Simulation Study on the Energy Consumption Characteristics of Individual and Cluster Thermal Storage Electric Heating Systems

Abstract

This study investigates the energy consumption characteristics of individual and clustered thermal storage electric heating systems, focusing on their sustainability implications for regional load distribution and user energy consumption patterns. Simulation results show that thermal storage electric heating shifts peak energy demand from daytime to nighttime low-price hours, reducing electricity costs and optimizing grid load balancing. As the proportion of thermal storage electric heating increases from 10% to 30%, the daytime minimum load reduction rate rises from 7% to 22%, while the nighttime maximum load increase rate increases from 16% to 63%. This operational mode supports sustainable energy usage by alleviating daytime grid peak pressure and leveraging low-cost, off-peak electricity for heat storage. The findings highlight the potential of thermal storage electric heating to enhance energy efficiency, integrate renewable energy, and promote grid stability, contributing to a more sustainable energy system.

1. Introduction

With the global transformation of energy structures and the increasing awareness of environmental protection, thermal storage electric heating has emerged as an efficient and clean heating method, gradually becoming a focal point for research and application [1,2]. The intermittency and volatility of renewable energy sources pose significant challenges to the operational efficiency and safety of power systems [3,4,5]. Thermal storage electric heating systems, by storing thermal energy during low-demand periods and releasing it during peak periods, can effectively reduce operational costs and enhance the flexibility and stability of power systems [6,7]. The objective of this study is to explore the potential of thermal storage electric heating systems in optimizing regional load distribution, reducing operational costs, and enhancing grid flexibility and stability by establishing thermodynamic and power system models for such systems.

Among various clean heating methods, the “coal-to-electricity” policy (a Chinese initiative aimed at replacing coal-fired heating systems with electric heating to reduce air pollution and improve energy efficiency) has not only provided users with substantial convenience but also demonstrated considerable growth potential, making it a crucial heating option in northern regions [8,9,10]. However, the rapid increase in rural electric heating users has resulted in a significant rise in the number of electric heating devices connected to the grid. This has further widened the gap between peak and off-peak electricity demands. This could trigger peak load issues, affecting the safety and stability of rural power systems [11]. If subsidies are reduced or eliminated, farmers might revert to using coal for heating, which would undermine the progress made in clean energy adoption [12,13]. Therefore, researchers have proposed multiple optimization methods to address these challenges [14,15]. Currently, there are three mainstream methods for analyzing the thermal performance of building envelopes in dynamic thermal simulations: the Finite Element Method (FEM), the Finite Difference Method (FDM), and the Thermal Network Method. The Finite Element Method (FEM) excels in accurately handling complex geometries and nonlinear boundary conditions but incurs higher computational costs. The Finite Difference Method (FDM) offers high computational efficiency and is suitable for large-scale simulations, though its accuracy diminishes when dealing with complex geometries. The Thermal Network Method strikes a balance between computational efficiency and precision by simplifying the heat conduction process; however, its ability to describe complex thermal processes is limited [16,17,18,19,20]. Papavasiliou A et al. argued that the “heat-driven power generation” constraint is the primary reason for the sharp decline in peak load regulation capabilities during the winter heating season and the substantial curtailment of wind power. They suggested that configuring thermal storage devices could effectively solve these issues [21]. Bruninx K et al. modeled electric heating systems and analyzed the impact of various electric heating technologies, such as electric boilers, heat pumps, and air conditioners, on power systems. Their findings indicated that these devices have a greater impact on the grid compared to thermal storage electric heating systems [22]. Buber T et al. compared the peak shaving and valley filling potential of thermal storage electric heating systems and heat pumps in Germany, highlighting that thermal storage electric heating systems can reduce the peak thermal load of combined heat and power units while increasing the valley load of the grid [23]. Oliver David et al. conducted a techno-economic analysis of renewable energy technologies, evaluating the technical and economic characteristics and future prospects of GSHP and thermal storage electric heating systems. Their results showed that in regions with stringent environmental requirements, thermal storage electric heating systems significantly outperform traditional coal-fired boilers [24]. Akmal M and Flynn D et al. investigated the technology of matching thermal loads to wind power generation, providing valuable insights for optimizing the integration of thermal storage electric heating systems with distribution network loads [25]. Temperature and climate change have significant effects on the thermodynamic and power system models of thermal storage electric heating systems. Variations in temperature directly influence the efficiency of heat storage and release processes, while climatic conditions (such as wind speed and humidity) further impact the thermal performance and electricity demand of the system [26,27,28,29,30].

