Page 71 - Mathematical Models and Algorithms for Power System Optimization

Optimization of Annual Generator Maintenance Scheduling 61

Fig. 3.3
Fuzzy membership function curve of production expenses.
3.4.3 Formation of Fuzzy Constraints for GMS Problem

The constraint boundary of GMS may be described by the fuzzy membership function μ xðÞ.
c
(1) Fuzzy maintenance window constraint. Two edges of the maintenance window are the
earliest and latest maintenance start times of the unit. The fuzzy membership function is
expressed as:
8
ð
M slb iðÞ M st i, tÞ
>
1 W sle Þ < M stb
> , M sle M st i, tð
<
M stb iðÞ M sle iðÞ
μ ð i, tÞ ¼ (3.14)
c1
M st i, tÞ M st iðÞ
ð
>
> , M sle M st i, tð
: 1 W sll Þ < M sll
M sll iðÞ M slb iðÞ
where M st (i,t)—maintenance start time in state (i,t), M sle (i)—the earliest acceptable
maintenance start time for unit i, M sll (i)—the latest acceptable maintenance start time for
unit i, M slb (i)—the optimal maintenance start time for unit i, W sle —weight coefficient that
advances maintenance time, W sll —weight coefficient that delays maintenance time. The
fuzzy membership function curve of maintenance window is shown in Fig. 3.4.

Fig. 3.4
Fuzzy membership function curve of maintenance window.