Mobile Energy-Storage Technology in Power Grid: A Review of Models and Applications

Abstract

In the high-renewable penetrated power grid, mobile energy-storage systems (MESSs) enhance power grids’ security and economic operation by using their flexible spatiotemporal energy scheduling ability. It is a crucial flexible scheduling resource for realizing large-scale renewable energy consumption in the power system. However, the spatiotemporal regulation of MESS is affected by the complex operating environments in the power and transportation networks. Numerous challenges exist in modeling and decision-making processes, such as incorporating uncertainty into the optimization model and handling a considerable quantity of integer decision variables. This paper provides a systematic review of MESS technology in the power grid. The basic modeling methods of MESS in the coupled transportation and power network are introduced. This study provides a detailed analysis of mobility modeling approaches, highlighting their impact on the accuracy and efficiency of MESS optimization scheduling. The applications of MESS in the power grid are presented, including the MESS planning, operation, and business model. The key challenges encountered by MESS in power grid operations across various scenarios are analyzed. The corresponding modeling methods, solution algorithms, and typical demonstration projects are summarized. At last, this study also proposes the MESS system research and application prospects based on the consideration of its promotion.

1. Introduction

With the proliferation of low-carbon energy and the development of smart grids in recent years, advanced energy storage technology has been regarded as an essential resource in energy systems. The traditional stationary energy-storage system (ESS) is installed at fixed locations on the grid. It smooths out power fluctuations within a specific range due to line transmission capacity limitations or node voltage security constraints. MESS technology, on the other hand, breaks through spatial constraints and connects to different locations on the grid for charging and discharging. Multiple battery modules can be assembled in their carriers [1], or various carriers can be combined as a fleet for dispatch [2]. Therefore, compared with conventional stationary energy storage, MESS has more flexibility in space dispatch [3].

The charging behavior and load demands of electrical vehicles (EVs) influence the power system operation [4]. The EV cluster connected to the charging station can be considered as energy storage, and thus, it has the potential for vehicle-to-grid (V2G) optimal scheduling [5]. By regulating the charging behavior of EVs in the charging station, they can participate as flexible resources in the cooperative dispatch of multi-microgrid systems [6] or grid demand response [7] to improve the grid operation economy. Therefore, some studies state that EV clusters can be considered MESS devices in optimal grid dispatch [8]. However, EVs provide mobility services for vehicle owners most of the time. They only participate in the grid’s optimal operation when connected to the charging station with the owner’s permission. Therefore, the EV operation behavior is complex and has low controllability when participating in power system dispatch. At the same time, due to the limited battery size of EVs, the regulation capacity they provide to the grid is not significant.

The maturity of small-volume and large-capacity energy storage technology is the foundation for applying MESS. MESS is gradually being used in power and industrial production. Most MESS researches and projects are based on lithium-ion batteries [9,10]. A lithium iron phosphate battery has the advantage of operational safety, long cycle life, abundant metal resources, low cost, and environmental protection. It has become the main choice for energy-storage batteries in China. In the existing research and applications, in addition to high-performance battery-based MESS, mobile energy technology has been expanded to mobile hydrogen storage and mobile thermal energy storage, realizing the coupling of multiple energy systems and integrated energy supply applications. Hydrogen energy can be converted not only into electrical energy but also into thermal and chemical energy in many forms. Based on pyrolytic high-density solid hydrogen-storage materials [11], hydrogen energy can be transferred over long distances. Thus, mobile hydrogen energy storage often plays a coupling role in the coordinated operation of multi-energy systems [12,13]. Mobile thermal energy storage refers to the use of high-efficiency energy-storage equipment combined with delivery vehicles for the storage, transportation, and release of thermal energy and the use of high-efficiency heat-exchange technology for the storage of thermal energy, which is distributed in the form of mobile vehicles to the user end for steam output.

MESS is carried in trucks, electric bus fleets, trains, and even ships that can move between different grids or charging stations and have fast access capabilities [14,15]. It has large-capacity and high-power batteries, power electronic interfaces, and control systems. Unlike electric vehicles, MESSs are fully controlled to participate in grid optimization. Their batteries have more considerable rated power and capacity, and the scheduling strategies are formulated according to the grid operation energy support demands [16,17,18], ancillary service demands [19], or power transfer capacity enhancement [20,21,22]. A comparison of EV, MESS, and stationary ESS is summarized in

Table 1. Comparison of EV, MESS, and stationary ESS.

	Flexibility	Controllability	Scale	Typical Functions
EV	Spatiotemporal	Stochastic	· Large quantity · Small individual capacity	· Demand response
MESS	Spatiotemporal	Fully controllable	· Small quantity · Relatively large individual capacity	· Emergency or temporary charging and discharging
Stationary ESS	Temporal	Fully controllable	· Small quantity · Large individual capacity	· Regular charging and discharging

.

Many researchers have studied the optimization modeling and solution methods for MESS business and scheduling schemes. While the operation strategies of MESS are affected by the power and transportation operating environment and multiple uncertainties, its spatiotemporal decision process is complex. The current different modeling methods need to be comparative analyzed to guide MESS research in problems with different scale and application scenarios. To support the in-depth development of MESS technology, it is also necessary to systematically sort out the current MESS scheduling technology and operation mode in the power grids. In the application of MESS, the key problems to be solved under various regulation scenarios, decision-making techniques, and application effects need to be analyzed. MESS obtains considerable operating income through spatiotemporal scheduling, which is an important condition to promote its large-scale commercialization application. Therefore, in terms of the business model, it is necessary to summarize the key issues and technical difficulties in the operation framework, incentive mechanism, and pricing model of MESS and analyze the improvement effect of different methods on the MESS operation income.

Thus, this study presents applicable solutions for MESS in the power grid by summarizing the relevant research and progress of MESS modeling methods and grid applications. First, the MESS schedule modeling methods in the coupled transportation and power network are introduced in Section 2. Then, considering the complex operation environment, the grid application of the MESS from the perspective of planning, operation, and business model is summarized in Section 3. The future research and application prospects are proposed in the last section.

