Multi-Objective Hybrid WIPSO–GSA Algorithm-Based DG and Capacitor Planning for Reduction of Power Loss and Voltage Deviation in Distribution System

Abstract In electric distribution system, majority of load connected are inductive in nature and it results in increased system power loss and reduced bus voltage profile. In this study, in order to overcome these issues, optimal planning of DG and capacitor are presented by optimizing multiple objectives such as minimization of total active power loss (P loss total ) and reduction of voltage deviation (VD). Here, a hybrid configuration of weight improved particle swarm optimization (WIPSO) and gravitational search algorithm (GSA) called hybrid WIPSO–GSA algorithm is proposed to solve the optimization problem in multi-objective problem domain. In order to solve multi-objective optimization problem, the proposed hybrid WIPSO–GSA algorithm is integrated with two components. The first component is fixed-sized archive that is responsible for storing a set of non-dominated Pareto optimal solutions and the second component is a leader selection strategy that helps to update and identify the best compromised solution from the archive. The proposed methodology is tested on standard 33-bus and Indian 85-bus distribution system. Moreover, the total economic benefit due to optimal DG and capacitor planning are established and also the superiority of the proposed technique is illustrated by comparing the results with other existing optimization techniques.


Introduction
The distribution system is mainly responsible for reliable and quality supply of power to end customers and it is operated at low voltage when compared to high-voltage transmission system. Mostly distribution network is operating at lagging power factor since majority of loads connected to the distribution network are inductive in nature. The lag in load power factor causes wide range of technical issues such as enhanced network power loss and reduced bus voltage profiles. In order to overcome these technical issues compensation devices such as DG and capacitor are installed in distribution network. Generally, DG is a small-scale power generation unit that is usually connected closer to load in the distribution system and it has a significant impact on quality and reliable of power to the end consumers. In power systems, different DG technologies are involved in which some have been in use for a long time, while others are newly emerging. The two main categories of DG technologies are renewable DG technologies (e.g. photovoltaic and wind turbine) and non-renewable chaotic ABC (CABC) algorithm [22], and TLBO technique [23]. However, in [20][21][22][23], the weights assigned to different objectives are predefined resulting in unequal priority in optimizing different objectives. To overcome this problem multiple objectives are solved simultaneously by attaining non-dominated Pareto optimal solutions using optimization techniques such as non-dominated sorting GA (NSGA) [24], multi-objective PSO (MOPSO) [25], non-dominated sorting modified cuckoo search algorithm (NSMCSA) [26], and peer-enhanced multi-objective TLBO (PeMOTLBO) [27] for optimal planning of compensation devices in distribution network.
In this study, minimization of P loss total and reduction of VD objective functions are optimized to optimally allocate DG and capacitor in distribution network. Also, a novel multi-objective hybrid WIPSO-GSA algorithm is proposed to solve the multi-objective optimization problem. The main advantage of using hybrid optimization technique over non-hybrid is that, it will produce better optimization results by combining the strength of two optimization algorithms. In the proposed multi-objective hybrid WIPSO-GSA algorithm the hybridization is done by merging the skill of local search capability in GSA with the skill of social thinking in WIPSO. The proposed multi-objective hybrid WIPSO-GSA algorithm provides a set of non-dominated Pareto optimal solutions by simultaneously optimizing different objective functions and the best compromised solution is identified using a leader selection strategy that provides optimal location and sizing of DG and capacitor in distribution network. Here, DG supplying active power alone is considered along with capacitor. Moreover, the economic benefits achieved through optimal DG and capacitor installations are also established considering essential economic factors for the total planning period. The effectiveness of the proposed multi-objective hybrid algorithm is also demonstrated by comparing the results with other existing optimization techniques. The remainder of the paper is structured as follows: Section 2 contains problem formulation with necessary technical constraints and expressions to evaluate total economic benefit. Section 3 describes the concept behind hybrid WIPSO-GSA algorithm and implementation of proposed multi-objective hybrid WIPSO-GSA algorithm. Section 4 contains simulation results followed by conclusions.

