基于混沌理论的含分布式电源系统负荷预测研究
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摘要
电力负荷预测对于整个电力系统的运行与控制起着至关重要的作用,无论是经济调度、水火电协调还是发电计划的制定都是以负荷预测的数据为基础的。近年来随着风力发电、小型燃气轮机发电等新型发电方式的出现,以此为代表的分布式电源使传统的发、输电模式发生了巨大的变化。随着电网结构越来越复杂,以及电网规模的迅速扩大,系统对于电网稳定性的要求也不断提高,因此对负荷预测问题也提出了更新更有特点的要求。但在实际中取得的负荷数据中由于测量设备的误差、采样时间和地点的差异性等因素的影响,电力负荷时间序列呈现出复杂性、非线性、不确定性的特点。正是这些特点使得常规的预测方法无法很好的对含分布式电源的电系统负荷序列进行预测。
由于混沌被认为是解决确定性的非线性系统中出现的具有内在随机性的解的有效方法。混沌时间序列的奇怪吸引子中包含了丰富的动力学信息,从有限的时间序列中就可以恢复出包含整个系统动力学特征的奇怪吸引子。因此混沌方法被认为是研究非线性时间序列的动力学特征的最好方法。本文从时间序列的相空间重构出发,利用MATLAB数学工具,采用功率谱方法和最大Lyapunov指数法研究含分布式电源的电力负荷时间序列的混沌性。并通过绘制时间序列的功率谱图和计算时间序列的离散卷积积分,探讨了确定相空间重构的嵌入维数和延迟时间参数的不同方法,并首次将一种改进的C-C算法引入到电力负荷时间序列的相空间重构参数的选取中。从定量的角度,分析了采用不同的时间序列预测方法对同一序列进行预测时产生的不同精度的预测结果,以及同一方法对不同时间序列进行预测时产生的结果在精度上的差异性。通过算例发现混沌方法得出的负荷预测结果的预测精度令人满意。
The power load forecasting plays a vital role in the whole operation and control in electrical power system. Economic dispatch, hydro-thermal power coordination and power generation plan are all based on the load forecasting data. In recent years, with the arising of wind power generation, micro turbine generating and other new generating methods, distributed generators has greatly changed the traditional generation mode and transmission mode of power grid. The structure of power network becomes more and more complex and the scale continues to expand, which constantly raises the demand of power system stability. The accurate power load forecasting data can provide a solid protection for grid planning, scheduling and controlling. Because there are many influencing factors, the power load time series are complexity, nonlinearity and uncertainty. Because of these features, the load sequence is not accurately predicted by the conventional methods.
Chaos is considered as an effective method of solving inherent randomness solution which in the deterministic nonlinear system. The strange attractors of chaos time series contain abundant dynamics information, and recover the chaos attractors with dynamic characteristic in the limited time series. Therefore, the chaos method is known as the best way of researching dynamics characteristic of the nonlinearity time series. Proceed from the phase space reconstruction of time sequence, this test makes use of the MATLAB, adopts power spectrum and maximum Lyapunov exponent to research the chaos of electric power system load time series which containing distributed generators, and discusses embedded dimensions of determining phase space reconstruction and different ways for delaying time parameters. Moreover, the modified C-C algorithm is introduced to the parameter selection of phase space reconstruction’s power load time series for the first time. From the quantitative angle, when adopting different ways of time series forecasting predict the same time series, it will bring out different predicting precision; on the contrary, when adopting the same way of time series forecasting predicts different time series, it will bring out differences in the predicting precision. According to the calculations, the prediction accuracy of load predicting by the chaos method is satisfactory.
由于混沌被认为是解决确定性的非线性系统中出现的具有内在随机性的解的有效方法。混沌时间序列的奇怪吸引子中包含了丰富的动力学信息,从有限的时间序列中就可以恢复出包含整个系统动力学特征的奇怪吸引子。因此混沌方法被认为是研究非线性时间序列的动力学特征的最好方法。本文从时间序列的相空间重构出发,利用MATLAB数学工具,采用功率谱方法和最大Lyapunov指数法研究含分布式电源的电力负荷时间序列的混沌性。并通过绘制时间序列的功率谱图和计算时间序列的离散卷积积分,探讨了确定相空间重构的嵌入维数和延迟时间参数的不同方法,并首次将一种改进的C-C算法引入到电力负荷时间序列的相空间重构参数的选取中。从定量的角度,分析了采用不同的时间序列预测方法对同一序列进行预测时产生的不同精度的预测结果,以及同一方法对不同时间序列进行预测时产生的结果在精度上的差异性。通过算例发现混沌方法得出的负荷预测结果的预测精度令人满意。
The power load forecasting plays a vital role in the whole operation and control in electrical power system. Economic dispatch, hydro-thermal power coordination and power generation plan are all based on the load forecasting data. In recent years, with the arising of wind power generation, micro turbine generating and other new generating methods, distributed generators has greatly changed the traditional generation mode and transmission mode of power grid. The structure of power network becomes more and more complex and the scale continues to expand, which constantly raises the demand of power system stability. The accurate power load forecasting data can provide a solid protection for grid planning, scheduling and controlling. Because there are many influencing factors, the power load time series are complexity, nonlinearity and uncertainty. Because of these features, the load sequence is not accurately predicted by the conventional methods.
