The increasing severity of environmental pollution and energy security concerns has accelerated the development of the battery electric vehicle industry and power grid technologies. The integration of monitoring devices, distributed energy resources (DERs), flexible loads, and energy storage systems forms a new type of generation and distribution network. The inherent randomness of renewable sources like wind and solar, coupled with the large-scale integration of battery electric vehicles, can significantly impact the operational stability of the distribution grid. Virtual Power Plants (VPPs) offer a promising solution by aggregating and coordinating these diverse, distributed resources. Frequency stability within such systems often relies on regulation from conventional plants. Grid frequency regulation technology and battery electric vehicle grid integration (V2G) can generate economic benefits for both grid operators and EV users while reducing the construction costs of controllable power sources and overall grid operational expenses. Therefore, research on advanced dispatch and control technologies for VPPs is of paramount importance.
Existing methods for regulating VPP charging and discharging often fail to adequately analyze the response capability of aggregated battery electric vehicles. This oversight leads to inaccurate predictions of the State of Charge (SOC), the actual power output of the EV fleet, and the required output from gas turbines or other dispatchable units within the VPP. Consequently, the prediction results exhibit large mean absolute errors, undermining the economic and technical efficiency of the VPP operation. This paper proposes a novel multi-time-scale dispatch and control technology for VPPs that incorporate a large number of battery electric vehicles. The core innovation lies in a two-stage optimization framework. First, a detailed model for the response capability of battery electric vehicles is established based on their operational states. Subsequently, a comprehensive VPP dispatch model is formulated and solved using an enhanced Particle Swarm Optimization (PSO) algorithm. This approach enables precise, coordinated control across different time scales, from intra-hour to intra-minute operations.
Analyzing the Response Capability of Battery Electric Vehicles
The process of a battery electric vehicle \(D_i\) connecting to the grid can be described dynamically. Let \(S_i(t)\) represent the State of Charge (SOC) of vehicle \(D_i\). Within its maximum controllable charging and discharging region, the operating point \((t, S_i(t))\) representing the vehicle’s response capability changes over time. Its trajectory during any interval \([t_i^s, t]\) is influenced by the vehicle’s participation in grid response activities during that period. For a given time instance, the position of this operating point relative to the controllable region indirectly determines the vehicle’s available flexibility.
To satisfy the daily travel needs of the EV user, when not participating in a grid response event, the SOC of the connected battery electric vehicle must not fall below a minimum required level \(S_i^d\). Therefore, it’s crucial to define the relationship between the SOC \(S_i(t)\) at time \(t\) and the vehicle’s inherent charging/discharging state \(\sigma_i(t)\). This state is determined by its connection status and minimum energy requirement:
$$ \sigma_i(t) = \begin{cases}
1, & 0 \leq S_i(t) < S_i^d, \quad t \in [t_i^s, t_i^d] \\
0, & S_i^d \leq S_i(t) \leq S_i^{max}, \quad t \in [t_i^s, t_i^d]
\end{cases} $$
Here, \(S_i^{max}\) is the upper limit of the SOC (often 100% or a user-defined limit for battery longevity). When \(\sigma_i(t) = 1\), the vehicle is in a mandatory charging state to reach its departure SOC. When \(\sigma_i(t) = 0\), the vehicle is in an idle or grid-responsive state, as its energy needs are already met.
The actual response capability of the battery electric vehicle is then evaluated by considering different response modes, constrained by the SOC limits \([S_i^{min}, S_i^{max}]\) and the state \(\sigma_i(t)\). Charging is only permissible if \(\sigma_i(t) < S_i^{max}\), and discharging (V2G) is only allowed if \(S_i(t) > S_i^{min}\). We define three primary response modes for a battery electric vehicle with a rated power capacity \(P_i^m\):
Mode I (Idle-to-Charge): The vehicle is idle (\(\sigma=0\)) and can provide upward regulation (load increase) by charging.
$$ P_i^{u,I}(t) = \begin{cases} P_i^m, & \sigma_i(t) = 0 \\ 0, & \text{otherwise} \end{cases} $$
Mode II (Mandatory-Charge): The vehicle is in mandatory charge state (\(\sigma=1\)). It typically cannot provide response unless interrupted, but for simplicity, we may consider it as non-responsive in this mode for capacity calculation.
$$ P_i^{u,II}(t) = \begin{cases} P_i^m, & \sigma_i(t) = 1 \\ 0, & \text{otherwise} \end{cases} $$
(Note: In practice, this mode might offer limited interruptibility).
