Quantum Computing for Optimizing Power Flow in Energy Grids

Abstract

Quantum Computing is beginning to gather even more attention at a time where efforts are being made into familiarizing younger audiences into not only learning programming on a classical computer, but also on a quantum one.This new paradigm of computation is set to revolutionize several industries as the hardware keeps developing, with the potential to solve problems that a classical computer would consider intangible, as well as giving some specific problems a so sought after speed-up. This is done by applying the properties of quantum physics, like superposition and entanglement, for computation. These properties not only allow to process a larger amount of data simultaneously, but also allows to tackle problems in a completely different way that would not be possible in a classical computer.This thesis focuses on solving a known and relevant problem in the electrical industry and studying its application on a quantum environment. The Unit Commitment Problem, the problem in question, consists in minimizing the cost of power production, for a certain time horizon, by scheduling different generating units in order to meet a certain demand given by a valid forecast. Given that this is an NP-hard problem, it quickly becomes intractable on classical computers when considering real world scenarios on a large scale.A test scenario was also designed to study, by conducting an experimental analysis, the influences that each of the parameters have on the solution quality. To that end, the formulation of the Unit Commitment Problem was also translated to a suitable QUBO form which is then solved through a quantum annealer from D-Wave. For that test scenario, both the parameters from the problem formulation as well as the parameters related to the quantum computer were considered.The results from the experimental analysis suggest that most parameters do have an impact on the solution quality. With some having a greater impact overall such as Grids, that are representing how accurate the linearization of the problem is, as well the delta value associated with the first constraint, a value that is tied to how much of a weight the first constraint, that restricts each unit to a single production level, has. While the parameters with the overall greater impact are tied to the formulation of the problem, parameters like chain strength that affects the strength of coupling between qubits representing a single variable also have a significant impact on the solution quality. While most parameters have a statistical impact on the solution quality, the delta associated with the second constraint, that restricts power generation to equal the demand, fails to have an impact.

Quantum Computing is beginning to gather even more attention at a time where efforts are being made into familiarizing younger audiences into not only learning programming on a classical computer, but also on a quantum one.This new paradigm of computation is set to revolutionize several industries as the hardware keeps developing, with the potential to solve problems that a classical computer would consider intangible, as well as giving some specific problems a so sought after speed-up. This is done by applying the properties of quantum physics, like superposition and entanglement, for computation. These properties not only allow to process a larger amount of data simultaneously, but also allows to tackle problems in a completely different way that would not be possible in a classical computer.This thesis focuses on solving a known and relevant problem in the electrical industry and studying its application on a quantum environment. The Unit Commitment Problem, the problem in question, consists in minimizing the cost of power production, for a certain time horizon, by scheduling different generating units in order to meet a certain demand given by a valid forecast. Given that this is an NP-hard problem, it quickly becomes intractable on classical computers when considering real world scenarios on a large scale.A test scenario was also designed to study, by conducting an experimental analysis, the influences that each of the parameters have on the solution quality. To that end, the formulation of the Unit Commitment Problem was also translated to a suitable QUBO form which is then solved through a quantum annealer from D-Wave. For that test scenario, both the parameters from the problem formulation as well as the parameters related to the quantum computer were considered.The results from the experimental analysis suggest that most parameters do have an impact on the solution quality. With some having a greater impact overall such as Grids, that are representing how accurate the linearization of the problem is, as well the delta value associated with the first constraint, a value that is tied to how much of a weight the first constraint, that restricts each unit to a single production level, has. While the parameters with the overall greater impact are tied to the formulation of the problem, parameters like chain strength that affects the strength of coupling between qubits representing a single variable also have a significant impact on the solution quality. While most parameters have a statistical impact on the solution quality, the delta associated with the second constraint, that restricts power generation to equal the demand, fails to have an impact.