基于稀疏贝叶斯学习方法的回归与分类在电力系统中的预测研究
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摘要
预测技术是一门复杂的交叉学科,它已经涉及到社会的各个领域,而在电力系统领域中,预测也起着至关重要的作用。不仅仅是电力负荷需要预测,电价、电压充裕性、功角曲线变化、谐波分析、稳定性、故障分类、系统可靠性、运行风险度等都需要进行预测,而这些内容都是回归预测和分类预测的一部分。如何提高预测精度和缩小预测时间是大家最关心的问题,好的预测方法和模型对电力系统的运行与控制、电力系统稳定与保护、电力网络的无功优化调度、电力系统规划运行、发电机组的优化组合、电力市场的交易定价等一系列实际操作问题有着决定性的作用。由于电力系统是一个大规模非线性动态系统,其中必然存在着许多极为复杂的工程计算和非线性优化问题,而且需要很高的时效性,特别是随着电网的不断发展和电力走向市场化,工程师们面临的问题越来越复杂,而人们对电网的安全性和供电可靠性的要求却越来越高。虽然长期以来电力系统自动化研究者一直在寻找高效可靠的方法来解决这些问题,然而电力系统中仍存在许多问题无法得到快速与精确的结果。
与传统的计算方法相比较,人工智能(Artificial Intelligence, AI)法对于复杂的非线性系统问题求解有着不可替代的极大优势。它弥补了传统方法的单纯依靠精确数学求解的不足,解决了某些传统计算方法难于求解或不能解决的问题。由于它具有处理各种非线性的能力,以及容许模型不精确性和参数不确定性等特性,近几年来,人工智能技术的应用研究已经几乎渗透到电力系统和电工技术的所有方面,其中不少研究已有实际应用,人工智能技术必然将在较长的时期内和现有传统数学模型计算方法并存,相互协调地形成各种实用的控制和优化策略。
利用人工智能的核心是内容——机器学习(Machine Learning, ML),将回归分析(Regression Analysis, RA)和模式识别(Pattern Recognition, PR)进行综合分析是本文研究的重点。针对目前机器学习技术在电力系统应用的发展,本文在总结了现有机器学习方法在电力系统应用现状的基础上,引入了全新的以基于概率的稀疏贝叶斯学习理论的机器学习方法在电力系统数据回归和状态分类上的建模研究,改变了过去电力系统中的回归和分类进行各自单独研究的状态,将回归和分类进行了综合预测分析,同时利用数据挖掘(Data Mining,DM)技术、核主成分分析(Kernel Principal Components Analysis, KPCA)、核函数构造、以及粒子群优化(Particle Swarm Optimization, PSO)算法对模型进行改进,经实验和仿真,在电力系统中期负荷预测和暂态稳定评估模型研究上都得到了令人满意的结果,论文的主要研究内容和创新性成果如下：
(1)利用全新的以基于概率学习的稀疏贝叶斯理论机器学习方法及其实用模型：相关向量机(Relevance Vector Machine, RVM),在电力系统数据回归和状态分类两个方面上分别构建了中期负荷预测模型和暂态稳定评估模型,以这两个模型为例子,从机器学习的回归和分类两方面进行全面验证。在同等条件下,与当前最流行的支持向量机(Support Vector Machine, SVM)模型和径向基人工神经网络(Radial Basis Function Artificial Neural Nets, RBF-ANN)模型相比都得到了更好的结果,由于其算法的高稀疏性和基于概率学习的结构,相关向量机不仅得到了很高的预测精度,而且与支持向量机相比它大大减少了核函数参与预测计算的数量,减少了预测计算时间,并且可以提供概率性预测和任意使用核函数等优点。可以预见,相关向量机在电力系统预测控制中有着非常广阔的应用前景,特别是其概率性预测和超高的稀疏性所带来的快速计算特点,对电力系统在线计算和分级控制策略的形成有着非常大实用价值。
(2)针对电力系统庞大的日负荷曲线时间序列数据库,提出了基于时间序列形状相似的多重聚类分析方法进行数据挖掘预处理。利用基于欧式距离分析的K-menas聚类方法和基于形状相似度量的凝聚式层次聚类方法对历史负荷数据进行多重聚类分析。该方法能准确对电力系统历史日负荷样本进行符合实际变化规律的分类,并能发现较特殊的日负荷样本。在结合相关向量机回归分析的中期负荷预测模型进行仿真计算后,结果表明使用该方法后在降低了输入向量空间维数的同时也得到了很好的预测精度。
(3)由于影响电力系统暂态稳定的因素很多,而且SCADA收集到的现场运行数据也是海量的,若直接对如此庞大的数据空间进行分析,不仅造成了“维数灾”而且往往不能取得很好的效果,针对这种情况提出了核主成分分析法对原始输入特征值进行主成分提取,从中剔除大部分不相关的或冗余的特征值。最后利用基于相关向量机分类的暂态稳定评估模型进行仿真比较,结果显示该方法在得到了良好的预测精度的同时,还大大压缩了输入空间。
(4)在相关向量机的核函数构造上创新利用组合核函数的思想,以典型的高斯核函数为基础,分别与之建立多项式核和张量积多维线性样条核的线性组合,并得到相应的组合核函数。为了提高组合核函数模型的效果,本文使用粒子群优化算法对组合核函数的核参数进行自动寻优,排除人为主观因素的影响,得到最优的核参数。在相关向量机中期负荷预测与相关向量机暂态稳定评估仿真中,即在机器学习的回归和分类两个方面,相关向量机的组合核函数模型都得到了比单一核函数模型更准确的预测结果,充分说明了利用组合核函数构造法来提高相关向量机预测模型的准确率是行之有效的方法。
