Hierarchical Control of EV Virtual Power Plants: A Strategy for Peak-Shaving Ancillary Services

Abstract

In recent years, the installed capacity of renewable energy sources, such as wind power and photovoltaic generation, has been steadily increasing in power systems. However, the inherent randomness and volatility of renewable energy generation pose greater challenges to grid frequency stability. To address this issue, this paper first introduces the Minkowski sum algorithm to map the feasible regions of dispersed individual units into a high-dimensional hypercube space, achieving efficient aggregation of large-scale schedulable capacity. Compared with conventional geometric or convex-hull aggregation methods, the proposed approach better captures spatio-temporal coupling characteristics and reduces computational complexity while preserving accuracy. Subsequently, aiming at the coordination challenge between day-ahead planning and real-time dispatch, a “hierarchical coordination and dynamic optimization” control framework is proposed. This three-layer architecture, comprising “day-ahead pre-dispatch, intraday rolling optimization, and terminal execution,” combined with PID feedback correction technology, stabilizes the output deviation within ±15%. This performance is significantly superior to the market assessment threshold. The research results provide theoretical support and practical reference for the engineering promotion of vehicle–grid interaction technology and the construction of new power systems.

1. Introduction

Against the backdrop of the global energy structure transition and the deepening implementation of low-carbon economy strategies, the new energy vehicle industry has witnessed explosive growth [1]. With the exponential increase in the electric vehicle (EV) fleet and the in-depth exploration of their battery energy storage characteristics, constructing a smart grid with synergistic interaction of “Generation-Grid-Load-Storage” has become a core direction for modern power system innovation [2]. This transformation is reflected not only in the structural adjustment on the energy supply side but also in a fundamental shift in the demand-side management paradigm—through innovative applications such as Vehicle-to-Grid (V2G) technology and clustered control of smart charging piles, EV populations are evolving from mere electricity consumers to mobile energy storage units with flexible regulation capabilities [3,4,5,6,7]. Moreover, emerging artificial intelligence technologies such as federated learning and digital twins are increasingly being applied to EV scheduling and grid ancillary services, enabling more accurate behavior prediction and privacy-preserving collaborative optimization [8,9].

The aggregate schedulable capacity (ASC) of naturally distributed EV clusters serves as a core metric for evaluating the capability of EV-aggregated Virtual Power Plants (VPPs) to participate in grid ancillary services. Its technical essence lies in the dynamic quantification of bidirectional energy interaction capability [10,11]. By establishing a spatio-temporal constraint model for the charging and discharging power of EV clusters, this metric accurately characterizes the maximum schedulable power boundary between the EV cluster, as a flexible load, and the power grid, while guaranteeing users’ travel needs [12]. Current research on EV capacity aggregation primarily follows two approaches: macro-modeling based on cluster statistics [13] and bottom-up modeling based on user behavior [14,15]. The former, while computationally efficient, often overlooks spatio-temporal heterogeneity; the latter, though accurate, suffers from high computational complexity when scaled [16]. In contrast, this paper proposes a novel Minkowski sum-based aggregation method that efficiently maps individual EV feasible regions into a high-dimensional hypercube, balancing accuracy with scalability.

As a key enabler for building new power systems, VPPs utilize information and communication technology, intelligent control algorithms, and market mechanisms to aggregate distributed generation, energy storage systems, and flexible load-side resources (represented by EVs), forming a coordinated “Generation-Grid-Load-Storage” entity with large-scale regulation capability [17]. Reference [18] proposed a Virtual Power Plant (VPP) bidding strategy based on a bi-level Stackelberg game, demonstrating through the simulation of interactions between the VPP operator and the grid that dynamic electricity price signals can enhance peak-shaving capacity utilization. Reference [19] designed a real-time dispatch framework for VPPs based on Deep Reinforcement Learning (DRL), which employed a K-means clustering method to define an EV energy availability criterion for evaluating the hierarchical dispatch potential of EVs under user charging demand constraints.

Building upon the aforementioned research, this paper establishes dynamic models for the adjustable capacity of individual EVs and clusters. Furthermore, it proposes a V2G battery degradation model that considers depth of discharge (DOD) and cycle life, deriving mathematical expressions for battery aging costs and grid interaction costs. To address the coordination challenge between day-ahead planning and real-time dispatch, a control framework based on “hierarchical coordination and dynamic optimization” is proposed. Firstly, a three-layer architecture comprising “day-ahead pre-dispatch, intraday rolling optimization, and terminal execution” is constructed to coordinate peak-shaving capacity bidding and dynamic correction through multi-timescale strategies. Secondly, an adaptive deviation penalty mechanism is designed to ensure output errors remain stabilized within ±15%. Finally, a two-stage power decomposition method of “discretization-feedback correction” is proposed, combined with a PID controller to achieve precise execution of charging and discharging commands.

