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New Algorithms Related to Power Flow 85

4.1.5 Overview of This Chapter

(1) The power flow calculation method based on SA is studied. In this chapter, the traditional
power flow model is first constructed as an unconstrained nonlinear quadratic
programming model, then the SA method is combined with the N-R method to construct a
new combinatorial algorithm. The new algorithm uses SA technology to determine the
appropriate step size of the solution variable in the N-R method so that it does not fall
into the local solution, thereby improving the problem of difficult convergence in
power flow calculation, and minimizing the divergence situation. For the calculation
of power flow in normal systems, the new algorithm has the same convergence as the
N-R algorithm, yet for the ill-conditioned systems where the N-R method is difficult to
converge, as long as the solution exists, the new algorithm may obtain a convergent
solution.
(2) A discrete OPF algorithm is studied. This algorithm requires an initial integer solution that
can be obtained by truncating the solution from traditional continuous OPF or a general
power flow solution. On this basis, the near-optimal solution can be obtained. Therefore,
even if the initial integer solution is infeasible, the algorithm proposed can still be applied to
searchforafeasibleintegersolution.Twoalgorithmsareproposed:thefirstalgorithmusesa
continuous OPF to calculate an initial value, then rounds off the corresponding integer
variables and finally searches for the discrete optimal solution; the second algorithm uses
thepowerflowmethodtocalculatetheinitialvalue,thenusestheLPmethodtocalculatethe
continuous optimal solution, in which corresponding integer variables are rounded off, and
finally searches for a discrete optimal solution based on SLP approach.

Section 4.2 in this chapter gives the basic ideas of formulating the unconstrained power flow
model; Section 4.3 provides the unconstrained power flow model in the form of a nonlinear
quadratic function; Section 4.4 shows the calculation process of solving unconstrained power
flow; Section 4.5 gives the detailed results from actual case studies and their analyses;
Section 4.6 introduces the discrete OPF model; Section 4.7 describes the discrete OPF
algorithm; Section 4.8 gives the concrete formulation of 5-Bus system and then the results of
135-Bus real scale system by using traditional OPF and LF as initial values respectively; and
Section 4.9 is a summary of the chapter.

4.2 Ideas of Modeling for Unconstrained Power Flow with
Objective Function

4.2.1 Description of Ill-Conditioned Power Flow Problem

As previously mentioned, the N-R method and the fast PQ decoupled load flow method are most
widely used. Both methods are efficient, however, in some special situations, nonconvergence
may be encountered. Whether a power flow calculation will converge or not depend on many
factors, such as operating conditions, reactive power distributions, and solution algorithms.