微网短期负荷预测“机理+辨识”策略中的白噪声分离
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摘要
科学的预测是正确决策的依据和保证。微网短期负荷预测是电力系统领域的一个前沿的重要研究课题,对含微网系统运行的安全性和经济性有重要的意义。对于一个特定的电力短期负荷记录(时间序列),存在预测准确率的上限。
对微网负荷,预测准确率上限的大部分由白噪声的不可预测性引起。因此,研究负荷序列中的白噪声分离,具有重要的实际意义。一般地,从复杂时间序列中识别白噪声的正确分布函数,是尚未解决的困难理论问题。
本文结合微网负荷预测,从理论上分析了白噪声与信号的相对性;采用小波等方法,研究了白噪声近似分离。依此进行了微网短期负荷模拟数据的白噪声分离研究。
具体研究内容和结果如下:
(1)结合微网负荷的特点,提出了微网负荷预测的“背景调整法”,并对背景形成的思路做了初步的探讨。
(2)从理论上分析了有限长度(样本容量)时间序列中信号与噪声的相对性。根据Cramer分解定理,可将非平稳时间序列分解为信号和白噪声两部分。发现对于有限长度时间序列,趋势项和随机项的区分是相对的,白噪声和信号的区分是相对的。并通过小波去噪等数值仿真证实:样本容量越大,这种区分越准确。大体符合卡方分布规律。
(3)得到了一个理想的白噪声序列,其性能显著优于用“伪随机数”生成的白噪声序列。
(4)采用白噪声、AR(1)序列,评估了小波去噪的效果。并采用Bior4.4、Sym8、Db4、Coif5小波,对微网负荷模拟序列进行了白噪声分离。发现在功率谱上信号与噪声可分条件下,小波去噪有一定的实际价值。
Scientific forecasting is the foundation and assurance of correct decision. Short-term load forecasting of microgrid system is a leading subject, which is important to the economy and stability of microgrid systems.
For a given load data series(a time series), there exists an upper limit of forecast accuracy. For microgrid load, most of the upper limit is caused by white noise, so the study of the denoise is of practical signifcance. Generally, to identify the distribution function of white noise from a complex time series is an unresolved difficult problem.
Here we study the relativity of noise and signal, combined with the microgrid load forecast; Study the white noise separation using strategies as the wavelet denoise, and apply the wavelet denoise to microgrid load.
The main contents and results are:
(1)According to the characteristic of microgrid, put forward a“background adjust strategy”, and study how to construct an ideal background.
(2) Study theoretically the relativity between signal and noise in limited time series.According to Cramer’s decomposition theorem, a given non-stationary time series can be decomposed into two uncorrelated different parts: signals and white noise. For a time-limited series, the difference between trend and random is relative, the difference between noise and signal is relative. Find that if the sample capacity is larger, the difference is bigger.
(3)Achieve an ideal white noise by processing a physical white noise. Its performance is much better than that achieved from pseudo-random number.
(4)Study the effect of wavelet denoise using white noise and an AR(1) time series. Apply wavelet denoise to microgrid load using wavelets like bior4.4, sym8, db4 and coif5. Find that when the power spectrums of signal and noise are separable, the wavelet denoise is very effective.
对微网负荷,预测准确率上限的大部分由白噪声的不可预测性引起。因此,研究负荷序列中的白噪声分离,具有重要的实际意义。一般地,从复杂时间序列中识别白噪声的正确分布函数,是尚未解决的困难理论问题。
本文结合微网负荷预测,从理论上分析了白噪声与信号的相对性;采用小波等方法,研究了白噪声近似分离。依此进行了微网短期负荷模拟数据的白噪声分离研究。
具体研究内容和结果如下:
(1)结合微网负荷的特点,提出了微网负荷预测的“背景调整法”,并对背景形成的思路做了初步的探讨。
(2)从理论上分析了有限长度(样本容量)时间序列中信号与噪声的相对性。根据Cramer分解定理,可将非平稳时间序列分解为信号和白噪声两部分。发现对于有限长度时间序列,趋势项和随机项的区分是相对的,白噪声和信号的区分是相对的。并通过小波去噪等数值仿真证实:样本容量越大,这种区分越准确。大体符合卡方分布规律。
(3)得到了一个理想的白噪声序列,其性能显著优于用“伪随机数”生成的白噪声序列。
(4)采用白噪声、AR(1)序列,评估了小波去噪的效果。并采用Bior4.4、Sym8、Db4、Coif5小波,对微网负荷模拟序列进行了白噪声分离。发现在功率谱上信号与噪声可分条件下,小波去噪有一定的实际价值。
Scientific forecasting is the foundation and assurance of correct decision. Short-term load forecasting of microgrid system is a leading subject, which is important to the economy and stability of microgrid systems.
For a given load data series(a time series), there exists an upper limit of forecast accuracy. For microgrid load, most of the upper limit is caused by white noise, so the study of the denoise is of practical signifcance. Generally, to identify the distribution function of white noise from a complex time series is an unresolved difficult problem.
Here we study the relativity of noise and signal, combined with the microgrid load forecast; Study the white noise separation using strategies as the wavelet denoise, and apply the wavelet denoise to microgrid load.