To address the aforementioned research questions, this paper proposes a simulation-based research method for thermal storage electric heating systems, grounded in thermodynamic and power system models. In the theoretical section, a thermodynamic model of the thermal storage electric heating system is established, providing a detailed description of its heat storage and release processes. For data collection, this study integrates simulation data with real-world engineering data to ensure the accuracy and reliability of the model. In terms of analytical methods, this paper employs simulation software to model the system, exploring energy consumption characteristics and economic performance under different operational strategies. The research findings demonstrate that thermal storage electric heating systems, by storing thermal energy during off-peak electricity hours and releasing it during peak hours, can effectively reduce operational costs, optimize regional load distribution, and enhance grid flexibility and stability.

2. Methods

2.1. Overview

The operation of thermal energy storage (TES) electric heating systems is closely linked to building thermal loads, necessitating the modeling of these loads to effectively integrate the “source–storage–load” components. Buildings are the primary energy-consuming entities on the load side of TES electric heating systems, and modeling and simulating their energy consumption characteristics is of significant importance. Currently, there are three main methods for the dynamic thermal simulation of building envelopes. The first method utilizes building energy simulation tools, such as DOE-2.2, EnergyPlus 23.1, and TRNSYS 18, to predict heating and cooling loads based on the mathematical relationships between the building and its surrounding environment. The second method involves constructing purely data-driven models, known as “black-box” models, which predict heating and cooling loads based on predefined factors. These black-box models include neural network models and support vector machine models. The third method is the “gray-box” model, which combines the principles of white-box and black-box models. In gray-box models, the RC (resistor–capacitor) thermal network model is commonly used to simplify energy flows within the building, such as heat transfer through the building’s external surfaces, to calculate the heating and cooling demands required to maintain the target indoor temperature. The RC thermal network model is constructed in a manner similar to multi-node models in power grids, where nodes represent measurement points. The temperature at each node is analogous to node voltage, the building envelope and indoor air quality are similar to one or more resistors and capacitors, and heat flows (e.g., HVAC cooling loads, solar radiation contributions, or human body heat) are comparable to electrical currents. Given the diverse types of buildings that utilize TES electric heating, the use of “white-box” or “black-box” models is not conducive to large-scale computations. Therefore, this study adopts the third approach, the “gray-box” model, for the analysis of building thermal loads.

2.2. Building Thermal Balance Equation and Heat Exchange Processes

Assuming a uniform temperature distribution within the building, the thermal balance equation for the building can be expressed as Equation (1):

$$\mathsf{\Delta }Q=\left(C_a+C_m\right){\displaystyle \frac{d{T}_z}{dt}}$$

(1)

where ΔQ represents the total heat exchange within the building, in kW; ${\displaystyle \frac{d{T}_z}{dt}}$ is the rate of temperature change per unit time; and C_a and C_m are the heat capacities of the air and thermal mass, respectively, in kJ/K. These heat capacities can be calculated using Equations (2) and (3):

$$C_a=c_a\cdot {\rho }_a\cdot A_z\cdot h_z$$

(2)

$$C_m=c_m\cdot {\rho }_m\cdot V_m$$

(3)

where c_a and c_m are the specific heat capacities of the air and thermal mass, respectively, in kJ/(kg·K); ρ_a and ρ_m are the densities of the air and thermal mass, respectively, in kg/m³; h_z is the height of the building, in m; and V_m is the volume of the thermal mass, in m³.

The heat exchange processes within the building are illustrated in Figure 1. To reduce model complexity, this study simplifies the thermal storage process of the building envelope. Due to the presence of the building envelope, there is a temperature difference between the indoor and outdoor environments, leading to the following three heat exchange processes:

(1)

Forced convective heat transfer from indoor air to the inner surfaces of the building walls (excluding doors), roof, and floor.

(2)

Conductive heat transfer between the building walls (excluding doors), roof, and floor envelope materials.

(3)

Natural convective heat transfer from the outer surfaces of the building walls (excluding doors), roof, and floor to the outdoor air.

Additionally, during the heating or cooling processes of indoor air and envelope materials, these materials absorb or release heat, thus providing a certain degree of thermal storage capacity within the building.

2.3. Building Thermal Load Modeling

The RC thermal network model was employed to model the building’s thermal load, as illustrated in Figure 2.

Based on the building’s thermal balance Equation (1) and thermal power balance constraint (4), the air thermal storage process within the building is described by Equation (5), establishing the mathematical relationship between T_z (indoor air temperature) and Q_s (heating power supplied by the HPFHS).

$$Q_s=Q_{hl,building}$$

(4)

where Q_hl,building is the thermal load of the building, in kW.

$$\left(c_a\cdot {\rho }_a\cdot A_z\cdot h_z+c_m\cdot {\rho }_m\cdot V_m\right)\cdot {\displaystyle \frac{d{T}_z}{dt}}=Q_{i,wall}+Q_{i,roof}+Q_{i,floor}+Q_{window}+Q_{swindow}+Q_s+Q_{vent}-Q_p$$

(5)

