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arXiv:2110.12624 · IEEE International Conference on Quantum Computing and Engineering (QCE)

Adapting Quantum Approximation Optimization Algorithm (QAOA) for Unit Commitment

Samantha Koretsky, Pranav Gokhale, Jonathan M. Baker, Joshua Viszlai, Honghao Zheng, Niroj Gurung, Ryan Burg, Esa Aleksi Paaso, Amin Khodaei, Rozhin Eskandarpour, Frederic T. Chong

Published Oct 1, 2021• 45 citations
arXivHTMLPDF

Abstract

In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment, which aims to satisfy a target power load at minimal cost. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Using Qiskit, we simulate results for sample systems to validate the effectiveness of our approach. We also compare to purely classical methods. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units. However, for larger problem instances, the classical solvers either scale exponentially in runtime or must resort to coarse approximations. This opens the door to potential quantum advantage for systems with several hundred units, though quantum error correction may be necessary at this scale.

DOI
10.1109/qce52317.2021.00035

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In the present Noisy Intermediate-Scale Quantum (NISQ), hybrid algorithms that leverage classical resources to reduce quantum costs are particularly appealing. We formulate and apply such a hybrid quantum-classical algorithm to a power system optimization problem called Unit Commitment, which aims to satisfy a target power load at minimal cost. Our algorithm extends the Quantum Approximation Optimization Algorithm (QAOA) with a classical minimizer in order to support mixed binary optimization. Using Qiskit, we simulate results for sample systems to validate the effectiveness of our approach. We also compare to purely classical methods. Our results indicate that classical solvers are effective for our simulated Unit Commitment instances with fewer than 400 power generation units. However, for larger problem instances, the classical solvers either scale exponentially in runtime or must resort to coarse approximations. This opens the door to potential quantum advantage for systems with several hundred units, though quantum error correction may be necessary at this scale.
This paper proposes a hybrid quantum-classical algorithm to solve a fundamental power system problem called unit commitment (UC). The UC problem is decomposed into a quadratic subproblem, a quadratic unconstrained binary optimization (QUBO) subproblem, and an unconstrained quadratic subproblem. A classical optimization solver solves the first and third subproblems, while the QUBO subproblem is solved by a quantum algorithm called quantum approximate optimization algorithm (QAOA). The three subproblems are then coordinated iteratively using a three-block alternating direction method of multipliers algorithm. Using Qiskit on the IBM Q system as the simulation environment, simulation results demonstrate the validity of the proposed algorithm to solve the UC problem.
Solving problems related to planning and operations of large-scale power systems is challenging on classical computers due to their inherent nature as mixed-integer and nonlinear problems. Quantum computing provides new avenues to approach these problems. We develop a hybrid quantum-classical algorithm for the Unit Commitment (UC) problem in power systems which aims at minimizing the total cost while optimally allocating generating units to meet the hourly demand of the power loads. The hybrid algorithm combines a variational quantum algorithm (VQA) with a classical Benders-type heuristic. The resulting algorithm computes approximate solutions to UC in three stages: i) a collection of UC vectors capable meeting the power demand with lowest possible operating costs is generated based on VQA; ii) a classical sequential least squares programming (SLSQP) routine is leveraged to find the optimal power level corresponding to a predetermined number of candidate vectors; iii) in the last stage, the approximate solution of UC along with generating units power level combination is given. To demonstrate the effectiveness of the presented method, three different systems with 3 generating units, 10 generating units, and 26 generating units were tested for different time periods. In addition, convergence of the hybrid quantum-classical algorithm for select time periods is proven out on IonQ's Forte system.
