基于NSTPNT的风电系统可靠性对风电预测误差灵敏度
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摘要
研究电力系统可靠性对风电预测误差的灵敏度,量化风电预测误差对可靠性的影响,可为风电并网系统的优化调度与备用规划提供参考依据.实际风电预测误差的分布未知,给灵敏度计算带来困难.本文首次提出非标准三阶多项式正态变换方法,推导非标准正态假设下多项式系数的解析表达式,实现将风电预测误差转换为同期望,标准差正态随机变量的多项式形式.将转换后的风电预测误差,代入含备用最优负荷削减模型,评估风电系统可靠性.提出可靠性指标对风电预测误差期望,标准差的灵敏度解析算法.算例验证了非标准三阶多项式正态变换方法与预测误差分布参数可靠性灵敏度算法的准确性.分析备用容量与标准差变化对预测误差可靠性灵敏度的影响.
The research of the sensitivities of the wind power system' reliability indices with respect to the distribution parameters of the wind power forecast error(WPFE) may help the reserve schedule, while the unknown distribution of the WPFE makes it difficult to calculate the sensitivities. The non-standard third-order polynomial normal transformation(NSTPNT) method is novelly proposed. And the analytical expressions of the polynomial coefficients are derived. Based on the NSTPNT, the sensitivities of the reliability indices with respect to the distribution parameters of the WPFE, including the expectation and standard deviation, are established respectively. The numerical results verify the accuracy of the proposed methods. The effects of the reserve capacity and the standard deviation of the WPFE on the reliability sensitivity are analyzed.
The research of the sensitivities of the wind power system' reliability indices with respect to the distribution parameters of the wind power forecast error(WPFE) may help the reserve schedule, while the unknown distribution of the WPFE makes it difficult to calculate the sensitivities. The non-standard third-order polynomial normal transformation(NSTPNT) method is novelly proposed. And the analytical expressions of the polynomial coefficients are derived. Based on the NSTPNT, the sensitivities of the reliability indices with respect to the distribution parameters of the WPFE, including the expectation and standard deviation, are established respectively. The numerical results verify the accuracy of the proposed methods. The effects of the reserve capacity and the standard deviation of the WPFE on the reliability sensitivity are analyzed.
引文
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[3]赵渊,何媛,芦晶晶.旋转备用对电网可靠性的影响及优化配置研究[J].电力系统保护与控制,2014, 42(8):40-46.Zhao Y, He Y, Lu J J. Allocation optimization of spinning reserve and its effect on bulk power systems reliability[J]. Power System Protection and Control, 2014, 42(8):40-46.
[4] Benidris M, Mitra J. Reliability and sensitivity analysis of composite power systems under emission constraints[J].IEEE Transactions on Power Systems, 2014, 29(1):404-412.
[5] Benidris M, Mitra J. Reliability and sensitivity analysis of composite power systems considering voltage and reactive power constraints[J]. IET Generation, Transmission&Distribution, 2015, 9(12):1245—1253.
[6] Gu Y, Xie L. Fast sensitivity analysis approach to assessing congestion induced wind curtailment[J]. IEEE Transactions on Power Systems, 2014, 29(1):101-110.
[7]王娟,马义中,汪建均.基于Kriging模型与重要性抽样的可靠性灵敏度分析[J].系统工程理论与实践,2017, 37(9):2440-2449.Wang J, Ma Y Z, Wang J J. Reliability sensitivity analysis based on Kriging model and importance sampling[J].Systems Engineering—Theory&Practice, 2017, 37(9):2440-2449.
[8]唐承,郭书祥,莫延或.基于灵敏度分析的系统可靠性稳健分配优化方法[J].系统工程理论与实践,2017, 37(7):1903-1909.Tang C, Guo S X, Mo Y Y. Robust allocation optimization method for system reliability based on sensitivity analysis[J]. Systems Engineering—Theory&Practice, 2017, 37(7):1903-1909.
[9]华玉婷,李生虎.基于SMP状态空间等值的智能变电站保护系统短期可靠性评估[J].系统工程理论与实践,2016, 36(9):2439-2448.Hua Y T, Li S H. Short-term reliability assessment of smart substation protection system using SMP state space equivalent model[J]. Systems Engineering—Theory&Practice, 2016, 36(9):2439-2448.
