Power Flow Calculation Based on Block-encoded Adiabatic Quantum Newton-Raphson Method

doi:10.16182/j.issn1004731x.joss.25-0506

Abstract

Abstract:

To overcome the efficiency bottleneck of the traditional Newton-Raphson(NR)method in high-dimensional power flow calculations for modern power systems and the constraints of variational quantum algorithm frameworks, this paper proposed a power flow calculation framework integrating block encoding technology and adiabatic quantum computing principles. Based on block encoding technology, adiabatic quantum theory, andthe NR method, a block-encoded adiabatic quantum power flow calculation framework (BQ-NR) was constructed. The NR correction equations were mapped to a quantum system, and the quantum state encoding of the correction equations was realized by constructing an extended Hermitian matrix and a projection operator; a discrete adiabatic evolution scheme was designed, and the continuous Hamiltonian was transformed into a sequence of unitary operators executable on quantum circuits by using Trotter-Suzuki decomposition and block encoding technology, realizing the dynamic coupling of the quantum solver and classical algorithms. Experimental results show that when the discrete evolution step M≥5×10⁶, the BQ-NR method can achieve convergence within three iterations, and its error accuracy (on the order of 1×10^-5) is comparable to that of the traditional NR method, which verifies the effectiveness of the block-encoded adiabatic quantum linear solver in solving correction equations; power flow calculation experiments verify the generalizability of the proposed algorithm, providing theoretical support for the engineering application of quantum computing in power system analysis.

Key words: adiabatic quantum computing, Newton-Raphson method(NR), power flow calculation, Trotter-Suzuki decomposition, block encoding

CLC Number:

TP391.9

Jiang Shengchao, Pei Yunqing, Zhai Hongying, Wu Guojian, Gao Fang. Power Flow Calculation Based on Block-encoded Adiabatic Quantum Newton-Raphson Method[J]. Journal of System Simulation, 2026, 38(5): 1453-1465.

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References 21

[1]	Cain M B, O'Neill R P, Castillo A. History of Optimal Power Flow and Formulations[J]. Federal Energy Regulatory Commission, 2012, 1: 1-36.
[2]	Radman G, Raje R S. Power Flow Model/Calculation for Power Systems with Multiple FACTS Controllers[J]. Electric Power Systems Research, 2007, 77(12): 1521-1531.
[3]	赵真, 袁旭峰, 徐玉韬, 等. 一种改进三点估计法的概率潮流计算方法[J]. 南方电网技术, 2020, 14(11): 43-48.
	Zhao Zhen, Yuan Xufeng, Xu Yutao, et al. An Improved Three-point Estimate Method for Probability Load Flow Calculation[J]. Southern Power System Technology, 2020, 14(11): 43-48.
[4]	朱怡莹, 周荣生, 林文硕. 考虑通信时延与中断的省地协同异步式潮流计算[J]. 南方电网技术, 2021, 15(6): 91-97.
	Zhu Yiying, Zhou Rongsheng, Lin Wenshuo. Provincial-local Coordinated Asynchronous Power Flow Calculation Considering Communication Delays and Interruptions[J]. Southern Power System Technology, 2021, 15(6): 91-97.
[5]	董清, 屈桐. 一种牛顿潮流算法收敛性定理的应用研究[J]. 电力科学与工程, 2021, 37(3): 16-22.
	Dong Qing, Qu Tong. A Study on the Application of Convergence Theorem of Newton Power Flow Algorithm[J]. Electric Power Science and Engineering, 2021, 37(3): 16-22.
[6]	徐震, 张大波, 杨贺钧, 等. 基于HHL算法的量子牛顿-拉夫逊法潮流计算[J]. 中国电机工程学报, 2025, 45(14): 5564-5576.
	Xu Zhen, Zhang Dabo, Yang Hejun, et al. Quantum Newton-raphson Power Flow Computation Based on HHL Algorithm[J]. Proceedings of the CSEE, 2025, 45(14): 5564-55760.
[7]	Feng Fei, Zhou Yifan, Zhang Peng. Quantum Power Flow[J]. IEEE Transactions on Power Systems, 2021, 36(4): 3810-3812.
[8]	韩平平, 吴家毓, 仇茹嘉, 等. 电力系统离散绝热变分量子潮流计算方法[J]. 电网技术, 2025, 49(7): 2852-2862.
	Han Pingping, Wu Jiayu, Qiu Rujia, et al. Discrete Adiabatic Variation Quantum Power Flow Calculation Method for Power Systems[J]. Power System Technology, 2025, 49(7): 2852-2862.
[9]	凌佳杰, 耿光超, 江全元. 基于变分量子算法的电力系统潮流计算[J]. 中国电机工程学报, 2023, 43(1): 28-36.
	Ling Jiajie, Geng Guangchao, Jiang Quanyuan. Power Flow Calculation of Power System Based on Variable Quantum Algorithm[J]. Proceedings of the CSEE, 2023, 43(1): 28-36.
[10]	刘成骏, 娄骐, 徐一骏, 等. 基于光量子计算机的电网停电后分区模型及量子比特扩容方法[J]. 电力系统自动化, 2025, 49(11): 80-90.
	Liu Chengjun, Lou Qi, Xu Yijun, et al. Partitioning Model and Qubit Expansion Method for Power Grid Blackout Based on Optical Quantum Computers[J]. Automation of Electric Power Systems, 2025, 49(11): 80-90.
[11]	李知艺, 许悦, 韩旭涛. 量子计算技术在新型电力系统决策优化中的应用[J]. 电力系统自动化, 2024, 48(6): 62-73.
	Li Zhiyi, Xu Yue, Han Xutao. Application of Quantum Computing Technology in Decision-making Optimization of New Power System[J]. Automation of Electric Power Systems, 2024, 48(6): 62-73.
[12]	Gao Fang, Wu Guojian, Guo Suhang, et al. Solving DC Power Flow Problems Using Quantum and Hybrid Algorithms[J]. Applied Soft Computing, 2023, 137: 110147.
[13]	Harrow A W, Hassidim A, Lloyd S. Quantum Algorithm for Linear Systems of Equations[J]. Physical Review Letters, 2009, 103(15): 150502.
[14]	Albash T, Lidar D A. Adiabatic Quantum Computation[J]. Reviews of Modern Physics, 2018, 90(1): 015002.
[15]	C S Costa Pedro, An Dong, Sanders Yuval R, et al. Optimal Scaling Quantum Linear-systems Solver via Discrete Adiabatic Theorem[J]. PRX Quantum, 2022, 3(4): 040303.
[16]	Alan Costa Dos Santos. Adiabatic Dynamics and Shortcuts to Adiabaticity: Fundamentals and Applications[EB/OL]. (2021-07-25) [2025-05-18]. .
[17]	Childs Andrew M, Kothari Robin, Somma Rolando D. Quantum Algorithm for Systems of Linear Equations with Exponentially Improved Dependence on Precision[J]. SIAM Journal on Computing, 2017, 46(6): 1920-1950.
[18]	Gilyén András, Su Yuan, Low G H, et al. Quantum Singular Value Transformation and Beyond: Exponential Improvements for Quantum Matrix Arithmetics[C]//Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. New York: ACM, 2019: 193-204.
[19]	Suzuki Masuo. Generalized Trotter's Formula and Systematic Approximants of Exponential Operators and Inner Derivations with Applications to Many-body Problems[J]. Communications in Mathematical Physics, 1976, 51(2): 183-190.
[20]	Lloyd S. Universal Quantum Simulators[J]. Science, 1996, 273(5278): 1073-1078.
[21]	Kashem M A, Ganapathy V, Jasmon G B, et al. A Novel Method for Loss Minimization in Distribution Networks[C]//DRPT2000. International Conference on Electric Utility Deregulation and Restructuring and Power Technologies. Proceedings. Piscataway: IEEE, 2000: 251-256.

