Page 67 - Mathematical Models and Algorithms for Power System Optimization

Optimization of Annual Generator Maintenance Scheduling 57

Based upon the modeling approaches in Section 3.2 and these notation definitions, the
following objective functions and constraints of GMS can be formed.

3.3.2 Objective Function

(1) The GMS may select the reserve margin of maintenance as the objective function for
systems of high load level and small system reserve:

f
max min P RM i, tð Þgg i 2 i, …, Ng, t 2 1, …, Tg (3.1)
f
f
f
The meaning of the objective function is that, for each unit i to be maintained, first find the
minimum values of maintenance reserve P RM (i,t) in every possible “maintenance period,”
then find the maximum among these minimum values. The “maintenance period”
corresponding to the maximum is considered the optimal maintenance arrangement time
of unit i.
(2) The GMS may select the production and maintenance expenses as the objective function
for systems of low load level and large system reserve:

( )
N T N
XX X
min C Pi P Gi 1 Y it Þ + C Mi Z i tðÞ (3.2)
ð
i¼1 t¼1 t¼1
3.3.3 Constraints

(1) Maintenance reserve constraint. In the GMS problem, relations between the
maintenance reserve and system output and forecast load of the system in interval t are
shown here:
N
X
P SC tðÞ ¼ P Gi + P HY tðÞ + P SC tðÞ + P EP tðÞ P SS tðÞ (3.3)
i¼1 !
N
X
P RM tðÞ ¼ P SC tðÞ P D tðÞ Y it P Gi (3.4)
i¼1
Based on Eq. (3.4), the maintenance reserve constraint of the system is given:
(3.5)
P RM tðÞ=P L tðÞ R t
In a practical system, R t is generally 10%–15% or P RM is equal to or greater than the
capacity of one or two units with the maximum capacity in the system.
(2) Maintenance window constraint, which means the earliest and latest maintenance start
time constraint of the unit. For unit i, it is expressed as:

0, t > E i or t > L i
Z i tðÞ ¼ (3.6)
1, E i t L i and t ¼ maintenance start time