Page 191 - Mathematical Models and Algorithms for Power System Optimization

182 Chapter 6

Start

Step 1 An initial load flow solution is obtained

Linearized master problem (LMP) is obtained by
Step 2
linearizing master problem (MP)

Step 3 Decomposition and coordination procedure

Step 4 Multi-state Improvement Procedure

No
Step 5 Are all variables convergent?
Yes

Stop
Fig. 6.4
Flow chart of multistate VAR planning algorithm.

Step 1: After formulating the overall nonlinear MIP problem as master problem MP, set
k
iteration count k 0; initial solution Z is calculated according to power flow solution for
each state. Here variable Z is defined as follows:

ð
Z ¼ X 1 , Y 1 , …, X M , Y M , Y C , W C Þ (6.37)
k
Step 2: Linearize main problem MP around the point Z , and the problem has a diagonal
block form, as shown by Eq. (6.34).
Step 3: Fix coordination variable Y C , and decompose linearized master problem into
linearized subproblems. The overall problem (LMP) is decomposed into several
linearized subproblems state by state, and each subproblem is solved independently.
The results are then coordinated to get solution z k+1 for the overall problem (LMP). On
this basis, adjust coordination variable Y C to reduce the infeasibility and objective function
of the whole problem, that is, to coordinate solutions of corresponding problems to get the
solution of linearized main problem LMP. Detailed explanation will be given in
Section 6.4.3.1.
Step 4: Maintain the feasibility of each state, and change the value of coordination variable
Y C , that is, execute multistate integer improvement procedure to further reduce investment
cost; two integers are changed simultaneously while maintaining the feasibility of all states.
The detailed solution procedure is given in Section 6.4.3.2.