The main contents and results are:
(1)According to the characteristic of microgrid, put forward a“background adjust strategy”, and study how to construct an ideal background.
(2) Study theoretically the relativity between signal and noise in limited time series.According to Cramer’s decomposition theorem, a given non-stationary time series can be decomposed into two uncorrelated different parts: signals and white noise. For a time-limited series, the difference between trend and random is relative, the difference between noise and signal is relative. Find that if the sample capacity is larger, the difference is bigger.
(3)Achieve an ideal white noise by processing a physical white noise. Its performance is much better than that achieved from pseudo-random number.
(4)Study the effect of wavelet denoise using white noise and an AR(1) time series. Apply wavelet denoise to microgrid load using wavelets like bior4.4, sym8, db4 and coif5. Find that when the power spectrums of signal and noise are separable, the wavelet denoise is very effective.
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]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
[3] Fan Jianqing, Yao Qiwei., Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag, 2003.
[4] Bouffard F, Galiana FD, Stochastic security for operations planning with significant wind power generation, IEEE Transactions on Power Systems, 2008, 23(2): 306-316.
[5] 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.
[6] Schiermeier Q, Tollefson J, Scully T, et al, Electricity without carbon. Nature, 2008, 454(7206): 816-823.
[7] Wai RJ, Wang WH,Grid-connected photovoltaic generation system., IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953-964.
[8] Bialasiewicz JT., Renewable energy systems with photovoltaic power generators: Operation and modeling, IEEE Transactions on Industrial Electronics, 2008, 55(7): 2752-2758.
[9] Katiraei F, Iravani R, Hatziargyriou N, et al, Microgrids management, IEEE Power & Energy Magazine, 2008, 6(3): 54-65.
[10] Sao CK, Lehn PW., Control and power management of converter fed microgrids, IEEE Transactions on power Systems, 2008, 23(3): 1088-1098.
[11] Bae IS, Kim JO, Reliability evaluation of customers in a microgrid, IEEE Transactions on Power Systems, 2008, 23(3): 1416-1422.
[12] Neville A., Microgrids promise improved power quality and reliability. Power, 2008, 152(6): 22-26.
[13] Tsikalakis AG, Hatziargyriou ND,Centralized control for optimizing microgrids operation, IEEE Transactions on Energy Conversion, 2008, 23(1): 241-248.
[14] Li YW, Vilathgamuwa DM, Loh PC., Robust control scheme for a microgrid with PFC capacitor connected, IEEE Transactions on Industry Applications, 2007, 43(5): 1172-1182.
[15] Marris E., Energy: Upgrading the grid. Nature, 2008, 454(7204): 570-573.
[16] Gooijer JGD, Hyndman RJ., 25 years of time series forecasting. International Journal of Forecasting, 2006, 22(3): 443– 473.
[17] Tsay RS, Time series and forecasting: Brief history and future research. Journal of the American Statistical Association, 2000, 95(450): 638-643.
[18]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.
[19]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.
[20]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.
[21]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.
[22] 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.
[23] 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.
[24] 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.
[25] 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.
[26] Nature Editorial, China's wind-power potential, Nature, 2009, 457(7228): 357.
[27] (美)David C. Hoaglin, (美)Frederick Mosteller, (美)John W. Tukey著,陈忠琏,郭德媛译.探索性数据分析.北京:中国统计出版社, 1998.
[28]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.
[29]于尔铿,刘广一,周京阳,能量管理系统(EMS).北京:科学出版社,1998.
[30]王惠文,吴载斌,孟洁,偏最小二乘回归的线性与非线性方法.北京:国防工业出版社,2006.
[31] Xu Yansun, John B W, Dennis M H, and Lu Jian, Wavelet Transform Domain Filters: A Spatially Selective Noise Filtration Technique, IEEE Transactions on Image Processing, 1994, 3(6): 747~758
[32]李平,李卫国,王志国,小波去噪理论及MATLAB实现研究,现代商贸工业,2008,9:399~400
[33] Pasti L, Walczak B, Massart D L, Reschiglian P, Optimization of signal denoising in discrete wavelet transform, Chemometrics and Intelligent Laboratory Systems, 1999, 48: 21~34
[34] (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
[35]胡细宝,孙洪祥,王丽霞,概率论数理统计随机过程,北京:北京邮电大学出版社,2004
[36] Cramer H, On some classes of nonstationary stochastic processes, Stockholm, 1961
[37]翟祥志,“机理+辨识”策略中电力负荷预测准确率的上限估计:[硕士学位论文],天津;天津大学,2008
[38] David Slepian,On Bandwidth,Proceedings of IEEE,1976,64(3):292~300
[39]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
[40] http://www.random.org/
[41]范剑青,姚琦伟著,陈敏译,非线性时间序列-建模、预报及应用,北京:高等教育出版社,2005
[42] http://lwf.ncdc.noaa.gov/oa/climate/onlineprod/drought/xmgr.html
[43] 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
[44] Cornelius Lanczos, Linear differential operators, USA: SIAM, 1996: 55
[45]康重庆,牟涛,夏清,电力系统多级负荷预测及其协调问题(一)研究框架,电力系统自动化,2008,32(7):35~38
[46] Yang Zheng-Ling (杨正瓴), Gao Yang (高阳), Gao Yong-Tao (郜永涛), Zhang Jun(张军), Behavior of logistic map driven by a white noise, Chinese Physics Letters, 2009, 26(6): 060506
[2]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
[3] Fan Jianqing, Yao Qiwei., Nonlinear Time Series: Nonparametric and Parametric Methods, New York: Springer-Verlag, 2003.
