微网短期负荷预测中的白噪声分离
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摘要
微网短期负荷预测对微网系统安全、经济的运行有重要的意义。微网短期负荷预测中,白噪声的存在导致了预测的准确率上限。如何从微网短期负荷序列中识别并分离白噪声,是尚未解决的难题。
准确的分离白噪声,可以确定比较优化的预测模型与方法,确定组合预测模型的数目,得出概率化预测结果,对于微网短期负荷预测具有十分重要的意义。本文具体研究内容和结果如下:
(1)采用Matlab进行了四种小波函数、软硬阈值函数下小波阈值去噪数值实验,验证了小波去噪与时间序列分析中的平滑法有相似之处,四种小波去噪效果的优劣与移动平均法和指数平滑法(接近于正态的)的好坏有某种对应关系,并从理论上推断构造更好的平滑系数的可能性。
(2)采用解析形式探索了功率谱分离白噪声的可能性,并对AR(1)序列、AR(2)序列进行去噪研究。小波去噪和差分去噪按频率划分信号与噪声,对于低频信号高频噪声序列去噪有效,而功率谱去噪按幅值划分信号与噪声,对于序列是低频噪声高频信号的情形仍有效。在信号和噪声在频率域上不存在相互抵消的情况下,功率谱分离噪声方差效果显著。
(3)在Smith和Wallis对预测之谜给出的经验解释的基础上,采用数理统计学进行了理论解释,研究了样本容量对组合权重的影响。
(4)采用差分法和小波对eunite原始负荷序列的48个抽样序列进行去噪研究,发现差分法去噪对低频信号高频噪声序列的效果要优于小波去噪,验证抽样序列方差比原序列方差大。
The research of microgrid short term load forecasting short-term is important for the safe and economic running of the system contains microgrid. For microgrid load, there exists an upper limit of forecast accuracy which is caused by unpredictable white noise. Generally speaking,it is an unresolved difficult problem to identify the distribution function of white noise and separate white noise from microgrid load time series .
Accurate separation of white noise, can determine more optimal prediction model and more optimal prediction method, can determine the number of combination forecasting model, achieve probabilistic predictions, is of great significancefor the microgrid short term load forecasting
The main contents and results are:
(1) Study the effect of wavelet denoise using four wavelet functions, hard and soft threshold function under Matlab simulation environment. Cofirm the similarities between wavelet denoising and the smoothing in time series analysis, the pros and cons of four types of wavelet denoising have something to do with the advantages and disadvantages between the moving average and exponential smoothing method which is close to normal, and infer the possibility of better smoothing coefficient in theoretically.
(2) Explore the possibility of power spectrum denoising with analytical method, study the effect of power spectrum denoising using an AR(1) time series and an AR(2) time series.Wavelet denosing and differential method distinguish signal from noise by frequency, are usually used for the higher frequency noise on the lower-frequency signal sequence, while power spectrum distinguish signal from noise by amplitude, lower frequency noise on higher frequency signal sequence is still valid for power spectrum. For the case of signal and noise do not offset in frequency domain, the effect of power spectrum denoising is remarkable.
(3) On the basis of empirical discovery of Smith and Wallis, give a mathematical statistics analytical explanantion for the forecast combination puzzle. Study the sample size’s effect on the combined weights.
(4) Study the effects of differential method and the wavelet for 48 sample load sequence from eunitel load sequence. Find differential method denoising is superior to wavelet denoising for higher frequency noise on lower frequency signal sequence. Confirm sample sequeces have larger variance.
