A control method for electric water heaters considering demand-side response

Abstract

The present invention provides a control method for an electric water heater considering demand-side response. First, based on the energy balance process, a hierarchical technique is used, and four main phenomena causing temperature changes inside the electric water heater are considered to construct an electric water heater model. Then, a Gaussian kernel smoother is used to preprocess the power profile, and K-means is used to classify the smoothed profiles of multiple clusters determined by the usage profile criterion. After that, a minimum cost objective function of the electric water heater is constructed. Immediately afterwards, an electric water heater demand response model is constructed based on the constructed electric water heater model, the data selected by the Gaussian kernel smoother, and the minimum objective function. Finally, MATLAB is used to solve the electric water heater demand response model. The present invention clusters users according to their power distribution, allowing part of the peak electricity consumption period to be transferred to the off-peak period, which can help users reduce electricity costs and help utility companies manage the electricity demand during peak periods.

Description

Technical Field

[0001] The present invention relates to the technical field of electric water heaters, and specifically to a regulation method for electric water heaters considering demand-side response. Background Technique

[0002] Electric water heaters (EWHs) have great potential in demand-side management applications. More precisely, because of their energy storage capacity, they can be used as shifting loads.

[0003] The k-means clustering algorithm is an iterative clustering analysis algorithm. Its steps are as follows: initially divide the data into k groups, then randomly select k objects as the initial clustering centers, and then calculate the distances between each object and each seed clustering center, and assign each object to the clustering center closest to it. The clustering centers and the objects assigned to them represent a cluster. Each time a sample is assigned, the clustering centers of the cluster are recalculated based on the existing objects in the cluster. This process will be repeated continuously until a certain termination condition is met. The termination condition can be that no (or the minimum number of) objects are reassigned to different clusters, no (or the minimum number of) clustering centers change anymore, or the sum of squared errors is locally minimized.

[0004] Demand Response, abbreviated as DR for short, refers to the short-term behavior in which when the wholesale electricity market price rises or the system reliability is threatened, after receiving a direct compensation notice for induced load reduction or an electricity price increase signal sent by the power supply side, electricity users change their inherent habitual electricity consumption patterns to reduce or shift the electricity load during a certain period to respond to the power supply, thereby ensuring the stability of the power grid and suppressing the rise of electricity prices. It is one of the solutions for demand-side management (DSM). Summary of the Invention

[0005] The present invention provides a regulation method for electric water heaters considering demand-side response, which can greatly reduce the energy consumption and cost in the oxygen production process.

[0006] A regulation method for electric water heaters considering demand-side response includes the following steps:

[0007] Step S1: Based on the energy balance process, use hierarchical technology and consider the four main phenomena that cause temperature changes inside the electric water heater to construct an electric water heater model;

[0008] Step S2: Use a Gaussian kernel smoother to preprocess the power profile, and use K-means to classify the smoothed profiles of multiple clusters determined by the usage profile criterion, so as to obtain the data required by the model;

[0009] Step S3: Construct the minimum - cost objective function of the electric water heater;

[0010] Step S4: Construct the demand - response model of the electric water heater based on the electric - water - heater model in Step S1, the data required for obtaining the model in S2, and the minimum - objective function in S3;

[0011] Step S5: Use MATLAB to solve the demand - response model of the electric water heater and obtain the regulation method of the electric water heater.

[0012] Furthermore, in Step S1, the four main phenomena that cause the internal temperature change of the electric water heater are:

[0013] 1) The heating element heats the water ($Q$ h );

[0014] 2) Heat loss to the environment ($Q$ env );

[0015] 3) Hot - water consumption ($Q$ flow );

[0016] 4) Internal convective heat transfer ($Q$ conv ).

