Page 60 - Mathematical Models and Algorithms for Power System Optimization

50 Chapter 3

3.1 Introduction

3.1.1 Description of the Problem

Generator maintenance scheduling (GMS) is one of the most important measures in the
economic operation of power systems. It can improve the system operating reliability, reduce
the generation cost, extend the generator lifetime, and relax the new installation pressure. Due
to the rapid increase of demand, the expansion of power system scale has made the GMS
problem more difficult and complex. The normal maintenance schedule is the basis of
increasing the security of generation equipment and avoiding imminent faults. A scheduled
maintenance outage has less impact on the power system than a forced outage.
Solution techniques for GMS have been investigated for several decades. Examples of these
techniques are integer programming and dynamic programming. An expert system (ES), fuzzy
dynamic programming (FDP), has been applied. However, these techniques are effective only
for some systems under certain conditions. A GMS problem is a large-scale integer-
programming problem. The objective function is to maximize the reserve margins or to
minimize the production costs. The constraints consist of a reserve margin, maintenance
windows (i.e., between the admissive earliest and latest start time of maintenance),
simultaneous maintenance, continuous maintenance, the maximum area maintenance capacity,
manpower, etc.

The number of integer variables of a GMS problem is very large, even for a middle-scale
system, at about 103–104 (equal to the number of units multiplied by time intervals), so the
existing integer-programming methods cannot be used to solve such a large-scale integer
problem. However, a GMS problem can be formulated into a multistage decision-making
problem with a noncontinuous objective function and constraints with nonanalytical equations,
which can be solved by dynamic programming. Recently, a prototype ES with FDP has been
shown to be effective for a special system. However, because of the complexity of the power
system, a prototype ES cannot satisfy the diversification of a GMS problem of different power
systems.
The ES with generalized construction is discussed in this chapter, which can be applied to
different power systems or different operation conditions of the same system. The ES can be
assembled from different rules that can be used to decide the maintenance priorities of the
generators and to treat the constraints of a GMS problem. The inherence of GMS is that a
feasible solution is very hard to find, but it must be obtained for practical purposes. If no
feasible solution exists, then the constraints must be modified, or the forecasting load in certain
time intervals should be curtailed by an amount that’s as small as possible. With the aid of the
ES and the “fuzzification” of constraints, the solution time and memory of GMS will be greatly
reduced, and a reasonable strategy will be more easily obtained.