Towards a Sustainable Power System: A Three-Stage Demand Response Potential Evaluation Model

Abstract

Developing flexible resources is a key strategy for advancing the development of new power systems and addressing the issue of climate change. Demand response is a crucial flexibility resource that is extensively employed due to its sustainability and economy. This work develops a three-stage demand response potential evaluation model based on “theoretical potential–realizable potential–multi-load aggregation potential” in response to the issues of inadequate consideration of numerous complicated agents and time in previous research. Firstly, the traditional method calculates the theoretical maximum demand response potential of a single industry in each period. Based on this, the industry characteristics are taken into account when establishing the demand response potential evaluation model. Lastly, the time variation of the demand response potential is taken into consideration when evaluating the demand response potential of multiple load aggregation. For the analysis, three industries are chosen as examples. The results show that the potential of peak shaving and valley filling obtained by using the model is smaller than that of the traditional method, the reduction range of peak cutting demand response potential calculated by multi-load aggregation is 19–100%, and the reduction range of valley filling demand response potential is 20–89%. The results are closer to reality, which is conducive to improving the accuracy of relevant departments in making relevant decisions and promoting the sustainable development of a new power system.

1. Introduction

1.1. Background and Motivation

With the intensification of climate change and the shortage of primary energy supply [1], the power system is gradually transitioning to the use of clean energy. Strong volatility, unpredictability, and intermittentness characterize the clean energy sources of our time [2]. The stability and dependability of the electrical system are under jeopardy as clean energy sources proliferate [3]. In order to smooth the uncertainty and intermittency of renewable energy output, the demand for flexible regulation resources is increasing [4]. Stimulating the potential of demand-side resource regulation and strengthening power demand-side management are of great significance for ensuring the stable operation of power grids and promoting sustainable development [5].

Demand-side management (DSM) consists of acts modifying the level or pattern of electricity consumption [6]. Demand-side flexibility is an important part of DSM, which is defined as the ability of power users to adjust their power consumption behavior according to the needs of power system operation. The primary use of demand-side flexibility is seen in demand response (DR). The categories of DR are displayed in Figure 1. The implementation of demand response can fully wake up the sleeping resources on the load side, guide users to optimize the electricity load, and improve the consumption of new energy. However, the implementation of demand response and the implementation of related policies need to have a more accurate assessment of the demand response potential of users, so as to improve the effectiveness of demand response and the economy of the new power system and promote the sustainable development of the power system.

In order to more accurately evaluate the potential of user demand response, it is necessary to further explore flexible resources [7] and minimize the evaluation error as much as possible. This is especially true for the assessment of the demand response potential of multiple users or multi-load aggregation. Two things to take into account while evaluating demand-side flexibility resource potential are as follows:

• What needs to be considered when assessing the potential for demand-side resource response?
• How should the potential for demand response be assessed when many demand-side resources are combined?

The answers to these queries will aid planners in understanding the evolution of power demand and creating effective development strategies as well as enabling them to better comprehend the demand response capability of demand-side resources. The power supply may be flexibly modified to maintain the power system’s balance and stability, increase the use of clean energy, and accomplish the flexibility and sustainable development of the power system by evaluating the demand response capability of regional multi-load aggregation.

1.2. Literature Review

In order to solve the above problems, scholars have carried out a lot of research on the potential of demand response. These studies include the following:

• Evaluation of individual resource potential for demand response

From an equipment standpoint, some researchers assess the potential for demand response by looking at the equipment itself or the ambient conditions in the immediate vicinity. For example, study [8] examined the impact of indoor climate conditions and building parameters on the demand response potential of a single air-conditioning system in the case of no cooling and heating. On this basis, study [9] established aggregate power models of multiple air conditioners to analyze the influences of indoor temperature, outdoor temperature, and the number of aggregate air conditioners on the demand response potential. Study [10] looked further into the topic of buildings, establishing models for thermal networks and investigating the impact of various building features and scenarios on the potential for demand response. Some scholars also consider the impact of user factors on demand response potential from the perspective of users. For instance, study [11] uses a top-down approach to determine demand response potential, taking into account the user’s participation in demand response based on conventional methodologies. However, the results are approximate and the time frame is annual. In addition to resident consumption patterns, study [12] considers users’ wishes when assessing the potential for time-varying demand response from air conditioners. In study [13], considering the impact of user consumption on demand response potential, thermal sensitivity was used to quantify the above factors and combined with neural network algorithm to calculate the demand response potential of users. Some academics forecast demand response potential by looking for a relationship between demand response potential and past data in addition to calculating demand response potential [14]. Nevertheless, industrial characteristics are rarely taken into account in these studies; instead, they primarily focus on equipment or user aspects. In actuality, due to certain industry features, the industry will not always respond when it engages in demand response; in fact, there may be non-response periods at times. A literature analysis of the variety of methods used in the meat business was performed [15]. The industry’s features were taken into account, but the results simply indicated that the sector had high potential for demand response; the real potential value was not determined.

