Optimization and estimation of reliability indices and cost of Power Distribution System of an urban area by a noble fuzzy-hybrid algorithm

Highlights

• The paper described fuzzy-hybrid algorithms in Power Distribution System (PDS).

• The paper explained hybridization between Genetic Algorithm (GA) and Quantum mechanized Particle Swarm Optimization (QPSO).

• The paper proposed minimization problem of reliability indices (SAIFI and SAIDI) and system cost.

• The paper suggested fuzzy-inference rule to describe dependency between load, failure-rate and SAIFI, SAIDI and system cost estimation using the Fuzzy Inference System.

• The paper introduced Fuzzy Linguistic Rule-based System.

Abstract

Power Distribution System (PDS) in an urban populated area suffers from interruptions due to uncertain faults, which degrades its reliability. Better performance of the PDS can be achieved by minimizing the most commonly used reliability indices like System Average Interruption Frequency Index (SAIFI) or System Average Interruption Duration Index (SAIDI) as well as minimizing PDS cost (both installation and maintenance cost). Number and position of Reclosers and fuses (protective devices) and switches in a PDS play an important role in enhances the performance of a PDS while lowering its cost. As the problem is inherently related to real-life activities, it can be modelled better by fuzzy logic. In this paper, the single, as well as a multi-objective optimization problem of minimizing the cost and reliability metrics, has been solved by the help of a noble fuzzy-hybrid algorithm. The outcome of the proposed algorithm is a PDS with a modified number of a recloser, fuse and switch and their arrangement in the network. Two well-known and well-organized meta-heuristic algorithms named as improved Genetic Algorithm (GA) and Quantum mechanized Particle Swarm Optimization (QPSO) are hybridized with fuzzified inputs and the outputs are defuzzified in order to minimize reliability metrics and cost. The obtained result set is compared with existing works of literature to establish that the model developed is more reliable in terms of fault tolerance as a fuzzy repair rate and the fuzzy failure rate has been considered in the experiment. As an offshoot, a rule-set is also obtained that may help the future decision process.

Introduction

The objective of designing a power distribution system (PDS) is to make it perform at an optimal level. Power distribution systems mainly consist of feeders, reclosers, circuit breakers, switches, fuses, etc. The location and number of these components are the most important factors to determine the effectiveness and cost-efficiency of the system. Switches can minimize the duration of customer interruption. Fuses guard the feeder section (main section) by isolating defective lateral sections (shown by thin lines in Fig. 1). Fuses are not present in the main section of the network because if a fault occurs, the main section should be disconnected from the network. A recloser acts as a protective as well as a switching device. It manages faults which are temporary or sudden and permanent or persistent. Whenever a fault occurs, reclosers have a unique ability to perform as an isolator to the downstream section, so that the upstream section remains undisturbed; this property is called trip or reclose function.

Two metrics, namely SAIFI and SAIDI, are most commonly used to determine the reliability of a PDS, Importance of these two metrics for determining the reliability of a PDS is explained in [1]. Another important aspect of this paper is that it captures uncertainties and catastrophes of a PDS using fuzzy concepts [2]. Uncertainties that affect system parameters in a PDS are many. This paper deals with two most important such parameters: (i) variation of load and (ii) differences in failure and repair rate depending upon various constraints. We have used a case study for introducing the fuzzy approach as reported the surveys by Sathya and Tyler (1991) [3] and Tongsopit and Greacen. (2013) [4]. More about these surveys are discussed in later sections.

Enhancement of system reliability by minimizing reliability indices such as SAIFI and SAIDI and optimization of cost of the corresponding system has been the main objectives of many researchers for the last few years. In the book by Allan (2013) [5], the central queries about the enhancement of reliability of Power Distribution System (PDS) are well explained. Tippachon and Rerkpreedapong (2009) [6], proposed an exclusive model to achieve higher reliability and the least cost by solving a multi-objective function using ant colony system (ACS) [7]. Their goal was to suggest the best positions of switches and protective devices (Fuses) to design a PDS. In 2005 Popović et al. [8] proposed an ideal assignment of reclosers as well as distributed generators to improve system reliability.

The problem of maximizing the reliability of a PDS and minimizing its cost is an optimization problem in general. Evolutionary Algorithms (EAs) have been considered as suitable techniques to solve such optimization problems to obtain global optima rather than local optima [9]. EAs describe heuristic methods based on population modification strategies inspired from natural evolution, such as GA [10], [11], Evolutionary Programming (EP) [12], [13], [14], Evolutionary Strategy (ES) [15], [16], Genetic Programming (GP) [17], Swarm Optimization [18], Ant Colony Optimization [19] etc. Among these, GA is the most popular EA [20] and it is considered as one of the foremost proficient and predominant heuristic search optimization technique [21], [22], [23] based on the technicalities of natural genetics and natural selection, which mimics the basic and primitive rule of “Survival of the fittest” of Charles Darwin. Prof. J. H. Holland first introduced the concept of this algorithm. The detailed research work on this topic is presented in many books and articles such as Goldberg (1989a) [24], Goldberg (1989b) [25], Michalewicz and Schoenauer (1996) [14], Mitchell (1996) [26], Sakawa (2002) [27] and others.

