水力机组系统参数全局敏感性分析
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摘要
以水力机组系统为研究对象,提出水力不平衡力解析表达式连接传统水电调节系统模型和机械子系统模型,从而构建系统的整体耦合动力学模型。采用扩展傅里叶幅度检验法(extended Fourier amplitude sensitivity test,EFAST)对复杂水电系统模型典型参数进行敏感性分析,以评估其对发电机角速度和转子质心偏移敏感特性。研究结果:(1)机组综合自调节系数、转轮进口直径、转轮出口直径、水轮机额定流量和主接力器额定位移为发电机电角速度重要敏感参数;(2)发电机转子质量偏心、水轮机转轮质量偏心、机组综合自调节系数、转轮入口直径、转轮出口直径、转轮入口直径和主接力器额定位移为发电机转子质心水平偏移敏感性参数;(3)质心主要敏感性参数与其他参数相互作用对X方向和Y方向振动摆度影响有明显区别;(4)发电机转子质心振动偏移参数敏感性强于发电机角速度值。因此,利用该模型分析具体电站振动演化时,模型调参顺序为先校准发电机角速度值,在校准心振动偏移参数。该研究为复杂水电系统模型个体化应用和模型调参提供重要科学指导依据。
Sensitivity analysis of a hydroelectric generating system is of great significance to the application and improvement of the modeling technologies. To describe the unbalanced hydraulic forces acting on the turbine blades, this paper presents analytical expressions that play a key role in linking the models of the governing system and generator units. And based on this, we develop a unified model of the hydroelectric generating system and conduct a sensitivity analysis of its 27 parameters using the extended Fourier amplitude sensitivity test(EFAST), focusing on the parameters sensitive to the angular speed and rotor centroid of the generator. Results show that 1) the generator angular speed sensitive parameters include unit self-adjustment coefficient, the penstock diameters of the runner inlet and outlet,rated flow, and rated main servomotor displacement. 2) The sensitive parameters to the rotor centroid at horizontal deflection offset are the mass eccentricity of the rotor and runner, self-adjustment coefficient,the diameters of the runner outlet and outlet, and rated servomotor displacement. 3) An obvious difference exists between the interaction effects of the global sensitivity parameters and other parameters on the oscillation swings in X-direction and Y-direction. 4) The sensitivity to oscillation offset is stronger than that to the parameters of generator speed. Hence, when using the unified model to analyze the vibration evolution, the generator speed should be adjusted first, then the generator rotor parameters.
Sensitivity analysis of a hydroelectric generating system is of great significance to the application and improvement of the modeling technologies. To describe the unbalanced hydraulic forces acting on the turbine blades, this paper presents analytical expressions that play a key role in linking the models of the governing system and generator units. And based on this, we develop a unified model of the hydroelectric generating system and conduct a sensitivity analysis of its 27 parameters using the extended Fourier amplitude sensitivity test(EFAST), focusing on the parameters sensitive to the angular speed and rotor centroid of the generator. Results show that 1) the generator angular speed sensitive parameters include unit self-adjustment coefficient, the penstock diameters of the runner inlet and outlet,rated flow, and rated main servomotor displacement. 2) The sensitive parameters to the rotor centroid at horizontal deflection offset are the mass eccentricity of the rotor and runner, self-adjustment coefficient,the diameters of the runner outlet and outlet, and rated servomotor displacement. 3) An obvious difference exists between the interaction effects of the global sensitivity parameters and other parameters on the oscillation swings in X-direction and Y-direction. 4) The sensitivity to oscillation offset is stronger than that to the parameters of generator speed. Hence, when using the unified model to analyze the vibration evolution, the generator speed should be adjusted first, then the generator rotor parameters.
