The problem is combinatorial, which precludes algorithms that guarantee a global optimum. Most existing reconfiguration algorithms fall into two categories. In the first, branch exchange, the system operates in a feasible radial configuration and the algorithm opens and closes candidate switches in pairs. In the second, loop cutting, the system is completely meshed and the algorithm opens candidate switches to reach a feasible radial configuration. Reconfiguration algorithms based on linearized transshipment, neural networks, heuristics, genetic algorithms, and simulated annealing have also been reported, but not widely used. These existing reconfiguration algorithms work with a simplified model of the power system, and they handle voltage and current constraints approximately, if at all.

The algorithm described here is a constructive method, using a full nonlinear power system model that accurately handles constraints. The system starts with all switches open and all failed components isolated. An optional network power flow provides a lower bound on the losses. Then the algorithm closes one switch at a time to minimize the increase in a merit figure, which is the real loss divided by the apparent load served. The merit figure increases with each switch closing. This principle, called discrete ascent optimal programming (DAOP), has been applied to other power system problems, including economic dispatch and phase balancing. For reconfiguration, the DAOP method's greedy nature is mitigated with a backtracking algorithm. Approximate screening formulas have also been developed for efficient use with partial load flow solutions. This method's main advantage is the accurate treatment of voltage and current constraints, including the effect of control action. One example taken from the literature shows how the DAOP-based algorithm can reach an optimal solution, while adjusting line voltage regulators to satisfy the voltage constraints.