Page 196 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 187

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Fig. 6.6
Schematic diagram of decomposition and coordination procedure.

6.4.3.3 Improvement of integer variables within main calculation procedure

In the previous section, integer variables are changed one by one, making it not satisfactory in
reducing fixed cost and requiring further improvement. This section introduces integer
improvement procedure in detail whose principle is similar to the integer improvement
procedure introduced in Section 6.2. However, this principle emphasizes selection among
states. To obtain a practical solution and to further decrease the installation cost, two integers
are changed simultaneously while keeping the feasibility of the overall problem. To accomplish
this, the improvement procedure is divided into two stages. In Stage I, for the purpose of
computational efficiency, the infeasibility is checked by using the simplex tableau without
executing pivot exchange operation. In Stage II, the most promising (but likely infeasible) pair
is tried by resolving the MIP problem to find a feasible solution.

Stage I: Select one pair of integers for infeasibility calculation. As the number of LPs is
calculated based on the number of states the number of reactive power nodes,
infeasibility is only expressed as simplex in the calculation without the pivoting operation
to improve calculation efficiency. If a pair of integers can be chosen, then plus one to one
integer and minus one from another. If a pair of integers cannot be chosen, rank the
infeasibility of each pair of integers, and move to Stage II.
Stage II: Choose the most possible pair of integers, that is, the pair of integers with lowest
infeasibility, and solve the problem with MILP method. If it is feasible and the integer
solution is improved, then accept the integer solution; otherwise, abandon the integer
solution.

6.4.4 Implementation

The algorithm is implemented with LP package HITACMPS-II. Numerical calculation is
carried out on the same 135-node practical system as in Section 6.3. In the test system, all