Page 32 - Mathematical Models and Algorithms for Power System Optimization

22 Chapter 2

(4) Generated output constraint of areas in each time period (inequality constraints with the
total number of N AREA )
X
AI k X i tðÞ AA k , k ¼ 1,…,N AREA ; t ¼ 1,…,24D (2.10)
i2Nk

(5) Reservoir capacity constraint of the pumped storage plant in each time period (inequality
constraints with the total number of 24D)
1. Original expression of reservoir capacity constraint

T T
X X
W min W 0 P pp t ðÞ PPC P pg t ðÞ PGC W max W 0 ,
t¼1 t¼1
t ¼ 1,…,24D; n t ¼ 1,…,24D
24D 24D
X X
W 0 W min P pg tðÞ 870 P pp tðÞ 640 W 0 W max
t¼1 t¼1
where PPC and PGC are transformation coefficients for water reserve/generated
energy during water pumping and power generation.
3
3
3
3
PPC 0:64 m =kWh ¼ 0:64 10 m =MWh ¼ 640 m =MWh
3
3
3
3
PGC 0:87 m =kWh ¼ 0:87 10 m =MWh ¼ 870 m =MWh
2. Final expression of the reservoir capacity constraint of the pumped storage plant
24D 24D
X X
ð
ð W 0 W max Þ=640 P pg tðÞ 1:36 165Y p tðÞ W 0 W min Þ=640 (2.11)
t¼1 t¼1
(6) Water quantity balancing constraint of the pumped storage plant in each time period
(equality constraints with the total number of 24D)
1. Original equation of water balancing constraint
24D 24D
X X
P pp tðÞ PPC P pg tðÞ PGC ¼ W 24 W 0
t¼1 t¼1
2. Final water quantity balancing expression of the pumped storage plant (transfer water
quantity balance into pump generation balance)

24D 24D
X X
P pg tðÞ 870 P pg tðÞ 640 ¼ W 0 W 24
t¼1 t¼1 (2.12)
24D 24D
X X
ð
P pg tðÞ 870=640 Y p tðÞ 165 ¼ W 0 W 24 Þ=640
t¼1 t¼1
(7) Generated output constraint of each unit in each time period (continuous variable
constraints with the total number of N 24D)