An auxiliary optimization method for electric heating renovation based on using a clustering algorithm

The large amount of pollutants emitted by coal heating in winter is one of the main causes of haze, which brings great trouble to people’s lives. To reduce air pollution caused by coal burning and improve air quality, the state advocates the transformation of traditional electric heating methods to accelerate the transformation of China’s energy system to a clean and low-carbon model and improve the utilization rate of renewable energy in China. Therefore, this article through the calculation of the residual capacity of the retrofit and the calculation of the air conditioning load to assist the electric heating transformation. Firstly, the average power of the transformer during a high power period is calculated instead of taking the maximum power directly, which solves the problem of small residual capacity caused by a large maximum load rate and maximizes the transformable capacity. Secondly, the cluster analysis of air conditioning heating as one of the typical electric heating methods is carried out by the K-means clustering method, and the air conditioning load is obtained as the data reference during the electric heating transformation to assist the optimization transformation of electric heating. The two methods are further studied and verified by two examples, and the theory guides the practice to assist the electric heating transformation and achieve the goal of energy saving and emission reduction.


Introduction
At present, with the introduction of national energy-saving and emission-reduction policies, low-carbon economic benefits are increasingly valued.Electric heating, as a new type of heating method, is also receiving great attention.Although central heating is adopted in the northern region, due to factors such as weather, season, and power supply time, some residents may use electric heating during non-heating periods, which can cause some parts of the power grid to exceed 80% of the load and increase the pressure on the power grid.

Research status
With the continuous popularization of renewable energy and the improvement of power systems, electric heating will become more environmentally friendly and sustainable.Domestic scholars' research on electric heating mainly focuses on the effectiveness, economy, and system operation of heating methods.
• Chen proposed a random forest short-term electric heating load data prediction model based on isolated forests and multiple stepwise feature selection, as well as a nonlinear multi-dimensional interpretable evaluation prediction model algorithm to predict and analyze the short-term electric heating load of universities [1].
• Analysing the urgent need for Australian households to reduce energy consumption through more efficient heating and cooling systems as rising temperatures and higher energy costs create, Peukes Ina Eileen deconstructed reference gas heaters and air conditioners and assessed their material composition [2].• Kiran P, by considering a restructured electricity market, Deploy a new interactive Variant Roth-Erev (VRE) combining GenCo's collaborative learning effects The analysis shows the effectiveness of the co-learning method used by agents in the power market.The method is tested on a standard IEEE system and the performance of the technology is verified on a real Indian power grid network [3].• Yang et al. verified the effectiveness of the distributed electric heating cluster hybrid control strategy by simulating and analyzing the wind power output consumption, start/stop of electric heating equipment, and indoor temperature changes under the distributed electric heating cluster hybrid control strategy [4].• Zhang used the enthalpy method model to establish a simplified mathematical model for the phase change thermal storage electric heating module.The reliability of the model was verified by comparing it with experimental data, and the thermal storage and release characteristics of the module were preliminarily analyzed [5].• Wang et al. researched the expansion and planning issues of the power grid caused by the connection of electric heating equipment in the electric thermal coupling energy system and obtained a distribution system planning plan that considers the connection of electric boiler equipment [6].• Yan et al. conducted in-depth research on distributed electric heating as the research object, focusing on exploring the potential of load-side resource regulation and promoting the mechanism of source-load interaction.They reduced the peak valley difference of the load curve, maximized the revenue of load aggregators, and reduced user heating costs [7].

Research content and innovation points
After research, traditional electric heating renovation is achieved by estimating the maximum power of transformers through experience and calculating the remaining capacity of distribution transformers to achieve optimization of electric heating.This method optimizes the waste of power resources to a certain extent.However, in sudden situations, there is a certain degree of error when facing the power mutation point within the normal range of the transformer.Therefore, to provide relevant departments with a more accurate remastered surplus, this article will assist in the electric heating renovation of newly developed residential areas through the following two aspects.
• The first is the calculation of the remaining exploitable capacity of the distribution transformer.Based on the annual power distribution data of 96 points in the Xinfa community, the remaining capacity for power supply and heating renovation is calculated by calculating the maximum load rate during the high-power period of transformer distribution.• The second is the calculation of the air conditioning load.Based on the annual power variation trend of the distribution transformer, the cluster analysis method is used to divide the seasons when air conditioning is used and the seasons when air conditioning is not used, and the air conditioning load is calculated.The analysis of the remaining open capacity of the distribution transformer can use a more scientific method to estimate the modifiable amount and can resist the impact of the maximum power mutation within a reasonable range on the remaining exploitable capacity, making the data more realistic and accurate.The calculation of air conditioning load can provide data support for the renovation process, to better assist the electric heating renovation of newly developed residential areas.By using these two methods, more accurate transformer capacity and air conditioning load can be obtained compared to traditional electric heating renovation.Subsequently, a specific analysis of the transformer capacity and air conditioning load in a residential area in Beijing in 2020 is conducted to further verify the feasibility of the method, thereby assisting in electric heating renovation, improving the reasonable utilization of