Forecasting technology is a complex cross-science, it has almost involved in every social fieled, in Electric power systems, and it also plays a very vital role. Not only does the power loaded need forecasting, but the power price, voltage adequacy, power-angle curve, harmonic wave analysis, stability assessment, fault classification, system reliability, working riskprofile, etc. need forecasting. In these forecasting, all belong to regression and classification. The problem and concerns is how to promote the forecasting accurancy and save the computing time. A good forecasting model is definitively for many questions in power systems, such as:system operation and control, system stability and protection, grid optimal reactive power attemper, system operation planning, generators'optimization, dealer pricing of power market etc.. Essentially, power system is a complicated large-scale dynamic nonlinear system. Consequentially, it has many problems about complex engineering calculation and nonlinear optimization; further more it has a sharp time-bound. Especially, along with the grid development and power market, engineers face the problems become complicated more and more, in the other side, customs need the grid safe and electric energy quality increasingly higher and higher. Although researchers of automation in electric power systems have sought many methods to resolve the problems for a long time, the problems can not be attained the faster and more accurate results.
Comparing with the traditional calculating method, artificial intelligence (AI) programs have the great irreplaceable advantages in complex nonlinear systems. It makes up the shortcomings of the traditional methods which purely lie upon the exactly mathematical models, and resolve the problems which can not be settled or difficult to be settled by traditional methods. As it has the ability which can deal with the nonlinear problem, and admit the models are uncertainty and inexactness, in recent years, AI technology applications research have infiltrated through the electric power system and electric engineering, and some of these have in practical, so AI and traditional mathematical models must be existing side by side in a long period, and mutually form the practical control and optimization strategy in concerted.
With the hardcore of AI:machine learning (ML) technology, applying pattern identification and regression analysis in power systems, is the dissertation's emphasis. Aim at the development of machine learning in power systems, the dissertation summarizes the machine learning technology applications for power systems in existence, and introduces a new machine learning technology which based on probability learning and sparse Bayesian theorem, and gives the modeling methods to power systems forecasting. For improving the model, data mining, kernel principal components analysis, kernel function construction, particle swarm optimization also are used, after experiment and emulation we get a satisfactory result both in regression and classification. The main contributions of the dissertation include the following.