2.

Evaluation of several resources’ potential for demand response

There are two types of evaluations for demand response potential: qualitative and quantitative. The results of the qualitative evaluation are subjective. For instance, study [16] builds an assessment framework to gauge the scores of different demand-side resources before utilizing an enhanced G1 (a kind of analytic hierarchy process) approach to assess the demand response potential of users. A system of index evaluation based on game theory and information value is designed in study [17]. These studies aim to increase demand-side resource utilization rates and facilitate demand-side resource adjustments for the power system. Some research has characterized the demand-side resource potential in regions according to a given level [18] in order to assess the existing state of regional demand response potential; nevertheless, these studies were unable to determine the precise potential value. Quantitative research has compensated for this deficiency. For example, study [19] analyzed the potential of peak clipping and valley filling with different sample numbers, and analyzed the change in the peak demand of user electrical appliances as the number of samples increased. Although a variety of electrical appliances were taken into account, an overall analysis was not made. Study [20] proposed an evaluation method of demand response potential considering multi-energy coupling, but did not analyze the demand response potential of multi-load superposition. Instead, it evaluated only one demand-side resource, and the objective function had the single goal of cost minimization. Study [21] evaluated the demand response potential of multiple regions in Germany on a 15 min time scale, taking into account time variability. However, it only assessed a single demand-side resource and did not evaluate the demand response potential of multiple-load superposition.

3.

Research on the multiple-load polymerization method

With the diversification of flexible resource types, scholars have proposed many methods to aggregate the load in order to further explore power demand-side resources. A common method of similar load aggregation is the clustering method. For example, study [22] first uses a K-nearest neighbor classification (KNN) algorithm to classify air-conditioning load, and then uses the K-means clustering method to aggregate the load. Heterogeneous loads can also use K-means clustering for data mining [23]; study [24] uses K-means ++ to build a load aggregation model. The above method adopts the principle of classification. Most of the obtained aggregated loads result in multiple scenarios. Many times, the outcome of a single aggregation is the superposition of several loads. For example, in [25], loads are divided into replaceable loads, reducible loads, transferable loads, and translational loads to establish an aggregation model, and then these four loads are superimposed to study related issues in the power market on this basis. In study [26], when studying the demand response potential of multi-load aggregation, the demand response potential of load aggregators is also obtained by means of superposition. However, in some studies, time variability is not considered in the stacking process, and only maximum demand response potential is considered.

Based on the existing literature, the following inquiries can be formulated:

• When evaluating the potential of flexible resource demand response, current research focuses on modeling and analysis based on the characteristics of certain equipment or the load characteristics of a certain industry, ignoring the other characteristics of the industry such as the response period and response duration of the industry.
• Qualitative and quantitative research are the two categories into which existing research can be separated. The conclusion of qualitative research is often to compare the demand response potential of various flexible resources, and an exact value cannot be obtained. Quantitative research compensates for this shortcoming, but the result is always a number, that is, the demand response potential of all-day peak-filling is a fixed value, which is obviously unreasonable, and a single-objective function will lead to a large difference between the result and the reality. Furthermore, there will be a higher error in the results due to this fault when examining the demand response potential of regional multi-load aggregation.
• Multiple load aggregation methods commonly used include K-means, K-means ++, and other clustering methods, and some studies also establish aggregation models according to classified data characteristics. The aggregation result is mostly the load in multiple scenarios, and the superposition is the final result. However, in some studies, the superposition is carried out according to the maximum or unique value, which ignores the timing, which can then easily cause inaccurate results.

1.3. Contribution and Article Organization

By taking industry features and scheduling into account, this research built a three-stage demand response potential evaluation model based on “theoretical potential–realizable potential–multi-load aggregation potential” to address the aforementioned issues. Figure 2 shows this structure. We determined the attainable demand response potential and assessed the demand response potential for various industries. Finally, the demand response potential of multi-load aggregation in the region was superimposed in time order, and the multi-time demand response potential of the region was determined. The sensitivity of the results was analyzed. The three main contributions of this study are as follows:

• Compared with the previous research on demand response potential, which has focused on the mining of load characteristics, this paper focuses on industry characteristics and realizable potential, and constructs a three-stage demand response potential assessment model to quantitatively assess the realizable demand response potential of users within different periods.
• Compared with the previous studies, which only considered the single objective of user cost or peak–valley difference minimization, this paper comprehensively considered two objectives and constructed a double-objective function considering user cost and peak–valley difference minimization to make the results more accurate.
• The theoretical potential value or maximum potential value has frequently been aggregated in prior research on the demand response potential of multi-load aggregation without taking the time variability of demand response potential into account. This factor is taken into consideration in this study, which refines the time scale and superimposes the demand response potential of various industries at a single time point to improve the accuracy of the multi-load demand response potential results.

The structure of this study is as follows. After the introduction, Section 2 describes the methodology used in this paper, and Section 3 presents an empirical analysis. The discussion and conclusions are given in Section 4 and Section 5, respectively.

2. Materials and Methods

The meanings of parameters in the model are summarized in Appendix A.

2.1. Theoretical Response Potential Evaluation Model for a Single Resource

Considering the variation in response types, the theoretical response potential of the response resource $i$ at time $t$ is determined:

$${{\displaystyle f}}_t(i)={{\displaystyle L}}_t(i)\ast {{\displaystyle \lambda }}_i$$

(1)

where $L_t(i)$ is industry $i$’s electrical load at time $t$ and $f_t(i)$ is the industry $i$’s theoretical demand response potential at time $t$. The industry’s flexible load proportion, or the ratio of the average load adjustment amount to the highest load when the demand response is applied, is represented by the ${\lambda }_i$ in the demand response measure.

The difference between the peak period load and the daily minimum load should not be exceeded by the theoretical potential value of industry participation in demand response peaking, and the difference between the daily maximum load and the trough period load should not be exceeded by the theoretical potential value of valley filling.

$$f^{\lim }=\frac{\left|{{\displaystyle l}}_{-}{\displaystyle \sum _{i\in t}{{\displaystyle l}}_i}\right|}{I}$$

(2)

The formula takes into account the following: $l$ is the highest or minimum daily load; $f^{\lim }$ is the maximum potential of peak cutting or valley filling; $t$ is the peak or trough duration; and $I$ is the number of peak or valley periods.

The demand response $F$’s theoretical potential is the lowest value between the two.

$$F=\min \left\{f,f^{\lim }\right\}$$

(3)

2.2. A Model for Assessing the Realizable Response Potential of a Single Resource

2.2.1. Objective Function

The goal function takes cost and peak–valley difference minimization into account. The multi-objective optimization issue is reduced to a single objective optimization problem using the weight coefficient method:

$$F_1=\mathit{min}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{t=t_0}^{t_f}{{\displaystyle D}}_{down}^t(i)}}$$

(4)

$$F_2={{\displaystyle L}}_{\mathit{max}}-{{\displaystyle L}}_{\mathit{min}}$$

(5)

$$F={{\displaystyle \omega }}_1{{\displaystyle F}}_1+{{\displaystyle \omega }}_2{{\displaystyle F}}_2$$

(6)

$${{\displaystyle \omega }}_1+{{\displaystyle \omega }}_2=1,0\le {{\displaystyle \omega }}_1,{{\displaystyle \omega }}_2\le 1$$

(7)

$L_{\max }$ refers to the maximum load; $L_{\min }$ refers to the minimum load; its participation cost in the peaking reaction at time $t$ is $D_{down}^t$; the peaking period’s beginning and ending moments are $t_0$ and $t_f$; $F_2$ is the minimum objective function of peak–valley difference; and the target weight coefficients are ${\omega }_1$ and ${\omega }_2$.

$${{\displaystyle D}}^t(i)={{\displaystyle L}}_t^{down}(i)\ast {{\displaystyle c}}_{down}(i)$$

(8)

where ${{\displaystyle L}}_t^{down}(i)$ represents the increase or decrease in the load at time $t$; $c_{down}(i)$ reduces the cost per unit load for industry $i$.

2.2.2. Constraints

①

Load reduction constraints

Each power industry’s maximum load reduction during the peak cutting period is limited to the current theoretical response potential.

$${{\displaystyle L}}_t^{down}\ast {{\displaystyle DR}}_{t,on}^{down}\le {{\displaystyle f}}_t(i)$$

(9)

The theoretical maximum response potential is denoted by $f_t(i)$ in the formula. $D{R}_{t,on}^{down}$ denotes the presence or absence of peak clipping at time $t$. The value is 1 in the event of a response and 0 in the absence of one.

②

Response duration constraints

The response duration constraint must be introduced because certain devices cannot reply for an extended period of time due to variations in equipment operating circumstances.

$${\displaystyle \sum _{t=0}^{23}{{\displaystyle DR}}_{t,on}^{down}}\le {{\displaystyle t}}^{down}$$

(10)

where ${{\displaystyle t}}^{down}$ indicates the maximum daily load reduction time.

