强模式耦合现象中复转矩系数法和开环模式判稳方法的等价性证明
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摘要
复转矩系数法和开环模式判稳方法采用相同的系统划分方式,都是将系统划分为2个子系统。当机械子系统的开环模式和电气子系统的开环模式相互靠近时,其中一个对应的闭环模式阻尼弱化甚至有可能处在复平面右半平面,这种现象称之为强模式耦合现象。这种现可以同时采用复转矩系数法和开环模式判稳方法进行分析。该文主要对强模式耦合现象中复转矩系数法和开环模式判稳方法的等价性进行证明。在理论上证明2种方法的稳定判据一致,从而说明2种方法的等价性,并结合算例对理论进行验证,发现不同场景下两种方法的稳定判断结果完全一致,和理论推导结果相符;同时采用复转矩系数法从阻尼机理的角度对强模式耦合现象做出解释,并提出根据开环模式的留数估算复转矩系数法中阻尼系数的公式,计算结果表明估算值和实际值较为接近。
The complex torque coefficient method and the open-loop mode stabilization judgement method use the same system division style, which divides the system into two subsystems. When the open loop mode of the mechanical subsystem and the open loop mode of the electrical subsystem are close to each other, one of the corresponding closed loop modes is weakened and may even be in the right half plane of the complex plane. This phenomenon is called strong mode coupling. In this case, the complex torque coefficient method can be used for analysis and the open-loop mode stabilization method can all be used for analysis. This paper mainly proved the equivalence of the complex torque coefficient method and the open-loop mode stabilization judgement method in the strong mode coupling phenomenon. It was proved theoretically that the stability criteria of the two methods are consistent,which explains the equivalence of the two methods. The theory was verified by the example. It is found that the stability judgment results of the two methods are completely consistent under different scenarios, which is consistent with the theoretical derivation. At the same time, complex torque coefficient method was used to explain the strong mode coupling from the perspective of damping mechanism, and the formula for estimating the damping coefficient in the complex torque coefficient method based on the residual of the open-loop mode was proposed. The calculation results show that the estimated value is close to the actual value.
The complex torque coefficient method and the open-loop mode stabilization judgement method use the same system division style, which divides the system into two subsystems. When the open loop mode of the mechanical subsystem and the open loop mode of the electrical subsystem are close to each other, one of the corresponding closed loop modes is weakened and may even be in the right half plane of the complex plane. This phenomenon is called strong mode coupling. In this case, the complex torque coefficient method can be used for analysis and the open-loop mode stabilization method can all be used for analysis. This paper mainly proved the equivalence of the complex torque coefficient method and the open-loop mode stabilization judgement method in the strong mode coupling phenomenon. It was proved theoretically that the stability criteria of the two methods are consistent,which explains the equivalence of the two methods. The theory was verified by the example. It is found that the stability judgment results of the two methods are completely consistent under different scenarios, which is consistent with the theoretical derivation. At the same time, complex torque coefficient method was used to explain the strong mode coupling from the perspective of damping mechanism, and the formula for estimating the damping coefficient in the complex torque coefficient method based on the residual of the open-loop mode was proposed. The calculation results show that the estimated value is close to the actual value.
引文
[1]Canay I M.A novel approach to the torsional interaction and electrical damping of the synchronous machine part I:theory[J].IEEE Transactions on Power Apparatus and Systems,1982,PAS-101(10):3630-3638.
[2]Canay I M.A novel approach to the torsional interaction and electrical damping of the synchronous machine part II:application to an arbitrary network[J].IEEETransactions on Power Apparatus and Systems,1982,PAS-101(10):3639-3647.
[3]Joos G,Ooi B T.Torsional interactions between synchronous generators and long transmission lines[J].IEEE Transactions on Power Systems,1987,2(1):17-22.
[4]Zhu Xinyao,Sun Haishun,Wen Jinyu,et al.Improved complex torque coefficient method using CPCM for multi-machine system SSR analysis[J].IEEE Transactions on Power Systems,2014,29(5):2060-2068.