(1) Utilizing the bran-new thought of probabilistic learning practical model: 'relevance vector machine' (RVM), a general Bayesian framework for obtaining sparse solutions to classify or regress predicting, respectively construct the medium term load forecasting model and transient stability assessment(TSA) model, validating the result from two sides of regression and classification. In the same condition, comparing with the popular and state-of-the-art'support vector machine' (SVM) and Radial Basis Function Artificial Neural Nets(RBF-ANN), RVM model achievs better results both in two sides. For its arithmetic's structure is high sparsity and based on probabilistic learning, RVM not only achieves good forecasting accuracy but also cut down the computing time, and it can offer the probabilistic prediction and arbitrary using kernel functions. Predictably, RVM must has a extraordinary board prospect in electric power system. Especially, for its probabilistic prediction and super sparsity, it has a good practical value for online computation and forming the hierarchical control strategy in electric power systems forecasting.
(2) Aim at the enormous database of day load time series, an electric load data clustering algorithm (CA) using multi-hierarchy analysis based on time series curve contour similarity is proposed, the performance is proved by theory also. The experiment result makes clear that the algorithm can exactly classify the historical load series accord with the practical regulation, and also can find the special movement in the samples. Application in a RVM short-term load forecasting model, decreasing the input vector dimension, at the same time we attain the high level of accuracy.
(3) As there are a great deal of factors influent the transient stability, further more SCADA collect the operation data are magnanimity, if we analyze the data space directly, not only brought out'Curse of Dimensionality', but could not achieve a good result. The dissertation gives kernel principal component analysis (KPCA) for feature abstract in TSA model, the method eliminate the irrelevance and redundancy from original input eigenvalues, The emulation in TSA model, result shows the method gives good prediction accuracy and the same time reduces the input dimension greatly.
(4) Utilizing the compound kernel function ideology, first-use for the RVM constructing kernel functions. Multi-linearity-compound kernels based on Gaussian kernel, polynomial kernel and tensor product spline kernel were built, and the compound kernel functions'parameters are automatic optimized by algorithm of particle swarm optimization (PSO), then attain the optimal kernel parameters to enhance the model's efficiency. Emulation of TSA models and short term load forecasting based on multi-kernel RVMs. The result shows the compound kernels RVM models give the better generalization capability than the single kernel ones. It indicates that using compound kernel construction method is a viable way to enhance RVM model's forecasting accuracy.
与传统的计算方法相比较,人工智能(Artificial Intelligence, AI)法对于复杂的非线性系统问题求解有着不可替代的极大优势。它弥补了传统方法的单纯依靠精确数学求解的不足,解决了某些传统计算方法难于求解或不能解决的问题。由于它具有处理各种非线性的能力,以及容许模型不精确性和参数不确定性等特性,近几年来,人工智能技术的应用研究已经几乎渗透到电力系统和电工技术的所有方面,其中不少研究已有实际应用,人工智能技术必然将在较长的时期内和现有传统数学模型计算方法并存,相互协调地形成各种实用的控制和优化策略。