[10] Bouffard F, Galiana F D. Stochastic security for operations planning with significant wind power generation[J].IEEE Transactions on Power Systems, 2008, 23(2):306-316.
[11]张昭遂,孙元章,李国杰,等.计及风电功率不确定性的经济调度问题求解方法[J].电力系统自动化,2011,35(22):125-130.Zhang Z S, Sun Y Z, Li G J, et al. A solution of economic dispatch problem considering wind power uncertainty[J].Automation of Electric Power Systems, 2011, 35(22):125-130.
[12]杨宏,苑津莎,张铁锋.一种基于Beta分布的风电功率预测误差最小概率区间模型和算法[J].中国电机工程学报,2015,35(9):2135-2142.Yang H, Yuan J S, Zhang T F. A model and algorithm for minimum probability interval of wind power forecast errors based on Beta distribution[J]. Proceedings of the CSEE, 2015, 35(9):2135-2142.
[13] Bludszuweit H, Dominguez-Navarro J A, Llombart A. Statistical analysis of wind power forecast error[J]. IEEE Transactions on Power Systems, 2008, 23(3):983-991.
[14]丁华杰,宋永华,胡泽春,等.基于风电场功率特性的日前风电预测误差概率分布研究[J].中国电机工程学报,2013,33(34):136-144.Ding H J, Song Y H, Hu Z C, et al. Probability density function of day-ahead wind power forecast errors based on power curves of wind farms[J]. Proceedings of the CSEE, 2013, 33(34):136-144.
[15]叶林,张亚丽,巨云涛,等.用于含风电场的电力系统概率潮流计算的高斯混合模型[J].中国电机工程学报,2017, 37(15):4379-4387.Ye L, Zhang Y L, Ju Y T, et al. Gaussian mixture model for probabilistic power flow calculation of system integrated wind farm[J]. Proceedings of the CSEE, 2017, 37(15):4379-4387.
[16] Fleishman A I. A method for simulating non-normal distributions[J]. Psychometrika, 1978, 43(4):521—532.
[17] Chen X, Tung Y K. Investigation of polynomial normal transform[J]. Structural Safety, 2003, 25:423-445.
[18] Tung Y K. Polynomial normal transforms in uncertainty analysis[C]//International Conference on Applications of Statistics and Probability, 1999:167-174.
[19] Greenwood J A, Landwehr J M, Matalas N C, et al. Probability weighted moments:Definition and relation to parameters of several distributions expressable in inverse form[J]. Water Resources Research, 1979, 15(5):1049-1054.
[20]谢应昭,卢继平.基于多项式正态变换和最大熵估计的含风电系统电压稳定分析[J].电力自动化设备,2015, 35(10):66-73.Xie Y Z, Lu J P. Probability voltage stability analysis based on polynomial normal transformation and maximum entropy estimation for power system containing wind power[J]. Electric Power Automation Equipment, 2015,35(10):66-73.
[21]蔡德福,石东源,陈金富.基于多项式正态变换和拉丁超立方采样的概率潮流计算方法[J].中国电机工程学报,2013,33(13):91-100.Cai F D, Shi D Y, Chen J F. Probabilistic load flow calculation method based on polynomial normal transformation and Latin hypercube sampling[J]. Proceedings of the CSEE, 2013, 33(13):91-100.
[22]吴巍,汪可友,李国杰.计及光伏发电相关性的多重积分法概率潮流计算[J].中国电机工程学报,2015, 35(3):568-575.Wu W, Wang K Y, Li G J. Probability load flow calculation method based on multiple integral method considering correlation of photovoltaic generation[J]. Proceedings of the CSEE, 2015, 35(3):568-575.
[23] Papavasiliou A, Oren S S, O'Neill R P. Reserve requirements for wind power integration:A scenario-based stochastic programming framework[J]. IEEE Transactions on Power Systems, 2011, 26(4):2197-2206.
[24] Wang Q J. Direct sample estimators of L moments[J]. Water Resources Research, 1996, 32(12):3617-3619.
