Page 161 - Mathematical Models and Algorithms for Power System Optimization

152 Chapter 6

adjustments, then calculate power flow more than 10 times, which will map the grid loss
curve to obtain the tap ratio number of adjustable transformers. For a real system
containing hundreds of nodes, the design of a calculation case itself is hard work.
(2) Continuous VAR optimization method: This method uses the continuous reactive
power optimization method to obtain a continuous optimal solution, then truncates the
nearest solution to the integer solution. The method is applicable when there are fewer
discrete variables, and the upper and lower limit values of the discrete variables are close.
For a real system with several hundred nodes, when there are many discrete variables
and the upper and lower limit values of the discrete variables are distant, the solution
obtained by simply truncating may not be feasible. It is even more difficult to obtain a
suboptimal solution. For radiator-like distribution networks, the tap position of the
transformer must be used as a discrete variable. When the number of discrete variables
(>50) is high, the truncated solution after continuous optimization generally does not
guarantee a discrete feasible solution. Truncation solutions can sometimes lead to an
increase in the objective function and may also lead to inequality constraints.
Another approach is to use a truncated solution fixed by the continuous optimization
method and to use the continuous optimization method to optimize continuous variables.
This approach will increase the workload of optimization calculations, which cannot
assure that the obtained discrete solution is feasible either.
Whether the optimized truncated solution is used as the final solution, or the optimized
truncated solution is fixed and then the continuous variable is reoptimized, neither the
discrete feasible solution nor the discrete optimal solution can be obtained.
(3) Discrete VAR optimization method: This method can directly lead to discrete solutions
for transformer tap position and capacitor bank number, for example, in a real power
supply system with 40 nodes, 2 units of generators, and 2 units of adjustable transformers,
as long as the bound of all variables are given. For systems of such small scale, there
are already solutions in some international literature. As long as there are solutions, it is
always possible to find the discrete optimal solution. However, for the large-scale real
systems containing hundreds of nodes, these methods cannot assure that discrete solutions
can be obtained. As the existing algorithms cannot assure obtaining a discrete feasible
solution or optimal solution, in this chapter, some explorations are made in this respect to
find the discrete feasible solution of a large-scale real system.

6.1.2 Overview of This Chapter

(1) Single-state discrete VAR optimization: In Section 6.3 of this chapter, the discrete reactive
power optimization algorithm is studied under the single operating mode of the power
system, namely, the study of the single-state algorithm in which only the number of
capacitor banks is treated as a discrete variable. The algorithm uses an approximate
algorithm for solving mixed-integer LP to deal with the reactive-optimized, mixed-integer
linear programming (MILP) problem and approximates the nonlinear problem of reactive