The problems of traditional electric heating methods
Although the research and development, investment, and utilization of new electric heating equipment have effectively reduced the emissions of harmful substances such as carbon dioxide and nitrogen oxides, and also significantly improved air quality, this traditional electric heating method still faces many problems and huge challenges in its development, which are specifically manifested in the following three aspects.
• The first is resource waste.From the perspective of distribution resources, using traditional methods to estimate the remaining modifiable capacity of electric heating will be smaller than the true value, so the capacity during the electric heating renovation will be slightly smaller, resulting in transformers that should be within a reasonable load range being in a low load state, causing waste of power resources.• The second is the high pressure on the power grid.From the perspective of power grid enterprises, the centralized use of electric heating equipment will bring a surge in load to the local power grid.To improve the adaptability of the power grid to the user power supply, it is necessary to modify the existing access methods, equipment conditions, and ability to resist power outage risks.The cost and engineering volume of the modification also puts great pressure on the power grid enterprises.• The third is that there are many heating methods.From the perspective of residential heating methods, there are other heating methods such as electric heating and thermal heating in newly developed residential areas.Due to the diversity of heating methods, relevant departments do not have a specific reference value during the renovation process, making electric heating renovation more difficult.The core of this article is to assist in the optimization of electric heating renovation and provide data foundation support for relevant departments.

Calculation of removable capacity
To provide a more accurate residual capacity for the distribution transformer and better assist in the completion of the electric heating renovation, this section will establish a modifiable residual capacity model based on the 96-point power data of the transformer (as shown in Figure 1) to study the residual capacity of the distribution transformer and assist in the planning of the electric heating renovation.the following aspects: first, processing the missing values of the 96-point power obtained; second, processing the data that does not meet the reasonable range, that is, calculating the power values of the transformer's maximum capacity exceeding the reported capacity, which is all within the unreasonable range and needs to be discarded; third, correcting the sudden changes in the data filled with missing values.If there is a point mutation in the 96-point power data, which is greater than 1.7 times the previous point, it will be replaced with the previous value (through curve validation, the most mutation occurs when the ratio of the previous data to the subsequent data is k=1.7, which is considered a mutation data when k ≥ 1.7, so the mutation data can be replaced with the previous value), and the fourth is to screen data that meets the rules for further processing.

Data calculation.
Based on the normal data obtained after processing and the definition of transformer overload, we establish a threshold calculation rule for the high power period of transformer operation and calculate the remaining modifiable capacity according to this rule.To calculate the scientific and reasonable maximum power of transformers, the transformers must be in a high-power operating state.After searching for data, it was found that the transformer can continue to operate for 180 minutes when overloaded by 10%, which is 110% of the transformer load.This means that the high power period is set as the highest and continuous three hours of transformer operation power throughout the day.Subsequently, we perform the following calculations on the data: • We process the daily 96-point data of the transformer into 24-point data (average the 4-point data per hour); • We calculate the daily maximum power.First, we determine the high power period of each day: we find the hour with the highest power of the day and mark it as two hours before and after the maximum power.If the power at the corresponding time is greater than 90% of the maximum power of the day, we mark it as 1, otherwise, mark it as 0. We observe the hourly data marked with 5 to identify consecutive high power periods: if the continuous period marked with 1 is greater than or equal to 3 hours, we select the three consecutive hours containing the highest power as the high power period; if marked as 1 is a discontinuity in the period, then we select the three consecutive hours including the highest power and marked power as the high power period; if there are no marked hours except for the highest power, we directly select the three consecutive hours closest to the highest power (including the hour where the highest power is located).Finally, we calculate the average power during the high power period of each day, which is the highest power of the day.• We calculate the maximum power of the transformer throughout the year.We calculate the maximum power for 365 days per day throughout the year, where the maximum value is the annual maximum power of the distribution transformer.• Based on the maximum power of the distribution transformer obtained in the previous step ω, combined with the multiplication of the distribution transformer table k, and the reported installed capacity C, we calculate the maximum load rate of the transformer throughout the year η.The calculation formula is as follows: • We calculate the remaining capacity ΔC of transformers that can be used for electric heating renovation by using the reported installed capacity C, and maximum load rate η by using the following formula: 2.2.3 Summary.After calculation, the difference between the remaining capacity obtained and the capacity obtained through traditional electric heating renovation is the modifiable capacity.This portion of capacity can be used for other purposes to make more reasonable use of transformer power.