③

Response time constraints

There are response time limits since users’ power usage varies and sometimes they are unable to respond to demand.

$${{\displaystyle DR}}_{t,on}^{down}=0,t\in {{\displaystyle \mathit{\tau }}}_1$$

(11)

The time during which the clipping response cannot be executed is represented by ${\tau }_1$ in the formula.

④

Energy balance constraint

The entire load value following load transfer cannot be greater than the initial load in order to satisfy the industry’s energy balancing requirements.

$${\displaystyle \sum _{t=0}^{23}{{\displaystyle \alpha }}_t\ast }{{\displaystyle L}}_t^{shift}\le 0$$

(12)

If time $t$ is the load acceptance time, then ${\alpha }_t=-1$; if time t is the load transfer time, then ${\alpha }_t=1$. Here, ${\alpha }_t$ denotes the direction of load transfer. ${{\displaystyle L}}_t^{shift}$ stands for load transfer at time t.

The above model is used to evaluate the potential of demand response peak cutting. When evaluating the potential of demand response valley filling, the concept related to peak cutting in the above model can be replaced by valley filling.

2.3. Multi-Load Interaction Response Aggregation Analysis Model

Most conventional methods for evaluating demand response are predicated on a straightforward superposition of an individual user’s maximum response capability. However, in such an evaluation approach, the maximum response potential of each user does not appear at the same time point, neglecting the issue that users’ maximum response potential cannot be fully developed in different periods of time. As a result, the real demand response potential at each time point is determined in this work. Next, by superimposing the sequential phase, the actual demand response potential of various loads is derived. Figure 3 illustrates this.

The formula is as follows:

$${{{\displaystyle f}}_t}^r={\displaystyle \sum _{\mathrm{i}=1}^n{{\displaystyle L}}_{\mathrm{t}}^r(i)}$$

(13)

$f_t^r$ represents the actual demand response potential of multiple loads at time $t$, and $i$ represents industry $i$.

3. Results

3.1. The Basic Information

The peak–valley electricity pricing strategy is adopted by the local populace, business community, and industry. In order to verify the rationality of the model, three industries with greater flexibility in a certain region of China are selected for analysis. The data come from the actual data of a power grid company.

Table 1. Local peak–valley time division and electricity price.

	Peak	Valley	Flat
Timeframe	9:00–11:00, 15:00–22:00	0:00–7:00, 12:00–14:00	Other time period
Price	0.9203	0.3249	0.6226

displays the precise time division and peak–valley electricity pricing.

3.1.1. Residential Industry

The residential industry’s adjustable loads primarily consist of lighting, water heaters, air conditioners, and electric heaters. Among these, the largest load in the summer is the air conditioner; in the winter, the largest loads are the water heater and electric heating. Figure 4 displays the usual daily load curve of the residential industry.

The chart shows that residential industry has a low load in the early morning and a peak load in the noon and evening hours. This indicates a high degree of coincidence with the local peak–valley period and a significant opportunity for peak cutting and valley filling.

3.1.2. Accommodation and Catering Industry

Lighting, air conditioning, cold kitchen storage, and other systems account for the majority of the electrical load in the accommodation and catering industry. Of these, the air conditioning system operates continuously around the clock, and the load change trend resembles that of people’s daily lives. More than 30% of the overall load is accounted for by the lighting system, and more than 40% is accounted for by the air conditioning system, which mostly uses split and central air conditioning. The consumption load of the cold kitchen storage is around 20%. The load characteristic curve is displayed in Figure 5.

Due to the significant influence of human behavior, the accommodation and catering industry has a load characteristic curve resembling that of the residential industry and a higher capacity for demand response.

3.1.3. Wholesale and Retail Industry

The primary adjustable loads for inhabitants in the wholesale and retail industry are those related to air conditioners and lighting. The load characteristic curve is displayed in Figure 6.

Due to industrial features, the wholesale and retail industry has a high daytime load. Additionally, different industry scales have distinct adjustable load proportions and vast variation ranges, which offer higher possibilities for responding to demand.

3.2. Assessment of Individual Industry Demand Response Potential

The demand response potential of the aforementioned three industry categories is assessed using the demand response potential evaluation model built in Section 2. Figure 7, Figure 8 and Figure 9 display the load curves and potential values of the three industry types that are involved in the demand response. Of them, the residential industry accounts for 13% of the adjustable load, the accommodation and catering industry accounts for 23%, and the retail and wholesale industry contributes for 10–30%; the proportion of adjustable load in the retail and wholesale industry is set at 20% in this paper.

