A Review and Prospective Study on Modeling Approaches and Applications of Virtual Energy Storage in Integrated Electric–Thermal Energy Systems

Abstract

The increasing use of renewable energy sources introduces significant fluctuations in power generation, demanding enhanced regulatory capabilities to maintain the balance between power supply and demand. To promote multi-energy coupling and the local consumption of renewable energy, integrated energy systems have become a focal point of multidisciplinary research. This study models adjustable sources, networks, and loads within electric–thermal integrated energy systems as energy storage entities, forming virtual energy storage systems to participate in the optimization and scheduling of integrated energy systems. This paper investigates the modeling and control strategies of virtual energy storage systems within electric–thermal integrated energy systems. Initially, it introduces the definition, logical architecture, and technical connotations of virtual energy storage. Next, it models temperature-controlled loads as virtual energy storage systems and compares them with traditional energy storage systems, analyzing their characteristic differences and summarizing virtual energy storage system modeling methods and characteristic indicators. This paper then focuses on the specific applications of virtual energy storage systems in four typical scenarios. Finally, it explores the future development directions of virtual energy storage.

1. Introduction

The high integration of renewable energy sources (RESs) has led to closer energy conversion and coupling among various energy types. Traditional power systems are gradually evolving into integrated energy systems (IESs). With the widespread adoption of combined heat and power (CHP) units, heat pumps (HPs), electric boilers (EBs), and air conditioners (ACs), among other energy conversion devices, the coupling between electricity and thermal systems is becoming more integrated. This evolution is forming integrated electricity and heat systems (IEHSs) [1,2]. Among the simplest and most widely used types of IESs, electric–thermal coupling systems utilize the easy storage characteristics of thermal energy for mutual complementation across multiple energy sources. They are a crucial platform for achieving high penetration of renewable energy consumption in the future. This concept has garnered extensive attention and research from scholars worldwide, leading to diverse research directions, including CHP flow calculation [3,4], CHP economic dispatch [5], CHP planning [6] and CHP state estimation [7].

Current research on electric–thermal integrated energy grids largely focuses on weakly coupled networks of a few large-scale CHP units. However, as the primary heat source for district heating, thermal power’s CHP units operate in a heat-first mode during the heating season, which improves their own energy efficiency but limits flexibility. This mode significantly contributes to curtailment issues in wind and solar power. It is evident that a reciprocal constraint exists between the flexibility of electricity systems and the efficiency of thermal systems. On one hand, the large-scale integration of renewable energy requires flexibility, yet CHP systems pursue efficiency at the expense of reducing electricity system flexibility. On the other hand, electricity is easily transmitted but difficult to store, whereas heat is easily stored [8] but hard to transmit, highlighting the inherent complementarity in the physical characteristics of electricity and thermal systems.

The comprehensive study of electric–thermal IESs aims to optimize the allocation of diverse energy forms over extensive temporal and spatial scales while meeting user demands for electricity and heat consumption. This includes enhancing the flexibility of system operations, thus providing new solutions to the integration of renewable energy [9,10]. However, electricity and thermal systems are distinct energy systems with unique physical properties, transmission laws, and conventional research methods. Their integration heightens the complexity of system analysis and optimization, presenting new challenges to the scheduling and optimization of IES operations.

In IESs, electricity systems exhibit fast transmission speeds and short response times, but electricity cannot be stored in large quantities. Thermal and cooling systems exhibit greater inertia. Thermal energy can be transmitted over long distances, while cooling systems typically operate within a transmission range of about 1 km [11]. Currently, many regions in China utilize centralized heating systems with heated buildings functioning as thermal storage devices [12]. Therefore, studying the transmission characteristics and scheduling methods of thermal systems is crucial.

In 2018, the concept of “virtual energy storage” (VES) was first introduced by Chinese scholars [13]. VES aggregates flexible electrical sources, energy grids, and loads, using surplus energy from storage units or injecting deficient energy into the system, thus balancing multiple energy sources, similar to physical energy storage [14]. VES is an innovative concept with significant importance both in China and globally. Unlike battery energy storage systems (BESSs), virtual energy storage systems (VESSs) do not require significant additional investment or space [15,16]. As of 2020, China’s urban building area reached approximately 50 billion square meters, with a total heating network length of about 500,000 km. Based on a room temperature fluctuation range of ±2 °C and a network temperature fluctuation range of ±5 °C, the virtual energy storage capacity of China’s heating system is estimated to be around 569.4 MWh. Consequently, VESSs may serve as an alternative to BESSs. Therefore, studying the transmission characteristics and scheduling methods of thermal systems is crucial [17,18].

Despite the extensive research on VESSs, particularly in regional heating and cooling systems [19,20,21,22], the literature reveals a gap in equivalent modeling methods for temperature-controlled loads (TCLs) and VESSs. For instance, Zhong et al. [23] developed models for electricity demand response (DR) and thermal inertia VES, integrating electrical and thermal energy storage in the economic dispatch of IESs; equivalent methods for TCLs and VESSs remain insufficiently explored. Xie et al. [24] summarized modeling and control strategies for VES in constant temperature-controlled loads (TCLs); equivalent methods for TCLs and VESSs remain insufficiently explored. Additionally, Amini et al. [25] coordinated and aggregated constant TCLs and electric vehicles to form VESSs, thus providing power adjustments traditionally managed by generators through load demand changes, but heterogeneous virtual energy storage modeling is not well integrated. This paper addresses this gap by focusing on the equivalent modeling and control strategies of TCLs and VESSs, offering a comprehensive review that contrasts with existing studies by delving deeper into this specific area.

The remainder of this paper is organized as follows: Section 2 presents a detailed analysis of the logical framework of VESSs and its technical implications for equivalent modeling. Section 3 focuses on VESS modeling methods, including individual and aggregated TCLs. Section 4 introduces VESS applications and corresponding control strategies. Section 5 explores future research directions for VESSs. Finally, Section 6 concludes the paper. The structure of this article is shown in Figure 1.

