计及行为特征的市场化用户电量数据拟合方法

doi:10.6040/j.issn.1672-3961.0.2023.077

摘要/Abstract

摘要：

针对市场化用户用电行为复杂多变、电量数据的规律难以精确表征的问题, 提出考虑行为特征的市场化用户电量数据拟合方法。采用K-means聚类算法对用户用电行为进行分类, 明确各类用户的典型特征; 构建基于正交多项式的电量数据拟合神经网络模型, 其中神经网络权值系数采用梯度下降算法进行训练, 正交多项式分别采用Chebyshev多项式、Hermite多项式、Legendre多项式及Laguerre多项式进行对比分析; 采用山东省济南市用户电量数据进行仿真分析, 对不同类别的用户分别采用基于4种不同正交多项式的实现方法进行电量数据拟合和评价指标计算, 总结具有不同行为特征的用户最适宜的拟合方法。仿真结果表明, 同类用户在不同的实现方法下电量数据拟合效果差异明显, 基于Hermite多项式及Laguerre多项式的神经网络模型拟合精度相对较高, 但不同类别用户电量数据拟合精度最高的多项式模型有所不同。根据用电行为类型选择相应正交多项式构成神经网络拟合模型, 是实现用户电量数据精确拟合的有效途径。

关键词: 正交多项式, 神经网络, 曲线拟合, 电量, 电力用户分类

Abstract:

To address the problem that the electricity consumption behavior of market-based users was complex and variable, and the laws of electricity data were difficult to be accurately characterized, a market-based user electricity data fitting method considering behavioral characteristics was proposed. The K-means clustering algorithm was used to classify the electricity consumption behavior of customers and clarify the typical characteristics of each type of customers; the neural network model based on orthogonal polynomials was constructed, in which the neural network weight coefficients were trained by gradient descent algorithm and the orthogonal polynomials were Chebyshev polynomials, Hermite polynomials, Legendre polynomials and Laguerre polynomials. The simulation analysis was carried out using the electricity data of users in Jinan, Shandong Province, and four different orthogonal polynomials were used to fit the electricity data and calculate the evaluation indexes for different categories of users, so as to summarize the most suitable fitting methods for users with different behavioral characteristics. The simulation results showed that the power data fitting effect differed significantly among different implementation methods for similar users, and the fitting accuracy of the neural network models based on Hermite polynomials and Laguerre polynomials was relatively high, but the polynomial models with the highest power data fitting accuracy for different categories of users were different. Selecting the corresponding orthogonal polynomials to form a neural network fitting model according to the type of electricity consumption behavior was an effective way to achieve accurate fitting of user electricity data.

Key words: orthogonal polynomial, neural network, curve fitting, power consumption, electricity user classification

中图分类号:

TM71

于泓,杜娟,魏琳,张利. 计及行为特征的市场化用户电量数据拟合方法[J]. 山东大学学报 (工学版), 2023, 53(4): 113-119.

Hong YU,Juan DU,Lin WEI,Li ZHANG. Data fitting method for electricity consumption of power market users considering behavioral characteristics[J]. Journal of Shandong University(Engineering Science), 2023, 53(4): 113-119.

