A novel two-stage evolutionary optimization method for multiyear expansion planning of distribution systems in presence of distributed generation

Highlights

• A new multiyear planning model for distribution system expansion is presented.

• A binary modified imperialist competitive algorithm (BMICA) is proposed.

• An improved shark smell optimization (ISSO) is suggested.

• By combination of BMICA and ISSO, a novel two-stage solution approach is presented.

• The efficacy of the proposed BMICA + ISSO is extensively investigated.

Abstract

In this paper, a new approach for multiyear expansion planning of distribution systems (MEPDS) is presented. The proposed MEPDS model optimally specifies the expansion schedule of distribution systems including reinforcement scheme of distribution feeders as well as sizing and location of distributed generations (DGs) during a certain planning horizon. Moreover, it can determine the optimal timing (i.e. year) of each investment/reinforcement. The objective function of the proposed MEPDS model minimizes the total investment, operation and emission costs while satisfying various technical and operational constraints. In order to solve the presented MEPDS model as a complicated multi-dimensional optimization problem, a new two-stage solution approach composed of binary modified imperialist competitive algorithm (BMICA) and Improved Shark Smell Optimization (ISSO), i.e. BMICA + ISSO, is presented. The performance of the suggested MEPDS model and also two-stage solution approach of BMICA + ISSO is verified by applying them on two distribution systems including a classic 34-bus and a real-world 94-bus distribution system as well as a well-known benchmark function. Additionally, the achieved results of BMICA + ISSO are compared with the obtained results of other two-stage solution methods.

Introduction

Distribution systems as substantial sectors of power systems play a key role in electrical power delivery to the end-line customers. Regarding the essential matters, such as load growth, limited capacity of distribution equipment, and the competitive incentives of distribution system operators (DSOs) to give agreeable electrification services to their customers, totally stimulate such organizations to design appropriate expansion plans for future of their systems.

Nowadays, within both research and practical enviroments, utilization of distributed generation (DG) as an effectual and reliable choice for expansion planning of distribution systems (EPDS) has been broadly taken into account. Generally speaking, the DG technology comprises the micro-to-medium size generation units installed and operated close to the load centers in low voltage (LV) side, or directly connected to medium voltage (MV) section of distribution systems [1], [2]. The concern of global warming due to increasing emission of greenhouse gases [3] in addition to economic subjects such as unrestrained instabilities of electricity price [4] have persuasively corroborate the employment of DG through the EPDS policies of DSOs. Less time for construction as well as lower pollution rate compared to the conventional large-scale generators of power systems, modular size, power losses' reduction and voltage profile improvement are among other technical and operational advantages of DG [5]. However, the aforesaid advantages extremely depend on the DG location, installation/generation capacity and its type [6]. Therefore, to earn the maximum DG advantages, it is required to take it into consideration as a benefitical alternative in EPDS decision-making tools.

From mathematical perspective, DG-integrated EPDS is a complicated multi-dimentional optimization problem including both binary and integer decision variables and copious local optima. The most widely-used objective function for DG-integrated EPDS is minimizing the total investment and operation costs aiming to efficiently serve the load demand of customers subject to various technical and operational constraints for both DG and distribution system. Owning to the difficulties of mathematical programming methods for solving EPDS problem, like trapping in local optima leading to premature convergence, solving it with evolutionary optimization methods has been broadly presented in recent research works on EPDS. In [7], an integrated EPDS model incorporating DG as an effective alternative for peak load shaving is presented. The model of [7] optimizes the total investment and operation costs associated with DG units and distribution systems. The authors of [8] suggested a multistage EPDS framework including DG technologies. Also, they have utilized a hybrid PSO and shuffled frog leaping (SFL) algorithm to solve their EPDS optimization problem. At the same context, a homogeneous research work on EPDS modeling is presented in [9] taking the total investment and operation costs into consideration as objective to be minimized. Also, a multiobjective framework for multistage EPDS is introduced in [10] solved by multiobjective tabu search (MTS). Biswas et al. proposed an EPDS model in [11] to find the optimum location and size of DG units. Their model aims to reduce the voltage sag in LV distribution systems using the flexible alternative of DG. In [12], a time-based model for EPDS, with the aim of providing the growing load demand of customers during anuual planning horizon, is introduced. The authors of [12] suggested a hybrid genetic algorithm (GA) and optimal power flow (OPF), i.e.GA-OPF, to solve their EPDS model. Another hybrid solution method, attained by combination of GA and immune algorithm (i.e. IGA), is proposed in [13] to solve the dynamic multiobjective EPDS model consideing DGs. Modified particle swarm optimization (MPSO) is employed in [14] to solve the yearly EPDS model including DG and storage units. In [15], a multistage DG-integrated EPDS model is presented using artificial bee colony (ABC) as the solution approach. A time-based model for expansion planning of distribution systems is presented in [16] considering DGs. However, the emission cost is not considered as a component of the objective function in [16]. Additionally, the OPF subproblem isn't incorporated into the expansion model of [16]. A dynamic EPDS model is suggested in [17] considering the total investment and operation costs as the components of objective function which should be simultaneously minimized. The proposed model of [17] is solved by original PSO. However, the presented model of [17] does not include binary and integer decision variables. Additionally, the model of [17] does not incorporate the DG emission cost into the objective function. In addition to different models, the solution methods of this paper and [17] are different. While the solution method of [17] only utilizes original PSO, the proposed solution approach of this paper includes two evolutionary optimization methods and each of these two methods is an enhanced version of an original evolutionary optimization approach (binary modified version of ICA or BMICA for the first stage and improved version of SSO or ISSO for the second stage).

Despite the worthwhile research works carried out for modeling and solving of EPDS problem, more proficient models and solution approaches are still desired. The principal contributions of this paper are twofold:

• A novel optimization model for multiyear EPDS (MEPDS) in presence of DG is presented. In this model, the investment and operation costs as well as emission cost are considered as the objectives, which are concurrently minimized within a planning horizon. As the suggested MEPDS is time-based, it can also define the optimal time schedule (i.e. year) of both DG investment and feeders’ reinforcement. To the best of the authors’ knowledge, there is no MEPDS model simultaneously optimizing investment, operation and emission costs in the literature.

• The proposed MEPDS model is mathematically a non-smooth, non-convex, and mixed-integer non-linear programming (MINLP) optimization problem. This problem cannot be easily solved by conventional numerical optimization methods. Additionally, single-stage evolutionary optimization methods may not be able to solve this problem, since it includes binary, integer, and continuous variables together. Accordingly, a new two-stage evolutionary optimization approach, named BMICA + ISSO, with high global search (i.e. exploration) and local search (i.e. exploitation) capabilities, is introduced to solve the proposed MEPDS problem. In the first stage of the suggested solution approach, i.e. BMICA, the binary and integer decision variables are optimized. By doing this, the optimal expansion schedule including location, capacity and installation year of DG units in addition to reinforcement timing of distribution feeders are specified. In the second stage, ISSO optimizes the continuous variables. It solves the associated optimal power flow (OPF) problem optimizing the operation point of both DG units and distribution system. It is worthwhile to note that the introduced BMICA + ISSO solution approach has been specifically designed in this paper for solving the MEPDS problem and has not been presented elsewhere in the area.

The reminder of this paper is set as follows. In Section 2, the proposed MEPDS model is described. In Section 3, the proposed two-stage solution method, i.e. BMICA + ISSO, is introduced. Section 4 presents the numerical results achieved by application of the suggested MEPDS and BMICA + ISSO on two distribution test systems and one well-known benchmark function besides the comparitive results of other two-stage solution methods. Concluding remarks are presented in Section 5.