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International Conference on Sustainable Mobility Applications, Renewables and Technology (SMART)

Newton-Raphson Method Using HHL Algorithm for Power Flow Quantum Computing

Ziad El-Khatib, Sherif Moussa

Published Nov 22, 2024• 1 citation
Publisher

Abstract

This paper presents Newton-Raphson method using HHL algorithm for power flow quantum computation. The proposed Newton-Raphson HHL Quantum method converges to the solution within four iterations compared to the Newton-Raphson classical solution which converged in five iterations. The Newton-Raphson classical solution voltage$\mathrm{V}_{2}=0.96674$pu, angle$\delta_{2}=-0.04816$rads, angle$\delta_{3}=0.04096$rads. The Newton-Raphson-HHL Quantum method voltage$\mathrm{V}_{2}= 0.98173$pu, angle$\delta_{2}=-0.05018$rads, angle$\delta_{3}=0.04021$rads. This work Newton-Raphson HHL Quantum method for 3-bus time to converge is O.$228\mathrm{s}$. The fidelity is calculated to be 0.981436 with circuit width of 4 which is the number of qubits used in the circuit and the circuit depth gate layers is 126.

DOI
10.1109/smart63170.2024.10815146

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This paper presents Newton-Raphson method using HHL algorithm for power flow quantum computation. The proposed Newton-Raphson HHL Quantum method converges to the solution within four iterations compared to the Newton-Raphson classical solution which converged in five iterations. The Newton-Raphson classical solution voltageV2=0.96674\mathrm{V}_{2}=0.96674V2​=0.96674pu, angleδ2=−0.04816\delta_{2}=-0.04816δ2​=−0.04816rads, angleδ3=0.04096\delta_{3}=0.04096δ3​=0.04096rads. The Newton-Raphson-HHL Quantum method voltageV2=0.98173\mathrm{V}_{2}= 0.98173V2​=0.98173pu, angleδ2=−0.05018\delta_{2}=-0.05018δ2​=−0.05018rads, angleδ3=0.04021\delta_{3}=0.04021δ3​=0.04021rads. This work Newton-Raphson HHL Quantum method for 3-bus time to converge is O.228s228\mathrm{s}228s. The fidelity is calculated to be 0.981436 with circuit width of 4 which is the number of qubits used in the circuit and the circuit depth gate layers is 126.
The goal of the load flow study is to ensure that electrical power is delivered efficiently and reliably to end-users while maintaining the stability and security of the power system. Newton-Raphson is a numerical method used widely for load flow analysis. One of the most computationally expensive steps in this method is an equation-solving step. We propose to replace this step with HHL, a quantum algorithm for solving linear systems of equations. HHL is exponentially faster, but with caveats. In this study, a hybrid quantum algorithm is proposed for solving load flow. The Newton-Raphson method is used as a benchmark to compare the performance of the hybrid quantum algorithm. Although the simulation of the hybrid quantum algorithm takes much time, these preliminary results are encouraging and point to the potential for the use of quantum algorithms to develop hybrid quantum algorithms for load flow analysis and related problems.
In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm for the solution of a system of linear equations (SLE) offers an exponential speedup over the classical computers. The speedup advantage is more significant when the size and the frequency of solving the power flow problem become more substantial. Verified quantum computing applications to power systems are merely nonexistent at this point. Through this paper, we plan to (1) provide a proof-of-concept that practical power system problems can be solved using quantum technology, (2) build a quantum-grid foundation by solving a fundamental power system problem with applications in many other critical grid problems, and (3) apply HHL to solve an SLE which has broad applications in many power system problems. A small 3-bus system is used for testing and demonstration purposes, considering the limitations of the available quantum computing hardware and software. The proposed method's merits and effectiveness are demonstrated using IBM open-source quantum computer and reported through proof-of-concept experimental demonstration using a 4-qubit quantum information processor.
Significant progress in the construction of physical hardware for quantum computers has necessitated the development of new algorithms or protocols for the application of real-world problems on quantum computers. One of these problems is the power flow problem, which helps us understand the generation, distribution, and consumption of electricity in a system. In this study, the solution of a balanced 4-bus power system supported by the Newton-Raphson method is investigated using a newly developed dissipative quantum neural network hardware. This study presents the findings on how the proposed quantum network can be applied to the relevant problem and how the solution performance varies depending on the network parameters.
Harrow-Hassidim-Lloyd (HHL) is a quantum computation algorithm that can solve a system of linear equations in a logarithmic time scale; hence, an exponential speed-up over best-known classical computers, which have polynomial time complexity, is accessible. This paper studies the integration of HHL into the DC optimal power flow problem. Optimality conditions are formulated as a system of equations in the form of Ax=bAx=bAx=b that is solved by HHL. The performance of HHL for A-matrices appearing in DCOPF problems is discussed. The initialization of HHL for encoding data from classical data to a quantum state in an efficient manner is also investigated. The impact of HHL calculation error on DCOPF convergence and solution accuracy is analyzed. Qiskit module is used to test the HHL-based DCOPF problem on a 3-bus system. The impact of quantum computers and HHL errors on DCOPF is simulated for the IEEE 14- bus system.
This paper aims to contextualize the requirements for Quantum Computing (QC) algorithms to achieve a quantum advantage in solving the alternating current power flow (ACPF) problem, with a focus on runtime complexity. First, we establish a benchmark for a QC iterative solver to demonstrate an advantage over the classical Newton-Raphson Load Flow (NRLF) algorithm. Next, we derive a baseline expression for the end-to-end runtime complexity of any Gate-based QC algorithm as Ω(Nκ/ε),Ω(N κ/\varepsilon),Ω(Nκ/ε), reflecting dependence on system size NNN, condition number κκκ, and error tolerance ε\varepsilonε. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.
Abstract The development of quantum algorithms is facilitated by quantum circuit designs. A floating-point number can represent a wide range of values and is extremely useful in digital signal processing. A quantum circuit model to implement the floating-point division problem using the Newton-Raphson division algorithm is proposed in this paper. The proposed division circuit offers a significant savings in T-gates and qubits used in the circuit design when correlated with the state of art works proposed on fast division algorithms. The qubits savings are estimated around 17% and 20%, T-count savings are around 59.03% and 20.31%. Similarly, T-depth savings is estimated around 77.45% and 24.33% over the existing works.