The decarbonization of electricity systems is increasing the complexity of operational planning and energy-system optimization. Higher penetration of variable renewable generation, distributed resources, storage, and flexible demand require system operators to evaluate a growing number of possible operating schedules under tighter decision-making timeframes. Unit Commitment is one of the central problems in this context, since it determines which generation units should be committed to meet demand at minimum operating cost while respecting system constraints. Although Mixed-Integer Linear Programming remains the operational standard for this class of problems, the increasing dimensionality and constraint complexity of future power systems motivate the exploration of complementary computational approaches. This thesis investigates whether a near-term quantum optimization algorithm can reproduce and analyze a simplified Unit Commitment decision. The study focuses on the Quantum Approximate Optimization Algorithm (QAOA), not as a replacement for classical solvers, but as a diagnostic tool for understanding how an energy-system scheduling problem behaves when reformulated for quantum computation. A four-generator isolated energy-system case study is considered, consisting of a baseload gas unit, a peak gas unit, a wind unit, and a solar unit. The system demand is set to 180 MW, with total installed capacity of 200 MW. The classical benchmark identifies the least-cost feasible dispatch as committing the baseload gas unit, peak gas unit, and wind unit, producing exactly 180 MW at a normalized operating cost of 51. To make the Unit Commitment problem compatible with QAOA, the constrained classical formulation is converted into a Quadratic Unconstrained Binary Optimization problem. The demand inequality is transformed into an equality using a binary-expanded slack variable representing surplus generation. This increases the model from four physical commitment variables to a nine-qubit quantum representation with 512 possible basis states. The resulting formulation is implemented using a reproducible simulation pipeline based on Qiskit validation and an exact statevector simulator, allowing the full probability distribution of the optimized quantum state to be evaluated. The final tuned QAOA configuration recovers the same dispatch as the classical benchmark, achieving an approximation ratio of 1.0. The optimized distribution assigns 79.9% of its probability mass to physically feasible dispatches, compared with a 12.5% uniform baseline, and assigns 1.24% probability to the exact optimum, making it observable with an expected measurement budget of approximately 80 shots. These results show that QAOA can solve the controlled small-scale benchmark and can meaningfully amplify feasible energy schedules. However, the analysis also identifies an important limitation for energy-system applications. The slack-variable encoding required to represent the demand constraint expands the search space and spreads probability over many feasible or near-feasible states, rather than concentrating it strongly on the unique least-cost dispatch. Increasing circuit depth improves broad physical feasibility but does not improve exact optimum extraction beyond the best observed depth. The thesis therefore concludes that QAOA is mathematically capable on the simplified Unit Commitment instance studied here, but practical relevance for realistic energy-system modeling will require more efficient constraint encodings, constraint-preserving mixers, and validation on larger multi-period problems including storage, ramping, and renewable uncertainty.
La decarbonizzazione dei sistemi elettrici sta aumentando la complessità della pianificazione operativa e dell’ottimizzazione energetica. La crescente presenza di generazione rinnovabile variabile, risorse distribuite, sistemi di accumulo e domanda flessibile richiede agli operatori di valutare un numero sempre maggiore di possibili programmi operativi in tempi decisionali più ristretti. In questo contesto, lo Unit Commitment rappresenta un problema centrale, poiché determina quali unità di generazione debbano essere impegnate per soddisfare la domanda al minimo costo operativo, rispettando i vincoli del sistema. Sebbene la Programmazione Lineare Intera Mista rimanga lo standard operativo, la crescente complessità dei futuri sistemi elettrici motiva l’esplorazione di approcci computazionali complementari. Questa tesi analizza se il Quantum Approximate Optimization Algorithm (QAOA) possa riprodurre e interpretare una decisione semplificata di Unit Commitment. QAOA non viene considerato come sostituto dei solutori classici, ma come strumento diagnostico per studiare il comportamento di un problema energetico quando viene riformulato per il calcolo quantistico. Il caso studio considera un sistema energetico isolato con quattro generatori: gas di base, gas di picco, eolico e solare. La domanda è fissata a 180 MW, con una capacità installata totale di 200 MW. Il benchmark classico identifica come soluzione ottima l’impegno delle unità gas di base, gas di picco ed eolica, che producono esattamente 180 MW con un costo operativo normalizzato pari a 51. Per rendere il problema compatibile con QAOA, la formulazione vincolata viene convertita in un problema Quadratic Unconstrained Binary Optimization (QUBO). Il vincolo di domanda viene trasformato