Generational and Steady-State Genetic Algorithms for Generator Maintenance Scheduling Problems

The aim of generator maintenance scheduling (GMS) in an electric power system is to allocate a proper maintenance timetable for generators while maintaining a high system reliability, reducing total production cost, extending generator life time etc. In order to solve this complex problem a genetic algorithm technique is proposed here. The paper discusses the implementation of GAs to GMS problems with two approaches: generational and steady state. The results of applying these GAs to a test GMS problem based on a practical power system scenario are presented and analysed. The effect of different GA parameters is also studied. 1 Problem description Generator maintenance scheduling (GMS) is an essential part of the problem of economic operation and control of power systems, and involves finding the optimum timing of the outages of generating units. This is important primarily because other planning activities are directly affected by such decisions. In modern power systems the demand for electricity has increased with related expansions in system size, which has resulted in higher numbers of generators and lower reserve margins making the GMS problem more complicated. A good maintenance schedule increases system operating reliability, reduces generation cost, extends equipment life time and relaxes new installation pressure. The GMS problem is a complex combinatorial constrained optimisation problem. There are generally two categories of objective functions in GMS based on reliability or economic cost criteria. The problems have the following general constraints to be satisfied. • Maintenance window defines the limitation on the earliest and latest times and the duration of maintenance for a unit. • Sequence constraints the maintenance of certain units is allowed only after the maintenance of other specified units. • Non-simultaneous constraints the simultaneous maintenance of certain units is not allowed. • Crew and resource constraints consider the availability of manpower and resources. • Load constraints consider the demand and the reliability of power supply. Mathematically, GMS problems can be formulated as integer programming problems using binary variables associated with answers to "When does maintenance start?". The use of these variables instead of the variables associated with answers to "When does maintenance occur?" reduces the number of variables [1]. The first formulation satisfy the constraints on the periods and duration of maintenance. The answer to the first question automatically provides the answer to the second. Several deterministic mathematical methods and heuristic techniques are reported in the literature for solving these problems [1,2,3]. General solution methods are based on integer programming, branch-and-bound techniques, dynamic programming, etc. However, such approaches are severely limited by the 'curse of dimensionality' and are poor in handling the non-linear objective and constraint functions that characterise the GMS problem. The heuristic approach uses a trial-anderror method to evaluate the maintenance objective function in the time interval under examination. This requires significant operator input and in some situations it fails to produce even feasible solutions [3]. Genetic algorithms (GAs) provide a new approach to the solution of complex combinatorial optimisation problems. This paper describes the procedure for implementing GAs for solving the GMS problem. Two GA approaches, namely generational and steady state, have been applied to test GMS problems which include features of real systems. The paper discusses the application of GAs to GMS problems using a reliability criteria based on levelling reserve generation [3]. This is achieved by minimising the sum of squares of the reserves over the entire operational planning period.