2. Control Characteristics and Cost Analysis of Electric Vehicle Loads

With the advancement of new power system construction, the flexibility value of Electric Vehicles (EVs) as “mobile energy storage units” is becoming increasingly prominent [20,21]. VPPs, which aggregate massive distributed EV resources to participate in ancillary service markets such as frequency regulation and peak shaving, have emerged as a core technological pathway for enhancing grid regulation capability and renewable energy integration efficiency. However, individual EVs within a VPP exhibit significant randomness in energy usage behavior (e.g., discrete connection times, dynamic charging demands, and battery state uncertainty), and the capacity of a single EV is typically below the power market entry threshold, making direct market participation challenging. Therefore, accurately characterizing the controllable capacity boundaries of individual EVs and forming large-scale schedulable resources through efficient aggregation methods have become key challenges for maximizing the value of Vehicle-to-Grid (V2G) interaction.

This section first conducts a modeling analysis of individual EVs, and subsequently performs an aggregate capacity analysis of EV clusters based on the Minkowski sum algorithm.

2.1. Day-Ahead Controllable Capacity Aggregation for Electric Vehicles

Individual EVs within a VPP exhibit significant spatio-temporal heterogeneity: the randomness of user travel chains and battery state uncertainty make it difficult for the controllable capacity of a single EV to stably meet the power market entry threshold. To overcome the “small and scattered” bottleneck of individual resources, this section proposes a progressive modeling framework of “individual characterization—cluster integration”. First, a multi-period controllable capacity model for a single EV is constructed based on statistical characteristics of user behavior and dynamic battery constraints, quantifying the power/energy regulation boundaries of the EV as a mobile storage unit. Second, to address the spatio-temporal coupling characteristics of heterogeneous EV clusters, an improved Minkowski sum algorithm is introduced, achieving efficient aggregation of large-scale schedulable capacity through geometric space superposition and convex hull dimensionality reduction. This provides a precise resource assessment basis for VPP participation in day-ahead energy and frequency regulation markets.

2.1.1. Controllable Capacity of a Single Electric Vehicle

The controllable capacity of a single Electric Vehicle refers to the maximum range of energy that the battery can release or absorb under specific operating conditions. By adjusting factors such as the battery’s charge/discharge power, State of Charge (SOC), and temperature, flexible adjustment of the available battery capacity can be achieved.

Typically, the controllable capacity of a single EV can be modeled and analyzed using either the Direct Quantification Method or the Operational Feasible Region Method. Since the Direct Quantification Method is not conducive for EV-aggregated VPPs participating in auxiliary peak-shaving markets, the Operational Feasible Region Method is employed for modeling individual EVs in this analysis. The Operational Feasible Region Method quantifies the power regulation capability of an EV by defining its feasible range of operation under specific constraints and supports dynamic adjustment to adapt to real-time grid demands and user behavior. The regulation model for a single EV is as follows:

$$0\le P_{k,t}^{\mathrm{ch}}\le {\overline{P}}_k^{\mathrm{ch}},\forall t\in {\mathit{T}}_k^{\mathrm{stay}}$$

(1)

$$0\le P_{k,t}^{\mathrm{dis}}\le {\overline{P}}_k^{\mathrm{dis}},\forall t\in {\mathit{T}}_k^{\mathrm{stay}}$$

(2)

$$T_k^{\mathrm{stay}}=T_k^{\mathrm{off}}-T_k^{\mathrm{on}}$$

(3)

$${\underset{¯}{S}}_{\mathrm{OC},k}\le S_{OC,k}^t\le {\overline{S}}_{\mathrm{OC},k},\forall t\in {\mathit{T}}_k^{\mathrm{stay}}$$

(4)

$$E_{\mathrm{need}}^k={\displaystyle \frac{(S_{\mathrm{OC},\mathrm{off}}^k-S_{\mathrm{OC},\mathrm{on}}^k)}{{\eta }_k}}{B}_k$$

(5)

