An Optimal Solution is Not Enough: Alternative Solutions and Optimal Power Systems

TL;DR

This paper explores the concept of alternative solutions in power system optimization, emphasizing their theoretical basis, generation methods, and practical applications in optimal power flow problems.

Contribution

It introduces a new perspective on alternative solutions using sublevel sets, expands on solution generation methods beyond existing techniques, and demonstrates their use in power system modeling.

Findings

Provides a theoretical framework for alternative solutions in optimization.

Identifies methods and tools for generating alternative solutions.

Demonstrates practical use cases in optimal power flow analysis.

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.