Page 137 - Mathematical Models and Algorithms for Power System Optimization

128 Chapter 5

After expanding and transposing, then it becomes:

0 0 0 0
A P P b A P + A P A P + P b (5.7)
L C G L
Thus, it can be expressed as linear programming range constraints:

B 0 1 B 0 1 B 0 1 P 0 C B 0 1
0
0
B b R P P b B b R B b R B b R P + P b (5.8)
L
L
0 0 0 P 0 G 0
(5) Bound constraints. Output constraints of generation bus and curtailment constraints of
load bus can be processed as bound constraints.

0 P C P L
(5.9)
P G P G P G

(6) Specific expressions. Based on the previous processing results of the LCO model, combine
Eqs. (5.1), (5.3), (5.8), and (5.9) to derive the following linear programming model:

P C
min ½ C 0Š (5.10)
P G
Equality constraints:

P C
½ 11Š ¼ 1 P L (5.11)
P G
Range constraints:

0 1 0 1 0 1 0 0 1
B B B P C B
B b R P P b B b R B b R B b R P + P b (5.12)
0
0
L
L
0 0 0 P 0 G 0
Bound constraints:

0 P C P L
(5.13)
P
G P G P G
5.3.5 The Derivation Process of LP Model for LSC

(1) Developing process of model. The linear programming model of maximizing LSC is
similar to the linear programming model of minimizing LC, but only their variables are
different. Therefore, the linear programming model of maximizing LSC can be derived
similarly to that of processing the linear programming model of minimizing LC, according
to the principles given in Table 5.2.