2. Basic Features of Virtual Energy Storage

2.1. The Basic Logic of Virtual Energy Storage

Figure 2 illustrates the structure of a typical IES virtual energy storage system. The IES centers around the power system, synergistically integrating with thermal, gas, cooling, and water networks. It utilizes diverse energy sources and technologies such as wind power, photovoltaics, CHP units, EBs, electric vehicles, batteries, thermal storage tanks, and gas storage facilities to supply energy to integrated energy clusters.

Given the diversity and complexity of devices and networks within IESs and the differences in timescales of various energy forms, energy storage can be modeled from the perspective of energy balance and normalization. This approach enables the storage-based modeling of sources, grids, and loads with uniform adjustable characteristics, thus forming a VESS that participates in IES optimization and scheduling. Energy storage equivalence principles can be flexibly selected based on device or network characteristics and regulatory requirements [26]. In electric–thermal IES, temperature-controlled loads, such as ACs and refrigerators [27], can adjust energy consumption by slightly altering temperatures within specified ranges. By effectively utilizing the inherent energy storage characteristics of inertial networks (thermal, gas, cooling, and water networks) [28], it is possible to regulate the temperature of the storage medium to control its energy storage capacity. Additionally, buildings possess significant thermal inertia; changes in electrical equipment characteristics result in indoor temperature changes with a certain lag. Adjusting the temperature change curve within an acceptable range for users can enhance the flexibility of thermal and cooling loads.

2.2. The Essence of Virtual Energy Storage

The operational characteristics of VES are akin to those of traditional BESSs. Some scholars have proposed a virtual battery model [29,30] that defines energy storage indicators such as charging/discharging power, virtual storage capacity, charging/discharging time, and the state of virtual energy (SOVE) for VES. The charging/discharging power of VES represents the equivalent power utilized when energy devices or networks participate in IES optimization and scheduling. For device-level VES, this value is contingent on the device’s operational status. The virtual storage capacity reflects the performance characteristics and specifications of the VES. The charging/discharging time of VES determines its sustained response capability [31]. The state of virtual energy (SOVE) can be viewed as an indicator of the remaining energy in VES, directly representing the device’s or the system’s response capability [32]. The core component of the thermal VES studied in this paper is temperature. As shown in Figure 3, when the temperature is at its lowest, the system’s state of charge (SOC) is zero. When the system absorbs more heat, it enters a charging state; conversely, for cooling systems, the opposite is true.

The integration of VES into electric–thermal IESs provides novel methods for system optimization and scheduling. VES plays several critical roles, including the following:

• Efficiency improvement: By controlling flexible resources and interacting with real-time energy prices, the modulation of energy output from devices or networks equates to the discharge or charge of a VES. This linear macroscopic storage model simplifies the complex microscopic dynamic models of flexible loads (FLs), thereby reducing the scale of system optimization and enhancing solution efficiency.
• Economic benefits: VES acts as a buffer energy source based on changes in energy device output or network capacity. It improves the economic efficiency and renewable energy absorption capacity of the power system by leveraging the synergistic flexibility of multi-energy complementarity while maintaining stable system operation. This can significantly reduce the investment required for traditional energy storage systems (ESSs), providing substantial economic benefits.
• Unified energy management: VES enables the digital abstraction and virtualization of various heterogeneous energy elements, such as electricity, heat, and cooling. This method integrates diverse physical and chemical energy characteristics into a unified framework, breaking down spatial and temporal barriers, enhancing energy visualization and controllability, and achieving dynamic optimization and scheduling with spatial–temporal variability and granular control.

We have compared the micro-dynamic model and the virtual energy storage model for flexible loads and the results are shown in

Table 1. Comparison between micro-dynamic model of FL and virtual energy storage model.

Aspect	Micro-Dynamic Model of Flexible Load	Virtual Energy Storage Model
Concept	Analyzes dynamic responses of individual loads to varying conditions.	Utilizes equivalent parameters to simulate energy storage behavior.
Complexity	Involves detailed modeling of load dynamics and interaction effects.	Simplifies dynamic processes by focusing on energy input and output.
Applicability	Suitable for systems with fast-changing load characteristics.	Effective in scenarios requiring energy balance and flexible scheduling.
Accuracy	High accuracy in modeling load behaviors under specific conditions.	Sacrifices some accuracy for simplicity and efficiency in optimization.
Optimization	Requires comprehensive data and computational resources for optimization.	Streamlines optimization by focusing on key energy variables.

.

3. Research on VES Modeling Methodology

This section summarizes modeling methods for virtual energy storage (VES) in energy systems, networks, and devices within electric–thermal IESs. Optimizing and scheduling electric–thermal IESs can significantly enhance their capacity to integrate new energy sources by effectively utilizing the VES potential of heating system. Under certain conditions, the heating system, acting as a natural thermal storage device, can replace physical storage units, thereby reducing construction costs [33]. Furthermore, the heating system collaborates with physical thermal storage [34] and buildings possessing thermal inertia [35]. This section primarily examines VES modeling methods for controllable indoor temperature loads and heating networks with adjustable supply and return water temperatures based on regulatory principles. It also summarizes characteristic VES indicators under various regulatory principles and methodologies. Refer to

Table 2. Comparison of metrics for virtual energy storage in buildings and heating networks.

Virtual Energy Storage Type	Charging and Discharging Power	Energy Storage Capacity	Charging and Discharging Time	Energetic State Description
Temperature-controlled load	Reflects differences in transient and steady-state power.	Affected by heat source power, pipe network heat loss, and heat load requirements.	Influenced by the rate of temperature change perceived by users.	Ratio of real-time temperature difference to user comfort interval.
Heating pipe network	Affected by heat source power, pipe network heat loss, and heat load requirements.	Dependent on upper and lower limits of water supply temperature.	Related to the rate of change in heat medium temperature.	Ratio of heat medium temperature to upper and lower limits of pipeline bearing temperature.

for the related VES indicators.