2. MESS Modeling

The MESS operation in the transportation and power networks is coupled through charging stations. There is a correlation between their traveling states and battery power, as shown in Figure 1.

The MESS travel path and power dispatch strategies follow the instructions of power grid control centers. Still, the travel distance and traffic flow influence the arrival time and available energy. In the simulation scenarios, traffic flows in road networks are usually allocated based on the Wardrop principle [23], and the quantitative model of the traffic flow’s effect on travel time is established based on the road resistance function. In practical applications, the real-time road condition monitoring system can also obtain historical and real-time data on the road conditions of transportation networks [24]. Based on the road information, the coupling relationship between mobility and battery energy is described, and the joint modeling of MESS in power and transportation networks is achieved. The mobility model and battery energy model are the two main parts of MESS modeling, followed by a detailed description of the modeling methodology and model characteristics, respectively.

2.1. Mobility Model

Most studies combine the mobility constraints in transportation networks and battery operation constraints in power grids to build mathematic models of MESS operation. The commonly used mobility models are given as follows:

(1)

Sliding time window-based model

As shown in Figure 2, the MESS mobility is characterized by its parking state at stations, which is also modeled as

$${\displaystyle {\sum }_{i\in N}{s}_{i,t}}\le 1,m_t^{}=1-{\displaystyle {\sum }_{i\in N}{s}_{i,t}},\forall t\in T$$

(1)

where m_t is the binary variable that equals 1 if an MESS is traveling at time t, and s_i,t is the binary variable that equals 1 if an MESS is connected to station i at time t. Equation (1) shows that each MESS is connected to at most one of its candidate stations during each time period and the states of connecting to stations and traveling on roads are mutually exclusive.

The transition delay constraints are designed considering the travel time between stations [25,26], as stated below:

$$s_{i,t+\tau }+s_{j,t}\le 1,\forall i,j\in N,\tau \in T_{ij},t+\tau \le T$$

(2)

where T_ij is the travel time between stations i and j.

To improve the scheduling efficiency of MESSs in large-scale systems, the parking state and the traveling state transition variables are introduced to build linear constraints between adjacent time periods [27]:

$${\displaystyle {\sum }_{i\in N}{m}_{i,t}^{}}=1-{\displaystyle {\sum }_{i\in N}{s}_{i,t}},\forall t\in T$$

(3)

$$s_{i,t}-D_{i,t}\le s_{i,t+1}\le s_{i,t}+U_{i,t},\forall i\in N,t\in T\backslash \left\{D\right\}$$

(4)

$$\begin{array}{l}{\mathrm{\Delta }}_{(1)i,t}=m_{i,t}-m_{i,t+1},\forall i\in N,t\in T\backslash \left\{D\right\}\\ {\mathrm{\Delta }}_{(2)t}={\displaystyle {\sum }_{i\in N}{m}_{i,t}}-{\displaystyle {\sum }_{i\in N}{m}_{i,t+1}},t\in T\backslash \left\{D\right\}\end{array}$$

(5)

$$\left[\begin{array}{c}{D}_{i,t}\\ U_{i,t}\end{array}\right]=\left[\begin{array}{cc}{a}_1& b_1\\ a_2& b_2\end{array}\right]\left[\begin{array}{c}{\mathrm{\Delta }}_{(1)i,t}\\ {\mathrm{\Delta }}_{(2)t}\end{array}\right]+\left[\begin{array}{c}{c}_1\\ c_2\end{array}\right]$$

(6)

Equation (4) is a preliminary constraint of parking state transition between adjacent time periods. Although the value of auxiliary variables D_i,t and U_i,t are unknown, their values restrict whether the parking state changes in the following time period. Equation (5) is the constraint of traveling state transition, Δ_(1)i,t is the MESS traveling state transition on node i, and Δ_(2)t is the MESS state transition between travel and parking. For ease of solving, variables D_i,t and U_i,t are modeled as linear functions of Δ_(1)i,t and Δ_(2)t, as shown in (6). Replacing D_i,t and U_i,t in Equation (4) with the expressions in (5) and (6), a linear constraint between the parking and traveling states is built.

Also, the travel time between two stations needs to be considered in the mobility model:

$$S_t\ge s_{i,t-1}{\displaystyle {\sum }_{k\in N}{T}_{ik}}+{\displaystyle {\sum }_{k\in N}{m}_{k,t}{T}_{ik}}-{\displaystyle {\sum }_{k\in N}{T}_{ik}},\forall i\in N,t\in T\backslash \left\{0\right\}$$

(7)

$$S_t\ge 0,\forall t\in T\backslash \left\{0\right\}$$

(8)

$$R_t=R_{t-1}+S_t-{\displaystyle {\sum }_{i\in N}{m}_{i,t-1}},\forall t\in T\backslash \left\{0\right\}$$

(9)

$$R_t/M\le {\displaystyle {\sum }_{i\in N}{m}_{i,t}}\le R_t$$

(10)

$$w_t\ge {\displaystyle {\sum }_{i\in N}{m}_{i,t-1}}+{\displaystyle {\sum }_{i\in N}{m}_{i,t}}-2+\epsilon ,\forall t\in T\backslash \left\{0\right\}$$

(11)

$$-\left(1-w_t\right)\le m_{i,t}-m_{i,t-1}\le \left(1-w_t\right),\forall i\in N,t\in T\backslash \left\{0\right\}$$

(12)

$$x_{i0,0}=1,S_0=0,R_0=0,w_0=0$$

(13)

where S_t is the travel time of MESSs, R_t is the rest travel time of an MESS on its travel path, M is a large positive number, ε is a small positive number, T_ik is the travel time from station i to k, and w_t is the auxiliary binary variable. Equations (7) and (8) present the required travel time between two stations, and the travel time is 0 when the MESS does not travel at time t. Equations (9) and (10) are designed to maintain the traveling state until the end of the travel time. Equations (11) and (12) are designed to maintain the travel direction of MESSs during traveling. Equation (13) is the constraint of initial conditions.

(2)

Time–space network model

Based on the weighted and directed graph of transportation networks, the spatiotemporal coupling constraints of MESS mobility are constructed in [28]. The charging station is set as graph nodes, and the travel time between stations is the weight.

