Harnessing the Power of Quantum Computing for Renewable Energy Systems
Open Access
- Author:
- Jing, Hang
- Graduate Program:
- Electrical Engineering (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- December 18, 2023
- Committee Members:
- Madhavan Swaminathan, Program Head/Chair
Minghui Zhu, Major Field Member
Chunhao Wang, Outside Field Member
Yan Li, Chair & Dissertation Advisor
Daniel Cullina, Major Field Member
Xiantao Li, Outside Unit Member - Keywords:
- Quantum computing
Renewable energy systems - Abstract:
- This dissertation focuses on the quantum computing for renewable energy systems. With the rapidly develop of power systems, more and more challenge computational problems need to be resolved urgently. For these challenge problems, the classical computer needs high computational effort, or even is impossible to solve them due to the dimension curse. To overcome these issues, by leveraging quantum properties, this dissertation aims at designing or applying quantum algorithms, which is running in quantum computer. This dissertation shows the author's developed works and the corresponding research statement, which are abstracted as follows. First, there are some critical and challenge combinatorial optimization problems in power systems. For a typical category, the Quadratic Binary Combinatorial Optimization (QUBO) problems, the Quantum Approximate Optimization Algorithm (QAOA) is a quantum-classical hybrid approach to provide high-quality approximation solution based on the adiabatic theorem. However, the performance of QAOA highly relies on the critical parameters in the ansatz, which need high computational effort for parameter training. To address this issue, by taking the Max-Cut problem, a famous binary combinatorial problem, as an instance, the author presents a data-driven QAOA with the parameter transfer strategy, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. Without any parameter optimization, the proposed data-driven QAOA is comparable with the famous classical algorithm, the Goemans-Williamson algorithm. The proposed strategy advances QAOA and pilots the practical application of quantum technique to power systems in noisy intermediate-scale quantum (NISQ) devices. In future work, the proposed strategy will be extended from the Max-Cut problem to the generic QUBO problem. Besides, considering QAOA is a promising quantum algorithm in NISQ era, the implementation in simulator will also be extended to the real quantum computer for further validating the proposed strategy. Second, in the Model Predictive Control (MPC) problem in renewable power systems, or the power flow calculation problem in power systems, solving the linear algebraic equations is a fundamental step. The quantum algorithm, the Harrow-Hassidim-Lloyd (HHL) algorithm, is utilized to speed up this fundamental step by solving the Quantum Linear Systems Problem (QLSP). However, there are some limitation of current HHL algorithm applications or implementations. The limitation 1: the existing implementation of original HHL algorithm may only deal with QLSP whose all eigenvalues are either positive or negative. The limitation 2: the key component of the HHL algorithm, the controlled rotation is cumbersome to implement. The limitation 3: the HHL algorithm provides a quantum state, which contains the solution of linear equations in quantum computer. For practical application in classical computer, the quantum tomography is needed to determine or estimate the elements of the solution in quantum state. The exponential speedup cannot kept due to the extra computational effort for quantum tomography. To overcome these limitations, the revised HHL algorithm, and the Matrix Extension for Amplifying Sampling Probabilities of Intended Solution (ME-ASPI) method are proposed. The revised HHL algorithm containing the well-designed mapping function and quantum operator enables the ordinary implementation of HHL algorithm to handle the limitation 1 and 2. For limitation 3, the author considers the case that when the partial information in quantum state is interested. The partial solutions are very meaningful in engineering problems. For instances, in the MPC problem, only the first element of optimal control input sequence is needed. in large-scale power flow problem, only the state of key buses are required for timely operation. By leveraging the properties of engineering problems, the proposed ME-ASPI method achieves the speedup of HHL algorithm when the quantum tomography is needed. In other words, the designed ME-ASPI method can determine the partial solution of linear equations by using the revised HHL algorithm and levering the nature of quantum tomography. In addition, the author also designs a universal quantum observable to extract the solutions of interest from the linear system of equations. The observable can be applied on many state-of-art quantum algorithms for the Quantum Linear Systems Problem (QLSP). The author also proposes two implementations for the deigned observable based on Hadamard test. In the future work, more applications will be implemented to verify the proposed revised HHL algorithm, ME-ASPI method, and quantum observable. Third, the author introduces a novel approach to address the computational challenges inherent in optimal control by leveraging quantum computing technology. The author proposes a hybrid quantum algorithm to theoretically address quadratic programming problems in MPC with inequality constraints. This approach aims to improve computational efficiency and provide innovative solutions to the challenges in power systems. Specifically, the method integrates the interior point method with variational quantum algorithm, utilizing the parameter shift rule to solve quadratic programming problems with inequality constraints in MPC. Meanwhile, the author also introduce how quantum computing can be employed to handle quadratic programming problems with various types of constraints, such as equality, inequality, or binary constraints. In addition, the author achieves polynomial speedup in parameter design for MPC to ensure system stability by using quantum computing. The author also demonstrates the Quantum Singular Value Decomposition (QSVD) under the framework of the variational quantum algorithm is implemented by both integrated with the non-gradient-based optimization method, and the gradient-based method driven by parameter shift rule. The QSVD method can efficiently provides Singular Value Decomposition (SVD) for the dynamic mode decomposition control. In the future work, the author will design the ansatz for MPC and SVD problems by considering the properties of the engineering problem. In summary, quantum technology offers a groundbreaking methodology to address challenging computational issues in power systems. This dissertation showcases the author's developed work and aims to delve deeper into the application of quantum computing in power systems. Future research endeavors will be conducted from both an application perspective and a quantum algorithm design perspective. This dissertation is organized as follow. Chapter 1 will introduce the backgrounds and motivations of this dissertation. Chapter 2 will introduce the proposed data-driven QAOA for combinatorial problem in power system. Chapter 3 will introduce the improved HHL algorithm and the proposed ME-ASPI method for the MPC problem in microgrids. Chapter 4 will introduce the proposed quantum observable for the partial information estimation problem in power system. Chapter 5 will present the variational quantum algorithm for the optimal control problems in microgrids. Chapter 6 will show the conclusions and future works.