Abstract
High penetrations of wind and photovoltaic (PV) generation increase temporal and scenario-dependent source–load variability in distribution networks, complicating the planning and operation of mobile energy resources. This paper proposes a multi-scenario-driven planning–operation co-optimization method that incorporates mobile energy storage vehicles (MESVs), transportable battery energy storage systems (TBESSs), mobile hydrogen fuel-cell power supply vehicles (MHSVs), power-to-hydrogen (P2H), and on-site hydrogen storage into a two-stage stochastic optimization framework. Probability-weighted representative scenarios characterize wind, photovoltaic, and load uncertainty. The first stage determines resource types, quantities, ratings, candidate-node activation, and P2H/hydrogen-storage capacities; the second stage determines scenario-dependent deployment and hourly operation. A second-order cone-relaxed DistFlow model represents battery operation, the P2H–storage–refueling–MHSV chain, road accessibility, and relocation costs. Representative cases for renewable energy integration, peak shaving, congestion mitigation, and black-start active-power support are tested on the IEEE 33-bus system. In the renewable-integration case, three TBESSs totaling 4.50 MW/11.25 MWh reduce monthly wind/PV curtailment from 571.908 to 461.385 MWh, a 19.3% reduction. In the peak-shaving case, road constraints increase the monthly economic objective from CNY 310,462.56 to CNY 344,079.39 (10.8%), showing that accessibility can materially alter deployment and operating outcomes. The results also show that MESVs provide peak-shaving and local network support, whereas MHSVs provide sustained active-power support through the electricity–hydrogen chain.
1 Introduction
As increasing capacities of distributed wind and photovoltaic generation are connected to distribution networks, power flows are gradually changing from unidirectional supply to bidirectional power exchange. Voltage fluctuations and local line congestion are consequently becoming more pronounced, increasing the need for flexible regulation resources. Battery energy storage systems can provide coordinated voltage regulation in renewable-rich distribution networks and are important flexible resources for improving distribution-network operating flexibility (). Stationary energy storage remains connected to designated nodes over the long term and is therefore suited to continuous local regulation, whereas mobile energy storage can change its connection location according to operating requirements, transfer regulation capability among nodes, and provide both power and energy support (). When changes in source–load conditions shift the constrained branches and required support locations, stationary and mobile storage can complement each other through sustained local regulation and cross-node support. Their suitability depends on the spatial distribution of renewable generation, resource-dispatch requirements, transportation conditions, and configuration scale (; ). Meanwhile, the deployable locations and effectiveness of mobile energy resources are also constrained by road conditions, arrival times, and grid-connection conditions (). Therefore, studying the siting and sizing of mobile energy storage under source–load uncertainty and its coordinated operation with renewable generation is of practical significance for improving renewable energy integration, alleviating local network constraints, and strengthening power-supply support.
A variety of modeling methods have been developed for the planning and operation of mobile battery energy storage. Time–space network models construct connections between locations and time periods to describe departure, travel, arrival, dwelling, and grid-connection states (). Two-stage models link resource configuration with scenario-dependent deployment and operation and have been used for pre-disaster pre-positioning and post-disaster support (; ). To reduce the combinatorial complexity of joint transportation–electricity optimization, some studies use virtual connections or equivalent reconfiguration to represent service transfers of mobile storage among distribution-network nodes (). In terms of applications, mobile batteries have been used to transfer renewable energy across regions (); two-stage stochastic planning has been applied to coordinate resource configuration and multi-scenario operation (); and battery degradation (), dynamic microgrid formation (), and post-disaster restoration with renewable generation () have gradually been incorporated into relevant models. These studies provide a foundation for the siting, configuration, and operation of mobile battery storage.
However, most existing studies focus on a single type of battery-based mobile storage and cannot fully represent the differences among mobile energy resources in deployment mode, power rating, energy duration, and replenishment conditions. Stationary and mobile battery storage differ in their configuration and operating roles in bidirectional active distribution networks (Zhu et al., 2025). A resource that integrates batteries, power conversion, and grid-connection components in a container and is transported by truck to different substations or feeder connection points is referred to as a TBESS (). Other coordinated mobile electricity–hydrogen planning studies simultaneously consider MESVs and MHSVs (). In this study, MESVs, TBESSs, and MHSVs are collectively referred to as mobile energy resources; they respectively represent fast vehicle-mounted battery support, large-capacity transportable battery storage, and sustained electricity–hydrogen energy supply. They differ in response speed, power and energy scale, continuous supply capability, and replenishment requirements (Zhu et al., 2025; ; ). Consequently, the three resources have different suitability, configuration scales, and operating modes in renewable energy integration, peak shaving, congestion mitigation under normal operation, and black-start active-power support. A single mobile-storage model cannot reflect how changes in application requirements affect resource-type selection, capacity configuration, and operating characteristics. It is therefore necessary to formulate separate power, energy-storage, hydrogen-storage, and replenishment constraints for MESVs, TBESSs, and MHSVs within the same distribution-network siting-and-sizing framework and to analyze their configuration results and operating characteristics using consistent evaluation indicators.
Road conditions are an important factor that distinguishes mobile-storage planning from stationary-storage configuration. Existing studies model transportation at different levels of detail. Some jointly optimize the travel process of mobile resources with distribution-network restoration, microgrid formation, or operating dispatch through time–space networks or route variables (; ; ; Zhou K. et al., 2024; ; ). Some first identify grid-side support requirements and then perform vehicle–task matching and route scheduling (). Others use equivalent reconfiguration or parameter mapping to reduce the scale of joint distribution–road-network models (). Detailed route models can describe specific vehicle movements but also increase the number of integer variables, road-data requirements, and computational burden. Studies focused on equipment siting and sizing and multi-scenario operating evaluation therefore require a balance between the fidelity of road-information representation and the scale of the planning model.
The introduction of MHSVs gives mobile energy resources fuel constraints and sustained supply characteristics that differ from those of battery storage. Coordinated planning of mobile electricity–hydrogen resources indicates that battery-based mobile storage and hydrogen fuel-cell mobile power resources can undertake support tasks with different response speeds and supply durations (). Mobile solid-state hydrogen storage planning incorporates electrolytic hydrogen production, hydrogen storage, and fuel-cell generation into uncertainty models (). Coordinated operation of hydrogen storage and hydrogen vehicles shows that the onboard hydrogen state and refueling process affect power-supply support (), while the layout of hydrogen-production, storage, and refueling facilities affects hydrogen availability (). Hydrogen consumption, energy-conversion efficiency, and lifetime constraints also alter the operating schedules of fuel-cell mobile power supplies (Zhou Z. et al., 2024). Therefore, MHSV configuration and operation must jointly consider P2H production, on-site hydrogen storage, and vehicle refueling.
