水电直流孤岛系统的Hopf分岔和极限环
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摘要
以水电为主的直流孤岛送出系统中多次出现具有长振荡周期和稳定振幅的超低频频率振荡事件。考虑到水轮机的非线性特性,建立了水电孤岛系统的非线性描述方程进行研究。并对比了非线性系统和其线性化模型下的稳定性和表现,发现了水电孤岛系统中非线性模型下的Hopf分岔和稳定极限环现象。在一定的参数范围内,系统平衡点不稳定,但出现稳定的极限环,系统轨迹收敛到极限环而呈现出等幅振荡。进一步分析得到极限环特性与Hopf分岔参数的关系。分析结果为研究水电直流孤岛中频率稳定问题提供了一种理论上的可能,最后说明了考虑水轮机非线性的重要性。
Ultra-low frequency oscillation with long cycle and stable amplitude has occurred in several hydro-dominant islands, attracting people's attention. To solve this problem, this paper takes nonlinearity of hydraulic turbine, the main nonlinearity source of the system, into account and sets up islanded system's nonlinear model with dynamic equations. Furthermore, this paper compares the effect of stability analysis and performance of the system with linear and nonlinear models. Different from linear model, Hopf bifurcation and limit cycle appears in the result of nonlinear dynamic model. In a certain range of the model parameters, the system equilibrium point is not stable. Instead, the attractor is stable, meaning that the system trajectories converge to this attractor and oscillate with stable amplitude. Relationship between limit cycle and Hopf bifurcation is further analyzed. Results show that attractor in the nonlinear model can explain the ultra-low frequency oscillation in the test and provides a theoretical possibility for analyzing frequency stability problem in hydroelectric islands. The research also explains importance of considering the hydraulic turbine's nonlinear model.
Ultra-low frequency oscillation with long cycle and stable amplitude has occurred in several hydro-dominant islands, attracting people's attention. To solve this problem, this paper takes nonlinearity of hydraulic turbine, the main nonlinearity source of the system, into account and sets up islanded system's nonlinear model with dynamic equations. Furthermore, this paper compares the effect of stability analysis and performance of the system with linear and nonlinear models. Different from linear model, Hopf bifurcation and limit cycle appears in the result of nonlinear dynamic model. In a certain range of the model parameters, the system equilibrium point is not stable. Instead, the attractor is stable, meaning that the system trajectories converge to this attractor and oscillate with stable amplitude. Relationship between limit cycle and Hopf bifurcation is further analyzed. Results show that attractor in the nonlinear model can explain the ultra-low frequency oscillation in the test and provides a theoretical possibility for analyzing frequency stability problem in hydroelectric islands. The research also explains importance of considering the hydraulic turbine's nonlinear model.
引文
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[2]马进,赵大伟,钱敏慧,等.大规模新能源接入弱同步支撑直流送端电网的运行控制技术综述[J].电网技术,2017,41(10):3112-3120.Ma Jin,Zhao Dawei,Qian Minhui,et al.Reviews of control technologies of large-scale renewable energy connected to weaklysynchronized sending-end DC power grid[J].Power System Technology,2017,41(10):3112-3120(in Chinese).
[3]Zhang M,Liu C,Han Y,et al.Research on frequency oscillation of HVDC sending system in islanded mode of hydro power units[C]//2014 International Conference on Power System Technology(POWERCON).Chengdu:CSEE,2014:2394-2400.
[4]贺庆,张宝家,易俊,等.蒙西—天津南特高压交流输电工程系统调试中电网稳定特性与运行方式[J].电网技术,2017,41(9):2749-2754.He Qing,Zhang Baojia,Yi Jun,et al.Power grid stability and operation modes in commissioning tests of Mengxi-Tianjinnan UHV AC transmission system[J].Power System Technology,2017,41(9):2749-2754(in Chinese).
[5]许达.特高压直流输电系统孤岛运行研究[D].广州:华南理工大学,2012.
[6]王华伟,韩民晓,范园园,等.呼辽直流孤岛运行方式下送端系统频率特性及控制策略[J].电网技术,2013,37(5):1401-1406.Wang Huawei,Han Minxiao,Fan Yuanyuan,et al.Frequency characteristics and control strategy of the feed-end system in the operation mode of the cold island DC[J].Power System Technology,2013,37(5):1401-1406(in Chinese).
[7]陈亦平.直流孤岛运行特性和安全稳定控制措施的研究[D].广州:华南理工大学,2014.
[8]陈亦平,陈磊,叶骏,等.云广直流孤岛动态稳定问题的广域电力系统稳定器解决方案[J].电力系统自动化,2014,4(5):31-35.Chen Yiping,Chen Lei,Ye Jun,et al.Solution of dynamic stability problems in islanded Yunnan-Guangdong DC transmission system based on wide-area power system stabilizer[J].Automation of Electric Power Systems,2014,4(5):31-35(in Chinese).
[9]陈亦平,陈磊,叶骏,等.云广直流孤岛运行“5?26”双极闭锁原因分析及改进措施[J].电力系统自动化,2014,38(8):129-135.Chen Yiping,Chen Lei,Ye Jun,et al.Analysis and improvement of“5?26”bi-pole trip of Yunnan-Guangdong HVDC islanded operation[J].Automation of Electric Power Systems,2014,38(8):129-135(in Chinese).
[10]袁林.直流送端孤岛系统的频率控制研究[D].沈阳:沈阳工业大学,2013.
[11]范园园,韩民晓,刘崇茹,等.水电孤岛高压直流送出协调控制策略[J].电网技术,2012,36(7):237-242.Fan Yuanyuan,Han Minxiao,Liu Chongru,et al.Coordinated control strategy for HVDC transmission from hydropower islands[J].Power System Technology,2012,36(7):237-242(in Chinese).
[12]胡铭,金小明,高鹏,等.云广特高压直流输电系统孤岛运行的稳定控制措施[J].电网技术,2009,33(18):5-8.Hu Ming,Jin Xiaoming,Gao Peng,et al.Stability control strategies for±800 k V DC transmission system from Yunnan to Guangdong under islanded operation[J].Power System Technology,2009,33(18):5-8(in Chinese).
[13]Huang H,Li F.Sensitivity analysis of load-damping characteristic in power system frequency regulation[J].IEEE Transactions on Power Systems,2013,28(2):1324-1335.
[14]Kundur P.Power system stability and control[M].New York:Mc Graw-hill,1994.
[15]Zhang Z C,Zhang Y,Zhang J S,et al.Routh criterion for Hopf bifurcation and its application to electric power systems[J].Relay,2005,33(1):34-37.