Optimal Solar Photovoltaic Placement as a Distributed Generation in Radial Distribution Networks using Particle Swarm Optimization

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1 Nigerian Journal of Solar Energy, Vol. 26, Solar Energy Society of Nigeria (SESN) All rights reserved. Optimal Solar Photovoltaic as a Distributed Generation in Radial Distribution Networks using Particle Swarm Optimization Lawal, S. M.,* Shehu R.S. and Yusuf, A.B. Electrical and Electronic Engineering Department, College of Engineering, Kaduna Polytechnic, Kaduna-Nigeria. Abstract - The optimal solar photovoltaic placement as a distributed generation (DG) in radial distribution networks using particle swarm optimization was investigated. The optimal placement and sizing of Solar Photovoltaic (as a DG) problem is formulated as a constraint nonlinear optimization problem with both locations and sizes of solar photovoltaic being continuous. The objective functions adopted in this paper are the total active power loss function and voltage deviation function. The multiple nature of the problem, made it necessary to form a multi-objective function in search of the solution that consist of both the location and size. The output indicates that Particle Swarm Optimization (PSO) algorithm technique shows an edge over other types of search methods due to its effectiveness and computational efficiency. The proposed method was tested on the standard IEEE 34-bus and validated with 33- bus test systems distribution networks. Results indicate that the sizing and location of Solar Photovoltaic DG are system dependent and should be optimally selected before installing the solar photovoltaic system as a distributed generator in the network. The optimal placement of DG location and best sizes, improved the voltages profile of the network while power losses reduced substantially. Keywords: Solar Photovoltaic System, Distributed Generation, Particle Swarm Optimization, Power Loss, Voltage Deviation 1.0 INTRODUCTION In a conventional power system, the electrical power generation unit is expected to function as reliable as possible in both voltage and frequency stability of the network. This is to avoid all unnecessary disturbances which can jeopardize the electrical system performance (El-Hawary, 2008). The transmission aspect of power system network transfers the bulk energy generated through a long distance to the distribution network. It uses the interconnected neighboring utility that allows the economic dispatch of power within regions during normal conditions (El-Hawary, 2008). The distribution system otherwise known as medium or low voltage systems transfer the energy to the consumer or load centers as the end user. These voltages are transferred based on the nominal voltage of the energy generated. This type of generation is called the conventional or centralized system of electrical power generation. The generation plant can be thermal power, hydro power station, nuclear power station etc. But due to general concern for the environment and also conservation of fossil fuels. Alternative sources are now being considered so as to preserve and minimize the negative impact caused by these conventional power generating plants to the environment. This alternative source of power generation option is known as Distributed Generation as mentioned in Lawal et al, (2015). *Corresponding author Tel: sanimlawal@gmail.com 84 Distributed Generation (DG) has become one of the options in electrical power provision in order to curtail or reduce the problems posed by the conventional power systems. As DG is becoming increasingly popular with high level of acceptability, the problem of optimum placement of the DG in the distribution networks with the correct capacity are the main challenges for power utilities (Satish et al., 2011). A number of works have been reported in this area of optimal location and sizing in power system using different optimization techniques. A good number of publications have looked at optimizing the location and sizing of DG based on different criteria. In (Celli and Pilo 2001), the authors employed Genetic algorithm optimization technique for optimal DG allocation in medium voltage distribution networks. Power demands of the loads and their growth versus time, duration of the planning period were considered. Cost parameters such as inflation and interest rates, unit cost of kwh lost due to Joule effect (cost of losses), construction and maintenance costs of feeders of different cross-sections were all evaluated in the objective function. In their work, De Souza and De Albuquerque (2006) made use of Evolutionary Programming for optimal placement of DG in distribution networks so as to minimize the active power losses of the feeder and the total network supply cost. The method used is highly efficient for distributed generation economic analysis because the generators allocation and sizing proposed by the algorithm could significantly reduce the total load