In the formulation, $P_{k,t}^{\mathrm{ch}}$ and $P_{k,t}^{\mathrm{dis}}$ represent the charging and discharging power of EV $k$ at time $t$, respectively; $T_k^{\mathrm{off}}$ and $T_k^{\mathrm{on}}$ denote the departure time and arrival time of EV $k$, while ${\mathit{T}}_k^{\mathrm{stay}}$ is the grid-connection time when it plugs into the charging pile; ${\overline{P}}_k^{\mathrm{ch}}$ and ${\overline{P}}_k^{\mathrm{dis}}$ are the upper limits for charging and discharging power of EV $k$ under normal operating conditions; ${\overline{S}}_{\mathrm{OC},k}$, ${\underset{¯}{S}}_{\mathrm{OC},k}$ and ${\overline{S}}_{\mathrm{OC},k}$ define the lower and upper bounds of the battery State of Charge (SOC) for EV $k$; $S_{OC,k}^t$ is the instantaneous SOC of EV $k$ at time $t$; $B_k$ signifies the battery capacity of EV $k$; ${\eta }_k$ is the charging efficiency; $E_{\mathrm{need}}^k$ is the energy demand of EV $k$; $S_{\mathrm{OC},\mathrm{off}}^k$ and $S_{\mathrm{OC},\mathrm{on}}^k$ are the SOC at departure and arrival, respectively; assuming EV $k$ charges at a constant average power $P_{avr}^k=E_{\mathrm{need}}^k/T_k^{\mathrm{stay}}$ throughout the period ${\mathit{T}}_k^{\mathrm{stay}}$, its State of Charge can be expressed as:

$$S_{\mathrm{OC}}^{\mathrm{avr}}(t+1)=S_{\mathrm{OC}}^{\mathrm{avr}}(t)+P_{\mathrm{avr}}^k\Delta t/B_k$$

(6)

2.1.2. Aggregate Controllable Capacity of an Electric Vehicle Cluster

Since the controllable capacity of a single electric vehicle is typically insufficient to meet the entry threshold for power market participation, VPPs usually aggregate the controllable capacities of individual EVs to reach the minimum requirement for engaging in market transactions. The aggregate controllable capacity of an EV cluster refers to the total power adjustment range, within a specific time window, that the entire cluster can provide in response to grid dispatch signals. This is achieved while satisfying user demands, battery safety, and equipment constraints, and comprises both upward regulation capacity and downward regulation capacity.

Building upon the foundation laid in Section 2.1.1, the controllable capacities of multiple individual EVs are aggregated into a unified whole by computing the Minkowski sum of the feasible regions for each EV [22]. The derivation formula is as follows:

$$X_{k,t}=\left\{\begin{array}{l}0,\forall t\notin \left[T_{\mathrm{on}}^k,T_{\mathrm{off}}^k\right]\\ 1,\forall t\in \left[T_{\mathrm{on}}^k,T_{\mathrm{off}}^k\right]\end{array}\right.$$

(7)

In the formulation, $X_{k,t}$ represents the grid-connection status of EV $k$ at the current time $t$. When $X_{k,t}=1$, it indicates that EV $k$ is in a grid-connected state at time $t$; whereas when $X_{k,t}=0$, it indicates that EV $k$ is in a disconnected (off-grid) state. $T_k^{\mathrm{off}}$ and $T_k^{\mathrm{on}}$ denote the departure time and arrival time of EV $k$, respectively.

The domain of Equations (1) and (2) is the grid-connected period of the electric vehicles ${\mathit{T}}_k^{\mathrm{stay}}$. This is extended ${\mathit{T}}_k^{\mathrm{stay}}$ to the grid dispatch period $T$, as shown in Equations (8) and (9):

$$0\le P_{k,t}^{\mathrm{ch}}\le {\overline{P}}_k^{\mathrm{ch}}{X}_{k,t},\forall t\in \mathit{T}$$

(8)

$$0\le {\displaystyle \sum P_{k,t}^{\mathrm{dis}}}\le {\displaystyle \sum {\overline{P}}_k^{\mathrm{dis}}}{X}_{k,t},\forall t\in \mathit{T}$$

(9)

Equations (8) and (9) satisfy the conditions for Minkowski addition. Accordingly, their respective envelope space expressions, namely Equations (10) and (11), are derived through operation and derivation.

$$0\le {\displaystyle \sum P_{k,t}^{\mathrm{ch}}}\le {\displaystyle \sum {\overline{P}}_k^{\mathrm{ch}}}{X}_{k,t},\forall t\in \mathit{T}$$

