马尔科夫链在中长期负荷组合预测中的应用
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摘要
中长期负荷预测是城市电网规划的基础工作之一,它为电网规划提供了必不可少的基础数据,是保证电力系统可靠供电和经济运行的前提。合理而精准的负荷预测将直接影响到电力投资、网络布局和运行的合理性,具有很大的经济效益和社会效益。
由于中长期负荷预测受到很多不定因素的影响,单一预测模型难以保证在任何情况下都能获得满意的预测结果。如何获得简单实用、稳定性好的预测模型以及如何提高负荷预测的精度成为了学者们研究的重点。本文在学习和消化马尔科夫链的基础上,将其引入到中长期负荷组合预测中,分别从串联组合预测和并联组合预测两个方面来进行分析计算。
本文首先概述了电力负荷预测的研究现状以及负荷预测的目的和意义,讨论了负荷预测的分类和中长期负荷预测的方法,同时介绍了马尔科夫基本理论,为后文的发展做了铺垫。在此基础上,考虑马尔科夫链的特性并将其应用到组合预测中去。对于串联组合预测,结合马尔科夫链中转移概率可以反映随机因素的影响、适用于随机波动较大的动态过程的特点,将其与灰色预测模型进行有机结合。该方法弥补了灰色预测模型在预测结果的精确性和可信任性方面所表现出的固有缺陷。预测结果表明该方法在提高预测精度上具有可行性；对于并联组合预测,一方面,针对单一模型都有特定的适用范围和条件的情况,利用马尔科夫过程无后效性的特点将其应用于负荷模型的筛选。算例证实了相对于用没有经过筛选的模型进行的预测,用筛选模型进行的预测其预测结果更为理想。另一方面,以最小误差为准则给出了马氏链的状态和状态概率的初步估计,再用马氏链拟合状态概率分布的时变规律。通过将一步转移概率矩阵的估计问题转化为多元约束自回归模型,然后利用一步转移概率矩阵的估计和初始状态概率分布来动态获取组合权重。实例表明,该方法计算量小、精确度高。最后,结合马尔科夫在中长期负荷预测中的应用情况,分析并总结了预测误差的来源,并进一步探讨了提高负荷预测精度的方法。
Mid-long term forecasting of power system loading is one of the basic work of power grid planning for cities. It provides the required and basic data for power grid planning, and it's the premise of reliable supplying and economic running of power system. The precision of the forecasting shall directly affect the rationality of investment, network layout and its running.
Due to the fact that the mid-long term forecasting is affected by many uncertain factors, no single model can guarantee the satisfaction for the result under any circumstances. How to get the forecast model, how to apply simplicity, practicality, and stability, and how to improve the accuracy of load forecasting has become a research key point. Based on the well comprehension of Markov theory, which is introduced in this paper into mid-long term forecasting, and analyzed and calculated separately form series combination forecast and parallel combination forecast aspect.
To begin with, this paper gives a brief introduction of the definition, goal and significance of electricity load forecasting, and makes an analysis of the current conditions and prospects of mid-long term electricity load forecasting both at home and abroad, and discusses the classification of electricity load forecasting and methods for mid-long term electricity load forecasting, and meanwhile, describes the Markov theory, all of which doing foreshadowing for the following discussion. Based on this, consideration of the quality of Markov theory which is applied to combined forecast is developed. For series combination forecast, the features of Markov theory which can reflect the influence on random factors and be extended to the stochastic process which is dynamic and fluctuating is considered, and it is seamless integrated with the GM(1, 1)model. This method makes up the inherent deficiency which showed by the GM(1, 1)model's load forecasting that in precision and dependability aspect. The results of the load forecasting indicated that this method can improve the accuracy. For parallel combination forecast, on the one hand in view of the specific utilization and condition of each single forecasting model, the properties of no aftereffect is implemented to multi-model sifting. The example demonstrated that relative to primeval method, the result which produced by the new method is more ideal. On the other hand, firstly, Markov chain is used to fit the law of status probability distribution of these filtered models, and then the estimating problem of the one-step status probabilities transition matrix is translated into constrained multivariate self-regression analysis model. Secondly, the combination weights of these filtered models are determined through the estimate of the one-step status probabilities transition matrix and the distribution of status probability. Results of calculation examples show that the forecasting results generated by the proposed model is accurate and the proposed method is practicable.
