Research on the Optimal Design of Seasonal Time-of-Use Tariff Based on the Price Elasticity of Electricity Demand

Abstract

Building a new power system with renewable energy as its main component is a key measure proposed by China to address the climate change problem. Strengthening demand-side management (DSM) is an important way to promote the development of a new power system. As an important economic incentive measure in DSM, the current TOU tariff is faced with the problem of a weak incentive effect due to the small tariff difference between the peak and valley periods. Against this background, a novel hybrid three-stage seasonal TOU tariff optimization model is proposed in this paper. First, the K-means++ algorithm is adopted to select the typical days of the four seasons through load curve clustering. Then, the price elasticity of the electricity demand model is constructed to calculate the self-elasticity and cross-elasticity in four seasons. Finally, the seasonal TOU tariff optimization model is constructed to determine the optimal TOU tariff. Through the proposed model, the tariff in the peak period has increased by 8.06–15.39%, and the tariff in the valley period has decreased by 18.48–27.95%. The result shows that the load in the peak period has decreased by 4.03–8.02% and the load in the valley period has increased by 6.41–9.75% through the proposed model.

1. Introduction

1.1. Background and Motivation

To cope with the increasingly serious climate change problem, China proposed carbon peaking and carbon neutrality goals at the 75th United Nations General Assembly in 2021 [1,2]. According to the IEA (IEA: https://www.iea.org/data-and-statistics (accessed on 27 December 2022)), the carbon emissions of the power sector account for more than 40% of China’s total carbon emissions. Therefore, building a new power system with renewable energy as the main body is the key to achieving the “dual carbon” goals [3]. However, the inherent uncertainty and volatility of renewable energy generation will increase the risk of power supply and demand mismatch, thus affecting the power system’s operation [4,5].

To ensure the security and stability of power system operation, on the one hand, it is necessary to improve the prediction accuracy of renewable energy generation. On the other hand, it is essential for strengthening demand-side management (DSM). DSM refers to adjusting user load or power consumption mode through certain incentive policies and price mechanisms so as to guide users to use power scientifically and reasonably [6]. The current incentive means and price mechanism are mainly shown in

Table 1. The current incentive means and pricing mechanism.

Type	Means	Characteristics
Incentive means	direct load control (DLC) [7]	The power grid can directly control the user’s electrical equipment through the remote-control device.
	interruptible load (IL) [8]	Users interrupt or reduce the load according to the contract.
	demand side bidding (DSB) [9]	Users can participate in demand response (DR) projects through bidding or contract orders.
	emergency demand response (EDR) [10]	Users spontaneously reduce load during peak hours or emergencies (If the users do not respond, they will not be punished).
	ancillary service market (ASM) [11]	DR can provide frequency regulation and system backup.
Price mechanism	time-of-use (TOU) price [12]	TOU price refers to dividing 24 h of a day into several periods according to the system operation status.
	real-time price (RTP) [13]	RTP is the marginal cost of providing electricity to users in a very short period of time (such as 30 min, 15 min, and 5 min).
	critical peak price (CPP) [14]	CPP is formed by superimposing flexible peak rates on TOU price.

.

As shown in Table 1, there are mainly two types of DSM mechanisms: incentive means and price mechanisms, of which the latter is mainly composed of TOU, RTP, and CPP. Due to the late start of China’s power market, the spot market is mainly conducted in several pilots, so there are relatively few regions implementing the RTP. In contrast, the TOU tariff is widely implemented as a price-based DR method. Through the introduction of TOU, users can transfer the power load in the peak period to the valley period to reduce the power consumption cost, so as to achieve the effect of “peak-cutting” and “valley-filling” [15]. On 26 July 2021, the National Development and Reform Commission (NDRC) issued a notice on further improving the TOU tariff mechanism (NDRC: http://www.gov.cn/zhengce/zhengceku/2021-07/29/content_5628297.htm (accessed on 27 December 2022)). The notice proposed that all regions should reasonably determine the price difference between peak and valley electricity prices. However, the practical effect of the TOU tariff is not satisfactory. On the one hand, the tariff gap between the peak and valley periods is not obvious, and the power users are unwilling to transfer or reduce the load during peak hours. Such unreasonable electricity prices cannot mobilize the enthusiasm of users, which leads to difficulty in solving the congestion of the power system. On the other hand, the TOU tariff implemented in most regions is a set of all-year TOU tariffs. Only a few provinces, such as Anhui and Hebei, have proposed to establish seasonal TOU tariffs. In fact, power users have significantly different load characteristics and electricity consumption habits in different seasons. If the same set of TOU tariffs is adopted for each season, it may lead to poor implementation effects of DR for power users in other seasons. Therefore, it is necessary to design a more reasonable seasonal TOU tariff according to the differentiated load curve of power users in different seasons.

The seasonal TOU tariff designed in this paper can effectively improve the DR enthusiasm of power users, reduce the power load in the peak period, and ensure the stable operation of the power system without increasing the cost of power users.

1.2. Literature Review and Contribution

The optimal design of the TOU tariff is also a hot issue among scholars. One is the time division of the peak-flat-valley (PFV) period. Charwand and Gitizadeh [16] proposed an intuitionistic fuzzy diverge thresholding model to cluster the load into three periods. Liu et al. [17] proposed a seasonal PFV time division method based on an improved fuzzy C-means clustering (IFCM) algorithm, which can overcome inaccurate user load selection and simple classification problems. Due to the lack of consideration of user DR in traditional time-division methods, Cheng and Zhai [18] established a TOU time-division model based on the user response.