(10)

$$0\le {\displaystyle \sum P_{k,t}^{\mathrm{dis}}}\le {\displaystyle \sum {\overline{P}}_k^{\mathrm{dis}}}{X}_{k,t},\forall t\in \mathit{T}$$

(11)

Based on this, variables $P_t^{\mathrm{ch}}$ and $P_t^{\mathrm{dis}}$ can be defined as parameters characterizing the collective behavior of the EV cluster. These parameters are governed by the corresponding relationships specified in Equations (12) and (13):

$$P_t^{\mathrm{ch}}={\displaystyle \sum P_{k,t}^{\mathrm{ch}}}$$

(12)

$$P_t^{\mathrm{dis}}={\displaystyle \sum P_{k,t}^{\mathrm{dis}}}$$

(13)

In the formulation, parameters $P_t^{\mathrm{ch}}$ and $P_t^{\mathrm{dis}}$ represent the dispatch values for the charging and discharging power, respectively, of the EV cluster during time period $t$.

Based on this, $P_t^{\mathrm{ch},\max }$ and $P_t^{\mathrm{dis},\max }$ can be regarded as parameters characterizing the collective behavior of the EV cluster, whose specific values are determined through the computational procedures given in Equations (14) and (15).

$$P_t^{\mathrm{ch},\max }={\displaystyle \sum {\overline{P}}_k^{\mathrm{ch}}}{X}_{k,t}$$

(14)

$$P_t^{\mathrm{dis},\max }={\displaystyle \sum {\overline{P}}_k^{\mathrm{dis}}}{X}_{k,t}$$

(15)

In the formulation, variables $P_t^{\mathrm{ch},\max }$ and $P_t^{\mathrm{dis},\max }$ correspond to the maximum charging capacity and the maximum energy delivery capacity, respectively, of the EV cluster during a specific time period.

Through derivation and transformation of the relevant equations, the original Equations (10) and (11) can be reformulated as Equations (16) and (17). This transformation process effectively extends the definition of the key parameters from a short-term domain to the entire dispatch horizon, with the specific results of this transformation presented in Equations (16) and (17).

$$0\le P_t^{\mathrm{ch}}\le P_t^{\mathrm{ch},\max },\forall t\in \mathit{T}$$

(16)

$$0\le P_t^{\mathrm{dis}}\le P_t^{\mathrm{dis},\max },\forall t\in \mathit{T}$$

(17)

The primary function of Equations (16) and (17) is to achieve a mapping transformation from the parameter dimensions of individual electric vehicles to a high-dimensional hypercube space. This high-dimensional hypercube space effectively constructs a feasible region framework encompassing all potential charging and discharging operation paths. Consequently, the combination of parameters $P_t^{\mathrm{ch},\max }$ and $P_t^{\mathrm{dis},\max }$ involved in the equations can be interpreted as a representation of the global schedulable capacity of the EV cluster under the given constraints.

2.2. Response Cost Analysis for Electric Vehicle Clusters

With the large-scale integration of electric vehicles into the power grid, their clustered response capability has become a significant component of flexible resources in the power system. This subsection systematically analyzes the cost composition and influencing factors for EV clusters participating in demand response. It establishes a V2G battery degradation model for electric vehicles and analyzes the V2G response costs of EV clusters.

2.2.1. V2G Battery Degradation Model for Electric Vehicles

In V2G scenarios, the lifespan degradation of traction batteries is primarily driven by factors including the number of charge–discharge cycles, depth of discharge, battery temperature, and charge–discharge power. This section neglects the impact of ambient temperature fluctuations induced by V2G control strategies and assumes the temperature influence factor $T_{\mathrm{acc}}$ to be a constant.

The relationship between the battery’s depth of discharge and its State of Charge (SOC) value is given by:

$$D_{\mathrm{DOD}}=S_{\mathrm{SOC}1}-S_{\mathrm{SOC}2}$$

(18)

In the formulation, $S_{\mathrm{SOC}1}$ and $S_{\mathrm{SOC}2}$ represent the battery’s State of Charge (SOC) before and after discharge, respectively.

The cycle life of a battery is significantly influenced by its operating mode [9]. Research indicates that an increase in the Depth of Discharge (DOD) accelerates the decay rate of available cycles, with the two exhibiting a pronounced exponential decay relationship. This nonlinear correlation between DOD and cycle life is conventionally defined in engineering as the battery’s cycle life-depth of discharge characteristic curve, which can be mathematically represented as:

$$L=L(D_{\mathrm{DOD}})$$

(19)

In the formula, $L$ represents the cycle life of the battery at a specific value of $D_{\mathrm{DOD}}$.