Chaos is considered as an effective method of solving inherent randomness solution which in the deterministic nonlinear system. The strange attractors of chaos time series contain abundant dynamics information, and recover the chaos attractors with dynamic characteristic in the limited time series. Therefore, the chaos method is known as the best way of researching dynamics characteristic of the nonlinearity time series. Proceed from the phase space reconstruction of time sequence, this test makes use of the MATLAB, adopts power spectrum and maximum Lyapunov exponent to research the chaos of electric power system load time series which containing distributed generators, and discusses embedded dimensions of determining phase space reconstruction and different ways for delaying time parameters. Moreover, the modified C-C algorithm is introduced to the parameter selection of phase space reconstruction’s power load time series for the first time. From the quantitative angle, when adopting different ways of time series forecasting predict the same time series, it will bring out different predicting precision; on the contrary, when adopting the same way of time series forecasting predicts different time series, it will bring out differences in the predicting precision. According to the calculations, the prediction accuracy of load predicting by the chaos method is satisfactory.
引文
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[2]梁志珊,王丽敏,付大鹏.应用混沌理论的电力系统短期负荷预测.控制与决策,1998,13:87-90.
[3]权先璋,蒋传文,张勇传.电力负荷的混沌预测方法.华中理工大学学报,2000,28:92-94.
[4]杨正领,林孔元.电力系统负荷记录混沌特性成因的探索.电力系统自动化,2002,5:18-22.
[5] Kim K H,Lee Y J,Rhee S B,et al.Dispersed generator placement using fuzzy-GA in distribution systems [C].Proc. 2002 IEEE Power Engineering Society. Aummer Meeting,2002,3:1148-1153.
[6] Borges C.L.T,Falcao D.M.Optimal distributed generation allocation for reliability,losses and voltage improvement [J]. International Journal of Power and Energy Systems.2006,28 (6):413-420.
[7]陈海众,陈金富,杨雄平,陈波,陈驾宇.配电网中计及短路电流约束的分布式发电规划.电力系统自动化,2006,30(21):16-21.
[8]杨培宏,刘文颖.分布式发电的种类及前景.农村电气化,2007,238:54-56.
[9] RA HMAN T K A,RA HIM S R A,MU SIRIN I. Optimal allocation and sizing of embedded generators//Proceedings of National Power&Energy Conference, November 29230,2004,Kuata L umpur,Malaysia:288-294.
[10] Ng C H, Lie T T, Goel L. Impacts of distributed generation on system reliability in competitive electricity markets [J].Power Engineering Conference, Singapore, 2007: 735-740.
[11]郑漳华,艾芊,顾承红,蒋传文.考虑环境因素的分布式发电多目标优化配置.中国电机工程学报,2009,29(13):23-28..
[12]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002,1.
[13]刘式达,刘式适,非线性动力学和复杂现象北京:气象出版社,1989,4-6.
[14]卢侃,孙建华,混沌学传奇.上海:上海翻译出版社公司,1991,10-12
[15] F.Takens Determing strange attractors in turbulence.Lecture notes in Math,1981, 898:361-381.
[16] L.Rodriguez-Iturbe et al. Chaos in rainfall. Water Resources Res,1989, 25:1667-1675.
[17] P.Grassberger and L.Procaccia. Measuring the strangeness of strange. Physica D,1983, 9:712-716.
[18] Breaford P. Wilcox et al. Searching for chaotic dynamics in snowmelt runoff. Water Resources Research,1991,27:1005-1010.
[19]赵汉清,文必洋.短时间序列的混沌检测方法及其在高频地波雷达海杂波混沌特性研究中的应用,信息处理,2003,19:92-94.
[20] D.O.Krimer, S.Residori. Thermomechanical effects in uniformly aligned dye-doped nematic liquid crystals. The European Physical Journal E,2006, 1:77-82.
[21] Ajjarapu V, Lee B. Bifurcation. Theory and its application to nonlinear dynamical phenomena in an electrical power system. IEEE PWRS, 1992,7:424-431.