Another one is the setting of the TOU price. Kong et al. [19] built a TOU price optimization model based on cost-benefit analysis, which can effectively improve the stability and economy of the power system. Huang et al. [20] proposed an optimal TOU price strategy for selecting the user’s range based on cost, which can reflect the adjusting process of the user’s electricity consumption behavior. However, the above research mainly focuses on the measurement of the cost of each period and lacks an analysis of the user’s responsiveness. Therefore, some scholars design the optimal TOU pricing model from the user side. Taik and Kiss [21] proposed a TOU pricing strategy based on the price elasticity of electricity demand (PEED). Hu et al. [22] constructed the TOU price optimization model based on the master-slave game theory and considering customer satisfaction. In contrast, the TOU pricing method based on PEED is much simpler and more efficient. According to the time scale, the PEED coefficient can be further divided into long-term and short-term. The former is mainly used to analyze the matching degree of energy development and economic development of a country or an industry [23,24]. The latter is more suitable for the optimal design of the TOU tariff during the PFV periods studied in this paper. However, the determination of the short-term PEED coefficient in existing research is mainly based on questionnaires or direct settings [25,26].

Through the literature review mentioned above, the existing TOU tariff optimization model based on the short-term PEED coefficient has mainly the following shortcomings:

(1)

The traditional PEED matrix is mostly constructed as (3 × 3), including three stages of peak-flat, flat-valley, and peak-valley. Such a simple matrix may lead to an inaccurate calculation of load fluctuation in each period, which will lead to unreasonable TOU pricing.

(2)

Not all users are aware of their PEED and DR abilities, so the method of determining PEED based on a questionnaire in the existing literature is not universal. Meanwhile, direct setting of PEED based on expert experience also has strong subjectivity.

(3)

At present, most of the existing studies are based on the original set of TOU tariffs to optimize a new set of TOU tariffs, which means the designed tariff is the same in each month/season. However, as mentioned above, power users have different electricity consumption characteristics in different seasons, and electricity price optimization in a single season is not universal.

Against this background, this paper proposes a three-stage TOU tariff optimization model. First, the K-means++ algorithm is adopted for load clustering to obtain the load curve of typical days in four seasons. Then, the PEED matrix is established to calculate the user’s self-elasticity coefficient and cross-elasticity coefficient in the PFV period. Finally, a PEED-based TOU pricing optimization model is established to design the optimal TOU price in the different seasons. The load and TOU tariff data used in this paper are from a province in China. The superiority and scientificity of the proposed three-stage TOU tariff optimization model are verified through the case study. The innovations and contributions of this paper are as follows:

(1)

The clustering of a typical day’s load curve based on the K-means++ algorithm is first adopted in this paper, which is proven to have better clustering performance than the traditional methods.

(2)

Compared with the traditional (3 × 3) matrix, the (24 × 24) PEED matrix established in this paper is more comprehensive. In addition, the PEED coefficient is calculated based on the actual load data, which is more accurate than questionnaires or direct settings in the existing studies.

(3)

The seasonal characteristics are incorporated into the traditional TOU tariff optimization design model. Through this study, the optimal TOU tariff for four seasons can be obtained instead of one, which is more practical and universal.

The structure of this study is as follows: After the introduction, the second part introduces the methodology applied in this paper. Section 3 illustrates the TOU tariff optimization model. Section 4 introduces the case study, and the conclusions are given in Section 5.

2. Methodology

2.1. K-Means++ Algorithm

Due to its characteristics of fast convergence speed and strong interpretability, the K-means algorithm is widely used in clustering [27]. However, its convergence mainly depends on the initialization of the cluster center. To avoid the aforementioned problem, Arthur and Vassilvitskii proposed a novel K-means++ algorithm in 2006 [28]. The steps of the traditional K-means algorithm are listed as follows:

➢

Step 1: Select $k$ objects from the load data $L=\{l_1,l_2,\dots ,l_n\}$ as the initial cluster center $C=\{c_1,c_2,\dots ,c_k\}$.

➢

Step 2: Calculate the Euclidean distance from each cluster object to the cluster center.

➢

Step 3: Recalculate each cluster center.

➢

Step 4: Repeat Step 1 and Step 2 until the position of the cluster center does not change anymore.

Compared with the traditional K-means algorithm, the K-means++ algorithm mainly improved the way of initializing the cluster center as follows:

➢

Step 5: Take one center $c_1$, chosen uniformly at random from $L$.

➢

Step 6: Calculate the shortest distance $D(l)$ between each sample and the existing cluster center. Then, calculate the probability $P(l)$ that each sample point is selected as the next cluster center, and select the sample point corresponding to the maximum probability value as the next cluster center. The probability can be expressed as follows:

$$P(l)=\frac{D{(l)}^2}{{\displaystyle {\sum }_{l\in L}D{(l)}^2}}$$

(1)

➢

Step 7: Repeat Step 6 until $k$ cluster centers are obtained.

This paper mainly takes the annual hourly load data as the empirical object, so $n=365$. In addition, in order to design a seasonal TOU tariff, this paper clusters the load curves of typical days in four seasons (spring, summer, autumn, and winter), so that the cluster center $k=4$.

2.2. Price Elasticity of Electricity Demand Model

The electricity demand of power users is closely related to the electricity price. The PEED is the ratio of the electricity demand change rate to the electricity price change rate in a certain period, which can measure the sensitivity of power users to electricity price mechanisms [29]. In general, the electricity demand in a certain period is not only related to the electricity price in that period but also affected by the electricity price in other periods. Hence, the PEED can be further divided into self-elasticity and cross-elasticity. Of which, the self-elasticity coefficient can be expressed as follows [30]:

$$\epsilon (t)=\frac{\partial l(t)/l(t)}{\partial u(t)/u(t)}$$

(2)

where $\epsilon (t)$ represents the self-elasticity coefficient, which refers to the impact of the change in electricity price on the electricity demand of users at time $t$, $l(t)$ represents the load demand at time $t$, and $u(t)$ represents the electricity price at time $t$.

The cross-elasticity coefficient can be expressed as follows [31]:

$$\epsilon (t,h)=\frac{\partial l(t)/l(t)}{\partial u(h)/u(h)}$$

(3)

where $\epsilon (t,h)$ represents the cross-elasticity coefficient, which refers to the impact of the change of electricity price at time $h$ on the electricity demand of users at time $t$, and $u(h)$ represents the electricity price at time $h$.

