Page 218 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 209

calculation using the stochastic search method. The SA based on simulated metal welding
process has even been used for the reactive power optimization and ill-conditioned power flow
calculation.

Similar to the SA algorithm, GA is also a stochastic search method, but it is based on the
searching algorithm of natural selection and natural biological mechanism. The query
algorithm will exchange the most suitable chromosomal structure of the string with the
structural but random chromosome to form a new chromosome structure, so as to achieve
the goal of evolution. This algorithm uses the chromosome to indicate the variables of the
problems and can be combined into many exploration points. The multipoint search in the
solution space can avoid the local point optimization and possibly obtain the global optimal
point in which the objective function and constraint function are not required to be continuous,
and thus can adapt to the discrete reactive power optimization.
The combination of GA with power system expert rules and traditional algorithms can handle
the integer variables and improve the solution’s efficiency. The calculation results in this
section show that GA can give a number of integer-feasible solutions for engineering
technicians to make the final decision, whereas the traditional algorithm can generally give
only one solution.

6.6.3 GA-based Model for Discrete VAR Optimization

There can be numerous objective functions for VAR optimization, such as active power loss
minimization, VAR source investment minimization, voltage deviation minimization, etc. The
algorithm in this section applies to a real distribution system, with the following selected
objective function:
ð
f ¼ min system active power lossÞ
The following constraints must be satisfied:

(1) Node reactive and active power flow equations.
(2) Upper and lower limits of generator voltage.
(3) Upper and lower limits of generator reactive output.
(4) Upper and lower limits of transformer tap.
(5) VAR limits for all new capacitor installation nodes.
(6) VAR limits for all existing capacitor installation nodes.

Constraints (1)–(3) are the same as those in Section 6.3. Considering that the algorithm
is essentially an unconstrained algorithm, the voltage deviations and the reactive
power deviations must be considered within the objective function. Therefore, the fitness of
GAF is