Figure 7 shows the potential for demand response in the residential industry. Valley filling potential is represented by a positive number and peak cutting potential is represented by a negative number. The right axis in the figure represents the load before and after the participation in demand response; the blue line is the typical daily load curve before the participation in demand response, and the red line is the result of the model in this paper. The next two graphs have the same format. In the residential industry, demand response times can be measured in minutes or even seconds. It can respond continuously or intermittently within an hour. For example, users can respond constantly from 0:00 to 1:00, or they can respond frequently but for a short time. However, no matter how often they respond during this time, the total response potential is fixed. In other words, the demand response potential at 1:00 is equal to the potential over the time period 0:00–1:00. In general, the residential industry responds sustainably during the filling period, and there is no response period during the peak cutting period, so this is classified as intermittent response.

According to the theoretical demand response potential calculated in Section 2, the theoretical demand response potential of the residential industry’s peak is 27.07 MW, and the theoretical potential of valley filling is 17.27 MW.

Table 2. Demand response potential of the residential industry.

Time	0	1	2	3	4	5	6	7	8	9	10	11
Potential value/MW	9.45	15.96	14.33	13.21	12.47	12.43	13.79	16.28	0.00	0.00	−22.30	0.00
Time	12	13	14	15	16	17	18	19	20	21	22	23
Potential value/MW	0.00	0.00	17.27	0.00	−24.44	−24.30	0.00	0.00	0.00	−27.07	−27.07	0.00

displays the residential industry’s realizable potential for demand response over several time periods. Excluding the non-response period and flat period, the filling period’s response potential ranges from 9.45 MW to 17.27 MW, and its demand response potential peaks around 14:00, matching the filling period’s theoretical capacity. The full theoretical potential of peak clipping was only attained at 2 p.m. and 22 p.m.; other periods fell between 22.3 MW and 24.44 MW below this figure.

The potential for demand response in the accommodation and catering industry is depicted in Figure 8. The accommodation and catering industry does not participate in demand response from 11:00 to 13:00 and 18:00 to 20:00, nor does it respond to the same time frames as the residential industry. The maximum duration of demand response in the accommodation and catering industry is 3 h. The reaction persists throughout the middle period, as shown in the figure, and there is no response potential at 2 o’clock and 6 o’clock. In the flat segment, there is participation in the demand response at 15:00 and 23:00. The maximum demand response potential is 9.27 MW in the filling period and 14.08 MW in the clipping period.

The accommodation and catering industry has a theoretical maximum peak cutting potential of 14.09 MW and a theoretical maximum valley filling potential of 9.43 MW.

Table 3. Demand response potential of the accommodation and catering industry.

Time	0	1	2	3	4	5	6	7	8	9	10	11
Potential value/MW	7.82	8.11	0.00	7.23	7.01	7.28	0.00	9.27	0.00	0.00	−14.08	0.00
Time	12	13	14	15	16	17	18	19	20	21	22	23
Potential value/MW	0.00	0.00	0.00	10.51	−13.09	−14.08	0.00	0.00	0.00	−13.41	−11.65	9.08

illustrates the demand response potential that the accommodation and catering industry can achieve over several timeframes. The filling demand response potential is 0 during the valley period because of the restricted reaction duration between 2:00 and 6:00. The filling demand response reaches its realizable maximum potential at 7:00. Additionally, there is a time when the demand response potential is 0 due to the short reaction duration, and at 17:00, the realizable maximum peak demand response potential is reached. The highest filling demand response potential in the flat sector is 10.51 MW, with participation from 15:00 and 23:00 as well. According to the method of calculating the theoretical demand response potential of peak and valley, the theoretical demand response potential of the flat segment is 11.79 MW, so the demand response potential of 15 points and 23 points is reasonable.

The wholesale and retail industry’s potential for demand response is depicted in Figure 9. The wholesale and retail industry does not respond from 9:00 to 11:00 and from 15:00 to 17:00; response times are limited to four hours. As can be seen from the figure, the flat segment hardly participates in the demand response. There is a maximum filling demand response potential of 17.05 MW during the valley period and a maximum clipping demand response potential of 38.1 MW during the peak period, neither of which obtain the theoretical maximum demand response potential.

Table 4. Demand response potential of the wholesale and retail industry.