利用人工智能的核心是内容——机器学习(Machine Learning, ML),将回归分析(Regression Analysis, RA)和模式识别(Pattern Recognition, PR)进行综合分析是本文研究的重点。针对目前机器学习技术在电力系统应用的发展,本文在总结了现有机器学习方法在电力系统应用现状的基础上,引入了全新的以基于概率的稀疏贝叶斯学习理论的机器学习方法在电力系统数据回归和状态分类上的建模研究,改变了过去电力系统中的回归和分类进行各自单独研究的状态,将回归和分类进行了综合预测分析,同时利用数据挖掘(Data Mining,DM)技术、核主成分分析(Kernel Principal Components Analysis, KPCA)、核函数构造、以及粒子群优化(Particle Swarm Optimization, PSO)算法对模型进行改进,经实验和仿真,在电力系统中期负荷预测和暂态稳定评估模型研究上都得到了令人满意的结果,论文的主要研究内容和创新性成果如下：
(1)利用全新的以基于概率学习的稀疏贝叶斯理论机器学习方法及其实用模型：相关向量机(Relevance Vector Machine, RVM),在电力系统数据回归和状态分类两个方面上分别构建了中期负荷预测模型和暂态稳定评估模型,以这两个模型为例子,从机器学习的回归和分类两方面进行全面验证。在同等条件下,与当前最流行的支持向量机(Support Vector Machine, SVM)模型和径向基人工神经网络(Radial Basis Function Artificial Neural Nets, RBF-ANN)模型相比都得到了更好的结果,由于其算法的高稀疏性和基于概率学习的结构,相关向量机不仅得到了很高的预测精度,而且与支持向量机相比它大大减少了核函数参与预测计算的数量,减少了预测计算时间,并且可以提供概率性预测和任意使用核函数等优点。可以预见,相关向量机在电力系统预测控制中有着非常广阔的应用前景,特别是其概率性预测和超高的稀疏性所带来的快速计算特点,对电力系统在线计算和分级控制策略的形成有着非常大实用价值。
(2)针对电力系统庞大的日负荷曲线时间序列数据库,提出了基于时间序列形状相似的多重聚类分析方法进行数据挖掘预处理。利用基于欧式距离分析的K-menas聚类方法和基于形状相似度量的凝聚式层次聚类方法对历史负荷数据进行多重聚类分析。该方法能准确对电力系统历史日负荷样本进行符合实际变化规律的分类,并能发现较特殊的日负荷样本。在结合相关向量机回归分析的中期负荷预测模型进行仿真计算后,结果表明使用该方法后在降低了输入向量空间维数的同时也得到了很好的预测精度。
(3)由于影响电力系统暂态稳定的因素很多,而且SCADA收集到的现场运行数据也是海量的,若直接对如此庞大的数据空间进行分析,不仅造成了“维数灾”而且往往不能取得很好的效果,针对这种情况提出了核主成分分析法对原始输入特征值进行主成分提取,从中剔除大部分不相关的或冗余的特征值。最后利用基于相关向量机分类的暂态稳定评估模型进行仿真比较,结果显示该方法在得到了良好的预测精度的同时,还大大压缩了输入空间。
(4)在相关向量机的核函数构造上创新利用组合核函数的思想,以典型的高斯核函数为基础,分别与之建立多项式核和张量积多维线性样条核的线性组合,并得到相应的组合核函数。为了提高组合核函数模型的效果,本文使用粒子群优化算法对组合核函数的核参数进行自动寻优,排除人为主观因素的影响,得到最优的核参数。在相关向量机中期负荷预测与相关向量机暂态稳定评估仿真中,即在机器学习的回归和分类两个方面,相关向量机的组合核函数模型都得到了比单一核函数模型更准确的预测结果,充分说明了利用组合核函数构造法来提高相关向量机预测模型的准确率是行之有效的方法。
Forecasting technology is a complex cross-science, it has almost involved in every social fieled, in Electric power systems, and it also plays a very vital role. Not only does the power loaded need forecasting, but the power price, voltage adequacy, power-angle curve, harmonic wave analysis, stability assessment, fault classification, system reliability, working riskprofile, etc. need forecasting. In these forecasting, all belong to regression and classification. The problem and concerns is how to promote the forecasting accurancy and save the computing time. A good forecasting model is definitively for many questions in power systems, such as:system operation and control, system stability and protection, grid optimal reactive power attemper, system operation planning, generators'optimization, dealer pricing of power market etc.. Essentially, power system is a complicated large-scale dynamic nonlinear system. Consequentially, it has many problems about complex engineering calculation and nonlinear optimization; further more it has a sharp time-bound. Especially, along with the grid development and power market, engineers face the problems become complicated more and more, in the other side, customs need the grid safe and electric energy quality increasingly higher and higher. Although researchers of automation in electric power systems have sought many methods to resolve the problems for a long time, the problems can not be attained the faster and more accurate results.
