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Multi-objective planning of electrical distribution systems incorporating sectionalizing switches and tie-lines using particle swarm optimization

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Abstract

A multi-objective planning approach for electrical distribution systems using particle swarm optimization is presented in this paper. In this planning, the number of feeders and their routes, number and locations of sectionalizing switches, and number and locations of tie-lines of a distribution system are optimized. The multiple objectives to determine optimal values for these planning variables are: (i) minimization of total installation and operational cost and (ii) maximization of network reliability. The planning optimization is performed in two steps. In the first step, the distribution network structure, i.e., number of feeders, their routes, and number and locations of sectionalizing switches are determined. In the second step, the optimum number and locations of tie-lines are determined. Both the objectives are minimized simultaneously to obtain a set of non-dominated solutions in the first step of optimization. The solution strategy used for the first step optimization is the Strength Pareto Evolutionary Algorithm-2 (SPEA2) based multi-objective particle swarm optimization (SPEA2–MOPSO). In the second step, the solutions/networks obtained from the previous step are further optimized by placement of tie-lines. SPEA2-based binary MOPSO (SPEA2–BMOPSO) is used in the second step of optimization. The proposed planning algorithm is tested and evaluated on different practical distribution systems.

Introduction

The power system deregulation has opened a competitive market for power system utilities. After being unbundled, it is challenging for power companies to hold profit while keeping customers satisfied. This affects more to distribution utilities due to their direct link with end users. Thus, an efficient planning of distribution networks is essential for all utilities. The computerized distribution system planning has a rich literature spanning over past three decades. A review of the existing models can be found in [1], [2], [3]. The distribution system planning is basically an optimization process to obtain a number of planning variables, such as: (i) size and location of distribution substation, (ii) number of feeders and their routes, (iii) number and locations of sectionalizing switches, and (iv) number and locations of tie-lines. The planning objectives are minimization of installation cost of new facilities (i.e., substations and feeders), minimization of operational (maintenance and lost energy) cost, and enhancement of system reliability. These objectives are subjected to several network constraints, such as substation and feeder capacity, maximum node voltage deviation, and network radiality. This planning optimization can be performed as that of a static planning, i.e., one-step planning for a brand new network and as an expansion planning, i.e., addition of new nodes to an existing network as well.

In the initial works [1], [2], [3], reliability is not considered in the planning, where the only objective is minimization of total installation and operational cost. In present scenario, the reliability is an important factor accounting for customer satisfaction. It is now considered as one of the planning objectives [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. From this point of view, in this work, the two objectives are considered: (i) total installation and operational cost, and (ii) a reliability indicator named contingency-load-loss index (CLLI). The CLLI is a contingency based reliability assessment indicator formulated in [17]. It is defined as the ratio of average non-delivered load due to failure of all branches, considered one at a time, to the total load. This index can distinguish the reliability levels of different network structures (such as single feeder with and without sectionalizing switches, multiple feeders with different sectionalizing switches etc.) as shown in [17]. The reliability improvement of a distribution network can be done using sectionalizing switches and tie-lines. Sectionalizing switches are placed in a network to isolate faulty segment(s) and thereby keeping the upstream sections healthy. Tie-lines are used to provide supply to some feeder branches due to faults occurring in an upstream branch. However, provision of sectionalizing switches and tie-lines improves system reliability at the expense of additional installation costs. Thus, a trade-off between cost and reliability is required. It is done by using the Pareto-dominance principle [19].

The distribution system planning problem is a typical nonlinear, non-convex, non-differentiable, constrained optimization problem with integer and continuous decision variables. The problem dimension increases with the number of nodes. Traditionally, numerical optimization tools, such as nonlinear programming (NLP) [4], [7], [8], Benders’ decomposition [5], and dynamic programming (DP) [6], [9] have been used to solve this problem for small scale systems. Then, some heuristics-based algorithms, for example network flow programming [11], Tabu search [15] etc. have been used. In the recent times, population-based meta-heuristic algorithms, for example genetic algorithm (GA) [10], [12], [13], [14], artificial immune system [16], and particle swarm optimization (PSO) [17], [18] are used. The advantage of these algorithms is that they use multi-point search. Thus, they can yield a set of non-dominated solutions in a single run.