3.1. A VES Modeling Approach for TCLs

Temperature-controlled loads, as a crucial component of residential electricity consumption, demonstrate excellent adjustability. These loads encompass ACs, refrigerators, HPs, and water heaters. Power-to-Heat (P2H) loads, in particular, constitute a significant portion of peak electricity demand during summer and winter, presenting considerable regulatory opportunities. Existing studies predominantly examine the virtual energy storage characteristics of air-conditioning loads [36]. Thus, this section primarily focuses on air-conditioning loads as the main subject of investigation.

3.1.1. P2H-Building Virtual Energy Storage Model

• ETP model

The Equivalent Thermal Parameter (ETP) model is extensively employed to model TCLs, describing the transfer and dissipation of thermal energy within a room. The first-order ETP model is represented by an equivalent circuit, illustrated in Figure 4a [37,38,39]. It is highly practical and suitable for scenarios involving gradual temperature changes within a room. However, it considers fewer factors influencing indoor temperature, leading to less precise results. Additional factors, such as AC compressor frequency, outdoor temperature, and building structure, have been explored in the existing literature to complement and enhance established virtual energy storage models for air-conditioned buildings. Wang et al. [40] and Yin et al. [41] examined the influence of outdoor temperature on the virtual energy storage of ACs, revealing a significant correlation and time sensitivity. A dual-parameter model was developed to characterize the heat exchange process between indoor air and building envelope and furniture surfaces, comprehensively considering these elements [36,42,43]. In another study, AC compressor frequency served as an intermediary variable, and a discrete virtual charging state model of air-conditioning loads was established using a linear function model of electricity and cooling capacity [27,44,45]. Additionally, multiple distributed temperature-controlled loads were managed through virtual energy storage aggregation control [46]. Higher-order ETP models, namely 2R2C [46], 3R2C [47], and 4R4C [48], are depicted in Figure 4b, c, and d, respectively. The second-order ETP equivalent model (2R2C) accounts for the temperature conditions of indoor air and solids. Subsequent studies integrated factors including solar radiation, outdoor temperature, equivalent thermal capacity and resistance of the building envelope, window and roof equivalent thermal resistance, internal equipment heat generation, and cold air infiltration and ventilation losses.

These thermal conduction parameters are analogous to electrical conduction and can be calculated using Ohm’s Law. Q represents the cooling or heating capacity of the building. T_in and T₀ denote the indoor and ambient temperatures, respectively. R and C signify the equivalent thermal resistance and thermal capacitance, respectively.

Typical values for thermal parameters of air-conditioning loads are provided in the literature, as shown in

Table 3. Comparison of related indexes between virtual energy storage and physical energy storage.

Parameter Name	Parameter Symbol	Parameter Value	Parameter Unit
Equivalent thermal resistance	R	1~3	W/(°C·m2)
Equivalent thermal capacity	C	47~230	kJ/(°C·m2)

[49].

Based on the circuit principle, the first-order ETP model can be described as Equation (1):

$${\displaystyle \frac{\mathrm{d}{T}_{\mathrm{in}}\left(t\right)}{dt}}={\displaystyle \frac{Q_{ac}\left(t\right)}{C}}+{\displaystyle \frac{\left(T_{out}\left(t\right)-T_0\right)}{RC}}$$

(1)

where T_in(t) is indoor temperature, °C; T_out(t) is outdoor temperature, °C; Q_ac(t) is the cooling capacity of the air-conditioning system, W; R is the building equivalent thermal resistance, °C/W; and C is the equivalent heat capacity of the building, J/C.

The relationship between indoor temperature and user comfort is typically referred to as the comfort level. The closer the indoor temperature is to the optimal temperature and the smaller the temperature fluctuations, the higher the comfort level of the occupants. Conversely, the farther the indoor temperature deviates from the optimal range and the greater the temperature fluctuations, the lower the comfort level. The acceptable temperature range and the acceptable temperature fluctuation range for indoor heating and cooling are given by Equations (2) and (3).

$$T_{\min }⩽T(t)⩽T_{\max }$$

(2)

$$\mathsf{\Delta }{T}_{\min }⩽\left|T(t+1)-T(t)\right|⩽\mathsf{\Delta }{T}_{\max }$$

(3)

where T_min is the upper limit of the acceptable indoor temperature range of the building envelope for comfort purposes, °C; T_max is the lower limit of the acceptable indoor temperature range of the building envelope for comfort purposes, °C; ΔT_min is the lower limit of the acceptable indoor temperature variation interval for the building envelope to ensure comfort, °C; and ΔT_max is the upper limit of the acceptable indoor temperature variation interval for the building envelope to ensure comfort, °C.

Considering the primary factors affecting heat inside buildings, the differential equation is given as Equation (4):

$$(k_{wall}{S}_{wall}(T_{out}(t)-T_{in}(t))+k_{win}{S}_{win}(T_{out}(t)-T_{in}(t))+G(t)S_{win}{S}_c+P_{in}(t)-P_{air}(t))\mathsf{\Delta }t=\rho V{C}_{\mathrm{in}}(T_{in}(t+1)-T_{in}(t))$$

(4)

where k_wall is the heat transfer coefficient of the exterior wall of a building, which indicates the amount of heat that passes through the wall per second for every 1 °C difference between the indoor and outdoor temperatures during steady-state heat transfer; S_wall is the area of building facades, m²; k_win is the heat transfer coefficient of exterior building windows; S_win is the area of exterior building windows, m²; G(t) is solar radiant power, which represents the amount of heat received per second per square meter when exposed perpendicular to the light; S_c is the shading coefficient, the value of which is related to the presence or absence of a sunshade, glazing material, etc.; P_in is the heating power of indoor heat sources, such as the human body and electrical equipment; P_air is the power of electric heating equipment; ρ is the room air density; V is the room air volume; and C_in is the specific heat capacity of the room air.

2.

