Optimal Power Distribution Planning Using Improved Particle Swarm Optimization

In planning of radial power distribution system, optimal feeder routing and optimal branch conductor selection plays an important role. Economical distribution system requires effective planning method, which involves optimization procedure to connect the given load to the substations. In the paper, a generalized algorithm is developed for obtaining the optimal feeder path and the optimal location of substation on minimum loss criterion. Forward/Backward sweep load flow technique is applied to calculate the energy loss costs and select the minimum energy loss cost path for the power distribution. Finally, the optimal branch conductor selection of radial distribution system is performed by using particle swarm optimization (PSO). The proposed method has been tested on several radial distribution systems and results were found encouraging.


Introduction
Designing a distribution network optimally requires number of technically feasible alternatives and utilization of enhancement tools [1]. The choice of options and streamlining apparatus rely upon the demands with worthy unwavering quality levels, power transportation breaking points of distribution lines and the radial structure of the network [2].The issue of distribution framework planning is to locate the optimum substation location and the faultless feeder configuration to connect the load to the substation [3]. The distribution system planning is huge to give reliable and cost effective operation to consumers [4]. The planning issue of distribution networks might be expressed as an improvement issue, so that for a given geographical area or region with an arrangement of load demands already evaluated, the attributes of the network are resolved, including the area of the transformation centres, limiting the total installation and operation costs, subject to the technical requirements for a satisfactory operation of the system [5]. To deal with such issues new optimization tools and frameworks are basic considering the range and size of substations and feeders, the improvement of new feeders and furthermore new substations [6]. Power distribution planning is a complex problem for the researchers. There are two approaches used for solving this complex problem, i.e classical search algorithm and evolutionary algorithm. Now a day's researcher have used different evolutionary algorithm for planning a optimal power distribution system because EA is superior over classical approach. There are different types of EAs, e.g PSO, GA, ACO, AIS and Tabu Search. In earlier literature GA has been mostly used for the power distribution planning but the recent literature survey indicates that the PSO is a powerful challenger of the GA [7]. In this paper multi objective planning problem is solved by using particle swarm optimization (PSO). This problem involves a number of planning variables such as: optimal location of substation, optimal feeder path and optimal selection of conductors. These planning objectives are achieved by minimizing the objective function which consists of installation cost of new facility (substation and feeder) and energy loss cost. The association of this paper presents the related work is section 2, the proposed distribution system planning algorithm in section 3, the simulation results of the proposed work in section 4 took after by the conclusion in section 5.

Related Work
Mostafa Esmaeeli et al. [8] have proposed a risk-based planning technique in LV distribution networks for ideally deciding the size, number, and the situation of distribution transformers. In that approach, three different risk techniques are characterized for distribution system operator (DSO). They are named risk-seeker, risk-neutral, and risk-averse. Marina Lavorato et al. [9] have proposed a constructive heuristic algorithm (CHA) to comprehend distribution system planning (DSP) issue. The DSP is a particularly complex mixed binary nonlinear programming issue. A CHA was aimed to get an awesome quality response for the DSP issue. The proposed method has been tested on two test systems and one real system. Singh et al. [10] presented a simple and easy method for power distribution planning without using any optimization technique. But the limitation of this method is that the connection of new node is dependent upon the sequence of appearance of node in data file. Amin Hajizadeh and Ehsan Hajizadeh [11] presented a multiobjective planning algorithm based on PSO for optimal siting and sizing of DGs in radial distribution systems by minimizing the objective function. The algorithm has been tested on IEEE 33 bus system. Mohammadian et al. [12] presented a PSO based algorithm for practical planning of radial distribution systems includes optimal selection of conductor and placement of capacitor in radial distribution system.

Optimal Power Distribution System Planning
This paper provides an optimal power distribution in the following stages, initially all the possible paths are identified using the uploaded system data and then for each identified path forward/backward sweep load flow technique is applied to calculate the energy loss costs. The minimum energy loss cost path is selected for the power distribution. Then the optimal branch conductor selection of radial distribution system is performed by using particle swarm optimization (PSO). Here, the optimization is improved by the parameters such as power loss, voltage profile and Depreciation on capital investment. The PSO optimization results the optimal conductor and the location of the optimal conductor is chosen as the optimal substation and then through the optimal substation power distribution. The block diagram of proposed work is given in figure1.