引文
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[13]杨华,陈云良,徐永,等.基于VMD-HHT方法的水电机组启动过渡过程振动信号分析研究[J].工程科学与技术,2017,49(2):92-99.YANG Hua,CHEN Yunliang,XU Yong,et al.Analysis of the hydropower unit vibration signal in the start transient process based on VMD-HHT method[J].Advanced Engineering Sciences,2017,49(2):92-99.(in Chinese)
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[15]曾云,张立翔,郭亚坤,等.共用管段的水力解耦及非线性水轮机模型[J].中国电机工程学报,2012,32(14):103-108.ZENG Yun,ZHANG Lixiang,GUO Yakun,et al.Hydraulic decoupling and nonlinear hydro turbine model with sharing common conduit[J].Proceedings of the CSEE,2012,32(14):103-108.(in Chinese)
[16]程永光,陈鉴治,杨建东.水电站调压室涌浪最不利叠加时刻的研究[J].水利学报,2004,35(7):109-113.CHENG Yongguang,CHEN Jianzhi,YANG Jiandong.Study on the most unfavorable superposition moment of surge in surge tank of hydropower station[J].Journal of Hydraulic Engineering,2004,35(7):109-113.(in Chinese)
[17]程永光,陈鉴治,杨建东,等.连接管长度对调压井水位波动和水锤压力的影响[J].水利学报,2003,34(5):46-51.CHENG Yongguang,CHEN Jianzhi,YANG Jiandong,et al.Influence of length of connecting pipe on water level fluctuation and water hammer pressure of surge tank[J].Journal of Hydraulic Engineering,2003,34(5):46-51.(in Chinese)
[18]LI C S,ZHANG N,LAI X J,et al.Design of a fractionalorder PID controller for a pumped storage unit using a gravitational search algorithm based on the Cauchy and Gaussian mutation[J].Information Sciences,2017,396:162-181.
[19]P.雷诺兹,刘明,方丽杰.欧洲各国及俄罗斯的水电站现代化改造[J].水利水电快报,2016,37(8):14-16.LNZ P,LIU Ming,FANG Lijie.Modernization of hydropower stations in Europe and Russia[J].Express Water Resources&Hydropower Information,2016,37(8):14-16.(in Chinese)
[20]XU B B,CHEN D Y,BEHRENS P,et al.Modeling oscillation modal interaction in a hydroelectric generating system[J].Energy Conversion and Management,2018,174:208-217.
[21]SUDRET B.Global sensitivity analysis using polynomial chaos expansions[J].Reliability Engineering&System Safety,2008,93(7):964-979.
[22]KLEPPER O.Multivariate aspects of model uncertainty analysis:tools for sensitivity analysis and calibration[J].Ecological Modelling,1997,101(1):1-13.
[23]邢会敏,相诗尧,徐新刚,等.基于EFAST方法的AquaCrop作物模型参数全局敏感性分析[J].中国农业科学,2017,50(1):64-76.XING Huimin,XIANG Shiyao,XU Xingang,et al.Global sensitivity analysis of aquacrop model paramters based on EFAST method[J].Scientia Agricultura Sinica,2017,50(1):64-76.(in Chinese)
[24]IOOSS B,LEMAITRE P.A review on global sensitivity analysis methods[J].Operations Research/Computer Science Interfaces,2015,59:101-122.
[25]SALTELLI A,RATTO M,ANDRES T,et al.Global sensitivity analysis.The Primer[M].Wiley John,2008:304.
[26]何亮,赵刚,靳宁,等.不同气候区和不同产量水平下APSIM-Wheat模型的参数全局敏感性分析[J].农业工程学报,2015,31(14):148-157.HE Liang,ZHAO Gang,JIN Ning,et al.Global sensitivity analysis of APSIM-Wheat paramters in different climate zones and yield levels[J].Transactions of the Chinese Society of Agricultural Engineering,2015,31(14):148-157.(in Chinese)
[27]KULASIRI D,LIANG J,YAO H,et al.Global sensitivity analysis of a model related to memory formation in synapses:Model reduction based on epistemic parameter uncertainties and related issues[J].Journal of Theoretical Biology,2017,419:116-136.