[5]Bahrman M,Larsen E V,Piwko R J,et al.Experience with HVDC-turbine-generator torsional interaction at square butte[J].IEEE Transactions on Power Apparatus and Systems,1980,PAS-99(3):966-975.
[6]Kim D J,Nam H K,Moon Y H.A practical approach to HVDC system control for damping subsynchronous oscillation using the novel eigenvalue analysis program[J].IEEE Transactions on Power Systems,2007,22(4):1926-1934.
[7]倪以信,王艳春,陈寿荪,等.多机系统HVDC引起的轴系扭振的扫频:复数力矩系数分析[J].电力系统及其自动化学报,1991,3(2):44-55.Ni Yixin,Wang Yanchun,Chen Shousun,et al.The frequency scanning:complex torque ceofficient analysis of HVDC-caused shaft torsional oscillations in multimachine system[J].Proceedings of the EPSA,1991,3(2):44-55(in Chinese).
[8]Choo Y C,Agalgaonkar A P,Muttaqi K M,et al.Analysis of subsynchronous torsional interaction of HVDC system integrated hydro units with small generator-to-turbine inertia ratios[J].IEEE Transactions on Power Systems,2014,29(3):1064-1076.
[9]Padiyar K R.Analysis of subsynchronous resonance in power systems[M].Norwell,MA:Kluwer,1999.
[10]Padiyar K R,Sai Kumar H V.Investigations on strong resonance in multimachine power systems with STATCOM supplementary modulation controller[J].IEEETransactions on Power Systems,2006,21(2):754-762.
[11]Dobson I.Strong resonance effects in normal form analysis and subsynchronous resonance[C]//Bulk Power System Dynamics and Control V.Onomichi:IREP,2001.
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[13]Alawasa K M,Mohamed A R I.Impedance and damping characteristics of grid-connected VSCs with power synchronization control strategy[J].IEEE Transactions on Power Systems,2015,30(2):952-961.
[14]谢小荣,刘华坤,贺静波,等.直驱风机风电场与交流电网相互作用引发次同步振荡的机理与特性分析[J].中国电机工程学报,2016,36(9):2366-2372.Xie Xiaorong,Liu Huakun,He Jingbo,et al.Mechanism and characteristics of subsynchronous oscillation caused by the interaction between full-converter wind turbines and AC systems[J].Proceedings of the CSEE,2016,36(9):2366-2372(in Chinese).
[15]Du Wenjuan,Bi Jingtian,Wang Haifeng.Damping degradation of power system low-frequency electromechanical oscillations caused by open-loop modal resonance[J].IEEE Transactions on Power Systems,2018,33(5):5072-5081.
[16]Du Wenjuan,Chen Xiao,Wang Haifeng.Power system electromechanical oscillation modes as affected by dynamic interactions from grid-connected PMSGs for wind power generation[J].IEEE Transactions on Sustainable Energy,2017,8(3):1301-1312.
[17]Du Wenjuan,Chen Xiao,Wang Haifeng.PLL-induced modal resonance of grid-connected PMSGs with the power system electromechanical oscillation modes[J].IEEE Transactions on Sustainable Energy,2017,8(4):1581-1591.
[18]Du Wenjuan,Fu Qiang,Wang Haifeng.Small-signal stability of an AC/MTDC power system as affected by open-loop modal coupling between the VSCs[J].IEEETransactions on Power Systems,2018,33(3):3143-3152.
[19]Du Wenjuan,Fu Qiang,Wang Haifeng.Open-loop modal coupling analysis for a multi-input multi-output interconnected MTDC/AC power system[J].IEEETransactions on Power Systems,2019,34(1):246-256.
[20]Du Wenjuan,Zhen Zijing,Wang Haifeng.Sub-synchronous oscillations caused by the control of LCC HVDC transmission line under the condition of open-loop modal coupling[J].IET Generation,Transmission&Distribution,2018,12(19):4310-4318.