Under the implementation of the TOU tariff, users adjust their electricity consumption behavior according to the change in electricity price in each period, so as to maximize their own benefits. The change in power load can be expressed as follows [32]:

$$l(t)=l^0(t)\left[1+\epsilon (t)\frac{u(t)-u^0(t)}{u^0(t)}+{\displaystyle \sum _{\begin{array}{l}h=1\\ h\ne t\end{array}}^{24}\epsilon (t,h)\frac{u(h)-u^0(h)}{u^0(h)}}\right]$$

(4)

where $l^0(t)$ represents the original load before optimization at time $t$, and $u^0(t)$ and $u^0(h)$ respectively represent the original tariff before optimization at time $t$ and $h$.

3. TOU Tariff Optimization Model based on the PEED

3.1. Objective Function

The TOU tariff optimization model proposed in this paper aims to reduce the load in the peak period and increase the load in the valley period, as follows [33]:

$$\left\{\begin{array}{l}\min f_1=l{(t)}_{peak}\\ \max f_2=l{(t)}_{valley}\end{array}\right.$$

(5)

where $l{(t)}_{peak}$ and $l{(t)}_{valley}$ respectively represent the load in the peak period and valley period.

The load of the power system is high during the peak period and low during the valley period, so Equation (5) is often converted to minimize the peak-valley difference of the power grid. However, the power consumption characteristics of industrial users are diametrically opposite from those of the power system. Their maximum power consumption often occurs at midnight (the peak period of the power grid), and their minimum power consumption often occurs during the peak period of the grid. Therefore, for industrial users, Equation (5) can be converted into Equation (6):

$$\max f=\min [l{(t)}_{valley}]-\max [l{(t)}_{peak}]$$

(6)

3.2. Constraints

➢

Consumer electricity cost constraint.

When implementing the optimized TOU tariff, the electricity cost paid by power users cannot exceed the electricity cost before optimization [34]. The consumer electricity cost constraints can be expressed as follows:

$${\displaystyle \sum _{t=1}^{24}[l(t)\times u(t)]}\le {\displaystyle \sum _{t=1}^{24}[l^0(t)\times u^0(t)]}$$

(7)

➢

Peak-valley tariff constraints.

According to the NDRC, the price difference between peak and valley periods shall not be less than 3:1. The peak-valley price difference constraint can be expressed as follows:

$$\frac{u{(t)}_{peak}}{u{(t)}_{valley}}\ge 3$$

(8)

where $u{(t)}_{peak}$ and $u{(t)}_{valley}$ respectively represent the electricity price in the peak period and valley period.

In addition, the peak-valley tariff has upper and lower limit constraints, as follows:

$$\left\{\begin{array}{l}u{(t)}_{peak}\ge u^0{(t)}_{peak}\\ u{(t)}_{valley}\le u^0{(t)}_{valley}\end{array}\right.$$

(9)

where $u^0{(t)}_{peak}$ and $u^0{(t)}_{valley}$ respectively represent the original electricity price in the peak period and valley period.

➢

Power consumption balance constraint.

Before and after electricity price optimization, the total electricity consumption of users should remain unchanged [35]. The power consumption balance constraint can be expressed as follows:

$${\displaystyle \sum _{t=1}^{24}l(t)}={\displaystyle \sum _{t=1}^{24}{l}^0(t)}$$

(10)

4. Case Study

4.1. Data Sources

The load data used in this paper is from a province in China, and the time scale of the sample is 365 days (8760 observation points). Considering the different TOU tariffs implemented by different sectors, this paper focuses on the power load of industrial users as the empirical analysis object. The annual hourly power load of industrial users is shown in Figure 1.

The Spring Festival is a traditional festival in China, and industrial users often stop production during the festival. Therefore, the power load of industrial users drops sharply during the Spring Festival. In addition, the latest TOU tariff and PFV time division implemented by industrial users in the province are shown in

Table 2. The latest TOU tariff and PFV time division implemented by industrial users in the province.

	Peak	Flat	Valley
Time division (Hour)	8:00–11:00 15:00–21:00	11:00–12:00 13:00–15:00 21:00–23:00	12:00–13:00 23:00–8:00
Tariff (Yuan/MWh)	0.8791	0.5951	0.3111

.

As shown in Table 2, the current electricity price in the peak period is 2.8 times that in the valley period and has not reached the stipulated three times.

4.2. Clustering of Typical Daily Load Curves in Four Seasons based on K-Means++ Algorithm

The clustering of typical daily load curves in four seasons is shown in Figure 2.

As shown in Figure 2, the grey lines represent the daily load curve and the red lines represent the typical daily load curves in four seasons clustered by K-means++ algorithm. To verify that the K-means++ algorithm used in this paper has a better clustering effect, the clustering results were compared with the traditional K-means clustering results, as shown in

Table 3. The clustering performance of the K-means++ algorithm and K-means algorithm.

	K-Means++	K-Means
${\xi }_{SSE}$	3.20 × 108	5.39 × 108

. The sum of squared errors criterion (SSE) was selected as the evaluation criterion for the clustering effect [36], as shown in Equation (11):

$${\xi }_{SSE}={\displaystyle \sum _{i=1}^k{\displaystyle {\sum }_{l_j\in c_i}{‖l_j-m_i‖}^2}}$$

(11)

where $m_i$ is the centroid of the cluster $c_i$.

As shown in Table 3, the SSE value of the K-means algorithm is smaller than that of the K-means algorithm. Hence, compared with the traditional K-means algorithm, the K-means++ algorithm adopted in this paper has better clustering performance.

4.3. TOU Tariff Optimization Results Analysis

(1)

Optimization results for TOU tariffs in spring.