As shown in Figure 3, the time–space network is built based on the spatiotemporal road conditions, and the MESS mobility arc is described by binary decision variables γ_(o,d),t0. The mobility arc in the time–space network describes all possible traveling and parking states of MESSs. It reflects the beginning and destination of travel paths and time. The parking state is defined by the arc with the same beginning and destination station [29]. The mobility model is described as

$${\displaystyle \sum _{(o,d),t_0\in {\mathit{A}}_{\tau }}{\gamma }_{(o,d),t_0}}=1,\forall \tau \in \mathit{T}$$

(14)

$${\displaystyle \sum _{(o,d),t_0\in {\mathit{A}}_{n,{\tau }_0,\mathrm{in}}}{\gamma }_{(o,d),t_0}}={\displaystyle \sum _{(o,d),t_0\in {\mathit{A}}_{n,{\tau }_0,\mathrm{out}}}{\gamma }_{(o,d),t_0}},\forall \tau \in \mathit{T}$$

(15)

$${\displaystyle \sum _{(o,d),t_0\in {\mathit{A}}_{\mathrm{dep},1,\mathrm{out}}}{\gamma }_{(o,d),t_0}}=1$$

(16)

$${\gamma }_{(o,d),t_0}+{\gamma }_{(d,o),t_0+1}\le 1$$

(17)

where t₀ and τ₀ represent the beginnings of time intervals t and τ, respectively, (o,d) is the origin–destination station pair, (o,d), t₀ represents the MESS mobility from Station o to Station d at time t₀, A is the set of all mobility strategies, and γ_(o,d),t0 is a binary variable for MESS mobility. When MESS mobility strategy (o,d),t₀ is chosen, γ_(o,d),t0 = 1; otherwise, γ_(o,d),t0 = 0. Equation (14) indicates that the MESS mobility is unique in any period, meaning that the mobility must be either traveling or parking and cannot be simultaneously in the traveling and parking states. Equation (15) describes that the MESS mobility is coherent in adjacent periods, i.e., the starting position of the next instant and the ending position of the current instant need to be consistent. Equation (16) indicates that the initial station is fixed for some MESSs, like electric buses. Equation (17) guarantees that the MESS is forbidden to turn around and travel back immediately.

(3)

Virtual switch model

In addition to directly modeling MESS mobility in transportation networks, the “virtual switch” is also used to model the MESS mobility [30]. It describes the parking state and travel time of MESSs in different nodes based on virtual switches’ opening and closing state.

The switching state of the virtual switch model is similar to the traveling and parking constraints in Equations (1) and (2):

$${\displaystyle \sum _{i\in N}{s}_{i,t}\le 1},\forall t\in T$$

(18)

$${\displaystyle \sum _{i\in N}{\displaystyle \sum _{j\in N\backslash \left\{i\right\}}{m}_{ij,t}}}\le 1,\forall t\in T$$

(19)

$${\displaystyle \sum _{i\in N}{s}_{i,t}=1-{\displaystyle \sum _{i\in N}{\displaystyle \sum _{j\in N\backslash \left\{i\right\}}{m}_{ij,t}}}},\forall t\in T$$

(20)

where s_i,t is a binary variable for the virtual switch state. When the virtual switch is closed at station i, s_i,t =1. m_ij,t is the flag for virtual switch state change. When the virtual switch is open at station i and closed at station j, m_ij,t = 1.

Then, the travel time between two stations is modeled by the switching action time constraints:

$$\left\{\begin{array}{l}{\varphi }_{i,t}-{\phi }_{i,t}=s_{i,t}-s_{i,t-1},\forall i\in N,t\in T\backslash \left\{0\right\}\\ {\displaystyle \sum _{i\in N}({\varphi }_{i,t}+{\phi }_{i,t})}\le 1,\forall t\in T\end{array}\right.$$

(21)

$$\left\{\begin{array}{l}{\varphi }_{j,t}-{\mu }_{j,t}={\displaystyle \sum _{i\in N\backslash \left\{j\right\}}(m_{ij,t-1}-m_{ij,t}),\forall j\in N,t\in T\backslash \left\{0\right\}}\\ {\displaystyle \sum _{j\in N}({\varphi }_{j,t}+{\mu }_{j,t})\le 1,\forall t\in T}\end{array}\right.$$

(22)

$$m_{ij,t}\ge m_{ij,t+t{r}_{ij,t}-1}-m_{ij,t+t{r}_{ij,t}},\forall i\in N,j\in N\backslash \left\{i\right\},t+t{r}_{ij,t}\le T$$

(23)

$${\displaystyle \sum _{j\in N\backslash \left\{i\right\}}{m}_{ij,t}\ge {\phi }_{i,t}},\forall i\in N,t\in T$$

(24)

where ${\varphi }_{i,t}$ and ${\phi }_{i,t}$ describe the access state of the virtual switch at station i. When the virtual switch at station i switches from open to closed at time t, ${\varphi }_{i,t}=1$. When the virtual switch at station i switches from closed to open states at time t, ${\phi }_{i,t}=1$. μ_j,t is an auxiliary binary variable to ensure the equation always holds. Equation (21) describes the relationship between the virtual switching action and its switch state. Equation (22) shows the relationship between closed switching and state flags. Equation (23) shows that a specific time interval has to be satisfied between different virtual switch actions, which is the time required on the way to MESS scheduling. Equation (24) describes the constraints between the virtual switch access station and the switching state. The model (18)–(24) is also linear, which is convenient to solve.

The above three types of approaches reflect different modeling ideas and have different model scale. The researches can choose the appropriate model to use or make further improvements based on the problem scenario and problem size.

The sliding window approach is the basic MESS modeling method, which uses two sets of binary variables to describe the traveling and parking states. The spatiotemporal model is a graph-based scheduling model that provides intuitive descriptions of the spatiotemporal mobility of MESSs in transportation networks. The virtual switch models the MESS mobility state as the switching state in the power network, which reflects the transportation network constraints into power grid connection constraints.