In the equation, Q_i,wall, Q_i,roof, and Q_i,floor represent the convective heat transfer powers from the indoor air to the internal surfaces of the building walls, roof, and floor, respectively, in kW. Q_window denotes the convective heat transfer power between the indoor and outdoor environment through the windows, in kW. Q_swindow is the heat power contributed to the indoor environment by solar radiation passing through the windows, in kW. The terms on the right-hand side of the equation can be calculated using Equations (6)–(26). Q_s represents the heat supply power provided by the Heat Pump and Fresh Air System (HPFHS) to the building, in kW, without considering the heat losses from radiators. Q_vent is the power loss due to ventilation, in kW, which includes both the infiltration through gaps (such as window and door cracks) and the intentional opening of windows to ensure adequate CO₂ levels and humidity. Q_p is the heat power resulting from user behavior, in kilowatts (kW), encompassing internal heat generation from the human body, heat production from electrical appliances, and heat loss from using cold water. The values of Q_p are provided as input data and are not calculated. The terms on the right-hand side of the equation are computed using Equations (6)–(13).

$$Q_{i,wall}={\displaystyle \sum _{j=1}^4{U}_{i,wall}\cdot A_{wall,j}\cdot \left(T_{i,wall,j}-T_z\right)}$$

(6)

$$Q_{i,roof}=U_{i,roof}\cdot A_z\cdot \left(T_{i,roof}-T_z\right)$$

(7)

$$Q_{i,floor}=U_{i,floor}\cdot A_z\cdot \left(T_{i,floor}-T_z\right)$$

(8)

$$Q_{window}={\displaystyle \sum _{j=1}^4{U}_{window}\cdot A_{window,j}\cdot (T_e-T_z)}$$

(9)

$$Q_{window}={\displaystyle \sum _{j=1}^4{\tau }_{window}\cdot SC\cdot A_{window,j}\cdot I_{T,j}}$$

(10)

$$Q_s=c_w\cdot {\rho }_w\cdot q_2\cdot \left(T_{s2}-T_{r2}\right)$$

(11)

$$Q_{vent}=c_a\cdot {\rho }_a\cdot (L_{al}\cdot A_z\cdot h_z+L_{ac})\cdot (T_e-T_z)$$

(12)

$$Q_p=-\left(q_{body}+q_{bodyw}+q_{bodyel}\right)\cdot n_{body}$$

(13)

In the equation, U_i,wall, U_i,roof, and U_i,floor represent the convective heat transfer coefficients for the indoor air to the internal surfaces of the building walls, roof, and floor, respectively, in W/(m²·K). U_window is the overall heat transfer coefficient for the indoor air to the inner surface of the windows and the outdoor air to the outer surface of the windows, accounting for both forced convection and natural convection, in W/(m²·K). A_wall,j and A_window,j are the surface areas of wall j and window j, respectively, in m². I_T,j is the total solar radiation intensity incident on the surface of window j, in kW/m². τ_window is the transmittance coefficient of the glass. SC is the shading coefficient of the window. L_al is the air leakage rate per unit volume, in 1/h. L_ac is the volumetric flow rate of air due to intentional window opening for ventilation, in m³/h. n_body is the real-time number of occupants in the home. q_body denotes the total heat generation rate of the human body, q_bodyw indicates the heat generated by the human body through evaporative cooling, and q_bodyel represents the heat dissipated by the human body through radiation and convection, measured in kilowatts (kW).

The heat storage processes in the materials on the inner surfaces of the building walls, roof, and floor can be described by Equations (14)–(16):

$$\left({\displaystyle \frac{{\sum }_{l=1}^{n_{wall}}{c}_{wall,l}\cdot {\rho }_{wall,l}\cdot A_{wall,j}\cdot d_{wall,l}}{2}}\right)\cdot {\displaystyle \frac{d{T}_{i,wall,j}}{dt}}=Q_{en,wall,j}-Q_{i,wall,j}$$

(14)

$$\left({\displaystyle \frac{{\sum }_{l=1}^{n_{roof}}{c}_{roof,l}\cdot {\rho }_{roof,l}\cdot A_z\cdot d_{roof,l}}{2}}\right)\cdot {\displaystyle \frac{d{T}_{i,roof}}{dt}}=Q_{en,roof}-Q_{i,roof}$$

(15)

$$\left({\displaystyle \frac{{\sum }_{l=1}^{n_{floor}}{c}_{floor,l}\cdot {\rho }_{floor,l}\cdot A_z\cdot d_{floor,l}}{2}}\right)\cdot {\displaystyle \frac{d{T}_{i,floor}}{dt}}=Q_{en,floor}-Q_{i,floor}$$

(16)