图/表 9

图1

表1

表2

图2

图3

表3

表4

表5

图4

参考文献 17

1	郑亚先, 杨争林, 冯树海, 等. 碳达峰目标场景下全国统一电力市场关键问题分析[J]. 电网技术, 2022, 46 (1): 1- 20.
	ZHENG Yaxian , YANG Zhenglin , FENG Shuhai , et al. Key issue analysis in national unified power market under target scenario of carbon emission peak[J]. Power System Technology, 2022, 46 (1): 1- 20.
2	刘宣, 唐悦, 卢继哲, 等. 基于概率预测的用电采集终端电量异常在线实时识别方法[J]. 电力系统保护与控制, 2021, 49 (19): 99- 106.
	LIU Xuan , TANG Yue , LU Jizhe , et al. Online real time anomaly recognition method for power consumption of electric energy data acquisition terminal based on probability prediction[J]. Power System Protection and Control, 2021, 49 (19): 99- 106.
3	顾天奇, 张雷, 冀世军, 等. 封闭离散点的曲线拟合方法[J]. 吉林大学学报(工学版), 2015, 45 (2): 437- 441. doi: 10.13229/j.cnki.jdxbgxb201502015
	GU Tianqi , ZHANG Lei , JI Shijun , et al. Curve fitting method for closed discrete points[J]. Journal of Jilin University(Engineering and Technology Edition), 2015, 45 (2): 437- 441. doi: 10.13229/j.cnki.jdxbgxb201502015
4	崔晗, 王允, 邱丽荣, 等. 基于二次曲线拟合的共焦拉曼光谱探测方法[J]. 光谱学与光谱分析, 2016, 36 (12): 3958- 3962.
	CUI Han , WANG Yun , QIU Lirong , et al. Confocal Raman spectroscopy method based on quadratic curve fitting[J]. Spectroscopy and Spectral Analysis, 2016, 36 (12): 3958- 3962.
5	阮文骏, 王蓓蓓, 李扬, 等. 峰谷分时电价下的用户响应行为研究[J]. 电网技术, 2012, 36 (7): 86- 93.
	RUAN Wenjun , WANG Beibei , LI Yang , et al. Customer response behavior in time-of-use price[J]. Power System Technology, 2012, 36 (7): 86- 93.
6	杨松浩, 孟倩戎, 张宇博, 等. 基于功频特性多项式拟合的电力系统暂态频率最低点在线预测模型[J]. 中国电机工程学报, 2022, 42 (增刊1): 115- 125.
	YANG Songhao , MENG Qianrong , ZHANG Yubo , et al. An online prediction model of power system frequency nadir based on polynomial fitting of power-frequency characteristics[J]. Proceedings of the CSEE, 2022, 42 (Suppl.1): 115- 125.
7	周沙, 景亮. 基于矩特征与概率神经网络的局部放电模式识别[J]. 电力系统保护与控制, 2016, 44 (3): 98- 102.
	ZHOU Sha , JING Liang . Pattern recognition of partial discharge based on moment features and probabilistic neural network[J]. Power System Protection and Control, 2016, 44 (3): 98- 102.
8	MA Y , YANG J , FENG J , et al. Load data recovery method based on SOM-LSTM neural network[J]. Energy Reports, 2022, 8, 129- 136.
9	杨思明, 单征, 丁煜, 等. 深度强化学习研究综述[J]. 计算机工程, 2021, 47 (12): 19- 29.
	YANG Siming , SHAN Zheng , DING Yu , et al. Survey of research on deep reinforcement learning[J]. Computer Engineering, 2021, 47 (12): 19- 29.
10	杨胡萍, 王承飞, 朱开成, 等. 基于相空间重构和Chebyshev正交基神经网络的短期负荷预测[J]. 电力系统保护与控制, 2012, 40 (24): 95- 99.
	YANG Huping , WANG Chengfei , ZHU Kaicheng , et al. Short-term load forecasting based on phase space reconstruction and Chebyshev orthogonal basis neural network[J]. Power System Protection and Control, 2012, 40 (24): 95- 99.
11	ERYILMAZ S B , DUNDAR A . Understanding how orthogonality of parameters improves quantization of neural networks[J]. Institute of Electrical and Electronics Engineers (IEEE), 2022, (9): 1- 10.
12	GOVINDHARAJ A , MARIAPPAN A , AMBIKAPA-THY A , et al. Real-time implementation of adaptive neuro backstepping controller for maximum power point tracking in photo voltaic systems[J]. IEEE Access, 2021, 9, 105859- 105875.
13	SALDANA G , SAN MARTÍN J I , ZAMORA I , et al. Empirical calendar ageing model for electric vehicles and energy storage systems batteries[J]. Journal of Energy Storage, 2022, 55, 105676.
14	高元海, 王淳. 级数展开法拟合概率潮流分布函数的局限及改进[J]. 中国电机工程学报, 2021, 41 (17): 5900- 5911.
	GAO Yuanhai , WANG Chun . Limitation analysis and improvement for series expansion methods to fit the distribution function of probabilistic power flow[J]. Proceedings of the CSEE, 2021, 41 (17): 5900- 5911.
15	李莎, 曾喆昭. 基于Chebyshev多项式的神经网络中长期负荷预测研究[J]. 经济数学, 2015, 32 (1): 99- 102.
	LI Sha , ZENG Zhezhao . The medium and long forecasting based on Chebyshev polynomial neural-network[J]. Journal of Quantitative Economics, 2015, 32 (1): 99- 102.
16	WANG S F, WU S C, LIU T, et al. Power user classification strategy of multi view clustering[C]//Proceedings of the 2016 16th International Symposium on Communications and Information Technologies (ISCIT). Qingdao, China: IEEE, 2016: 671-675.
17	邓莎. 计及用电行为特征的负荷数据分类方法研究[D]. 沈阳: 沈阳工业大学, 2021.
	DENG Sha. Power load classification method based on user behavior characteristics[D]. Shenyang: Shenyang University of Technology, 2021.

