Page 190 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 181

is 29, and the number of states is 7, then the number of continuous variables shall be
(135 2+36+1+17+7¼331) 7¼2317, and the number of discrete variables shall be
20 2+29¼69.
(2) The number of problem constraints: (the number of system nodes N 2) the number of
states+the number of capacitor nodes N C +N E .
If the number of nodes is 135, the number of newly installed capacitors is 20, the number
of existing capacitors is 29, and the number of states is 7, then the number of constraints
shall be 2 135 7+20+29+7¼1946.
(3) Cost function is a linear expression.
(4) Constraint function is a nonlinear function.
(5) Variables are divided into two types: continuous variables and discrete variables, and there
is a large number of integer variables.
(6) Both the number of constraints and variables are more than a thousand.

The listed points show that multistate discrete reactive power optimization is an MIP problem
of super-large scale.

6.4.3 Overall Solution Procedure of Multistate VAR Optimization

6.4.3.1 Main calculation procedure
Although the algorithm in Section 6.3 can effectively solve a nonlinear MIP problem for a
single state, it cannot directly be applied to a multistate problem because of the large numbers of
constraint equations and integer variables.
In the solution algorithm of this section, the nonlinearity is resolved by using the successive
linearization technique, and the decomposition and coordination techniques are employed to
overcome the huge scale of the problem. The approximation algorithm employed in Section 6.3
is also applicable to treat the integral nature of variables.
The generalized overall solution algorithm is shown in the flow chart in Fig. 6.4.

The outline of the solution procedure proposed here is that the multistate VAR planning
problem (Master Problem: MP) is decomposed into subproblems (LSP) state by state, and each
LSP is solved by using the decomposition and coordination procedure. Further, an improved
procedure is employed to enhance the solution. After that, the master problem is linearized
again, and this procedure is repeated until a nonlinear solution is obtained. A little more detailed
explanation of each procedure is given as follows: