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.

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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