相关文章 15

[1]	黄芳,王欣,高国海,沈玲珍,付勋,方宇. 融合主客观评价的图数据Top-k频繁模式挖掘[J]. 山东大学学报 (工学版), 2025, 55(6): 1-12.
[2]	邵孟伟,袁世飞,周宏志,王乃华. 基于BP神经网络和遗传算法的翅片管结构优化[J]. 山东大学学报 (工学版), 2025, 55(6): 76-82.
[3]	邓彬, 张宗包, 赵文猛, 罗新航, 吴秋伟. 基于云边协同和图神经网络的电动汽车充电站负荷预测方法[J]. 山东大学学报 (工学版), 2025, 55(5): 62-69.
[4]	董明书,陈俐企,马川义,张珠皓,孙仁娟,管延华,庄培芝. 沥青路面内部裂缝雷达图像智能判识算法研究[J]. 山东大学学报 (工学版), 2025, 55(3): 72-79.
[5]	贾轩,许吉凯,任艺婧,刘德才,许强,张利. 基于样本扩容和数据驱动的台区理论线损计算方法[J]. 山东大学学报 (工学版), 2025, 55(3): 158-164.
[6]	祝明,石承龙,吕潘,刘现荣,孙驰,陈建城,范宏运. 基于优化长短时记忆网络的深基坑变形预测方法及其工程应用[J]. 山东大学学报 (工学版), 2025, 55(3): 141-148.
[7]	李伟豪,王苹苹,许万博,魏本征. 结构先验引导的多模态腰椎MRI图像分割算法[J]. 山东大学学报 (工学版), 2025, 55(1): 66-76.
[8]	孙尚渠,张恭禄,蒋志斌,李朝阳. 盾构滚刀磨损的影响因素敏感性分析及预测[J]. 山东大学学报 (工学版), 2025, 55(1): 86-96.
[9]	林振宇,邵蓥侠. 基于盖根堡多项式最佳平方近似的谱图网络[J]. 山东大学学报 (工学版), 2024, 54(5): 93-100.
[10]	常新功,苏敏惠,周志刚. 基于进化集成的图神经网络解释方法[J]. 山东大学学报 (工学版), 2024, 54(4): 1-12.
[11]	马翔悦,徐金东,倪梦莹. 基于多尺度特征模糊卷积神经网络的遥感图像分割[J]. 山东大学学报 (工学版), 2024, 54(3): 44-54.
[12]	赵涛,张宁,王小超,马川义,田源,张圣涛,杨梓梁. 基于图神经网络轨迹预测的合流区交通冲突预测方法[J]. 山东大学学报 (工学版), 2024, 54(2): 36-46.
[13]	李璐,张志军,范钰敏,王星,袁卫华. 面向冷启动用户的元学习与图转移学习序列推荐[J]. 山东大学学报 (工学版), 2024, 54(2): 69-79.
[14]	范黎林,刘士豪,李源,毛文涛,陈宗涛. 基于课程正则化的物理信息神经网络渐进式训练策略[J]. 山东大学学报 (工学版), 2024, 54(1): 11-24.
[15]	孙园,曾惠权,欧阳苏建,高佳倩,王绮楠,林智勇. 基于粒子群算法的模糊大脑情感学习非线性系统辨识[J]. 山东大学学报 (工学版), 2024, 54(1): 25-32.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

