基于变分模态分解-BA-LSSVM算法的配电网短期负荷预测
2019-10-12赵凤展杜松怀单葆国井天军赵婷婷
赵凤展,郝 帅,张 宇,杜松怀,单葆国,苏 娟,井天军,赵婷婷
基于变分模态分解-BA-LSSVM算法的配电网短期负荷预测
赵凤展1,郝 帅1,张 宇2,杜松怀1,单葆国3,苏 娟1,井天军1,赵婷婷2
(1.中国农业大学信息与电气工程学院,北京 100083; 2. 国网北京市电力公司,北京 100031;3. 国网能源研究院,北京 102209)
配电台区日负荷序列呈现为既包含变化趋势、又含有波动细节的不规则曲线,该文借助变分模态分解(variational mode decomposition,VMD)将包含这些信息的原始日负荷序列分解为不同频率尺度的子序列,并结合一系列复杂的环境因素,分别利用不同的最小二乘支持向量机(least squares support vector machine,LSSVM)模型进行负荷预测,最后将基于不同频率分量的预测结果相加得到最终的日负荷预测结果。为了提高LSSVM预测能力,采用蝙蝠算法(bat algorithm,BA)对各LSSVM的参数进行寻优,同时,该文分析了影响负荷变化的环境因素,设计了一套因素归一化方法,预测过程考虑了环境因素的影响。仿真结果表明,该文提出的考虑复杂环境因素的预测思想及对历史日负荷进行VMD分解、BA优化、LSSVM预测的组合预测方法能有效提高短期日负荷预测的准确性。
算法;电能;配电台区负荷预测;变分模态分解;最小二乘支持向量机;蝙蝠算法;复杂环境因素
0 引 言
随着全球能源日益紧缺和污染加重,电能正逐渐替代化石能源,成为人们生产生活的主要能量来源。中华人民共和国国家发展和改革委员会于2017年6月发布了《电力发展“十三五”规划》,“升级改造配电网,推进智能电网建设”已经成为中国电力发展的重点任务[1]。电力需求增加,用电负荷迅速增长,将对配电网规划和运行可靠性带来巨大冲击[2-4]。因此,研究短期日负荷预测成为《规划》中的重要一环。
现有的短期负荷预测方法主要是多种传统预测方法[5]及以人工神经网络、支持向量机(support vector machine,SVM)等为代表的机器学习方法[6-7]。机器学习方法在处理多因素问题(如气象因素)方面具有更强的学习和模拟能力,预测效果更好。SVM具有小样本预测、泛化能力强等特征;最小二乘支持向量机(least squares support vector machine,LSSVM)是SVM的一种改进,继承了SVM的优点,用平方差损失函数代替不敏感损失函数,用等式约束代替不等式约束,将二次规划问题转为求解线性方程,降低了求解复杂性,更适用于短期快速预测[8-9]。
由于负荷运行的不确定性及负荷影响因素的复杂性,单一的负荷预测方法很难做到准确地预测短期负荷,因此,组合方法已成为近年来短期负荷预测主流方法[10]。文献[11]采用灰色模型及LSSVM组合预测方法及历史负荷数据学习、日内预测的思路,文献[12]采用LSSVM预测、改进并行粒子群算法优化LSSVM参数的方法,都取得了较好的预测效果。
在预测前对数据进行预处理可有效降低数据的不规律性带来的干扰[10]。文献[13]采用集成经验模态分解(ensemble empirical mode decomposition,EEMD)将原始非平稳负荷序列分解成一系列具有不同特征的子序列。变分模态分解(variational mode decomposition,VMD)是一种非递归、变模式的分解方法,克服了EEMD递归求解的缺点,谐波分离效果更好[14]。文献[15]采用VMD-模态重构方法得到了信号的3个分量,各分量在不同频率尺度上特点明显;但对于短期日负荷预测来说,还需着重分析各分量在一日内的变化特性。
另外一些最新的负荷预测文献考虑利用人工智能算法对预测模型进行参数优化[16]。文献[17]和文献[18]分别采用粒子群算法(particle swarm optimization,PSO)和BBFMA(bare bones fireworks algorithm)进行LSSVM参数优化。文献[19]采用蝙蝠算法(bat algorithm,BA)对SVM参数进行优化,结果表明借助参数优化可以降低预测误差;而LSSVM与SVM相比待优化参数更少,所以,采用LSSVM预测可加快参数优化及预测速度。文献[20]采用BA-LSSVM优化最小二乘支持向量机的惩罚参数和核参数,与PSO-LSSVM相比具有更高的精度。
本文从分析短期日负荷的复杂环境因素入手,依次介绍了时序信号的VMD序列分解方法及BA优化LSSVM的原理,进而提出了基于VMD-BA-LSSVM模型的日负荷预测方法,最后以北京近郊某台区配电变压器一段时间的负荷数据及当地气象数据为基础,利用所提模型进行日负荷预测,并与其他几种典型方法进行比较,验证了所提预测方法的有效性。
1 负荷影响因素分析