Virtual energy storage model

However, the Equivalent Thermal Parameter (ETP) model is limited to simulating scenarios without external disturbances. Therefore, this paper integrates dynamics, uncertainties, and human behavior, as illustrated in Figure 5. Expanding on the ETP model discussed earlier, a TCL adjusts its operating power by setting temperatures or switching states to provide regulation services. By leveraging the thermal inertia of buildings [40,50,51,52], adjustments to a TCL’s operating power within the range of human thermal comfort have minimal impact on indoor temperatures. Similar to battery characteristics, a set of parameters defines the state variables of VESSs, encompassing energy upper and lower limits, power upper and lower limits, state of charge, and efficiency, detailed in

Table 4. State parameters of virtual energy storage.

Parameter Name	Parameter Symbol
Baseline power	$P_{\mathrm{base}}\left(t\right)$
Virtual charging power	$P_{ch}\left(t\right)$
Virtual discharging power	$P_{dis}\left(t\right)$
Virtual energy storage capacity	$Q_{ca}$
Charge and discharge duration	$t_{ch/dis}$
State of charge	$VSOC(t)$

.

According to Meng et al. [45], when the heat generated by an AC matches the heat dissipated by the building, the indoor temperature reaches the set temperature. The heating power required (P_base) to maintain this temperature serves as the baseline power for a VESS. The virtual charging and discharging power of the energy storage system can then be derived from this baseline power:

$$P_{\mathrm{base}}={\displaystyle \frac{Q}{\eta }}={\displaystyle \frac{T_{\mathrm{out}}-T_{\mathrm{in}}}{\eta R}}$$

(5)

where η is the AC energy efficiency ratio.

$$\left[P_{ch/dis}\left(t\right)\right]=\left\{\begin{array}{c}\left[P_{\mathrm{air}}\left(t\right)\right]-\left[P_{base}\left(t\right)\right]>0,\mathrm{charging} \mathrm{state}\\ \left[P_{\mathrm{air}}\left(t\right)\right]-\left[P_{base}\left(t\right)\right]<0,\mathrm{discharging} \mathrm{state}\end{array}\right.$$

(6)

where P_ch/dis is the charging and discharging power.

The Virtual Heat Storage Capacity (VHSC) correlates with the building’s equivalent thermal capacity parameters and the indoor temperature comfort range [T_max, T_min]. It remains unaffected by outdoor temperature or solar radiation:

$$Q_{ca}=C(T_{\max }-T_{\min })$$

(7)

where Q_ca is the virtual energy storage capacity.

Alongside the building’s inherent parameters, the charging and discharging times are influenced by internal and external temperatures, switch function states, and electrical power levels:

$$t_{ch/dis}=RC\ln ({\displaystyle \frac{T_{in}(t_0)-T_{\mathrm{out}}(t)-R{P}_{\mathrm{AC}}(t)}{T_{in}(t)-T_{\mathrm{out}}(t)-R{P}_{\mathrm{AC}}(t)}})$$

(8)

where t_ch/dis is the charging and discharging time.

The Virtual State of Charge (VSOC) is defined as the ratio of the thermal energy stored in the VESS to the Virtual Heat Storage Capacity (VHSC). Equation (9) illustrates its role in describing the VESS’s state of charge, with values ranging from 0 to 1. The VSOC equals 0 when the indoor temperature T_in = T_min and 1 when T_in = T_max.

$$VSOC(t)={\displaystyle \frac{E(t)}{C_{ca}}}$$

(9)

where E(t) is the energetic state.

3.1.2. Virtual Energy Storage Models for Other TCLs

Other temperature-controlled loads, akin to air-conditioning systems, regulate their temperature by adjusting their power output, demonstrating characteristics akin to charging and discharging. These loads possess adjustable power due to their variable temperature ranges. For instance, the operational range of electric water heaters is defined by their upper and lower temperature limits, refrigerators adjust their output according to acceptable food refrigeration temperatures, and HPs and EBs vary their output based on indoor temperature bounds. However, due to varying physical properties and functionalities among temperature-controlled loads, there are differences in the modeling of virtual energy storage (VES) for HPs, refrigerators, EBs, and air-conditioning systems [53]. Research on the VES characteristics of other temperature-controlled loads remains limited.

For HP loads, their virtual energy storage characteristics closely resemble those of air-conditioning systems. The distinction lies in the purpose: air-conditioning systems primarily store energy to cool indoor spaces, while HPs primarily store energy to heat indoor spaces. A common approach involves integrating the operational state of HPs with indoor temperatures to develop a virtual energy storage model [54]. Studies indicate that coordinating the operation of HPs with batteries can effectively stabilize power fluctuations in microgrid interconnections. However, practical applications must consider the impact of operational cycles on the virtual energy storage capabilities of HPs [50]. Additionally, the rated capacity of virtual energy storage in refrigerators can be accurately forecasted and integrated into grid scheduling [55]. The rated capacity of refrigerator virtual energy storage can be effectively projected and utilized for grid scheduling [56]. Concerning water heater loads, a virtual energy storage model utilizing adjustable water temperatures has been developed and implemented within IESs, thereby enhancing system economic efficiency and power system frequency characteristics [57].

3.2. A VES Modeling Approach for Heating Pipe Networks

A centralized heating system consists of a heat source, a primary heat exchange station, a primary network, a secondary heat exchange station, a secondary network, and heat users. The primary network serves as a transmission network, characterized by significant transmission delays and dynamic properties, whereas the secondary network functions as a distribution network with shorter transmission delays and less-pronounced dynamic properties [58,59]. This study exclusively focuses on the thermal model of the primary heating network. The following assumptions are made for the heating network:

• The hot water in the pipeline is treated as an incompressible fluid;
• Only the temperature distribution along the pipeline length is taken into account;
• Heat conduction along the pipeline length is negligible compared to convective heat transfer and is therefore disregarded.