[25] Prudnikov A P, Brychkov Y A, Marichev O I. Integrals and series:Special functions[M]. New York:Gordon and Breach Science Publishers, 1998:122-123.
[26] Negnevitsky M, Nguyen D H, Piekutowski M. Risk assessment for power system operation planning with high wind power penetration[J]. IEEE Transactions on Power Systems, 2015, 30(5):1359-1368.
[27] University of Washington. PECO PSAP file format description[EB/OL].[2017-4-24]. https://www2.ee.washington.edu/research/pstca/pf14/ieeel4cdf.txt.
[28] Bonneville Power Administration. Wind power forecasting data[EB/OL].[2018-3-14]. https://www.bpa.gov/Projects/Initiatives/Wind/Pages/Wind-Power-Forecasting-Data.aspx.
[29] Elia System Operator. Wind power generation data[EB/OL].[2018-9-5]. http://www.elia.be/en/grid-data/powergeneration/wind-power.
[2]赵渊,周念成,谢开贵,等.大电力系统可靠性评估的灵敏度分析[J].电网技术,2005, 29(24):25-30.Zhao Y, Zhou N C, Xie K G, et al. Sensitivity analysis on reliability assessment of bulk power system[J]. Power System Technology, 2005, 29(24):25-30.
[3]赵渊,何媛,芦晶晶.旋转备用对电网可靠性的影响及优化配置研究[J].电力系统保护与控制,2014, 42(8):40-46.Zhao Y, He Y, Lu J J. Allocation optimization of spinning reserve and its effect on bulk power systems reliability[J]. Power System Protection and Control, 2014, 42(8):40-46.
[4] Benidris M, Mitra J. Reliability and sensitivity analysis of composite power systems under emission constraints[J].IEEE Transactions on Power Systems, 2014, 29(1):404-412.
[5] Benidris M, Mitra J. Reliability and sensitivity analysis of composite power systems considering voltage and reactive power constraints[J]. IET Generation, Transmission&Distribution, 2015, 9(12):1245—1253.
[6] Gu Y, Xie L. Fast sensitivity analysis approach to assessing congestion induced wind curtailment[J]. IEEE Transactions on Power Systems, 2014, 29(1):101-110.
[7]王娟,马义中,汪建均.基于Kriging模型与重要性抽样的可靠性灵敏度分析[J].系统工程理论与实践,2017, 37(9):2440-2449.Wang J, Ma Y Z, Wang J J. Reliability sensitivity analysis based on Kriging model and importance sampling[J].Systems Engineering—Theory&Practice, 2017, 37(9):2440-2449.
[8]唐承,郭书祥,莫延或.基于灵敏度分析的系统可靠性稳健分配优化方法[J].系统工程理论与实践,2017, 37(7):1903-1909.Tang C, Guo S X, Mo Y Y. Robust allocation optimization method for system reliability based on sensitivity analysis[J]. Systems Engineering—Theory&Practice, 2017, 37(7):1903-1909.
[9]华玉婷,李生虎.基于SMP状态空间等值的智能变电站保护系统短期可靠性评估[J].系统工程理论与实践,2016, 36(9):2439-2448.Hua Y T, Li S H. Short-term reliability assessment of smart substation protection system using SMP state space equivalent model[J]. Systems Engineering—Theory&Practice, 2016, 36(9):2439-2448.
[10] Bouffard F, Galiana F D. Stochastic security for operations planning with significant wind power generation[J].IEEE Transactions on Power Systems, 2008, 23(2):306-316.
[11]张昭遂,孙元章,李国杰,等.计及风电功率不确定性的经济调度问题求解方法[J].电力系统自动化,2011,35(22):125-130.Zhang Z S, Sun Y Z, Li G J, et al. A solution of economic dispatch problem considering wind power uncertainty[J].Automation of Electric Power Systems, 2011, 35(22):125-130.
[12]杨宏,苑津莎,张铁锋.一种基于Beta分布的风电功率预测误差最小概率区间模型和算法[J].中国电机工程学报,2015,35(9):2135-2142.Yang H, Yuan J S, Zhang T F. A model and algorithm for minimum probability interval of wind power forecast errors based on Beta distribution[J]. Proceedings of the CSEE, 2015, 35(9):2135-2142.