Existing studies generally examine one or a small number of mobile-storage resources, including cross-regional renewable energy transfer (), post-disaster restoration (; ; ), voltage–reactive-power regulation (), bidirectional power-flow operation (Zhu et al., 2025), and mobile electricity–hydrogen resource configuration (). The mobile-resource types, network operating states, scheduling horizons, and evaluation indicators differ among studies, making their results unsuitable for direct comparison of MESVs, TBESSs, and MHSVs under different distribution-network requirements. For siting-and-sizing decisions involving multiple mobile-resource types, representative application scenarios should be established under a consistent distribution network, source–load scenario set, and parameter system. The response characteristics and functional division of the three resources can then be analyzed using the configuration results, intraday operating processes, and system operating indicators.
The treatment of source–load uncertainty should match the available information and the planning objective. Existing stochastic-planning studies analyze how different active-management measures affect active-distribution-network planning () and use two-stage stochastic optimization to coordinate renewable-energy planning and multi-scenario operation of distribution systems with electric vehicles (). Stochastic programming (SP) coordinates planning and operation through probability-weighted representative scenarios. It is suitable when probabilistic scenarios can be formed from historical data or simulated samples and when the expected operating effect across multiple scenarios is the primary concern (; ; ). Two-stage robust optimization can also be used to address source–load uncertainty in distribution-network planning (). Robust optimization (RO) does not rely on an exact probability distribution and emphasizes the feasibility of a configuration within a prescribed uncertainty set, but its results may become increasingly conservative as the uncertainty set expands (). Distributionally robust optimization (DRO) instead optimizes over an ambiguity set of probability distributions; recent formulations combine robust ambiguity sets with risk measures such as conditional value-at-risk to control distributional uncertainty and tail risk (Zhong et al., 2026). The suitability of each method depends on the data basis and decision objective. In this study, candidate scenarios can be generated from wind, photovoltaic, and load samples, and probability-weighted representative scenarios can be obtained through scenario reduction. The objective is to determine mobile-resource siting-and-sizing schemes that accommodate multiple typical source–load conditions and to evaluate their operating performance comprehensively. Two-stage stochastic optimization is therefore adopted to address source–load uncertainty.
In summary, existing studies provide methodological foundations for mobile-battery planning, road-condition modeling, and mobile-hydrogen resource configuration, but four limitations remain. First, most studies focus on a single battery-based mobile-storage technology, and relatively few simultaneously consider multiple types of mobile energy resources within the same distribution-network planning framework while distinguishing their operating characteristics. Second, existing distribution–road-network studies commonly use route variables, time–space states, and traffic constraints to represent vehicle movement. Although these formulations describe specific routes, they require extensive data, many integer variables, and substantial computation. Conversely, ignoring the road differences among resource–candidate-node combinations cannot capture their accessibility and relocation-cost differences. Road-information representations suited to mobile-resource siting and sizing and distribution-network operating evaluation therefore require further study. Third, the power-supply capability of mobile hydrogen resources depends jointly on P2H production, on-site storage, and vehicle refueling, and a fixed initial-fuel constraint alone cannot represent the complete electricity–hydrogen replenishment relationship. Fourth, application tasks and evaluation indicators are dispersed among studies, making it difficult to characterize the operation of different mobile energy resources across multiple applications under a consistent network, source–load scenario set, and indicator definition. The main contributions of this study are as follows.
A multi-resource coupled siting-and-sizing model is developed for distribution networks. Based on DistFlow constraints and renewable-energy operating constraints, three representative mobile energy resources—MESVs, TBESSs, and MHSVs—are introduced together with P2H production and on-site hydrogen storage. The model determines resource types, equipment specifications and quantities, rated power, battery-energy and onboard-hydrogen capacities, activation of candidate connection nodes, and the scale of electricity–hydrogen facilities.
To account for road constraints on mobile-resource deployment, the accessibility status and one-way relocation cost of each resource–candidate-node combination are calculated externally and embedded in the second-stage scenario-dependent deployment constraints and objective function. These parameters restrict deployment feasibility under each source–load scenario and quantify the corresponding deployment cost.
A multi-scenario-driven two-stage stochastic mixed-integer quadratically constrained programming model is formulated to co-optimize mobile-resource and electricity–hydrogen-facility planning with scenario-dependent operation. The first stage determines mobile-resource configuration, candidate-node activation, and the siting and sizing of P2H and on-site hydrogen storage facilities. Subject to the first-stage scheme, the second stage determines resource deployment and hourly operation under each source–load scenario. Representative cases are established for renewable energy integration, peak shaving, congestion mitigation under normal operation, and black-start active-power support, and the operating characteristics of multiple resource types are analyzed in terms of siting and sizing, representative operating trajectories, road-condition effects, and multidimensional evaluation.
The remainder of this paper is organized as follows. Section 2 presents the distribution-network model, MESV and TBESS models, the MHSV–P2H electricity–hydrogen coupling model, the road-network model, and the operating evaluation indicators. Section 3 introduces source–load scenario generation and reduction and formulates the multi-scenario-driven two-stage stochastic planning–operation co-optimization model. Section 4 describes the distribution network, flexible resources, road conditions, source–load scenarios, and representative cases, and analyzes the planning configuration, overall operating results, single-resource characteristics, joint operation, road-condition effects, and multidimensional performance of multiple resource types. Section 5 summarizes the conclusions and future research directions.
2 Configuration and operation models for multiple types of mobile energy resources
Figure 1 presents the siting-and-sizing framework for multiple types of mobile energy resources under source–load uncertainty. Wind, photovoltaic, and load time series are processed through scenario generation and reduction to form representative scenarios. The distribution-network model, MESV and TBESS models, the MHSV–P2H electricity–hydrogen coupling model, the road-network model, and corresponding operating evaluation indicators are then established. The model minimizes the sum of first-stage planning cost and the expected second-stage scenario operating cost to determine the siting, sizing, and operating schemes.