Air conditioning load calculation
As one of the common winter heating methods, air conditioning has important reference significance for the renovation of electric heating.Therefore, this section will take air conditioning as an example to calculate the load of air conditioning heating and provide relevant departments with load data for using air conditioning heating, to better estimate the load of other electric heating methods.
To make the seasonality more apparent, K-Means clustering was performed on the average power of transformers for each month throughout the year.We identify the season in which each transformer uses air conditioning this year (default the high-power season as the season in which air conditioning is used) and classify the transformer into K categories based on the clustering results.Figure 2 shows the model for calculating air conditioning load.The specific calculation steps are as follows: • We extract 96-point power data for each transformer and calculate the daily average power of each transformer.• We calculate the monthly average power, maximum power, and variance of the transformer based on the results of the previous step.• We cluster the monthly data of each transformer in 2020 and determine the number of clusters based on the curve contour coefficient.We cluster the data based on the input data and the obtained number of clusters K. • We export the clustered data and observe the characteristics of each type of data, calculate their power for 2019 and 2021 respectively, and observe the curves.• Then we divide the data processed in the previous step into two parts based on the season when air conditioning is used and the season when air conditioning is not used.• We calculate the average load between the seasons when air conditioning is used and the seasons when air conditioning is not used, and make a difference, believing that the difference is the air conditioning load.(When using air conditioning in both summer and winter, winter is the season for using air conditioning for heating).The air conditioning load obtained through calculation can provide references for other electric heating systems to better assist in electric heating renovation.

Examples of removable capacity
To study the remaining capacity that can be retrofitted, this section selects the 96-point data of the annual transformer power data of a residential area in Changping District, Beijing in 2020.We average the hourly data to obtain the 24-point data in Table 1.The power variation curve is shown in Figure 3.Then, we obtain the power data for the hour with the highest power in the 24-point data in the table, which is 1.7845 kW at 19 h.We observe the transformer power before and after 19 h.If the power at a certain point is greater than 90% of the maximum power (1.6061 kW), we mark it as 1, otherwise, mark it as 0. The results are shown in Table 2.
Table 2 Therefore, the three consecutive hours of 17 h, 18 h, and 19 h were ultimately selected as the highpower periods of the day.After calculation, the average power of the 12 o'clock data within these 3 hours is 1.6734 kW, which is considered to be the maximum power of the day.By analogy, we calculate the maximum power per day for 365 days throughout the year, compare and select the maximum daily power within 365 days, and this maximum value is the maximum power of the transformer, which can be used to calculate the remaining capacity for retrofitting.

Calculation.
The maximum power of the transformer in the community in 2020 was finally obtained to be 1.675 kW.After inspection, the reported installed capacity of the transformer was 315 kW, and the multiplication rate in the table was 80.The maximum load rate and remaining capacity that can be modified can be calculated by using the following formula.
• Maximum load rate=(maximum power × multiplication of the table)/reported capacity • Remaining capacity=contract capacity × 80% -contract capacity × maximum load rate After calculation, the maximum load rate of the transformer is 42.54%, and the remaining modifiable capacity is 118.00 kW.

Verification.
If the maximum power value is used as the maximum power for calculation, the maximum power of the transformer in the community is 1.785 kW.Taking the reported installed capacity of the transformer as 315 kW and the multiplication rate of the table as 80, the highest load rates are 45.33% respectively, and the remaining modifiable capacity is 109.21kW.118.00 kW>109.21kW.The method of directly taking the maximum power as the maximum power to calculate the remaining modifiable capacity is smaller than the actual remaining capacity.Therefore, the data calculated by statistical analysis to obtain the maximum power is more accurate and can serve as a theoretical basis to guide practice.