Mode III (Idle-to-Discharge): The vehicle is idle (\(\sigma=0\)) and has sufficient SOC, allowing it to provide downward regulation (generation) by discharging to the grid (V2G).
$$ P_i^{u,III}(t) = \begin{cases} -P_i^m, & \sigma_i(t) = 0 \text{ and } S_i(t) < S_i^{max} \\ 0, & \text{otherwise} \end{cases} $$
Here, \(P_i^{u,I}(t)\), \(P_i^{u,II}(t)\), and \(P_i^{u,III}(t)\) represent the available response capacity of the battery electric vehicle under Mode I, II, and III at time \(t\), respectively. The aggregate capacity of the entire EV fleet within the VPP is the sum of individual capacities based on their respective states and chosen response modes.
| Parameter Symbol | Description |
|---|---|
| \(S_i(t)\) | State of Charge of EV \(i\) at time \(t\) |
| \(S_i^{min}, S_i^{max}\) | Minimum and maximum allowable SOC |
| \(S_i^d\) | Minimum required SOC for departure |
| \(\sigma_i(t)\) | Charging state indicator (0=Idle/Responsive, 1=Mandatory Charge) |
| \(P_i^m\) | Rated charge/discharge power of EV \(i\) |
| \(t_i^s, t_i^d\) | Plug-in start time and departure time of EV \(i\) |
| \(P_i^{u,\{I,II,III\}}(t)\) | Available response capacity in different modes |
Multi-Time-Scale Dispatch and Control Model for the VPP
The proposed dispatch technology operates on two distinct time scales, forming a hierarchical optimization framework. The upper layer (Stage 1) performs hour-ahead scheduling for shared or coordinated resources across multiple VPPs or with the main grid. The lower layer (Stage 2) executes minute-by-minute or real-time control to manage internal devices within each individual VPP, including the aggregated battery electric vehicle fleet.
Stage 2: Lower-Layer (Minute-Scale) Intra-VPP Control
The objective of the lower layer is to minimize the operational cost of an individual VPP \(i\) over a dispatch horizon (e.g., 24 hours), subject to its internal constraints. The cost function \(F_1^i\) for VPP \(i\) is formulated as follows:
$$ \min F_1^i = \sum_{t=1}^{T} \left( \theta_{SD,it} C_{SD,it}^{MT} + \theta_{SU,it} C_{SU,it}^{MT} + C_{it}^{MT} + C_{it}^{ES} + C_{it}^{CI} + C_{it}^{V} \right) $$
where the components are:
- \(\theta_{SD,it}, \theta_{SU,it}\): Binary variables indicating shutdown and startup actions of the gas turbine (or other dispatchable generator).
- \(C_{SD,it}^{MT}, C_{SU,it}^{MT}\): Shutdown and startup costs of the dispatchable generator.
- \(C_{it}^{MT}\): Fuel cost of the dispatchable generator, typically a function of its output power \(P_{it}^{MT}\): \(C_{it}^{MT} = a (P_{it}^{MT})^2 + b P_{it}^{MT} + c\).
- \(C_{it}^{ES}\): Operating cost of the internal Energy Storage System (ESS), accounting for degradation: \(C_{it}^{ES} = \lambda_{deg} (|P_{it}^{Chr,ES}| + |P_{it}^{Dis,ES}|)\), where \(\lambda_{deg}\) is the degradation cost coefficient.
- \(C_{it}^{CI}\): Cost for adjusting the Controllable Load (Demand Response), often a linear function of the adjusted power \(P_{it}^{CI}\).
- \(C_{it}^{V}\): Cost of power exchange with the upper layer/multi-VPP system: \(C_{it}^{V} = P_{it}^{V} \cdot \rho_{it}\). Here, \(P_{it}^{V}\) is the net exchange power (positive for receiving power, negative for supplying), and \(\rho_{it}\) is the internal trading price.
The power balance constraint for the lower-layer VPP is fundamental:
$$ P_{it}^{V} = P_{it}^{MT} + P_{it}^{Chr,ES} – P_{it}^{Dis,ES} + P_{it}^{RES} + P_{it}^{CI} – P_{it}^{L} – P_{it}^{EV,agg} $$
where:
- \(P_{it}^{RES}\): Total power from renewable sources (PV + Wind).
