Page 111 - Mathematical Models and Algorithms for Power System Optimization

New Algorithms Related to Power Flow 101

Many excellent algorithms have been developed for OPF calculation. In these algorithms, the
OPF problem is formulated as a continuous nonlinear problem in which the number of
transformer taps and the numbers of capacitor and reactor units are all treated as continuous
variables. However, some of the variables in the OPF problem can be adjusted only by discrete
steps: transformer ratios are changed tap by tap, and capacitors and reactors are adjusted by unit
operations.
If the OPF problem is solved by the existing algorithms, the number of transformer taps and the
number of capacitor and reactor units are determined by the discrete values closest to optimum
continuous values, and the supplied reactive power is settled according to these discrete values.
Therefore,theoperatingpointsobtainedbysuchalgorithmsmightbenonoptimumand/orunfeasible.

From the foregoing viewpoint, transformer tap ratios and the number of capacitor units, as well
as the number of reactor units, should be treated as discrete variables in the OPF problem.
When taking into account the discrete nature of the number of transformer taps and the number
of capacitor and reactor units, the OPF problem becomes a nonlinear MIP problem with
numerous integer variables. Hence, in this chapter, such a discrete problem is referred to as a
“discrete OPF problem.” Until now, the existing general mathematical programming
techniques could not solve such a large-scale nonlinear MIP problem accurately from the
viewpoint of memory size and computing time.

To solve the practical discrete OPF problem, this section presents a new algorithm that can
obtain a good near-optimal discrete solution. This algorithm is based on an optimization
procedure in which the nonlinear discrete OPF problem is linearized iteratively and solved by
an approximation method (see Appendix C).

To obtain a nonlinear load flow solution, the algorithm exploits the concept of the SLP method.
Because LP is carried out repeatedly in the approximation method, the computer code of this
algorithm can easily be developed by making use of existing LP software options.

In the proposed algorithm, an initial solution is generated by rounding off the discrete variables
of the solution of a continuous OPF. When the solution of the continuous OPF is infeasible after
the discrete variables are rounded off, the proposed algorithm becomes very effective.

4.6.3 Features of the Problem

The discrete OPF studied in this section is an operation planning problem whose objective is to
minimize the generator operation cost under the operational constraints of the power system.
For convenience of description, both capacitor and reactor are referred to as reactive devices.
The number of capacitor banks and reactor banks installed at each bus is deemed as an integer
variable, whereas the transformer tap is considered a discrete variable. The objective functions
and constraints of the discrete OPF are explained here.