[22]刘晨晖.电力系统负荷预报理论与方法.哈尔滨:哈尔滨工业大学出版社,1987.
[23]牛东晓,曹树华等.电力负荷预测技术及其应用.北京:中国电力出版社,1998.
[24]姚建刚,章建,银车来.电力市场运营及其软件开发.北京:中国电力出版社,2002.
[25] P.Grassberger and I.Procaccia. Measuring the strangeness of strange attractors. Physica D,1983, 8:1585-1590.
[26]唐巍,李殿璞.电力系统经济负荷分配的混沌优化方法.中国电机工程学报,2000,20:36-40.
[27]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化,2000,24:32-35.
[28] N.H.Packard,J.P.Crutchfield,J.D.Farmer and R.S.Shaw. Geometry from a time series. Phys.Rev.Lett, 1980, 45:712-716.
[29] D.Kugiumtais. States space reconstruction in the anaysis of chaotic time series—the role of the time window length. Physica D,1996,95:13-28.
[30]林嘉宇,王跃科,黄芝平等.语音信号相空间重构中的时间延迟的选择——复自相关法.信号处理,1999,15:220-225.
[31] Henry D.I.Abarbanel. The analysis of observed chaotic data in physical systems. Reviews of Modern Physics, 1993, 65:1331-1392.
[32]孙海云,曹庆杰.混沌时间序列建模及预测.系统工程理论与实践. 2001,5:106-109.
[33]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报,2007,19:2527-2538.
[34]宋学锋.混沌经济学理论及其应用研究.徐州:中国矿业大学出版社,1996.
[35] P.Graassberger, I.Procaccia. Estimical of the Kolmogorov entropy from a chaotic signals Physical Review A, 1983,28:2591-2593.
[36] A.Wolf.J.B.Swifh, H.L.Swinney and J.A.Vastano. Determing Lyapunov exponents from a time series. Physica D, 1985:285-317.
[37] G.Barana and I. Tsuda. A new method for computing Lyapunov exponents. Phys. Lett. A, 1993,175:421-427.
[38] K.Briggs. An improved method for estimating Lyapunov exponents of chaotic time series. Phys. Lett. A, 1990,151:27-32.
[39] R.Brown, P.Bryant and H.D.I.Abarbanel. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys.Rev.A, 1990,42:5817-5826.
[40]魏宏森,宋永华.开创复杂性研究的新科学.成都:四川教育出版社,1991.
[41]梁志珊,王丽敏等.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,18:368-371.
[42]赵翔,孙月明.Lyapunov指数在转子剩余寿命预报中的应用.中国电机工程,1999,18:10-13.
[43] Farmer J.D. and Sidorowich J.J. Predicting chaotic time series. Phys. Rev. Lett,1987,18:368-371.
[44]王承熙,张源.风力风电.北京:中国电力出版社,2002.
[45]吴学光,张学成,印永华,戴慧珠,陈允平.异步风力发电系统动态稳定性分析的数学模型及其应用.电网技术,1998:6-7.
[2]梁志珊,王丽敏,付大鹏.应用混沌理论的电力系统短期负荷预测.控制与决策,1998,13:87-90.
[3]权先璋,蒋传文,张勇传.电力负荷的混沌预测方法.华中理工大学学报,2000,28:92-94.
[4]杨正领,林孔元.电力系统负荷记录混沌特性成因的探索.电力系统自动化,2002,5:18-22.
[5] Kim K H,Lee Y J,Rhee S B,et al.Dispersed generator placement using fuzzy-GA in distribution systems [C].Proc. 2002 IEEE Power Engineering Society. Aummer Meeting,2002,3:1148-1153.
[6] Borges C.L.T,Falcao D.M.Optimal distributed generation allocation for reliability,losses and voltage improvement [J]. International Journal of Power and Energy Systems.2006,28 (6):413-420.
[7]陈海众,陈金富,杨雄平,陈波,陈驾宇.配电网中计及短路电流约束的分布式发电规划.电力系统自动化,2006,30(21):16-21.
[8]杨培宏,刘文颖.分布式发电的种类及前景.农村电气化,2007,238:54-56.
[9] RA HMAN T K A,RA HIM S R A,MU SIRIN I. Optimal allocation and sizing of embedded generators//Proceedings of National Power&Energy Conference, November 29230,2004,Kuata L umpur,Malaysia:288-294.
[10] Ng C H, Lie T T, Goel L. Impacts of distributed generation on system reliability in competitive electricity markets [J].Power Engineering Conference, Singapore, 2007: 735-740.
[11]郑漳华,艾芊,顾承红,蒋传文.考虑环境因素的分布式发电多目标优化配置.中国电机工程学报,2009,29(13):23-28..