准确的分离白噪声,可以确定比较优化的预测模型与方法,确定组合预测模型的数目,得出概率化预测结果,对于微网短期负荷预测具有十分重要的意义。本文具体研究内容和结果如下:
(1)采用Matlab进行了四种小波函数、软硬阈值函数下小波阈值去噪数值实验,验证了小波去噪与时间序列分析中的平滑法有相似之处,四种小波去噪效果的优劣与移动平均法和指数平滑法(接近于正态的)的好坏有某种对应关系,并从理论上推断构造更好的平滑系数的可能性。
(2)采用解析形式探索了功率谱分离白噪声的可能性,并对AR(1)序列、AR(2)序列进行去噪研究。小波去噪和差分去噪按频率划分信号与噪声,对于低频信号高频噪声序列去噪有效,而功率谱去噪按幅值划分信号与噪声,对于序列是低频噪声高频信号的情形仍有效。在信号和噪声在频率域上不存在相互抵消的情况下,功率谱分离噪声方差效果显著。
(3)在Smith和Wallis对预测之谜给出的经验解释的基础上,采用数理统计学进行了理论解释,研究了样本容量对组合权重的影响。
(4)采用差分法和小波对eunite原始负荷序列的48个抽样序列进行去噪研究,发现差分法去噪对低频信号高频噪声序列的效果要优于小波去噪,验证抽样序列方差比原序列方差大。
The research of microgrid short term load forecasting short-term is important for the safe and economic running of the system contains microgrid. For microgrid load, there exists an upper limit of forecast accuracy which is caused by unpredictable white noise. Generally speaking,it is an unresolved difficult problem to identify the distribution function of white noise and separate white noise from microgrid load time series .
Accurate separation of white noise, can determine more optimal prediction model and more optimal prediction method, can determine the number of combination forecasting model, achieve probabilistic predictions, is of great significancefor the microgrid short term load forecasting
The main contents and results are:
(1) Study the effect of wavelet denoise using four wavelet functions, hard and soft threshold function under Matlab simulation environment. Cofirm the similarities between wavelet denoising and the smoothing in time series analysis, the pros and cons of four types of wavelet denoising have something to do with the advantages and disadvantages between the moving average and exponential smoothing method which is close to normal, and infer the possibility of better smoothing coefficient in theoretically.
(2) Explore the possibility of power spectrum denoising with analytical method, study the effect of power spectrum denoising using an AR(1) time series and an AR(2) time series.Wavelet denosing and differential method distinguish signal from noise by frequency, are usually used for the higher frequency noise on the lower-frequency signal sequence, while power spectrum distinguish signal from noise by amplitude, lower frequency noise on higher frequency signal sequence is still valid for power spectrum. For the case of signal and noise do not offset in frequency domain, the effect of power spectrum denoising is remarkable.
(3) On the basis of empirical discovery of Smith and Wallis, give a mathematical statistics analytical explanantion for the forecast combination puzzle. Study the sample size’s effect on the combined weights.
(4) Study the effects of differential method and the wavelet for 48 sample load sequence from eunitel load sequence. Find differential method denoising is superior to wavelet denoising for higher frequency noise on lower frequency signal sequence. Confirm sample sequeces have larger variance.
引文
[1]王成山(天津大学),分布式发电供能系统相关基础研究,973计划项目资助(2009CB219700),2009
[2] Nature Editorial. China's wind-power potential. Nature, 2009, 457(7228): 357
[3] Bouffard F, Galiana FD. Stochastic security for operations planning with significant wind power generation. IEEE Transactions on Power Systems, 2008, 23(2): 306~316
