灰色预测模型及中长期电力负荷预测应用研究
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摘要
电力是关系国计民生的重要基础产业和公用事业。中长期电力系统负荷预测作为电力规划、投资、生产、调度和交易等工作的基础,在电力安全和经济运行中发挥着至关重要的作用。我国中长期电力负荷,既有逐年增长的确定性,又有随机变化的不确定性,可以视为典型的灰色系统,适合使用灰色模型建模预测。然而随着电力系统复杂性和电力市场化程度的不断提高,传统灰色预测方法逐渐不能适应电力负荷预测的需要,亟待丰富和完善。全文主要从GM(1,1)模型优化、多变量预测、区间灰数预测、变权缓冲优化等方面研究灰色预测的模型和方法及其在中长期负荷预测中的应用。
本文研究了GM(1,1)模型的建模机理,系统分析了GM(1,1)模型存在的问题,包括边值问题、背景值构造问题、最小二乘参数辨识问题等,根据模型的时间响应式,提出了使用蚁群算法直接辨识GM(1,1)模型边值x(0)(1)和发展系统a和灰作用量b的优化方法,构建了基于蚁群算法的优化GM(1,1)预测模型。该模型既修正了边值影响,又避免了背景值构造和最小二乘参数估计带来的误差,能够有效提高预测精度。通过负荷数据仿真验证了该优化模型的有效性。
中长期电力负荷不是独立存在的,相反,它与经济社会发展紧密相关。考虑多种因素互相联系和互相制约,建立多变量预测模型,更具实际意义。针对多变量灰色建模预测问题,本文阐述了均值生成在减弱或消除随机噪声方面的作用,分析了逆均值生成所带来的系统误差,提出了基于均值生成的多变量灰色MGMmv(1,N)模型及其残差修正EMGMmv(1,N)模型。算例分析和实际应用验证了该模型既能克服外界扰动影响,又能避免自身系统误差,可以应用于实际的中长期负荷预测。
现有的灰色负荷预测方法大多是点预测,对区间预测问题研究较少。本文提出了基于论域的合成灰数灰度的概念,阐述了合成灰数灰度的性质,首次提出了合成灰数灰度的线性收敛特性。在此基础上,分析了基于核和灰度的区间灰数预测模型存在的问题,并建立灰数序列的预测模型,以代替原有模型中的灰度预测值的确定方法,改进和完善了原有区间灰数预测模型。改进模型从核和灰度两个方面同时发掘区间灰数序列的内蕴信息与发展趋势,克服了原有模型存在的不足,且支持误差分析和精度检验。通过尖峰负荷预测的实际应用,验证了改进模型的有效性和可用性。
在缓冲算子应用研究方面,首先,基于调和平均数的概念和缓冲算子三公理,提出调和平均弱化缓冲算子,并将之应用于实际的中长期负荷预测；其次,引入变权缓冲算子,阐述了变权缓冲算子在动态调节缓冲强度和增加建模序列光滑度方面的性质和作用,提出了变权缓冲灰色预测模型及其参数优化方法。该方法基于灰色关联分析和粒子群算法,以预测结果与实际值的灰色关联度最大为适应度函数目标,对模型进行参数优选,能够有效提高模型精度以及拟合和预测的稳定性。最后,将该模型应用于实际的中国全社会用电量预测,结果证明了该模型的有效性和可用性。
上述研究对于完善灰色预测理论,丰富中长期负荷预测手段均具有十分重要的现实意义。
The electric power sector is an important basic industry and a key public utility, which is crucial to the country's development and people's livelihood. The medium-and long-term power system load forecasting, as the basis of planning, investment, production, dispatching, trading and etc., is playing a significant role in the safe and economic operation of power sector. The country's medium-and long-term power load is featured with both a certainty of annual increment and an uncertainty of random variation. Thus, it can be seen as a typical grey system and shall be suitable for grey prediction modeling. However, with the increasing complexity and improving marketization of power sector, the traditional grey prediction method gradually cannot meet the requirement of power load forecasting, and needs to be enriched and improved. This dissertation studies on various models and methods of grey prediction and their applications in medium-and long-term power load prediction, and mainly focus on optimal GM(1,1) model, multi-variable prediction model, interval grey number prediction model, variable weights buffer grey model, and etc.
