OPTIMAL SCHEDULING IN THERMAL GENERATING SYSTEMS

Abstract

As power system generating facilities increase in size, number and complexity, the power utility is faced with a range of decision scheduling problems. The simple rules of thumb, based on human judgement alone are no longer applicable in the solution of intricate cases. The applica tion of mathematical programming techniques as a supplement to human judgement has aroused considerable interest among power system engineers. The present work is primarily con cerned with the development of mathematical models and sche duling algorithms for a range of decision making situations arising in the daily and/or periodic functioning of a power plant or group of power plants under centralized administra tion. Based on the structure of the mathematical models used the work is classified into two parts. In the first part,a number of maintenance scheduling and allied problems are formulated as integer linear and nonlinear programs. In the second part, generation scheduling problems are formulated as mixed integer nonlinear and continuous variable nonlinear programs. First of all, the problem, of preventive maintenan ce scheduling is discussed. A 0-1 integer programming model is presented for obtaining minimum maintenance cost schedules. A set of comprehensive and interacting cons traints, such as sequencing of generating units, security

considerations , resources limitation etc. are transformed into the integer programming format. The problem becomes an involved one, when a large number of units are to be maintained during the multiperiod scheduling horizon. A new, simple and efficient optimization technique is deve loped for the solution of the problem„ The method is supe rior to the other known integer programming procedures as, it exploits the special properties of the model. In the overhauling of power plants? the maintenance staff is inter changed between stations at times of overhauls. A mathema tical description of the problem of staff interchange sche duling is presented and solved through the 0-1 programming approach. Thus, the program makes available the required number of craftsmen of each category at the minimum cost. Next, the problem of corrective maintenance schedul ing is presented. To have built-in maintenance at the design or planning stage is referred to as the problem of corrective maintenance. A system analyst / designer is faced with the problem of designing systems having failure free operation. Such an objective is fulfilled by designing critical subsystems having a high degree of reliability. A nonlinear programming formulation of the corrective maintenance scheduling problem is presented. The analysis results in the optimal number of standby components and repair facilities to achieve a specific level of system iii reliability. A new scheduling algorithm is devised and the results of computatj m are presented for generator r> excitation system and turbine cooling system . T — In the next section, the problem of maintenance budgetary control is discussed. Choosing a sound and effective maintenance policy reduces the system down-time and thus increases the revenue to the utility. The objec tive is aimed at selecting that set of proposals which will maximize the net present value of its total expected return. The problem is discussed under conditions of cer tainty and uncertainty. Amathematical version of the problem is presented and scheduling algorithms are develo ped for deterministic and probabilistic cases. After the units have been scheduled for preven tive maintenance on annual basis, the next problem is the selection of units out of the available set for real time operation. This is referred to as the problem of unit commitment scheduling. The total production cost to be minimized is the sum of running cost, shut down cost and time dependent start up cost . The security model incor porated provides a means for assessing system security in hour-to-hour operation on a probabilistic basis., An eff icient computation procedure is/ developed based on the premise of feasibility and economic dispatch. Results of computation are presented to obtain a 2^hour schedule

for a medium size system drawn from the literature. In the end a continuous variable nonlinear model is presented for the real power scheduling. A linearized representa tion of the network is used to include the effect of trans mission losses. An efficient multivariable constrained search iterative procedure is developed for the solution of coordinating equations. A scheduling algorithm is developed and results are presented for a sample system. The computation time and storage are encouragingly small- Avenues of future research in the area are discussed.