Page 68 - Mathematical Models and Algorithms for Power System Optimization

58 Chapter 3
0, t > E i or > L i

Y it tðÞ ¼
1, E i t L i +MD i
(3.7)
E i ¼ Period iðÞ Shift iðÞ
L i ¼ Period iðÞ + Shift iðÞ
where E i —the feasible earliest maintenance start time of unit i, L i —the feasible latest
maintenance start time of unit i,MD i —maintenance duration of unit i.
(3) Maintenance time nonoverlapping constraint, which reflects the technical requirements of
two or more units generally unable to be maintained simultaneously in the same power
plant, is expressed as:
X
Y it ¼ 1 (3.8)
i2F
where F—power plant F in the system.
(4) Area maintenance capacity constraint, which limits the total capacity of units maintained
simultaneously in the area, is expressed as:

X
P Gi Y it M g JðÞ (3.9)
max
i2J
where J—area J in the system, M g (J)max—maximum capacity of units maintained
simultaneously in the area J.
(5) Maintenance manpower constraint, which limits the number of units to be maintained at
the same time for those power plants not staffed with full-time maintenance personnel, is
expressed as:
N
X
(3.10)
M Pi Y it M Pmax
i¼1
where M Pi —maintenance manpower required for unit i, M Pmax —maximum human
resources available for maintenance of the system.
Because GMS is a problem of medium- and long-term planning, its optimization objective and
constraint boundary are often uncertain and even fuzzy. Such uncertainty and fuzzy factors
make it sometimes difficult to carry out accurate numerical evaluation for optimization results,
often with larger trends based on experiential knowledge. For instance, different maintenance
scheduling in a specific time window will produce different expense indexes or reserve margin
indexes. However, the uncertainty in load, unit output, and other factors in the time window
make it unable to determine which index is the optimal one. At present, the empirical subjective
evaluation with “satisfaction degree” is more appropriate for the actual situation. Thus, proper
fuzzification of the GMS objective function and constraints will make the GMS solution
procedure more flexible.