FIGURE 1
Figure 2 shows the distribution–road-network structure and the connection relationships of mobile energy resources. The distribution-network layer includes distributed wind generation, photovoltaic generation, loads, critical loads, and candidate connection nodes for mobile energy resources. The road-network layer includes the resource depot, service nodes, and hydrogen-supply facilities. MESVs and TBESSs travel through the road network to candidate connection nodes for charging and discharging, while deployed MHSVs provide active-power support to the distribution network. P2H facilities use electricity to produce hydrogen, and on-site hydrogen storage facilities store hydrogen and refuel the MHSVs. Candidate-node activation is determined in the first stage, and mobile energy resources are deployed in the second stage only to activated and road-accessible candidate nodes.
FIGURE 2
2.1 Distribution-network model
Let , , , , and denote the sets of distribution-network buses, branches, time periods, application scenarios, and source–load scenarios, respectively, and let denote the root bus. Bus loads and the maximum available wind and photovoltaic outputs are determined by the base loads or installed capacities, source–load scenario time-series coefficients, and application-scenario adjustment factors, as given in Equations 1a–d:where and are the base active and reactive loads at bus , respectively; and are the installed photovoltaic and wind capacities at bus ; and , , and are collectively termed the source–load scenario time-series coefficients. They describe the intraday load, photovoltaic, and wind profiles in source–load scenario , where is the load coefficient and and are the photovoltaic and wind output coefficients. is the load-level adjustment factor; and are the photovoltaic and wind output adjustment factors; and and are the photovoltaic and wind installed-capacity adjustment factors. is the additional charging load. is the per-unit base capacity, and the relevant power quantities are converted to per-unit values for calculation. is the duration of each period.
The actual grid-connected active power and curtailed power of wind and photovoltaic generation satisfy Equations 2a–c:where and are the actual grid-connected active powers of photovoltaic and wind generation, while and are the curtailed photovoltaic and wind powers. Reactive-power outputs are constrained by fixed proportions of installed capacity, as given in Equations 3a, b:where and are the photovoltaic and wind reactive-power outputs, respectively, and is the reactive-power capability coefficient of renewable generation.
Let denote the set of mobile battery-storage resources. and are the charging and discharging powers of resource , is the MHSV generation power, is the P2H electricity consumption, and is the load-shedding power. The active-power balance at each bus is given by Equation 4:
The reactive-power balance is given by Equation 5:where is the active power purchased by the distribution network from the upstream grid, and is the reactive-power exchange with the upstream grid. and are the active and reactive power flows at the sending end of branch from bus to bus ; and are the branch resistance and reactance; is the squared current magnitude; and is the root-bus indicator.
A second-order cone-relaxed DistFlow model is used. The branch voltage drop, current-power relationship, and capacity constraints are given in Equations 6a–e:where is the squared voltage magnitude at bus , is the branch-capacity limit, is the branch-capacity slack, and are the lower and upper limits of the squared voltage magnitude, is the substation voltage, and is the upper limit of the squared branch-current magnitude. Equation 6c treats the branch apparent-power limit as a penalized soft constraint, and is the nonnegative excess allowance in squared apparent power and is penalized in the objective function. The root-bus power exchange and load-shedding power satisfy Equations 7a–c:where is the upstream-grid supply limit in period under application scenario , and is the limit on reactive-power exchange between the distribution network and the upstream grid.
2.2 MESV and TBESS models
Let denote the set of three types of mobile energy resources, and let denote a candidate equipment specification. is the configured number of type-, specification- units, and is the type-activation variable. The relationship between equipment quantity and type activation is given by Equations 8a–c:where is the upper limit on the total number of type- units, and is the upper limit on the configurable number of units with the corresponding specification.
For , the aggregate rated power and energy capacity are given by Equations 9a, b:where and are the rated power and energy capacity of one unit, and and are the aggregate power and energy capacities corresponding to the siting-and-sizing result. is an upper bound determined by the maximum total number of units and the maximum rated power per unit.
Let denote the candidate connection-node set. indicates that resource type is deployed to node in application scenario and source–load scenario , indicates whether candidate node is activated, and indicates whether resource type is applicable to application scenario . Scenario-dependent deployment satisfies Equations 10a–c:
Units of the same type are represented as an aggregated fleet. The deployment node and hourly operating states are determined under each source–load scenario. For compactness, define the operating-state set and define the aggregate charging/discharging power as follows in Equation 11:
The node-level power, aggregate power, and charging/discharging states of MESVs and TBESSs satisfy Equations 12a–d:where is the discharging-state variable. The initial aggregate stored energy and its temporal recursion are given by Equations 13a, b:
The energy limits and terminal-state constraint are given by Equations 14a, b:where is the aggregate stored energy; and are the charging and discharging efficiencies; , , and are the initial, minimum, and maximum state-of-charge ratios; and is the terminal period of the scheduling horizon.
The total mobile-resource connection power at each candidate node satisfies Equation 15:where is the connection-power limit of candidate node .
2.3 MHSV–P2H electricity–hydrogen coupling model
The aggregate rated power and onboard hydrogen-storage capacity of MHSVs are given by Equations 16a, b:where is the onboard hydrogen-storage capacity of one MHSV, and is an upper bound determined by the maximum number of MHSVs and the maximum rated power per vehicle. Define the aggregate MHSV generation power as given in Equation 17:
The node-level and aggregate generation powers satisfy Equations 18a, b:
The hydrogen consumed by MHSVs in period is given by Equation 19:where is MHSV hydrogen consumption, is the fuel-cell generation efficiency, is the lower heating value of hydrogen, and the factor 1,000 converts MW to kW.
Let be the hydrogen supplied by the P2H station at node to MHSVs, and let be the onboard hydrogen inventory. The aggregate refueling amount is given by Equation 20:
The refueling capability and onboard hydrogen inventory satisfy Equations 21a–f:where is the single-period refueling limit at station , is the single-period refueling limit per MHSV, and , , and are the initial, minimum, and maximum onboard-hydrogen ratios.
Let denote the candidate P2H construction-node set, the P2H-facility construction variable, and and the electrolyzer power and on-site hydrogen-storage capacity, respectively. The siting-and-sizing constraints for P2H and on-site hydrogen-storage facilities are given by Equations 22a–e:where is the upper limit on the number of P2H facilities; and are the lower and upper limits on the electrolyzer power of one station; and are the lower and upper limits on the on-site hydrogen-storage capacity of one station; and is the upper limit on total electrolyzer capacity.