2 Lawal, S. M., Shehu, R.S. and Yusuf, A.B. supply cost, and its applicability has been tested in a feeder with high losses index. Vallem and Mitra (2005) made use of Simulated Annealing optimization technique for optimal sitting and Sizing of Distributed Generation for Micro-grid Architecture, which involved the planning issues such as optimally designing the interconnections, sizing and sitting the DG units to maximize reliability, reduce costs and improve security of the system, and also an estimated capacity and location of the DG has been achieved with level of reliability. In Anantasate et al., (2008), Bee Colony optimization (BCO) was adopted for Multi-objectives optimal placement of DG, where the optimal number, size and location of the DG simultaneously minimized real power loss, violation function of contingency analysis and power generation limits. And the simulation result on IEEE 30 bus shows that the BCO can obtain the optimal solution with less computing time compared to simulated annealing, genetic algorithm, and tuba search with an average computing time. In Akorede et al., (2010), the authors tackled the issue of misplacement or inappropriate allocation of DG in distribution network by using a fuzzy controller to adjust the crossover and mutation rates to maintain the proper population diversity during the Genetic Algorithm operation, so as to overcomes the premature convergence problems of the simple Genetic Algorithm. Ghosh et al., (2010) made used of a simple conventional iterative search technique together with Newton Raphson method for optimal sizing/placement of DG and the power flow analysis on a modified IEEE test systems where weighting factors balanced between the cost and the loss factors which formed the objective functions. In Hung et al., (2011) employed an Improved Analytical (IA) method in conjunctions with loss sensitivity factor (LSF) and exhaustive load flow (ELF) methods in multiple distributed generation placement in primary distribution networks for loss reduction based on different types of DG s. Result shows that DG is capable of delivering both real and reactive power reduce loss more than that of DG capable of delivering real power only in one, two or three DG cases. Santoso et al., (2007) made used of intelligent techniques for planning distributed generation systems in solving the DG planning based on investment, cost minimization, sizing and sitting of the distributed generators, islanding with DG, and optimal placement of capacitors. To address these issues, this paper focuses mainly on the optimal placement and sizing of DG in the distribution networks, but distribution networks has been found to be exhibiting significant voltage drop due to their high R/X ratio that could cause substantial power losses along the feeders. In the light of this aforementioned problem, installations of DG within the radial distribution networks level will have an overall 85 positive impact towards reducing the power losses, voltage deviation as well as improving the network voltage profiles. A forward/backward sweep method was adopted for the load flow analysis due to its distinctive solution techniques on distribution networks that outweigh other conventional load flow methods in terms robustness and efficiency performance in distribution networks system (Le et al., 2006). The problems were formulated and solved using intelligent system techniques. In this paper, optimal placement and sizing of DG in radial distribution networks were determined. The objectives of this study are to minimize power loss and voltage deviation as well as maximize voltage profile in the distribution networks by means of particle swarm optimization (PSO). 2.0 METHODOLOGY A careful observation on the different methodologies adopted by other authors was observed in order to develop an idea for the right approach to be used in this study. Eventually the following steps were followed as in Satish et al., (2011). 2.1 Problem formulation The optimal placement and sizing of Solar Photovoltaic (as a DG) problem was formulated as a constraint nonlinear optimization problem with both locations and sizes of solar photovoltaic being continuous as in the work done by Lawal et al., (2014). The objective functions adopted in this paper are the total active power loss function and voltage deviation function. The multiple nature of the problem, made it necessary to form a multi-objective function in search of the solution that consist of both the location and size. 2.2 Constraints Along with the objective function, there is another significant part of the optimization model that needs to be defined and that is the constraints. In real applications, there are always limits on the choices of control variables. The constraints considered in this paper are of two types: equality and inequality constraints. 