Comparing with the traditional calculating method, artificial intelligence (AI) programs have the great irreplaceable advantages in complex nonlinear systems. It makes up the shortcomings of the traditional methods which purely lie upon the exactly mathematical models, and resolve the problems which can not be settled or difficult to be settled by traditional methods. As it has the ability which can deal with the nonlinear problem, and admit the models are uncertainty and inexactness, in recent years, AI technology applications research have infiltrated through the electric power system and electric engineering, and some of these have in practical, so AI and traditional mathematical models must be existing side by side in a long period, and mutually form the practical control and optimization strategy in concerted.
With the hardcore of AI:machine learning (ML) technology, applying pattern identification and regression analysis in power systems, is the dissertation's emphasis. Aim at the development of machine learning in power systems, the dissertation summarizes the machine learning technology applications for power systems in existence, and introduces a new machine learning technology which based on probability learning and sparse Bayesian theorem, and gives the modeling methods to power systems forecasting. For improving the model, data mining, kernel principal components analysis, kernel function construction, particle swarm optimization also are used, after experiment and emulation we get a satisfactory result both in regression and classification. The main contributions of the dissertation include the following.
(1) Utilizing the bran-new thought of probabilistic learning practical model: 'relevance vector machine' (RVM), a general Bayesian framework for obtaining sparse solutions to classify or regress predicting, respectively construct the medium term load forecasting model and transient stability assessment(TSA) model, validating the result from two sides of regression and classification. In the same condition, comparing with the popular and state-of-the-art'support vector machine' (SVM) and Radial Basis Function Artificial Neural Nets(RBF-ANN), RVM model achievs better results both in two sides. For its arithmetic's structure is high sparsity and based on probabilistic learning, RVM not only achieves good forecasting accuracy but also cut down the computing time, and it can offer the probabilistic prediction and arbitrary using kernel functions. Predictably, RVM must has a extraordinary board prospect in electric power system. Especially, for its probabilistic prediction and super sparsity, it has a good practical value for online computation and forming the hierarchical control strategy in electric power systems forecasting.
(2) Aim at the enormous database of day load time series, an electric load data clustering algorithm (CA) using multi-hierarchy analysis based on time series curve contour similarity is proposed, the performance is proved by theory also. The experiment result makes clear that the algorithm can exactly classify the historical load series accord with the practical regulation, and also can find the special movement in the samples. Application in a RVM short-term load forecasting model, decreasing the input vector dimension, at the same time we attain the high level of accuracy.
(3) As there are a great deal of factors influent the transient stability, further more SCADA collect the operation data are magnanimity, if we analyze the data space directly, not only brought out'Curse of Dimensionality', but could not achieve a good result. The dissertation gives kernel principal component analysis (KPCA) for feature abstract in TSA model, the method eliminate the irrelevance and redundancy from original input eigenvalues, The emulation in TSA model, result shows the method gives good prediction accuracy and the same time reduces the input dimension greatly.
(4) Utilizing the compound kernel function ideology, first-use for the RVM constructing kernel functions. Multi-linearity-compound kernels based on Gaussian kernel, polynomial kernel and tensor product spline kernel were built, and the compound kernel functions'parameters are automatic optimized by algorithm of particle swarm optimization (PSO), then attain the optimal kernel parameters to enhance the model's efficiency. Emulation of TSA models and short term load forecasting based on multi-kernel RVMs. The result shows the compound kernels RVM models give the better generalization capability than the single kernel ones. It indicates that using compound kernel construction method is a viable way to enhance RVM model's forecasting accuracy.
引文
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