Distribution Load Flow (DLF)
In any DG and capacitor placement problem, DLF analysis plays a vital role in the solution process. In this study, backward sweep and forward sweep method of DLF [28] is used in order to achieve accurate results. DG technologies (e.g. fuel cells, micro-turbines, and combustion turbines). The review over basic DG definition, potential DG benefits and various DG technologies were presented in [1,2]. The installation of DG and capacitor in distribution network has various technical and economic benefits and their positive impacts on distribution system operation are being analyzed. Even though the integration of DG and capacitor provides various benefits, they may impose certain problems and limitations if they are not optimally planned at appropriate bus location and capacity (i.e. size) in the distribution network. Since installation of compensation devices in distribution system is an optimization problem, several approaches were employed in literature for optimal location and sizing of compensation devices in distribution system. In [3,4], optimal capacitor installation problem was solved using analytical method and in [5,6], analytical methods were also used for optimal installation of DG in distribution network. Even though analytical methods were used to solve capacitor and DG allocation problem, they require complex calculations and formulation of impedance bus matrix. To overcome these problems artificial intelligent techniques are generally used. In recent years, there has been a significant interest among researchers in using artificial intelligent techniques. In [7][8][9], optimal capacitor allocation problem was addressed using particle swarm optimization (PSO) [7], plant growth simulation algorithm (PGSA) [8], and teaching learning-based optimization (TLBO) [9]. In [10][11][12][13][14], optimal DG allocation problem was solved using genetic algorithm (GA) [10], shuffled frog leap algorithm (SFLA) [11], artificial bee colony (ABC) algorithm [12], intelligent water drop algorithm [13], and combination of improved-PSO and gravitational search algorithm (GSA) [14]. In [15][16][17], optimal simultaneous DG and capacitor allocation problem was addressed using bacterial foraging optimization algorithm (BFOA) [15], intersect mutation differential evolution (IMDE) algorithm [16], and gbestguided ABC (GABC) algorithm [17].
The studies addressed in [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] utilize minimization of P loss total as main objective and also minimization of total operation cost is another single objective commonly used for allocating compensation devices in distribution network [18,19]. In the single objective DG and capacitor planning problem, the solutions attained optimizes only one objective function, whereas the other important factors involved are left unattended. In order to overcome this drawback, multiple objectives can be solved simultaneously using multi-objective optimization methodologies. In [20][21][22][23], different objectives were combined into a single scalar objective optimization problem using weight sum method and the optimization problem was solved using combination of GA and PSO algorithm [20], sequential quadratic programming deterministic technique [21],

Multi-Objective Problem Formulation
In order to find trade-off solutions among different objectives, a Pareto-based multi-objective technique is used. In this study, the objective functions to be optimized are minimization of P loss total and reduction of VD. Mathematically, the objective functions are formulated as follows:

Minimization of P loss total
For N bus radial distribution system, minimization of P loss total problem is formulated as follows: where P SS total is the injected active power at bus 1 from the substation; P DG(a) is the active power output of a th DG unit; P load(i) is the active power load connected at bus i; ndg is the total number of DG units installed in the distribution network; N bus is the total number of buses in the distribution network.

Minimization of VD
For N bus radial distribution system, minimization of VD problem is formulated as follows [27]: where V i is the voltage magnitude of bus i in p.u.; V rated is the rated voltage magnitude and it is taken as 1 p.u.

Technical Constraints
The objective functions formulated are optimized subjected to the following technical constraints:

Power Limits of DG and Capacitor
(1) where P DG min and P DG max are the lower and upper total active power generation limits of DG units, respectively; Q Cap min and Q Cap max are the lower and upper total reactive power generation limits of capacitors, respectively; Q Cap(b) is the reactive power output of b th capacitor; P load(i) and Q load(i) are the active and reactive power load connected at bus i, respectively; ncap is the total number of capacitors installed in the distribution network. In order to maintain quality and reliable supply of power to end consumers and also to achieve potential economic benefit, minimized power loss, and reduced voltage deviation, 80% of system total active load is taken as the upper limit for active power generation of total installed DG units and 80% of system total reactive power load is taken as the upper limit for reactive power generation of total installed capacitors [12].

