Journal of ELECTRICAL ENGINEERING, VOL. 55, NO. 3-4, 2004, 57–63 ANT COLONY OPTIMIZATION FOR NEW REDESIGN PROBLEM OF MULTI–STATE ELECTRICAL POWER SYSTEMS Rabah Ouiddir * — Mostefa Rahli * — Rachid Meziane ** — Abdelkader Zeblah *** The most important phase in many industrial 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 a new design is predicted. This paper uses an ant colony optimization (ACO) method to solve the new redesign problem for multi-state series-parallel power systems. The study horizon is divided into several periods. A multiple-choice of components can be chosen and included into subsystem component at any stage to improve the system performance. The components are characterized by their cost, performance and availability. The objective is to minimize the investment over the study period while satisfying availability or performance constraints. A universal generating function technique is applied to evaluate power system availability. The ant colony approach is required to identify the optimal combination of components with different parameters to be allocated in parallel. Keywords: new redesign, ant colony, multi-state, power system, universal generating moment function 1 INTRODUCTION In many industrial systems, new systems designs have been considered as an important problem, eg , in power systems and in manufacturing systems. For instance, modifying the existing structure, designing a new struc- ture and adding new components (reinforcement) belong- ing to the redundancy optimization problem (ROP) as suggested in (Levitin, Lisnianski, Ben-Haim and Elmakis, 1997). This latter is a well- known combinatorial opti- mization problem where the new design is achieved by numerous discrete choices made from components avail- able on the market. Based on the cost, availability and performance, the objective function is to minimize the investment-costs over each study period within the plan- ning horizon for a certain availability or (reliability) re- quirement. Figure 1 shows a typical series-parallel power structure. However, the capacity of many power produc- tion systems is defined by multiple heterogeneous units. In this situation the system can have several levels of per- formance: from perfect working to total failure. In this case it is considered as a multi-state system (MSS). The MSS system consists of n subsystems C i ( i = 1, 2,...,n ) in series arrangement. Each subsystem C i can contain several components of type i connected in par- allel from various versions on the market. Each version in turn can contain one or more identical components in parallel. Components are characterized by their cost, availability and performance according to their version. Different versions of components may be chosen for any given subsystem. Besides, a lot of alternatives lead to a change in performance and reliability, such as series- parallel modernization as in (Levitin, 1999). The simplest method in this work to help system performance to face the increased demand is a new design. Component 1 Subsystem C 1 Component 2 Component 3 Component K1 Component 1 Component 2 Component 3 Component K2 Component 1 Component 2 Component 3 Component Kn Subsystem C 2 Subsystem C n . . . . . . . . . ... Fig. 1. Series-parallel power system structure The classical reliability theory is based on the binary assumption that the system is either working perfectly or completely fails. However, in many real life situations we are actually able to distinguish among various lev- els of performance for systems. In this case, it is impor- tant to develop MSS reliability theory. Most of research works in MSS reliability analysis extend the results to the multi-state case. A recent review of the literature can be found in (Ushakov, Levitin and Lisnianski, 2002). Gener- ally, the methods of MSS reliability assessment are based on four different approaches: (1) The structure function approach; (2) The stochastic process (Markov) approach; (3) The Monte-Carlo simulation technique; (4) The uni- versal moment generating function (UMGF) approach. The total investment-cost minimization problem, sub- ject to reliability constraints, is a well-known sequence ∗ University of Oran USTO, Engineering Faculty, Electrical Department, B.P. 89 El M Naoura, Oran, Algeria E-mail: rahlim@yahoo.fr ∗∗ University of Bechar, Electrical Department, Engineers Sciences Faculty, B.P. 8000, Bechar, Algeria ∗∗∗ University of Sidi Bel Abbes, Engineering Faculty, Electrical Department, B.P. 22000, Sidi Jillali, Sidi Bel Abbes, Algeria ISSN 1335-3632 c  2004 FEI STU