Page 202 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 193

system with complete functions is used. Calculation results show that the algorithm is able to
perfectly deal with the discrete VAR optimization problem.

The algorithm in this section is, in fact, closely related to functions of a programming system. If
a mathematical programming system capable of running on a mainframe computer is not
available, for the convenience of applying the algorithm, the mathematical system used in this
section is a LP programming program package that can be operated under existing PC
conditions. At present, such a programming package does not have some functions that a
mainframe computer LP programming system possesses, so it is impossible in the LP
calculation to return to specified base and change constraints or modify the fixed value of a
variable. Thus, each time an integer is changed, it is necessary to recalculate the LP once more,
increasing the computational effort, as the algorithm itself is still valid.

Sections 6.3 and 6.4 of this chapter focused on the effectiveness of the algorithm, that is,
finding the discrete feasible solution under the condition without limiting the initial value too
much, so it is unnecessary to have a discrete feasible initial value. It is well known that the
optimization problem, once described as a mathematical problem, is the most pressing problem
to find the solution. To satisfy some strict conditions, such as convexity and continuous
differentiable, the nonlinear optimization algorithm can only obtain the local optimal solution.
Therefore, for the algorithm adopted in this section, the results must be related to the initial
value. Generally speaking, a better initial value can simplify and speed up the solution
process and increase the possibility of finding discrete feasible solutions. Therefore, it is
necessary to further study the initial value selection method.

An expert system can help solve some problems that cannot be solved with analytical
mathematics, which is of great importance in recent years. Study of the application of an
expert system in power system calculation combines the expert system with a traditional
optimization algorithm, which is able to solve some problems that are difficult to solved with a
traditional optimization algorithm; it can also reach better solutions than those obtained with
traditional optimization algorithms. However, so far, there are no researchers who noticed
that expert rules may be used to seek initial values. Based on real physical background on
power systems, it may sometimes find better initial values that cannot be given by analytical
mathematics.
To achieve better initial value, the concept of expert rules is introduced in this section to solve
the rounded-off problems of the integer initial value of transformer ratio and reactive power
compensation equipment. This section determines what kind of rounded-off method to use
depending on the degree of fuzziness of integer initial value, that is, a simple rounded-off
method or an expert rule based on a rounded-off method. The rounded-off method based on
expert rules judges the transformer type according to the direction of active power flow, then
determines whether the tap ratio shall be geared up or geared down according to node voltage.
This method reduces the possibility of voltage violation after the gearing of tap ratio, shortens
calculation time, and lays a solid foundation for further finding of discrete solution.