Bus Voltage Limits
where V min and V max are the lower and upper limits of bus voltage magnitude, respectively; V i is the voltage at bus i. Here, the lower and upper limits of bus voltage magnitude are taken as 0.90 p.u. and 1.05 p.u., respectively [5].

Economic Benefit Evaluation of DG and Capacitor
In this study, all the costs are expressed in Indian Rupee (₹). The mathematical formulation involving different DG and capacitor cost terminologies for the total planning period is presented as follows [25]:

DG and Capacitor Investment Cost
Here, the investment cost includes DG unit cost, site for installing DG, equipment, monitoring, and construction. The investment cost of DG (C IDG ) is evaluated by: where IC DG is the installation cost of DG in ₹/MW.
where P SS total,aft.loc is the injected active power (in MW) at bus 1 from the substation after DG and capacitor location.
After optimal DG and capacitor installation, the cost benefit due to reduction in cost of energy purchased from the substation including energy loss (C SS pp,benefit ) for the total planning period is evaluated by subtracting (16) from (15) and it is expressed as follows: The total economic benefit after considering various DG and capacitor cost terminologies for the total planning period (Total benefit pp ) is given by:

Solution Technique
In recent years there has been several heuristic evolutionary optimization techniques developed and the main aim of all these techniques is to achieve best solution (i.e. global optimum) amid all possible inputs. In order to achieve global optimum a heuristic technique should have two main features such as exploration and exploitation. For any heuristic technique, the ability to search the whole problem space is termed as exploration and the convergence ability to achieve global optimum near a good solution is termed as exploitation. In order to achieve global optimum, the ultimate aim of any heuristic optimization technique is to find the fine balance between the ability of exploration and exploitation. According to [29], the strengthening of either one ability will weaken the other and vice versa. Thus, the previously mentioned features make the existing heuristic optimization techniques capable of solving only finite set of problems. Merging the strength of optimization techniques is one of the best possible ways to find balance between overall exploration and exploitation abilities. Therefore, in order to maintain good balance between exploration and exploitation abilities, the authors are motivated to hybrid WIPSO and GSA in this study.

Hybrid WIPSO-GSA Algorithm
PSO proposed by Kennedy [30] has attracted many researchers owing to its simplicity thereby making it one of the most widely used optimization technique in hybrid The investment cost of capacitor (C ICap ) is evaluated by: where IC Cap is the installation cost of capacitor in ₹/MVAr.

Operational and Maintenance Cost of DG and Capacitor
Here, the operational and maintenance cost includes fuel cost, renovation cost, and electrical and mechanical annual inquiry. The DG operational and maintenance cost (C OMDG pp ) for the total planning period is given by: and the capacitor maintenance (C MCap pp ) cost for the total planning period is evaluated as: where PWF is the present worth factor for the total planning period and it is formulated as follows: InfR is the inflation rate; IntR is the interest rate; P DG(a) is the operating active power output of a th DG unit (MW); OC DG and MC DG is the operational cost (₹/MWh) and annual maintenance cost (₹/year) of DG, respectively; MC Cap is the annual maintenance cost (₹/year) of capacitor; T is the total number of operating hours in a year (T = 8760); pp is the total planning period (in years).

Economic Benefit
The purchased cost of energy from the substation including energy loss before DG and capacitor location (C SS pp,bef.loc ) for the total planning period is given by: where K SS is the grid electricity price in ₹/MWh; P SS total,bef.loc is the injected active power (in MW) at bus 1 from the substation before DG and capacitor location.
By optimally installing DG and capacitor, the distribution companies can supply portion of system power demand and also compensates system power loss. The purchased cost of energy from the substation including energy loss after DG and capacitor location (C SS pp,aft.loc ) for the total planning period is given by: where x l d is the current position vector of particle l in a D-dimensional search space; v l d is the velocity vector of particle l in a D-dimensional search space; N p is the total number of particles; k is the current iteration number; Iter max is the total number of iterations; rand 1 , rand 2 , and rand 3 are the random numbers between 0 and 1; x gbest d is the gbest of particle group until iteration k; acc l d (k) is the acceleration of particle l and it is evaluated using expression given in equation (25); F l d (k) is the resultant force acting on particle l acquired from every other particles in the search space; M l (k) is the inertia mass proportional to the fitness of particle l. The expressions to evaluate F l d (k) and M l (k) are given in [34].
In classical PSO [30] and also in hybrid methods involving PSO [20,31,32], a fixed value (usually fixed to 2) is assigned for acceleration coefficients c 1 (cognitive component) and c 2 (social component). The fixed value of c 1 and c 2 will result in less accurate results and occurrence of premature convergence [33]. Therefore, quality solution is achieved using proposed hybrid WIPSO-GSA algorithm by modifying c 1 and c 2 in an adaptive way such that c 1 is decreased and c 2 is increased as the iteration proceeds [33], so that adaptive weights can be assigned to exploration and exploitation abilities thereby resulting in better global optimum and greater convergence speed. Therefore, the new modified c 1 and c 2 is represented as c 1new and c 2new and are formulated as shown in (23) and (24), respectively, where c 1initial and c 1final are the initial and final values of cognitive component, respectively; c 2initial and c 2final are the initial and final values of social component, respectively.

Multi-Objective Hybrid WIPSO-GSA Algorithm
The multi-objective hybrid WIPSO-GSA algorithm almost inherits all the basic features of hybrid WIPSO-GSA algorithm, which means the search space is being explored and exploited by the search agents in a same manner. However, the main difference is that, multi-objective hybrid WIPSO-GSA algorithm searches around a set of non-dominated Pareto optimal solutions stored in the archive, whereas the hybrid WIPSO-GSA algorithm only saves and improves one global optimum. In this study, in order to accomplish multi-objective optimization by hybrid WIPSO-GSA technique, two new components are integrated and they are very similar to (24) methods [20,31,32]. However, classical PSO has certain drawbacks such as it suffers from premature convergence while solving complex problems and also it relies on users to alter control parameters [19,33]. Therefore, the classical PSO is enhanced to WIPSO [33] by modifying PSO parameters adaptively without changing the inherent structure of the algorithm. GSA proposed by Rashedi [34] is a heuristic optimization technique and it is inspired from Newton's theory of law of gravity. In GSA, agents contain the candidate solutions and they have masses proportional to their fitness value. In terms of exploration ability, in WIPSO, even though the weight and acceleration coefficients are modified in an adaptive way, the involvement of pbest (local best position) alone in exploration will cause premature local optimum [31], whereas in GSA better exploration can be achieved by considering agent's mass along with overall force acquired from every other masses [34]. In terms of exploitation ability, in WIPSO, the involvement of gbest (global best position) provides greater exploitation ability [31], whereas in GSA, its 'memory-less' nature [35] have adverse effect on exploitation ability resulting in higher convergence time when nearing global optimum. Therefore, in this study, in order