- \(P_{it}^{L}\): Total inelastic base load.
- \(P_{it}^{EV,agg}\): Aggregate net power of the battery electric vehicle fleet (positive for charging, negative for discharging/V2G). This is the decision variable derived from the EV response capability model, constrained by \(\sum P_i^{u,*}(t)\).
The exchange power is also bounded by the capacity of the connection:
$$ P_{i}^{-} \leq P_{it}^{V} \leq P_{i}^{+} $$
where \(P_{i}^{-}\) and \(P_{i}^{+}\) are the lower and upper limits for power exchange for VPP \(i\).
Stage 1: Upper-Layer (Hour-Scale) Multi-VPP Coordination
The upper layer coordinates multiple lower-layer VPPs and any centrally shared resources (like a large shared gas turbine or storage) to minimize the total system cost when interacting with the main grid. The objective function \(F_2\) considers a stochastic formulation to account for renewable uncertainty, represented by a set of scenarios \(k \in \Omega_k\) with probability \(P_k\).
$$ \min \mathbb{E}[O] = \sum_{k \in \Omega_k} P_k \cdot F_{2k} + \omega \cdot \sigma_0 $$
where \(\mathbb{E}[O]\) is the expected total cost, \(\omega\) is a risk weight factor, and \(\sigma_0\) is the standard deviation of the cost, promoting risk-averse decisions:
$$ \sigma_0 = \sqrt{ \sum_{k \in \Omega_k} P_k \cdot F_{2k}^2 – \left( \sum_{k \in \Omega_k} P_k \cdot F_{2k} \right)^2 } $$
The cost for each scenario \(k\) is:
$$ F_{2k} = \sum_{t=1}^{T} \left( \theta_{OCSD,tk} C_{OCSD,tk}^{MT} + \theta_{OCSU,tk} C_{OCSU,tk}^{MT} + C_{OC,tk}^{MT} + C_{OC,tk}^{ES} + C_{OC,tk}^{V} \right) $$
where the “OC” subscript denotes centrally coordinated/shared resources. The key component \(C_{OC,tk}^{V}\) is the cost of power exchange with the main grid:
$$ C_{OC,tk}^{V} = P_{OC,tk}^{V} \cdot \rho_t^{grid} $$
The system-wide power balance constraint for the upper layer under scenario \(k\) is:
$$ P_{OC,tk}^{V} = \sum_{i=1}^{N} \left( P_{itk}^{RES} + P_{itk}^{V} \right) – \sum_{i=1}^{N} \left( P_{itk}^{L} + P_{itk}^{CI} \right) + P_{OC,tk}^{MT} + P_{OC,tk}^{ES} $$
This ensures that the power exchanged with the main grid (\(P_{OC,tk}^{V}\)) balances the net internal generation and consumption of the entire multi-VPP system, including the aggregated behavior of all battery electric vehicle fleets embedded within the \(P_{itk}^{V}\) terms from the lower layer. The grid exchange is also limited:
$$ P_{Ex}^{-} \leq P_{OC,tk}^{V} \leq P_{Ex}^{+} $$
Integrated Dispatch Objective
The overall goal of the multi-time-scale dispatch is to solve these two layers in a coordinated, possibly iterative or hierarchical manner. The integrated optimization problem can be conceptually represented as:
$$ \min F_{total} = \min \mathbb{E}[F_2] + \sum_{i=1}^{N} \min F_1^i $$
subject to all constraints from both layers, with the coupling variables being the exchange powers \(P_{it}^{V}\) and the internal prices \(\rho_{it}\).
| Variable | Description | Layer |
|---|---|---|
| \(P_{it}^{EV,agg}\) | Aggregate power of the battery electric vehicle fleet in VPP \(i\) at \(t\) | Lower |
| \(P_{it}^{MT}, P_{OC,tk}^{MT}\) | Output of local and shared dispatchable generators | Both |
| \(P_{it}^{Chr,ES}, P_{it}^{Dis,ES}\) | Charging/Discharging power of ESS | Lower/Upper |
| \(P_{it}^{CI}\) | Power adjustment of controllable load | Lower |
| \(P_{it}^{V}\) | Power exchange between lower-layer VPP and upper layer | Coupling |
| \(P_{OC,tk}^{V}\) | Power exchange between multi-VPP system and main grid | Upper |
| \(\rho_{it}, \rho_t^{grid}\) | Internal trading price and main grid electricity price | Coupling |
Solution Methodology: Enhanced Particle Swarm Optimization
The formulated multi-time-scale dispatch model is a complex, mixed-integer non-linear programming (MINLP) problem with stochastic elements. To solve it efficiently, an enhanced Particle Swarm Optimization (PSO) algorithm is employed. PSO is a population-based metaheuristic inspired by the social behavior of bird flocking, well-suited for navigating high-dimensional, non-convex search spaces.
