An Efficient Algorithm for QCDP and Implementation

This work formulates optimal power flow with continuous and discrete variables problems (OPFCDP) and state estimation with continuous and discrete variables problems (SECDP) as classes of quadratic programming with continuous and discrete variables problems (QCDP). This work also applies an ordinal optimization (OO) theory-based two-stage algorithm to solve the QCDP. This work first constructed a crude but efficient model to select $N$ excellent settings from a sample space. A scheme with enhanced accuracy based on sensitivity theory was applied to rank the $N$ samples and identify the top $s$ samples to form the selected subset. Finally, these $s$ discrete samples in the selected subset were solved by the exact model and the top setting with the smallest objective value was the good enough solution. Via numerous tests, this work demonstrates the efficiency of the proposed algorithm and compares with those of other heuristic methods, such as tabu search, genetic algorithm, and the ant colony system, for solving the SECDP and OPFCDP on IEEE 118-bus and 244-bus systems.