in un’uguaglianza mediante una variabile di slack espansa in forma binaria, che rappresenta la generazione in surplus. Questa trasformazione aumenta il modello da quattro variabili fisiche di commitment a una rappresentazione quantistica a nove qubit, con 512 possibili stati di base. La formulazione viene implementata tramite una pipeline riproducibile, validata con Qiskit e con un simulatore statevector esatto, così da analizzare l’intera distribuzione di probabilità dello stato quantistico ottimizzato. La configurazione finale di QAOA recupera lo stesso dispacciamento del benchmark classico, raggiungendo un rapporto di approssimazione pari a 1,0. La distribuzione ottimizzata assegna il 79,9% della probabilità a dispacciamenti fisicamente ammissibili, rispetto a un baseline uniforme del 12,5%, e assegna l’1,24% all’ottimo esatto, rendendolo osservabile con circa 80 shot attesi. Tuttavia, la codifica tramite variabili di slack espande lo spazio di ricerca e distribuisce la probabilità su molti stati ammissibili o quasi ammissibili, invece di concentrarla fortemente sull’unico dispacciamento a costo minimo. La tesi conclude quindi che QAOA è matematicamente efficace sull’istanza semplificata studiata, ma che la sua rilevanza pratica per sistemi energetici realistici richiederà codifiche dei vincoli più efficienti, mixer che preservino l’ammissibilità e validazione su problemi multi-periodo più ampi con accumulo, vincoli di rampa e incertezza rinnovabile.
Exploring Quantum Algorithms for energy system modeling: a NISQ-era benchmark on Unit Commitment
ALBAALAWY, AHMED TAREK MOHAMED ABDELLATIF
2025/2026
Abstract
The decarbonization of electricity systems is increasing the complexity of operational planning and energy-system optimization. Higher penetration of variable renewable generation, distributed resources, storage, and flexible demand require system operators to evaluate a growing number of possible operating schedules under tighter decision-making timeframes. Unit Commitment is one of the central problems in this context, since it determines which generation units should be committed to meet demand at minimum operating cost while respecting system constraints. Although Mixed-Integer Linear Programming remains the operational standard for this class of problems, the increasing dimensionality and constraint complexity of future power systems motivate the exploration of complementary computational approaches. This thesis investigates whether a near-term quantum optimization algorithm can reproduce and analyze a simplified Unit Commitment decision. The study focuses on the Quantum Approximate Optimization Algorithm (QAOA), not as a replacement for classical solvers, but as a diagnostic tool for understanding how an energy-system scheduling problem behaves when reformulated for quantum computation. A four-generator isolated energy-system case study is considered, consisting of a baseload gas unit, a peak gas unit, a wind unit, and a solar unit. The system demand is set to 180 MW, with total installed capacity of 200 MW. The classical benchmark identifies the least-cost feasible dispatch as committing the baseload gas unit, peak gas unit, and wind unit, producing exactly 180 MW at a normalized operating cost of 51. To make the Unit Commitment problem compatible with QAOA, the constrained classical formulation is converted into a Quadratic Unconstrained Binary Optimization problem. The demand inequality is transformed into an equality using a binary-expanded slack variable representing surplus generation. This increases the model from four physical commitment variables to a nine-qubit quantum representation with 512 possible basis states. The resulting formulation is implemented using a reproducible simulation pipeline based on Qiskit validation and an exact statevector simulator, allowing the full probability distribution of the optimized quantum state to be evaluated. The final tuned QAOA configuration recovers the same dispatch as the classical benchmark, achieving an approximation ratio of 1.0. The optimized distribution assigns 79.9% of its probability mass to physically feasible dispatches, compared with a 12.5% uniform baseline, and assigns 1.24% probability to the exact optimum, making it observable with an expected measurement budget of approximately 80 shots. These results show that QAOA can solve the controlled small-scale benchmark and can meaningfully amplify feasible energy schedules. However, the analysis also identifies an important limitation for energy-system applications. The slack-variable encoding required to represent the demand constraint expands the search space and spreads probability over many feasible or near-feasible states, rather than concentrating it strongly on the unique least-cost dispatch. Increasing circuit depth improves broad physical feasibility but does not improve exact optimum extraction beyond the best observed depth. The thesis therefore concludes that QAOA is mathematically capable on the simplified Unit Commitment instance studied here, but practical relevance for realistic energy-system modeling will require more efficient constraint encodings, constraint-preserving mixers, and validation on larger multi-period problems including storage, ramping, and renewable uncertainty.| File | Dimensione | Formato | |
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https://hdl.handle.net/10589/260592