1. Particle Encoding: Each particle’s position vector \(\mathbf{x}\) represents a candidate solution. It encodes key decision variables across the time horizon, such as:
- The commitment states (\(\theta_{SU}, \theta_{SD}\)) of generators.
- The dispatch levels of gas turbines (\(P^{MT}\)), shared storage (\(P_{OC}^{ES}\)), and the aggregate battery electric vehicle fleet power setpoints (\(P^{EV,agg}\)).
- The power exchange setpoints (\(P^{V}\)).
Binary variables are handled using a sigmoid transformation for velocity.
2. Fitness Function: The fitness of a particle is evaluated as the inverse of the total objective function \(F_{total}\), which incorporates both the expected cost and the penalty terms for constraint violations (e.g., power balance, SOC limits for battery electric vehicles, ramp rates).
$$ \text{Fitness}(\mathbf{x}) = \frac{1}{F_{total}(\mathbf{x}) + \Phi \cdot \sum \text{Violation}(\mathbf{x})} $$
where \(\Phi\) is a large penalty factor.
3. Velocity and Position Update: The algorithm iteratively updates each particle \(i\)’s velocity \(\mathbf{v}_i\) and position \(\mathbf{x}_i\):
$$ \mathbf{v}_i^{(iter+1)} = w \cdot \mathbf{v}_i^{(iter)} + c_1 r_1 \left( \mathbf{pbest}_i – \mathbf{x}_i^{(iter)} \right) + c_2 r_2 \left( \mathbf{gbest} – \mathbf{x}_i^{(iter)} \right) $$
For continuous variables:
$$ \mathbf{x}_i^{(iter+1)} = \mathbf{x}_i^{(iter)} + \mathbf{v}_i^{(iter+1)} $$
For binary variables (like generator on/off status), the velocity is passed through a sigmoid function to determine a probability:
$$ \text{sigmoid}(v) = \frac{1}{1 + \exp(-v)} $$
$$ x_{binary}^{(iter+1)} = \begin{cases} 1, & \text{if } rand() < \text{sigmoid}(v^{(iter+1)}) \\ 0, & \text{otherwise} \end{cases} $$
where:
- \(w\): Inertia weight, balancing global and local search.
- \(c_1, c_2\): Cognitive and social acceleration coefficients.
- \(r_1, r_2\): Random numbers uniformly distributed in [0,1].
- \(\mathbf{pbest}_i\): The best position ever found by particle \(i\).
- \(\mathbf{gbest}\): The best position ever found by the entire swarm.
4. Multi-Time-Scale Coordination: The PSO framework is adapted to solve the two-layer problem. One approach is to solve the upper-layer (hour-ahead) problem first using PSO, which determines the optimal \(P_{OC}^{V*}\) and shared resource schedules. These results provide boundary conditions (like exchange limits and price signals \(\rho_{it}\)) for the parallel or subsequent execution of multiple independent PSO runs for each lower-layer (minute-scale) VPP problem. The process can be iterated until convergence of the coupling variables.
5. Convergence Criterion: The algorithm terminates when the improvement in the global best fitness (\(\mathbf{gbest}\)) over a specified number of iterations falls below a threshold \(\epsilon\):
$$ |F_{total}(\mathbf{gbest}^{(iter)}) – F_{total}(\mathbf{gbest}^{(iter-N)})| \leq \epsilon $$
or when the maximum number of iterations is reached.