First, the price elasticity coefficient of industrial users’ electricity demand in spring was calculated, as shown in

Table A1. Price elasticity coefficient of electricity demand in spring.

	0:00	1:00	2:00	3:00	4:00	5:00	6:00	7:00	8:00	9:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00	18:00	19:00	20:00	21:00	22:00	23:00
0:00	−0.038	−0.038	−0.024	−0.009	0.010	0.024	0.028	0.031	0.036	0.034	0.030	0.023	0.009	0.001	0.002	0.012	0.024	0.025	0.017	−0.007	−0.037	−0.051	−0.056	−0.047
1:00	−0.038	−0.037	−0.038	−0.023	−0.008	0.010	0.024	0.028	0.031	0.036	0.035	0.030	0.023	0.008	0.001	0.001	0.012	0.023	0.025	0.017	−0.007	−0.037	−0.051	−0.055
2:00	−0.024	−0.038	−0.037	−0.038	−0.024	−0.009	0.010	0.024	0.027	0.031	0.036	0.035	0.030	0.023	0.008	0.001	0.001	0.012	0.024	0.025	0.017	−0.007	−0.036	−0.051
3:00	−0.009	−0.023	−0.038	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.027	0.032	0.036	0.035	0.030	0.023	0.008	0.001	0.001	0.012	0.024	0.025	0.017	−0.007	−0.036
4:00	0.010	−0.008	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.023	0.008	0.001	0.002	0.013	0.024	0.025	0.017	−0.007
5:00	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.023	0.008	0.001	0.002	0.013	0.024	0.025	0.017
6:00	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.023	0.009	0.002	0.002	0.013	0.024	0.025
7:00	0.031	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024	0.009	0.002	0.002	0.013	0.024
8:00	0.036	0.031	0.027	0.024	0.010	−0.009	−0.024	−0.039	−0.039	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024	0.009	0.002	0.002	0.013
9:00	0.034	0.036	0.031	0.027	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024	0.009	0.002	0.002
10:00	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024	0.009	0.002
11:00	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024	0.009
12:00	0.009	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030	0.024
13:00	0.001	0.008	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035	0.030
14:00	0.002	0.001	0.008	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036	0.035
15:00	0.012	0.001	0.001	0.008	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032	0.036
16:00	0.024	0.012	0.001	0.001	0.008	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028	0.032
17:00	0.025	0.023	0.012	0.001	0.001	0.008	0.023	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024	−0.009	0.010	0.024	0.028
18:00	0.017	0.025	0.024	0.012	0.002	0.001	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.039	−0.039	−0.024	−0.009	0.010	0.024
19:00	−0.007	0.017	0.025	0.024	0.013	0.002	0.002	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.039	−0.039	−0.024	−0.009	0.010
20:00	−0.037	−0.007	0.017	0.025	0.024	0.013	0.002	0.002	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.039	−0.039	−0.024	−0.009
21:00	−0.051	−0.037	−0.007	0.017	0.025	0.024	0.013	0.002	0.002	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039	−0.024
22:00	−0.056	−0.051	−0.036	−0.007	0.017	0.025	0.024	0.013	0.002	0.002	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038	−0.039
23:00	−0.047	−0.055	−0.051	−0.036	−0.007	0.017	0.025	0.024	0.013	0.002	0.002	0.009	0.024	0.030	0.035	0.036	0.032	0.028	0.024	0.010	−0.009	−0.024	−0.039	−0.038

. Then, the TOU tariff and load optimization results in spring were calculated, as shown in

Table 4. The TOU tariff optimization results in spring.

	Peak	Flat	Valley
Original tariff (Yuan/MWh)	0.8791	0.5951	0.3111
Optimized tariff in spring (Yuan/MWh)	0.9499	0.6623	0.2375

and Figure 3.

Compared with the original tariff, the tariff in the peak period increased by 8.06%, and the tariff in the valley period decreased by 23.66%. Due to the adjustment of electricity prices, users spontaneously change their electricity consumption behavior. As shown in Figure 3, the maximum load growth during the valley period reached 6.41% (3:00 a.m.), and the maximum load reduction during the peak hours reached 4.03% (16:00 p.m.). Through the TOU tariff optimization, the gap between the maximum load and the minimum load of industrial users expanded from 654.01 MW to 927.49 MW.

(2)

Optimization results for TOU tariffs in summer.

First, the price elasticity coefficient of industrial users’ electricity demand in summer is calculated, as shown in

Table A2. Price elasticity coefficient of electricity demand in summer.

