Page 166 - Mathematical Models and Algorithms for Power System Optimization

Discrete Optimization for Reactive Power Planning 157

as the initial value, and MINOS nonlinear software package can reach the same continuous
optimal solution as the calculation results in this chapter.
(5) Comparison with power flow calculation results: Under the conditions that voltage of the
generator terminal, node angle of the balancing machine, and integer variable are fixed,
and bound of other variables are infinitely slack, then calculating power flow with the
calculation procedure based on the algorithm proposed in this chapter can lead to the same
power flow solution as the Newton-Raphson algorithm.
(6) Comparison with manual programming results: The manual programming method
normally only makes a few cases. It is obvious that the results of a discrete optimization
algorithm are better than the manual programming method. However, results of this
chapter are still compared with that of a manual programming method to prove the
superiority of the algorithm. Furthermore, when some variables cross the threshold and
some variables reach their limits after optimization calculation, if a feasible solution still
cannot be obtained, the discrete optimization algorithm therefore may only reach one
conclusion: the problem is unsolvable. In contrast, manual programming may adjust the
limits for variables to obtain the feasible solution. If the engineer’s experience is
summarized to form a rule library or reasoning procedure, then combined with the
outcomes from optimization mathematics, the obtained results will be much better than
any of the solely used methods.
Verification of procedure validity is a complicated problem in itself. As the algorithm
in this chapter is newly proposed, it is hereby important to verify its validity in the study.

6.2.7 Special Treatments for Practical Problems

Discrete reactive power optimization procedure developed based on the algorithm in this
chapter deals with not only discrete variables but also special problems incurred in practical
calculation, such as installing new reactive power compensation equipment at the original
reactive power compensation equipment location; setting the upper limit for new reactive
power compensation equipment; using the habitual tap position to express the transformer
ratio and ensuring the transformer ratio integer solutions of the transformers in series must be
equal; verifying data according to infeasible solution information; etc. It is quite often that
practical problems may not be expressed with mathematical formulas. As for this, researchers
should have a good mathematical foundation and engineering background to abstract
mathematical models and common rules, or to adopt flexible methods acceptable to
engineering practices in solving problems. In applying the procedure, this chapter has solved
some problems. However, there is still a great deal of work to do before solving all practical
problems.