Abstract：As the frequency of power electronic switches increases, the traditional electromagnetic transient (EMT) real-time simulation based on CPUs fails to describe the high-frequency characteristics of switches accurately. It has become a trend to take FPGAs as the hardware platforms for real-time simulation. However, the following challenges exist: (1) the high programming threshold and long development cycle make it difficult to conduct a real-time simulation based on FPGAs; (2) it is hard to ensure the real-time performance of simulation while completing high complexity and large-scale iterative calculation. Therefore, this paper proposes a real-time EMT simulation universal solver for power electronic systems based on FPGAs. Firstly, a method that the node equation is reorganized into the form of a state space equation is proposed, and only the state quantity and measurement quantity in the simulation model are considered. As a result, the calculation quantity is reduced, and the calculation parallelism is increased. Secondly, the general framework of the FPGA real-time simulation solver is designed. The solver regards the fixed admittance matrix nodal method (FAMNM) as the switch modeling and circuit analysis method, and takes the multiply accumulator (MAC) for the basic computing unit. Its framework includes two parts, namely offline preprocessing and online calculation. The offline program of the solver can automatically obtain the parameters of the simulation models and generate the calculation data. A new organization method of FPGA ROM initialization data considering multiple simulation conditions is applied to improve the utilization of storage resources when generating calculation data, which splices and writes multiple data into the same initialization file. As the core of the online program, the matrix-vector multiplication (MVM) computing architecture can not only automatically configures computing resources and control logic according to parameters, but also automatically configure the reuse degree of resources by users. Finally, an implementation method of low-delay single-cycle floating-point accumulation is proposed. Rather than through a unidirectional shift, the alignment of the float-pointing accumulator is finished by a bidirectional shift, moving the shift alignment step out of the critical path of floating-point accumulation and realizing high-speed accumulation. The performance of the proposed solver is analyzed from two aspects of simulation speed and simulation scale: it can achieve a running speed of 400 MHz and a simulation step of 100 ns. Compared with the eHS solver from OPAL-RT under the same conditions, its simulation speed is doubled, and its simulation scale increases by 29.69 %~79.17 %. A two-level bridge converter and a three-level NPC converter are taken as test examples separately to verify the correctness and generality of the proposed solver. The real-time simulation at a high switching frequency is compared with the eHS solver based on an OP5700 simulator and the offline simulation based on Matlab. The results show that the maximum simulation errors of the proposed solver for the two examples are 3.47 % and 3.08 %, respectively. The following conclusions can be drawn from the theoretical analysis and simulations. The proposed general solver based on FPGAs, with high-speed MAC as the basic computing unit, can achieve a running speed of 400 MHz, a simulation step of 100ns, and maintain a high simulation accuracy. It has the characteristics of strong versatility, high automation, and flexible configuration. Under the same hardware conditions, its simulation speed, simulation scale, resource utilization, and use flexibility are all superior to the eHS solver of OPAL-RT.
周斌, 汪光森, 李卫超, 王志伟, 揭贵生. 基于FPGA的电力电子系统电磁暂态实时仿真通用解算器[J]. 电工技术学报, 2023, 38(14): 3862-3874.
Zhou Bin, Wang Guangsen, Li Weichao, Wang Zhiwei, Jie Guisheng. An FPGA-Based General Solver for Electromagnetic Transient Real-Time Simulation of Power Electronic Systems. Transactions of China Electrotechnical Society, 2023, 38(14): 3862-3874.