[21]王旭斌,杜文娟,王海风.开环模式谐振引发含变速风电机组电力系统振荡的机理分析[J].中国电机工程学报,2017,37(22):6481-6491.Wang Xubin,DU Wenjuan,Wang Haifeng.Oscillations caused by open-loop modal resonance in power system with variable-speed wind generator[J].Proceedings of the CSEE,2017,37(22):6481-6491(in Chinese).
[22]王旭斌,杜文娟,王海风.直驱风电并网系统中锁相环引起次同步振荡的开环模式谐振机理分析[J].中国电机工程学报,2018,38(7):1935-1950.Wang Xubin,Du Wenjuan,Wang Haifeng.Mechanism analysis of open-loop modal resonance on subsynchronous oscillations caused by PLL in power systems with integrated PMSGs[J].Proceedings of the CSEE,2018,38(7):1935-1950(in Chinese).
[23]任必兴,杜文娟,王海风.UPFC与同步机轴系的动态相互作用研究:模式谐振的诱发与评估[J/OL].中国电机工程学报,2018,https://doi.org/10.13334/j.0258-8013.pcsee.181029.Ren Bixing,Du Wenjuan,Wang Haifeng.Dynamic interaction between UPFC and generator shaft:induction and evaluation based on modal resonance[J/OL].Proceedings of the CSEE,2018,https://doi.org/10.13334/j.0258-8013.pcsee.181029(in Chinese).
[24]First benchmark model for computer simulation of subsynchronous resonance[J].IEEE Transactions on Power Apparatus and Systems,1977,96(5):1565-1572.
[25]安德森,福阿德王奔.电力系统控制与稳定[M].北京:电子工业出版社,2012.Anderson P M,Fouad A A.Power system control and stability[M].Beijing:Electronic Industry Press,2012(in Chinese).
[2]Canay I M.A novel approach to the torsional interaction and electrical damping of the synchronous machine part II:application to an arbitrary network[J].IEEETransactions on Power Apparatus and Systems,1982,PAS-101(10):3639-3647.
[3]Joos G,Ooi B T.Torsional interactions between synchronous generators and long transmission lines[J].IEEE Transactions on Power Systems,1987,2(1):17-22.
[4]Zhu Xinyao,Sun Haishun,Wen Jinyu,et al.Improved complex torque coefficient method using CPCM for multi-machine system SSR analysis[J].IEEE Transactions on Power Systems,2014,29(5):2060-2068.
[5]Bahrman M,Larsen E V,Piwko R J,et al.Experience with HVDC-turbine-generator torsional interaction at square butte[J].IEEE Transactions on Power Apparatus and Systems,1980,PAS-99(3):966-975.
[6]Kim D J,Nam H K,Moon Y H.A practical approach to HVDC system control for damping subsynchronous oscillation using the novel eigenvalue analysis program[J].IEEE Transactions on Power Systems,2007,22(4):1926-1934.
[7]倪以信,王艳春,陈寿荪,等.多机系统HVDC引起的轴系扭振的扫频:复数力矩系数分析[J].电力系统及其自动化学报,1991,3(2):44-55.Ni Yixin,Wang Yanchun,Chen Shousun,et al.The frequency scanning:complex torque ceofficient analysis of HVDC-caused shaft torsional oscillations in multimachine system[J].Proceedings of the EPSA,1991,3(2):44-55(in Chinese).
[8]Choo Y C,Agalgaonkar A P,Muttaqi K M,et al.Analysis of subsynchronous torsional interaction of HVDC system integrated hydro units with small generator-to-turbine inertia ratios[J].IEEE Transactions on Power Systems,2014,29(3):1064-1076.
[9]Padiyar K R.Analysis of subsynchronous resonance in power systems[M].Norwell,MA:Kluwer,1999.
[10]Padiyar K R,Sai Kumar H V.Investigations on strong resonance in multimachine power systems with STATCOM supplementary modulation controller[J].IEEETransactions on Power Systems,2006,21(2):754-762.
[11]Dobson I.Strong resonance effects in normal form analysis and subsynchronous resonance[C]//Bulk Power System Dynamics and Control V.Onomichi:IREP,2001.
[12]Dobson I,Zhang J,Greene S,et al.Is strong modal resonance a precursor to power system oscillations?[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2001,48(3):340-349.