[4] Bouffard F, Galiana FD, Stochastic security for operations planning with significant wind power generation, IEEE Transactions on Power Systems, 2008, 23(2): 306-316.
[5] 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.
[6] Schiermeier Q, Tollefson J, Scully T, et al, Electricity without carbon. Nature, 2008, 454(7206): 816-823.
[7] Wai RJ, Wang WH,Grid-connected photovoltaic generation system., IEEE Transactions on Circuits and Systems I-Regular Papers, 2008, 55(3): 953-964.
[8] Bialasiewicz JT., Renewable energy systems with photovoltaic power generators: Operation and modeling, IEEE Transactions on Industrial Electronics, 2008, 55(7): 2752-2758.
[9] Katiraei F, Iravani R, Hatziargyriou N, et al, Microgrids management, IEEE Power & Energy Magazine, 2008, 6(3): 54-65.
[10] Sao CK, Lehn PW., Control and power management of converter fed microgrids, IEEE Transactions on power Systems, 2008, 23(3): 1088-1098.
[11] Bae IS, Kim JO, Reliability evaluation of customers in a microgrid, IEEE Transactions on Power Systems, 2008, 23(3): 1416-1422.
[12] Neville A., Microgrids promise improved power quality and reliability. Power, 2008, 152(6): 22-26.
[13] Tsikalakis AG, Hatziargyriou ND,Centralized control for optimizing microgrids operation, IEEE Transactions on Energy Conversion, 2008, 23(1): 241-248.
[14] Li YW, Vilathgamuwa DM, Loh PC., Robust control scheme for a microgrid with PFC capacitor connected, IEEE Transactions on Industry Applications, 2007, 43(5): 1172-1182.
[15] Marris E., Energy: Upgrading the grid. Nature, 2008, 454(7204): 570-573.
[16] Gooijer JGD, Hyndman RJ., 25 years of time series forecasting. International Journal of Forecasting, 2006, 22(3): 443– 473.
[17] Tsay RS, Time series and forecasting: Brief history and future research. Journal of the American Statistical Association, 2000, 95(450): 638-643.
[18]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.
[19]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.
[20]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.
[21]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.
[22] 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.
[23] 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.
[24] 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.
[25] 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.
[26] Nature Editorial, China's wind-power potential, Nature, 2009, 457(7228): 357.
[27] (美)David C. Hoaglin, (美)Frederick Mosteller, (美)John W. Tukey著,陈忠琏,郭德媛译.探索性数据分析.北京:中国统计出版社, 1998.
[28]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.
[29]于尔铿,刘广一,周京阳,能量管理系统(EMS).北京:科学出版社,1998.
[30]王惠文,吴载斌,孟洁,偏最小二乘回归的线性与非线性方法.北京:国防工业出版社,2006.
[31] Xu Yansun, John B W, Dennis M H, and Lu Jian, Wavelet Transform Domain Filters: A Spatially Selective Noise Filtration Technique, IEEE Transactions on Image Processing, 1994, 3(6): 747~758
[32]李平,李卫国,王志国,小波去噪理论及MATLAB实现研究,现代商贸工业,2008,9:399~400
[33] Pasti L, Walczak B, Massart D L, Reschiglian P, Optimization of signal denoising in discrete wavelet transform, Chemometrics and Intelligent Laboratory Systems, 1999, 48: 21~34
[34] (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
[35]胡细宝,孙洪祥,王丽霞,概率论数理统计随机过程,北京:北京邮电大学出版社,2004
[36] Cramer H, On some classes of nonstationary stochastic processes, Stockholm, 1961
[37]翟祥志,“机理+辨识”策略中电力负荷预测准确率的上限估计:[硕士学位论文],天津;天津大学,2008
[38] David Slepian,On Bandwidth,Proceedings of IEEE,1976,64(3):292~300
[39]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
[40] http://www.random.org/
[41]范剑青,姚琦伟著,陈敏译,非线性时间序列-建模、预报及应用,北京:高等教育出版社,2005
[42] http://lwf.ncdc.noaa.gov/oa/climate/onlineprod/drought/xmgr.html
[43] 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
[44] Cornelius Lanczos, Linear differential operators, USA: SIAM, 1996: 55
[45]康重庆,牟涛,夏清,电力系统多级负荷预测及其协调问题(一)研究框架,电力系统自动化,2008,32(7):35~38
[46] Yang Zheng-Ling (杨正瓴), Gao Yang (高阳), Gao Yong-Tao (郜永涛), Zhang Jun(张军), Behavior of logistic map driven by a white noise, Chinese Physics Letters, 2009, 26(6): 060506