An Optimal Solution is Not Enough: Alternative Solutions and Optimal Power Systems
Matthew Viens, J. Kyle Skolfield, William E. Hart, Michael Ferris
TL;DR
This work argues that optimal power systems modeling should routinely consider alternative optimal solutions (AOS), not just a single optimal decision. It presents a unifying framework built on sublevel sets, minimal representations, and projections to analyze and generate AOS beyond traditional MGA methods, with a focused application to optimal power flow (OPF). The authors show how AOS concepts apply across DC-OPF, network-flow, and copper-plate relaxations, and demonstrate in a 3-bus OPF example that multiple AOS exist and can reveal secondary tradeoffs such as AC feasibility and line losses. The paper also surveys theoretical methods and software tools for AOS generation, highlighting practical routes for practitioners to incorporate AOS into planning, analysis, and policy discussions.
Abstract
Power systems modeling and planning has long leveraged mathematical programming for its ability to provide optimality and feasibility guarantees. One feature that has been recognized in the optimization literature since the 1970s is the existence and meaning of multiple exact optimal and near-optimal solutions, which we call alternative solutions. In power systems modeling, the use of alternative solutions has been limited to energy system optimization modeling (ESOM) applications and modeling to generate alternative (MGA) techniques. We present three key results about alternative solutions for power systems modeling. First, we give a perspective, based on sublevel sets and projection, for characterizing alternative solutions as a facet of general optimization theory. Second, we include pointers to alternative solution generation methods and tools beyond MGA-style techniques. Third, we demonstrate the use cases for alternative solutions in power system modeling on the fundamental optimal power flow problem.