According to the law of energy conservation, a one-dimensional thermal dynamic model of the heating pipeline is developed:

$${\rho }_{\mathrm{w}}S{C}_{\mathrm{p}}{\displaystyle \frac{\partial T_{\mathrm{P}}}{\partial t}}+m{C}_{\mathrm{p}}{\displaystyle \frac{\partial T_{\mathrm{P}}}{\partial x}}={\displaystyle \frac{T_{\mathrm{a}}-T_{\mathrm{P}}}{R_{\mathrm{P}}}}$$

(10)

where ${\rho }_{\mathrm{w}}$ is the density of water; S is the inner cross-sectional area of the pipe; $C_{\mathrm{p}}$ is the specific heat capacity of water; T_p is the temperature of the water in the pipes; m is the mass flow rate; T_a is the ambient temperature outside the pipe; $R_{\mathrm{p}}$ is the total heat transfer thermal resistance from the tube to the surroundings; and t and x are temporal and spatial variables.

Equation (10) is differentiated and arranged as

$$(1+{\displaystyle \frac{3m\mathsf{\Delta }t}{2{\rho }_{\mathrm{w}}S\mathsf{\Delta }x}}+{\displaystyle \frac{\mathsf{\Delta }t}{{\rho }_{\mathrm{w}}S{c}_{\mathrm{p}}{R}_{\mathrm{p}}}})T_n^i=T_n^{i-1}+{\displaystyle \frac{\mathsf{\Delta }t}{{\rho }_{\mathrm{w}}S{c}_{\mathrm{p}}{R}_{\mathrm{p}}}}{T}_{\mathrm{a}}+{\displaystyle \frac{m\mathsf{\Delta }t}{{\rho }_{\mathrm{w}}S\mathsf{\Delta }x}}(2T_{n-1}^i-{\displaystyle \frac{1}{2}}{T}_{n-2}^i)$$

(11)

where $T_n^i$ is the temperature of the pipe at time step number i and space step number n; Δt and Δx are time and space steps.

$$T_n^i=C_0+C_1{T}_n^{i-1}+C_2(2T_{n-1}^i-{\displaystyle \frac{1}{2}}{T}_{n-2}^i)$$

(12)

where C₀, C₁, and C₂ is a constant.

The presence of transmission delay effects in the thermal system provides the heating network with an inherent thermal storage capability, further enhanced when regulating supply and return water temperatures. Thermal storage in the system manifests as an increase in the return water temperature. If the heat source output exceeds the load demand during a period, the return water temperature increases after transmission and heat exchange at the secondary station, indicating network thermal storage. Conversely, a decrease in the return water temperature reflects heat release from the network.

Due to temperature fluctuations across the network, a single location cannot accurately gauge current thermal storage. To enhance the model from previous references, an equivalent average temperature is defined as follows:

$$T_{\mathrm{eq}}^t=(\sum _{j=1}^{\mathrm{K}}\sum _{n=1}^{\mathrm{M}}(T_{n,j}^t\mathsf{\Delta }x{S}_j))/(\sum _{j=1}^{\mathrm{K}}\mathsf{\Delta }x{S}_j)$$

(13)

where $T_{\mathrm{e}\mathrm{q}}^t$ is the equivalent average temperature of the water supply or return network at time t; $T_{n,j}^t$ is the temperature of the pipe numbered j at spatial location n at time t; and K and M are the total number of pipes and the total number of spatial steps of pipes numbered j, respectively.

To describe the thermal storage level of the heating network, the Virtual Heat Storage Tank (VHST) model established is used to derive the State of Virtual Thermal Storage (SOVTS) index. The virtual thermal storage of the heating network can be broadly determined by the difference between heat supply and heat consumption, fundamentally influenced by the pipeline temperature and with certain limitations.

In the following, the heat storage capacities of the supply water network and the return water network are defined based on a reference temperature. To ensure the safe and stable operation of the heating system, the upper and lower limits of the supply and return water temperatures are set according to design specifications, thereby determining the upper and lower bounds of the network’s thermal storage:

$$Q_{\mathrm{eq}}^t=C_{\mathrm{p}}{\rho }_{\mathrm{w}}{V}_{\mathrm{p}}(T_{\mathrm{eq}}^t-T_{\mathrm{p}}^{\mathrm{ref}})$$

(14)

where $Q_{\mathrm{e}\mathrm{q}}^t$ is the real-time heat storage in the pipe network; V_p is the water capacity of the pipe network; and $T_{\mathrm{p}}^{ref}$ is the reference temperature.

$$Q_{\mathrm{eq}}^{\max }=C_{\mathrm{p}}{\rho }_{\mathrm{w}}{V}_{\mathrm{p}}(T_{\mathrm{p}}^{\max }-T_{\mathrm{p}}^{\mathrm{ref}})$$

(15)

$$Q_{\mathrm{eq}}^{\min }=C_{\mathrm{p}}{\rho }_{\mathrm{w}}{V}_{\mathrm{p}}(T_{\mathrm{p}}^{\min }-T_{\mathrm{p}}^{\mathrm{ref}})$$

(16)

where $Q_{\mathrm{e}\mathrm{q}}^{max}$ and $Q_{\mathrm{e}\mathrm{q}}^{min }$ are maximum and minimum heat storage capacities; $T_{\mathrm{p}}^{max }$ and $T_{\mathrm{p}}^{min }$ are maximum and minimum temperature of thermal storage.

Therefore, the unified virtual thermal storage of the secondary heating network in the heating system can be expressed as follows, obtaining the SOVTS of the heating network. Assuming equal water capacities in both the supply and return water networks, this can be further simplified to

$$S_{\mathrm{OVTS}}(t)={\displaystyle \frac{T_{\mathrm{eq}}^t-T_{\mathrm{p}}^{\min }}{T_{\mathrm{p}}^{\max }-T_{\mathrm{p}}^{\min }}}$$

(17)

The VES model for heating networks discussed above is mainly developed for single heat source and radial heating network structures, with sparse research on complex ring heating networks involving multiple heat sources [60]. While most VES models for heating networks adjust supply and return water temperatures, this mode necessitates high flow rates, resulting in elevated circulation pump speed and power consumption. Consequently, some studies have explored VES models for heating networks that focus on regulating flow rates [61,62]. Research suggests that the proposed mode of adjustment and scheduling can optimize heat loss power and circulation power consumption, showing better economic and flexibility performance than temperature adjustment methods. However, frequent adjustments in flow rate can cause hydraulic imbalance in the heating network, jeopardizing thermal system stability. Hence, research on VES in heating networks primarily focuses on temperature regulation.