The electricity consumption of the electrolyzer and hydrogen production satisfy Equations 23a, b:where is the hydrogen production and is the electrolytic-hydrogen production efficiency. The on-site hydrogen inventory satisfies Equations 24a–e:where is the on-site hydrogen inventory, and are the initial and terminal hydrogen-storage ratios, and is the upper limit on the net increase in on-site hydrogen inventory. These constraints form the P2H production–on-site hydrogen storage–vehicle refueling–MHSV generation electricity–hydrogen supply chain.
In this study, “black-start active-power support” refers specifically to a simplified hourly active-power support subproblem during a prescribed no-grid-import interval, rather than a complete dynamic black-start restoration process. The corresponding constraint is given by Equation 25:where is the black-start active-power support requirement in period , and is the unmet active-power support in source–load scenario .
2.4 Road-network model
For each mobile-resource type, candidate connection node, and application scenario, the road layer first provides a prescribed one-way travel time and an application-specific response-time limit. Their comparison determines the binary accessibility parameter: the resource–node pair is accessible only when the travel time does not exceed the response-time limit. The one-way relocation-cost parameter is then calculated from the same travel time using the corresponding resource/application movement-cost coefficient. Scenario-dependent deployment satisfies Equation 26:where is a binary parameter. When , the corresponding resource–candidate-node combination cannot be deployed. The relocation cost of one scenario-dependent deployment of an aggregated type- fleet in application scenario and source–load scenario is given by Equation 27:
This provides a parameterized road–grid interface in which the optimization selects feasible resource–node deployments and accounts for relocation cost, whereas detailed vehicle paths, departure/arrival sequences, and traffic-flow states remain outside the current planning model.
2.5 Operating evaluation indicators
To evaluate mobile-resource configurations, operating indicators are constructed for renewable energy integration, power-supply support, network operation, and road accessibility. The monthly expected curtailed wind and photovoltaic energy in application scenario is given by Equation 28:
The monthly load-shedding energy in application scenario is given by Equation 29:where and are the monthly expected curtailed wind and photovoltaic energy and the monthly load-shedding energy in application scenario , respectively; is the equivalent number of operating days per month for application scenario , which converts representative-day results to monthly values; is the effective source–load scenario set; and is the effective scenario probability.
The maximum line loading ratio is given by Equation 30:
The inaccessibility rate of candidate deployment combinations is given by Equation 31:
There are 18 resource–candidate-node combinations in this study. This indicator represents the proportion restricted by road accessibility. Indicators with different dimensions are converted to relative values using min-max normalization, as given in Equation 32:where denotes an object included in the comparison of the same type of indicator, and denotes the indicator category. If the maximum and minimum values of an indicator are equal, its normalized value is set to zero. The multidimensional evaluation of the three mobile energy resources includes economic benefit, peak shaving, congestion mitigation, total load-shedding reduction, renewable-energy coordination, and deployment flexibility. The economic-benefit score is the arithmetic mean of the standardized cost-saving, return-on-investment, and peak–valley arbitrage scores, with a weight of 1/3 assigned to each sub-indicator. The congestion-mitigation score averages the standardized congestion-cost and line-loading scores with equal weights of 1/2, and the deployment-flexibility score similarly averages the road-accessibility and applicable-scenario scores with equal weights of 1/2. Peak shaving, total load-shedding reduction, and renewable-energy coordination each use their respective single standardized indicator. The applicable-scenario score is determined by the number of application scenarios in which the resource is allowed to participate according to the resource-service matrix. No further weighted aggregation is applied across the six dimensions; Figure 3 therefore presents a multidimensional comparative profile rather than a single overall performance score. All dimension scores are converted to a 0–100 scale for comparison among the three resources under the current evaluation set.
FIGURE 3
3.1 3 Two-stage stochastic optimization under source–load uncertainty
Source–load scenario generation and reduction
Candidate source–load scenarios are generated from wind, photovoltaic, and load time-series forecasts. Monte Carlo sampling first produces 500 candidate samples, after which scenario reduction retains eight representative scenarios and their original probabilities, forming the complete representative scenario set. Let denote the original probability of representative scenario s. The complete and effective scenario probabilities satisfy Equations 33a, b:
For the reported siting-and-sizing case studies, scenarios s1–s4 are activated as the effective scenario set . Here, “effective” denotes the scenarios included in the reported planning calculation rather than the result of a second scenario-reduction step; scenarios s5–s8 remain part of the complete representative scenario set but are not included in these planning runs. The original probability mass of s1–s4 is 0.570, and their probabilities are renormalized using Equation 33b so that the probabilities of the active scenarios sum to one.
The representative scenarios obtained after reduction differ in load level, wind and photovoltaic output level, and ramping characteristics, and therefore represent multiple typical source–load operating states.
3.2 Two-stage siting-and-sizing model
Two-stage stochastic programming is used to describe the relationship between mobile-resource planning and operation under source–load uncertainty. Before the source–load scenario is realized, the first-stage planning decisions are determined and shared by all representative scenarios. First-stage variables include the equipment specifications and quantities of each mobile-resource type, type-activation status, candidate-node activation status, and the construction locations and capacities of P2H and on-site hydrogen-storage facilities. These variables do not carry a source–load scenario index. After a representative source–load scenario is realized, the second-stage decisions can be adjusted according to the realized scenario, subject to the fixed first-stage planning scheme. Second-stage variables are scenario dependent and include mobile-resource deployment, MESV and TBESS charging and discharging, MHSV generation, P2H hydrogen production, onboard and on-site hydrogen states, renewable-energy utilization, load shedding, and distribution-network operation in each period. The deployment variable has no time index. Thus, after a source–load scenario is realized, units of the same resource type are treated as an aggregated fleet and assigned to one activated and road-accessible candidate node for the representative day, while their power and energy/hydrogen states are optimized hourly. This scenario-level assumption represents day-level resource deployment for planning and operating evaluation, but does not capture fleet splitting among multiple nodes or within-day relocation between nodes. Equations 14b and 21f require terminal battery energy and onboard hydrogen not below their initial levels, while (24d)–(24e) constrain terminal on-site hydrogen storage and its net increase; inter-day state continuity and multi-day relocation are not modeled.