[1] 孙鹏琨, 葛琼璇, 王晓新, 等. 基于硬件在环实时仿真平台的高速磁悬浮列车牵引控制策略[J]. 电工技术学报, 2020, 35(16): 3426-3435. Sun Pengkun, Ge Qiongxuan, Wang Xiaoxin, et al.Traction control strategy of high-speed maglev train based on hardware-in-the-loop real-time simulation platform[J]. Transactions of China Electrotechnical Society, 2020, 35(16): 3426-3435. [2] 王成山, 李鹏, 王立伟. 电力系统电磁暂态仿真算法研究进展[J]. 电力系统自动化, 2009, 33(7): 97-103. Wang Chengshan, Li Peng, Wang Liwei.Progresses on algorithm of electromagnetic transient simulation for electric power system[J]. Automation of Electric Power Systems, 2009, 33(7): 97-103. [3] 王潇, 张炳达, 乔平. 一种面向微电网实时仿真的分块分层并行算法[J]. 电工技术学报, 2017, 32(7): 104-111. Wang Xiao, Zhang Bingda, Qiao Ping.A block hierarchical parallel method for real-time simulation of microgrid[J]. Transactions of China Electro- technical Society, 2017, 32(7): 104-111. [4] Chalangar H, Ould-Bachir T, Sheshyekani K, et al.Methods for the accurate real-time simulation of high-frequency power converters[J]. IEEE Transa- ctions on Industrial Electronics, 2022, 69(9): 9613-9623. [5] Mahseredjian J, Dinavahi V, Martinez J A.Simulation tools for electromagnetic transients in power systems: overview and challenges[J]. IEEE Transactions on Power Delivery, 2009, 24(3): 1657-1669. [6] 郝琦, 葛兴来, 宋文胜, 等. 电力牵引传动系统微秒级硬件在环实时仿真[J]. 电工技术学报, 2016, 31(8): 189-198. Hao Qi, Ge Xinglai, Song Wensheng, et al.Micro- second hardware-in-the-loop real-time simulation of electric traction drive system[J]. Transactions of China Electrotechnical Society, 2016, 31(8): 189-198. [7] 朱建鑫, 胡海兵, 陆道荣, 等. 应用于级联STATCOM的高精度低成本全FPGA实时仿真模型研究[J]. 电工技术学报, 2019, 34(4): 777-785. Zhu Jianxin, Hu Haibing, Lu Daorong, et al.The research on fully FPGA-based real-time simulation with high fidelity and low cost for the cascaded STATCOM[J]. Transactions of China Electrotech- nical Society, 2019, 34(4): 777-785. [8] 李浩洋, 李泽, 郭源博, 等. 考虑开关管开路故障的三电平STATCOM建模与硬件在回路实时仿真[J]. 电工技术学报, 2019, 34(3): 552-561. Li Haoyang, Li Ze, Guo Yuanbo, et al.Modeling and hardware-in-the-loop real-time simulation of three- level STATCOM considering switch open-circuit faults[J]. Transactions of China Electrotechnical Society, 2019, 34(3): 552-561. [9] Dufour C, Cense S, Ould-Bachir T, et al.General- purpose reconfigurable low-latency electric circuit and motor drive solver on FPGA[C]//Annual Con- ference on IEEE Industrial Electronics Society, Montreal, 2012: 3073-3081. [10] Bachir T O, Dufour C, David J P, et al.Floating-point engines for the FPGA-based real-time simulation of power electronic circuits[C]//International Conference on Power Systems Transients (IPST), Delft, 2011: 1-7. [11] Ould Bachir T, Dufour C, Bélanger J, et al.A fully auto- mated reconfigurable calculation engine dedi- cated to the real-time simulation of high switching frequency power electronic circuits[J]. Mathematics and Computers in Simulation, 2013, 91: 167-177. [12] Razzaghi R, Paolone M, Rachidi F.A general purpose FPGA-based real-time simulator for power systems applications[C]//IEEE/PES Innovative Smart Grid Technologies Europe, Istanbul, 2014: 1-5. [13] Razzaghi R, Mitjans M, Rachidi F, et al.An automated FPGA real-time simulator for power electronics and power systems electromagnetic transient applications[J]. Electric Power Systems Research, 2016, 141: 147-156. [14] 王成山, 丁承第, 李鹏, 等. 基于FPGA的配电网暂态实时仿真研究(一): 功能模块实现[J]. 中国电机工程学报, 2014, 34(1): 161-167. Wang Chengshan, Ding Chengdi, Li Peng, et al.Research on FPGA-based transient real-time simu- lation of distribution network, part Ⅰ: realization of functional modules[J]. Proceedings of the CSEE, 2014, 34(1): 161-167. [15] 王成山, 丁承第, 李鹏, 等. 基于FPGA的配电网暂态实时仿真研究(二): 系统架构与算例验证[J]. 中国电机工程学报, 2014, 34(4): 628-634. Wang Chengshan, Ding Chengdi, Li Peng, et al.Real- time transient simulation for distribution systems based on FPGA, part II: system architecture and algorithm verification[J]. Proceedings of the CSEE, 2014, 34(4): 628-634. [16] Wang Zhiying, Zeng Fanpeng, Li Peng, et al.Kernel solver design of FPGA-based real-time simulator for active distribution networks[J]. IEEE Access, 2018, 6(1): 29146-29157. [17] Majstorovic D, Celanovic I, Teslic N D, et al.Ultralow-latency hardware-in-the-loop platform for rapid validation of power electronics designs[J]. IEEE Transactions on Industrial Electronics, 2011, 58(10): 4708-4716. [18] Pejovic P, Maksimovic D.A method for fast time- domain simulation of networks with switches[J]. IEEE Transactions on Power Electronics, 1994, 9(4): 449-456. [19] Dagbagi M, Hemdani A, Idkhajine L, et al.ADC- based embedded real-time simulator of a power con- verter implemented in a low-cost FPGA: application to a fault-tolerant control of a grid-connected voltage- source rectifier[J]. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1179-1190. [20] Guo Xizheng, Tang Yiguo, Wu Mingkang, et al.FPGA-based hardware-in-the-loop real-time simu- lation implementation for high-speed train electrical traction system[J]. IET Electric Power Applications, 2020, 14(5): 850-858. [21] 穆清, 周孝信, 王祥旭, 等. 面向实时仿真的小步长开关误差分析和参数设置[J]. 中国电机工程学报, 2013, 33(31): 120-129, 15. Mu Qing, Zhou Xiaoxin, Wang Xiangxu, et al.Small- step switching error analysis and parameter setting for real-time simulation[J]. Proceedings of the CSEE, 2013, 33(31): 120-129, 15. [22] Dufour C. Method and system for reducing power losses and state-overshoots in simulators for switched power electronic circuit: US, 9665672[P].2017-05-30. [23] Li Zirun, Xu Jin, Wang Keyou, et al.A discrete small-step synthesis real-time simulation method for power converters[J]. IEEE Transactions on Industrial Electronics, 2022, 69(4): 3667-3676. [24] Dommel H W. Digital computer solution of electro- magnetic transients in single and multiphase net- works[J]. IEEE Transactions on Power Apparatus and Systems, 1969, PAS-88(4): 388-399. [25] Ho C W, Ruehli A, Brennan P.The modified nodal approach to network analysis[J]. IEEE Transactions on Circuits and Systems, 1975, 22(6): 504-509. [26] Mahseredjian J.Computation of power system transients: overview and challenges[C]//IEEE Power Engineering Society General Meeting, Tampa, 2007: 1-7. [27] Marti J R, Lin J.Suppression of numerical oscillations in the EMTP[J]. IEEE Power Engineering Review, 1989, 9(5): 71-72. [28] 徐晋. 通用电力电子实时仿真方法研究及应用[D]. 上海: 上海交通大学, 2019. [29] Ould-Bachir T, Dufour C, Bélanger J, et al.Effective floating-point calculation engines intended for the FPGA-based HIL simulation[C]//International Sym- posium on Industrial Electronics, Hangzhou, 2012: 1363-1368. [30] Ould-Bachir T, Merdassi A, Cense S, et al.FPGA- based real-time simulation of a PSIM model: an indirect matrix converter case study[C]//Annual Con- ference of the IEEE Industrial Electronics Society, Yokohama, 2016: 3336-3340. [31] Xilinx Inc. Block memory generator v8.4: LogiCORE IP product guide[EB/OL]. (2021-08-06)[2022-05-30]. https://docs.xilinx.com/content/dam/xilinx/support/documents/ip_documentation/blk_mem_gen/v8_4/pg058- blk-mem-gen.pdf. [32] Vangal S R, Hoskote Y V, Borkar N Y, et al.A 6.2-GFlops floating-point multiply-accumulator with conditional normalization[J]. IEEE Journal of Solid State Circuits, 2006, 41(10): 2314-2323. [33] Zhuo Ling, Morris G R, Prasanna V K.High- performance reduction circuits using deeply pipelined operators on FPGAs[J]. IEEE Transactions on Parallel and Distributed Systems, 2007, 18(10): 1377-1392. [34] Chen Yuan, Dinavahi V.An iterative real-time non- linear electromagnetic transient solver on FPGA[J]. IEEE Transactions on Industrial Electronics, 2011, 58(6): 2547-2555. [35] Ould-Bachir T, David J P.Performing floating-point accumulation on a modern FPGA in single and double precision[C]//IEEE Annual International Symposium on Field-Programmable Custom Computing Machines, Charlotte, 2010: 105-108. [36] Ould-Bachir T, David J P.Self-alignment schemes for the implementation of addition-related floating-point operators[J]. ACM Transactions on Reconfigurable Technology and Systems, 2013, 6(1): 1-21. [37] Oklobdzija V G.An algorithmic and novel design of a leading zero detector circuit: comparison with logic synthesis[J]. IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 1994, 2(1): 124-128. [38] IEEE Standards 754-2008. IEEE standard for floating- point arithmetic 754-2008. IEEE standard for floating- point arithmetic[S]. New York: IEEE Computer Society Microprocess Standards Committee, 2008. [39] OPAL-RT Inc. eFPGAsim v1.5: eHS user guide[EB/OL]. (2019-03-12)[2022-05-30]. https://www.opal-rt.com/ display/FPET/Main+features.
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