Analysis of multi-objective cooperative optimization strategy for residential load under extreme weather

In recent years, the problem of seasonal power supply shortages in extreme weather has frequently occurred across China, which has brought great inconvenience to people’s production and life. At the same time, with the advancement of the energy revolution, the proportion of electric energy in the terminal energy is increasing, which also poses a severe challenge to China’s energy security. Our research, by constructing a residential electricity consumption model and conducting multiple electricity price response experiments, has collected data that assesses various factors involved in user responses. It has also explored and inferred the impact of these factors on user-side responses. This study introduces new research directions aimed at alleviating electricity supply-demand imbalances during different periods, contributing to the optimization and enhancement of the national power system.


Introduction
In recent days, various regions in China have experienced frequent incidents of occasional power shortages during extreme weather conditions, especially during the high electricity demand peaks in summer and winter.This has led to the implementation of temporary measures such as power rationing in some areas, causing noticeable inconveniences in people's production and daily lives [1].Meanwhile, as the ongoing energy revolution continues [2][3], the proportion of electricity in the end-use energy mix is steadily increasing.As one of the world's largest energy-consuming nations, China's demand for electricity will further accelerate with the continuous pace of urbanization and industrialization [4].In this context, traditional national and grid construction methods would require substantial capital investments.Therefore, a scientific analysis of and adjustments to local electricity demand become critically important.
Electricity demand response, as a significant measure in demand-side management [5], is widely applied worldwide.Particularly, demand response based on price signals and incentive measures has received increasing attention for guiding users towards more energy-efficient behavior [6].Both domestic and international scholars have initiated research on comprehensive energy services and demand response for industrial and commercial users.However, research in the area of comprehensive energy services and demand response for urban and rural residents is still in its early stages [7][8].Due to the characteristics of residential electricity consumption including small individual loads, dispersed distribution, strong randomness, and low controllability, it poses significant challenges for demand-side management in households [9].It is worth noting that there is currently a lack of research databases focusing on the individual demand response behaviors of Chinese residents.Therefore, the widespread implementation of residential demand response still faces the challenge of insufficient foundational sample data.Our study assesses user participation in response and explores and deduces the impact of these factors on user-side responses.

Data sources and data collection
This essay conducts an investigation by collecting data on residential electricity conservation responses in pilot areas following the sending of incentive text messages.It selects electricity conservation response rate and per-household electricity savings as metrics for measuring residents' responsiveness to electricity demand.Factors such as subsidy rates, geographical location, baseline values and meteorological variables (temperature, humidity, wind speed) are considered as influencing factors.As shown in figure 1, subsidized prices will significantly affect the level of residents' demand response, showing a negative correlation.Because the sample size is too small and affected by factors such as large price fluctuation and time effect, there is a reverse effect.

Figure 2.
Correlation between power saving response rate, power saving per household and regional and benchmark power.
As can be seen from figure 2, there are obvious regional differences between the residents' powersaving response rate and the average power-saving amount per household.Among county residents, township residents and rural residents, the average power-saving amount per household of county residents is the highest, while that of rural residents is the lowest, and the power-saving response rate of township residents is higher than that of county residents and rural residents.Figure 3 shows the relationship between the power saving per household and the power saving response rate and the temperature difference, humidity difference and wind difference.There is a positive correlation between the average household power saving, power saving response rate and the absolute values of temperature difference and humidity difference.The sample wind difference only exists between -1 and 1, and the average household power saving and response rate are the same.
The price decline strategy refers to the gradual reduction of the subsidized price in the three power responses which are respectively 10 yuan/KWH, 8 yuan/KWH and 5 yuan/KWH, which is only applied to the six-country communities.The price increment strategy refers to the gradual increase of the subsidized price in the three power responses which are respectively 2 yuan/KWH, 5 yuan/KWH and 8 yuan/KWH, which is applied to other cells in the data set except the six cells.With the passage of time, the overall response rate of users who applied the price-decreasing strategy and price-increasing strategy continued to rise, according to the experimental data in Table 1.In each response stage, the response rate of users applying the increasing-price strategy is higher than that of No reply 236 Table 2 and 3 indicate that the response of users applying the price-decreasing strategy and the priceincreasing strategy both reflect high user viscosity, that is, after users make a reply in a certain power response stage, the proportion of users still making a reply in the next power response stage is larger.In the reply users, the proportion of actual energy-saving users can better represent the user's willingness to participate.In Figures 4, among the users who applied the price reduction strategy, the proportion of actual power-saving users in the first round of power response was about 50%.Then, with the continuous reduction of the subsidy price, the proportion of actual power-saving users decreased rapidly.
Figure 5 shows that among the users who applied the price-increasing strategy, the increase of subsidy price increased the proportion of actual power-saving users to a certain extent, but the second increase of subsidy price had a negative effect on the increase of actual power-saving users.The marginal effect was diminishing.Once again, it confirms that the willingness of users to participate in the power response is sensitive to the subsidized price.
In addition, in the third response, temperature and humidity have increased significantly, which has a certain impact on the basic electricity consumption of residents.The impact of factors other than subsidized prices on the power saving of users still needs to be further verified by experiments.According to figure 6, for the users with the decreasing price strategy and the increasing price strategy, the baseline power of the users who reply is higher than that of the users who do not reply.Among the users who applied the price reduction strategy, the average power saving of the replying users was lower than that of the non-replying users, indicating that the price reduction strategy caused the loss of participants to a certain extent.They were not willing to take the initiative to save power again under the lower price subsidy.

