SEQUENCING AND SCHEDULING OF GENERATING SYSTEMS

Abstract

With the increasing population growth tho problei of optimal sequencing and scheduling of generating systems has gained great momentum. The different capacities, sites and times of construction of various units pose wide variety of problems. Minimum and maximum capacities of the plants at various sites, capital and operating costs, reliability of supply are some of factors to be taken into consideration. In general, this involves the determination of capacity, sequence and schedule of the generating facilities, watch. «e to be installed during a planning horizon so as to meet the forecasted demand with some percentage reserve margin. The present work is primarily concerned with the development of mathematical models and sequencing and scheduling algorithms for a range of decision making situations arising in the planning of generating systems. First, the sequencing and sizing of electric generating facilities i3?eccfi8^de^d.The. sequencing and sizing problem.- is to determine over certain planning horizon, the capacity and sequence of generating facilities that should be brought out into a power system in order to satisfy the forecasted demands for electricity. The objective is to minimize the present worth of all the investment and operating costs incurred for power generation over the planning horizon. It is further assumed that one type of plant can be expanded only once in the whole planning period. Sequencing constraints have also been neatly imbedded in the mathematical model developed. The mathematical model thus formulated takes the ?m

form of a mixed integer nonlinear program. A new algorithm capable of handling efficiently nonlinear mixed integer programming problems, has been presented and used for the solution of the above problem. The mode of approach is by converting the constrained mixed integer nonlinear programming problem into unconstrained mixed integer non linear programming problem with the help of interior point discretization penalty function. Powell's method is used for the unconstrained search process. In the next section, the problem of expansion planning of generating systems is considered in still more broader perspective. The problem attacked here is to determine for each year over some planning horizon, what * types and sizes of generating plants should be brought into the system and what should be their generation schedule over the span of each year so as to meet the system forecasted demands for electricity. The objective is to minimize the present month of all the investment and operating costs incurred for generation over the planning horizon. The mathematical model developed is capable of handling different types of electric power generating technologies that are available to satisfy time variable power demands. For different demand situations, different generation schedules are required, hence correspondingly different operating costs are incurred. To reflect this and properly evaluate the operating costs, the load duration curve is segmented into various subintervals for each planning horizon Modified Bender's algorithm is used for the analysis of (iii) sequencing and scheduling problem. The technique is computationally much more powerful than classical Bender's algorithm. Next, the sequencing and scheduling of water resources systems is presented. Mathematical structures are formulated involving optimal selection, sequencing and timing of a set of water resources development projects which in the aggregate must satisfy the large number of continuous time demand projections at every point in a finite planning horizon. The problem is complicated by both the number and nature of the individual capacity expansion projects (e.g. reservoirs, hydro-electric power projects). An optimization technique is presented for the solution of the problem. The method is superior to other well known integer programming procedures as it exploits the special properties of the model. Next, the problem of optimizing the production of electric power, when hydro-electric and thermal plants are available, is presented. The optimum hydro-thermal generation scheduling problem is to find out the water discharge from the reservoirs for power generation and corresponding thermal generation so as to minimize the fuel cost while satisfying the load demand constraints, constraints on reservoir levels, limits an hydro and thermal generations of each unit and the continuity equation. A new decomposition technique has been developed so as to reduce the size of the problem and computer time and memory requirements.

The number of variables in the decomposed subproblem are also reduced by variable elimination. Hence large size hydro-thermal scheduling problems can be easily handled by this approach. Lastly, the problem of optimal maintenance scheduling of generating systems is considered. The general purpose of determining a maintenance schedule is to find the time and sequence of outages of generating units over a given period such that a minimum level of specified security is achieved and the costs involved are minimized. A new mathematical model is developed for this problem by considering -power import and uncertainty. The model considers the effect of uncertainties on the power forecasts and the forced outages of generators on scheduling. The objective is expressed as the minimization of the average weighted unavailability, it combines the effect of unit planned outage length and the unit deterioration between outages. Modifiexf Bender's algorithm is used for the solution of the problem. .. .. The computer-programs are developed for all the algorithms discussed so far and have been applied to solve sequencing and scheduling problems of various generating systems. To illustrate the method of attack, numerical examples are incorporated. At the end future avenues of research in the area are discussed.