Time	0	1	2	3	4	5	6	7	8	9	10	11
Potential value/MW	7.55	17.05	0.00	13.60	12.65	12.35	13.47	0.00	6.12	0.00	0.00	0.00
Time	12	13	14	15	16	17	18	19	20	21	22	23
Potential value/MW	0.00	5.85	13.68	0.00	0.00	0.00	−38.10	0.00	−35.52	−28.72	0.00	0.02

shows the demand response potential of the wholesale and retail industry during different periods. Excluding the non-responsive period and the period of zero demand response potential, the demand response potential of valley filling ranges from 0.02 MW to 17.05 MW, and the demand response potential of peak cutting ranges from 28.72 MW to 38.1 MW.

3.3. Multi-Load Demand Response Potential Evaluation

The demand response potential of multi-load aggregation was evaluated according to Formula (13) in Section 2, and the results are shown in Figure 10.

In Figure 10, different colors represent different industries, and the result is the aggregate demand response potential of the three industries. The demand response potential varies greatly at different times. Peak cutting demand response potential is maximal at 21:00, reaching 69.20 MW, while the maximum valley filling demand response is at 1:00, reaching 41.12 MW; the potential of demand response even decreases to 0 at certain time points.

4. Discussion

Since the data in this paper are used for the first time in this paper, in order to verify the superiority of the three-stage demand response potential assessment model framework designed in this paper, we combined it with the theoretical methods of other studies to compare it in three aspects. In addition, we also analyze the sensitivity of the model.

4.1. Comparison of Individual Industry Results

In this section, the elastic coefficient method [27] mentioned in other studies is compared with the results of the model in this paper, and the results are shown in Figure 11. In Figure 11, the gray curve represents the original load of the accommodation and catering industry that is not involved in the demand response; the green curve is the result calculated by using the elastic coefficient method, and the red curve is the method used in this paper. On the whole, the two methods can achieve the effect of peak cutting and valley filling, but the results obtained by the elastic coefficient method vary greatly compared with the original load curve, and the specific comparison of the results of the two methods is shown in

Table 5. Comparative analysis of the results of the two methods.

	Elastic Coefficient Method	Textual Method
Maximum load (MW)	76.36	69.12
Minimum load (MW)	36.22	33.16
Difference between peak and valley (MW)	40.14	35.96
Similarity to the original data curve (MW)	11.65	5.53

. Among them, the average value of the absolute difference between the two numbers in the corresponding positions of the two groups of data is used to describe the similarity of the two groups of data. The smaller the value, the more similar the two columns of data are.

As can be seen in Table 5, the maximum peak-to-valley load difference of the load curve obtained by the elastic coefficient method is larger than the result in this paper, the similarity to the original load curve is less than the result in this paper, and the demand response potential of some moments is also greater than the result in this paper. According to the traditional theory, the greater the demand response potential, the better the model effect; however, in practice, there is the theoretical maximum demand response potential at every moment, and the greater the demand response potential at the time point, the closer it is to the theoretical potential. In the case of not exploiting the demand response potential of flexible resources as much as possible, the probability will be greater, because the model’s results are inaccurate due to too few factors being taken into account. The calculation results of this paper are in line with the actual situation, and the model is reasonable.

4.2. Comparison of Multiple Load Aggregation Results

When studying the demand response potential of a region, some studies have analyzed the demand response potential of a single industry but re-analyzed the regional load instead of using a bottom-up aggregate analysis method when analyzing the whole region [28]. Study [26] introduced the concept of the aggregator, but the evaluation of demand response potential in multi-load aggregation has often focused on the maximum potential while ignoring the time-varying demand response potential. This section focuses on the effect of timing on the demand response potential of multi-load aggregation.

Table 6. Three industries’ peak-filling theoretical maximum potential.

Type of Industry	Valley Filling Potential	Peak Clipping Potential
Residential industry	17.27 MW	27.07 MW
Accommodation and catering industry	9.43 MW	14.09 MW
Wholesale and retail industry	24.59 MW	43.82 MW
Total	51.29 MW	84.98 MW

displays the demand response potential of multi-load aggregation using traditional methods.

Table 7. Demand response potential under multi-load aggregation.

Time	0	1	2	3	4	5	6	7	8	9	10	11
Potential value/MW	24.82	41.12	14.33	34.03	32.12	32.07	27.26	25.55	6.13	0.00	−36.37	0.00
Time	12	13	14	15	16	17	18	19	20	21	22	23
Potential value/MW	0.00	5.85	30.95	10.51	−37.53	−38.38	−38.10	0.00	−35.52	−69.20	−38.72	9.11

displays the demand response potential of the multi-load aggregation computed in this work. Using the traditional method, the demand response potential of valley filling is 51.29 MW, and the demand response potential of peaking is 84.98 MW. The maximum peak clipping demand response potential under the proposed method is 69.2 MW, which is 15.78 MW less than that of the traditional method, representing a decrease of 18.57%; the maximum valley filling demand response potential is 41.12 MW, which is 10.17 MW less than that of the traditional method, representing a decrease of 19.83%. The peak clipping and valley filling potential values are smaller in other periods, which accurately describes the demand response potential of multi-load polymerization. The results are more accurate than those of traditional methods.

