Accurate regional wind power prediction plays an important role in the security and reliability of power systems.For the performance improvement of very short-term prediction intervals(PIs),a novel probabilistic predi...Accurate regional wind power prediction plays an important role in the security and reliability of power systems.For the performance improvement of very short-term prediction intervals(PIs),a novel probabilistic prediction method based on composite conditional nonlinear quantile regression(CCNQR)is proposed.First,the hierarchical clustering method based on weighted multivariate time series motifs(WMTSM)is studied to consider the static difference,dynamic difference,and meteorological difference of wind power time series.Then,the correlations are used as sample weights for the conditional linear programming(CLP)of CCNQR.To optimize the performance of PIs,a composite evaluation including the accuracy of PI coverage probability(PICP),the average width(AW),and the offsets of points outside PIs(OPOPI)is used to quantify the appropriate upper and lower bounds.Moreover,the adaptive boundary quantiles(ABQs)are quantified for the optimal performance of PIs.Finally,based on the real wind farm data,the superiority of the proposed method is verified by adequate comparisons with the conventional methods.展开更多
Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionall...Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.展开更多
基金This work was supported by the National Key R&D Program of China“Technology and Application of Wind Power/Photovoltaic Power Prediction for Promoting Renewable Energy Consumption”(No.2018YFB0904200)Complement S&T Program of State Grid Corporation of China(No.SGLNDKOOKJJS1800266).
文摘Accurate regional wind power prediction plays an important role in the security and reliability of power systems.For the performance improvement of very short-term prediction intervals(PIs),a novel probabilistic prediction method based on composite conditional nonlinear quantile regression(CCNQR)is proposed.First,the hierarchical clustering method based on weighted multivariate time series motifs(WMTSM)is studied to consider the static difference,dynamic difference,and meteorological difference of wind power time series.Then,the correlations are used as sample weights for the conditional linear programming(CLP)of CCNQR.To optimize the performance of PIs,a composite evaluation including the accuracy of PI coverage probability(PICP),the average width(AW),and the offsets of points outside PIs(OPOPI)is used to quantify the appropriate upper and lower bounds.Moreover,the adaptive boundary quantiles(ABQs)are quantified for the optimal performance of PIs.Finally,based on the real wind farm data,the superiority of the proposed method is verified by adequate comparisons with the conventional methods.
文摘Unlike height-diameter equations for standing trees commonly used in forest resources modelling,tree height models for cut-to-length(CTL)stems tend to produce prediction errors whose distributions are not conditionally normal but are rather leptokurtic and heavy-tailed.This feature was merely noticed in previous studies but never thoroughly investigated.This study characterized the prediction error distribution of a newly developed such tree height model for Pin us radiata(D.Don)through the three-parameter Burr TypeⅫ(BⅫ)distribution.The model’s prediction errors(ε)exhibited heteroskedasticity conditional mainly on the small end relative diameter of the top log and also on DBH to a minor extent.Structured serial correlations were also present in the data.A total of 14 candidate weighting functions were compared to select the best two for weightingεin order to reduce its conditional heteroskedasticity.The weighted prediction errors(εw)were shifted by a constant to the positive range supported by the BXII distribution.Then the distribution of weighted and shifted prediction errors(εw+)was characterized by the BⅫdistribution using maximum likelihood estimation through 1000 times of repeated random sampling,fitting and goodness-of-fit testing,each time by randomly taking only one observation from each tree to circumvent the potential adverse impact of serial correlation in the data on parameter estimation and inferences.The nonparametric two sample Kolmogorov-Smirnov(KS)goodness-of-fit test and its closely related Kuiper’s(KU)test showed the fitted BⅫdistributions provided a good fit to the highly leptokurtic and heavy-tailed distribution ofε.Random samples generated from the fitted BⅫdistributions ofεw+derived from using the best two weighting functions,when back-shifted and unweighted,exhibited distributions that were,in about97 and 95%of the 1000 cases respectively,not statistically different from the distribution ofε.Our results for cut-tolength P.radiata stems represented the first case of any tree species where a non-normal error distribution in tree height prediction was described by an underlying probability distribution.The fitted BXII prediction error distribution will help to unlock the full potential of the new tree height model in forest resources modelling of P.radiata plantations,particularly when uncertainty assessments,statistical inferences and error propagations are needed in research and practical applications through harvester data analytics.