用户的用电行为受环境影响,在日负荷预测过程中考虑影响负荷的环境因素可以更真实预测该日实际用电情况。以北京某台区配电变压器一段时间的负荷数据及当地气象数据为例,分析得到影响负荷变化的复杂环境因素主要包括日最低温度、日平均温度、天气情况、天气变化情况、负荷日类型以及季节情况,其中天气情况包括:晴、多云、阴、小雨、中雨、大雨、暴雨、雨夹雪、小雪、中雪、大雪、暴雪、霜冻、雾、微风、大风、冰雹;天气变化情况包括正常天气和突变天气;负荷日类型包括工作日和休息日。
2 变分模态分解
日负荷序列看似波动且无规律,但是经过变分模态分解(variational mode decomposition,VMD),便可得到由不同频率表征的趋势分量及波动分量。与EEMD的递归筛选原理不同,VMD采用非递归、变模态原理将信号分解成一系列有限带宽子序列;VMD具有更好的谐波分离能力,并且每个分序列具有更好的规律性[21-22]。
2.1 变分模态分解的具体步骤
VMD包括3个步骤,分别为建立约束变分模型、拉格朗日变换和交替更新:
式中{u}为分解所得到的个模态分量,为模态函数总个数;{}为各模态分量的频率中心;()为狄拉克分布;()为一个序列,是采样时刻。
2)拉格朗日变换。以上约束变分问题通过引入增广Lagrange函数消除约束变分模型的约束性,得到Lagrange函数表示的变分约束模型
式中为Lagrange乘法算子,用以确保严格执行约束条件;为二次惩罚因子,用以确保转换的准确性。
3)交替更新。步骤2)中的优化问题公式(2)可以根据下面的2个更新方程来求解。
2.2 变分模态分解的算法流程
VMD算法流程总结如下:
1)输入待分解的序列()。
5)重复步骤3)、4)进行迭代,直到满足
由此得到分解后的个子序列,其模态函数为u,中心频率为。
3 蝙蝠算法–最小二乘支持向量机
采用蝙蝠算法确定最小二乘支持向量机的预测参数,在结合蝙蝠算法的良好收敛性的同时,保留了最小二乘支持向量机的小样本和计算快速的预测特点[23-24]。
3.1 最小二乘支持向量机及其回归过程
最小二乘支持向量机(least squares support vector machine,LSSVM)是一种成熟的机器预测方法,作为SVM的扩展,LSSVM将最小二乘损失函数作为损失函数,并用等式约束条件替代SVM中的不等式约束条件;LSSVM保留了结构风险最小化、小样本等特点,大大降低了计算复杂度[24]。
LSSVM的回归过程如下:
2)根据结构风险最小化准则,式(7)对应的LSSVM优化问题可以表示为
3)求解上述优化问题,构建Lagrange函数
式中为Lagrange乘法算子。
式中为核函数宽度。
3.2 蝙蝠优化算法
蝙蝠算法(bat algorithm,BA)是一种新兴的寻优算法,BA克服了遗传算法、粒子群算法(particle swarm optimization,PSO)等算法执行时间长,性能与初始值有关及参数敏感等缺点[24-25];BA可以在局部搜索和全局搜索之间动态转换,搜索过程具有更好的收敛性[26]。
2)随机初始化蝙蝠搜索位置x,其中包含LSSVM中和2个参数信息。
3)对比所有个体的适应度,寻找当前全局最优解*。
4)根据式(13)至式(15)更新每轮蝙蝠的搜索速度、搜索脉冲频率和搜索位置
式中(,)、(,)分别为预测日的负荷真实值、负荷预测值;为预测点数,本文=24。
基于VMD-BA-LSSVM的短期日负荷组合预测流程图如图2所示。
5 算例分析
5.1 算例概况
1)数据来源:北京某配变台区变压器低压侧有功功率数据,并已经过不良数据处理。
2)输入数据:分别为2017年1月10日至2017年1月23日、2017年2月2日至2017年2月15日、2017年2月17日至2017年3月2日的24 h负荷数据及日环境数据,见表2。
3)预测模型:本文所提VMD-BA-LSSVM及其他5种组合预测模型:EEMD-LSSVM、VMD-LSSVM、VMD-BA-SVM、VMD-PSO-LSSVM、不含有天气变化类型的VMD-BA-LSSVM(即原VMD-BA-LSSVM模型中前14天的变量()设为0),该方法简称为“VMD-BA-LSSVM(0)”。
4)预测目标:分别预测2017年1月24日、2017年2月16日、2017年3月3日这3 d的24 h负荷值。
5.2 预测结果对比分析
采用以上6种组合预测模型得到的2017年1月24日、2017年2月16日、2017年3月3日24个时刻的负荷预测结果,前2天的预测结果如图3所示。由图3可得,利用VMD-BA-LSSVM的预测结果与实际值最为贴合;在实际值波动较大的时刻(如2017年1月24日22:00),VMD-BA-LSSVM预测值最接近实际值,说明VMD-BA-LSSVM对负荷波动预测最准确。
图2 基于VMD-BA-LSSVM的短期日负荷组合预测流程图
表2 2017年1月10日至23日的负荷及环境数据
注:()为负荷日类型变量;()为天气变化类型变量。 Note:() is load day type variable;() is weather change type variable.