The size of the above four mobility models are compared in Table 2 [31], where M is the number of MESSs, D is the scheduling time spans, N is the number of charging stations, N_v is the number of virtual nodes in the transportation network, and T_ik is the time spans from node i to node k. The number of binary variables and constraints are mainly influenced by the system scale and scheduling time span. When the sliding window-based model with linear-constrained travel behavior is applied to large-scale systems, the variable or constraint number does not grow with the system size or time span.

Table 2. Mobility model comparison.

Model	Characteristic	Decisions	Travel Time	Number of Binary Variables	Number of Constraints
(1)–(2)	Sliding window-based model [25]	Traveling and parking state	Modeled by transition delay constraints	M(D + 1)(N + 1)	M[(2D + 1) ${\sum }_{i=1}^{N-1}$${\sum }_{k=1}^{N-1}$Tik − ${\sum }_{i=1}^{N-1}$${\sum }_{k=1}^{N-1}$T2 ik + 4D + 4]/2
(3)–(13)	Linear-constrained travel behavior [27]	Traveling and parking state	Modeled by traveling state transition constraints	M(D + 1)(2N + 1)	MD(5N + 6) + 7M
(14)–(17)	Time–space network [29]	Mobility arc	Modeled by arcs	DM(N2 + 2Nv), where Nv = ${\sum }_{i=1}^{N-1}$Σk>iTik − N(N − 1)/2	DM(N2 + 3Nv + 1) − M(N2 − N + 2Nv)
(18)–(24)	Virtual switch model [30]	Switch state	Modeled by switching time	M(D + 1)(N2 + 3N)	M[(D + 1)(N + 5) + 2DN + Σi∈NΣj∈N\{i} (D + 1 − Tij,D + 1)]

Table 2. Mobility model comparison.

Model	Characteristic	Decisions	Travel Time	Number of Binary Variables	Number of Constraints
(1)–(2)	Sliding window-based model [25]	Traveling and parking state	Modeled by transition delay constraints	M(D + 1)(N + 1)	M[(2D + 1) ${\sum }_{i=1}^{N-1}$${\sum }_{k=1}^{N-1}$Tik − ${\sum }_{i=1}^{N-1}$${\sum }_{k=1}^{N-1}$T2 ik + 4D + 4]/2
(3)–(13)	Linear-constrained travel behavior [27]	Traveling and parking state	Modeled by traveling state transition constraints	M(D + 1)(2N + 1)	MD(5N + 6) + 7M
(14)–(17)	Time–space network [29]	Mobility arc	Modeled by arcs	DM(N2 + 2Nv), where Nv = ${\sum }_{i=1}^{N-1}$Σk>iTik − N(N − 1)/2	DM(N2 + 3Nv + 1) − M(N2 − N + 2Nv)
(18)–(24)	Virtual switch model [30]	Switch state	Modeled by switching time	M(D + 1)(N2 + 3N)	M[(D + 1)(N + 5) + 2DN + Σi∈NΣj∈N\{i} (D + 1 − Tij,D + 1)]

2.2. Battery Energy Model

The battery provides energy for its mobility. After the MESS is parked and connected to the charging station, its battery energy is affected by the charging and discharging power. The battery energy is modeled as follows:

$${\left(p_{e,i,t}^{\mathrm{ch}}-p_{e,i,t}^{\mathrm{di}}\right)}^2+{\left(q_{e,i,t}^{\mathrm{ess}}\right)}^2\le {\left(s_{i,t}{S}_{{}^e}^{{}^{ess}}\right)}^2,\forall t\in \mathit{T}$$

(25)

$$p_{e,i,t}^{\mathrm{ch}},p_{e,i,t}^{\mathrm{di}}\ge 0,\forall t\in \mathit{T}$$

(26)

$$C_{e,t}=C_{e,t-1}+\mathrm{\Delta }t\left(\eta {\displaystyle \sum _{i\in \mathrm{Node}}{p}_{e,i.t}^{\mathrm{ch}}}-{\displaystyle \frac{1}{\eta }}{\displaystyle \sum _{i\in \mathrm{Node}}{p}_{e,i,t}^{\mathrm{di}}}-p_{e,t}^{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}}\right),\forall t\in \mathit{T}$$

(27)

$$p_{e,t}^{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}}=m_t{p}_e^{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}},\forall t\in \mathit{T}$$

(28)

$$\mathrm{S}\mathrm{O}{\mathrm{C}}_{e,\min }{C}_e^{\mathrm{ess}}\le C_{e,t}\le \mathrm{S}\mathrm{O}{\mathrm{C}}_{e,\max }{C}_e^{\mathrm{ess}},\forall t\in \mathit{T}$$

(29)

where $p_{e,i,t}^{\mathrm{c}\mathrm{h}}$ and $p_{e,i,t}^{\mathrm{d}\mathrm{i}}$ are the active charging and discharging power, respectively; $q_{e,i,t}^{\mathrm{e}\mathrm{s}\mathrm{s}}$ is the reactive power; $S_e^{\mathrm{e}\mathrm{s}\mathrm{s}}$ is the rated power; C_e,t is the stored energy; η is the energy storage efficiency; $p_{e,t}^{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}}$ is the power consumption during travel and $p_e^{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{v}\mathrm{e}\mathrm{l}}$ is the unit power consumption at each time interval; $C_e^{\mathrm{e}\mathrm{s}\mathrm{s}}$ is the rated energy capacity; SOC_e,min and SOC_e,max are the lower and upper states of charge level of the battery; s_i,t is the state for MESS connection to the stations, and in particular, it is equivalent to ${\gamma }_{e,(i,i),t_0}$ in model (3); and m_t is the mobility state of MESS, which is equivalent to m_t in model (1)–(2) m_i,t in model (3)–(13), $(1-{\displaystyle {\sum }_{i\in N}{\gamma }_{e,(i,i),t_0}})$ in model (14)–(17), and m_ij,t in model (18)–(24). Equations (25) and (26) are the constraints for battery operation power. Equations (27)–(29) are the constraints for battery storage energy.

Therefore, compared with the stationary energy storage battery energy model, the SOC of MESS is not only related to its charging and discharging power to the grid but also needs to consider its power consumption during mobility, as summarized in

Table 3. Battery status during operation.