In the equations, n_wall, n_roof, and n_floor represent the number of material layers in the building walls, roof, and floor, respectively. c_wall,l, c_roof,l, and c_floorl,l are the specific heat capacities of the l-th layer of the building walls, roof, and floor, respectively, in kJ/(kg/K); ρ_wall,l, ρ_roof,l, and ρ_loorl,l are the densities of the l-th layer of the building walls, roof, and floor, respectively, in kg/m³. d_wall,l, d_roof,l, and d_loorl,l are the thicknesses of the l-th layer of the building walls, roof, and floor, respectively, in m. T_i,wall, T_i,roof, and T_i,floor are the temperatures of the inner surfaces of the building walls (ignoring the effect of doors), roof, and floor, respectively, in °C. Q_enwall, Q_en,roof, and Q_en,floor are the heat conduction powers through the building walls (ignoring the effect of doors), roof, and floor, respectively, in kW, which can be calculated using Equations (17)–(19).

$$Q_{en,wall,j}={\displaystyle \frac{1}{R_{en,wall}}}\cdot A_{wall,j}\cdot \left(T_{o,wall,j}-T_{i,wall,j}\right)$$

(17)

$$Q_{en,roof}={\displaystyle \frac{1}{R_{en,roof}}}\cdot A_z\cdot \left(T_{o,roof}-T_{i,roof}\right)$$

(18)

$$Q_{en,floor}={\displaystyle \frac{1}{R_{en,floor}}}\cdot A_z\cdot \left(T_e-T_{i,floor}\right)$$

(19)

In the equations, T_o,wall and T_o,roof are the temperatures of the outer surfaces of the building walls (ignoring the effect of doors) and roof, respectively, in °C. R_en,wall, R_en,roof, and R_en,floor are the equivalent thermal resistances for heat conduction between the layers of the building walls (ignoring the effect of doors), roof, and floor, respectively, in (m²·K)/W, which can be calculated using Equations (20)–(22).

$$R_{en,wall}={\sum }_{l=1}^{n_{wall}}\left({\displaystyle \frac{d_{wall,l}}{{\lambda }_{wall,l}}}\right)$$

(20)

$$R_{en,roof}={\sum }_{l=1}^{n_{roof}}\left({\displaystyle \frac{d_{roof,l}}{{\lambda }_{roof,l}}}\right)$$

(21)

$$R_{en,floor}={\sum }_{l=1}^{n_{floor}}\left({\displaystyle \frac{d_{floor,l}}{{\lambda }_{floor,l}}}\right)$$

(22)

In the equations, λ_j is the thermal conductivity of the j-th layer of the building envelope, in W/(m·K).

The heat storage processes in the materials on the outer surfaces of the building walls (ignoring the effect of doors) and roof can be described by Equations (23) and (24):

$$\left({\displaystyle \frac{{\sum }_{l=1}^{n_{wall}}{c}_{wall,l}\cdot {\rho }_{wall,l}\cdot A_{wall,j}\cdot d_{wall,l}}{2}}\right)\cdot {\displaystyle \frac{d{T}_{o,wall,j}}{dt}}=Q_{o,wall,j}+Q_{swall,j}-Q_{en,wall,j}$$

(23)

$$\left({\displaystyle \frac{{\sum }_{l=1}^{n_{roof}}{c}_{roof,l}\cdot {\rho }_{roof,l}\cdot A_z\cdot d_{roof,l}}{2}}\right)\cdot {\displaystyle \frac{d{T}_{o,roof}}{dt}}=Q_{o,roof}+Q_{sroof}-Q_{en,roof}$$

(24)

In the equations, Q_o,wall and Q_o,roof are the natural convective heat transfer powers from the outer surfaces of the building walls (ignoring the effect of doors) and roof to the outdoor air, respectively, in kW; Q_swall and Q_sroof are the heat powers contributed by solar radiation to the outer surfaces of the walls and roof, respectively, in kW. The terms on the right-hand side of the equations can be calculated using Equations (25)–(28).

$$Q_{o,wall,j}=U_{o,wall}\cdot A_{wall,j}\cdot \left(T_e-T_{o,wall,j}\right)$$

(25)

$$Q_{swall,j}=\left({\alpha }_{w,wall}/U_{o,wall}\right)\cdot U_{wall}\cdot A_{wall,j}\cdot I_{T,j}$$

(26)

$$Q_{o,roof}=U_{o,roof}\cdot A_z\cdot \left(T_e-T_{o,roof}\right)$$

(27)

$$Q_{sroof}=\left({\alpha }_{w,roof}/U_{o,roof}\right)\cdot U_{roof}\cdot A_z\cdot I_{T,j}$$

(28)

In the equations, α_w,wall andα_w,roof are the absorptivity coefficients of the outer surfaces of the building walls (ignoring the effect of doors) and roof, respectively. U_o,wall and U_o,roof are the natural convective heat transfer coefficients from the outer surfaces of the building walls (ignoring the effect of doors) and roof to the outdoor air, respectively. U_wall and U_roof are the total heat transfer coefficients of the building wall and roof envelope structures, respectively, in W/(m²·K), which can be calculated using Equations (29) and (30).