Identification of all possible paths
In the proposed method, all possible radial paths are initially identified by the following steps. Let us consider an 'n'-node distribution network. The path selection algorithm has following steps [13]:  Initiate from the substation node (let node -1), check the nodes which are directly connected to substation node and form a connection matrix 'q'.  Check the last node's connections of 'q'matrix and update matrix with new connections.  Updated node's connections are entering in new rows of matrix 'q'.  Repeat the second and third step for next iteration until last node having no remaining connection. So in this way all possible radial paths for energizing all nodes (2 to n -node) are obtained.  Now separate possible paths for respective energizing nodes (2 to n -node) i.e. create n-1 matrices q2, q3, …qn-1.
Row of matrices represents the path for energizing node.

Load flow on each path
The load node for each possible paths matrix represented by q2, q3, …qn-1. To calculate the energy losses in each path of respective load node, the forward/backward sweep load flow technique is used [14]. Step Step: 3 calculate the nodal current injections Starting from the end nodes and moving towards the root node calculate the branch currents.
This is backward sweep which is application of Kirchhoff's current law at each node.
Step: 4 Starting from the root node and travelling towards the end nodes calculate the node voltages.
This is forward sweep and is application of Kirchhoff's voltage law.
Step: 5 Calculate the maximum mismatch in the bus voltage , then repeat the steps from 2 to 5.
then the algorithm has converged.
Where  is the maximum voltage mismatch,

Particle swarm optimization (PSO)
Particle Swarm Optimization (PSO) algorithm is developed by Kennedy and Elbehart in 1995 [15]. PSO is initialized by population of random solutions called as particles and updating themselves continuously. Over a number of iterations, a group of variables have their values adjusted closer to the member whose value is closest to the target at any given moment. It's an algorithm that's simple and easy to implement.

Performance of particle swarm optimization using inertia weights
Shi and Eberhart in 1998 [16] proposed an inertia weight 'w' to have a better balance between the local and global search. Use of this 'w' has improved performance of basic PSO in many applications.
The following describes the position and velocity update equations with weight factors included.
Xid is present position vector Vid is present velocity vector Pid best position vector Pgd is global best position vector W is inertia weight ɛ1 and ɛ2 are random number generators. C1, C2 are positive constants. With a proper selection of 'w' number of iterations also reduces. Hence, it is required to keep the value of 'w' varying and linearly decreasing from 0.9 to 0.4. A large weight factor facilitates a global search while a small inertia weight facilitates a local search. Value of 'w' is determined by using equation (6) [17].
Where and are maximum and minimum values of the inertia weight, is the current iteration and is the maximum number of iterations.

Optimal conductor selection
The load flow analysis designs a system that has a good voltage profile during normal operation and that will continue to operate acceptably when one or more lines become inoperative due to line damage, lightning strokes, failure of transformers, etc. To obtain the optimal conductor, the power loss, voltage profile and depreciation on capital investment of the transmission line is must be low. The objective function is the sum of the conductor annual energy loss cost and the conductor depreciation cost [18]. These are calculated by C= Cf + Cl (7) Where, Cf is annual fixed cost of connected feeder lines and substations, Cl is annual energy losses cost of network.

Calculation of total energy loss cost
The major cost in electrical distribution network is the energy losses cost. The total annual cost of radial distribution network is expressed as:

Cl=
[Kp + Ke × Lsf × 8760] (8) Total energy loss cost is calculated for each path by the equation (8) and selects the minimum energy loss cost path as the optimal path.

Power Loss
The real power loss of distribution network is given by (9) Where, j is the branch number, Rj is the resistance and Ij is the current of j th branch, respectively. PLis the total real power loss of N-bus distribution network.

Depreciation on capital investment:
The annual capital cost for branch j with k type conductor is, Cf= α×[cost(k)×len(j)] (10) Where, α is the interest and depreciation factor, cost(k)is the cost of k type conductor (Rs/km), len(j) is the length of branch j in (km)

