Journal of Shandong University(Engineering Science) ›› 2023, Vol. 53 ›› Issue (4): 113-119.doi: 10.6040/j.issn.1672-3961.0.2023.077

• Electrical Engineering • Previous Articles     Next Articles

Data fitting method for electricity consumption of power market users considering behavioral characteristics

Hong YU1(),Juan DU2,Lin WEI3,*(),Li ZHANG3   

  1. 1. Jinan Power Supply Company, State Grid Shandong Electric Power Company, Jinan 250012, Shandong, China
    2. Editorial Department of the Journal of Shandong University of the Arts, Jinan 250014, Shandong, China
    3. School of Electrical Engineering, Shandong University, Jinan 250061, Shandong, China
  • Received:2023-04-24 Online:2023-08-20 Published:2023-08-18
  • Contact: Lin WEI E-mail:1524372002@qq.com;wl1243483679@163.com

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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

CLC Number: 

  • TM71

Fig.1

The structure of the orthogonal polynomial feedforward neural network"

Table 1

Four types of orthogonal polynomial and recurrence equation"

正交多项式 数学表达式 递推关系式
Chebyshev多项式 Ti(x)=cos(i arccos x), x∈[-1, 1], 多项式系{Ti(x)}关于权函数$\rho(x)=\frac{1}{\sqrt{1-x^2}}$正交 T0(x)=1; T1(x)=x; …; Tk(x)=2xTk-1(x)-Tk-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{Li(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{Hi(x)}关于权函数ρ(x)=e-x2正交 H0(x)=1; H1(x)=2x; …; Hk(x)=2xHk-1(x)-2(k-1)Hk-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{Ψi(x)}关于权函数ρ(x)=e-x正交 Ψ0(x)=1; Ψ1(x)=1-x; …; Ψk(x)=(2k-1-x)Ψk-1(x)-(k-1)2Ψk-2(x), k=2, 3, …

Table 2

User classification and its characteristics"

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

Fig.2

Fitting results based on Hermite polynomials for electricity consumption of two-shift type power customers"

Fig.3

Fitting results and goodness of fit based on Laguerre polynomials for electricity consumption of night-shift type power customers"

Table 3

Goodness of fitting based on Hermite polynomials for electricity consumption of two-shift type power customers"

时刻 MAPE/% 时刻 MAPE/%
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

Table 4

Goodness of fitting based on Laguerre polynomials for electricity consumption of night-shift type power customers"

时刻 MAPE/% 时刻 MAPE/%
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

Table 5

Fitted evaluation index results of four orthogonal polynomial neural network models"

多项式 指标 单峰型 避峰型 波动型 双峰型
ChebyshevMAPE/% 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
RMSE 0.003 5 0.003 6 0.003 8 0.002 4
Hermite MAPE/% 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
RMSE 0.003 1 0.001 4 0.003 9 0.000 6
Legendre MAPE/% 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
RMSE 0.004 3 0.002 0 0.005 6 0.003 2
Laguerre MAPE/% 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
RMSE 0.004 5 0.002 0 0.002 1 0.005 1

Fig.4

Missing data filling of real power consumption curves for two-shift type customers"

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