$$U_{wall}={\displaystyle \frac{1}{\left(R_{i,wall}+R_{en,wall}+R_{o,wall}\right)}}$$

(29)

$$U_{roof}={\displaystyle \frac{1}{\left(R_{i,roof}+R_{en,roof}+R_{o,roof}\right)}}$$

(30)

3. Implementation

3.1. Case Study Description

Taking the winter heating scenario of rural residences in northern China that have undergone electric heating retrofitting as an example, this study applies the aforementioned thermal storage electric heating system model. Based on the “Technical Specification for Thermal Storage Electric Heating Systems (10 kV and Below): Part 3,” it is recommended to integrate heat pump thermal storage to enhance the system efficiency of thermal storage electric heating when technically and economically feasible. The thermal storage electric heating system operates by converting electrical energy into thermal energy using a heat pump during off-peak electricity hours and storing it in a thermal storage water tank. During peak electricity hours, the stored thermal energy is released to meet user demand. This mechanism ensures a continuous supply of hot water, and even under limited power supply conditions, the thermal energy stored in the water tank can still meet the basic needs of users. Using a typical heat pump–thermal storage water tank–user model as an example, the energy consumption characteristics of a single thermal storage electric heating unit are analyzed through simulation. The structural diagram of the thermal storage electric heating unit system is shown in Figure 3. The air-source heat pump heating system consists of an air-source heat pump, a thermal storage water tank, radiators, a heat pump circulation pump, a heating network circulation pump, a battery, and heating pipelines.

3.2. Analysis of Energy Consumption Characteristics of Single Thermal Storage Electric Heating Systems

The example considers a typical day during the heating season in Tianjin, with the outdoor temperature profile shown in Figure 4. To better align with real-world scenarios, it is assumed that users will utilize the thermal storage function of the electric heating system to modify their electricity usage patterns based on the impact of time-of-use (TOU) electricity rates. Therefore, an energy consumption strategy that optimizes economic benefits is generated, with the objective function given by Equation (39) and the constraints given by Equations (31)–(33).

min{μ_e P_e,tl}

(31)

P_min ≤ p_j ≤ p_max

(32)

$$k_{cp}^{\min }\le k_{cp}\le k_{cp}^{\max }$$

(33)

In the equations, P_e,tl represents the output power of the heat pump in the thermal storage electric heating system. μ_e represents the electricity price. p_min and p_max represent the lower and upper bounds of the heating equipment’s output power. $k_{cp}^{\min }$ and $k_{cp}^{\max }$ represent the lower and upper bounds of the thermal storage capacity.

Figure 5 shows the optimized operation results of the single thermal storage electric heating system. Through simulation analysis, it is found that compared to traditional electric heating, the energy consumption characteristics of users with thermal storage electric heating exhibit significant changes in their temporal distribution. From the figure, it is evident that the energy consumption peak of the thermal storage electric heating system is concentrated in the time periods of 0–4 h and 20–23 h, while the energy consumption load is significantly lower during the periods of 4–9 h and 17–24 h. This change in the temporal distribution is primarily due to the operational strategy of the thermal storage electric heating system, which takes advantage of the lower electricity prices at night to store heat and then releases the stored heat during the higher electricity price periods during the day. Specifically, the figure shows that from 0 to 4 h, the thermal storage electric heating device operates at a high heating output. From 4 to 9 h, the heating output of the device significantly decreases, indicating that the device is mainly releasing the stored heat during this period. From 20 to 23 h, the heating output increases again, suggesting that the device is preparing to store heat for the night. Figure 5 also clearly reflects the impact of time-of-use (TOU) electricity pricing policies on the operation of the thermal storage electric heating system. During the low-price periods of 0–4 h and 20–23 h, the heating output of the thermal storage electric heating system significantly increases. Conversely, during the high-price periods of 4–9 h and 17–24 h, the heating output significantly decreases. This operational strategy effectively utilizes the low-cost off-peak electricity at night. It also avoids running the system during the higher electricity price periods during the day, thereby minimizing electricity expenses and achieving the goal of economic optimality.

