基于块编码绝热量子牛顿‒拉夫逊法的潮流计算

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

摘要/Abstract

摘要：

为突破传统牛顿‒拉夫逊(Newton-Raphson, NR)法在新型电力系统高维潮流计算中的效率瓶颈，以及变分量子算法框架的制约，提出融合块编码技术和绝热量子计算原理的潮流计算框架。基于块编码技术、绝热量子理论和NR法构建块编码绝热量子潮流计算框架(BQ-NR)。将NR法修正方程映射至量子系统，通过构造厄密扩展矩阵与投影算符实现修正方程的量子态编码；设计离散绝热演化方案，并利用Trotter-Suzuki分解和块编码技术将连续哈密顿量转化为量子线路可执行的酉算子序列，实现量子求解器与经典算法的动态耦合。实验结果表明：当离散演化步数M≥5×10⁶时，BQ-NR法可在3次迭代内实现收敛，其误差精度达1×10^‒5量级，与传统NR法相当，验证了块编码绝热量子线性求解器在修正方程求解中的有效性；潮流计算实验进一步验证了所提算法的可推广性，为量子计算在电力系统分析中的工程应用提供了理论支撑。

关键词: 绝热量子计算, 牛顿?拉夫逊法, 潮流计算, Trotter-Suzuki分解, 块编码

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

中图分类号:

TP391.9

蒋圣超,裴云庆,翟宏营等 . 基于块编码绝热量子牛顿‒拉夫逊法的潮流计算[J]. 系统仿真学报, 2026, 38(5): 1453-1465.

Jiang Shengchao,Pei Yunqing,Zhai Hongying,et al . 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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参考文献 21

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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