[28]XU B B,CHEN D Y,ZHANG H,et al.Dynamic analysis and modeling of a novel fractional-order hydro-turbinegenerator unit[J].Nonlinear Dynamics,2015,81(3):1263-1274.
[29]丁聪,把多铎,陈帝伊,等.混流式水轮机调节系统的建模与非线性动力分析[J].武汉大学学报(工学版),2012,45(2):187-192.DING Cong,BA Duoduo,CHEN Diyi,et al.Modeling and nonlinear dynamic analysis of Francis hydro-turbine governing system[J].Engineering Journal of Wuhan University,2012,45(2):187-192.(in Chinese)
[30]许贝贝.水力发电系统分数阶动力学模型与稳定性[D].杨凌:西北农林科技大学,2017.XU Beibei.Fractional-order dynamic model of a hydropower generation system and its stability[D].Yangling:Northwest A&F University,2017.(in Chinese)
[31]曾云,张立翔,张成立,等.水轮发电机组轴系横向振动的大扰动暂态模型[J].固体力学学报,2013(S1):137-142.ZENG Yun,ZHANG Lixiang,ZHANG Licheng,et al.Large disturbance transient model of lateral vibration of turbine generator shaft system[J].Chinese Journal of Solid Mechanics,2013(S1):137-142.(in Chinese)
[32]张雷克,马震岳,宋兵伟.水轮发电机组在不平衡磁拉力及密封力下振动特性分析[J].水电能源科学,2010,28(9):117-120.ZHANG Leike,MA Zhenyue,SONG Bingwei.Vibration analysis of hydrogenerator set under unbalanced magnetic pulling force and sealing force[J].Water Resources and Power,2010,28(9):123-126.(in Chinese)
[33]白冰,张立翔.随机水力激励下机组轴系的动力响应[J].排灌机械工程学报,2017,35(5):398-403.BAI Bing,ZHANG Lixiang.Dynamic response of hydroturbine set shaft system under stochastic hydraulic excitation[J].Journal of Drainage and Irrigation Machinery Engineering,2017,35(5):398-403.(in Chinese)
[34]常近时.水力机械装置过渡过程[M].北京:高等教育出版社,2005.CHANG Jinshi.Transient process of hydraulic machinery[M].Beijng:Higher Education Press,2005.(in Chinese)
[2]沈祖诒.水轮机调节系统分析[M].北京:水利电力出版社,1991.SHEN Zuyi.Hydraulic turbine governing system[M].Beijing:Water Resources and Electric Power Press,1991.(in Chinese)
[3]郑源,陈德新.水轮机[M].北京:中国水利水电出版社,2011.ZHENG Yuan,CHEN Xinde.Hydraulic turbine[M].Beijing:China Water&Power Press,2011.(in Chinese)
[4]ZHANG Y N,LIU K H,XIAN H Z,et al.A review of methods for vortex identification in hydroturbines[J].Renewable and Sustainable Energy Reviews,2018,81(Part 1):1269-1285.
[5]陈帝伊.非线性动力学分析与控制的若干理论问题及应用研究[D]:杨凌:西北农林科技大学,2013.CHEN Diyi.Nonlinear dynamical analysis,control and their applications[D].Yangling:Northwest A&FUniversity,2013.(in Chinese)
[6]ZENG Y,GUO Y K,ZHANG L X,et al.Nonlinear hydro turbine model having a surge tank[J].Mathematical Modelling of Systems,2013,19(1):12-28.
[7]SU W T,LI X B,LAN C F,et al.Chaotic dynamic characteristics of pressure fluctuation signals in hydroturbine[J].Journal of Mechnical Science and Technology,2016,30(11):5009-5017.
