Page 146 - Mathematical Models and Algorithms for Power System Optimization

Load Optimization for Power Network 137

5.5.1.3 Result of 5-bus system for state 1
According to the linear programming model of optimizing 5-bus system LC, use the linear
programming STYRP1.10 software package developed in China to calculate LCO for Status 1.

STYRP1.10 solves the linear programming problem by using a modified simplex method. It
only requires a general form of linear programming, and the program will automatically process
range and bound constraints. The specific input data requirements and formats are described in
the following section:

(1) The objective function, equality constraints, and inequality constraints are written into the
coefficient A matrix (as variable C in the program), which designates the location of
objective function by IOB¼1; the right hand side constraint variable is D; set the right
hand side constraint of the objective function to 0.
(2) The type of equation is represented with ITYPE ( 1 indicates less than or equal to, or
maximizing; 1 indicates more than or equal to, or minimizing; 0 indicates equal to).
(3) The bound constraints of linear programming are represented with variable IBD
(boundary index) and BD (boundary value): if the nth variable has bound constraints, then
n indicates upper bound constraint and –n indicates lower bound constraint; BD is the
specific upper and lower boundary values of each variable.
Thus, according to the expressions for two linear programming models of state 1 of 5-bus
system discussed previously, the input variables A, D, ITYPE, IBD, and BD from the
STYRP1.10 solution are expressed as follows:
(4) Input variable coefficient for the linear programming software package:

2 3
1 1 1 0 0
6 1 1 1 1 1 7
6 7
6 0:3344 0:3282 0 0:3282 0 7
6 7
A ¼ 0:3365 0:6698 0 0:6698 0 ,
7
6
6 7
6 0:6656 0:3313 0 0:3313 0 7
6 7
4 0 0 0 1 0 5
1 1 1 1 0
2 3 2 3
1 0
3:3
0 7
6 6 7
6 7 6 7
1 1:1843
6 7 6 7 2 3 2 3
6 7 6 7 1 1:2
1 1:9656
6 7 6 7
2 0:6
6 7 6 7 6 7 6 7
6 1 7 6 1:9776 7 6 7 6 7
6 7 6 7 6 3 7 6 1:5 7
6 1 7 6 1:5000 7 6 7 6 7
ITYPE ¼ 6 7 , D ¼ 6 7 , IBD ¼ 4 , BD ¼ 0:3 7
6
6
7
6 1 7 6 6:3000 7 6 7 6 7
6 7 6 7 6 4 7 6 1:4 7
6 1 7 6 0:7757 7 6 7 6 7
6 7 6 7 4 5 5 4 2:0 5
6 1 7 6 0:3544 7
6 7 6 7 5 3:0
6 1 7 6 0:0176 7
6 7 6 7
4 1 5 4 1:5000 5
1 0:3000