[13]Alawasa K M,Mohamed A R I.Impedance and damping characteristics of grid-connected VSCs with power synchronization control strategy[J].IEEE Transactions on Power Systems,2015,30(2):952-961.
[14]谢小荣,刘华坤,贺静波,等.直驱风机风电场与交流电网相互作用引发次同步振荡的机理与特性分析[J].中国电机工程学报,2016,36(9):2366-2372.Xie Xiaorong,Liu Huakun,He Jingbo,et al.Mechanism and characteristics of subsynchronous oscillation caused by the interaction between full-converter wind turbines and AC systems[J].Proceedings of the CSEE,2016,36(9):2366-2372(in Chinese).
[15]Du Wenjuan,Bi Jingtian,Wang Haifeng.Damping degradation of power system low-frequency electromechanical oscillations caused by open-loop modal resonance[J].IEEE Transactions on Power Systems,2018,33(5):5072-5081.
[16]Du Wenjuan,Chen Xiao,Wang Haifeng.Power system electromechanical oscillation modes as affected by dynamic interactions from grid-connected PMSGs for wind power generation[J].IEEE Transactions on Sustainable Energy,2017,8(3):1301-1312.
[17]Du Wenjuan,Chen Xiao,Wang Haifeng.PLL-induced modal resonance of grid-connected PMSGs with the power system electromechanical oscillation modes[J].IEEE Transactions on Sustainable Energy,2017,8(4):1581-1591.
[18]Du Wenjuan,Fu Qiang,Wang Haifeng.Small-signal stability of an AC/MTDC power system as affected by open-loop modal coupling between the VSCs[J].IEEETransactions on Power Systems,2018,33(3):3143-3152.
[19]Du Wenjuan,Fu Qiang,Wang Haifeng.Open-loop modal coupling analysis for a multi-input multi-output interconnected MTDC/AC power system[J].IEEETransactions on Power Systems,2019,34(1):246-256.
[20]Du Wenjuan,Zhen Zijing,Wang Haifeng.Sub-synchronous oscillations caused by the control of LCC HVDC transmission line under the condition of open-loop modal coupling[J].IET Generation,Transmission&Distribution,2018,12(19):4310-4318.
[21]王旭斌,杜文娟,王海风.开环模式谐振引发含变速风电机组电力系统振荡的机理分析[J].中国电机工程学报,2017,37(22):6481-6491.Wang Xubin,DU Wenjuan,Wang Haifeng.Oscillations caused by open-loop modal resonance in power system with variable-speed wind generator[J].Proceedings of the CSEE,2017,37(22):6481-6491(in Chinese).
[22]王旭斌,杜文娟,王海风.直驱风电并网系统中锁相环引起次同步振荡的开环模式谐振机理分析[J].中国电机工程学报,2018,38(7):1935-1950.Wang Xubin,Du Wenjuan,Wang Haifeng.Mechanism analysis of open-loop modal resonance on subsynchronous oscillations caused by PLL in power systems with integrated PMSGs[J].Proceedings of the CSEE,2018,38(7):1935-1950(in Chinese).
[23]任必兴,杜文娟,王海风.UPFC与同步机轴系的动态相互作用研究:模式谐振的诱发与评估[J/OL].中国电机工程学报,2018,https://doi.org/10.13334/j.0258-8013.pcsee.181029.Ren Bixing,Du Wenjuan,Wang Haifeng.Dynamic interaction between UPFC and generator shaft:induction and evaluation based on modal resonance[J/OL].Proceedings of the CSEE,2018,https://doi.org/10.13334/j.0258-8013.pcsee.181029(in Chinese).
[24]First benchmark model for computer simulation of subsynchronous resonance[J].IEEE Transactions on Power Apparatus and Systems,1977,96(5):1565-1572.
[25]安德森,福阿德王奔.电力系统控制与稳定[M].北京:电子工业出版社,2012.Anderson P M,Fouad A A.Power system control and stability[M].Beijing:Electronic Industry Press,2012(in Chinese).