Figure 6 compares the actual power consumption and the optimization results of the Dasha Wo thermal storage electric heating station, which serves as a demonstration site. To validate the effectiveness of the proposed model for the energy consumption characteristics of thermal storage electric heating systems, we obtained the data from the electric boiler of the Dasha Wo demonstration site and normalized it. We then compared it with the optimization results generated by the proposed model. From Figure 6, it is evident that under the guidance of time-of-use (TOU) electricity pricing, the actual power consumption curve of the Dasha Wo demonstration site aligns well with the optimization results. Both curves show that the electric boiler is activated during the low-price night period (20–6 h) and shut down during the high-price day period (7–19 h). This clearly reflects the operational strategy of the thermal storage electric heating system to store heat during low-price periods and supply heat during peak periods. This operational mode effectively concentrates the load during the low-price night period, reducing overall electricity costs and benefiting the stability and balance of the power grid. However, there is a notable difference in the curves between 1 and 5 h. This discrepancy is due to the larger thermal storage tank capacity and relatively smaller electric boiler power specified in the optimization model. Therefore, during this period, the electric boiler operates at full load to meet the heat storage demand, resulting in a higher peak in the actual power consumption curve. This phenomenon highlights the importance of carefully designing and optimizing the thermal storage electric heating system, considering the matching relationship between the thermal storage tank capacity and the electric boiler power to ensure the system’s stability and economic efficiency in actual operation.

3.3. Cluster Energy Usage Characteristics of Thermal Storage Electric Heating Systems

This section is based on the actual electricity usage data from a village in Tianjin that has undergone a coal-to-electricity conversion. The data collected includes the load distribution over a single day after the village adopted electric heating. To facilitate a detailed analysis of energy usage characteristics, it is necessary to classify the village’s households and analyze the load data for each household, including both thermal loads and other loads (e.g., lighting). This will provide the specific data required for the energy usage analysis.

3.3.1. User Classification

(1)

User Classification Indicators

The households in the village exhibit differences, and to establish individual thermal load models and models for other loads (e.g., lighting), the following classification indicators are primarily considered:

(1) Heating Temperature Setpoint: Due to varying cold tolerance levels and family compositions, different households set different heating temperatures. The minimum heating temperature ranges from 16 °C to 17 °C, but the maximum heating setpoint is generally 20 °C for all households. For the purpose of this study, the maximum heating setpoint is assumed to be 20 °C for all users.

(2) Actual Heating Area: Differences in building structures and the number of residents result in actual heating areas ranging from 60 to 100 m².

(3) Family Heat Demand: Variations in family heat demand can roughly reflect the household size, electricity usage patterns, and economic status.

(2)

User Classification

In the heat load prediction model, user classification is based on the set heating temperature and the actual heating area. The specific temperature settings and heating areas are modeled using random numbers. For the prediction model of other loads aside from electric heating, user classification is derived from the heat load values obtained from the heat load prediction model.

In the development of an orderly electricity usage strategy, users are classified into four categories based on the start time of their heat storage: those who begin heat storage before 21:00, between 21:00 and 22:00, between 22:00 and 23:00, and between 23:00 and 24:00. This classification facilitates comparison and optimization of the strategy.

3.3.2. Heat Load Prediction Model

The heat load prediction model utilizes an estimation formula that takes into account the outdoor temperature and the building area to predict the heat load for residents. The heat load prediction model is given by Equation (34):

$$Q_{r.i}\left(t\right)=\alpha F\left(i\right)K\left(t_{n.i}\right(t)-t_{wn}(t\left)\right)/1000$$

(34)

In the equation, $Q_{r.i}(t)$ represents the basic heat consumption of the i-th household at time t in kW. α is the temperature difference correction coefficient for the building, which is taken as 1. Kis the heat transfer coefficient of the building, measured in $\mathrm{W}/\left({\mathrm{m}}^2\mathrm{k}\right)$. $F\left(i\right)$ is the building area of the i-th household in ${\mathrm{m}}^2$, which varies for different types of residents. $t_{n.i}\left(t\right)$ is the indoor heating temperature of the $i$-th household at time $t$ in °C, which also differs for different types of users. $t_{wn}\left(t\right)$ is the outdoor temperature at time $t$ in °C.

The method for determining the indoor heating temperature, $t_{n.i}\left(t\right)$, is as follows:

Assuming the heating demand is at its lowest during the daytime (10:00–17:00), the indoor heating temperature should be set to the minimum temperature of 16 °C or 17 °C. During the peak heating demand period from 18:00 to 21:00, the indoor heating temperature should be maintained at 19–20 °C. For the rest of the day, the indoor heating temperature should be set to 17–18 °C.

The outdoor design temperatures are as follows: −7 °C from 10:00 to 17:00, −11 °C from 18:00 to 21:00, −12 °C from 22:00 to 4:00 the following morning, and −9 °C for the remaining hours.

The method for determining the indoor heating temperature $t_{n.i}\left(t\right)$ is given by Equation (35):

$$t_{n.i}(t)=\left\{\begin{array}{l}16+\left[\eta \right] 10\le t\le 17\\ 19+\left[\beta \right] 18\le t\le 21\\ 17+\left[\mu \right] \mathrm{otherwise}\end{array}\right.$$

(35)

where $\eta$, $\beta$, and $\mu$ are random coefficients, and $\eta$, $\beta$, $\mu$ $\in \left[0,1\right]$; [ ] denotes the floor function (i.e., rounding down to the nearest integer).