Cluster analysis of user response behavior
According to the power-saving amount of users who reply to SMS in all three rounds, K-means cluster analysis is carried out for users who apply the decreasing-price strategy and the increasing-price strategy respectively.
The specific power-saving amount of each household in the three responses in the original data is taken as the clustering condition.K = 3 is set (that is, three clustering centers are selected) to construct a cluster and obtain three clustering labels of 0, 1 and 2. The clustering results are visualized as follows: As shown in figure 7, The clustering results of users applying the decreasing-price strategy and the increasing-price strategy are analyzed respectively.In Figure 8, purple indicates the user whose cluster label is 0, green indicates the user whose cluster label is 1, and yellow indicates the user whose cluster label is 2. The line chart shows the change in the average power saving of the three types of users, the pie chart shows the proportion of the three types of users in the number of reply users and the scatter chart shows the average base power of the three types of users.
In the user group of the application of the price reduction strategy, the average power saving of "0" users increases first and then decreases with the increase of subsidized price.On the whole, the change of subsidized price has a direct impact on its power-saving behavior, that is, the reduction of subsidized price will reduce the enthusiasm of such users.
"1" class users showed a very high enthusiasm for participation in the first electricity response, but the amount of electricity saving gradually decreased in the later period."2" type of users in the first two power responses in the power saving floating around 0 indicating that they did not participate in the first two basic response actions still maintain the habit of electricity consumption, which is a group of no response action.Among the users who apply the price reduction policy and reply to SMS messages three times, the number of users in descending order corresponds to the groups labeled 2, 0, and 1 respectively.According to figure 9 and 10, in the user group of the application of price increase strategy, "0" users in the first response season of high power compressed the power saving space after the power saving continued to decrease with the growth of the subsidized price, while in the third response, due to the impact of the time effect (September 5 is the weekend), its power-saving difference continued to fall.However, in the end, its power consumption level has an overall decline.The power saving of "1" users increases first and then decreases with the growth of the subsidized price.In the second response period, the power consumption changes from negative to positive due to the price incentive, and the growth is obvious, but it decreases to negative in the third response.In the first two response activities, the power saving amount of "2" users fluctuated around 0 value, that is, they did not participate in the response actions, and the power saving amount achieved a relatively obvious increase in the third response activity.
From the perspective of the proportion of three types of users and the power consumption benchmark, the proportion of users who apply the price escalation strategy and reply to SMS three times corresponds to the groups labeled 2, 1 and 0 respectively from high to low, of which "2" users account for more than 50%.From the difference and proportion of the three types of users' residence, county residents occupy the largest proportion of "0" users and "1" users, rural residents occupy the largest proportion of users and the proportion of township residents in the three types of users is the same.

Conclusion
The main conclusions are as follows: (1) Subsidy prices are negatively correlated with residential demand response, but there is a need to further investigate potential reverse effects.
(2) Regional differences significantly influence residential electricity conservation behavior with county town residents conserving the most, rural residents conserving the least and township residents exhibiting higher response rates, necessitating consideration in policy and resource allocation.
(3) Temperature, humidity and wind speed variances positively correlate with electricity conservation responses, offering a fresh perspective for more accurate demand response predictions.
(4) Subsidy prices have a significant impact on user participation in electricity response with users under a price-increasing strategy showing higher response rates.
(5) Cluster analysis reveals differences in electricity conservation behavior among user categories, providing valuable insights for crafting effective policies and optimizing the power system.

Figure 1 .
Figure 1.Correlation between power saving response rate, power saving per household and subsidy unit price.

Figure 3 .
Figure 3. Correlation between power saving response rate, power saving per household and temperature difference, humidity difference and wind difference.

Figure 4 .
Figure 4. Subsidy price reduction strategy -power saving ratio of SMS reply users.

Figure 5 .
Figure 5. Subsidy price increment strategy -power saving ratio of SMS reply users.

Figure 6 .
Figure 6.Comparison of average baseline electricity and average power saving of users who replied and did not reply.

Figure 7 .
Figure 7. Clustering results of power saving amount of users with decreasing price and increasing price strategy.

Figure 8 .
Figure 8. Price decline strategy -Power saving, benchmark power and number of users of three categories.

Figure 9 .
Figure 9. Price increment strategy -power saving and number of three types of users.

Figure 10 .
Figure 10.Price escalation strategy -baseline electricity and heterogeneity of three types of users.

Table 1 .
Comparison of the proportion of SMS replies of subsidy price increasing and decreasing strategies.

Table 2 .
Subsidy price decline strategy -SMS reply user viscosity.

Table 3 .
Subsidy price increment strategy -SMS reply user viscosity.