4.3. Comparison of Objective Function Results

In the process of constructing a demand response potential evaluation model, some studies only have a single-objective function and focus on the cost minimization objective function. For example, study [20] constructs an adjustable potential evaluation model of demand response with a lower operating cost as its goal, and study [28] constructs a potential evaluation model of demand response with the minimum power consumption per hour as the goal. In this paper, a double-objective function evaluation model is constructed, which considers the minimum cost and the minimum peak–valley difference. The results under different objective functions are shown in Figure 12.

In Figure 12, the black curve is the original load curve, the blue curve is the load curve whose objective function is the lowest peak–valley difference, the cyan curve is the load curve whose objective function is the lowest cost, and the red dashed line is the load curve under the double-objective function of this paper. It can be seen that the main differences are concentrated in 0:00–7:00, 12:00–15:00, and 17:00–22:00. On the whole, the models under the three objective functions can all achieve the effect of peak cutting and valley filling, and the overlap period is less, indicating that different objective functions have a great impact on the evaluation results of demand response potential. The potential values of each period under the three objective functions are shown in

Table 8. The potential value of the wholesale and retail industry under different objective functions.

	Peak–Valley Difference Minimization	Two-Objective Function	Cost Minimization
0:00	7.22	7.55	0.00
1:00	5.13	17.05	16.30
2:00	0.00	0.00	14.27
3:00	7.65	13.60	12.87
4:00	9.06	12.65	0.00
5:00	10.33	12.35	0.00
6:00	6.47	13.47	12.76
7:00	0.00	0.00	13.57
8:00	2.92	6.12	2.22
9:00	0.00	0.00	0.00
10:00	0.00	0.00	0.00
11:00	0.00	0.00	0.00
12:00	0.00	0.00	12.89
13:00	1.82	5.85	20.67
14:00	3.20	13.68	20.68
15:00	0.00	0.00	0.00
16:00	0.00	0.00	0.00
17:00	0.00	0.00	0.00
18:00	−12.84	−38.10	−37.47
19:00	7.22	7.55	0.00
20:00	5.13	17.05	16.30
21:00	0.00	0.00	14.27
22:00	7.65	13.60	12.87
23:00	9.06	12.65	0.00

Note: In the table, the valley is shown in orange, the peak is shown in green, and the period when the industry is not responsive is shown in yellow; some of the peak period is not a responsive period, also shown in yellow.

.

As can be seen from Table 8, under the double-objective function, the grain filling effect is more obvious between 0:00 and 7:00, with the maximum potential value at most time points. The grain filling effect at 13:00–14:00 is in the middle position, and the peak cutting period at some time points is obvious. Considering only the smallest difference between peak and valley, the effect of peak cutting and valley filling is the least obvious. The demand response potential of the double-objective function used in this paper is 0.71% lower than that of the single objective with minimal cost. The overall demand response potential was reduced by 1.32% compared to the single goal of minimizing the peak–valley difference.

4.4. Sensitivity Analysis of Adjustable Load Proportion

The percentage of variable load in the retail and wholesale industry ranges from 10% to 30%, depending on the size. This paper uses a 20% adjustable load to calculate the industry’s potential demand response. The load curves for the retail and wholesale industry at different adjustable load ratios are shown in Figure 12.

Figure 13 illustrates that the key factor influencing whether a response occurs over a given period is the load’s change, which occurs very regularly. The change in the fraction of adjustable load has less of an impact. The difference from the initial load grows as the proportion of changeable load increases. The demand response potential of different periods under different adjustable load ratios is shown in

Table 9. The potential value of the wholesale and retail industry under different adjustable load ratios.