PSO optimization algorithm
PSO is an optimization tool can solve an assortment of difficult optimization issues. In this paper the optimal power distribution is obtained using the PSO algorithm. The detailed algorithm to determine optimal conductor is given below, Step 1: Initialize the system data and population size.
Step 4: The objective is to select optimal size of the conductor in each branch of the path, which minimizes the total cost. From equation (7) the overall objective function can be calculated.
Step 5: The evaluation of fitness function is a procedure to determine the fitness of each string in the population. Since the PSO proceeds in the direction of evolving best-fit strings and the fitness value is the only information available to the PSO, the performance of the algorithm is highly sensitive to the fitness values. The fitness function f is calculated by the following equation. f = (11) Step 6: If fitness is better than fitness (pbest), replace it. If fitness is better than global fitness (gbest), replace it.
Step 7: Now update the velocity and position of the particle using equation (4) and (5).
Step 8: Increment iteration count. If iteration max  count . Count, go to Step 3. Else go to Step9.
Step 9 The algorithm results the optimal conductor for each branch. The flow diagram of proposed PSO optimization algorithm is given in figure 2. The proposed optimization algorithm results the optimal conductor for the power distribution. Location of the optimal conductor is selected as the optimal substation location. Then the total kilovolt-ampere (KVA) fed through a particular optimal substation. Here we pick that the substation is a node. The ideal location for substation is also processed by limiting the power loss.

Results and Discussion
The proposed strategy of optimal planning in power distribution system is implemented in the working platform of MATLAB (version 17). The proposed Algorithm is tested on 33 node radial distribution system, 69 node radial distribution system and 54 node radial distribution systems.

Testing on 33-nodes Radial Distribution Network:
The single line outline of 33-node radial distribution network is appeared in figure 3.  The results of proposed optimal power distribution planning using improved particle swarm optimization on 33 nodes radial distribution network is tabulated in table1 for single feeder case, two feeder case and three feeder cases. From table 1 we realize that the proposed distribution system planning Algorithm yields a minimum real power loss of 84.1729kW and least reactive power loss of 57.0730kVAr in three feeder case scenario. Furthermore, the minimum node voltage of 0.9635 is acquired in three-feeder case of 33-node radial distribution system. The figure 4 shows the comparison of voltage profile with and without proposed optimized distribution planning Algorithm. The results confirm that the proposed optimized distribution planning algorithm yields improved voltage profile. Figure 4 demonstrates the voltage profile of 33-node radial distribution system for proposed optimized distribution system with single, two and three feeder arrangements and existing without optimized distribution.

Testing on 69 node radial distribution network:
To demonstrate the adequacy of the planned technique, a 69node radial distribution system as shown in figure 5 is considered. The testing results of proposed optimal power distribution planning using improved particle swarm optimization on 69 nodes radial distribution network in terms of total real power loss, total reactive power loss and minimum voltage is given in table 2. The performance is also analyzed for single feeder case, two feeder case and three feeder cases.  From table 2 it is clear that the proposed distribution system planning Algorithm yields a minimum real power loss of 91.8865kW and least reactance power loss of 41.6773kVAr in three-feeder case of 69 node radial distribution systems. The minimum node voltage of 0.9657 is obtained in three-feeder case. The figure 6 shows the comparison of voltage profile with and without proposed optimized distribution Algorithm, The comparison results prove that the proposed optimized distribution planning results the improved voltage profile than the existing without optimization Algorithm

Testing on 54-nodes Radial Distribution Network
For established the effectiveness of the proposed Algorithm another test system is considered that has been used and reported by many researchers using different technique such that Knowledge Based Expert System [3], ACS [5] and PSO [19]. The single line outline of 54-node radial distribution network is shown in figure.7   The testing results of proposed Algorithm on 54node radial distribution systems with single feeder cases are shown in table3 and the comparative results of various feeder and with reported Algorithm [3] is given in table4 and table5. From table 4 and table5 we realize that the proposed distribution system planning method yields a minimum real power loss of 41.2776kW and least system cost 232150Rs. in three feeder case of 54 node radial distribution system. The performance comparison graph of proposed Algorithm with reference [3] is given in figure 6

Conclusion
In this paper optimal power distribution planning algorithm is proposed using improved particle swarm optimization (PSO) technique. Initially, algorithm is developed for obtaining the optimal feeder path, optimal location of substation based on minimum loss criterion. Then, the optimal branch conductor selection of radial distribution system is performed using particle swarm optimization (PSO). The optimization algorithm is improved by using the power loss and depreciation on capital investment parameters. The effectiveness of the proposed algorithm is tested on 33node, 69 node and 54 nodes radial distribution network with single and multiple feeder cases. The results are compared with the other reported methods and found effective.