	0:00	1:00	2:00	3:00	4:00	5:00	6:00	7:00	8:00	9:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00	18:00	19:00	20:00	21:00	22:00	23:00
0:00	−0.035	−0.039	−0.027	−0.016	−0.001	0.008	0.009	0.013	0.019	0.022	0.023	0.020	0.010	0.008	0.015	0.031	0.043	0.042	0.028	−0.001	−0.033	−0.047	−0.050	−0.041
1:00	−0.039	−0.035	−0.038	−0.027	−0.016	−0.001	0.008	0.009	0.013	0.019	0.022	0.023	0.020	0.011	0.008	0.015	0.031	0.043	0.042	0.028	−0.002	−0.033	−0.047	−0.050
2:00	−0.027	−0.038	−0.035	−0.038	−0.027	−0.015	−0.001	0.009	0.009	0.013	0.019	0.022	0.023	0.020	0.010	0.008	0.015	0.030	0.043	0.041	0.027	−0.002	−0.033	−0.047
3:00	−0.016	−0.027	−0.038	−0.034	−0.038	−0.027	−0.015	0.000	0.009	0.009	0.012	0.019	0.022	0.023	0.020	0.010	0.008	0.015	0.030	0.042	0.041	0.027	−0.002	−0.033
4:00	−0.001	−0.016	−0.027	−0.038	−0.034	−0.038	−0.026	−0.015	0.000	0.009	0.009	0.012	0.019	0.022	0.023	0.020	0.010	0.008	0.014	0.030	0.042	0.041	0.027	−0.002
5:00	0.008	−0.001	−0.015	−0.027	−0.038	−0.034	−0.038	−0.026	−0.015	0.000	0.008	0.009	0.012	0.019	0.022	0.023	0.020	0.010	0.007	0.014	0.030	0.042	0.041	0.027
6:00	0.009	0.008	−0.001	−0.015	−0.026	−0.038	−0.034	−0.037	−0.026	−0.015	−0.001	0.008	0.009	0.012	0.019	0.022	0.023	0.020	0.010	0.007	0.014	0.030	0.042	0.041
7:00	0.013	0.009	0.009	0.000	−0.015	−0.026	−0.037	−0.034	−0.037	−0.026	−0.015	−0.001	0.008	0.009	0.012	0.019	0.022	0.022	0.020	0.010	0.007	0.014	0.030	0.042
8:00	0.019	0.013	0.009	0.009	0.000	−0.015	−0.026	−0.037	−0.033	−0.037	−0.026	−0.015	−0.001	0.008	0.009	0.012	0.019	0.022	0.022	0.020	0.010	0.007	0.014	0.030
9:00	0.022	0.019	0.013	0.009	0.009	0.000	−0.015	−0.026	−0.037	−0.034	−0.038	−0.027	−0.015	−0.001	0.008	0.009	0.012	0.018	0.021	0.022	0.020	0.009	0.007	0.014
10:00	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.026	−0.038	−0.034	−0.038	−0.027	−0.015	−0.001	0.008	0.008	0.012	0.018	0.021	0.022	0.019	0.009	0.007
11:00	0.020	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.027	−0.038	−0.034	−0.038	−0.026	−0.015	−0.001	0.008	0.008	0.012	0.018	0.021	0.022	0.019	0.009
12:00	0.010	0.020	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.027	−0.038	−0.034	−0.038	−0.026	−0.015	−0.001	0.008	0.008	0.012	0.018	0.021	0.022	0.019
13:00	0.008	0.011	0.020	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.026	−0.038	−0.034	−0.038	−0.027	−0.016	−0.001	0.008	0.008	0.012	0.018	0.021	0.022
14:00	0.015	0.008	0.010	0.020	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.026	−0.038	−0.034	−0.038	−0.027	−0.016	−0.001	0.008	0.008	0.011	0.018	0.021
15:00	0.031	0.015	0.008	0.010	0.020	0.023	0.022	0.019	0.012	0.009	0.008	−0.001	−0.015	−0.027	−0.038	−0.034	−0.038	−0.027	−0.016	−0.001	0.007	0.008	0.011	0.018
16:00	0.043	0.031	0.015	0.008	0.010	0.020	0.023	0.022	0.019	0.012	0.008	0.008	−0.001	−0.016	−0.027	−0.038	−0.034	−0.038	−0.027	−0.016	−0.002	0.007	0.008	0.011
17:00	0.042	0.043	0.030	0.015	0.008	0.010	0.020	0.022	0.022	0.018	0.012	0.008	0.008	−0.001	−0.016	−0.027	−0.038	−0.034	−0.038	−0.027	−0.016	−0.002	0.007	0.008
18:00	0.028	0.042	0.043	0.030	0.014	0.007	0.010	0.020	0.022	0.021	0.018	0.012	0.008	0.008	−0.001	−0.016	−0.027	−0.038	−0.034	−0.038	−0.027	−0.016	−0.002	0.007
19:00	−0.001	0.028	0.041	0.042	0.030	0.014	0.007	0.010	0.020	0.022	0.021	0.018	0.012	0.008	0.008	−0.001	−0.016	−0.027	−0.038	−0.034	−0.038	−0.027	−0.016	−0.002
20:00	−0.033	−0.002	0.027	0.041	0.042	0.030	0.014	0.007	0.010	0.020	0.022	0.021	0.018	0.012	0.008	0.007	−0.002	−0.016	−0.027	−0.038	−0.035	−0.038	−0.027	−0.016
21:00	−0.047	−0.033	−0.002	0.027	0.041	0.042	0.030	0.014	0.007	0.009	0.019	0.022	0.021	0.018	0.011	0.008	0.007	−0.002	−0.016	−0.027	−0.038	−0.035	−0.039	−0.027
22:00	−0.050	−0.047	−0.033	−0.002	0.027	0.041	0.042	0.030	0.014	0.007	0.009	0.019	0.022	0.021	0.018	0.011	0.008	0.007	−0.002	−0.016	−0.027	−0.039	−0.035	−0.039
23:00	−0.041	−0.050	−0.047	−0.033	−0.002	0.027	0.041	0.042	0.030	0.014	0.007	0.009	0.019	0.022	0.021	0.018	0.011	0.008	0.007	−0.002	−0.016	−0.027	−0.039	−0.035

. Then, the TOU tariff and load optimization results in summer were calculated, as shown in

Table 5. The TOU tariff optimization results in summer.

	Peak	Flat	Valley
Original tariff (Yuan/MWh)	0.8791	0.5951	0.3111
Optimized tariff in summer (Yuan/MWh)	1.0144	0.5169	0.2536

and Figure 4.

Compared with the original tariff, the tariff in the peak period increased by 15.39%, and the tariff in the valley period decreased by 18.48%. Due to the adjustment of electricity prices, users spontaneously change their electricity consumption behavior. As shown in Figure 4, the maximum load growth during the valley period reached 6.84% (1:00 a.m.), and the maximum load reduction during the peak hours reached 5.72% (17:00 p.m.). Through the TOU tariff optimization, the gap between the maximum and minimum load of industrial users expanded from 488.23 MW to 901.12 MW.

(3)

Optimization results for TOU tariffs in autumn.

First, the price elasticity coefficient of industrial users’ electricity demand in autumn was calculated, as shown in

Table A3. Price elasticity coefficient of electricity demand in autumn.