Mobility	Power State	Energy State
Traveling	Discharging for travel	SOC decrease
Parking	Charging in the station	SOC increase
	Discharging in the station	SOC decrease
	Idle	-

.

3. Grid Application of MESS

The spatiotemporal operation characteristics of MESS give it a high potential to support power system operational flexibility. In recent years, the research on the power grid application of MESS has gained significant attention. The problem involves complex operating environments and grid demands, and power grid and transportation network operating environments impact MESS configuration and scheduling decisions. This section summarizes the MESS application in power grids, including the planning, operation, and business model considering different scenarios and grid demands. The respective system models and solution methods in existing research are compared.

3.1. MESS Planning

The MESS charging station siting and MESS battery sizing are decided to minimize the investment and operation costs in the MESS planning problem. The investment cost function includes the device and maintenance costs, considering MESS lifetime and capital recovery factors. Since MESS integrates the energy storage needs of multiple buses or users, it increases the utilization rate of batteries, improves investment revenue for investors, and reduces energy storage configuration costs for users [32,33]. The cost-effectiveness of MESS relative to reliability-driven investments in transmission infrastructure and stationary capacity is verified in [34] for restoration during low-frequency, high-impact events, considering the annual event frequency per region and the distance between regions. The MESS stations have different investment capacities and participants, and the current literature broadly explores two MESS planning methods: independent and shared investment.

(1)

Independent investment

In most existing studies and practical applications, MESS is invested in and operated independently by the grid according to its needs. In this way, the MESS only operates between stations in the grid to which it belongs.

The two-stage MESS investment and operation model is constructed considering normal grid operation and failure conditions [26]. The installation strategies for MESS, involving allocation and sizing decisions, are optimized in the first stage as here-and-now decisions to minimize MESS investment costs. Considering various operational scenarios’ probabilities, scheduling strategies for the grid and MESS are optimized to minimize expected grid operation costs in the second stage as wait-and-see decisions. The proposed model is decomposed into subproblems using the progressive hedging algorithm. MESS investment and placement decisions remain consistent across all scenarios, with subproblems being solved concurrently to determine routing decisions for each failure-recovery scenario. In [35], the first-stage problem optimizes the MESS pre-siting and investment strategy under normal grid-operation scenarios. Subsequently, the MESS-reallocation strategy is optimized to hedge against the worst-case failure scenario in the second stage. The column-and-constraint generation (C&CG) algorithm decomposes the two-stage robust optimization model and solves it iteratively.

In practical grid applications, MESS is often collaboratively planned with various devices, such as fossil-energy distributed generators, stationary ESS, renewable power units, and EV charging stations. This leads to optimization planning problems with a significant number of integer decision variables, concurrently addressing multi-objective collaborative optimization challenges, thereby complicating the problem-solving process. Heuristic algorithms, such as greedy, particle swarm, and bionic algorithms, offer feasible approaches for addressing complex planning problems. In addressing complex, large-scale mixed-integer decision problems, the particle swarm algorithm in [36] determines MESS’s location and rated power in each iteration. Subsequently, a mixed-integer linear programming model is formulated using these outputs to determine the capacity decisions for MESS batteries. To reach the optimal solution with low dispersion in the multi-objective planning model, the hybrid meta-heuristic algorithm is verified with better performance in optimization results and solution efficiency [37]. As proposed in [38], the improved preference-incentive coevolution algorithm demonstrates remarkable efficacy in addressing nonlinear multi-objective planning models. This is achieved by introducing a set of preferences coevolving with the candidate solution population. These preferences serve as a method for evaluating the merits and drawbacks of various solutions for subsequent optimization. Considering the stochastic profiles for load demands and multiple renewable energy sources, [39] addressed the mixed-integer nonlinear stochastic planning model by introducing a hybrid-solution technique. This approach involves generating an initial population of genetic algorithm (GA) chromosomes comprising planning decision variables. Subsequently, the optimal power flow problem is solved for each chromosome in the current generation using the Generalized Reduced Gradient (GRG) method. The interaction halts when the average relative change in the best fitness function value over a predetermined maximum number of stall generations falls below a selected small tolerance.

Given the challenges posed by the scale of the model and the complexity of solutions in centralized programming, [40] presents a decentralized approach for MESS planning aimed at enhancing grid resilience during high-impact extreme events. This approach is based on the defender–attacker–defender model. In this method, the upper-level model employs an adaptive genetic algorithm to determine MESS siting and sizing outcomes for a specific extreme event. Meanwhile, the subproblem integrates middle- and lower-level problems to identify the most severe extreme event.

(2)

Sharing investment

The investment budget for shared MESS deployment is relatively low for small-scale energy-storage users, such as distributed renewable energy sources and microgrids. Under the sharing investment model, allocating MESS resources requires considering different participants’ benefits balance and storage demands [41].

Previous studies have suggested two forms of investment sharing: either multiple participants collectively invest in MESS, or users lease the MESS service from third-party investors. The focus of the former has centered on how various investment entities allocate their investment costs. The proportional distribution method in [42], which accounts for the MESS’s active charging/discharging power over time, can solve this problem. For the latter one, users opted to rent MESS at a suitable price rather than engaging in further facility planning. This approach allows users to flexibly configure MESS as a complement to stationary ESS during temporary needs [43]. The investors establish the time-of-use rental price for their MESS, aiming to strike a balance between cost recovery for investors and the willingness of users to rent. Detailed methods will be presented in Section 3.3.

3.2. MESS Operation

Leveraging its spatial and temporal regulation capacities, MESSs support power grid optimal operation across diverse scenarios [44,45]. Several MESS demonstration projects around the world have validated its ability to support multiple aspects of the power grid. This subsection describes the scheduling of mobile energy storage in terms of theoretical approaches and demonstration applications, respectively.

(1)

Optimal operation models and solution methods

Scheduling MESS regarding both path and power is the focus of research on optimal operation. The coupling of power and transportation operation environments is complex, presenting challenges for the operation decisions. The typical application scenarios, including the modeling and solution methods, are summarized and compared in Table 4.