[4] Ochoa LF, Padilha-Feltrin A, Harrison GP. Time-series-based maximization of distributed wind power generation integration. IEEE Transactions on Energy Conversion, 2008, 23(3): 968~974
[5] Schiermeier Q, Tollefson J, Scully T, et al. Electricity without carbon. Nature, 2008, 454(7206): 816~823
[6] Wai RJ, Wang WH. Grid-connected photovoltaic generation system. IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953~964
[7] Bialasiewicz JT. Renewable energy systems with photovoltaic power generators: Operation and modeling. IEEE Transactions on Industrial Electronics, 2008, 55(7): 2752~2758
[8] Wai RJ, Wang WH. Grid-connected photovoltaic generation system. IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953~964
[9]康重庆,夏清,张伯明,电力系统负荷预测研究综述与发展方向的探讨,电力系统自动化,2004, 28(17): 1~11
[10]于尔铿,刘广一,周京阳,能量管理系统(EMS),北京:科学出版社,1998
[11]朱陶业,李应求,张颖,等.提高时间序列气象适应性的短期电力负荷预测算法.中国电机工程学报,2006, 26(23):14~19
[12]牛东晓,谷志红,邢棉,等,基于数据挖掘的SVM短期负荷预测方法研究,中国电机工程学报,2006, 26(18):6~12
[13]刘吉成,谭忠富,陈广娟,差价合约下电网公司购电费用最小化的离散优化模型,中国管理科学,2007, (6): 60~66
[14]罗滇生,姚建刚,何洪英,等,基于自适应滚动优化的电力负荷多模型组合预测系统的研究与开发,中国电机工程学报,2003, 23(5):58~61
[15] Methaprayoon K, Lee WJ, Rasmiddatta S, et al. Multistage artificial neural network short-term load forecasting engine with front-end weather forecast. IEEE Transactions on Industry Applications, 2007, 43(6): 1410~1416
[16] Taylor JW, McSharry PE. Short-term load forecasting methods: An evaluation based on European data. IEEE Transactions on Power Systems, 2007, 22(4): 2213~2219
[17] Asber D, Lefebvre S, Asber J, et al. Non-parametric short-term load forecasting. International Journal of Electrical Power & Energy Systems, 2007, 29(8):630~635
[18] Bashir ZA, El-Hawary ME. Applying wavelets to short-term load forecasting using PSO-Based Neural Networks. IEEE Transactions on Power Systems, 2009, 243(1): 20~27
[19]程正兴,杨守志,冯晓霞,小波分析的理论算进展和应用.北京:国防工业出版社, 2007,178~228
[20]崔锦泰,小波分析导论,程正兴,译,西安:西安交通大学出版社,1995
[21]程正兴,小波分析算法与应用,西安:西安交通大学出版社,1998,178~228
[22]成礼智,王红霞,罗永,小波的理论与运用,北京:科学出版社,2004
[23] (美)Donald B.Percival,(英)Andrew T.Walden,程正兴等译,时间序列分析的小波方法,北京:机械工业出版社,2006,56-156,340~391
[24] D.L. Donoho, De-Noising by Soft Thresholding, IEEE Trans. Info. 1993,933~936
[25] D. L. Donoho and I. M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage, Journal of American Statistical Assoc., 1995, 90(432): 1200~1224
[26] D. L. Donoho and I.M. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrica, 1994, 81: 425~455
[27] D.L. Donoho and I.M. Johnstone, Waveshrinkage: Asymptopia?, J.R. Stat.Soc. ser. B, 1995, 57( 2): 301~369
[28]何正友,钱清泉,电力系统暂态信号分析中小波基的选择原则,电力系统自动化,2003, 27(10): 45~49
[29]胡敏,陈强洪,多尺度分析方法中四种典型小波基的选择与比较,微机发展,2002,(3): 41~44
[30]杨位钦,顾岚,时间序列分析与动态数据建模,北京:北京工业学院出版社,1986,68~84
[31] Cramer H, On some classes of nonstationary stochastic processes, Stockholm, 1961
[32]沈允春,罗天放,沈东旭,随机信号分析,北京:国防工业出版社,2008
[33] Lonnie C. Ludeman著,邱天爽,李婷,毕英伟等译,Random Processes: Filtering, Estimation, and Detection,北京:电子工业出版社,2005
[34] Fan Jianqing, Yao Qiwei, Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag, 2003
[35]高阳,“微网短期负荷预测“机理+辨识”策略中的白噪声分离:[硕士学位论文],天津;天津大学,2008
[36] Barnard, G. A., New methods of quality control, Journal of the Royal Statistical Society A, 1963, 126: 255~258