[8]佟文敏.水轮机转轮水力不平衡引起主轴摆动的分析[J].四川水力发电,1986(1):42-46.TONG Wenmin.Analysis of vibration of spindle caused by hydraulic unbalance of hydraulic runner of hydraulic turbine[J].Sichuan Water Power,1986(1):42-46.(in Chinese)
[9]许贝贝,陈帝伊,张浩,等.随机转速波动下水轮机调节系统动力稳定性[J].振动与冲击,2018,37(12):226-231.XU Beibei,CHEN Diyi,ZHANG Hao,et al.Stability of a hydro-turbine governing system under stochastic fluctuating speed[J].Journal of Vibration and Shock,2018,37(12):226-231.(in Chinese)
[10]ZHANG C B,YANG M J,LI J Y.Detailed modelling and parameters optimisation analysis on governing system of hydro-turbine generator unit[J].IET Genertion Transimission&Distribution,2018,12(5):1045-1051.
[11]宋志强,刘云贺.基于正交多项式分解的水轮机竖向动荷载识别[J].水利学报,2016,47(11):1449-1455.SONG Zhiqiang,LIU Yunhe.Vertical dynamic load identification of hydraulic turbine based on orthogonal polynomial decomposition[J].Journal of Hydraulic Engineering,2016,47(11):1449-1455.(in Chinese)
[12]IEEE Group.Hydraulic-turbine and turbine controlmodels for system dynamic studies[J].IEEE Transactions on Power Systems,1992,7(1):167-179.
[13]杨华,陈云良,徐永,等.基于VMD-HHT方法的水电机组启动过渡过程振动信号分析研究[J].工程科学与技术,2017,49(2):92-99.YANG Hua,CHEN Yunliang,XU Yong,et al.Analysis of the hydropower unit vibration signal in the start transient process based on VMD-HHT method[J].Advanced Engineering Sciences,2017,49(2):92-99.(in Chinese)
[14]张浩,许贝贝,陈帝伊.变顶高尾水洞水轮机调节系统哈密顿模型[J].振动工程学报,2018,31(2):323-328.ZHANG Hao,XU Beibei,CHEN Diyi.Hamiltonian model of a hydro-turbine governing system with inclined ceiling tailrace[J].Journal of Vibration Engineering,2018,31(2):323-328.(in Chinese)
[15]曾云,张立翔,郭亚坤,等.共用管段的水力解耦及非线性水轮机模型[J].中国电机工程学报,2012,32(14):103-108.ZENG Yun,ZHANG Lixiang,GUO Yakun,et al.Hydraulic decoupling and nonlinear hydro turbine model with sharing common conduit[J].Proceedings of the CSEE,2012,32(14):103-108.(in Chinese)
[16]程永光,陈鉴治,杨建东.水电站调压室涌浪最不利叠加时刻的研究[J].水利学报,2004,35(7):109-113.CHENG Yongguang,CHEN Jianzhi,YANG Jiandong.Study on the most unfavorable superposition moment of surge in surge tank of hydropower station[J].Journal of Hydraulic Engineering,2004,35(7):109-113.(in Chinese)
[17]程永光,陈鉴治,杨建东,等.连接管长度对调压井水位波动和水锤压力的影响[J].水利学报,2003,34(5):46-51.CHENG Yongguang,CHEN Jianzhi,YANG Jiandong,et al.Influence of length of connecting pipe on water level fluctuation and water hammer pressure of surge tank[J].Journal of Hydraulic Engineering,2003,34(5):46-51.(in Chinese)
[18]LI C S,ZHANG N,LAI X J,et al.Design of a fractionalorder PID controller for a pumped storage unit using a gravitational search algorithm based on the Cauchy and Gaussian mutation[J].Information Sciences,2017,396:162-181.
[19]P.雷诺兹,刘明,方丽杰.欧洲各国及俄罗斯的水电站现代化改造[J].水利水电快报,2016,37(8):14-16.LNZ P,LIU Ming,FANG Lijie.Modernization of hydropower stations in Europe and Russia[J].Express Water Resources&Hydropower Information,2016,37(8):14-16.(in Chinese)
[20]XU B B,CHEN D Y,BEHRENS P,et al.Modeling oscillation modal interaction in a hydroelectric generating system[J].Energy Conversion and Management,2018,174:208-217.