The dissertation studies the modeling mechanism of GM(1,1) model, systematically analyzes its inherent flaw, including issues like boundary value, background value, least squares parameter identification, and etc. According to the time response expression of GM(1,1) model, the dissertation proposes a optimized method to directly identify the boundary value x(0)(1) of GM(1,1) model, developing coefficient a and grey coefficient b by using ant colony algorithm, so that it establishes a optimized GM(1,1) prediction model based on ant colony algorithm. This optimized model can reduce the impact of boundary value, and also avoid the errors brought by background value structure and least squares parameter estimation. And the effectiveness of the optimized model has been proved by the load data simulation.
The medium-and long-term power load does not exist in isolation. In contrast, it is closely related to economic and social development. Since power load and multiple factors are correlated to and checking each other, it shall be of more practical meaning to establish a multi-variable prediction model rather than a single-variable one. In terms of multi-variable grey modeling prediction issue, this dissertation elaborates the role of mean-value generation in reducing the disturbance of random noise, analyzes the system error brought by inverse mean-value generation, and proposes the multi-variable grey MGMmv(1,N) model and its error modified EMGMmv(1,N) model. And the example analysis and practical application demonstrate that this model can overcome the external disturbance and avoid the system deviation, and can be applied to the practical medium-and long-term load forecasting.
The existing grey power load prediction methods are mostly point predictions, and hardly focus on interval predictions. The dissertation raises the concept of grey degree of compound grey number based on the "field" and elaborates its characteristics, and proposes its linear convergence characteristics for the first time. Based on these, it analyzes the deficiencies of interval grey number prediction model, which is based on kernel and grey degree. Furthermore, a prediction model for grey degree is built to replace the identification method of grey degree prediction value so as to improve the original interval grey number prediction model. The improved model can explore both potential information and developing trend of interval grey number series from the perspectives of both "kernel" and "grey degree", thus overcomes the deficiency of the original model, and also supports error analysis and precision test. The effectiveness and availability of the improved model have been proved by the practical application in peak load forecasting.
In regard to the application research of buffer operator, firstly, this dissertation proposes three kinds of harmonic mean weakening buffer operators based on harmonic mean number concept and the three axioms of buffer operators, and applies them to the practical medium-and long-term load prediction; secondly, it also introduces the variable-weights buffer operator, illustrates its characteristics and functions in dynamically adjusting buffer amplitude and increasing the smoothness of modeling data series, and proposes the variable-weight buffer grey model and its parameters' optimizing method. This method, based on grey correlation analysis and particle swarm optimization (PSO), takes the maximum grey correlation degree between predicted value and actual value as objective function to select the optimal buffer factor. It can effectively increase the prediction precision and the stability of fitting and prediction. At last, the application results in practical national electricity consumption have been given to prove the effectiveness and availability of the proposed medium-and long-term load prediction model.
The study above shall have a practical significance in both improving grey prediction theory and enhancing the medium-and long-term prediction methods.
本文研究了GM(1,1)模型的建模机理,系统分析了GM(1,1)模型存在的问题,包括边值问题、背景值构造问题、最小二乘参数辨识问题等,根据模型的时间响应式,提出了使用蚁群算法直接辨识GM(1,1)模型边值x(0)(1)和发展系统a和灰作用量b的优化方法,构建了基于蚁群算法的优化GM(1,1)预测模型。该模型既修正了边值影响,又避免了背景值构造和最小二乘参数估计带来的误差,能够有效提高预测精度。通过负荷数据仿真验证了该优化模型的有效性。
中长期电力负荷不是独立存在的,相反,它与经济社会发展紧密相关。考虑多种因素互相联系和互相制约,建立多变量预测模型,更具实际意义。针对多变量灰色建模预测问题,本文阐述了均值生成在减弱或消除随机噪声方面的作用,分析了逆均值生成所带来的系统误差,提出了基于均值生成的多变量灰色MGMmv(1,N)模型及其残差修正EMGMmv(1,N)模型。算例分析和实际应用验证了该模型既能克服外界扰动影响,又能避免自身系统误差,可以应用于实际的中长期负荷预测。
现有的灰色负荷预测方法大多是点预测,对区间预测问题研究较少。本文提出了基于论域的合成灰数灰度的概念,阐述了合成灰数灰度的性质,首次提出了合成灰数灰度的线性收敛特性。在此基础上,分析了基于核和灰度的区间灰数预测模型存在的问题,并建立灰数序列的预测模型,以代替原有模型中的灰度预测值的确定方法,改进和完善了原有区间灰数预测模型。改进模型从核和灰度两个方面同时发掘区间灰数序列的内蕴信息与发展趋势,克服了原有模型存在的不足,且支持误差分析和精度检验。通过尖峰负荷预测的实际应用,验证了改进模型的有效性和可用性。
在缓冲算子应用研究方面,首先,基于调和平均数的概念和缓冲算子三公理,提出调和平均弱化缓冲算子,并将之应用于实际的中长期负荷预测；其次,引入变权缓冲算子,阐述了变权缓冲算子在动态调节缓冲强度和增加建模序列光滑度方面的性质和作用,提出了变权缓冲灰色预测模型及其参数优化方法。该方法基于灰色关联分析和粒子群算法,以预测结果与实际值的灰色关联度最大为适应度函数目标,对模型进行参数优选,能够有效提高模型精度以及拟合和预测的稳定性。最后,将该模型应用于实际的中国全社会用电量预测,结果证明了该模型的有效性和可用性。
上述研究对于完善灰色预测理论,丰富中长期负荷预测手段均具有十分重要的现实意义。