	0.1	0.15	0.2	0.25	0.3
0:00	0.04	3.21	7.55	10.83	9.26
1:00	8.52	12.78	17.05	21.31	25.57
2:00	0.00	0.00	0.00	0.00	0.00
3:00	6.80	10.20	13.60	17.00	20.40
4:00	6.32	9.49	12.65	15.81	18.97
5:00	6.18	9.27	12.35	15.44	18.53
6:00	6.73	10.10	13.47	16.83	20.20
7:00	0.00	0.00	0.00	0.00	0.00
8:00	0.04	2.18	6.12	11.15	21.00
9:00	0.00	0.00	0.00	0.00	0.00
10:00	0.00	0.00	0.00	0.00	0.00
11:00	0.00	0.00	0.00	0.00	0.00
12:00	0.00	0.00	0.00	0.00	0.00
13:00	5.85	5.85	5.85	5.85	5.85
14:00	10.69	13.68	13.68	13.68	13.68
15:00	0.00	0.00	0.00	0.00	0.00
16:00	0.00	0.00	0.00	0.00	0.00
17:00	0.00	0.00	0.00	0.00	0.00
18:00	−19.05	−28.57	−38.10	−47.63	−57.15
19:00	0.00	0.00	0.00	0.00	0.00
20:00	−17.76	−26.64	−35.52	−44.40	−53.28
21:00	−14.36	−21.54	−28.72	−35.90	−43.08
22:00	0.00	0.00	0.00	0.00	0.00
23:00	0.00	0.00	0.02	0.02	0.04

Note: In the table, the valley is shown in orange, the peak is shown in green, and the period when the industry is not responsive is shown in yellow; some of the peak period is not a responsive period, also shown in yellow.

.

Table 9 shows that for the majority of the time, demand response potential rises in tandem with the proportion of adjustable load. The main reason for this is that the increase in the proportion of adjustable load leads to an increase in the theoretical maximum demand response potential, and the upper limit of achievable potential also increases. The demand response potential is zero at 2:00 and 7:00 for every percentage of adjustable load. The primary justification for not responding between 2:00 and 7:00 is to take into account the response time limits. After reaching a certain value, the demand response potential at 13:00 and 14:00 does not rise, indicating that it has reached its maximum demand response potential at that particular moment. At 00:00, with the proportion of adjustable load increasing to 0.3, the demand response potential shows a downward trend from 10.83 MW to 9.26 MW.

5. Conclusions

With the increase in the number of different flexible resources, an increasing number of uncertain factors will have a certain impact on the stability of the power grid. It is becoming more and more crucial to appropriately assess demand-side resource response capacity in order to maintain the stability of the electrical grid and encourage sustainable development. Based on this background, this study proposes a three-stage demand response potential evaluation model of multi-load aggregation based on time series and industry features to assess the potential for demand response. The results show that the three-stage demand response potential assessment model proposed in this paper is reasonable and can effectively reduce expectations of industry demand response potential, make results more realistic, and provide accurate theoretical support for the subsequent practical applications and decision making of power grid companies. The following are our conclusions:

• Compared with the calculation results of the traditional theoretical demand response potential, the calculation results of the three industries in this model can reach the theoretical demand response potential at some time points, and the realizable potential at other time points is smaller than the theoretical demand response potential. The main reason for this is that due to the characteristics of the industry, the industry is not responsive or not fully responsive at certain timepoints. Demand response potential will not reach the theoretical value at every point in time.
• Compared with the multi-load polymerization results of the traditional method, the timing factors were considered in the polymerization process, and the results showed that the polymerization results were better than those of the traditional method. Following polymerization, the peak clipping potential was lowered by 19–100% and the valley filling potential was reduced by 20–89% when compared to the theoretical potential value. The demand response potential calculated by the traditional method is the maximum demand response potential under ideal conditions, while the actual demand response potential calculated in this paper is only equal to or less than this value. Following aggregation, the peak cutting potential will be lowered by 100% because the non-response periods of the three industries overlap and the demand response potential of individual time points is 0. The potential reduction ratio of the majority of time points is close, and the load variations during the filling period are more balanced. The proportion of potential reduction at each time point in the peak cutting period fluctuates greatly. The subdivision of the time scale of demand response potential assessment is helpful for the reasonable allocation of power grid resources, thus ensuring the stability of the power grid, and can be used as the basis for research into power grid scheduling and market decision making so as to make research results more refined.
• Compared with traditional research that only considers a single target, the results of this paper are more accurate. Compared with only considering the cost minimization target, the reduction is 0.71%, and compared with only considering the peak–valley minimization target, the reduction is 1.32%. The use of numerous objective functions improves resource utilization, lowers decision making costs, and advances the sustainable development of the power grid by bringing the evaluation results of demand response potential closer to reality.

It can be seen from the research in this paper that there are many factors that affect the result of demand response potential assessment. In order to bring the assessment result closer to reality, more factors should be considered when constructing the assessment model, and appropriate objective functions should be set up. The demand response potential assessment model can be expanded in the following ways in further research:

• To improve the accuracy of the evaluation outcome, psychological and environmental aspects might be added to the objective function or constraint.
• Taking into account reorganization of peak–valley division to more accurately represent the features of the sector.
• This paper only evaluates the demand response potential of load aggregation in three industries, and other factors such as power grid stability and inter-industry influence need to be taken into account when expanding to other regions.