In this paper, PSO is used as the solution strategy for its simplistic algorithmic structure that can easily be implemented. In PSO, a population of particles representing the potential solutions search for the optimal solution(s) by updating their respective positions and velocities in view of their individual fitness values [17]. In single objective optimization, the fitness of a particle is measured by the value of the objective function corresponding to its position. However, in multi-objective optimization, since there are multiple objective functions, the value of any single objective function will not represent the fitness of a particle. Hence, there should be a fitness assignment scheme so as to assign the fitness of a particle in view of the values of its multiple objective functions. In this paper, this is done using the fitness assignment scheme of Strength Pareto Evolutionary Algorithm-2 (SPEA2) [20]. In SPEA2, a variant of multi-objective GA (MOGA), the fitness of a particle is determined using its non-dominance strength and density among the other population members. After assigning a single fitness value for each particle using this method, any PSO neighborhood topology can be used to update the velocity and position of each particle in PSO population.

In the proposed multi-objective planning approach for electrical distribution systems, the overall algorithm consists of two sequential steps. In the first step, PSO is used to optimize network structure and number and locations of sectionalizing switches. In the second step, all solutions obtained from first step are reevaluated to obtain optimal number and locations of tie-lines using a binary PSO. In PSO formulation, a modified cost-biased encoding/decoding scheme is used to obtain feeder routes. It can prevent the creation of infeasible networks thereby overcoming a common drawback of direct encoding [12], [13], [14]. Since the fitness of a particle in PSO is determined using SPEA2, the algorithm used in this paper is named as SPEA2-based multi-objective PSO (SPEA2–MOPSO). Simulation results on three different distribution systems are presented to validate the proposed approach. The performance of PSO depends on information exchange among the particles, which is done by using various neighborhood topologies [21]. Hence, the performance of SPEA2–MOPSO with two different neighborhood topologies, i.e., global best (gbest) topology and ring topology, a kind of local best (lbest) topology, is assessed on this planning optimization problem by statistical tests.

The paper is organized as follows. The multi-objective distribution system planning problem is formulated in Section 2. In Section 3, a brief review on multi-objective PSO (MOPSO) is presented. The proposed planning approach for distribution systems using SPEA2–MOPSO is presented in detail in Section 4. Section 5 provides simulation results and discussions. Section 6 concludes the paper.

Section snippets

Multi-objective distribution system planning problem

The distribution system planning problem is a very complex optimization procedure due to the involvement of the following factors: (i) different types of decision variables (discrete/ continuous), (ii) simultaneous choice of optimum conductor size and feeder routing, (iii) objective function consisting of linear as well as nonlinear terms, (iv) simultaneous optimization of the conflicting objectives, i.e., cost and reliability, (v) considerations of geographical obstacles and social issues

Multi-objective PSO (MOPSO): a brief review

The MOPSO has a growing volume of literature with several proposals to make the algorithm more powerful and the state-of-art reviews can be obtained in [22], [23]. Most of the MOPSO approaches are Pareto-dominance based approaches. The main goals of those approaches are to reach closer to the set of the Pareto-optimal solutions (i.e., better convergence) and to get a set of diversified solutions (i.e., better diversity among the solutions). Thus, the research on the Pareto-based MOPSO is

Multi-objective planning using SPEA2–MOPSO

There are certain practical issues with the distribution system planning problem. The structure of a distribution network to be planned depends upon the area (i.e., rural, semi-urban, urban, metropolitan city etc.) where it is to be constructed, type of consumers (i.e., domestic, commercial, industrial etc.) in the area, and the utility’s CAPEX (Capital Expenditure) and OPEX (Operational Expenditure) budgets. The distribution system is purposefully designed as radial network in most cases to

Simulation results and analysis

The proposed multi-objective distribution system planning approach is evaluated via computer simulation studies on expansion planning of the 21-node system [13] and static planning on the 54-node [38] and 100-node [13] distribution systems. The system data for the 21- and 100-node systems are available in [17]. The system data for the 54-node system is available in [38]. The conductor specifications are given in [17]. In this section, the Pareto-approximation sets obtained in the first and

Conclusion

In this paper, a multi-objective planning scheme for electrical distribution systems incorporating sectionalizing switches and tie-lines using PSO has been investigated. Two objectives i.e., total installation and operational cost and contingency-load-loss index (CLLI) have been simultaneously optimized using the Pareto-dominance principle. The CLLI is computed by considering faults in all network branches, taken one at a time. The network planning optimization is done in two steps. In the

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