Alternating Current Optimal Power Flow Unit Commitment (AC-OPF-UC) is a difficult mixed-integer nonlinear optimization problem that combines binary generator commitment decisions with nonconvex continuous AC power-flow constraints. In this work, we investigate whether hybrid quantum-classical variational algorithms can improve the solution of single-period AC-OPF-UC relative to classical approaches. To the best of our knowledge, this is the first study to directly evaluate quantum or hybrid quantum-classical algorithms for the full AC-OPF-UC problem. We consider two candidate algorithms for improving AC-OPF-UC solution quality relative to purely classical methods on ideal quantum hardware. The first applies QAOA directly to a fully discretized formulation of the problem, with equality and inequality constraints incorporated through penalty terms and slack variables. Although conceptually straightforward, this approach requires a prohibitively large number of qubits even for small instances. The second, qubit-efficient approach encodes only the binary generator status variables on a quantum computer, while optimizing the continuous power-flow variables classically for each sampled bitstring. We benchmark this method on randomly generated AC-OPF-UC instances with 5 to 13 generators and compare it against SCIP, SMAC, and uniform random sampling. Our simulations show that the qubit-efficient hybrid method does not outperform uniform sampling. These results suggest that in order to establish potential advantage of the variational hybrid strategy considered here over the best classical algorithms, if any, much larger system sizes (25+ generators) need to be tested, which is beyond our computational capacity. Alternatively, different approaches, such as quantum versions of branch-and-bound methods, may be more promising.
The unit commitment (UC) problem stands as a critical optimization challenge in the electrical power industry. It is classified as NP-hard, placing it among the most intractable problems to solve. This paper introduces a novel hybrid quantum-classical algorithm designed to efficiently (approximately) solve the UC problem in polynomial time. In this approach, the UC problem is decomposed into two subproblems: a QUBO (Quadratic Unconstrained Binary Optimization) problem and a quadratic optimization problem. The algorithm employs the Quantum Approximate Optimization Algorithm (QAOA) to identify the optimal unit combination and classical methods to determine individual unit powers. The proposed hybrid algorithm is the first to include both the spinning reserve constraint (thus improving its applicability to real-world scenarios) and to explore QAOA warm-start optimization in this context. The effectiveness of this optimization was illustrated for specific instances of the UC problem, not only in terms of solution accuracy but also by reducing the number of iterations required for QAOA convergence. Hybrid solutions achieved using a single-layer warm-start QAOA (p=1) are within a 5.1 % margin of the reference (approximate) classical solution, while guaranteeing polynomial time complexity on the number of power generation units and time intervals.
Unit commitment is an important optimization problem in power system operations, classified as NP-hard. This paper presents a hybrid quantum-classical method for the unit commitment problem with time-dependent constraints, where decisions must be made about which generators to turn on/off and how much power they should produce over a planning horizon. We use a hybrid quantum-classical optimization procedure to determine the on/off schedules of the generating units and the corresponding power dispatch that satisfies operational constraints such as load balance, generator limits, ramping, and reserve requirements. We frame the optimization loop as a leader-follower structure, where the quantum optimizer leads to give the on/off decisions, and the classical optimizer follows to produce the power level schedule. Leveraging Pauli-Correlation Encoding, our method scales to horizon-wide unit commitment schedules by encoding the binary variables with far fewer qubits. By combining these components, the method can handle multi-period settings while using far fewer qubits than straightforward quantum encodings that allocate one qubit per decision variable as in prior approaches. We evaluate the approach on both small- and large-scale instances, up to 312 binary variables, and show that it reliably produces feasible schedules with competitive operating costs.
Abstract The quantum hybrid algorithm has recently become a very promising and speedy method for solving larger-scale optimization problems in the noisy intermediate-scale quantum (NISQ) era. The unit commitment (UC) problem is a fundamental problem in the field of power systems that aims to satisfy the power balance constraint with minimal cost. In this paper, we focus on the implementation of the UC solution using exact quantum algorithms based on the quantum neural network (QNN). This method is tested with a ten-unit system under the power balance constraint. In order to improve computing precision and reduce network complexity, we propose a knowledge-based partially connected quantum neural network (PCQNN). The results show that exact solutions can be obtained by the improved algorithm and that the depth of the quantum circuit can be reduced simultaneously.