[0017] The electric water heater is considered as a set of S layers of completely - mixed equal - volume segments. The stratified model includes the on / off of two heating elements. When the water is heated, the hotter water flowing out from the bottom of the water tank has a smaller density, so it will rise to the top; at the same time, the colder water in the water tank has a larger density and will sink to the bottom and then be heated. Therefore, the temperature of the upper layer of the water heater is higher than that of the lower layer, especially during the hot - water consumption process;

[0018] Two main assumptions are used when constructing the electric - water - heater model:

[0019] 1) The water in each layer is perfectly mixed at any time, and each segment is dynamically characterized by a temperature variable, simplifying the model formula while maintaining a good representation of the thermoelectric behavior;

[0020] 2) Under normal operating conditions, the heating elements have a master - slave control system, where the upper element has priority, so the two heating elements are not allowed to work simultaneously;

[0021] Solve the energy - balance equation of the S layer as follows:

[0022]

[0023] Where $m$ s is the mass of the water in the S layer, $c$ pw is the specific heat of water, $Q$ h,s is the heating amount when the heating element is working, and its value is related to the nominal power $p$ wIs directly proportional to the conduction Q conv,s The interlayer heat exchange of water caused depends on the layer position, where:

[0024]

[0025] Where T s+1 、T s 、T s-1 Are the temperatures of the (S + 1)-th layer, S-th layer, and (S - 1)-th layer of the electric water heater respectively, K s Is the interlayer conduction coefficient, and the heat exchange between the environmental Q env,s That constitutes the energy balance equation of the S-th layer and the heat exchange of the water extraction Q flow,s Are calculated as follows:

[0026] Q env,s =U s (T env -T s )

[0027]

[0028] Where, U S Is the loss coefficient between this layer and its environment, Is the water flow rate, c pw Is the specific heat of water, T s 、T s-1 Are the temperatures of the S-th layer and (S - 1)-th layer of the electric water heater respectively, T in Is the inlet water temperature.

[0029] Furthermore, the step S2 specifically includes:

[0030] (1) Preprocess the power profile using a Gaussian kernel smoother, and its specific implementation process is as follows:

[0031] Adopt the kernel smoothing technology. For N daily power consumption curves P w , N(x), each daily record contains N observations, and the kernel smoother defines a set of weights for each x Are defined as follows:

[0032]

[0033] To give less weight to more distant adjacent points, use the Gaussian kernel smoother as follows:

[0034]

[0035] The Gaussian smoothing uses two dimensions: one is the power value and the other is time. The selection of the length scale parameter b of the input space is related to the standard deviation + / -3σ; this ensures high smoothing and covers 99% of the area. The Gaussian kernel smoother for any x is as follows:

[0036]

[0037] (2) Use K-means to classify the multiple clusters determined using the silhouette criterion into smooth silhouettes. The specific implementation process is as follows:

[0038] The silhouette s(i) is estimated as the difference between the within-cluster compactness and the separation from other clusters, and is calculated for each cluster as follows:

[0039]

[0040] where a(i) corresponds to the average dissimilarity within the cluster k of all other objects to which I belong, b(i) is the minimum of the average distances between the observation point i and all objects in other clusters, the initial number of clusters selected is k = 2, and according to different scenarios, two classes will be formed to demonstrate an example of the proposed control method.

[0041] Furthermore, in step S3, considering a finite discrete time range t, the discrete time step length n: Δt = t(n) - t(n - 1);

[0042] The minimum cost objective function of the electric water heater constructed in step S3 is:

[0043]

[0044] where T sp is the defined thermostat set point, P w is the normalized control variable dependent on the heating power element, C p is the power penalty cost function for each control interval based on the average water heating power consumption, C te is the temperature penalty cost function considering the user satisfaction constraint. The optimization objective of the minimum cost objective function of the electric water heater is to reduce the power as much as possible while keeping the temperature close to the set value during critical time periods. Therefore, the optimization problem is formulated as:

[0045]

[0046] Furthermore, in step S4, constructing the electric water heater demand response model satisfies two important conditions in the design:

[0047] It must ensure that there is a sufficiently high and controllable water temperature at the outlet, always respecting the comfort level expected by the customer;

[0048] No new consumption peak exceeding the daily peak can be generated during the management process.