to achieve fine balance between exploration and exploitation ability, hybridization is done between WIPSO and GSA by merging the strength of exploration in GSA with the strength of exploitation in WIPSO. In other words, the strength of local search capability in GSA is merged with the strength of social thinking in WIPSO so as to achieve better global optimum and greater convergence speed. Therefore, in hybrid WIPSO-GSA algorithm, the velocity update (v l d (k + 1)) and position update (x l d (k + 1)) expressions of particle l is given by: Iter max ) × k selection mechanism. In hybrid WIPSO-GSA algorithm, gbest guides the other agents in the search space toward the global optimum. However, in a multi-objective search space, it is difficult to compare solutions owing to the Pareto optimality concepts discussed earlier. Therefore, in order to handle this issue the leader selection mechanism is used. The main feature of leader selection mechanism is to choose a leader from the set of best non-dominated Pareto optimal solutions stored in the archive. For this purpose, the least crowded segment of the archive is chosen by the leader selection component and one of its non-dominated solutions is considered as the leader. Here, the selection is done by the roulette-wheel method with the probability for hypercube h (i.e. prob h ) is formulated as follows: where const is a constant number greater than one; N h is the total number of obtained non-dominated Pareto optimal solutions in segment h. From (26), it can be seen that segments that are less crowded have higher probability of signifying new leaders. In other words, the probability of picking a segment to select a leader is increased when the number of attained solutions is decreased in the segment. In this study, the multi-objective optimization problem to solve two different objectives is mathematically formulated as follows: where F is the vector of objective functions; X is the decision variable for particles in the search space.
In multi-objective hybrid WIPSO-GSA algorithm, generally there is not one global optimum, but contains a set of so called non-dominated Pareto optimal solutions. Non-dominated solution is the one which is not dominated by any other solution and are located in the archive. A decision vector x 1 dominates vector x 2 if: where N obj is the total objective functions considered in the problem; x 1 and x 2 are the D-dimensional decision vectors, containing DG location (DG loc ) and DG size (DG size ) and also capacitor location (Cap loc ) and capacitor size (Cap size ) as shown in (30) and (31): The key component of the archive is an archive controller. The archive has a fixed number of members and the main feature of the archive controller is to control the archive when the archive is full or when a new solution wants to enter the archive. Once the archive is full, a mechanism called adaptive grid mechanism is triggered. The main role of the grid mechanism is to keep the solutions in the archive as diverse as possible when the archive is full. In the grid mechanism, the objective space is divided into several regions called hypercube (i.e. segment). If a newly attained solution occupies a space outside the grid, then the locations of the grid should be re-evaluated to accommodate the new solution. If a newly attained solution occupies a space within the grid, then it is accommodated to the segment of the grid that have lower number of particles by randomly omitting one of the resident in the most crowded segment. The main advantage of using grid mechanism is low computational cost and it does not require complete grid updating in each and every iteration like in the case of niching [37].
In power load, respectively, thereby resulting in reduced flow of active and reactive power through distribution feeder sections. Here, the reduced flow of both active and reactive power results in reduced flow of active and reactive current component through distribution feeder sections, respectively, which in turn provides a significant reduction of system power loss when compared to independent DG and capacitor installation cases. Moreover, in Case-3, the additional reactive power support from capacitor = 20; Iter max (total number of iterations) = 150; G 0 (gravitational constant) = 1; α (descending coefficient) = 23; c 1initial = 0.6; c 1final = 0.4; c 2initial = 1.4; c 2final = 1.6.