Let denote the application-scenario set included in the optimization. The five representative cases are solved separately, and each solution contains only its corresponding application scenario. For each application, the 24-h result under source–load scenario s is treated as a representative-day quantity; the effective scenario probabilities form its expected representative-day value, which is multiplied by the prescribed equivalent monthly operating/event days of that application to obtain the monthly statistical value. The objective therefore minimizes the monthly expected total cost, as given in Equation 34:
The planning cost includes the monthly equivalent costs of mobile energy resources, candidate connection nodes, and P2H and on-site hydrogen-storage facilities, as given in Equation 35:
The planning terms are converted independently of the equivalent monthly operating days: capital expenditures are annualized using the capital-recovery factor, annual operation and maintenance costs are included where applicable, and the annualized planning cost is converted to a monthly equivalent using a factor of 1/12. Accordingly, is the monthly equivalent configuration cost of a mobile resource, is the monthly equivalent activation cost of candidate connection node , and is the monthly equivalent cost of the P2H and on-site hydrogen-storage facilities. These planning terms enter the objective directly on a monthly-equivalent basis, whereas scenario-dependent operating costs are probability-weighted at the representative-day level and then multiplied by the corresponding equivalent monthly operating/event days. The resulting monthly basis is a statistical equivalent constructed from representative-day results rather than a chronological multi-day simulation. The scenario operating cost is given by Equation 36:where is the electricity-purchase price; and are photovoltaic- and wind-curtailment penalty coefficients; is the bus load-shedding penalty coefficient; is the line-congestion penalty coefficient; is the P2H operating and refueling cost; is the penalty coefficient for insufficient black-start active-power support; and is an auxiliary regularization term for the power-flow solution.
The monthly auxiliary regularization cost aggregates across application and source–load scenarios using the equivalent monthly operating days and scenario probabilities. Subsequent economic analysis uses the monthly economic objective after this term is deducted, namely, .
Equations 1–36 constitute a two-stage stochastic mixed-integer quadratically constrained programming model under source–load uncertainty. The model minimizes the monthly expected total cost, with first-stage planning variables and second-stage scenario-dependent deployment and hourly operating variables optimized jointly.
4 Case study
4.1 Parameter settings
The model is formulated in the General Algebraic Modeling System (GAMS) 44.4.0 and solved using CPLEX. The relative optimality-gap tolerance is set to 1%, and eight solution threads are used. Accordingly, the reported objective value is interpreted together with its solver best bound: when the incumbent–best-bound intervals of two schemes overlap, their economic objectives are not ranked; a ranking is made only when the difference is clearly separated at the attained solution accuracy. Monthly accumulated operating indicators follow the same probability-weighted representative-day aggregation defined in Section 3.2. The maximum line loading ratio is the peak apparent-power-to-rating ratio, whereas maximum congestion slack is the peak relaxation beyond the squared branch rating (MVA2), both taken over all effective scenarios, periods, and branches.
A modified IEEE 33-bus radial distribution system is used. Candidate connection nodes for mobile energy resources are i7, i17, i24, i25, i29, and i32, and the scheduling horizon is 24 h. The maximum numbers of MESVs, TBESSs, and MHSVs are three, three, and two, respectively.
To analyze the effect of road factors on planning and operation, two road conditions are considered: full accessibility and road constraints. Under full accessibility, every resource–candidate-node combination is treated as accessible and the one-way relocation cost is zero. Under road constraints, the accessibility status and one-way relocation-cost parameters defined in Section 2.4 are used; inaccessible combinations cannot be deployed, and their associated relocation costs are included in scenario operating costs. Mobile-resource configuration, candidate-node activation, scenario-dependent deployment, and intraday operation are re-optimized under both road conditions. Except for the road-condition comparison, all representative cases with mobile energy resources in Table 1 use the road-constrained condition.
TABLE 1
| Case | Application scenario | Optional resources and road condition |
|---|---|---|
| Case 1 | Renewable energy integration | No mobile energy resources |
| Case 2 | Renewable energy integration | TBESS optional; road-constrained condition |
| Case 3 | Peak shaving | MESV and TBESS optional; road-constrained condition |
| Case 4 | Congestion mitigation under normal operation | MESV and TBESS optional; road-constrained condition |
| Case 5 | Black-start active-power support | MESV and MHSV optional; P2H and on-site hydrogen storage may be constructed; road-constrained condition |
Representative case settings.
Five representative cases are established: no mobile energy resources, renewable energy integration, peak shaving, congestion mitigation under normal operation, and black-start active-power support. Each case corresponds to a different source–load stress and application requirement. The monthly economic objective is used only to compare schemes under the same application scenario and statistical definition. Case 5 applies this scope by imposing a 0.55 MW hourly active-power support requirement during hours 1–4, with grid import set to zero over the same interval.
Table 1 summarizes the settings of the five representative cases.
The original source–load scenario set contains 500 candidate samples. Scenario reduction yields eight representative scenarios with probabilities 0.134, 0.168, 0.154, 0.114, 0.114, 0.132, 0.108, and 0.076, which sum to 1.000. Figure 4 shows the eight representative source–load scenarios and their probabilities.
FIGURE 4
Across the eight representative scenarios, the 24 h sums of the load time-series coefficients range from 20.571 to 21.542, while the corresponding sums of the photovoltaic and wind output coefficients range from 6.396 to 7.685 and from 10.046 to 13.240, respectively. The maximum changes between adjacent periods are 0.253, 0.372, and 0.254 for the three coefficient types. The scenarios therefore differ in both source–load levels and intraday rates of change. For the reported siting-and-sizing calculations, scenarios s1–s4 are activated with renormalized probabilities of 0.235, 0.295, 0.270, and 0.200. Scenarios s5–s8 remain in the complete representative scenario set but are not included in these planning runs. Accordingly, Figure 4 presents the complete eight-scenario set and the original scenario probabilities, whereas Figures 3 and 15 present results obtained from the four effective scenarios.
4.2 Siting-and-sizing and overall operating results
Table 2 presents the planning results and scenario-dependent deployment nodes for the five representative cases. In the renewable energy integration case, node i7 is activated and three TBESSs are configured, with an aggregate rated power of 4.50 MW and an energy capacity of 11.25 MWh. The fleet is deployed to i7 in all four effective scenarios. In the peak-shaving case, nodes i7 and i25 are activated and three MESVs are configured, with an aggregate rated power of 2.00 MW and an energy capacity of 4.80 MWh. The fleet is deployed to i7 in s1 and s4 and to i25 in s2 and s3. Units of the same type are represented as an aggregated fleet and are jointly deployed to one candidate node in each source–load scenario. In the congestion-mitigation case, node i7 is activated and two MESVs are configured, and the fleet is deployed to i7 in all four effective scenarios. In the black-start active-power support case, node i25 is activated, and MESV, MHSV, P2H, and on-site hydrogen storage are configured; both the MESV and MHSV are deployed to i25.
