Page 160 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 151

not yet been able to solve large-scale mixed-integer nonlinear problems for power systems.
When the number of adjustable tap ratios and adjustable capacitor banks in the power system
are large, the method of processing the tap position and number of capacitor banks as
continuous variables and then rounding the transformer does not always provide a discrete
feasible solution. It is very difficult to directly apply the discrete optimization method to the
VAR optimization of the power system. Therefore, the approximate algorithm is one of the
approaches to solve the discrete VAR optimization problem.

The algorithm here employs an excellent approximation method for solving linear mixed-
integer programming (MIP) problems, because an exact optimal solution of MIP problems can
hardly be obtained. Furthermore, to solve a nonlinear MIP problem, the algorithm exploits the
concept of recursive LP so that it is capable of obtaining an AC load flow solution to the VAR
planning problem. The program can easily be developed based on this algorithm, by
incorporating the options of existing LP software.

This chapter combines the expert rules, fuzzy mathematical concepts, and genetic algorithms
(GA) with traditional optimization methods to improve the possibility of obtaining discrete
solutions. To verify the validity and reliability of the algorithm, the corresponding verification
procedures were developed, and the numerical calculations were performed using the
actual-scale power system. The results of a practical test system show that the proposed
algorithm can effectively solve the discrete optimization VAR problems of power systems and
power distribution systems in practical scale.

6.1.1 Practical Method for Discrete VAR Optimization

The difference of constraints are the key issues of various VAR optimization models, which are
identified as being with and without constraint functions, and with or without integer variables.
The main practical methods currently used for VAR optimization of a power system could be
described as follows:

(1) Power flow method: The number of capacitor banks and transformer tap positions are
taken as constant values that are manually adjusted by one’s experience, then repeatedly
executed until the feasible solution is obtained. Due to the large number of capacitors
and transformers, the wide adjustable range, and rapid increase in the number of
adjustment solutions, along with the increase in the number of devices, it is impossible to
consider all feasible solutions, which can only be adjusted according to engineering
experience. It is difficult to guarantee that the schemes made in this way are optimal or
superior by using the so-called current adjustment method to select the system’s reactive
operation or planning scheme. Normally, such a method can provide a feasible
solution at best at the cost of a great deal of labor power and time.
For example, in a real power supply system with 40 nodes, 2 generators, and 2 sets of
adjustable transformers, experienced system engineers must design more than 10 cases of