Page 72 - Mathematical Models and Algorithms for Power System Optimization

62 Chapter 3

(2) Fuzzy maintenance time nonoverlapping constraint, which reflects whether the units meet
the technical conditions for maintenance. The fuzzy membership function is expressed as:

8
0, D e i, tð Þ < D 1min
>
>
<
D 1 i ðÞ D 1 i, tÞ
ð
μ c2 1 W 1 , d 1 i, tð Þ D 1min (3.15)
e ¼
D 1 iðÞ D iðÞ
> 1
>
1, D 1 i, tÞ D ls
:
ð
where D l (i,t)—minimum maintenance interval time when reaching to state (i,t),
W l —weight of maintenance time nonoverlapping, D lmin —minimum acceptable
maintenance interval time, D ls —maintenance interval time meeting the normal
requirement, D 1 iðÞ max D 1 i, tð Þg; D iðÞ min D 1 i, tÞg:
f
ð
f
1
T T
The fuzzy membership function curve of maintenance time constraint is shown in Fig. 3.5.

Fig. 3.5
Fuzzy membership function curve under maintenance time constraint.

(3) Fuzzy area constraint. The area constraint divides the system into several areas by
geographical location, limits the concurrent maintenance capacity in each area, and
decreases the power exchange between areas so as to reduce the transmission loss and
maintain the reliability of power supply. The fuzzy membership function of constrained
boundary is expressed as:

0, M g i, tð Þ > M g jðÞ
8
> max
>
ð
< M g iðÞ M g i, tÞ
μ
e ¼ 1 W g , M g i, tð Þ M g jðÞ (3.16)
c3 max
M g iðÞ M iðÞ
> g
>
1, M g i, tÞ M g jðÞ
:
ð
where M g (i,t)—minimum maintenance capacity when reaching to state (i,t), M g (j)—
acceptable maintenance capacity in area j (the unit i is in the area), M g (j) max —maximum