TABLE 2
| Case | Activated nodes | Resource configuration | Scenario-dependent deployment |
|---|---|---|---|
| Case 1 | — | — | — |
| Case 2 | i7 | 3 × TBESS, 1.50 MW/3.75 MWh each; total: 4.50 MW/11.25 MWh | s1–s4: i7 |
| Case 3 | i7, i25 | 1 × MESV, 0.50 MW/1.20 MWh; 2 × MESV, 0.75 MW/1.80 MWh each; total: 2.00 MW/4.80 MWh | s1, s4: i7; s2, s3: i25 |
| Case 4 | i7 | 1 × MESV, 0.25 MW/0.60 MWh; 1 × MESV, 0.50 MW/1.20 MWh; total: 0.75 MW/1.80 MWh | s1–s4: i7 |
| Case 5 | i25 | 1 × MESV, 0.50 MW/1.20 MWh; 1 × MHSV, 0.25 MW and 40 kg H2; P2H: 0.058824 MW; on-site H2 storage: Approximately 120.030 kg | s1–s4: both MESV and MHSV at i25 |
Planning and scenario-dependent deployment results of representative cases.
These configurations reflect differences in the service target, source–load stress, response time, and required support duration. For renewable-energy integration, the dominant requirement is to absorb renewable surplus over multiple hours; TBESSs therefore provide the larger energy-capacity scale needed for intertemporal charging and discharging. Peak shaving combines the highest load stress with a 45-min road-response limit, under which MESVs remain reachable while TBESSs do not, so a larger MESV fleet is selected. In normal congestion mitigation, the lower load stress and 150-min response limit enlarge the feasible deployment range, and a smaller MESV configuration is sufficient for localized support. Black-start active-power support requires 0.55 MW during the first 4 hours without grid import; the model therefore combines MESV output with MHSV generation and the P2H–hydrogen-storage–refueling chain to extend the available support duration.
Figure 5 presents the operating indicators and mobile-resource-chain outputs of the five representative cases. Each indicator is normalized using Equation 32, and the original values are listed in Tables 3 and 4. A normalized value represents only the relative magnitude of an indicator among the five cases and does not imply that a higher value corresponds to better performance. The monthly economic objectives in Table 3 exclude the auxiliary power-flow regularization term.
FIGURE 5
TABLE 3
| Case | Economic objective | Relocation cost | Load shedding | Wind/PV curtailment | Max. line loading | Max. congestion slack |
|---|---|---|---|---|---|---|
| Case 1 | 1,837,886.200 | 0.000 | 0.000 | 571.908 | 1.173 | 0.195 |
| Case 2 | 1,492,317.700 | 24,300.000 | 0.000 | 461.385 | 1.170 | 0.191 |
| Case 3 | 344,079.390 | 3,730.863 | 0.064 | 0.000 | 1.203 | 0.542 |
| Case 4 | 377,077.630 | 3,888.000 | 0.000 | 0.000 | 1.117 | 0.299 |
| Case 5 | 236,964.600 | 76.000 | 2.432 | 0.000 | 0.445 | 0.000 |
Key operating indicators of representative cases.
Economic objective and relocation cost are in CNY/month; load shedding and wind/PV curtailment are in MWh/month; line loading is in p.u.; congestion slack is in MVA2.
TABLE 4
| Case | MESV discharge (MWh) | TBESS discharge (MWh) | MHSV generation (MWh) | P2H electricity consumption (MWh) | H2 production (kg) | H2 refueling (kg) |
|---|---|---|---|---|---|---|
| Case 1 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Case 2 | 0.000 | 189.922 | 0.000 | 0.000 | 0.000 | 0.000 |
| Case 3 | 25.844 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Case 4 | 17.888 | 0.000 | 0.000 | 0.000 | 0.000 | 0.000 |
| Case 5 | 0.197 | 0.000 | 0.119 | 0.280 | 7.139 | 7.139 |
Monthly outputs of mobile energy resources and the electricity–hydrogen chain.
The monthly curtailed wind and photovoltaic energy in Case 1 is 571.908 MWh. After TBESSs are configured, curtailment in Case 2 decreases to 461.385 MWh, a reduction of 110.523 MWh, indicating that TBESSs absorb part of the surplus renewable energy. The associated road relocation cost is CNY 24,300.000/month. MESVs are deployed in both Cases 3 and 4, which correspond to different load stresses, configuration scales, and scenario-dependent deployment nodes; the reported indicators characterize the line operating conditions under their respective application scenarios. In Case 5, the maximum line loading ratio is 0.445 p.u., the congestion slack is zero, and the monthly load-shedding energy is 2.432 MWh. This application is mainly constrained by available supply capacity, and the line loading remains relatively low.
The monthly TBESS discharge in Case 2 is 189.922 MWh, reflecting its large energy-throughput scale. Monthly MESV discharge is 25.844 MWh in Case 3 and 17.888 MWh in Case 4. In Case 5, the MESV and MHSV deliver 0.197 MWh and 0.119 MWh, respectively. Monthly P2H electricity consumption is 0.280 MWh, corresponding to both hydrogen production and refueling of 7.139 kg. These results show that MHSV generation in the black-start active-power support scenario is linked to the upstream hydrogen-production, storage, and refueling processes.
Figure 6 presents the 24 h probability-weighted expected power balance of the five cases.
FIGURE 6
In Case 1, the utilized wind and photovoltaic energy is 43.030 MWh, and grid-purchased energy is 5.629 MWh. After TBESSs are configured, utilized wind and photovoltaic energy in Case 2 increases to 49.170 MWh. The daily TBESS discharge and charge are 10.551 MWh and 11.741 MWh, respectively, indicating that the TBESSs shift energy by charging during low-net-load periods and discharging during other periods. In Case 3, the load energy, grid-purchased energy, storage discharge, and storage charge are 92.089, 49.468, 3.230, and 3.579 MWh, respectively. The corresponding values in Case 4 are 85.846, 42.964, 1.491, and 1.652 MWh. In Case 5, utilized wind and photovoltaic energy, grid-purchased energy, mobile-resource output, load-shedding energy, MESV charging, and P2H electricity consumption are 11.739, 24.000, 1.582, 12.159, 1.094, and 1.400 MWh, respectively. The MESV and MHSV jointly provide mobile power-supply support.
4.3 Operating characteristics of individual resources
Figure 7 first presents the source–load ranges, net load, and statistical charging/discharging response of the TBESSs in the renewable energy integration scenario.