图3 原始负荷序列及各模型预测序列
5.3 误差对比及效率分析
以上6种组合预测模型3日的预测误差平均值和平均预测用时及其优化模型的平均优化用时如表3所示。
表3 各组合模型3次预测的平均预测误差及计算用时
注:VMD-BA-LSSVM(0)不考虑天气变化类型。
Note: VMD-BA-LSSVM(0) is without considering weather change type.
通过比较6种组合预测方法的预测误差可以反映各方法预测精度的优劣性,同时比较各方法的运行程序时间可以反映各方法预测效率的优劣性。由表3比较得知,VMD-BA-LSSVM的预测误差MAPE、max最小,说明该方法预测精准度最高。同时,由表3比较得知,对于同一LSSVM预测模型,BA的平均优化用时比PSO的平均优化用时少,说明BA的优化效率更高;对于同一BA优化模型,LSSVM的平均预测用时比SVM的平均预测用时少,是因为LSSVM待优化参数比SVM少,所以参数优化速度更快。
因此,由表3可得到以下结论:
1)VMD-LSSVM比EEMD-LSSVM误差更低,预测速度更快,这表明相比EEMD而言,VMD有更好的序列分解能力,分解得到的分序列具有更好的规律。
2)VMD-BA-LSSVM比VMD-BA-SVM预测误差更低,预测速度及优化速度更快,这表明相比SVM而言,LSSVM有更好的负荷预测能力,预测精度更高,预测速度更快;LSSVM待优化参数比SVM少,参数优化速度更快。
3)VMD-BA-LSSVM比VMD-LSSVM、VMD-PSO- LSSVM误差更低,优化速度更快,这表明相比不优化或PSO优化,BA的优化结果更优,且参数优化速度更快。
4)含有天气变化类型的VMD-BA-LSSVM模型比不含有天气变化类型的同种模型误差更低,这表明本文设计的考虑复杂环境因素的预测方法提高了预测精度。
6 结 论
针对短期日负荷精准、高效预测方法的迫切需求,本文提出了一种基于变分模态分解和蝙蝠算法优化最小二乘支持向量机的短期日负荷组合预测方法,主要结论如下:
1)采用VMD对非线性、非平稳的日负荷序列进行分解,并将得到的不同频率尺度的负荷矩阵输入不同的LSSVM中进行预测。VMD可以更细致表征日负荷在不同频率尺度上的变化特性,分解结果具有更好的规律性。
2)采用LSSVM进行负荷预测,LSSVM的参数由BA进行寻优。LSSVM可以有效地预测短期负荷序列,与SVM相比预测精度更高,预测速度更快,并且待优化参数更少,寻优速度更快;同时BA参数优选方法具有比PSO参数优选方法更优秀的全局寻优能力。
3)考虑VMD、LSSVM、BA各自优点,综合设计了VMD-BA-LSSVM组合预测方法,该方法与算例中的其他5种组合预测方法相比预测精度最高,预测速度最快,适用于短期日负荷预测。
4)考虑了复杂环境因素对日负荷变化的影响,并将复杂环境因素数据量化输入到预测模型中,使预测结果更加准确。
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Short-term load forecasting for distribution transformer based on VMD-BA-LSSVM algorithm
Zhao Fengzhan1, Hao Shuai1, Zhang Yu2, Du Songhuai1, Shan Baoguo3, Su Juan1, Jing Tianjun1, Zhao Tingting2
(1.,100083,; 2.,100031,; 3.,102209,)
With the wide application of all kinds of electrical equipment in the distribution system, the power load has increased in recent years, which has a great impact on distribution network. Thus, forecasting the short-term daily load is required. Combining the advantages of VMD, LSSVM and BA, a novel VMD-BA-LSSVM short-term daily power load forecasting method was designed, and the complex environmental factors were considered in this paper. Least squares support vector machine (LSSVM) is a classical machine prediction method, which has the advantages of small sample size, powerful generalization ability and fast solution. However, with the gradual improvement of forecasting accuracy requirements, simple LSSVM can’t guarantee the accuracy of the forecasting work. The daily load sequence of the distribution transformer presents an irregular curve containing variation currents and fluctuation details. These information can be separated and predicted respectively in the prediction process, thus better prediction results can be obtained. Although the daily load sequence seems to be fluctuant and irregular, the trend component and wave components in different frequency scales can be obtained by the variational mode decomposition method (VMD). Compared with the process of recursion and screening in EEMD, VMD is characterized by its non-recursive and variable mode. VMD decomposes the original load sequence into a series of specific band-limited subsequences, which aims to decrease instability. VMD has the better capability of harmonic separation, and each subsequence has a better