正交多项式	数学表达式	递推关系式
Chebyshev多项式	T_i(x)=cos(i arccos x), x∈[-1, 1], 多项式系{T_i(x)}关于权函数$\rho(x)=\frac{1}{\sqrt{1-x^2}}$正交	T₀(x)=1; T₁(x)=x; …; T_k(x)=2xT_k-1(x)-T_k-2(x), k=2, 3, …
Legendre多项式	$L_i(x)=\frac{1}{2^i i !} \frac{\mathrm{d}^i}{\mathrm{~d} x^i}\left(x^2-1\right)^i$, x∈[-1, 1]，多项式系{L_i(x)}关于权函数ρ(x)≡1正交	L₀(x)=1; L₁(x)=x; …; $L_k(x)=\frac{2 k-1}{k} x L_{k-1}(x)-\frac{k-1}{k} L_{k-2}(x), k=2, 3, \cdots$
Hermite多项式	$H_i(x)=(-1)^i \mathrm{e}^{x^2} \frac{\mathrm{d}^{\prime}}{\mathrm{d} x^i}\left(\mathrm{e}^{-x^2}\right), x \in(0, +\infty)$, 多项式系{H_i(x)}关于权函数ρ(x)=e^-x²正交	H₀(x)=1; H₁(x)=2x; …; H_k(x)=2xH_k-1(x)-2(k-1)H_k-2(x), k=2, 3, …
Laguerre多项式	$\Psi_i(x)=\mathrm{e}^x \frac{\mathrm{d}^i}{\mathrm{~d} x^i}\left(x^i \mathrm{e}^{-x}\right)$, x∈[0, +∞), 多项式系{Ψ_i(x)}关于权函数ρ(x)=e^-x正交	Ψ₀(x)=1; Ψ₁(x)=1-x; …; Ψ_k(x)=(2k-1-x)Ψ_k-1(x)-(k-1)²Ψ_k-2(x), k=2, 3, …

用户类型	特点	样本数量
单峰型	用电高峰期集中于白天, 晚上负荷非常小, 日峰谷差大。此类型曲线多出现于第二产业的轻工业及第三产业的市政生活居民用户	250
避峰型	用电主要集中于夜晚, 白天用电量较低。出现此类曲线多属于第二产业的大型工业工厂等	250
波动型	实时负荷在24 h中多变, 表现在晚间与午间用电量上升, 其他时段用电量回落。此类曲线多出现于第三产业的公共设备用电等	176
双峰型	用电高峰时间多集中于白天, 出现2个时段高峰, 分别分布在9:00—12:00、14:00—18:30时段。此类曲线多出现于第三产业的餐饮业及生活服务类	281

时刻	M_APE/%	时刻	M_APE/%
1:00	0.830 5	13:00	0.055 5
2:00	0.126 8	14:00	0.265 6
3:00	2.257 3	15:00	0.171 2
4:00	1.775 4	16:00	0.127 0
5:00	1.040 6	17:00	0.084 1
6:00	0.768 3	18:00	0.071 2
7:00	0.312 0	19:00	0.085 9
8:00	0.287 8	20:00	0.188 5
9:00	0.136 2	21:00	0.050 2
10:00	0.233 6	22:00	0.077 5
11:00	0.137 0	23:00	0.339 7
12:00	0.082 9	24:00	0.216 5

时刻	M_APE/%	时刻	M_APE/%
1:00	0.941 6	13:00	2.352 1
2:00	0.637 0	14:00	7.119 0
3:00	0.373 2	15:00	8.303 5
4:00	0.312 1	16:00	1.634 2
5:00	0.042 2	17:00	1.312 9
6:00	0.259 7	18:00	7.202 6
7:00	0.966 9	19:00	2.903 2
8:00	1.546 0	20:00	0.660 3
9:00	1.255 6	21:00	0.204 6
10:00	1.646 2	22:00	0.051 3
11:00	4.291 0	23:00	0.336 4
12:00	3.569 2	24:00	0.166 0

多项式	指标	单峰型	避峰型	波动型	双峰型
Chebyshev	M_APE/%	2.104 7	1.902 2	1.120 0	2.016 7
	R²	0.999 8	0.999 9	0.998 7	0.999 9
	R_MSE	0.003 5	0.003 6	0.003 8	0.002 4
Hermite	M_APE/%	1.826 7	1.708 6	1.148 5	0.405 1
	R²	0.999 9	0.999 9	0.998 7	0.999 9
	R_MSE	0.003 1	0.001 4	0.003 9	0.000 6
Legendre	M_APE/%	2.489 9	2.405 0	1.770 3	1.952 0
	R²	0.999 7	0.999 9	0.997 2	0.999 8
	R_MSE	0.004 3	0.002 0	0.005 6	0.003 2
Laguerre	M_APE/%	2.256 5	2.003 6	0.930 7	1.600 9
	R²	0.999 7	0.999 9	0.999 0	0.999 7
	R_MSE	0.004 5	0.002 0	0.002 1	0.005 1