FIGURE 7
Across the four scenarios, load energy ranges from 47.382 to 49.618 MWh, utilized wind and photovoltaic energy ranges from 48.421 to 49.986 MWh, and the 24 h cumulative net-load energy ranges from −1.039 to −0.367 MWh. Daily TBESS charging ranges from 11.136 to 12.361 MWh and daily discharging ranges from 9.860 to 11.156 MWh; all scenarios exhibit net absorption. Source–load scenarios change the charging and discharging periods and energy throughput of the TBESSs but do not change their primary role in renewable energy integration.
Figures 8–10 present the three-dimensional net-power trajectories of TBESSs, MESVs, and the MHSV–P2H chain under the four scenarios.
FIGURE 8
FIGURE 9
FIGURE 10
The TBESS net-power range is approximately −1.500 to 1.500 MW. All four scenarios contain pronounced charging and discharging processes, while the specific periods and magnitudes vary with source–load conditions. The result shows that the same siting-and-sizing scheme can adjust the intraday energy-shifting process of TBESSs through scenario-dependent operation.
Daily MESV discharge ranges from 2.335 to 3.648 MWh, daily charging ranges from 2.587 to 4.042 MWh, and net power ranges from −1.476 to 1.401 MW. Under the same first-stage MESV planning configuration, the fleet is deployed at i7 in s1 and s4 and at i25 in s2 and s3, while its hourly net-power trajectories also vary across scenarios, demonstrating that scenario-dependent second-stage operation adapts both deployment and charging/discharging decisions to the realized source–load condition. In the representative peak-shaving case, MESV power changes are concentrated in periods with high load stress. Their energy throughput is lower than that of TBESSs in the renewable energy integration case, but their power actions are more concentrated.
Daily MHSV generation ranges from 0.581 to 0.600 MWh, daily P2H electricity consumption ranges from 1.367 to 1.412 MWh, and net power ranges from −0.059 to 0.214 MW P2H electricity consumption exceeds MHSV generation mainly because of conversion losses in electrolytic hydrogen production and fuel-cell generation. On-site hydrogen storage coordinates the intraday timing of hydrogen production and refueling and satisfies the terminal hydrogen-inventory constraint.
Figures 11–13 use scenario s2, which has a relatively high probability and representative equipment behavior, to analyze typical operating processes of the three mobile energy resources.
FIGURE 11
FIGURE 12
FIGURE 13
Daily TBESS charging and discharging are 12.065 MWh and 10.889 MWh, respectively, and aggregate stored energy varies from 1.125 to 10.125 MWh. Figure 11 shows that charging during 13–17 h increases the stored energy from 3.692 MWh at 12 h to 10.125 MWh at 17 h, followed by discharge during 18–21 h and a decrease to 5.552 MWh. This charge–storage–discharge sequence directly illustrates the intertemporal energy-shifting role of TBESSs.
Daily MESV charging and discharging are 4.042 MWh and 3.648 MWh, respectively, and aggregate stored energy varies from 0.480 to 4.320 MWh. In scenario s2, the MESV fleet is deployed at i25 and its discharge is concentrated during 18–21 h, when stored energy decreases from 4.320 to 0.480 MWh; charging during 23–24 h then restores the terminal energy to approximately 2.400 MWh. This concentrated node-specific response links the trajectory in Figure 12 to short-duration local power support in the peak-shaving scenario.
Daily MHSV generation is 0.600 MWh and daily P2H electricity consumption is 1.412 MWh. Figure 13 shows that MHSV output is sustained over 1–4 h, corresponding to the defined 4 h black-start active-power support window, while P2H continues operating throughout the day. MHSV hydrogen consumption and refueling are both approximately 36.004 kg; the on-site hydrogen inventory falls to approximately zero during the support period and subsequently recovers to 12.003 kg by 24 h. This sequence shows how P2H production, hydrogen storage and refueling, and MHSV generation coordinate across time to support consecutive hydrogen-based power delivery and subsequent inventory recovery.
4.4 Joint operation and effects of road conditions
Figure 14 is an illustrative joint-operation example based on an extended peak-shaving case with full accessibility and zero relocation cost, rather than one of the five representative planning cases in Table 1; it is used to show the within-day coordinated response of MESV and TBESS in scenario s2.
FIGURE 14
Daily MESV charging and discharging are 1.011 MWh and 0.912 MWh, respectively, while daily TBESS charging and discharging are 3.004 MWh and 2.711 MWh. Both resources discharge during 18–21 h and replenish energy successively during 22–24 h. The TBESS supplies a larger amount of sustained energy, whereas the MESV power action is more concentrated. The two resources therefore exhibit different operating roles within the same day under joint configuration.
Figure 15 compares the planning and operating results obtained by re-optimization under full accessibility and road constraints. The two road conditions use the same distribution-network model and statistical method and differ only in the resource–candidate-node accessibility status and one-way relocation cost. In Figure 15, C2 denotes the paired case with full accessibility and C3 denotes the paired case with road constraints. These local labels are used only for the road-condition comparison in this figure.
FIGURE 15
Table 5 lists the corresponding original indicators for the paired cases under the two road conditions.
TABLE 5
| Application | Road condition | Inaccessible (%) | Relocation cost | Economic objective | Load shedding | Max. line loading | Max. congestion slack |
|---|---|---|---|---|---|---|---|
| Black-start active-power support | Full accessibility | 0.0000 | 0.000 | 239,536.170 | 2.273 | 0.454 | 0.000 |
| Black-start active-power support | Road constraints | 66.6667 | 129.600 | 239,301.130 | 2.275 | 0.445 | 0.000 |
| Congestion mitigation under normal operation | Full accessibility | 0.0000 | 0.000 | 364,254.800 | 0.000 | 1.049 | 0.158 |
| Congestion mitigation under normal operation | Road constraints | 16.6667 | 3,888.000 | 377,077.630 | 0.000 | 1.117 | 0.299 |
| Peak shaving | Full accessibility | 0.0000 | 0.000 | 310,462.560 | 0.000 | 1.072 | 0.232 |
| Peak shaving | Road constraints | 50.0000 | 3,730.863 | 344,079.390 | 0.064 | 1.203 | 0.542 |
Key indicators of paired cases under different road conditions.
Inaccessible (%) denotes the proportion of resource–candidate-node combinations excluded by the road-reachability condition. Relocation cost and economic objective are in CNY/month; load shedding is in MWh/month; line loading is in p.u.; congestion slack is in MVA2.
