Reliability and cost optimisation of complex electric power networks using ant colony algorithm

ITM Web of Conferences 15, 02006 (2017) CMES’17 DOI: 10.1051/itmconf/20171502006 Reliability and cost optimisation of complex electric power networks using ant colony algorithm Łukasz Piątek1,* 1 Częstochowa University of Technology, Institute of Information Technology, 42-200 Częstochowa, Poland Abstract. The article presents a new approach towards reducing an overall cost of electric power network with maintaining its reliability. Goals are achieved by implementing an ant colony algorithm with a cut-set method as a method for reliability evaluation. The algorithm solves the problem of multi-objective optimisation, where both the network cost and network reliability index, known as unavailability, should be minimalised. The network cost is considered as a linear function of overall length of network’s connections. For reliability evaluation in the cut-set method, real empiric data of hazard rate for overhead power lines are used. Parallel-series network structure, equivalent by means of reliability to analysed network, is generated through the cut-set method to compute unavailability of trial solutions. Sections of the structure are generated on the basis of minimum cut set, found by the algorithm for finding one- and two- minimum cuts. As used algorithm for finding minimum cuts has linear complexity, the evaluation of trial solutions is computationally effective. An example, presented in this article, provides figure of optimal network configurations found by the algorithm. 1 Introduction Overhead power lines are exposed to various environmental conditions that threatens outages in continuity of electric power delivery to the end consumers. Various consumers have different endurance to power outages. As a typical household can bear up with several hours power outage, for industrial, business and utility customers, lack of power continuity could create damage and money loss. As some customers are willing to pay more for reliability of their power supply, it is up to electric grid operator to provide the best possible service. To achieve better reliability, the grid operator has two choices. Either an improvement in reliability of key components of the network or an introduction of some redundancy into the network. Both solutions come with drawbacks because usually they require additional spending on building and maintaining the network structure. Improving reliability of such network components as overhead lines cannot be easily done, as they are vulnerable to weather conditions. Thus, fast response repair teams are used, that can repair a fault as soon as possible. The second solution, adding redundancy, provides alternative paths the can be used while some components of the network are damaged and under repair. The designing of such power network that has the highest reliability with the lowest cost states a multi-objective optimisation problem. This paper addresses this problem by providing an approach based on adapted ant colony optimisation algorithm [1]. The * modification introduced into the algorithm involves pheromone value updates based on the value of fitness function, heuristic search of solution space, as well as effective reliability estimation of trial solutions. Similar problems of optimisation were considered in different studies. The approach in which there is a need to maintain connections between all network nodes was analysed in [2,3]. Networks where only k nodes must be connected where considered in [4,5,6,7]. Simulated annealing was considered in [8]. Heuristic algorithms were proposed in [4,5,6]. Genetic algorithms for network optimisation were proposed in [9,10,11]. In [11] a Monte-Carlo method it was used to evaluate the reliability of networks coded by the individuals in population. In [10,11] the reliability estimation it was done by computing the sum of maximum distance between nodes. The author of this paper also designed a genetic algorithm for this problem in [12]. 2 Ant colony optimisation Observation on biological processes and behaviours led to design of new algorithms used in problem solving. The ant colony optimisation algorithm is based on how insects search for food. First proposed in [1], it consists in allowing a population of ants searching for trial solutions by exploring the solution space through random walking. The crucial point is that each ant deposits an information about recent movements in the form of chemical component called in biology a pheromone. The levels of pheromones are then read by other ants and used by them as a guidance in their walk. Corresponding author: © The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/). ITM Web of Conferences 15, 02006 (2017) CMES’17 DOI: 10.1051/itmconf/20171502006 The more ants choose a path, the more likely it is for an ant to decide to follow that path. The probability of an ant choosing to move from state x to state y is given by: 𝑝𝑝 𝛼𝛼 ⋅𝜂𝜂 𝛽𝛽 𝜏𝜏𝑥𝑥𝑥𝑥 𝑘𝑘 𝑥𝑥𝑥𝑥 = 𝛼𝛼 ⋅𝜂𝜂 𝛽𝛽 𝑥𝑥𝑥𝑥 ∑𝑧𝑧∈𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑎𝑦𝑦 𝜏𝜏𝑥𝑥𝑥𝑥 𝑥𝑥𝑥𝑥 operational time, we can assume that simultaneous outage of more than two connection is very unlikely. This allows to consider only 1 and 2 elements minimal cut in the cut set method. Of course, any catastrophic failure, that involves all area of the network, like flood or weather storms, can destroy many connections. But for such events network redundancy is not enough to prevent failure anyway. In this paper, we deal only with connections failures that are independent. The reliability of network connections is usually measured empirically. Failures of the network elements occur with the mean time which is called Mean Time To Failure – MTTF. The repair rate is referred as Mean Time To Repair – MTTR. These are the two network component reliability indicants used as data for the optimisation algorithm. Additionally, an index named failure rate λ is frequently used for describing components reliability. Since a typical component of electric power network is characterised by a constant failure rate, the number of failures occurring over a period of time referred to original, total population has the exponential distribution. Then, the relationship between component’s MTTF and failure rate can be defined as MTTF= λ-1. The study in [14] provides values of failure rate and MTTR for various components of electric power networks. For typical overhead distribution lines, the value of hazard rate per circuit kilometre λP is 0.0625 per year and the value of MTTR is 4.0 hours, regardless of line length. Since the failure rate value is given per circuit kilometre, we need to treat a line as a series of one-kilometre length lines. Then, the following formula is used to compute reliability indices of a connection between two network’s nodes: (1) where τxy is the pheromone level assigned to the connection (x, y) and ηxy is some heuri (...truncated)