3.3. Modeling of Virtual Energy Storage Aggregation

Reference [26] examined the aggregation of air conditioning based on temporal characteristics. Another study also explored the aggregation of air conditioning based on temporal characteristics [63]. Furthermore, other research introduced a temperature-controlled load aggregation model that incorporates response uncertainty, assessing the scheduling potential of TCL, thus highlighting its significant engineering application value [64]. A stochastic battery model was also proposed to represent aggregated TCL flexibility using a concise set of power signals [65,66]. Reference [30] developed a simplified time-varying thermal energy storage model to illustrate aggregated TCL flexibility, calculating suboptimal control trajectories. Additionally, a leaky storage unit was proposed to represent aggregated TCL flexibility in optimizing multiservice portfolios [67].

A single VESS unit’s constant temperature-controlled load is usually insufficient to meet the minimum load requirement for participation in DR programs. Thus, aggregating individual VESS units through an aggregator proves effective in leveraging the benefits of DR programs. In this study, each residential community, consisting of hundreds of air-conditioned households, is managed by an aggregator. The total energy consumption of the VESS is expressed as

$$P_{VESSs}(t)=\sum _{j=1}^{N_{air}}{\displaystyle \frac{1}{{\eta }_j}}{P}_{ac,j}{S}_{ac,j}(t)$$

(18)

where PVESS represents the total power consumption of aggregated VESS units, Nair denotes the total number of air-conditioning units in the aggregator, and j denotes the j-th AC.

Various operational scenarios (e.g., different T_set, T_db, P_rate, and j) can be employed to characterize and aggregate a group of VESS units. Monte Carlo simulations are used for generation [68]. Simulating real residential scenarios across multiple building models models actual air-conditioning household situations. After establishing the aggregation model, estimating the maximum controllable capacity of each VESS aggregator is essential for upper-level control purposes.

$$\mathrm{Max}{P}_i^{max}(t)=\sum _{j=1}^{N_{air}}{\displaystyle \frac{1}{{\eta }_j}}\left(1-S_{ac,j}(t)\right)P_{rate,j}$$

(19)

where $P_i^{max}$ is the maximum controllable capacity in aggregator i. It is assumed that reactive power is fully compensated on the air conditioner side; hence, $P_i^{max}$ specifically means the maximum controllable active power in the aggregator. It is worth noting that the decision variable in (19) is S_ac,j(t), and hundreds of VESSs are controlled by the same aggregator.

The calculation of Formula (21) shall satisfy the following conditions:

$$S_{ac}(t)=\left\{\begin{array}{lll}0\hfill & \mathrm{if} S_{ac}(t-1)=1\&\hfill & T_r<T_r^{min}\hfill \\ 1\hfill & \mathrm{if} S_{ac}(t-1)=0\&\hfill & T_r>T_r^{max}\hfill \\ S_{ac}(t-1)\hfill & \mathrm{otherwise}\hfill \end{array}\right.$$

(20)

$$T_r^{min}⩽T_r(t)⩽T_r^{max}$$

(21)

$$T_w^{min}⩽T_w(t)⩽T_w^{max}$$

(22)

Formula (20)’s maximum capacity estimation model presents a nonlinear mixed-integer programming problem that is challenging to use in traditional mathematical methods. Therefore, an optimization approach based on genetic algorithms is employed to tackle the capacity estimation model. Once the maximum controllable active power is determined within the aggregator, it can be further applied for upper-level control objectives, including voltage regulation and load management.

The modeling methods for buildings and pipe networks are shown in

Table 5. Summary of virtual energy storage modeling methods.

VES Modeling for TCL	VES Modeling for Heating Pipe Networks
Equivalent modeling based on ETP	Equivalent to a heat storage tank
Essence: variable range of medium temperature
Responding to the energy state of the system in terms of medium temperature

.

4. VES Application Scenarios and Control Strategies

Previously, the logical framework and technical essence of virtual energy storage (VES) were summarized. Within electric–thermal IESs, VES can dynamically adjust its charging and discharging power by altering temperature settings, playing a pivotal role. However, numerous energy devices and networks can be considered as VES, yet existing research has not fully capitalized on all VES resources within IESs. Moreover, application scenarios vary depending on the research objectives. Therefore, this section focuses on analyzing four typical application scenarios and their corresponding control strategies for virtual energy storage.

4.1. Demand Response

The characteristics of thermal loads (heating and cooling) are akin to electrical loads, offering substantial potential for implementing DR scheduling. DR optimally utilizes the dispatchable value of various load types, thereby smoothing power fluctuations and effectively achieving peak shaving and load filling. DR aimed at distributed users typically falls into two categories: load-specific DR and user-oriented DR. In the former, aggregation entities such as load aggregators act as the implementation bodies, aggregating specific types of loads (such as thermal loads) from users to form load clusters. Incentive measures are then tailored specifically for these types of loads. In contrast, the latter type typically involves electricity retailers as the implementing entities, directly offering incentives to users. Users generally optimize the operation of all their adjustable loads based on these incentive signals.

Qi et al. [69] developed an incentive-based integrated DR framework that incorporates energy network coupling across various electricity pricing schemes. It devised DR mechanisms tailored to variations in electricity prices for different types of loads. Wang et al. [70] integrated subjective and objective user considerations to propose a centralized air-conditioning control strategy. From the perspective of load aggregators, a novel dual-layer optimization model was developed, comprehensively integrating user DR preferences to maximize aggregator profits. In a study by Xiao et al. [71], probabilistic scenarios are used to model the uncertainty of renewable distributed energy and loads, considering interruptible demands related to both electricity and heating loads and consumer comfort. However, this model lacks comprehensive network modeling. A heating load DR model was developed in a separate study considering temperature heat dissipation and sensitivity limits. Under compensation incentives, it effectively harnesses the flexibility of heating load adjustment [72]. Addressing the optimization of comprehensive energy system operations at the district level, another study proposes incorporating incentive-based DR and direct load control methods, suggesting modeling electricity and heating loads separately based on load classification [73]. Furthermore, a comprehensive heating load DR model has been established, covering electricity, gas, cold, and heat loads, along with various heating demand levels [74]. Furthermore, a comprehensive heating load DR model has been established, covering electricity, gas, cold, and heat loads, along with various heating demand levels [75].

