Abstract
The most important phase in many industrial power applications is the design problem. Usually the demand increases randomly with time in the form of a cumulative demand curve. To adapt the power system capacity to the demand, new power architecture is predicted. To build this latter, the reliability optimization plays an important role to find the realizable power system architecture. This chapter describes and uses different meta-heuristics optimization methods to solve the redundancy optimization problem for multi-state series-parallel power systems. The authors consider the case where redundant power components are chosen to achieve a desirable level of reliability. The power components of the system are characterized by their cost, capacity, and reliability. The proposed meta-heuristics seek the optimal architectures of series-parallel power systems in which a multiple choice of components are allowed from a list of products available in the market. The approach has the advantage of allowing power components with different parameters to be allocated in power systems. To allow fast reliability estimation, a Moment Generating Function (MGF) method is applied. An illustrative example is presented.
Top1. Introduction
Electrical power productions systems are frequently built with electrical power components connected in series parallel arrangement. New system architectures have been considered as an important problem in power systems and in manufacturing systems. For instance, modifying an existing architecture, designing a new architecture and adding new components (reinforcement) belonging to the redundancy optimization problem (ROP). This latter is a well-known combinatorial optimization problem where the new architecture is achieved by numerous discrete choices made from components available on the market.
This chapter describes and compares the implementation of some optimization algorithms as Particle Swarm, Harmony Search and Immune System (PSO, HS, IS) to solve the ROP involve the selection of electrical components and the appropriate levels of redundancy to maximize system reliability or minimize investment cost of series-parallel architecture, given architecture constraints (reliability, cost and performance). However, the capacity of many power production systems is defined by multiple heterogeneous units. In this situation, the system can have several levels of performance: from perfect working to total failure. In this case, it is considered as a multi-state system (MSS).
The MSS redundancy, addressed in this chapter is a common representation for many system design problems. The detailed seeks and allocation component method of system reliability discussed here is the designed to select the optimal solution in the context of reliability and/ or investment optimization of electrical power network analysis, given the overall restrictions on the system performance and cost. The problem is to determine which alternative (architecture) to select with the specified level of electrical device reliability, and what kind of components to use in order to achieve the minimal system investment or maximum system reliability.
This formulation of the redundancy allocation problem for series-parallel electrical network system, leads to the objective functions given by the components of each sub-system. In this work, the aim is to adapt different meta-heuristics which include a modern technique (Ushakov, 1973) to select and to evaluate the best architectures with minimal investment and/ or maximal reliability met the various constraints.
Literature Review
The vast majority of classical reliability or availability analysis and optimization assume that components and system are in either of two states (i.e., complete working state and total failure state). However, in many real life situations we are actually able to distinguish among various levels of performance for both system and components. For such situation, the existing dichotomous model is a gross oversimplification and so models assuming multi-state (degradable) (Maymin, 1973; Natvig, 1986, 1982; El-Neweihi, 1984) systems and components are preferable since they are closer to reliability.
Recently much works treat the more sophisticated and more realistic models in which systems and components may assume many states ranging from perfect functioning to complete failure. In this case, it is important to develop MSS reliability theory (Zeblah et al., 2010). In this chapter, an MSS reliability theory will be used, where the binary state system theory is extending to the multi-state case. As is addresses in recent review of the literature for example in (Ushakov et al., 2002; Levitin et al., 2001).
The problem of total investment-cost minimization, subject to reliability or availability constraints, is well known as the redundancy optimization problem (ROP). The ROP is studied in many different forms as summarized in (Tillman et al., 1977) and more recently in (Kuo et al., 1977). The ROP for the multi-state reliability was introduced in (Ushakov, 1987; Lisnianski et al., 1996; Levitin, 1997).
This chapter uses a different meta heuristic’s (PSO, HS and IS) optimization approach to solve the ROP for multi-state system.
Key Terms in this Chapter
Redundancy (ROP): Redundancy optimization problem. The provision of multiple interchangeable components to perform a single function in order to provide resilience (to cope with failures and errors). Redundancy normally applies primarily to hardware. For example, a cluster may contain two or three computers doing the same job.
Multi-States System (MSS): In natural life electrical, hydraulic and mechanical components or devices are prone to failure. The capacity of many production components systems is defined by multiple heterogeneous or homogeneous units. In this situation, the system can have several levels of performance: from perfect working to total failure. In this case, it is considered as a multi-state system (MSS). Generally the most of working consider the situation where component have only two state perfect and total failure, for this reason we consider the real case of component the MSS situation.
Genetic Algorithm (GA): In the computer science field of artificial intelligence, genetic algorithm is a search heuristic that mimics the process of natural selection. This heuristic (also sometimes called a meta-heuristic) is routinely used to generate useful solutions to optimization and search problems. Genetic algorithms belong to the larger class of evolutionary algorithms (EA), which generate solutions to optimization problems using techniques inspired by natural evolution, such as inheritance, mutation, selection, and crossover. Genetic algorithms find application in bioinformatics, phylogenetics, computational science, engineering, economics, chemistry, manufacturing, mathematics, physics, pharmacometrics, and other fields.
Particles Swarm Optimization (PSO): The Particles Swarm optimization is a meta-heuristic as it makes few or no assumptions about the problem being optimized and can search very large spaces of candidate solutions. However, meta-heuristics such as PSO do not guarantee an optimal solution is ever found. More specifically, PSO does not use the gradient of the problem being optimized, which means PSO does not require that the optimization problem be differentiable as is required by classic optimization methods such as gradient descent and quasi-Newton methods. PSO can therefore also be used on optimization problems that are partially irregular, noisy, change over time.
Universal Moment Generation Function (UMGF): In probability theory and statistics, the moment-generating function (UMGF) of a random variable is an alternative specification of its probability distribution. Thus, it provides the basis of an alternative route to analytical results compared with working directly with probability density functions or cumulative distribution functions. There are particularly simple results for the moment-generating functions of distributions defined by the weighted sums of random variables. Note, however, that not all random variables have moment-generating functions. The moment-generating function does not always exist even for real-valued arguments, unlike the characteristic function. There are relations between the behavior of the moment-generating function of a distribution and properties of the distribution, such as the existence of moments.
Harmony Search (HS): In computer science and operations research, harmony search (HS) is a phenomenon-mimicking algorithm (also known as meta-heuristic algorithm, soft computing algorithm or evolutionary algorithm) inspired by the improvisation process of musicians. In the HS algorithm, each musician (= decision variable) plays (= generates) a note (= a value) for finding a best harmony (= global optimum) all together. Proponents claim the following merits: 1. HS does not require differential gradients, thus it can consider discontinuous functions as well as continuous functions. 2. HS can handle discrete variables as well as continuous variables. 3. HS does not require initial value setting for the variables. 4. HS is free from divergence. 5. HS may escape local optima.
Artificial Immune System (AIS): In computer science, artificial immune systems (AIS) are a class of computationally intelligent systems inspired by the principles and processes of the vertebrate immune system. The algorithms typically exploit the immune system's characteristics of learning and memory to solve a problem. The field of Artificial Immune Systems (AIS) is concerned with abstracting the structure and function of the immune system to computational systems, and investigating the application of these systems towards solving computational problems from mathematics, engineering, and information technology. AIS is a sub-field of Biologically-inspired computing, and Natural computation, with interests in Machine Learning and belonging to the broader field of Artificial Intelligence.