[0049] A method for regulating electric water heaters considering demand-side response proposed by the present invention clusters users based on their power distribution, allowing some peak electricity consumption periods to be shifted to off-peak periods, which can help users reduce electricity costs and help utility companies manage peak electricity demand. Description of the Drawings

[0050] Figure 1 is a flowchart of a method for regulating an electric water heater considering demand-side response according to an embodiment of the present invention;

[0051] Figure 2 is a diversified profile of the demand for water heaters according to an embodiment of the present invention;

[0052] Figure 3 is the cumulative energy loss according to an embodiment of the present invention;

[0053] Figure 4 is a comparison of the impact of control scenarios on the total household consumption according to an embodiment of the present invention. Detailed Embodiments

[0054] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0055] An embodiment of the present invention provides a method for regulating an electric water heater considering demand-side response, including the following steps:

[0056] Step S1: Based on the energy balance process, use a hierarchical technique and consider four main phenomena that cause temperature changes inside the electric water heater to build an electric water heater model;

[0057] Step S2: Use a Gaussian kernel smoother to preprocess the power profile, and use K-means to classify the smoothed profiles of multiple clusters determined by the usage profile criterion to obtain the data required by the model;

[0058] Step S3: Construct a minimum-cost objective function for the electric water heater;

[0059] Step S4: Construct an electric water heater demand response model based on the electric water heater model in Step S1, the data required by the model obtained in S2, and the minimum objective function in S3;

[0060] Step S5: Use MATLAB to solve the electric water heater demand response model and obtain the electric water heater regulation method.

[0061] In the said step S1, the four main phenomena that cause the internal temperature change of the electric water heater are:

[0062] 1) The heating element heats the water (Q h );

[0063] 2) Heat loss to the environment (Q env );

[0064] 3) Hot water consumption (Q flow );

[0065] 4) Internal convective heat transfer (Q conv ).

[0066] The electric water heater is considered as a set of S-layer completely mixed equal-volume segments. The stratified model includes the on / off of two heating elements. When the water is heated, the hotter water flowing out from the bottom of the water tank has a smaller density, so it will rise to the top; at the same time, the colder water in the water tank has a larger density and will sink to the bottom and then be heated. Therefore, the temperature of the upper layer of the water heater will be higher than that of the lower layer, especially during the hot water consumption process;

[0067] Two main assumptions are used when constructing the electric water heater model:

[0068] 1) The water in each layer is perfectly mixed at any time, and each segment is dynamically characterized by a temperature variable, simplifying the model formula while maintaining a good representation of the thermoelectric behavior;

[0069] 2) Under normal operating conditions, the heating elements have a master-slave control system, where the upper element has priority, so the two heating elements are not allowed to work simultaneously;

[0070] The S-layer energy balance equation is solved as follows:

[0071]

[0072] Where m s is the mass of the water in the S-layer, c pw is the specific heat of water, Q h,s is the heating amount of the heating element during operation, and its value is proportional to the nominal power p w of the heating element. The heat exchange between water layers caused by conduction Q conv,s depends on the layer position, where:

[0073]

[0074] Where T s+1 、T s 、T s-1 are the temperatures of the (S + 1)-th layer, the S-th layer, and the (S - 1)-th layer of the electric water heater respectively, and K sis the interlayer conduction coefficient, and the environment Q that constitutes the energy balance equation of the S layer env,s The heat exchange between and the water extraction Q flow,s The heat exchange calculation is as follows:

[0075] Q env,s =U s (T env -T s )

[0076]

[0077] Among them, U S is the loss coefficient between this layer and its environment, is the flow rate of water, c pw is the specific heat of water, T s 、T s-1 are the temperatures of the S-th layer and the (S - 1)-th layer of the electric water heater respectively, and T in is the inlet water temperature.

[0078] The specific steps of step S2 include:

[0079] (1) Preprocess the power profile using a Gaussian kernel smoother, and its specific implementation process is as follows:

[0080] The selection of data is based on the water heater power profile. However, the water heater power curve is a pulse-shaped signal, and its amplitude is equal to the rated power of the heating element. Given the difficulty in processing such patterns, a smoothing technique is adopted. A smoothed continuous signal has been created, which captures the important data of the power profile, especially during peak periods. In fact, the main idea is to obtain an equivalent signal with similar energy, which is more suitable for clustering purposes. This is achieved by excluding noise or other fine-scale structures. Using the kernel smoothing technique, for N daily power consumption curves P w , N(x), each daily record contains N observations. The kernel smoother defines a set of weights for each x defined as follows:

[0081]

[0082] In order to give less weight to more distant adjacent points, use the Gaussian kernel smoother as follows:

[0083]

[0084] Gaussian smoothing uses two dimensions: one is the power value, and the other is time (regarded as an angle). The selection of the length scale parameter b of the input space is related to the standard deviation + / - 3σ; this ensures high smoothing and covers 99% of the area. The Gaussian kernel smoother for any x is as follows:

[0085]

[0086] (2) Classify the multiple clusters determined using the silhouette criterion using K-means, and the specific implementation process is as follows:

[0087] This paper adopts the partitioning clustering algorithm K-means, and the corresponding measurement distance is based on the Euclidean metric. The K-means algorithm requires a specific number of clusters. Therefore, the first step before applying the clustering algorithm is to identify the correct number k of classes. In the silhouette analysis method used in this study, this method is based on the measurement of cluster compactness. The silhouette s(i) is estimated as the difference between the intra-cluster compactness and the separation from other clusters, and is calculated for each cluster as follows:

[0088]

[0089] where a(i) corresponds to the average dissimilarity within the cluster k of all other objects to which I belong, and b(i) is the minimum of the average distances between the observation point i and all objects in other clusters. The initial number of clusters selected is k = 2, and according to different scenarios, two classes will be formed to demonstrate an example of the proposed control method.

[0090] The purpose of grouping users is to identify the typical load patterns of water heaters for residential users, so as to formulate specific control strategies for each group of users. In this way, the main control of electricity consumption is applicable to high-consumption users during peak electricity consumption periods. Therefore, two typical power patterns will be determined during this process. Compared with the high-power profile, the low-power mode has no peak values.

[0091] In step S3, considering a finite discrete time range t, the discrete time step length n: Δt = t(n) - t(n - 1);

[0092] The minimum cost objective function of the electric water heater constructed in step S3 is:

[0093]

[0094] where T sp is the defined thermostat setpoint, P w is the normalized control variable dependent on the heating power element, C p is the power penalty cost function for each control interval based on the average water heating power consumption, C te is the temperature penalty cost function considering the user satisfaction constraint. The optimization objective of the minimum cost objective function of the electric water heater is to reduce the power as much as possible while keeping the temperature close to the set value during critical time periods. Therefore, the optimization problem is formulated as:

[0095]

[0096] In step S4, two important conditions are met in the design of constructing the demand response model of the electric water heater:

[0097] It is necessary to ensure that the water temperature at the outlet is high enough and controllable, always respecting the comfort level expected by the customer;

[0098] No new consumption peak exceeding the daily peak can be generated during the management process.

[0099] Therefore, the main focus is to create a control technology that supplies power to the heating element according to an optimized schedule while ensuring user satisfaction and peak period restrictions. Regarding the use of the water heater as a shifted load, based on the analysis of the energy consumption profile of the water heater, a specific operation plan dynamic programming is generated. In addition, a classification process is applied to group users with similar consumption profiles and identify the clients that contribute the most to the highest energy consumption during peak periods. To compare the effectiveness of management strategies, different research scenarios with or without consumption classification are compared respectively. In addition, K - value clustering analysis is applied, and an evaluation stage is introduced to evaluate the clustering performance.

[0100] In step S5, MATLAB is used to solve the demand response model of the electric water heater and obtain the regulation method. The specific steps include:

[0101] In MATLAB, dynamic programming is used to evaluate all possible situations and reuse the solutions of the computed sub - problems. In theory, it is possible to obtain the global optimal solution of the stated problem. Considering that the optimality of a solution depends on many factors, such as assumptions, problem formulation, and optimization algorithms, the optimality of the proposed solution is evaluated for each scenario:

[0102] 1) Final cumulative energy consumption;

[0103] 2) Diversification of the water heater power demand (peak - shaving and rebound power);

[0104] 3) Consumer satisfaction (hot water temperature);

[0105] 4) Computation time.

[0106] The technical solution of the present invention will be described below through a specific embodiment:

[0107] To compare the impact of power consumption, energy, and hot water temperature supply when applying the optimal management strategy, four scenarios are considered, as shown in Table 1. Three scenarios consider user classification by applying the K - means technique, and the last scenario uses local control in addition to user classification.