4.2. New Energy Consumption

Electricity generated from renewable sources contributes to energy conservation and emission reductions. However, the inherent uncertainty often results in mismatches between generation and demand, thereby diminishing the power system’s reliability [76]. Some research has indicated that integrating VESSs can mitigate uncertainty in wind and solar power generation, thereby enhancing the integration of renewable energy [77]. Reference [78] proposed novel approaches to reducing uncertainty from RESs and improving the economic operation of power systems. A revenue equation formulated as the objective function comprehensively considers operational revenues, costs, uncertainties in renewable energy generation, and renewable energy prices. Optimal operation modes are determined using particle swarm optimization methods, ensuring VESSs reduce uncertainty economically [79]. Yang et al. [80] introduced a two-stage electric–thermal system coordination strategy based on thermal storage characteristics within district heating networks to enhance unit peak shaving capabilities and reduce wind curtailment costs. In practical applications, wind or solar curtailment costs are integrated into the economic dispatch of VESSs, improving system efficiency and renewable energy use.

The objective function reflecting the goal of integrating renewable energy can be formulated as follows:

$$F=\min \left(\sum _{t=1}^T{P}_t^{\mathrm{cut}}\right)$$

(23)

where $P_t^{\mathrm{c}\mathrm{u}\mathrm{t}}$ is the power disposal in time period t.

Ai et al. [81] explored aggregation methods for various types of air-conditioning loads, investigating their potential for demand-side response and advocating for their participation in related initiatives. Using wind energy integration as a case study, their research verifies the practicality of incorporating demand-side resources to support renewable energy integration. In contrast to prior studies [82] focusing on smoothing wind power fluctuations through air-conditioning loads, reference [81] introduced a control model that shifts from time-domain to temperature-domain considerations. This innovative approach offers a fresh perspective on how temperature-controlled loads can interact with RESs.

4.3. Smoothing Contact Line Power

Due to the uncertainty in renewable energy generation and electricity demand, discrepancies in grid power connections arise. Virtual energy storage (VES) systems can alleviate these discrepancies to some extent [50]. Ao et al. [82] examined energy storage in office buildings and present a power smoothing control method for microgrid connections, addressing discrepancies between daily and hourly schedules and real-world scenarios. Zhao et al. [83] explored the virtual energy storage characteristics of air-conditioning loads and introduce a variable structure sliding mode tracking control strategy. This approach employs a state-space model of grouped air-conditioning loads, utilizing wind-power-storage-clustered air-conditioning load joint output as the sliding mode surface to mitigate microgrid connection power fluctuations. In urban park microgrid systems, Chen et al. [84] investigated the collaborative operation of air-conditioning load virtual energy storage and energy storage batteries. Their study presents an optimal control strategy based on continuous state variable constraints, with the objective function formulated as follows:

$$J=\min \int {(y_{\mathrm{ref}}-y)}^2\mathrm{d}t$$

(24)

where y_ref is the reference value for the deviation of electricity generation from electricity consumption and y is the actual value of the deviation of electricity generation from electricity consumption.

Wang et al. [49] proposed a coordinated control strategy for mitigating power fluctuations in grid connections. By employing Butterworth filters with varying time constants [50], VESSs and ESSs can effectively attenuate both high-frequency and low-frequency power fluctuations. This strategy ensures user comfort and extends battery longevity [85]. However, depending solely on empirically determined time constants in traditional filtering algorithms is limited, as it may not achieve optimal outcomes.

4.4. Integrated Energy Optimized Dispatch

VES applications in IESs primarily aim to minimize overall operational costs. VES devices are typically deployed in integrated energy cities or industrial parks, forming systems consisting of single or multiple device clusters that participate in energy scheduling [27,86]. The virtual thermal storage characteristics of heating networks or buildings are commonly applied in integrated electric–thermal–gas energy systems, considering network architecture and co-managed with CHP units and energy conversion devices (such as EB and HP). These systems adjust thermal output in response to peak–valley electricity prices, storing or releasing heat to optimize operational costs [23,87]. Jin et al. [88] proposed an optimized scheduling strategy for cold–hot–electricity co-production microgrids integrating VESSs to reduce operational costs. This method integrates VESS models into microgrid optimization scheduling models based on building thermal characteristics. Additionally, it ensures that indoor temperatures remain within acceptable ranges to guarantee user comfort during economic dispatch periods [89]. Beyond user comfort considerations, pricing information within microgrids also plays a crucial role in enhancing economic benefits [90]. Wang et al. [91] explored the economic adjustment potential of heating networks’ virtual energy storage characteristics in electric–thermal IES operations under time-of-use electricity pricing incentives, maximizing the complementary energy attributes of electric and thermal systems to lower overall IES operational costs. The general objective function of that study can be broadly expressed as

$$\min F=C_{\mathrm{buy}}+C_{\mathrm{O}\&\mathrm{M}}+C_{\mathrm{VES}}$$

(25)

where C_buy is acquisition costs; C_O&M is O&M costs; and C_VES is VES calling costs.

Due to varying considerations in different literature sources, economic optimization objective functions differ, but they generally build upon Equation (25) and include additional cost modules to form economic dispatch optimization strategies tailored to specific scenarios. For instance, introducing penalty cost modules for user temperature comfort can reduce operational costs for cold–hot–electricity co-supplied buildings [89]. Incorporating penalty cost modules for deviations in CHP unit operational ranges, coupled with the thermal storage characteristics of heating systems (VES), enhances the operational flexibility and economic efficiency of electric–thermal combined systems. Introducing penalty cost modules for wind curtailment [92] leveraging the virtual thermal storage characteristics of heating networks and buildings significantly reduces system operation costs and wind curtailment.