Air conditioning load example
To study the air conditioning load situation and provide a reference for the modifiable capacity of other electric heating methods, this section calculates the air conditioning load by analyzing the electricity consumption of some residential areas in Changping District, Beijing in 2020.
We perform K-Means clustering on the average daily power of transformers throughout the year to identify the season in 2020 when each transformer used air conditioning (default the high power season throughout the year to the season when air conditioning was used).According to the clustering results, the stations are divided into three categories: higher power in summer compared to other seasons, higher power in summer and winter compared to spring and autumn, and higher power in winter compared to other seasons.The following is the calculation process of the air conditioning load.

3.2.1
Extract 96-point power data for each transformer separately.We calculate the daily average power of each transformer.The partial power data of transformer A as of May 17, 2020, is shown in Table 3, and the daily average power of May 17, 2020, is 0.57345 kW.  4. Figure 3 shows the monthly average power and maximum power curves of transformer A.

3.2.4
We calculate the power of transformers divided into three categories for 2019 and 2021 and observe the curves.It is found that the trend of power change is mostly similar to 2020, and also meets the characteristics of high power in summer, high power in winter, and high power in summer and winter seasons.

3.2.5
By inputting the average data of transformer A into the model, it was found that the power in summer and winter was higher than that in spring and autumn.

3.2.6
Transformer A uses air conditioning for heating in winter (January, February, December) and has an average power of 0.5441 kW; the non-air conditioning season is spring and autumn (3, 4, 5, 9, 10, 11), and the average power is 0.3569 kW.Therefore, the load of the transformer using air conditioning is 0.1872kW.

3.2.7
By calculation, the air conditioning load capacity is 14.98 kW.By modifying this part of the capacity, the transformer load can be reduced and power resource waste can be avoided.

Results
This section studies the remaining capacity of transformers through scientific methods based on transformer data from some residential areas in Changping District, Beijing in 2020, to obtain a more accurate modifiable capacity of transformers.Afterward, to assist in the better implementation of electric heating renovation, data support was provided for other electric heating methods by calculating the air conditioning load.After verification, the calculation of the remaining capacity of the transformer and the air conditioning load has achieved the expected effect and can be used as a data reference for electric heating renovation to guide practical work.

Conclusions
People's methods are becoming increasingly diverse, and the renovation of electric heating is constantly developing.Through this study, combined with cutting-edge technology at home and abroad, this article conducted research on community electric heating by using statistical analysis and K-means clustering analysis and calculated the remaining capacity of transformers that can be retrofitted and the load used for air conditioning.Further validate the feasibility, practicality, and scientificity of the method are adopted in this article through case studies.By using these two methods, the goal of accelerating the optimization of electric heating transformation, reducing environmental pressure, and promoting the full utilization of power resources can be achieved.
2.2.1 Data preprocessing.Firstly, we obtain the 96-point power data of the community transformer for 365 days within a year.Secondly, data processing is carried out on the obtained data, which includes ICEEPS-2023 Journal of Physics: Conference Series 2728 (2024) 012016 IOP Publishing doi:10.1088/1742-6596/2728/1/0120164

Figure 2 .
Figure 2. Calculation of air conditioning load model.

Figure 3 .
Figure 3. Reading average power and maximum power of transformer A in 2020.

Figure 4 .
Figure 4. Annual power trend of air conditioning users in summer.

3. 2 . 3
Data clustering analysis.We cluster the monthly data of each transformer in 2020 and determine the number of clusters based on the curve contour coefficient, the input data, and the obtained number of clusters K.We input the monthly data of each transformer in 2020 into the K-Means clustering model to obtain the optimal number of clusters of 3. The clustering results of the annual power trend of air conditioning users in summer are shown in Figure4, the annual power trend of air conditioning users in summer and winter is shown in Figure5, and the annual power trend of air conditioning users in winter ICEEPS-2023 Journal of Physics: Conference Series 2728 (2024) 012016 IOP Publishing doi:10.1088/1742-6596/2728/1/0120168 is shown in Figure 6.

Figure 5 .
Figure 5. Annual power trend of air conditioning users in summer and winter.

Figure 6 .
Figure 6.Annual power trend of air conditioning users in winter.

Table 1 .
24-point power data of a certain transformer.

Table 3 .
Partial power data of transformer A. Monthly power data.We calculate the monthly average power, maximum power, and variance of the transformer based on the results of the previous step (12-point data for the entire year).The detailed data of one transformer A are shown in Table

Table 4 .
12-point power data of transformer A.