由于中长期负荷预测受到很多不定因素的影响,单一预测模型难以保证在任何情况下都能获得满意的预测结果。如何获得简单实用、稳定性好的预测模型以及如何提高负荷预测的精度成为了学者们研究的重点。本文在学习和消化马尔科夫链的基础上,将其引入到中长期负荷组合预测中,分别从串联组合预测和并联组合预测两个方面来进行分析计算。
本文首先概述了电力负荷预测的研究现状以及负荷预测的目的和意义,讨论了负荷预测的分类和中长期负荷预测的方法,同时介绍了马尔科夫基本理论,为后文的发展做了铺垫。在此基础上,考虑马尔科夫链的特性并将其应用到组合预测中去。对于串联组合预测,结合马尔科夫链中转移概率可以反映随机因素的影响、适用于随机波动较大的动态过程的特点,将其与灰色预测模型进行有机结合。该方法弥补了灰色预测模型在预测结果的精确性和可信任性方面所表现出的固有缺陷。预测结果表明该方法在提高预测精度上具有可行性；对于并联组合预测,一方面,针对单一模型都有特定的适用范围和条件的情况,利用马尔科夫过程无后效性的特点将其应用于负荷模型的筛选。算例证实了相对于用没有经过筛选的模型进行的预测,用筛选模型进行的预测其预测结果更为理想。另一方面,以最小误差为准则给出了马氏链的状态和状态概率的初步估计,再用马氏链拟合状态概率分布的时变规律。通过将一步转移概率矩阵的估计问题转化为多元约束自回归模型,然后利用一步转移概率矩阵的估计和初始状态概率分布来动态获取组合权重。实例表明,该方法计算量小、精确度高。最后,结合马尔科夫在中长期负荷预测中的应用情况,分析并总结了预测误差的来源,并进一步探讨了提高负荷预测精度的方法。
Mid-long term forecasting of power system loading is one of the basic work of power grid planning for cities. It provides the required and basic data for power grid planning, and it's the premise of reliable supplying and economic running of power system. The precision of the forecasting shall directly affect the rationality of investment, network layout and its running.
Due to the fact that the mid-long term forecasting is affected by many uncertain factors, no single model can guarantee the satisfaction for the result under any circumstances. How to get the forecast model, how to apply simplicity, practicality, and stability, and how to improve the accuracy of load forecasting has become a research key point. Based on the well comprehension of Markov theory, which is introduced in this paper into mid-long term forecasting, and analyzed and calculated separately form series combination forecast and parallel combination forecast aspect.
To begin with, this paper gives a brief introduction of the definition, goal and significance of electricity load forecasting, and makes an analysis of the current conditions and prospects of mid-long term electricity load forecasting both at home and abroad, and discusses the classification of electricity load forecasting and methods for mid-long term electricity load forecasting, and meanwhile, describes the Markov theory, all of which doing foreshadowing for the following discussion. Based on this, consideration of the quality of Markov theory which is applied to combined forecast is developed. For series combination forecast, the features of Markov theory which can reflect the influence on random factors and be extended to the stochastic process which is dynamic and fluctuating is considered, and it is seamless integrated with the GM(1, 1)model. This method makes up the inherent deficiency which showed by the GM(1, 1)model's load forecasting that in precision and dependability aspect. The results of the load forecasting indicated that this method can improve the accuracy. For parallel combination forecast, on the one hand in view of the specific utilization and condition of each single forecasting model, the properties of no aftereffect is implemented to multi-model sifting. The example demonstrated that relative to primeval method, the result which produced by the new method is more ideal. On the other hand, firstly, Markov chain is used to fit the law of status probability distribution of these filtered models, and then the estimating problem of the one-step status probabilities transition matrix is translated into constrained multivariate self-regression analysis model. Secondly, the combination weights of these filtered models are determined through the estimate of the one-step status probabilities transition matrix and the distribution of status probability. Results of calculation examples show that the forecasting results generated by the proposed model is accurate and the proposed method is practicable.
引文
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