Page 162 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 153

power optimization through the loop iteration of LP. To effectively reduce the investment
cost of reactive power devices, an improved algorithm that simultaneously changes
two integers is also proposed.
(2) Multistate discrete VAR optimization: Because the operating mode of the system is
constantly changing, reactive power planning under specific operating modes is generally
difficult to meet the needs of multiple operating modes. Therefore, it is necessary to study
the reactive power optimization that can comprehensively consider the various operating
modes of the system, that is, to study VAR optimization under a multistate condition.
Section 6.4 of this chapter proposes a multistate reactive power optimization model and
decomposition coordination algorithm with a diagonal block shape. This algorithm
decomposes and coordinates each state with the amount of reactive equipment associated
with each state as a coupling quantity to achieve overall optimization. This algorithm
considers the influence of reactive power equipment quantity on each state
comprehensively, without considering optimization of a single state, and pursues overall
state optimality, so as to make the minimal total investment.
(3) Expertrule-baseddiscreteVARoptimization:Becausetheoptimizationalgorithmgenerally
depends on the initial value, to obtain a better initial value, the concept of the expert rule is
introduced in Section 6.5 of this chapter to obtain the initial value of the integer, so that the
proposed algorithm can effectively find a better discrete solution. The expert rule given in
this chapter determines the rounded-off direction of the discrete variable based on the
ambiguityofthe integerinitial value, reducing the possibilityofthe voltage over limits,after
changing the ratio grade and the number of reactive equipment groups, saving calculation
time and greatly improving the possibility of getting a better integer-feasible solution.
(4) GA-based discrete reactive power optimization: Because the traditional optimization
algorithm cannot ensure the global optimal solution, and the GA has the ability to obtain a
global optimal solution, in the discrete feasible solution obtained in Section 6.6 of this
chapter, the GA based on a natural biological mechanism is used to stochastically modify
the integer-feasible solution so as to arrive at a new solution. The use of GA techniques can
generate different stochastic initial values, which may lead to different feasible solutions.
Compared with traditional optimization algorithms that can only give a unique feasible
solution, GA techniques provide the possibility to filter better feasible solutions.

6.2 Basic Ideas of Forming an Optimization Model

6.2.1 Way of Processing Discreteness

Reactive power compensation equipment in a power system, such as capacitors and reactors,
are switched in groups, whereas the tap of a transformer is adjusted by steps. Thus, the number
of capacitors and reactors, and taps of a transformer shall be expressed as integer variables
rather than continuous variables.