The building area F is calculated using Equation (36):

$$F\left(i\right)=60+\left[(100-60)\ast \eta \right]$$

(36)

where $\eta$ is a random coefficient, and $\eta \in [0,1]$; [ ] denotes the floor function (i.e., rounding down to the nearest integer).

The building heat transfer coefficient K is given by Equation (37):

$$K={\displaystyle \frac{1}{\frac{1}{{\alpha }_n}+\sum \frac{\delta }{{\alpha }_{\lambda } \lambda }+R_k+\frac{1}{{\alpha }_{\omega }}}}$$

(37)

where the values of the relevant parameters are listed in

Table 1. Values of relevant parameters.

Parameter	Value
Interior Surface Heat Transfer Coefficient (${\alpha }_n$)	8.7
Exterior Surface Heat Transfer Coefficient (${\alpha }_{\omega }$)	23
Wall Material Thickness ($\delta$)	0.24
Thermal Conductivity of Wall Material (Clay Porous Brick) ($\lambda$)	0.58
Correction Coefficient for Material Thermal Conductivity (${\alpha }_{\lambda }$)	1.2
Thermal Resistance of Enclosed Air Layer ($R_k$)	0.7

.

3.3.3. Prediction Model for Non-Electrical Heating Loads

The base data for the load predictions is from a village in Tianjin that has adopted electrical heating. From the thermal load prediction model derived in the analysis of the energy characteristics of individual storage heaters, the thermal load for each household at each time can be obtained. Consequently, the non-electrical heating load for the entire village at each time can be calculated using Equation (38):

$$Q_q(t)=Q_z(t)-{\sum }_{i=1}^{num}{Q}_{r.i}(t)$$

(38)

In this equation, $Q_q\left(t\right)$ represents the non-electrical heating load for the entire village at time $t$ (in kW), $Q_z\left(t\right)$ is the total load for the entire village at time $t$ (in kW), and num is the total number of households in the village.

Assuming that the thermal load of each household can generally reflect the economic status and overall electricity consumption level of that household, the non-electrical heating load for each household at each time can be calculated using Equation (39):

$$Q_{q.i}(t)={\displaystyle \frac{Q_{r.i}\left(t\right)}{Q_r\left(t\right)}}\ast Q_q(t)$$

(39)

Here, $Q_{q.i}\left(t\right)$ is the non-electrical heating load for the $i$-th household at time $t$ (in kW), and $Q_r\left(t\right)$ is the total electrical heating load for the village at time $t$ (in kW).

3.3.4. Analysis of Energy Usage Characteristics of Storage Electric Heating Systems

Figure 7 illustrates the impact of integrating thermal storage electric heating systems at different proportions on regional load variations. The four curves represent the load profiles without thermal storage electric heating and with 10%, 20%, and 30% integration of thermal storage electric heating, respectively. Comparative analysis reveals that in the absence of thermal storage electric heating, the load curve exhibits a typical “double peak” characteristic, with distinct load peaks occurring during the daytime and evening, while the nighttime load remains relatively low and stable. As the proportion of thermal storage electric heating increases, the daytime load gradually decreases, and the curve tends to flatten, particularly from midday to evening. For instance, at a 30% integration level, the daytime peak load decreases by 22% compared to the scenario without thermal storage electric heating, indicating that thermal storage electric heating effectively alleviates daytime grid pressure. Simultaneously, the nighttime load significantly increases, forming a new load peak during the early morning hours. For example, at a 30% integration level, the nighttime load rises by 63% compared to the scenario without thermal storage electric heating, reflecting the characteristic of more thermal storage electric heating devices operating intensively during off-peak electricity pricing periods. Overall, as the proportion of thermal storage electric heating increases, the load curve transitions from a “double peak” to a “single peak” pattern, demonstrating that thermal storage electric heating optimizes regional load distribution through a “peak shaving and valley filling” operational strategy. This contributes to mitigating peak grid pressure during the daytime and enhances the economic efficiency and stability of grid operation.

From

Table 2. Daytime load reduction and nighttime load increase after integration of 10% thermal storage electric heating.

	Daytime Minimum Load (kW)	Nighttime Maximum Load (kW)
Without Thermal Storage Electric Heating	436.02	668.37
With 10% Thermal Storage Electric Heating	404.28	772.38
Load Change Rate	7%	16%

Note: Load change rate = change ÷ daytime minimum/nighttime maximum load when not connected to thermal storage electric heating, the same below.

,

Table 3. Daytime load reduction and nighttime load increase after integration of 20% thermal storage electric heating.

