Goswami SK. Optimum allocation of distributed generations based on nodal pricing for profit, loss reduction and voltage improvement including voltage rise issue. Electric Power Energy Syst 2010;32(6):637–44. [8] Gozel T, Hocaoglu MH. An analytical method for the sizing and placement of distributed generators in radial systems. Electric Power Syst Res 2009;79(6):912–8. [9] Acharya N, Mahat P, Mithulananthan N. An analytical approach for DG allocation in primary distribution network. Electrical Power Energy Syst 2006;28(10):669–78. [10] Willis HL. Analytical methods and rules of thumb for modeling DGdistribution interaction. IEEE power engineering society summer meeting, vol. 3; 2000. p. 1643–4. [11] Koutroumpezis GN, Safigianni AS. Optimum allocation of the maximum possible distributed generation penetration in a distribution network. Electric Power System Research 2010;80(12):1421–7. [12] Hosseini RK, Kazemzadeh R. Optimal DG allocation by extending an analytical method to minimize losses in radial distribution systems. In: 2011 19th Iranian conference on electrical engineering (ICEE); May 2011. p. 1. [13] Kazemi A, Sadeghi M. Distributed generation allocation for loss reduction and voltage improvement. In: IEEE Power and Energy Engineering Conference, 2009 (APPEEC 2009). Asia-Pacific; March 2009. p. 1–6.

373

[14] Moradi MH, Abedinie M, Tolabi HB. Optimal multi-distributed generation location and capacity by Genetic algorithm. In: 4th International power engineering and optimization conf. (PEOCO2010). IEEE; 2010. p. 440–4. [15] Aliabadi MH, Behbahani B, Jalilvand A. Combination of GA and OPF for allocation and active and reactive power optimization in distributed generation units. In: 2nd IEEE international conference on power and energy (PECon 08). IEEE; 2008. p. 1541–4. [16] Gomez M-Gonzalez, Lopez A, Jurado F. Optimization of distributed generation systems using a new discrete PSO and OPF. Electric Power Syst Res 2012;84(1):174–80. [17] Moradi MH, Abedini M. A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems. Electrical Power Energy Syst 2012;34(1):66–74. [18] Sultana S, Roy PK. Multi-objective quasi-oppositional teaching learning based optimization for optimal location of distributed generator in radial distribution systems. Int J Electrical Power Energy Syst 2014;63(1):534–45. [19] Moradi MH, Reza Tousi SM, Abedini M. Multi-objective PFDE algorithm for solving the optimal siting and sizing problem of multiple DG sources. Electrical Power Energy Syst 2014;56(1):117–26. [20] Esmaili M, Firozjaee EC, Shayanfar HA. Optimal placement of distributed generations considering voltage stability and power losses with observing voltage-related constraints. Appl Energy 2014;113(1):1252–60. [21] Ishak R, Mohamed A, Abdalla AN, Wanik MZC. Optimal placement and sizing of distributed generators based on a novel MPSI index. Electr Power Energy Syst 2014;60(1):389–98. [22] Aman MM, Jasmon GB, Bakar AHA, Mokhlis H. A new approach for optimum simultaneous multi-DG distributed generation Units placement and sizing based on maximization of system loadability using HPSO (hybrid particle swarm optimization) algorithm. Energy 2014;66(1):202–15. [23] Devi S, Geethanjali M. Application of modified bacterial foraging optimization algorithm for optimal placement and sizing of distributed generation. Expert Syst Appl 2014;41(6):2772–81. [24] El-Fergany A. Optimal allocation of multi-type distributed generators using backtracking search optimization algorithm. Electrical Power Energy Syst 2015;64(1):1197–205. [25] Mohandas N, Balamurugan R, Lakshminarasimman L. Optimal location and sizing of real power DG units to improve the voltage stability in the distribution system using ABC algorithm united with chaos. Electrical Power Energy Syst 2015;66(1):41–52. [26] Falaghi H, Haghifam MR. ACO based algorithm for distributed generation sources allocation and sizing in distribution networks. IEEE lausanne power tech 2007; 2007. p. 5–560. [27] Khalesi N, Rezaei N, Haghifam MR. DG allocation with application of dynamic programming for loss reduction and reliability improvement. Electrical Power Energy Syst 2011;33(2):288–95. [28] Pattnaik SS, Bakwad KM, Sohi BS, Ratho RK, Devi S. Swine influenza models based optimization (SIMBO). Appl Soft Comput 2013;13(1):628–53. [29] Chakravorty M, Das D. Voltage stability analysis of radial distribution networks. Int J Electr Power Energy Syst 2001;23(2):pp–135. [30] Vovos PN, Bialek JW. Direct incorporation of fault level constraints in optimal power flow as a tool for network capacity analysis. IEEE Trans Power Syst 2005;20(4):2125–34. [31] Tizhoosh H. Opposition-based learning: a new scheme for machine intelligence. In: International conference on computational intelligence for modeling control and automation, Austria; November 2005. p. 695-01. [32] Wang H, Wu ZJ, Rahnamayan S, Liu Y, Ventresca M. Enhancing particle swarm optimization using generalized opposition-based learning. Inform Sci 2011;181(20):4699–714. [33] Roy PK, Mandal D. Oppositional biogeography-based optimization for optimal power flow. Int J Power Energy Convers 2014;5(1):47–69. [34] Qingzheng X, Lei W, Baomin H, Na W. Modified opposition-based differential evolution for function optimization. J Comput Inform Syst 2011:1582–91. [35] Simon D, Ergezer M, Du D. Oppositional biogeography-based optimization. . [36] Roy PK, Mandal D. Quasi-oppositional biogeography-based optimization for multi-objective optimal power flow. Electric Power Compon Syst 2011;40(2):236–56. [37] Rahnamayan S, Tizhoosh HR, Salalma MMA. Quasi oppositional differential evolution. In: Proceeding of IEEE congress on evolutionary computation, CEC 2007, Singapore, 25th–28th September; 2007. p. 2229–36. [38] Mandal B, Roy PK. Optimal reactive power dispatch using quasi-oppositional teaching learning based optimization. Int J Electr Power Energy Syst 2013;53:123–34. [39] Kashem MA, Ganapathy V, Jasmon GB, Buhari MI. A novel method for loss minimization in distribution networks. In: International conference on electric utility deregulation and restructuring and power technologies 2000, City University, London; 4–7 April 2000. p. 251–6. [40] Murthy KK, Jaya Ram Kumar SV. Three-phase unbalanced radial distribution load flow method. Int Referred J Eng Sci 2012;1(1):039–42.