Page 170 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 161

subject to:
1. Investment cost constraint:

(6.2)
C i C i W i , i 2 N C
where

(6.3)
C i ¼ 0,1,…,C i , i 2 N C [E C
(6.4)
W i ¼ 0,1, i 2 N C
2. Operation constraint
Power flow balance equation:

F 1i ¼ P i U, θ, Tð Þ P Gi P Li , i 2 N (6.5)
F 2i ¼ Q i U, θ, T, Cð Þ Q Gi Q Li , i 2 N (6.6)
where

X

P i ¼ U i U j G ij cosθ ij + B ij sinθ ij
j2i
X

Q i ¼ U i U j G ij sinθ ij B ij cosθ ij
j2i
Active power output limits of generator balance node:

(6.7)
P P Si P Si
Si
Generator reactive power output limits:
(6.8)
Q Q Gi Q , i 2 N G
Gi
Gi
Voltage limits of all nodes:
U U i U i , i 2 N (6.9)
i
Transformer tap limits:

(6.10)
T T i T i , i 2 N T
i
Problem P is a minimization problem with integer variables and nonlinear constraints.
When C i ¼0, the value of W i shall be 0 as well, so that equation of d i W i in objective
function shall be:
0,C i ¼ 0
(
d i W i ¼ (6.11)
d i ,C i ¼ 1,2,…,C i