	0:00	1:00	2:00	3:00	4:00	5:00	6:00	7:00	8:00	9:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00	18:00	19:00	20:00	21:00	22:00	23:00
0:00	−0.053	−0.049	−0.027	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.017	0.001	−0.005	0.001	0.012	0.014	0.005	−0.024	−0.062	−0.080	−0.084	−0.070
1:00	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.017	0.001	−0.005	0.001	0.012	0.014	0.005	−0.024	−0.062	−0.080	−0.084
2:00	−0.027	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.017	0.001	−0.005	0.001	0.012	0.015	0.005	−0.024	−0.062	−0.080
3:00	−0.004	−0.028	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.017	0.001	−0.005	0.001	0.012	0.015	0.006	−0.024	−0.062
4:00	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.028	−0.004	0.024	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.017	0.001	−0.005	0.001	0.013	0.015	0.006	−0.024
5:00	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.005	0.025	0.048	0.057	0.063	0.065	0.061	0.050	0.039	0.018	0.001	−0.005	0.001	0.013	0.015	0.006
6:00	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.051	0.039	0.018	0.001	−0.005	0.001	0.013	0.015
7:00	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.051	0.039	0.018	0.001	−0.005	0.001	0.013
8:00	0.065	0.063	0.057	0.048	0.024	−0.005	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.051	0.039	0.018	0.002	−0.005	0.001
9:00	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.065	0.061	0.051	0.039	0.018	0.002	−0.005
10:00	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.057	0.063	0.066	0.061	0.051	0.040	0.018	0.002
11:00	0.039	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.058	0.064	0.066	0.061	0.051	0.040	0.018
12:00	0.017	0.039	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.058	0.064	0.066	0.061	0.051	0.040
13:00	0.001	0.017	0.039	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.054	−0.049	−0.028	−0.004	0.025	0.048	0.058	0.064	0.066	0.061	0.051
14:00	−0.005	0.001	0.017	0.039	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.028	−0.004	0.025	0.048	0.058	0.064	0.066	0.061
15:00	0.001	−0.005	0.001	0.017	0.039	0.050	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.027	−0.004	0.025	0.048	0.058	0.064	0.066
16:00	0.012	0.001	−0.005	0.001	0.017	0.039	0.051	0.061	0.065	0.063	0.057	0.048	0.025	−0.004	−0.028	−0.049	−0.053	−0.049	−0.027	−0.004	0.025	0.048	0.058	0.064
17:00	0.014	0.012	0.001	−0.005	0.001	0.018	0.039	0.051	0.061	0.065	0.063	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049	−0.027	−0.004	0.025	0.048	0.058
18:00	0.005	0.014	0.012	0.001	−0.005	0.001	0.018	0.039	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049	−0.027	−0.004	0.025	0.048
19:00	−0.024	0.005	0.015	0.012	0.001	−0.005	0.001	0.018	0.039	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049	−0.027	−0.004	0.025
20:00	−0.062	−0.024	0.005	0.015	0.013	0.001	−0.005	0.001	0.018	0.039	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049	−0.027	−0.004
21:00	−0.080	−0.062	−0.024	0.006	0.015	0.013	0.001	−0.005	0.002	0.018	0.040	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049	−0.027
22:00	−0.084	−0.080	−0.062	−0.024	0.006	0.015	0.013	0.001	−0.005	0.002	0.018	0.040	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053	−0.049
23:00	−0.070	−0.084	−0.080	−0.062	−0.024	0.006	0.015	0.013	0.001	−0.005	0.002	0.018	0.040	0.051	0.061	0.066	0.064	0.058	0.048	0.025	−0.004	−0.027	−0.049	−0.053

. Then, the TOU tariff and load optimization results in autumn were calculated, as shown in

Table 6. The TOU tariff optimization results in autumn.

	Peak	Flat	Valley
Original tariff (Yuan/MWh)	0.8791	0.5951	0.3111
Optimized tariff in spring (Yuan/MWh)	0.9545	0.6604	0.2386

and Figure 5.

Compared with the original tariff, the tariff in the peak period increased by 8.57%, and the tariff in the valley period decreased by 23.30%. Due to the adjustment of electricity prices, users spontaneously change their electricity consumption behavior. As shown in Figure 5, the maximum load growth during the valley period reached 9.75% (23:00 p.m.), and the maximum load reduction during the peak hours reached 5.73% (10:00 a.m.). Through the TOU tariff optimization, the gap between the maximum and minimum load of industrial users expanded from 566.69 MW to 825.49 MW.

(4)

Optimization results for TOU tariff in winter.

First, the price elasticity coefficient of industrial users’ electricity demand in winter was calculated, as shown in

Table A4. Price elasticity coefficient of electricity demand in winter.