[37] Bates J. M. and Granger C. W. J, The combination of forecasts, Operational Research Quarterly, 1969, 20: 451~468
[38] Clemen R. T., Combining forecasts: a review and annotated bibliography, International Journal of Forecasting, 1989, 5: 559~583
[39] Gooijer, J. G. D., Hyndman R. J., 25 years of time series forecasting, International Journal of Forecasting, 2006, 22: 443~473
[40] Granger C. W. J., Combining forecasts - twenty years later, Journal of Forecasting, 1989, 8(3): 167~173
[41] Makridakis S.,Winkler R. L., Averages of forecasts: some empirical results, Manage.Sci., 1983, 29: 987~996
[42] Hibon M., Evgeniou T., To combine or not to combine: selecting among forecasts and their combinations, International Journal of Forecasting, 2005, 21: 15~24
[43] Koning A. J., Franses P. H., Hibon M., Stekler H.O., The M3 competition: statistical tests of the results, International Journal of Forecasting, 2005, 21: 397~409
[44] Kang H., Unstable weights in the combination of forecasts, Management Science, 1986, 32: 683~695
[45] Smith J., Wallis K. F., A simple explanation of the forecast combination puzzle, Oxford Bulletin Of Economics And Statistics, 2009, 71(3): 331~355
[46] Bernstein R., Bernstein S., Schaum’s Outline of Elements of Statistics II: Inferential Statistics, McGraw-Hill, New York, 1999
[47] Dickinson J. P., Some statistical results in the combination of forecasts, Operational Research Quarterly, 1973, 24: 253~260
[2] Nature Editorial. China's wind-power potential. Nature, 2009, 457(7228): 357
[3] Bouffard F, Galiana FD. Stochastic security for operations planning with significant wind power generation. IEEE Transactions on Power Systems, 2008, 23(2): 306~316
[4] Ochoa LF, Padilha-Feltrin A, Harrison GP. Time-series-based maximization of distributed wind power generation integration. IEEE Transactions on Energy Conversion, 2008, 23(3): 968~974
[5] Schiermeier Q, Tollefson J, Scully T, et al. Electricity without carbon. Nature, 2008, 454(7206): 816~823
[6] Wai RJ, Wang WH. Grid-connected photovoltaic generation system. IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953~964
[7] Bialasiewicz JT. Renewable energy systems with photovoltaic power generators: Operation and modeling. IEEE Transactions on Industrial Electronics, 2008, 55(7): 2752~2758
[8] Wai RJ, Wang WH. Grid-connected photovoltaic generation system. IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953~964
[9]康重庆,夏清,张伯明,电力系统负荷预测研究综述与发展方向的探讨,电力系统自动化,2004, 28(17): 1~11
[10]于尔铿,刘广一,周京阳,能量管理系统(EMS),北京:科学出版社,1998
[11]朱陶业,李应求,张颖,等.提高时间序列气象适应性的短期电力负荷预测算法.中国电机工程学报,2006, 26(23):14~19
[12]牛东晓,谷志红,邢棉,等,基于数据挖掘的SVM短期负荷预测方法研究,中国电机工程学报,2006, 26(18):6~12
[13]刘吉成,谭忠富,陈广娟,差价合约下电网公司购电费用最小化的离散优化模型,中国管理科学,2007, (6): 60~66
[14]罗滇生,姚建刚,何洪英,等,基于自适应滚动优化的电力负荷多模型组合预测系统的研究与开发,中国电机工程学报,2003, 23(5):58~61
[15] Methaprayoon K, Lee WJ, Rasmiddatta S, et al. Multistage artificial neural network short-term load forecasting engine with front-end weather forecast. IEEE Transactions on Industry Applications, 2007, 43(6): 1410~1416
[16] Taylor JW, McSharry PE. Short-term load forecasting methods: An evaluation based on European data. IEEE Transactions on Power Systems, 2007, 22(4): 2213~2219
