Page 113 - Mathematical Models and Algorithms for Power System Optimization

New Algorithms Related to Power Flow 103

4.6.4 Mathematical Model

In the discrete OPF problem addressed in this section, the objective function is to minimize
operation cost of generator and the constraint function is the operation conditions of the power
system. The formulated model is shown here.

OPF Problem:
Objective function:

To minimize operation cost of generator (equivalent to minimize loss).

X
min f i P Gi Þ (4.10)
ð
i2NG
Constraints:
Constraint of power flow balance (add variables such as transformer tap T, number of the
capacitor banks “C,” and number of the reactor banks “R”):

P i U, θ, Tð Þ P Gi P Li ¼ 0, i 2 N (4.11)

Q i U, θ, T, C, Rð Þ Q Gi Q Li ¼ 0, i 2 N (4.12)
Constraint of active and reactive outputs of generators:

P P Gi P Gi , i 2 N (4.13)
Gi
Q Q Gi Q , i 2 N (4.14)
Gi Gi
Constraint of bus voltage magnitude and phase angle:

U U i U i , i 2 N (4.15)
i
θ θ i θ i , i 2 N (4.16)
i
Constraint of transformer tap:

(4.17)
i
T T i T i , i 2 N T
Constraint of capacitor:

C C i C i , i 2 N C [E C (4.18)
i
Constraint of reactor:

(4.19)
R R i R i , i 2 N R
i
In which:
f i P Gi Þ ¼ a 0i + a 1i P Gi + a 2i P 2 (4.20)
ð
Gi