Jin et al. [93] proposed a dynamic economic dispatch model for a Hybrid Microgrid (H-Microgrid) considering user comfort and real-time electricity prices. The H-Microgrid integrates detachable distributed generators, RESs, and low-carbon buildings. Dynamic economic dispatch methods help reduce operating costs, minimize startup and shutdown cycles of distributed generators, and increase their available capacity [94].

Due to the limited number of individual TCLs and their smaller capacity, lower power, and greater uncertainty of VESSs in a single microgrid compared to the main grid, coordination with generators in the microgrid or other traditional energy storage devices (such as wind, solar, and batteries) is necessary to mitigate these drawbacks. Therefore, further research is needed to develop effective coordination control methods.

5. Discussion

Many scholars have made substantial advancements in modeling and applying VESSs using thermal control loads. However, within the context of China’s “Dual Carbon” objectives, there remains considerable scope for further research. This section investigates future research avenues for leveraging thermal control loads on the demand side to deliver ancillary services, aligning with the “Dual Carbon” objectives.

• Adaptation of VESS Control to Different Application Scenarios

VESS control strategies must account for a broader range of application scenarios and adapt to each specific case. The stability challenges encountered by power systems are varied, yet current VESS control strategies typically offer only a single type of ancillary service, thereby limiting their problem-solving capabilities. Investigating how VESSs can deliver multiple ancillary services within a unified control framework may help maintain system stability comprehensively while avoiding inconsistencies arising from disparate control strategies. Therefore, exploring methods for controlling load groups to deliver various ancillary services in diverse environments warrants further investigation.

2.

Coordinated Control of Multiple Types of VESSs

Current research on VESSs’ provision of ancillary services primarily focuses on con-trolling similar types of loads, resulting in the underutilization of a VESS’s overall regula-tion potential. Different types of VESSs demonstrate complementary characteristics con-cerning operating time and spatial distribution. Properly coordinating multiple VESS types for participation in control could further exploit their potential to provide ancillary services. However, challenges emerge in coordinating these types, particularly concerning the distribution of control responsibilities and benefits. Thus, further research is required to determine how to effectively coordinate multiple load types to provide ancillary services in terms of control methods, effects, and benefits.

3.

Research on Adjustable Potential of VESSs Under Limited Information and Random Factors

As China’s electricity market evolves, the diversity of market participants and trading models increases, requiring system control strategies to consider more factors. For VES systems, initial capacity estimates can be made through modeling, but the potential of a time-varying system to provide ancillary services to the power system at different times varies. Accurately estimating this adjustable potential is crucial. However, obtaining large amounts of accurate data, such as electricity usage and load parameters, can be challenging due to privacy concerns, increasing the difficulty of assessment. Therefore, accurately assessing adjustable potential under limited information and considering various unknown factors should be a key focus of future research.

4.

Improvement of Market Mechanisms for VESS Participation in Ancillary Services

Utilizing VES for ancillary services to the grid can significantly enhance the system’s regulatory capabilities. Certain provinces and cities in China have already established regulations for ancillary service markets, explicitly defining market participants to include third parties offering integrated energy services. As market participants shift from traditional generation to the demand side, research on employing Load Aggregators (LA) to consolidate VES resources for participation in ancillary services should be expedited. Leveraging LA to consolidate VES participation in the ancillary services market can integrate demand-side adjustable resources, thereby enhancing the system’s regulatory capacity. Additionally, a flexible pricing mechanism can bolster user engagement in regulation, thus promoting the implementation and long-term sustainability of VES in providing ancillary services.

6. Conclusions

To accurately focus on virtual energy storage systems, this paper comprehensively reviews equivalent modeling methods for temperature-controlled loads and virtual energy storage system control strategies. Firstly, it examines the equivalence of virtual energy storage systems for individual and aggregated temperature-controlled loads, comparing them with the physical parameters of traditional energy storage systems. Secondly, it explores virtual energy storage system control strategies in various application scenarios. This systematic analysis centers on current domestic and international research on virtual energy storage system modeling methods and application scenarios within electric–thermal integrated energy systems, leading to the following key conclusions:

(1)

Virtual energy storage represents an aggregation of sources, grids, and load flexibility devices/systems. It balances multiple energy sources by storing surplus energy or releasing deficient energy, exerting regulatory effects equivalent to physical energy storage. The introduction of virtual energy storage technologies offers new avenues for optimizing system operations, enhancing the economic viability of power systems, increasing renewable energy integration capacity, breaking down temporal and spatial barriers in energy, and enabling dynamic optimization scheduling in integrated energy systems.

(2)

By analyzing relevant literature from both domestic and international sources, this study summarizes virtual energy storage system modeling methods for air-conditioning and heating networks. It identifies a current research focus primarily on modeling air-conditioning loads within electric–thermal integrated energy systems, while overlooking other equipment such as electric boilers and heat pumps. Future advancements, particularly with the evolution of fifth-generation heating networks, underscore the growing potential for HPs and refrigeration units to engage in demand response, necessitating further research into their virtual energy storage system equivalent modeling methods.

(3)

Based on practical applications of virtual energy storage in various scenarios and referencing relevant literature, this paper analyzes and categorizes four typical application scenarios: demand response, new energy integration, smoothing interconnector line power, and comprehensive energy optimization scheduling. Despite significant strides in virtual energy storage research, several challenges persist. These include enhancing the accuracy of adjustment potential estimation to fully exploit virtual energy storage system capabilities; investigating hierarchical coordination control strategies integrating virtual energy storage systems, energy storage systems, and renewable energy sources; and prioritizing parameters such as the reliability and rapid response capabilities of virtual energy storage systems.

This synthesis aims to provide a scholarly exploration into the evolving landscape of virtual energy storage, laying the groundwork for future advancements and solutions in energy system optimization and integration.