	0:00	1:00	2:00	3:00	4:00	5:00	6:00	7:00	8:00	9:00	10:00	11:00	12:00	13:00	14:00	15:00	16:00	17:00	18:00	19:00	20:00	21:00	22:00	23:00
0:00	−0.033	−0.037	−0.020	−0.001	0.027	0.052	0.058	0.063	0.064	0.058	0.045	0.027	0.000	−0.018	−0.024	−0.016	0.002	0.007	0.002	−0.021	−0.055	−0.065	−0.065	−0.048
1:00	−0.037	−0.032	−0.035	−0.019	0.000	0.028	0.053	0.059	0.065	0.063	0.057	0.043	0.026	0.002	−0.019	−0.024	−0.017	0.001	0.006	0.000	−0.022	−0.056	−0.066	−0.065
2:00	−0.020	−0.035	−0.030	−0.034	−0.017	0.002	0.030	0.055	0.061	0.063	0.061	0.055	0.043	0.028	0.001	−0.019	−0.025	−0.018	−0.001	0.004	−0.001	−0.024	−0.057	−0.066
3:00	−0.001	−0.019	−0.034	−0.030	−0.034	−0.017	0.002	0.030	0.055	0.061	0.063	0.061	0.055	0.043	0.028	0.001	−0.019	−0.026	−0.019	−0.001	0.004	−0.002	−0.024	−0.057
4:00	0.027	0.000	−0.017	−0.034	−0.029	−0.033	−0.016	0.003	0.031	0.054	0.060	0.062	0.060	0.056	0.043	0.027	0.000	−0.020	−0.027	−0.020	−0.002	0.003	−0.002	−0.024
5:00	0.052	0.028	0.002	−0.017	−0.033	−0.029	−0.032	−0.016	0.004	0.031	0.054	0.059	0.062	0.061	0.056	0.043	0.027	0.000	−0.021	−0.027	−0.020	−0.003	0.003	−0.002
6:00	0.058	0.053	0.030	0.002	−0.016	−0.032	−0.028	−0.032	−0.015	0.003	0.030	0.053	0.059	0.062	0.061	0.056	0.043	0.027	−0.001	−0.021	−0.028	−0.021	−0.003	0.003
7:00	0.063	0.059	0.055	0.030	0.003	−0.016	−0.032	−0.028	−0.031	−0.016	0.003	0.030	0.053	0.059	0.062	0.061	0.055	0.042	0.026	−0.001	−0.022	−0.028	−0.021	−0.003
8:00	0.064	0.065	0.061	0.055	0.031	0.004	−0.015	−0.031	−0.029	−0.030	−0.015	0.004	0.030	0.052	0.060	0.062	0.062	0.056	0.043	0.027	0.000	−0.021	−0.028	−0.020
9:00	0.058	0.063	0.063	0.061	0.054	0.031	0.003	−0.016	−0.030	−0.028	−0.030	−0.014	0.004	0.030	0.052	0.060	0.063	0.062	0.057	0.044	0.028	0.000	−0.021	−0.028
10:00	0.045	0.057	0.061	0.063	0.060	0.054	0.030	0.003	−0.015	−0.030	−0.026	−0.028	−0.014	0.002	0.030	0.053	0.062	0.065	0.064	0.059	0.046	0.030	0.001	−0.020
11:00	0.027	0.043	0.055	0.061	0.062	0.059	0.053	0.030	0.004	−0.014	−0.028	−0.026	−0.028	−0.014	0.002	0.030	0.054	0.062	0.065	0.065	0.060	0.047	0.030	0.001
12:00	0.000	0.026	0.043	0.055	0.060	0.062	0.059	0.053	0.030	0.004	−0.014	−0.028	−0.025	−0.028	−0.014	0.002	0.031	0.055	0.063	0.066	0.066	0.060	0.047	0.030
13:00	−0.018	0.002	0.028	0.043	0.056	0.061	0.062	0.059	0.052	0.030	0.002	−0.014	−0.028	−0.025	−0.028	−0.014	0.002	0.031	0.054	0.063	0.066	0.065	0.060	0.047
14:00	−0.024	−0.019	0.001	0.028	0.043	0.056	0.061	0.062	0.060	0.052	0.030	0.002	−0.014	−0.028	−0.025	−0.028	−0.013	0.004	0.032	0.056	0.065	0.068	0.066	0.061
15:00	−0.016	−0.024	−0.019	0.001	0.027	0.043	0.056	0.061	0.062	0.060	0.053	0.030	0.002	−0.014	−0.028	−0.025	−0.027	−0.012	0.005	0.034	0.057	0.066	0.068	0.066
16:00	0.002	−0.017	−0.025	−0.019	0.000	0.027	0.043	0.055	0.062	0.063	0.062	0.054	0.031	0.002	−0.013	−0.027	−0.022	−0.025	−0.009	0.007	0.036	0.059	0.066	0.068
17:00	0.007	0.001	−0.018	−0.026	−0.020	0.000	0.027	0.042	0.056	0.062	0.065	0.062	0.055	0.031	0.004	−0.012	−0.025	−0.020	−0.023	−0.007	0.009	0.038	0.060	0.067
18:00	0.002	0.006	−0.001	−0.019	−0.027	−0.021	−0.001	0.026	0.043	0.057	0.064	0.065	0.063	0.054	0.032	0.005	−0.009	−0.023	−0.018	−0.020	−0.005	0.012	0.039	0.060
19:00	−0.021	0.000	0.004	−0.001	−0.020	−0.027	−0.021	−0.001	0.027	0.044	0.059	0.065	0.066	0.063	0.056	0.034	0.007	−0.007	−0.020	−0.016	−0.018	−0.003	0.012	0.039
20:00	−0.055	−0.022	−0.001	0.004	−0.002	−0.020	−0.028	−0.022	0.000	0.028	0.046	0.060	0.066	0.066	0.065	0.057	0.036	0.009	−0.005	−0.018	−0.014	−0.016	−0.002	0.013
21:00	−0.065	−0.056	−0.024	−0.002	0.003	−0.003	−0.021	−0.028	−0.021	0.000	0.030	0.047	0.060	0.065	0.068	0.066	0.059	0.038	0.012	−0.003	−0.016	−0.012	−0.016	−0.002
22:00	−0.065	−0.066	−0.057	−0.024	−0.002	0.003	−0.003	−0.021	−0.028	−0.021	0.001	0.030	0.047	0.060	0.066	0.068	0.066	0.060	0.039	0.012	−0.002	−0.016	−0.012	−0.016
23:00	−0.048	−0.065	−0.066	−0.057	−0.024	−0.002	0.003	−0.003	−0.020	−0.028	−0.020	0.001	0.030	0.047	0.061	0.066	0.068	0.067	0.060	0.039	0.013	−0.002	−0.016	−0.011

. Then, the TOU tariff and load optimization results in winter were calculated, as shown in

Table 7. The TOU tariff optimization results in winter.