Depending upon the swarming characteristic of fish or birds, Eberhart and Kennedy (1995) [28] proposed an algorithm called particle swarm optimization (PSO) for solving optimization problems. Different variants of PSOs have been invented by different researchers [29], [30], [31], [32], [33]. Sun et al. (2004) [34] developed a new algorithm called Quantum-mechanized Particle Swarm Optimization (QPSO) which draws ideas from the quantum property of particles.

Many researchers have used Genetic Algorithm (GA) and Quantum mechanized Particle Swarm Optimization (QPSO) to get an optimal PDS design by maximizing reliability and minimizing cost. In [35], authors have found out the optimal placement of reclosers and distributed generators in a PDS for maximizing reliability and minimizing cost. Li and Brown (2004) [36] achieved a PDS with higher reliability and the least cost by ranking based on the “benefit-to-cost ratio” parameter. Cost analysis and cost-effectiveness of any different heat pump system can be easily understood by articles of Esen et al. [37], [38], [39].

As different bio-inspired optimization techniques have their advantages and disadvantages, many researchers have developed hybrid meta-heuristic optimization techniques [40], [41]. This paper describes different variants of hybrid approaches based on GA and QPSO.

Researchers have proposed different hybridization techniques for single, as well as multi-objective optimization problems [27], [42], [43]. Hybridization of evolutionary algorithms can be described as a selection of different improved and/or traditional operators [43]. Application of Hybrid evolutionary algorithm in case of the single-objective function can be well understood by the proposed research works of Elhossini et al. (2010), and Li and Wang (2007) [42], [43].

Objective and contribution: The objective of this paper is to design a PDS in which reliability indices namely, SAIFI and SAIDI, and the operational cost are minimized. In order to do so, two meta-heuristic algorithms (GA and QPSO) have been considered for hybridization. QPSO is chosen as it is more robust than the PSO algorithm.

For solving single as well as Multi-Objective problems, different techniques to hybridize certain evolutionary algorithms have been reported in several works of literature. When hybridization of two evolutionary algorithms takes place, it is expected that they can compensate each other’s drawbacks effectively. GA is often hybridized with PSO technique (Sahoo et al. 2014) [41]. Both these algorithms have their advantages and disadvantages. Generally, PSO is known to be a local search technique and it always reaches some local optimal solution (swarm) from the solution space. The choice of the initial point (personal best position) is very important for PSO and it is selected using randomness techniques depending on the problem. During local search personal best position is modified and the search approaches some global best position. On the other hand, the performance of a global search technique such as GA is less dependent on its initial position(s) and it tends to converge to the global optima. However, PSO is usually faster than GA and may quickly converge to a solution if the initial choice (personal best position) is good. If one phase of GA is followed by another phase of PSO and this interleaving continues, the shortcoming of one algorithm may be compensated by the other in successive phases [42], [43]. This possibility motivated us to hybridize these two techniques.

We have used a fuzzy number system to deal with the inherent uncertainties of the system. The hybrid GA–QPSO algorithm is further modified to develop another algorithm, namely fuzzy GA–QPSO algorithm to take care of the real-life uncertainties inherent in a PDS. As another offshoot of our paper, a Fuzzy Linguistic Rule-based System has been generated by which Load and failure/repair rates are used to predict the reliability indices (SAIFI and SAIDI) and the cost of the network. The input variables are chosen carefully. Only the ones which have a high impact on the performance of a PDS are chosen as input parameters in the rule-based system.

We have used the survey [Annu. Rev. Energy. Environ. 1991.16:295-335 and Summary of Thailand power development plan 2012–2030] [4] as a case study in this paper. Loads in different section-paths have been considered as interval numbers while failure rate and repair rate have been considered as fixed over the time-period. Results and analysis as presented in Table 7, Table 8, Table 9, Table 10, Table 11, Table 12, Table 13, Table 14, Table 15 indicate that the PDS designed by our approach is better than one reported in the existing works of literature.

The outline of the paper is as follows. Section 1 enumerates the symbols used in this paper and its meaning. The problem definition, motivation, and contributions are described in Section 2. The problem is formulated in clear mathematical terms in Section 2. The design of the hybrid algorithm for the problem is discussed in Section 3. Introduction to the fuzzy approach and the fuzzy hybrid algorithms are discussed in Sections 4 Introduction to the fuzzy approach, 5 Development of the Fuzzy GA-QPSO algorithm. Results and discussions are presented in Section 6. In Section 7, we conclude.