Page 135 - Mathematical Models and Algorithms for Power System Optimization

126 Chapter 5

Table 5.1 Mathematical notations—Cont’d
Notations Descriptions

The column vector of branch active power; P bj : the active power of the branch j.
P b
The upper limit column vector of branch active power (specified); P bj : the upper limit of the
P b
branch j for active power.
θ The column vector of nodes for phase angle; θ : the column vector of nodes for phase angle but
0

θ 0
slack node, after ordered, θ ¼ .
0
R The connection matrix of node and branch.
B 0 The node susceptance transport matrix (the slack node is eliminated); B ij (¼1/x ij ): the mutual
0 1
P
B C
susceptance of node i and j; B ii ¼
@ B ijA: the self-susceptance of node i.
j2i
j6¼i
The diagonal matrix of branch susceptance.
B b
5.3.2 Model of Load Curtailment Optimization (LCO)
(1) Objective function:
X
min C i P Ci
i2N D
(2) Constraints of LCO model:
1. Equality constraints. Power balance constraints (DC power flow):
Power balance in the whole grid (no loss).
N N N
P P P
(a) Grid power balance: P Gi P Li + P Ci ¼ 0.
i¼1 i¼1 i¼1
(b) Bus power balance: P G P L +P C ¼Bθ.
(c) Branch power balance: P 0 ¼B b Rθ.
2. Inequality constraints.
(a) Network branch power constraints: |P bj | P bj , j 2 N B .
(b) Variable constraints.
a. Generation bus output constraint: P P Gi P Gi , i 2 N G .
Gi
b. Load bus capacity constraint: 0 P Ci P Li , i2N D .
5.3.3 Model of Load Supply Capability (LSC)

(1) Objective function:
X
max C i P Li
i2N D
(2) Constraints of LSC optimization model:
1. Equality constraints. Power balance constraints (DC power flow).
N N
P P
(a) Grid power balance: P Gi P Li ¼ 0.
i¼1 i¼1
(b) Bus power balance: P G P L ¼Bθ.
(c) Branch power balance: P b ¼B b Rθ.