	Peak	Flat	Valley
Original tariff (Yuan/MWh)	0.8791	0.5951	0.3111
Optimized tariff in winter (Yuan/MWh)	0.9665	0.6491	0.2241

and Figure 6.

Compared with the original tariff, the tariff in the peak period increased by 9.95% and the tariff in the valley period decreased by 27.95%. Due to the adjustment of electricity prices, users spontaneously change their electricity consumption behavior. As shown in Figure 6, the maximum load growth during the valley period reached 7.95% (23:00 p.m.), and the maximum load reduction during the peak hours reached 8.02% (10:00 a.m.). Through the TOU tariff optimization, the gap between the maximum load and the minimum load of industrial users expanded from 469.95 MW to 662.14 MW.

(5)

Discussion of TOU tariff optimization results.

Through the TOU tariff optimization design model built in this paper, the gap between the electricity price at the peak stage and the electricity price at the low stage of the four seasons was further widened.

Before optimization, the electricity price in the peak period was 0.3111 yuan/MWh, and the electricity price in the valley period was 0.8791 yuan/MWh, with a gap of 0.568 yuan/MWh. However, after optimization, the maximum gap between the two is 0.7608 yuan/MWh, which occurs in summer. The reason for this phenomenon may be the high-power load during the summer peak period. Of the four seasons, the maximum power load in the summer peak period is 3887.51 MWh, which is significantly higher than 3349.05 MWh in autumn and 3264.91 MWh in winter and is the same as 3938.92 MWh in spring. However, the maximum power load in the summer valley period is 4026.26 MWh, which is lower than 4261.95 MWh in the spring valley period.

Such a feature of “high demand in the peak period and low demand in the valley period” makes the TOU price of industrial users more adjustable in summer, and its peak-valley price difference can further expand compared with other seasons.

4.4. Comparison Results

The traditional TOU optimization design model only calculates a single set of TOU tariffs. To verify the superiority of the seasonal TOU optimization model proposed in this paper, the following comparative tests were designed (

Table 8. The comparative tests of the TOU optimization design model.

Experiment	Details
Control	Different TOU tariffs are adopted in different seasons.
Treatment	The same TOU tariff is adopted in all seasons (based on the traditional TOU tariff optimization model).

).

First, the clustering of the typical daily load curve for all years was obtained (Figure 7).

Then, the TOU tariff was calculated, as shown in

Table 9. The TOU tariff optimization result based on the traditional TOU optimized model.

	Peak	Flat	Valley
Original tariff (Yuan/MWh)	0.8791	0.5951	0.3111
Optimized tariff (Yuan/MWh)	0.9257	0.6911	0.2314

.

Based on the traditional TOU electricity price optimization model, the peak-valley price difference was 0.6943 yuan/MWh, which is lower than the seasonal TOU tariff designed in this paper. The effects of the control group and treatment group were compared in two dimensions: load and cost, as shown in

Table 10. The effect of the control group and treatment group.

Dimension	Experiment	Spring	Summer	Autumn	Winter	Total
Gap increase between the maximum load and the minimum load (MW)	Control	273.48	412.89	258.80	192.19	1137.36
	Treatment	264				1056
Cost (Yuan)	Control	53,641.19	52,897.09	44,640.22	42,105.24	193,283.74
	Treatment	48,985.92				195,943.69

.

Compared with the traditional method, the proposed model has a better effect on “peak-cutting” and “valley-filling” and lower costs for power users.

5. Conclusions and Suggestions

5.1. Conclusions

With the accelerated construction of new power systems, it is difficult to meet the safe and efficient operation requirements only by considering the use of regulatory resources on the power supply side and grid side. DSM plays a key role in alleviating the contradiction between power supply and demand, promoting the consumption of renewable energy, and improving the energy efficiency of the whole society. Of which, the economic means based on the TOU tariff are most effective in optimizing the power consumption structure of users. In this context, this paper proposes a novel hybrid three-stage seasonal TOU tariff optimization model, including typical day selection, price elasticity of electricity demand measurement, and TOU tariff optimization. The following conclusions can be obtained:

(1)

Compared with the traditional K-means algorithm, the K-means++ algorithm used in this paper has a better clustering effect. The typical daily load curve of four seasons obtained through K-means++ clustering is more scientific and reasonable.

(2)

To improve the accuracy of the PEED matrix, this paper expands the original (3 × 3) matrix to the (24 × 24) matrix. The results show that the elastic coefficients (including self-elastic and cross-elastic) at different times are not the same, even within the same period. A more accurate and comprehensive PEED matrix is significant for the rational design of the TOU tariff.

(3)

The seasonal TOU tariff optimization model constructed in this paper obtains the TOU tariff and typical daily load curve in four seasons. Compared with the original TOU tariff, the optimized seasonal TOU tariff increases by 8.06–15.39% in the peak period and decreases by 18.48–27.95% in the valley period. The TOU tariff optimization also results in a decrease of 4.03–8.02% of the load in the peak period and an increase of 6.41–9.75% of the load in the valley period.

(4)

Compared with the traditional TOU optimization models, the proposed model can increase the peak-valley load difference by 7.70% and reduce the power consumption cost by 1.36%.

5.2. Limitations and Future Outlook

Although this paper proposes a novel and comprehensive seasonal TOU tariff optimization design model, there are also some limitations:

(1)

From the perspective of methodology, although the model proposed in this paper has excellent effects, it is easy to understand how it could lead to problems such as low computational efficiency and long computation times.

(2)

Due to the data constraints, this paper only conducts TOU tariff optimization design for the industrial sector, and the empirical object only comes from the actual data of one province in China.

Therefore, our future research will be carried out and improved in the following aspects:

(1)

In the future, we will evaluate the electricity consumption habits and laws of power users in different regions and industries so as to calculate a more abundant PEED coefficient.

(2)

In the future, we will further expand the data samples to different sectors in more provinces, making the optimized TOU tariff more universal and practical.