[13] Bludszuweit H, Dominguez-Navarro J A, Llombart A. Statistical analysis of wind power forecast error[J]. IEEE Transactions on Power Systems, 2008, 23(3):983-991.
[14]丁华杰,宋永华,胡泽春,等.基于风电场功率特性的日前风电预测误差概率分布研究[J].中国电机工程学报,2013,33(34):136-144.Ding H J, Song Y H, Hu Z C, et al. Probability density function of day-ahead wind power forecast errors based on power curves of wind farms[J]. Proceedings of the CSEE, 2013, 33(34):136-144.
[15]叶林,张亚丽,巨云涛,等.用于含风电场的电力系统概率潮流计算的高斯混合模型[J].中国电机工程学报,2017, 37(15):4379-4387.Ye L, Zhang Y L, Ju Y T, et al. Gaussian mixture model for probabilistic power flow calculation of system integrated wind farm[J]. Proceedings of the CSEE, 2017, 37(15):4379-4387.
[16] Fleishman A I. A method for simulating non-normal distributions[J]. Psychometrika, 1978, 43(4):521—532.
[17] Chen X, Tung Y K. Investigation of polynomial normal transform[J]. Structural Safety, 2003, 25:423-445.
[18] Tung Y K. Polynomial normal transforms in uncertainty analysis[C]//International Conference on Applications of Statistics and Probability, 1999:167-174.
[19] Greenwood J A, Landwehr J M, Matalas N C, et al. Probability weighted moments:Definition and relation to parameters of several distributions expressable in inverse form[J]. Water Resources Research, 1979, 15(5):1049-1054.
[20]谢应昭,卢继平.基于多项式正态变换和最大熵估计的含风电系统电压稳定分析[J].电力自动化设备,2015, 35(10):66-73.Xie Y Z, Lu J P. Probability voltage stability analysis based on polynomial normal transformation and maximum entropy estimation for power system containing wind power[J]. Electric Power Automation Equipment, 2015,35(10):66-73.
[21]蔡德福,石东源,陈金富.基于多项式正态变换和拉丁超立方采样的概率潮流计算方法[J].中国电机工程学报,2013,33(13):91-100.Cai F D, Shi D Y, Chen J F. Probabilistic load flow calculation method based on polynomial normal transformation and Latin hypercube sampling[J]. Proceedings of the CSEE, 2013, 33(13):91-100.
[22]吴巍,汪可友,李国杰.计及光伏发电相关性的多重积分法概率潮流计算[J].中国电机工程学报,2015, 35(3):568-575.Wu W, Wang K Y, Li G J. Probability load flow calculation method based on multiple integral method considering correlation of photovoltaic generation[J]. Proceedings of the CSEE, 2015, 35(3):568-575.
[23] Papavasiliou A, Oren S S, O'Neill R P. Reserve requirements for wind power integration:A scenario-based stochastic programming framework[J]. IEEE Transactions on Power Systems, 2011, 26(4):2197-2206.
[24] Wang Q J. Direct sample estimators of L moments[J]. Water Resources Research, 1996, 32(12):3617-3619.
[25] Prudnikov A P, Brychkov Y A, Marichev O I. Integrals and series:Special functions[M]. New York:Gordon and Breach Science Publishers, 1998:122-123.
[26] Negnevitsky M, Nguyen D H, Piekutowski M. Risk assessment for power system operation planning with high wind power penetration[J]. IEEE Transactions on Power Systems, 2015, 30(5):1359-1368.
[27] University of Washington. PECO PSAP file format description[EB/OL].[2017-4-24]. https://www2.ee.washington.edu/research/pstca/pf14/ieeel4cdf.txt.
[28] Bonneville Power Administration. Wind power forecasting data[EB/OL].[2018-3-14]. https://www.bpa.gov/Projects/Initiatives/Wind/Pages/Wind-Power-Forecasting-Data.aspx.
[29] Elia System Operator. Wind power generation data[EB/OL].[2018-9-5]. http://www.elia.be/en/grid-data/powergeneration/wind-power.
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