2.3 Equality constraints The equality constraints are those associated with the nonlinear power flow equations. It was observed that in many published papers the power flow equations are the real and reactive power mismatch equations. The reason for this is that modified versions of conventional power flow programs such as Newton-Raphson method and Gauss- Siedel method are widely used. In this work, the power flow representation was based on bus current injections and the equality constraints are the bus current mismatch equations. Mathematically speaking, the

3 Lawal, S. M., Shehu, R.S. and Yusuf, A.B. equality constraints can be always expressed in a vector form as follows: H(x, u) = Q (1) Where: x: the vector of state (dependent) variables, and u: the vector of control (independent) variables. 2.4 Inequality constraints The inequality constraints are those associated with the bus voltages, total current flow, and DG(s) to be installed. 2.5 Bus voltage and current limits The bus voltage magnitudes are to be kept within acceptable operating limits throughout the optimization process. Vmax > V >Vmin Imin < I <I max Where; Vmin: the lower bound of bus voltage limits, Vmax: the upper bound of bus voltage limits, and V : the rms value of the ith bus voltage The same applicable to the current in the system, from minimum to maximum 2.6 Active power loss: The total active power loss in an electric power system is given by, P loss b l 1 n n 2 Vi i1 j1, i j R I 2 l l 2 [ Vj 2VV i j cos( i j)] Yii cosij (2) Where; b is the number of lines, R l is the resistance of line l, I l is the current through line l, V i and i are the voltage magnitude and angle at node i and Y ij and ij are the magnitude and angle of the line admittance, respectively. 2.7 Voltage deviation The voltage improvement index for a power system is defined as the deviation of voltage magnitudes at each from unity. Thus, for a given system, the voltage improvement index is defined as; 2 n V iref Vi L v i1 V (3) iref Where; n is the number of buses, Viref is the reference voltage at bus i and V i is the actual voltage at bus i. The objective function for solving the DG optimal placement problem is computed using equations (2)-(3). Due to the fact that the two objectives are different, it would be impossible to incorporate all the constraints in the same mathematical function. An overall fitness function is considered such that each objective function is normalized in a comparative manner with the base case system without DG. 86 This fitness function is given by; (4) P Where; loss and L v are total active power loss and voltage deviation index, respectively. Loss Is the total base case active power loss in base : the network and V : Is the total base case voltage deviation. base 3.0 Multi-Objective Functions (MOBF) Due to peculiar nature of the nonlinear optimization problem with more than one objective functions that are to be combined and solve simultaneously; it is therefore a Multi-objective function. In this case multi-objective is being formulated in searching for a solution consisting of both the DG location and size that minimizes the voltage deviation and active power loss as described by the percentage in each objective function base on the individual weight assigned to the objective function base on its magnitude. Therefore; This fitness function is given by; Ploss Lv f ( x) W1. W2. Lossbase V (5) base Where; W 1 and W 2 are the corresponding coefficients the corresponding objective functions; The weighting factors W1 + W2 =1; (0.5 and 0.5 respectively) In this study, the corresponding coefficients for each objective are defined as 50%. The 50% was chosen due to the importance of both coefficients and its minimization. Since total the sum of W1 + W2 = 100% (w1+w2=1) Bus Radial Distribution System Fig 1: Single Line Diagram of IEEE 34 Bus Distribution System (Kannan et al, 2010)