The MESS operation strategy is integrated into the power grid scheduling model and operation objective. When restoring de-energized loads in islanded microgrids, the placement of MESS is determined by the load’s recovery priority. The Dijkstra algorithm is introduced to determine a network graph’s quickest route between source and target nodes. Charging and discharging power are optimized using the same model as stationary ESS [46]. Considering the influence of traffic conditions, most existing research co-optimizes the MESS mobility and power strategy [47]. The authors of [48] analyzed the impact of MESS operation on the operation of conventional units based on the security-constrained unit commitment combined with the MESS mobility model (3) and energy model (5). The authors of [49] developed a voltage-regulation cost curve for MESS utilizing day-ahead predictions of renewable power generation, load, and traffic conditions. Piece-wise linear functions were employed to model the curves, increasing the cost of control devices as they near the power limits. This approach ensures the reserve of a certain amount of reactive power margin of MESS to address unexpected voltage violations. The studies above proposed day-ahead scheduling results for MESS based on deterministic predictive operational scenarios, providing valuable insight into its impact on the power grid.

Different devices and multi-energy systems in the renewable distribution system have different scheduling timescales, and even MESS scheduling on the transportation network and grid side have different timescales [50,51]. Challenges arise in coordinating scheduling decisions between MESSs, renewable energy sources, and traditional grid devices. Multi-stage models are commonly used in the studies that focus on this problem, but the specific modeling approaches are quite different. In addressing resilience enhancement in distribution networks, [52] tackles multi-device diverse operational characteristics by presenting a scheduling model that integrates long and short operation timescales. In contrast, [53] built a three-stage optimization model, considering the distribution network’s pre-disturbance, post-disturbance, and recovery phases.

The complex uncertainty in coupled power-transportation environments can significantly impact the scheduling of mobility and power for MESS, which need to be modeled and incorporated into the optimization model for enhanced operational precision, such as employing the chance-constrained optimization model [54]. Several linearization methods are designed for chance-constrained model reformulation, in which the Boolean reformulation method introduces fewer integer variables that can solve the joint chance-constrained model efficiently. The variable travel time and traffic congestion in the transportation network influence the MESS scheduling results [55,56]. However, the uncertainties in the transportation network are affected by various unexpected factors and are difficult to predict. The authors of [57] treat the road saturation parameter, which reflects the degree of road congestion, as a fuzzy number and use the expected value approach. The proposed fuzzy route planning model avoids road congestion and ensures time satisfaction during MESS operation. To deal with the inaccuracy of forecasts over the long horizon and leverage dynamically updated power grid and transportation state forecasts, the rolling optimization framework is adopted to solve the MESS scheduling strategies recursively. MESS optimal operation modeling becomes complicated when considering the uncertain power-transportation coupling operational conditions, compounded by large-scale integer decision variables, intensifying the solution’s complexity. However, the rolling optimization framework requires high solution efficiency due to a rolling time window. The authors of [58] proposed an MILP model for grid dynamic restoration using a scenario-based stochastic optimization method. The multi-stage robust economic optimization model in [59] is transformed to MILP based on the mixed affine decision rule, lifted uncertainty set, and duality theory. Generally, commercial solvers can quickly solve the MILP model. The penalty alternating direction algorithm could be employed to obtain a suboptimal solution to meet the demand for higher solution efficiency [60].

Recent research indicates that obtaining a precise uncertainty model is challenging, which affects model-based MESS scheduling performance. Deep reinforcement learning (DRL) methods make decisions based on statistical information from historical data, thus reducing reliance on models. The Markov decision process for MESS scheduling comprises state space, action space, transition probability functions, immediate reward, and discount factor [61]. The action space includes MESS mobility (represented by discrete variables) and charging/discharging power (represented by continuous variables). The deep Q network and the policy network for expected return benefits of online optimization are often trained by the twin-delayed deep deterministic policy gradient. The well-trained DRL model can be utilized for online MESS scheduling with high computational efficiency [62]. Considering the interaction between MESS agents and the users’ operating environment, a multi-agent DRL method is proposed in [63]. Unlike the single-agent DRL described previously, this method employs a finite Partially Observable Markov Game (POMG) with discrete time steps. It is formed with the observation space, action space, transition probability functions, immediate reward of all agents, and the environment state. The training process based on the deterministic policy gradient (DPG) theorem is similar to the conventional DRL but requires the consideration of other agents’ states.

In the above study, all kinds of resources belong to the distribution network and are centralized in scheduling by the distribution network. When the line switches, distributed power supplies, loads, and MESS are managed by multiple agents, and communication and collaborative restoration between agents are achieved through a hierarchical information–power–transport multi-agent system architecture [64].

Table 4. Grid operation research with MESS participation.

Ref.	Purpose	Mobility Model	Uncertainty	Optimization Model	Solution Method
[55]	Resilience improvement	(1)	-	MIQCP	commercial solver
[52,54]	Resilience improvement	(1)	Power grid	MINLP	reformulation
[53]	Resilience improvement	(1)	Power grid	MILP	heuristic method
[50]	Resilience improvement	(1)	Power grid	MISOCP	decomposition
[62]	Resilience improvement	(3)	Power grid	-	deep learning
[63]	Resilience improvement	(1)	Power grid	-	deep learning
[58]	Resilience improvement	(3)	transportation network and power grid	MILP	commercial solver
[48]	Renewable consumption	(3)	-	MILP	commercial solver
[59]	Renewable consumption	(3)	transportation network and power grid	MINLP	reformulation
[57]	Renewable consumption	(4)	transportation network and power grid	MINLP	decomposition
[61]	Renewable consumption	(3)	transportation network and power grid	-	deep learning
[49]	Security operation	(1)	Power grid	MISOCP	commercial solver

Table 4. Grid operation research with MESS participation.