[21]SUDRET B.Global sensitivity analysis using polynomial chaos expansions[J].Reliability Engineering&System Safety,2008,93(7):964-979.
[22]KLEPPER O.Multivariate aspects of model uncertainty analysis:tools for sensitivity analysis and calibration[J].Ecological Modelling,1997,101(1):1-13.
[23]邢会敏,相诗尧,徐新刚,等.基于EFAST方法的AquaCrop作物模型参数全局敏感性分析[J].中国农业科学,2017,50(1):64-76.XING Huimin,XIANG Shiyao,XU Xingang,et al.Global sensitivity analysis of aquacrop model paramters based on EFAST method[J].Scientia Agricultura Sinica,2017,50(1):64-76.(in Chinese)
[24]IOOSS B,LEMAITRE P.A review on global sensitivity analysis methods[J].Operations Research/Computer Science Interfaces,2015,59:101-122.
[25]SALTELLI A,RATTO M,ANDRES T,et al.Global sensitivity analysis.The Primer[M].Wiley John,2008:304.
[26]何亮,赵刚,靳宁,等.不同气候区和不同产量水平下APSIM-Wheat模型的参数全局敏感性分析[J].农业工程学报,2015,31(14):148-157.HE Liang,ZHAO Gang,JIN Ning,et al.Global sensitivity analysis of APSIM-Wheat paramters in different climate zones and yield levels[J].Transactions of the Chinese Society of Agricultural Engineering,2015,31(14):148-157.(in Chinese)
[27]KULASIRI D,LIANG J,YAO H,et al.Global sensitivity analysis of a model related to memory formation in synapses:Model reduction based on epistemic parameter uncertainties and related issues[J].Journal of Theoretical Biology,2017,419:116-136.
[28]XU B B,CHEN D Y,ZHANG H,et al.Dynamic analysis and modeling of a novel fractional-order hydro-turbinegenerator unit[J].Nonlinear Dynamics,2015,81(3):1263-1274.
[29]丁聪,把多铎,陈帝伊,等.混流式水轮机调节系统的建模与非线性动力分析[J].武汉大学学报(工学版),2012,45(2):187-192.DING Cong,BA Duoduo,CHEN Diyi,et al.Modeling and nonlinear dynamic analysis of Francis hydro-turbine governing system[J].Engineering Journal of Wuhan University,2012,45(2):187-192.(in Chinese)
[30]许贝贝.水力发电系统分数阶动力学模型与稳定性[D].杨凌:西北农林科技大学,2017.XU Beibei.Fractional-order dynamic model of a hydropower generation system and its stability[D].Yangling:Northwest A&F University,2017.(in Chinese)
[31]曾云,张立翔,张成立,等.水轮发电机组轴系横向振动的大扰动暂态模型[J].固体力学学报,2013(S1):137-142.ZENG Yun,ZHANG Lixiang,ZHANG Licheng,et al.Large disturbance transient model of lateral vibration of turbine generator shaft system[J].Chinese Journal of Solid Mechanics,2013(S1):137-142.(in Chinese)
[32]张雷克,马震岳,宋兵伟.水轮发电机组在不平衡磁拉力及密封力下振动特性分析[J].水电能源科学,2010,28(9):117-120.ZHANG Leike,MA Zhenyue,SONG Bingwei.Vibration analysis of hydrogenerator set under unbalanced magnetic pulling force and sealing force[J].Water Resources and Power,2010,28(9):123-126.(in Chinese)
[33]白冰,张立翔.随机水力激励下机组轴系的动力响应[J].排灌机械工程学报,2017,35(5):398-403.BAI Bing,ZHANG Lixiang.Dynamic response of hydroturbine set shaft system under stochastic hydraulic excitation[J].Journal of Drainage and Irrigation Machinery Engineering,2017,35(5):398-403.(in Chinese)
[34]常近时.水力机械装置过渡过程[M].北京:高等教育出版社,2005.CHANG Jinshi.Transient process of hydraulic machinery[M].Beijng:Higher Education Press,2005.(in Chinese)