4 Lawal, S. M., Shehu, R.S. and Yusuf, A.B. 5.0 Particle Swarm Optimization (PSO) Particle Swarm Optimization is a population based metaheuristic optimization technique that was first developed by Kennedy and Eberhart in 1995 inspired by the social behavior of bird flocking or fish schooling, on which individuals (particles) change their position (state) with time. Particle moves or fly around in a multidimensional direction in search of space, on which during the flight, each particle adjust or change its position according to its own experience (This value is called Pbest) and the neighboring particle (This value is called Gbest) experience, and finally made use of the best position encountered by itself and its neighbor (Lalitha et al., 2010) (see fig 2). Fig. 2: Concept of a searching point by particle swarm optimization Where sk is current searching point, sk +1 is modified searching point, vk is current velocity, vk +1 is modified velocity of agent i, pbest v is velocity based on pbest, gbest v is velocity based on gbest, n is number of particles in a group, m is number of members in a particle, pbesti is pbest of agent i, gbesti is gbest of the group, ωi is weight function for velocity of agent i, ci is weight coefficients for each term. PSO has same effectiveness as the genetic algorithm but with significantly better computational efficiency in terms of less functional evaluations by implementing statistical analysis and formal hypothesis testing (Hassan et al. 2004). Start Input Data Run the load flow and calculate the power loss and voltage deviation at base case Put DG randomly on busses and initialize the PSO Objnfunc = W1 PLindex + W2 VDindex Evaluate the fitness of each particle Check and update Pbest and Gbest of the particles Minimum best solution K= k+1 Update the velocity of the particles Update individuals Display Result Check the stopping criterion Not Satisfied Satisfied End success Fig 3: Flow Chart of the Solution Procedure Using Particle Swarm Optimization Algorithm 87

5 Bus Voltage Magnitude (p.u) Nigerian Journal of Solar Energy, Vol. 26, Solar Energy Society of Nigeria (SESN) All rights reserved. 6.0 SIMULATION RESULTS AND DISCUSSION The study was conducted on 34-bus Radial Distribution network system as shown in Fig 1, where the developed algorithms were tested on an IEEE-34-bus radial distribution system. The test system (34-Bus- Radial Distribution networks System) is an unbalanced radial distribution system used as a standard test system and validated with 33-bus test systems as presented in Satish et al., (2011). The power loss minimization was close to each other even though voltage has been considered in this work unlike in the referred paper. In order to check the efficiency and working performance of the PSO algorithm, another algorithm was developed using Genetic Algorithm (GA) for comparison. The results were carried out based on single and double DG placement in radial networks Voltage-Magnitude Number of Buses Fig. 4: Voltage Profile of the System at Baseload V-mag 6.1 Optimal placement and sizing of Solar Photovoltaic as a single DG in 34-bus RDS: A single DG source is to be installed in the 34-bus RDS. The PSO was used to investigate the optimal DG size and bus location simultaneously. The PSO maximum number of iterations, swarm particles and acceleration constant parameters are tuned for optimal result as presented in the program. The obtained PSO results for this case are tabulated in Table 1. The PSO method obtained both the single DG optimal bus location and rating simultaneously. It returned a different bus location for the DG to be installed in both cases than that of the GA method. The PSO proposed bus No. 12 for the single DG, while the bus location obtained by the GA method is No. 31. The mean values of the real power losses for cases are comparable to that of the GA method for both cases. The simulation time of the PSO method to reach both location and sizing results simultaneously outperforms that of its counterpart (GA). The convergence of the Table 1: Solar Photovoltaic placement results using different optimization methods Base GA PSO Case The best Location of DG (No. of Bus) The best Size on 2400 on of DG(kW) (31) (12) Power Loss (kw) Voltage Deviation Objective Function Value proposed PSO in the single DG case is shown in Fig 5, for a maximum. PSO number of iterations is 200. And also this shows that even if the number of the iterations is increased, the PSO algorithm has already settled to its final value. The base case load flow to determine the Power loss and voltage deviation was found to be KW and respectively at an objective function value of 1. The Optimal and Sizing of a single DG in an electrical distribution network using PSO revealed that the best location of the DG in the network was found to be bus number 12 with a size of 2400KW with a dropped in power loss to KW and voltage deviation of from KW and V as can be seen in Table 1, while That of GA settled at bus number 31 as it best location with a maximum size of DG to be 2500KW. The power loss was reduced KW as against the initial value of KW with a reduction also in voltage deviation to from at an objective function of The PSO convergence characteristic is shown in Fig 5, while that of GA is presented in Fig 6, Comparing the two output results, it is clear that the proposed PSO algorithm is more efficient and faster in terms of convergence (at 144) as against it counterpart GA which converged at 184, and also when it minimized the power loss and voltage deviation much lower than that of GA, therefore the proposed PSO algorithm has shown an aged performance over GA as shown in table 1. Voltage deviation has been minimized greatly that helps the distribution networks to regain it nominal voltage within the network because the smaller the voltage deviation the better for the distribution network as the nominal voltage maintain it status, as can be seen in Fig 7, the voltage profile improved within the networks while Fig 8, shows how voltage deviation has controlled and minimized as it moves towards 1p.u. 88