[0108] Table 1 Main characteristics of the control scenarios

[0109]

[0110]

[0111] 1) Reference scenario: The heating element is always available. The local thermostat applies power consumption to maintain the temperature within the recommended limits;

[0112] 2) First scenario: During each time period, the individual schedule of the heating elements of the profile under study is determined by the dynamic programming method without using the classification process;

[0113] 3) Second scenario: First, it applies a user classification process to the profile under study. Subsequently, no control is applied when using the first category (defined as low-consumption consumers), and the heating elements of each water heater are controlled when using the second group of users (identified as high-consumption consumers). It should be noted that the control schedule is determined by dynamic programming within each interval. By only controlling the high-energy-consuming group, the degree of its impact on peak power generation in diverse power demands can be determined;

[0114] 4) Third scenario: Similar to the second scenario, a user classification process is applied to the profile under study. No controls are applied to the first category. The grouped control schedule for the second category of heating elements is determined by dynamic programming within each time period. The grouped control schedule is determined using a reference profile representing the second category of users;

[0115] 5) Fourth scenario: The same control method as in the third case is adopted. However, individual local control in the water heater heating elements is added to the heating elements. When the output temperature drops below 58 °C, the controller omits the initial control provisions provided by dynamic programming, which may affect the comfort level in the next step.

[0116] The first and second scenarios involve individual control of the water heaters based on the hot water consumption of each customer. The third and fourth scenarios focus on group control by broadcasting a common control signal to each group.

[0117] The simulation for each of the above cases was carried out for a whole day (weekday). Figure 2Shows the diversified distribution map of the water heater power under all simulated scenarios. In the first scenario, as expected, the power consumption during peak periods is greatly reduced. However, when the heating element becomes available again without control, a new peak appears. In the second scenario, by implementing user classification and applying the control strategy only to the category identified as high-consumption consumers, the new peak created in the first scenario is reduced because only one group of customers is controlled. Nevertheless, in the second case, the intensity of the reduction in energy consumption during peak periods is less than that in the first case. This is because only users belonging to Class 2 are controlled. In the third scenario, dynamic programming is applied only once to create a scheduling reference profile for the second class within two time intervals. Moreover, using the same scheduling reference profile for all users in the class will potentially have a negative impact on user satisfaction (assuming similar (although not identical) water consumption behaviors among users belonging to each class).

[0118] Dynamic programming requires a large amount of computational effort, even when the state variable Pw is only discretized into two states (ON / OFF) and the control time is divided into time intervals. In all cases, the final energy consumption of the users is almost the same, as expected (see Figure 3 ). In fact, in the first scenario, when dynamic programming is applied to each user without a classification process or a controlled scheduling reference profile, the response time is very long. When classification is applied without considering the control progress reference profile, the computational time is still very high. Nevertheless, it is less than that in the first case.

[0119] We evaluated the impact of each control scheme on global household consumption (including space heating and household appliances). As Figure 4 shown, the results indicate that only in the first case did an important power rebound occur and new peak loads might be generated. The control scenarios with user classification perform better and might be more interesting in terms of reducing the global peak power. The evaluations and results obtained in this study reveal some advantages of using the proposed control schemes. It can be confirmed that:

[0120] 1) The individual optimization and control of each corona unit can both reduce the higher energy consumption during peak periods and generate a higher energy consumption rebound;

[0121] 2) The individual and category optimization of the operation of high-consumption EWHs provides a similar reduction in consumption during peak periods.

[0122] 3) The proposed optimized control of EWHs, which clusters them based on the power distribution of users, allows for the transfer of part of the peak electricity consumption period to off-peak periods. Specifically, it has the potential to transfer approximately 500 Wh without the problem of power rebound.

[0123] Therefore, a method for regulating an electric water heater considering demand-side response proposed by the present invention can help users reduce electricity costs and help utility companies manage electricity demand during peak hours.

