Page 136 - Mathematical Models and Algorithms for Power System Optimization

Load Optimization for Power Network 127

2. Inequality constraints.
(a) Network branch power constraint: |P bj | P bj , j 2 N B .
(b) Variable constraints.
a. Generation bus output constraint: P Gi P Gi P Gi , i 2 N G .
b. Load bus capacity constraint: P Li P Li P Li , i 2 N D .

5.3.4 The Derivation Process of LP Model for LCO

Select the LC and generation output of buses as state variables. The linear programming model
of LCO is derived from the following procedures:

P C
(1) Variables. State variable x ¼ , cost coefficient vector c¼[C 0].
P G
(2) Objective function.

P C
½
min C 0Š (5.1)
P G
(3) Equality constraints.
N N N
X X X
P Gi P Li + P Ci ¼ 0 (5.2)
i¼1 i¼1 i¼1

is expressed as linear programming equality constraints:

P C
½ 1 1 n 1 1 n Š ¼ 1 1 n P L (5.3)
P G

(4) Range constraints.
1. Based on the DC power flow model, bus phase angle variables can be eliminated to
obtain the relationship matrix between branch power and bus power.

P b ¼ AP P + P 0 (5.4)
0
0
G L C
where
0 1
B
A ¼ B b R
0
2. The branch power constraint P bj P bj P bj ð j 2 N B Þ can be expressed as the
following matrix formation:

P b P b P b (5.5)
3. Eq. (5.2) is substituted into Eq. (5.3) to obtain:

0
0
P b AP P + P 0 (5.6)
G L C P b