6 Voltage Deviation Bus Voltage Magnitude (p.u.) Lawal, S. M., Shehu, R.S. and Yusuf, A.B Number of Buses Before DG Using GA Using PSO Fig 8: Total Voltage Deviations Fig 5: PSO (Converged in Iteration No. 144) Fig 6: GA (Converged in Iteration No. 182) Number of Buses Fig 7: Voltage Profile and Its improvement Before DG Using GA Using PSO Optimal placement and sizing of double DGs in 34-bus RDS: The proposed PSO algorithm was utilized to optimally size and place two DG units in the 34-bus RDS. Table 2 presents the double DG case simulations results of the PSO and GA respectively. The PSO consistently chooses buses 22 and 27 for the two optimally sized DG units to be installed after several runs of the simulation. The PSO metaheuristic technique obtained the optimal DG locations and sizes simultaneously. The corresponding PSO results are compared to that of the GA method, as shown in Table 1.6. The PSO active power losses results are close to each other, i.e. GA losses are higher by 0.3%. Table 2: Two Solar Photovoltaics placement results using different optimization methods Base GA PSO Case The best Location of DGs (No. of Buses) & & 27 The best Sizes of DGs(kW) on (17) & 490 on (28) 1100 on (22) & 840 on (27) Total Size of DG (kw) Power Loss (kw) Voltage Deviation Objective Value Function Distribution System network real power losses were reduced by approximately 5% when compared to the losses of the GA method, as shown in Table 2. For both double DG cases, the Distribution System bus voltages range not only within limits but their deviation from the nominal voltage value is minimal and is similar to that of the GA method.

7 Bus Voltage Magnitude (P.U) Lawal, S. M., Shehu, R.S. and Yusuf, A.B. displayed an edge over GA in terms of convergence. Therefore this work can be extended by including more parameters in the optimization problem. REFERENCES Akorede, M. F., Hashim H., Aris I. and Abkadir M. Z. A. (2010). "Effective Method for optimal allocation of distributed generation units in meshed electric power systems," The institution of Engineering and Technology, vol. 5, pp Fig 9: GA (Converged in Iteration No. 179) Anantasate, S., Chokpannyasuwan, C., Pattaraprakor, W. and Bhasaputra, P. (2008). "Multiobjectives Optimal of Distributed Generation Using Bee Colony optimization," Proceedings for the GMSARN International Conference on Sustanable Development: Issues and Prospects for the GMS. Vol. 2, pp Celli, G. and Pilo, F. (2001). "Optimal Distribution Generation Allocation in MV Distribution Networks," IEEE Transactions,vol. 24, pp De Souza, B. A. and De Albuquerque, J. M. C. (2006). "Optimal of Distributed Generators Networks Using Evolutionary Programming," IEEE Transactions, pp Fig 10: PSO (Converged in Iteration No. 102) No. of Buses Fig 11: Voltage Profile and Its improvement Before DG Using GA Using PSO El-Hawary, M. E., (2008). Introduction to Electrical Power Systems. New jersey: John Wiley & son Inc.pp4-15. Ghosh, S. and Ghosal, S. (2010). "Optimal sizing and placement of distributed generation in a network system," Electric power and Energy system vol. 32, pp Hung, D. Q., Mithulanathan, N. and Bansal, R.C. (2011). "Multiple Distributed Generators in Primary Distribution Networks for loss Reduction," IEEE Transactions, vol.20, pp Hassan, R., Cohanim, B., de Weeck, O. and Venter, G. (2004). "A Comparison of Partcle Swarm Optimization and The Genetic Algorithm," American Institute of Aeronautics and Astronautics,vol.9, p CONCLUSION The optimized value of weighting factors was computed and the optimum solar photovoltaic location and its best size have been achieved, both as single DG and Double DGs. Due to the placement of an optimal DG location and best sizes, the voltages profile of the network also improved while power losses reduced substantially. Comparing the two heuristic methods, PSO 90 Kannan, S.M., Renuga, P., Rathina, A. and Monica, G. (2010). "Optimal capacitor placement and sizing using combined fuzzy-hpso method," International Journal of Engineering, Science and Technology, vol. 2, pp Lalitha, M. P., Reddy, V.C.V. and Usha, V. (2010). "Optimal DG for Minimum Real Power Loss

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