节点编号	有功功率	无功功率	节点编号	有功功率	无功功率
1	0	0	18	0.090	0.039
2	0.099	0.060	19	0.090	0.039
3	0.090	0.039	20	0.090	0.039
4	0.120	0.081	21	0.090	0.039
5	0.060	0.030	22	0.090	0.039
6	0.060	0.021	23	0.090	0.051
7	0.201	0.099	24	0.420	0.210
8	0.201	0.099	25	0.420	0.210
9	0.060	0.021	26	0.060	0.024
10	0.060	0.010	27	0.060	0.024
11	0.045	0.030	28	0.060	0.021
12	0.060	0.036	29	0.120	0.069
13	0.060	0.036	30	0.201	0.60
14	0.120	0.081	31	0.150	0.069
15	0.060	0.009	32	0.210	0.099
16	0.060	0.021	33	0.060	0.039
17	0.060	0.021

方法	是否收敛	迭代周期	收敛时误差值
NR	是	3	4.108 9×10⁵
BQ-NR(M=1×10⁴)	否
BQ-NR(M=5×10⁴)	否
BQ-NR(M=1×10⁵)	是	13	1.302 9×10⁵
BQ-NR(M=5×10⁵)	是	5	7.611 6×10⁶
BQ-NR(M=1×10⁶)	是	5	3.417 6×10⁵
BQ-NR(M=5×10⁶)	是	3	6.487 0×10⁶
BQ-NR(M=1×10⁷)	是	3	7.611 9×10⁵
BQ-NR(M=5×10⁷)	是	3	4.725 2×10⁶

测试系统	迭代周期		收敛时误差值
测试系统	传统NR	BQ-NR	收敛时误差值
IEEE-5	2	2	8.300 3×10⁵
IEEE-9	3	3	3.764 7×10⁷
IEEE-14	1	1	5.660 8×10⁵
IEEE-18	3	3	5.499 9×10⁶
IEEE-22	2	2	2.122 0×10⁷
IEEE-30	2	2	6.653 0×10⁵
IEEE-39	2	2	2.122 0×10⁷
IEEE-57	2	2	5.235 2×10⁶
IEEE-69	3	3	2.204 1×10⁷
IEEE-85	3	3	2.454 1×10⁷
IEEE-118	2	2	9.843 3×10⁶