regularity. In this paper, the VMD was used to decompose daily load sequence of a day and yield a series of subsequences with specific frequencies. Subsequences were put into four LSSVMs for the respective forecast. Different parameters in LSSVMs were optimized by the bat algorithm (BA). Meanwhile, the affection of the complex environmental factors was studied and the normalization approach of those factors was proposed. Thus, complex environmental factors were considered in forecasting. The procedures of this prediction method were as following: Firstly, the input data of the method was the daily load data with a one-hour interval and daily environmental data with a one-day interval of the previous 14 days. The daily load sequence (1 row and 24 columns, 1×24) was decomposed by the VMD method and yielded four low-to-high frequency subsequences. Secondly, the four subsequences of the previous 14 days were combined into four 14×24 matrices. Thirdly, the normalized data of the four matrices and environmental data were put into four LSSVMs to forecast the load of the 15th day. Meanwhile, the parameters of LSSVM were optimized by BA. The last, the four LSSVMs results were summed and yielded the final prediction result. In this paper, the VMD was used to decompose nonlinear, fluctuant daily load sequence and yield subsequences with different frequency scales. Subsequences were combined and put into LSSVMs for the respective forecast. Simulation results showed that the forecasting accuracy of VMD-based forecasting method was higher than EEMD-based method. At the same time, LSSVM was used to forecast, and BA was used to optimize the uncertain parameters. The simulation results showed that compared with SVM, LSSVM had a better capability to approximate the load sequence, and got higher prediction efficiency. LSSVM had less uncertain parameters than SVM, thus the efficiency of parameter optimization was higher. Furthermore, BA had excellent capability of global optimization and rapid convergence. Simulation results showed that the proposed method was the most accurate and efficient method, compared with other five forecasting methods.
algorithms; power; load forecasting for the distribution transformer; variational mode decomposition; least squares support vector machine; bat algorithm; complex environmental factor
2018-12-12
2019-06-25
国家电网公司科技项目(《市场交易环境下电力供需技术模型和应用研究》);国家重点研发项目(2016YFB0900100)
赵凤展,博士,副研究员,研究方向为智能配电网分析、规划、评价与优化运行等。Email:zhaofz@cau.edu.cn
10.11975/j.issn.1002-6819.2019.14.024
TM 715
A
1002-6819(2019)-14-0190-08
赵凤展,郝 帅,张 宇,杜松怀,单葆国,苏 娟,井天军,赵婷婷. 基于变分模态分解-BA-LSSVM算法的配电网短期负荷预测[J]. 农业工程学报,2019,35(14):190-197. doi:10.11975/j.issn.1002-6819.2019.14.024 http://www.tcsae.org
Zhao Fengzhan, Hao Shuai, Zhang Yu, Du Songhuai, Shan Baoguo, Su Juan, Jing Tianjun, Zhao Tingting. Short-term load forecasting for distribution transformer based on VMD-BA-LSSVM algorithm[J]. Transactions of the Chinese Society of Agricultural Engineering (Transactions of the CSAE), 2019, 35(14): 190-197. (in Chinese with English abstract) doi:10.11975/j.issn.1002-6819.2019.14.024 http://www.tcsae.org