Page 66 - Mathematical Models and Algorithms for Power System Optimization

56 Chapter 3

such an arrangement will also sometimes affect the reliability of the power
transmission. The area maintenance capacity constraint regulates the maximum
capacity or the maximum number of units for simultaneous maintenance in the area.
2. Maintenance time nonoverlapping constraint, which is an important constraint related
to the actual operation of GMS. Due to limitations such as site, tool, equipment,
available manpower, etc., it is generally not feasible to have two or more units
maintained in the same power plant. Therefore, the maintenance time of all units
should not be overlapped. In other words, in each power plant, only one unit can be
maintained at a time generally.

3.3 Formulation of the GMS Problem

3.3.1 Notations

Notations are shown in Table 3.2.

Table 3.2 Notations
Notation Description
N Total number of units involved in the GMS
T Total number of time intervals in the GMS period (one time interval¼one time unit)
i Count variable of units
t Count variable of time intervals
P sc (t) The total generation capacity in interval t,in MW
P Gi The rated capacity of unit i,inMW
P L (t) The system forecast load in interval t,inMW
P EL (t) The system equivalent load in interval t,inMW
P HY (t) Dependable system capacity of hydropower plant not involved in the GMS in interval t,in MW
P SG (t) Dependable system capacity of small thermal power plant not involved in the GMS in interval t,in
MW
Exchange power with external system in interval t
P EP (t)
P EP (t)>0: with input power; P EP (t)<0: without output power; P EP (t)¼0: no exchange power
P SZ (t) Sum of disabled capacities where the units fail to reach full capacity in interval t or the minimum
reserve capacity of the system, in MW
P RM (i,t) Maintenance reserve margin in interval t,inMW
Y it Maintenance state variable, Y it ¼1 or 0, meaning that unit i is either under or not under
maintenance in interval t
Z i (t) Maintenance start variable, Z i (t)¼1,0 means that t-th interval is either the maintenance start
time or not of unit i,I
C Pi Unit production expenses (or coal consumption) of unit i
C Mi Maintenance expenses of unit i
R t Lower limit of the ratio (maintenance reserve power/forecast load)
Number of time intervals in maintenance cycle of unit i
Period(i)
Number of shiftable time intervals within maintenance cycle of unit i
Shift(i)