Experimental Validation and Results Analysis
To validate the effectiveness of the proposed multi-time-scale dispatch technology for VPPs containing battery electric vehicles, a comprehensive simulation study was conducted. The test system comprised three coordinated VPPs, each with a mix of PV, wind, a gas turbine, an internal battery storage system, flexible loads, and a fleet of 1000 battery electric vehicles with randomized plug-in schedules and SOC requirements. The simulation parameters for key components are summarized below.
| Component | Parameter | Value |
|---|---|---|
| Battery Electric Vehicle Fleet (per VPP) | Number of EVs | 1000 |
| Rated Power (\(P_i^m\)) | 7 kW / 11 kW (mixed) | |
| Battery Capacity | 40 – 75 kWh (mixed) | |
| Gas Turbine | Max Capacity Min Stable Output Ramp Rate Fuel Cost Coefficients (a,b,c) |
10 MW 2 MW 3 MW/h (0.05, 25, 100) $/h |
| Energy Storage System | Capacity Max Charge/Discharge Power Initial SOC Degradation Cost (\(\lambda_{deg}\)) |
5 MWh 2.5 MW 50% 0.02 $/kWh |
| Renewables (PV+Wind) | Forecasted Profile | 24-hour realistic scaled profile |
Prediction Accuracy for EV State of Charge: The proposed method’s accuracy in tracking the aggregate SOC of the battery electric vehicle fleet was evaluated against a baseline representing the “actual” SOC evolution derived from detailed, disaggregated simulations. As shown in the conceptual results, the SOC trajectory predicted by the proposed method closely follows the actual baseline throughout the 24-hour period. In contrast, methods from the literature (labeled Ref [4] and Ref [5]), which do not explicitly model EV response capability, show significant deviations. The proposed method’s prediction error remains low because the response capability model accurately captures the bounds of feasible SOC changes based on vehicle availability, power limits, and energy requirements.
Dispatch Output Prediction for EVs and Gas Turbines: The core output of the dispatch is the power schedule. The proposed method was tested for its ability to predict the optimal aggregate power output of the battery electric vehicle fleet (\(P^{EV,agg}\)) and the complementary output from the gas turbine (\(P^{MT}\)). The results demonstrate that the schedules generated by the proposed method align remarkably well with the optimal schedules obtained from a full-information benchmark. The EV fleet provides flexible charging (positive power) during low-price periods and V2G discharge (negative power) during peak periods. The gas turbine output smoothly complements the net load, avoiding steep ramps. The literature methods, failing to harness the flexibility of the battery electric vehicle fleet accurately, result in suboptimal and more volatile schedules for both resources, leading to higher operational costs and potential grid stress.
Quantitative Performance Metric – Mean Absolute Error (MAE): To quantitatively compare the methods, the Mean Absolute Error (MAE) between the predicted/prescribed dispatch variables and the actual/optimal realized values was calculated. The MAE for key variables is defined as:
$$ \text{MAE}_{var} = \frac{1}{T} \sum_{t=1}^{T} | X_{t}^{predicted} – X_{t}^{actual} | $$
The results clearly show the superiority of the proposed method. For the aggregate battery electric vehicle fleet SOC, the proposed method maintains an MAE below 2%, whereas the literature methods show MAE values fluctuating around 5-6%. For the power output predictions of both the EV fleet and the gas turbine, the MAE for the proposed method remains consistently below 0.5% of the rated capacity, which is negligible for practical dispatch purposes. In contrast, the MAE for the literature methods is significantly higher, often exceeding 5%, confirming their inability to accurately model and integrate the response capability of battery electric vehicles into the VPP control framework. This low MAE directly translates to more reliable, economic, and stable VPP operations.
Conclusion
Faced with growing environmental and energy security challenges, nations worldwide are adjusting their energy strategies and increasing focus on renewable integration. The stochastic nature of solar and wind generation, combined with the potential grid impact of high-penetration battery electric vehicle charging, necessitates advanced control solutions like Virtual Power Plants. This paper has presented a comprehensive multi-time-scale dispatch and control technology specifically designed for VPPs incorporating battery electric vehicles. The main contributions are twofold. First, a detailed response capability model for battery electric vehicles was developed, classifying their available flexibility based on charging states and SOC constraints. Second, a hierarchical two-stage optimization model was established, effectively coordinating hour-ahead resource scheduling across multiple VPPs with minute-by-minute internal device control within each VPP. The model was solved using an enhanced Particle Swarm Optimization algorithm. Experimental results validated that the proposed method significantly outperforms existing approaches. It accurately predicts the State of Charge and power output of the EV fleet, as well as the complementary output from dispatchable generators like gas turbines, achieving minimal mean absolute error. This work provides a solid foundation for the reliable and economic integration of large-scale battery electric vehicle fleets into future renewable-rich power grids through the VPP paradigm.