Ref.	Purpose	Mobility Model	Uncertainty	Optimization Model	Solution Method
[55]	Resilience improvement	(1)	-	MIQCP	commercial solver
[52,54]	Resilience improvement	(1)	Power grid	MINLP	reformulation
[53]	Resilience improvement	(1)	Power grid	MILP	heuristic method
[50]	Resilience improvement	(1)	Power grid	MISOCP	decomposition
[62]	Resilience improvement	(3)	Power grid	-	deep learning
[63]	Resilience improvement	(1)	Power grid	-	deep learning
[58]	Resilience improvement	(3)	transportation network and power grid	MILP	commercial solver
[48]	Renewable consumption	(3)	-	MILP	commercial solver
[59]	Renewable consumption	(3)	transportation network and power grid	MINLP	reformulation
[57]	Renewable consumption	(4)	transportation network and power grid	MINLP	decomposition
[61]	Renewable consumption	(3)	transportation network and power grid	-	deep learning
[49]	Security operation	(1)	Power grid	MISOCP	commercial solver

(2)

Demonstration projects

In recent years, numerous MESS demonstration projects have been conducted worldwide to validate its operational benefits in the power grid, as outlined in

Table 5. Typical demonstration projects [66].

Year	Country	MESS Size	Application
			Resilience Improvement	Economic Operation	Security Operation
2016	USA	500 kW/800 kWh	√	√
2016	China	megawatt scale			√
2019	China	1 MW/2 MWh	√
2020	Germany	500 kW/1000 kWh		√
2020	China	34 MWh	√	√	√
2022	China	10 MW/9 MWh		√
2022	The Netherlands	20 MWh		√
2023	China	6 MW/7.2 MWh	√

. Several of these projects have yielded notable results. For example, at the demonstration site Friedland in Mecklenburg–Western Pomerania, 200% of the renewable energy required in the region is already being generated locally with the operation of MESS [65].

3.3. Business Model

With flexible configuration and scheduling ability, MESS provides a flexible energy-storage capacity and charging and discharging services for different users. Due to the lack of mature commercial mechanisms and scheduling technologies, the MESS investment relies on policy support currently. The MESS technology is not attractive enough for investors, which limits its application in actual projects. Therefore, the MESS business model needs to be designed to fully exploit the MESS flexibility operation potential and facilitate the energy interaction of multiple users through benefits. Generally, the MESS has two profit-making modes. One is to directly participate in grid operation and utilize grid time-sharing tariffs to arbitrage peaks and valleys through charging and discharging. And the other is to share the energy-storage device and collect sharing fees and power trading fees.

(1)

Electricity arbitrage

The MESS has the spatiotemporal arbitrage opportunity by traveling between different charging stations in a congested power grid. It purchases low-price electricity from nodes with surplus renewable energy and sells to high-demand nodes at higher prices. Thus, the incentive electricity price guides the user-side MESS to provide flexible scheduling services to the grid [67]. The design of incentive electricity prices needs to consider multiple factors or application scenarios. For user-side applications, e.g., [68], the MESS supplies low-cost electricity to commercial and industrial users, while it is compensated proportionally based on the demand charge cost reduction. MESS profits from the user side can also be based on the value of its flexibility. The users in [69] paid flexibility tariffs to MESSs as a reward for the parking time period. Thus, the MESS flexibility value in participating grid user scheduling is considered in community-level transaction energy markets.

The locational marginal price (LMP) and MESS-scheduling strategies are optimized considering the maximum social welfare under MESS and grid operation constraints [70]. However, the uncertainty of renewable energy sources has an impact on the operational benefits of mobile energy storage in addition to a significant impact on its scheduling decisions. In the uncertain environment, introducing the risk factor [71] or the chance-constrained model [72] can effectively control the influence of uncertain renewable power on decisions and guide the MESS participation in the day-ahead electricity market as a flexible ancillary resource. In addition, the uncertainty marginal price (UMP) is a novel concept that defines the marginal cost of immunizing the next increment in uncertainty at a specific location [73]. A market-based methodology combined with the LMP and UMP enhances the MESS operation flexibility in power grids [74]. In the proposed master-follower game model, the independent system operator releases the time-varying LMP and UMP based on stochastic security-constrained economic dispatch at the upper level. Then, the MESS owners provide energy and reserve capacity as flexibility services to maximize their benefits at the lower level.

The MESS arbitrage revenue is also tested in real-world systems. The authors of [75] applied a spatiotemporal arbitrage optimization model to MESS operating over 1131 case areas in California. It is verified that the life-cycle revenue of spatiotemporal arbitrage can fully compensate for the costs of a portable energy-storage system in several regions in California. To meet the peak charging demand in urban highway charging stations, the location and charging and discharging status of MESS systems are dynamically optimized based on the intraday electricity price to maximize the operational revenue of MESS systems [76].

(2)

Energy-storage service sharing and pricing

There are many types of participants for MESS-sharing services, such as investors, operators, and users. The investors rent out the MESS for revenue during the idle time, while other users rent the devices to meet the temporary load surges that are difficult to handle with the stationary ESS [77]. For example, an MESS plant with a 1 MWh battery is deployed in the Southern California grid to provide storage service for grid-planned outage management, load management, emergency outages, and public safety power shutoff according to seasons during the year [78]. The US-based Nomad Transportable Power Systems (NOMAD) offers plug-and-play, utility-scale MESS services and a proprietary docking system to the public. There are three versions of MESS: 1 MW/2 MWh, 500 kW/1.3 MWh, and 250 kW/660 kWh. It provides power backup; emergency response; and seasonal load mitigation for utilities, industrial and commercial entities, and renewable generation assets.

The sharing of mobile energy storage realizes the maximization of the value of idle energy-storage resources. However, due to the conflict of interest between different participants, the sharing of MESS requires solving the pricing and resource-allocation problem. Energy storage sharing can be described as a spot market that trades unused stored electricity. A central operator or platform is necessary to manage the centralized MESS trading and scheduling. In the electricity and ancillary services markets, the concept of promised energy storage and efficient energy storage is defined in [79] as the basis for the MESS-bidding strategy that maximizes the MESS benefits. To manage the operation risks in an uncertain operation environment, the conditional value-at-risk is introduced in the MESS-bidding model with the consideration of uncertain market prices, renewable power productions, and load demands [80]. Conflicts of interest and pricing games are unavoidable when there are different investors and users of shared mobile energy storage. A non-convex, non-cooperative game framework is proposed in [81] for various investors to compete against each other in the spot market for sharing energy. It has been proved that a Nash equilibrium exists under a mild-alignment condition, and it supports social welfare.