The electric power sector is an important basic industry and a key public utility, which is crucial to the country's development and people's livelihood. The medium-and long-term power system load forecasting, as the basis of planning, investment, production, dispatching, trading and etc., is playing a significant role in the safe and economic operation of power sector. The country's medium-and long-term power load is featured with both a certainty of annual increment and an uncertainty of random variation. Thus, it can be seen as a typical grey system and shall be suitable for grey prediction modeling. However, with the increasing complexity and improving marketization of power sector, the traditional grey prediction method gradually cannot meet the requirement of power load forecasting, and needs to be enriched and improved. This dissertation studies on various models and methods of grey prediction and their applications in medium-and long-term power load prediction, and mainly focus on optimal GM(1,1) model, multi-variable prediction model, interval grey number prediction model, variable weights buffer grey model, and etc.
The dissertation studies the modeling mechanism of GM(1,1) model, systematically analyzes its inherent flaw, including issues like boundary value, background value, least squares parameter identification, and etc. According to the time response expression of GM(1,1) model, the dissertation proposes a optimized method to directly identify the boundary value x(0)(1) of GM(1,1) model, developing coefficient a and grey coefficient b by using ant colony algorithm, so that it establishes a optimized GM(1,1) prediction model based on ant colony algorithm. This optimized model can reduce the impact of boundary value, and also avoid the errors brought by background value structure and least squares parameter estimation. And the effectiveness of the optimized model has been proved by the load data simulation.
The medium-and long-term power load does not exist in isolation. In contrast, it is closely related to economic and social development. Since power load and multiple factors are correlated to and checking each other, it shall be of more practical meaning to establish a multi-variable prediction model rather than a single-variable one. In terms of multi-variable grey modeling prediction issue, this dissertation elaborates the role of mean-value generation in reducing the disturbance of random noise, analyzes the system error brought by inverse mean-value generation, and proposes the multi-variable grey MGMmv(1,N) model and its error modified EMGMmv(1,N) model. And the example analysis and practical application demonstrate that this model can overcome the external disturbance and avoid the system deviation, and can be applied to the practical medium-and long-term load forecasting.
The existing grey power load prediction methods are mostly point predictions, and hardly focus on interval predictions. The dissertation raises the concept of grey degree of compound grey number based on the "field" and elaborates its characteristics, and proposes its linear convergence characteristics for the first time. Based on these, it analyzes the deficiencies of interval grey number prediction model, which is based on kernel and grey degree. Furthermore, a prediction model for grey degree is built to replace the identification method of grey degree prediction value so as to improve the original interval grey number prediction model. The improved model can explore both potential information and developing trend of interval grey number series from the perspectives of both "kernel" and "grey degree", thus overcomes the deficiency of the original model, and also supports error analysis and precision test. The effectiveness and availability of the improved model have been proved by the practical application in peak load forecasting.
In regard to the application research of buffer operator, firstly, this dissertation proposes three kinds of harmonic mean weakening buffer operators based on harmonic mean number concept and the three axioms of buffer operators, and applies them to the practical medium-and long-term load prediction; secondly, it also introduces the variable-weights buffer operator, illustrates its characteristics and functions in dynamically adjusting buffer amplitude and increasing the smoothness of modeling data series, and proposes the variable-weight buffer grey model and its parameters' optimizing method. This method, based on grey correlation analysis and particle swarm optimization (PSO), takes the maximum grey correlation degree between predicted value and actual value as objective function to select the optimal buffer factor. It can effectively increase the prediction precision and the stability of fitting and prediction. At last, the application results in practical national electricity consumption have been given to prove the effectiveness and availability of the proposed medium-and long-term load prediction model.
The study above shall have a practical significance in both improving grey prediction theory and enhancing the medium-and long-term prediction methods.
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