Page 203 - Mathematical Models and Algorithms for Power System Optimization

194 Chapter 6

Basic procedure of the algorithm in this section: First set the power flow initial value, then
determine discrete solution with continuous operation and expert rules; eventually calculate
optimized power flow. If there is still violation variable with optimized power flow, then the
algorithm in Chapter 4 will be used to carry out the calculation. Shown by calculation
results with the help of expert rules, there is no violation variable in optimized power flow
calculation results. The algorithm in this section is very pragmatic, which improves the
possibility of finding a feasible solution.

6.5.2 Necessity of Introducing Expert Rules

In reactive power optimization calculation, setting of transformer ratio is very important. It is
held in previous studies that transformer ratio may be taken as a continuous variable, so that
the adjustment range of each tap position is small, such as 0.25%, then obtain the discrete
solution by truncating it. However, when the number of tap ratios increases, such as 106
adjustable tap ratios in the test system in this chapter, a qualitative change will be elicited by
quantitative change. Thus, the truncated solution processed with the method is sometimes
infeasible. There are two types of transformers: step-up and step-down transformers.
However, this is not differentiated in input data, and their calculation model are not different
either, which is always the case in both power flow calculation and optimization calculation.
As the reverse transmission of reactive power is likely to occur, then the voltage at the
receiving end may be higher than that of the sending end. Thus, it is impractical to judge
whether it is a step-up transformer or a step-down transformer simply with the voltage drop
method. Active power flow method must be used to identify the type of transformer: the
transformer with active power flow flowing from low voltage end to high voltage end is taken
as a step-up transformer, whereas a transformer with active power flow flowing from high
voltage end to low voltage end is taken as a step-down transformer.

In a power flow calculation, tap ratio position and the number of VAR source installations
are given manually. However, in a continuous optimization calculation, the position and
number of VAR installations are figured throughout calculation. In the end, there is also the
problem of truncation. Generally, in continuous reactive power optimization calculation,
transformer ratio and capacitor bank number are truncated following a round-off principle, and
the calculation ends there. Such purely truncation method does not take into consideration the
relation between tap ratio and voltage, so it is hard to avoid voltage violation at the
corresponding node after tap ratio truncation. In this chapter, the approximation MIP
method also uses an initial integer solution obtained with truncation method as the initial value,
then finds the integer solution close to optimum.

In accordance with fuzzy mathematics, fuzzy numbers close to 0.5 have the highest fuzziness
degree. That is, membership function values of 0.49 and 0.51 are quite close, which cannot be