However, the centralized MESS-pricing model is complex and challenging to solve in cases with a large number of MESSs and users. Decentralized decision methods are applied in cases where distributed energy resources interact directly. There are fewer studies on distributed trading methods for mobile energy storage, but some literature has proposed distributed trading methods for shared stationary ESS and electric vehicle aggregators. To address decentralized transactions in the context of complex trading mechanisms, decentralized pricing can be achieved by decomposing the pricing problem into multiple sub-problems, such as the hierarchical pricing and scheduling structure. The community manager decides the day-ahead market price by integrating MESSs, stationary ESSs, and users into multiple economic agents [82]. Then, each agent proposes intra-day operation strategies for its participants according to the clearing price and the uncertain renewable energy generation. The peer-to-peer (P2P) trading model is another typical decentralized pricing method and is widely used in distributed energy trading [83,84]. Direct transactions between ESSs and users are achieved in P2P trading, with less need for interactive information and better privacy protection [85]. Considering the benefits of the MESS operators and users, the day-ahead auction mechanism for MESS usage rights [86] or power trading [87] is designed based on a P2P trading platform, and then deviation assessment and default settlement are conducted during the actual operation.

Overall, the appropriate incentive electricity price and market mechanism help guide the MESS’s flexible and efficient configuration and scheduling. Improving MESS revenue enhances its attractiveness to investors and promotes its applications in the grid. However, designing a business model for MESS still requires careful consideration of the energy management mode for specific application scenarios. The business model of MESS is still in the process of exploration, and the sharing operation mechanism of MESS needs to be further clarified.

4. Research and Application Prospect

Currently, research on MESS operation in coupled energy-transportation systems is still in the development stage. There are still difficulties in finding an efficient solution for the MESS business and scheduling model, which also leads to the under-exploitation of the regulation characteristics and potential of MESS resources. The following topics need to be further studied in the future.

4.1. Modeling and Solution of MESS Operation Problem

In MESS operation modeling, there is a conflict between the modeling accuracy of the transportation network operating environment and the difficulty of solving the model.

The dynamic and uncertain characteristics of the environment in the transportation network have a significant impact on MESS scheduling. Although the travel time is continuously varying, the MESS available time periods for the grid are modeled as discrete random variables considering the grid scheduling time interval. For uncertainty optimization models that consider discrete and continuous random variables, there are challenges to be solved in both model reconfiguration and efficient solutions.

The MESS traveling state is described by binary decision variables in all existing models and is related to departure, destination station, and travel time. Thus, the binary decision variable scale significantly increases in large application systems with long scheduling time spans. For the modeling methods, the spatiotemporal scheduling for MESS in transportation networks needs to be further improved to reduce the model size and enhance its applicability in large-scale systems. For solution methods, applying DL can effectively improve decision-making efficiency. Some researchers indicate that model-free methods lack interpretability and decision accuracy to a certain extent. The combination of mathematic modeling and DL is a promising method to solve the solution efficiency problem [88,89].

4.2. Comprehensive Application of MESS in Power Grids

To fully realize the comprehensive regulation capability of the power grid, the coordinate planning and hierarchical dynamic scheduling strategies of MESS with multiple flexible resources need to be further explored, which takes into account the regulation characteristics of each grid. In the MESS capacity and station-configuration process, it is necessary to fully integrate the multi-type needs of users to achieve the maximum utilization of MESS resources. Decision-making methods that consider multiple operational goals of different users or game theory to reach the equilibrium of interests among different participants can provide solution ideas for MESS regulation in complex application scenarios. The scheduling process needs to consider the probability of application scenarios in future periods and the users’ demands regarding MESS’s available power and capacity. Based on the grid situation awareness, adjusting the operation area and battery energy reserve strategy dynamically puts forward higher requirements for MESS’s flexible scheduling and efficient decision-making ability.

4.3. Business Model

Considering the different transaction needs of various MESS owners and grids, a more flexible and efficient business model needs to be designed to achieve an efficient match between the supply and demand sides. It is necessary to propose a comprehensive trading model that considers the trading periods of energy storage services (e.g., fixed periods, reservations, and temporary leases) to provide more flexible MESS services.

The type of MESS operators will also gradually increase; in addition to energy-storage stations, individual users configured with MESS can also rent their idle devices. With a huge number of MESS operators and users participating in trading together, centralized trading methods are unsuitable. Blockchain-based energy management and trading platforms implement bilateral trading mechanisms while considering the network constraints and without the involvement of a decision center [90]. This has been applied in studies related to energy storage trading [91] and microgrid energy markets [92]. The blockchain-based MESS business model can be further studied based on the superiority of blockchain-based distributed energy-trading technology.

5. Conclusions

As a flexible dispatching resource, MESS will provide comprehensive support for constructing smart power grids. At the same time, the development of MESS technology integrates smart energy and smart transportation, which is conducive to promoting the construction of a low-carbon smart city. This paper summarizes the existing studies from two aspects: the modeling method and grid application of MESS.

The different scales of regulation models for mobile energy storage under different modeling ideas will have an impact on its optimization decision model solution. The complex grid-transportation operating environments lead to MESS operation models in power grid applications containing complex model structures or large-scale mixed integer decision variables, which are the major challenges for MESS-scheduling problems. Existing research has made some progress in addressing this challenge in terms of model-based reformulation and algorithm design, as well as data-based deep learning optimization approaches. In terms of business model, the MESS can profit from electricity arbitrage and shared revenue, but its profit potential is still based on theoretical analysis, and there are few application projects for verification.

Future research needs to explore the MESS comprehensive application model further, refine its investors’ and users’ operation mode and profit demand modeling, and improve the MESS scheduling efficiency and effectiveness from the external business model and internal scheduling strategy. Meanwhile, with the increasingly complex operation environment, detailed modeling methods and efficient solution strategies for mixed integer programming need to be proposed to provide technical support for MESS promotion and application.