[0124] As described above, only the specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. A control method for an electric water heater considering demand-side response, characterized in that, It includes the following steps: Step S1: Based on the energy balance process, use the layering technique and consider the four main phenomena that cause temperature changes inside the electric water heater to build an electric water heater model; Step S2: Use a Gaussian kernel smoother to preprocess the power profile, and use K-means to classify the smoothed profiles of multiple clusters determined by the usage profile criterion, so as to obtain the data required by the model; Step S3: Build the minimum cost objective function of the electric water heater; Step S4: Build an electric water heater demand response model based on the electric water heater model in Step S1, the data required by the model obtained in S2, and the minimum objective function in S3; Step S5: Use MATLAB to solve the electric water heater demand response model and obtain the electric water heater control method; The specific content of Step S2 includes: (1) Use a Gaussian kernel smoother to preprocess the power profile, and its specific implementation process is as follows: Using the kernel smoothing technique, for N daily power consumption curves P w , N(x), each daily record contains N observations, and the kernel smoother defines a set of weights for each x which is defined as follows: To give less weight to farther adjacent points, use the Gaussian kernel smoother as follows: Gaussian smoothing uses two dimensions: one is the power value and the other is time. The selection of the length scale parameter b of the input space is related to the standard deviation + / -3σ; this ensures high smoothing and covers 99% of the area. The Gaussian kernel smoother for any x is as follows: (2) Use K-means to classify the smoothed profiles of multiple clusters determined by the usage profile criterion, and its specific implementation process is as follows: The silhouette s(i) is estimated as the difference between the within-cluster compactness and the separation from other clusters, and is calculated for each cluster as follows: where a(i) corresponds to the average dissimilarity within the observed cluster k to all other objects in cluster k, and b(i) is the minimum of the average distances between the observation point i and all objects in other clusters. The initial number of clusters selected is k = 2. According to different scenarios, two classes will be formed to demonstrate an example of the proposed control method.

2. The electric water heater control method considering demand side response according to claim 1, characterized in that, In Step S1, the four main phenomena that cause temperature changes inside the electric water heater are: 1) The heating element heats water (Q h ); 2) Heat loss to the environment (Q env ); 3) Hot water consumption (Q flow ); 4) Internal convective heat transfer (Q conv ); The electric water heater is considered a set of S layers of completely mixed equal-volume segments. The layering model includes the on / off of two heating elements. When the water is heated, the hotter water flowing out from the bottom of the water tank has a smaller density, so it will rise to the top; at the same time, the colder water in the water tank has a larger density and will sink to the bottom and then be heated. Therefore, the temperature of the upper layer of the water heater will be higher than that of the lower layer, especially during the hot water consumption process; Two main assumptions are used when building the electric water heater model: 1) The water in each layer is perfectly mixed at any time, and each segment is dynamically characterized by a temperature variable, which simplifies the model formula while maintaining a good representation of the thermoelectric behavior; 2) Under normal operating conditions, the heating elements have a master-slave control system, where the upper element has priority, so the two heating elements are not allowed to work simultaneously; Solve the energy balance equation of the S layer as follows: where m s is the mass of the water in the S layer, c pw is the specific heat of water, Q h,s is the heating amount of the heating element during operation, and its value is proportional to the nominal power p w of the heating element. The heat exchange between water layers caused by conduction Q conv,s depends on the layer position, where: Among them, T s+1 , T s , T s-1 are the temperatures of the (S + 1)-th layer, the S-th layer, and the (S - 1)-th layer of the electric water heater respectively. K s is the interlayer conduction coefficient. The heat exchange between the environment Q env,s constituting the energy balance equation of the S-th layer and the heat exchange of the water extraction Q flow,s are calculated as follows: Q env,s = U s (T env - T s ) Among them, U S is the loss coefficient between this layer and its environment, is the water flow rate, c pw is the specific heat of water, T s and T s-1 are the temperatures of the S-th layer and the (S - 1)-th layer of the electric water heater respectively, and T in is the inlet water temperature.

3. The electric water heater control method considering demand-side response according to claim 1, wherein In Step S3, consider a finite discrete time range t, and the discrete time step n: Δt = t(n) - t(n - 1); The minimum cost objective function of the electric water heater built in Step S3 is: where T sp is the defined thermostat setpoint, P w is the normalized control variable dependent on the heating power element, C p is the power penalty cost function for each control interval based on the average water heating power consumption, C te is the temperature penalty cost function considering the user satisfaction constraint. The optimization objective of the minimum cost objective function of the electric water heater is to minimize the power as much as possible while maintaining the temperature close to the set value during critical time periods. Therefore, the optimization problem is formulated as:

4. The electric water heater control method considering demand-side response according to claim 1, characterized in that In Step S4, building the electric water heater demand response model meets two important conditions in the design: It is necessary to ensure that the water outlet has a sufficiently high and controllable water temperature, always respecting the comfort level desired by the customer; No new consumption peak exceeding the daily peak can be generated during the management process.

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