A Submodular Approach for Electricity Distribution Network Reconfiguration
For power system operators, this work provides the first theoretical performance guarantee for the widely used branch exchange heuristic in distribution network reconfiguration.
This paper proves that loss minimization via distribution network reconfiguration is strongly NP-hard, formulates it as supermodular function minimization under a matroid basis constraint, and proposes a polynomial-time local search algorithm equivalent to branch exchange with a theoretical performance bound. On a 33-bus network, the algorithm matches or outperforms existing methods.
Distribution network reconfiguration (DNR) is a tool used by operators to balance line load flows and mitigate losses. As distributed generation and flexible load adoption increases, the impact of DNR on the security, efficiency, and reliability of the grid will increase as well. Today, heuristic-based actions like branch exchange are routinely taken, with no theoretical guarantee of their optimality. This paper considers loss minimization via DNR, which changes the on/off status of switches in the network. The goal is to ensure a radial final configuration (called a spanning tree in the algorithms literature) that spans all network buses and connects them to the substation (called the root of the tree) through a single path. We prove that the associated combinatorial optimization problem is strongly NP-hard and thus likely cannot be solved efficiently. We formulate the loss minimization problem as a supermodular function minimization under a single matroid basis constraint, and use existing algorithms to propose a polynomial time local search algorithm for the DNR problem at hand and derive performance bounds. We show that our algorithm is equivalent to the extensively used branch exchange algorithm, for which, to the best of our knowledge, we pioneer in proposing a theoretical performance bound. Finally, we use a 33-bus network to compare our algorithm's performance to several algorithms published in the literature.