Road accessibility affects the three applications differently because the application-specific response-time limits remove different resource–node combinations from the feasible deployment set. For peak shaving, the 45-min limit excludes all TBESS routes and the MESV route to i24, which are used in the full-accessibility solution, so the optimum shifts from a MESV–TBESS combination to a larger MESV fleet. For normal congestion mitigation, the 150-min limit leaves most combinations accessible but excludes the preferred TBESS deployment at i24 because its one-way travel time is 158 min, so the solution shifts to MESVs. In the extended black-start comparison, although the 35-min limit gives the highest inaccessible proportion, the full-accessibility MESV deployment at i25 remains reachable within 32 min, so the road constraint mainly changes the selected MESV size and location. The relative optimality gaps of the paired black-start cases are 0.9993% and 0.9288%. Their incumbent–best-bound intervals overlap, and the relative difference between the two reported monthly economic objectives is only 0.0981%; therefore, the economic objectives under the two road conditions are not ranked at the current solution accuracy. The black-start road comparison in Table 5 uses an extended mobile-battery case; the core Case 5 configuration of MESV, MHSV, and P2H is not included in this paired comparison. The normalized values and colors in Figure 15 are used only for relative comparison within the same indicator and should not be interpreted as a common performance score across different indicators.
4.5 Multidimensional evaluation of multiple resource types
Figure 3 compares MESV, TBESS, and MHSV scores in six dimensions: economic benefit, peak shaving, congestion mitigation, total load-shedding reduction, renewable-energy coordination, and deployment flexibility. Each component score is calculated using the method described in Section 2.5.
Under the current evaluation samples and resource-applicability settings, TBESSs obtain relatively high scores for renewable-energy coordination, peak shaving, and congestion mitigation, consistent with their energy-throughput and network-support results in the relevant samples. MESVs obtain relatively high scores for total load-shedding reduction and deployment flexibility. Figure 3 uses six MESV samples, four TBESS samples, and one MHSV sample. Some economic indicators of mixed-resource cases are allocated according to resource quantity shares. The resulting six-dimensional profiles therefore characterize functional differentiation only under the selected applications, resource-service matrix, indicator definitions, equal-weight rule, and sample composition used in this study; they should not be interpreted as a universal ranking of MESV, TBESS, and MHSV technologies. In particular, the MHSV profile should be interpreted cautiously because it is based on only one evaluation sample.
5 Conclusion
This paper develops a multi-scenario-driven two-stage stochastic planning–operation co-optimization model that accounts for source–load uncertainty, road accessibility, and relocation costs and analyzes the planning and operation of MESVs, TBESSs, MHSVs, and the P2H electricity–hydrogen chain. The main conclusions are as follows.
First, different application requirements lead to different resource types, configuration scales, and connection nodes. The renewable energy integration case configures three TBESSs with an aggregate rated power of 4.50 MW and an energy capacity of 11.25 MWh. Both the peak-shaving and congestion-mitigation cases select MESVs. The black-start active-power support case configures MESVs, MHSVs, P2H, and on-site hydrogen storage. In the peak-shaving case, the same MESV configuration is deployed to i7 and i25 under different source–load scenarios, indicating that source–load scenarios affect the deployment location of mobile energy resources.
Second, the three types of mobile energy resources exhibit distinct operating characteristics. Through intertemporal charging and discharging, TBESSs reduce monthly curtailed wind and photovoltaic energy from 571.908 to 461.385 MWh. MESVs respond to peak-shaving and local network-support requirements. In the black-start active-power support case, P2H production, on-site hydrogen storage, and vehicle refueling supply fuel to the MHSV, while the MESV and MHSV jointly provide hourly active-power support.
Finally, road constraints reduce the deployable range of mobile energy resources and affect resource configuration, candidate-node activation, and operating outcomes. In the peak-shaving and congestion-mitigation cases, road constraints increase the monthly economic objective, maximum line loading ratio, or congestion slack. Road accessibility and relocation costs should therefore be incorporated into planning and operation of mobile energy resources. Overall, the results show that multi-resource planning and operation should be coordinated across probabilistic source–load scenarios and road-network deployment conditions.
Future work may further consider time-varying traffic conditions, vehicle-level route planning and coordinated dispatch, multi-day continuous scheduling, and the dynamic black-start restoration process to improve the planning and operation model for multiple flexible-resource types.
Statements
Data availability statement
The datasets presented in this article are not readily available because they contain confidential information and are subject to authorization by the relevant data-owning organization and applicable confidentiality requirements. Requests to access the datasets should be directed to tongzhucsgzh@outlook.com, ZT.
Author contributions
ZT: Writing – original draft, Writing – review and editing. HZ: Writing – review and editing. XZ: Writing – review and editing. YG: Writing – review and editing. XS: Writing – review and editing. XQ: Writing – review and editing. LY: Writing – review and editing.
Funding
The author(s) declared that financial support was received for this work and/or its publication. This work was supported in part by the Science and Technology Program of Guangdong Power Grid Co., Ltd. (030400KC25080010 (GDKJXM20250602)).
Conflict of interest
Authors ZT, HZ, XZ, and YG were employed by Zhuhai Power Supply Bureau of Guangdong Power Grid Co., Ltd.
Authors XS, XQ, and LY were employed by National Institute of Guangdong Advanced Energy Storage Co., Ltd.
Generative AI statement
The author(s) declared that generative AI was not used in the creation of this manuscript.
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Summary
Keywords
coordinated planning and operation, electricity–hydrogen coupling, mobile energy resources, multi-resource coupling, multi-scenario-driven optimization, renewable energy integration, two-stage stochastic optimization
Citation
Tong Z, Zeng H, Zhou X, Gu Y, Su X, Qiao X and Yang L (2026) Two-stage stochastic optimization for planning and operation of multiple types of mobile energy resources in distribution networks. Front. Energy Res. 14:1954798. doi: 10.3389/fenrg.2026.1954798
Received
31 July 2026
Revised
21 August 2026
Accepted
31 August 2026
Published
25 September 2026
Volume
14 - 2026
Edited by
Yi Su, Xiangtan University, China
Reviewed by
Yanjian Peng, Changsha University of Science and Technology, China
Zhineng Fei, Aalto University, Finland
Updates
Copyright
© 2026 Tong, Zeng, Zhou, Gu, Su, Qiao and Yang.
This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
*Correspondence: Zhu Tong, tongzhucsgzh@outlook.com
Disclaimer
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.