Numerical Results and Discussions
In this study, a standard 33-bus radial distribution system with 32 feeder sections [38] and an Indian 85-bus radial distribution system with 84 feeder sections [39] are considered. For 33-bus system, the total active and reactive power load is 3.72 MW and 2.3 MVAr, respectively. For Indian 85-bus system, the total active and reactive power load is 2.55 MW and 2.60 MVAr, respectively. The base kVs for standard 33-bus and Indian 85-bus system is 12.66 kV and 11.00 kV, respectively. The optimization process using the proposed multi-objective hybrid WIPSO-GSA algorithm is carried out in MATLAB environment. Here, DG operating at unity power factor (i.e. injecting active power alone) is considered along with capacitor. The different DG and capacitor installation cases are listed as follows: • Case-1: Multiple installation of capacitor. • Case-2: Multiple installation of DG. • Case-3: Simultaneous multiple installation of DG and capacitor.
The non-dominated Pareto optimal solutions of proposed multi-objective hybrid WIPSO-GSA algorithm for different DG and capacitor installation cases are shown in Figures 2 and 3 for standard 33-bus and Indian 85-bus system, respectively. In the set of non-dominated Pareto optimal solutions attained from the proposed multi-objective hybrid WIPSO-GSA algorithm, the best compromise solution is determined using leader selection mechanism and is tabulated in Tables 1 and 2 for standard 33-bus and Indian 85-bus system respectively. The value of P loss total and VD without installing any DG and capacitor (i.e. base case) is 210.9983 kW and 0.1338 p.u., respectively, for standard 33-bus system and it is 311.4151 kW and 0.8102 p.u., respectively, for Indian 85-bus distribution system. In both standard 33-bus and Indian 85-bus system, among independent DG and capacitor installation cases, it is observed that independent installation of DG (i.e. Case-2) which compensates portion of system active power load alone results in significant reduction of P loss total and VD when compared to independent installation of capacitor (i.e. Case-1) that supports portion of system reactive power load alone. In both standard 33-bus and Indian 85-bus system, it is observed that, there is considerable amount of reactive power load in addition to active power load. Therefore, in such system conditions, simultaneous installation of DG and capacitor at multiple bus locations (i.e. Case-3) supplies portion of system active and reactive only restriction in capacitor installation cases (i.e. Case-1 and Case-3) is that the capacitors are available in fixed sizes only. This restriction can be overcome by cascading the capacitors in parallel in order to attain the required size at appropriate bus locations. The enhancement in bus voltage magnitude for different installation cases are shown in Figures 4 and 5 for standard 33-bus and Indian 85-bus system, respectively. From Figures 4 and 5, it is evident that Case-3 which supplies portion of system active and reactive power load results in enhanced bus voltage profiles at majority of buses when compared to other installation cases.
Determining suitable location and size of DG and capacitor in radial distribution system is significant for achieving potential technical benefits. However, apart from the technical benefits, the optimal DG and capacitor installations also yields greater economic benefits for distribution companies for the total planning period. The commercial information of DG and capacitor are taken from [40] and all the costs are expressed in Indian Rupee (₹). The values of various cost terminologies involved are: K SS = 5000 (₹/ MWh); IC DG = 25 x 10 6 (₹/MW); IC Cap = 100 x 10 3 (₹/ MVAr); OC DG = 2.5 x 10 3 (₹/MWh); MC DG = 10000 + 20% of IC DG (₹/year); MC Cap = 5000 + 20% of IC Cap (₹/year); InfR = 9%; IntR = 12.5%; pp = 10 (years). After optimal DG and capacitor installation, the reduction in cost of energy purchased from the substation including energy loss and the total cost benefit after considering various DG and capacitor cost terminologies that are evaluated using expressions given in (15), (16), (17), and (18) are presented in Tables 3 and 4 for standard 33-bus and Indian 85-bus system, respectively. From Tables 3 and 4, among different DG and capacitor installation cases, it is evident that Case-3 provides greater economic benefit followed by Case-2 and Case-1, respectively, in both standard 33-bus and Indian 85-bus system.
Finally, in order to show the computational supremacy of proposed multi-objective hybrid WIPSO-GSA algorithm over other existing techniques, comparison is made with literature that uses same case study. The best compromised solution of existing techniques and the proposed multi-objective hybrid WIPSO-GSA algorithm for different DG and capacitor installation cases are tabulated in Tables 5 and 6 for standard 33-bus and Indian 85-bus system, respectively. From Tables 5 and  6, it is perceived that, the proposed technique provides at appropriate multiple bus locations along with active power compensation by DG provides much reduced voltage deviation when compared to Case-2 and Case-1. The     1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

Base case
Case-1 Case-2 Case-3 Figure 5. Voltage profile at each bus for indian 85-bus distribution system. Table 3. total economic benefit results for standard 33-bus distribution system.

Disclosure Statement
No potential conflict of interest was reported by the authors.
proposed multi-objective hybrid WIPSO-GSA technique highly suitable for solving multi-objective optimization problems, thereby resulting in best compromised optimal planning of DG and capacitor in distribution network.

Conclusion
The proposed novel multi-objective hybrid WIPSO-GSA algorithm is employed to determine a set of non-dominated Pareto optimal solutions for optimal planning of DG and capacitor in distribution network and the leader selection strategy has been used to identify the best compromised location and sizing of DG and capacitor in distribution network. From the simulation results, it is concluded that the best compromised optimal DG and capacitor planning using the proposed multi-objective hybrid WIPSO-GSA algorithm results in reduction of P loss total and VD. Apart from technical benefits, the