Journal of Optimization

Volume 2018, Article ID 6258350, 19 pages

https://doi.org/10.1155/2018/6258350

## A Heuristic Approach for Optimal Planning and Operation of Distribution Systems

^{1}Engineering and Natural Sciences Facility, Altinbas University, Istanbul, Turkey^{2}Department of Computer Science, Faculty of Sciences, University of Diyala, Diyala, Iraq

Correspondence should be addressed to Khalid Mohammed Saffer Alzaidi; moc.oohay@sm5002ahk

Received 3 January 2018; Revised 14 April 2018; Accepted 29 April 2018; Published 3 June 2018

Academic Editor: Wei Wei

Copyright © 2018 Khalid Mohammed Saffer Alzaidi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The efficient planning and operation of power distribution systems are becoming increasingly significant with the integration of renewable energy options into power distribution networks. Keeping voltage magnitudes within permissible ranges is vital; hence, control devices, such as tap changers, voltage regulators, and capacitors, are used in power distribution systems. This study presents an optimization model that is based on three heuristic approaches, namely, particle swarm optimization, imperialist competitive algorithm, and moth flame optimization, for solving the voltage deviation problem. Two different load profiles are used to test the three modified algorithms on IEEE 123- and IEEE 13-bus test systems. The proposed optimization model uses three different cases: Case 1, changing the tap positions of the regulators; Case 2, changing the capacitor sizes; and Case 3, integrating Cases 1 and 2 and changing the locations of the capacitors. The numerical results of the optimization model using the three heuristic algorithms are given for the two specified load profiles.

#### 1. Introduction

Power systems have been evolving in the last two decades, exhibiting such changes as deregulation and the integration of renewables into the philosophical and operational mentalities. From the operational point of view, control means that involving the coordinated operation of tap changing transformers, such as capacitors, is required because loads are not constant over time and the outputs of renewable energy sources are intermittent. Voltage optimization (VO) is an effective technology that has been saving the industry millions of dollars in wasted electrical energy since the beginning of the new millennium [1]. High demand used to be managed by voltage reduction [2]. Another way of helping system operation is using capacitors to improve the power factor and the voltage profile and reduce power losses [3]. Furthermore, tap operations of voltage regulators are helpful in enhancing voltage profiles. Capacitors and voltage regulators are integrated, and improved voltage profiles are obtained. However, the life span of these devices is shortened by frequent operation because they are based on mechanical switch operations. New technological developments have made electronics-based voltage regulators and capacitors available [4], thereby bringing additional flexibility into the operation of smart grids.

On the planning side, optimal capacitor locations are sought [4]. For instance, in an algorithm that depends on dynamic programming, fuzzy logic and genetic algorithm (GA) approaches are used for capacitor distribution in distribution feeders. Gravitational search algorithm was used for optimal capacitor placement in [5], whereas a teaching-learning-based optimization was used for the same aim in [6]. Capacitors can also be used to reduce the effects of harmonics in distribution systems; the harmony search algorithm was applied for this goal in [7]. Capacitor location and sizing problem have been solved by other heuristics, such as clonal selection algorithm [8], ant colony optimization algorithm [8], and PSO [9].

Producing the best possible result with the available resources is always an objective in engineering problems. Optimization problems are generally solved using two approaches. The first is based on mathematical analysis, and the second is based on numerical calculations. Numerical optimization methods can be divided into derivative-based and non-derivative-based methods. If the derivatives of the encountered model are not easy to find or a mathematical function related to the model does not exist, then non-derivative-based methods are applied. These methods are generally inspired by nature. The most popular model is GA, which reflects the evolution process in nature [10]. Subsequently, methods inspired by the behaviors of birds and fish (particle swarm optimization [PSO]) [11], improvisation process of musicians (harmony search) [12], and the navigation approach of moths in nature, which is named transverse orientation (moth flame optimization [MFO]) [13], were developed.

This work models the voltage optimization problem using three different heuristic algorithms, namely, imperialist competitive algorithm (ICA), particle swarm optimization (PSO), and moth flame optimization (MFO). Cases 1 and 2 are applicable to operation, and Case 3 is applicable to planning in distribution systems.(i)The first model changes and uses the tap positions of the voltage regulators and obtains the optimal voltage value for given load conditions of the distribution system.(ii)The second model uses only the capacitors and optimizes the sizes of these devices for given load conditions.(iii)The third model uses the voltage regulators and the capacitors and finds the optimal tap positions, capacitor sizes, and locations.

MATLAB and a free power distribution system simulation tool OpenDSS [14, 15] are used in the simulations.

The rest of the paper is organized as follows. Section 2 proposes the voltage optimization models. Section 3 briefly explains ICA, PSO, MFO, and modified algorithm-based voltage deviation. Section 4 presents the experiments and the simulation results. Section 5 presents the conclusions.

#### 2. Model

We model three different cases.

*Case 1. *This case considers tap changers for the voltage regulators to minimize voltage deviations. The optimization model is as follows: where denotes the fitness values (cost), is the number of buses, is the voltage magnitude of bus , Tap_{i} is the tap position of the regulator, and and represent the minimum and maximum positions that a tap in a regulator can take, respectively. These values are in the range of .

*Case 2. *This case considers changing the size of the capacitors, and the model is as follows: where represents the fitness values (cost), is the number of buses, is the voltage magnitude of bus , is the size of the bank capacitor, and is the maximum size of the bank capacitor.

*Case 3. *This case integrates Cases 1 and 2 and changes the locations of the capacitors. The mathematical model is as follows: where represents the fitness values (cost), is the number of buses, is the voltage magnitude of bus , is the tap position of the regulator, and represent the minimum and maximum positions that a tap in a regulator can take, respectively (these values are in the range of ), is the size of the bank capacitor, is the maximum size of the bank capacitor, represents the location of the capacitors, and represents the maximum bus location.

#### 3. Heuristic Algorithms

##### 3.1. Imperialist Competitive Algorithm (ICA)

###### 3.1.1. General Approach

ICA was recently developed in 2007 by Esmaeil Gargari and Caro Lucas for continuous optimization problems [16]. The working philosophy corresponds to other evolutionary algorithms and initially creates random solution candidates called countries. The cost function of each solution candidate shows the power of each country. Hence, populations are composed of either colonized or imperialist countries. According to random rules, a part of a population is selected as the imperialists or the powerful countries, and the remaining part of the population comprises the colonized. Figure 1 presents a flowchart of ICA [16].