Page 163 - Mathematical Models and Algorithms for Power System Optimization

154 Chapter 6

In this chapter, a nonlinear integer programming model is used to represent the discrete
reactive power optimization, and discrete variables are used to represent tap position and the
number of capacitor banks and reactors. Moreover, a linear integer programming model is used
in iteration calculation to represent discrete reactive power optimization. The relationship
between objective function values for an MIP problem is as follows: the objective function
value upon integer constraint slack is the lower limit of the problem; the objective function
value upon integer variable rounded-off is the upper limit of the problem; and the objective
function value obtained with an integer programming method falls between the two limits.
Thus, an approximation algorithm based on solving a linear integer programming problem is
designed to search for a discrete linear optimization solution around a continuous linear
optimization solution. The basic idea of the algorithm is to slack integer variable constraint in
the linear integer programming problem, which uses LP method to obtain the lower limit of
objective function of the problem, so as to form the exploration space of integer solution based
on the slack solution, and to obtain a discrete solution within a calculation procedure of limited
steps. In other words, the basic idea of the algorithm is to transform complicated discrete
optimization into an LP problem, so as to obtain the discrete solution within a short period.

6.2.2 Way of Processing Nonlinearity

The balance condition for power system operation is power balance, which is the condition
that the reactive power optimization must meet, whereas in a power balance equation, the
voltage has a nonlinear relation with power. If the discrete characteristics of the transformer tap
and capacitor bank number are taken into account, the reactive power optimization will be
a MINLP problem.

Unlike the LP simplex method, the continuous nonlinear algorithm has no common algorithm.
The existing nonlinear algorithms have rigorous rules on the mathematical characteristics of
the problem, such as convexity, the objective function is a secondary function, etc. Otherwise,
it would be impossible to prove that the obtained solution is the global optimal solution. In
this chapter, under the assumption that most constraint functions are linear, nonlinear constraint
functions can be adjusted continuously and slightly. The successive linear programming
(SLP) algorithm is used to deal with the nonlinearity of discrete reactive power optimization.

6.2.3 Way of Processing Multiple States

A power system has different operating modes, which may change in different seasons,
days, or even in a single day. In addition, equipment maintenance of a line, generator, or
transformer may also lead to a change of operating mode. Because the system operating mode
is changing all the time, certainly reactive power planning made under a specific operating
mode can hardly meet the needs of multiple operating modes, so many kinds of system
operating modes should be comprehensively taken into consideration. Therefore, to meet the