[12]吕金虎,陆君安,陈士华.混沌时间序列分析及其应用.武汉:武汉大学出版社,2002,1.
[13]刘式达,刘式适,非线性动力学和复杂现象北京:气象出版社,1989,4-6.
[14]卢侃,孙建华,混沌学传奇.上海:上海翻译出版社公司,1991,10-12
[15] F.Takens Determing strange attractors in turbulence.Lecture notes in Math,1981, 898:361-381.
[16] L.Rodriguez-Iturbe et al. Chaos in rainfall. Water Resources Res,1989, 25:1667-1675.
[17] P.Grassberger and L.Procaccia. Measuring the strangeness of strange. Physica D,1983, 9:712-716.
[18] Breaford P. Wilcox et al. Searching for chaotic dynamics in snowmelt runoff. Water Resources Research,1991,27:1005-1010.
[19]赵汉清,文必洋.短时间序列的混沌检测方法及其在高频地波雷达海杂波混沌特性研究中的应用,信息处理,2003,19:92-94.
[20] D.O.Krimer, S.Residori. Thermomechanical effects in uniformly aligned dye-doped nematic liquid crystals. The European Physical Journal E,2006, 1:77-82.
[21] Ajjarapu V, Lee B. Bifurcation. Theory and its application to nonlinear dynamical phenomena in an electrical power system. IEEE PWRS, 1992,7:424-431.
[22]刘晨晖.电力系统负荷预报理论与方法.哈尔滨:哈尔滨工业大学出版社,1987.
[23]牛东晓,曹树华等.电力负荷预测技术及其应用.北京:中国电力出版社,1998.
[24]姚建刚,章建,银车来.电力市场运营及其软件开发.北京:中国电力出版社,2002.
[25] P.Grassberger and I.Procaccia. Measuring the strangeness of strange attractors. Physica D,1983, 8:1585-1590.
[26]唐巍,李殿璞.电力系统经济负荷分配的混沌优化方法.中国电机工程学报,2000,20:36-40.
[27]丁军威,孙雅明.基于混沌学习算法的神经网络短期负荷预测.电力系统自动化,2000,24:32-35.
[28] N.H.Packard,J.P.Crutchfield,J.D.Farmer and R.S.Shaw. Geometry from a time series. Phys.Rev.Lett, 1980, 45:712-716.
[29] D.Kugiumtais. States space reconstruction in the anaysis of chaotic time series—the role of the time window length. Physica D,1996,95:13-28.
[30]林嘉宇,王跃科,黄芝平等.语音信号相空间重构中的时间延迟的选择——复自相关法.信号处理,1999,15:220-225.
[31] Henry D.I.Abarbanel. The analysis of observed chaotic data in physical systems. Reviews of Modern Physics, 1993, 65:1331-1392.
[32]孙海云,曹庆杰.混沌时间序列建模及预测.系统工程理论与实践. 2001,5:106-109.
[33]陆振波,蔡志明,姜可宇.基于改进的C-C方法的相空间重构参数选择.系统仿真学报,2007,19:2527-2538.
[34]宋学锋.混沌经济学理论及其应用研究.徐州:中国矿业大学出版社,1996.
[35] P.Graassberger, I.Procaccia. Estimical of the Kolmogorov entropy from a chaotic signals Physical Review A, 1983,28:2591-2593.
[36] A.Wolf.J.B.Swifh, H.L.Swinney and J.A.Vastano. Determing Lyapunov exponents from a time series. Physica D, 1985:285-317.
[37] G.Barana and I. Tsuda. A new method for computing Lyapunov exponents. Phys. Lett. A, 1993,175:421-427.
[38] K.Briggs. An improved method for estimating Lyapunov exponents of chaotic time series. Phys. Lett. A, 1990,151:27-32.
[39] R.Brown, P.Bryant and H.D.I.Abarbanel. Computing the Lyapunov spectrum of a dynamical system from an observed time series. Phys.Rev.A, 1990,42:5817-5826.
[40]魏宏森,宋永华.开创复杂性研究的新科学.成都:四川教育出版社,1991.
[41]梁志珊,王丽敏等.基于Lyapunov指数的电力系统短期负荷预测.中国电机工程学报,1998,18:368-371.
[42]赵翔,孙月明.Lyapunov指数在转子剩余寿命预报中的应用.中国电机工程,1999,18:10-13.
[43] Farmer J.D. and Sidorowich J.J. Predicting chaotic time series. Phys. Rev. Lett,1987,18:368-371.
[44]王承熙,张源.风力风电.北京:中国电力出版社,2002.
[45]吴学光,张学成,印永华,戴慧珠,陈允平.异步风力发电系统动态稳定性分析的数学模型及其应用.电网技术,1998:6-7.