	Daytime Minimum Load (kW)	Nighttime Maximum Load (kW)
Without Thermal Storage Electric Heating	436.02	668.37
With 20% Thermal Storage Electric Heating	371.31	923.61
Load Change Rate	15%	38%

and

Table 4. Daytime load reduction and nighttime load increase after integration of 30% thermal storage electric heating.

	Daytime Minimum Load (kW)	Nighttime Maximum Load (kW)
Without Thermal Storage Electric Heating	436.02	668.37
With 30% Thermal Storage Electric Heating	338.24	1091.05
Load Change Rate	22%	63%

, it can be observed that as the proportion of storage electric heating systems increases, the minimum daytime load decreases significantly, while the maximum nighttime load rises substantially. Specifically, when 10% of traditional electric heating systems are replaced with storage electric heating systems, the minimum daytime load decreases from 436.02 kW to 404.28 kW, a reduction of 31.74 kW, with a load reduction rate of 7%. Simultaneously, the maximum nighttime load increases from 668.37 kW to 772.38 kW, an increase of 104.01 kW, with a load increase rate of 16%. As the proportion increases to 20%, the minimum daytime load further decreases to 371.31 kW, a reduction of 64.71 kW, with a load reduction rate of 15%. The maximum nighttime load rises to 923.61 kW, an increase of 255.24 kW, with a load increase rate of 38%. When the proportion reaches 30%, the minimum daytime load decreases to 338.24 kW, a reduction of 97.78 kW, with a load reduction rate of 22%. The maximum nighttime load increases to 1091.05 kW, an increase of 422.68 kW, with a load increase rate of 63%.

These results demonstrate that the integration of storage electric heating systems significantly alters the load distribution within the region. The reduction in daytime load becomes more pronounced as the proportion of storage electric heating systems increases, which is crucial for alleviating peak pressure on the daytime grid. Conversely, the nighttime load also increases, particularly when the proportion reaches 30%, with a 63% increase in the maximum nighttime load. This indicates that a large number of storage electric heating devices operate during the nighttime off-peak electricity periods, creating new load peaks. The reason for this phenomenon is that storage electric heating systems typically store heat during the nighttime when electricity prices are lower and then release the heat during the daytime when electricity prices are higher, effectively achieving load shifting and peak shaving. When 10% of thermal storage electric heating is integrated, the nighttime maximum load increases by 16%, exerting a relatively minor impact on the grid. However, when the integration proportion rises to 30%, the nighttime maximum load surges by 63%, resulting in a significant load peak. This concentrated increase in nighttime load may pose challenges to grid stability, particularly during periods of rapid load escalation, necessitating enhanced grid dispatching and reserve capacity management. Despite the significant increase in nighttime load, the grid can effectively manage load fluctuations through demand response coordination, such as time-of-use pricing and user-side load management. Additionally, reasonable planning of grid upgrade costs ensures stability. Moreover, the design of thermal storage electric heating systems has fully considered the grid’s regulation capacity. This ensures that the nighttime load increase remains within manageable limits and does not impose new pressures on the grid.

4. Conclusions

Through both simulation and empirical analysis, this study has conducted an in-depth exploration of the operational characteristics of storage electric heating systems and their impact on regional load distribution. The main conclusions are as follows:

(1)

Optimization of Energy Consumption Time Distribution: The thermal storage electric heating system significantly alters the temporal distribution of user energy consumption by shifting the peak energy usage period from daytime to nighttime during low electricity pricing hours, effectively reducing users’ electricity expenses.

(2)

Changes in Regional Load Distribution: With the increasing proportion of thermal storage electric heating, the regional daytime load decreases significantly, while the nighttime peak load rises markedly. Specifically, as the proportion of thermal storage electric heating increases from 10% to 30%, the daytime minimum load reduction rate increases from 7% to 22%, and the nighttime maximum load increase rate rises from 16% to 63%.

(3)

Mitigation of Grid Peak Pressure: The integration of thermal storage electric heating significantly reshapes the regional load distribution, playing a crucial role in alleviating daytime grid peak pressure. As the proportion of thermal storage electric heating increases, the regional daytime load decreases substantially, and the nighttime load rises, thereby effectively mitigating the daytime grid peak pressure.

Future research should focus on optimizing grid dispatching and exploring the regional application potential of thermal storage electric heating systems. In terms of regional applications, the adaptability of thermal storage electric heating systems under different electricity pricing policies and climatic conditions warrants in-depth investigation, particularly in regions with significant peak–valley electricity price differences. In such areas, these systems not only reduce users’ energy costs but also enhance grid stability and operational efficiency by optimizing load distribution. Additionally, along with smart grid technologies, the potential of thermal storage electric heating systems in renewable energy integration and comprehensive energy management can be further explored, providing new technical pathways for the efficient and low-carbon transformation of energy systems.