[17] Asber D, Lefebvre S, Asber J, et al. Non-parametric short-term load forecasting. International Journal of Electrical Power & Energy Systems, 2007, 29(8):630~635
[18] Bashir ZA, El-Hawary ME. Applying wavelets to short-term load forecasting using PSO-Based Neural Networks. IEEE Transactions on Power Systems, 2009, 243(1): 20~27
[19]程正兴,杨守志,冯晓霞,小波分析的理论算进展和应用.北京:国防工业出版社, 2007,178~228
[20]崔锦泰,小波分析导论,程正兴,译,西安:西安交通大学出版社,1995
[21]程正兴,小波分析算法与应用,西安:西安交通大学出版社,1998,178~228
[22]成礼智,王红霞,罗永,小波的理论与运用,北京:科学出版社,2004
[23] (美)Donald B.Percival,(英)Andrew T.Walden,程正兴等译,时间序列分析的小波方法,北京:机械工业出版社,2006,56-156,340~391
[24] D.L. Donoho, De-Noising by Soft Thresholding, IEEE Trans. Info. 1993,933~936
[25] D. L. Donoho and I. M. Johnstone, Adapting to unknown smoothness via wavelet shrinkage, Journal of American Statistical Assoc., 1995, 90(432): 1200~1224
[26] D. L. Donoho and I.M. Johnstone, Ideal spatial adaptation via wavelet shrinkage, Biometrica, 1994, 81: 425~455
[27] D.L. Donoho and I.M. Johnstone, Waveshrinkage: Asymptopia?, J.R. Stat.Soc. ser. B, 1995, 57( 2): 301~369
[28]何正友,钱清泉,电力系统暂态信号分析中小波基的选择原则,电力系统自动化,2003, 27(10): 45~49
[29]胡敏,陈强洪,多尺度分析方法中四种典型小波基的选择与比较,微机发展,2002,(3): 41~44
[30]杨位钦,顾岚,时间序列分析与动态数据建模,北京:北京工业学院出版社,1986,68~84
[31] Cramer H, On some classes of nonstationary stochastic processes, Stockholm, 1961
[32]沈允春,罗天放,沈东旭,随机信号分析,北京:国防工业出版社,2008
[33] Lonnie C. Ludeman著,邱天爽,李婷,毕英伟等译,Random Processes: Filtering, Estimation, and Detection,北京:电子工业出版社,2005
[34] Fan Jianqing, Yao Qiwei, Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag, 2003
[35]高阳,“微网短期负荷预测“机理+辨识”策略中的白噪声分离:[硕士学位论文],天津;天津大学,2008
[36] Barnard, G. A., New methods of quality control, Journal of the Royal Statistical Society A, 1963, 126: 255~258
[37] Bates J. M. and Granger C. W. J, The combination of forecasts, Operational Research Quarterly, 1969, 20: 451~468
[38] Clemen R. T., Combining forecasts: a review and annotated bibliography, International Journal of Forecasting, 1989, 5: 559~583
[39] Gooijer, J. G. D., Hyndman R. J., 25 years of time series forecasting, International Journal of Forecasting, 2006, 22: 443~473
[40] Granger C. W. J., Combining forecasts - twenty years later, Journal of Forecasting, 1989, 8(3): 167~173
[41] Makridakis S.,Winkler R. L., Averages of forecasts: some empirical results, Manage.Sci., 1983, 29: 987~996
[42] Hibon M., Evgeniou T., To combine or not to combine: selecting among forecasts and their combinations, International Journal of Forecasting, 2005, 21: 15~24
[43] Koning A. J., Franses P. H., Hibon M., Stekler H.O., The M3 competition: statistical tests of the results, International Journal of Forecasting, 2005, 21: 397~409
[44] Kang H., Unstable weights in the combination of forecasts, Management Science, 1986, 32: 683~695
[45] Smith J., Wallis K. F., A simple explanation of the forecast combination puzzle, Oxford Bulletin Of Economics And Statistics, 2009, 71(3): 331~355
[46] Bernstein R., Bernstein S., Schaum’s Outline of Elements of Statistics II: Inferential Statistics, McGraw-Hill, New York, 1999
[47] Dickinson J. P., Some statistical results in the combination of forecasts, Operational Research Quarterly, 1973, 24: 253~260