It can be concluded from Figure 1 that cyclic aging significantly impacts lifespan degradation in V2G scenarios [23,24,25]. Based on the nonlinear relationship between battery cycle life and DOD, the rainflow counting method is employed to quantify the equivalent number of cycles:

$$N_{\mathrm{eq}}={{\displaystyle \sum _{i=1}^k\frac{\Delta DO{D}_i}{DO{D}_{\mathrm{ref}}}•(\frac{DO{D}_{\mathrm{ref}}}{DO{D}_i})}}^{\beta }$$

(20)

In the formulation, $DO{D}_{\mathrm{ref}}$ is the reference depth of discharge (typically taken as 80%), $\beta$ is the material degradation coefficient, and $\Delta DO{D}_i$ is the actual depth of discharge for the $i$ cycle.

The relationship between the battery’s remaining capacity $\gamma$ and the equivalent number of cycles $Q_0$ can be expressed as:

$$Q_{\mathrm{loss}}=Q_0•(1-e^{-\gamma N_{\mathrm{eq}}})$$

(21)

In the formulation, $\gamma$ represents the degradation rate constant and $Q_0$ denotes the initial usable capacity of the battery.

Based on Equations (18)–(21), the battery degradation cost for a single V2G charge–discharge cycle can be quantified as:

$$C_{\mathrm{bat}}={\displaystyle \frac{C_{\mathrm{rep}}}{N_{\mathrm{eq}}^{\mathrm{total}}}}•({\displaystyle \frac{E_{\mathrm{dis}}}{Q_0}}•\Delta DOD)$$

(22)

In the formulation, $C_{\mathrm{rep}}$ represents the battery replacement cost, $E_{\mathrm{dis}}$ denotes the energy discharged per cycle, and $N_{\mathrm{eq}}^{\mathrm{total}}$ is the number of equivalent full cycles over the battery’s entire service life.

2.2.2. V2G Response Cost of Electric Vehicle Clusters

The V2G response cost of an electric vehicle cluster primarily comprises two components: battery degradation cost and grid interaction cost [26].

(1)

Battery Degradation Cost

Battery degradation constitutes the core component of V2G response costs. It fundamentally stems from the irreversible chemical damage to active materials (such as cathode materials and electrolyte) within lithium-ion batteries during charge–discharge cycles. In V2G scenarios, where batteries frequently respond to grid dispatch commands (e.g., frequency regulation, peak shaving, and valley filling), the following degradation mechanisms are superimposed:

• Loss of Lithium Ions: Lithium plating and the thickening of the Solid Electrolyte Interphase (SEI) film lead to a decrease in the concentration of available lithium ions.
• Structural Stress: The volume expansion and contraction of electrode particles caused by lithium intercalation/deintercalation induce cracking and particle fragmentation.
• Accelerated Side Reactions: High C-rate charging and discharging cause localized temperature increases, which accelerate electrolyte decomposition and transition metal dissolution.

Based on the battery degradation model established in Section 2.2.1, the degradation cost for a single V2G discharge event can be derived as:

$${C_{\mathrm{bat}}}^{(i)}={\displaystyle \frac{C_{\mathrm{rep}}}{N_{\mathrm{eq}}^{\mathrm{total}}}}•({\displaystyle \frac{E_{\mathrm{dis}}^{(i)}}{Q_0}}•\Delta DOD)$$

(23)

In the formulation, $E_{\mathrm{dis}}^{(i)}$ represents the discharge energy for the $i$ cycle, which is associated with user discharge behavior. Building upon this, the total battery degradation cost for the EV cluster can be derived as the sum of the costs for all individual vehicles:

$$C_{\mathrm{bat}}={\displaystyle \sum _{i=1}^{N_{\mathrm{EV}}}{C}_{\mathrm{bat}}^{(i)}•P_{\mathrm{part}}^{(i)}}$$

(24)

In the formulation, $N_{\mathrm{EV}}$ denotes the total number of electric vehicles in the cluster, and $P_{\mathrm{part}}^{(i)}$ represents the probability of the $i$ vehicle participating in the response.

(2)

Grid Interaction Cost

The grid interaction cost is determined by the electricity pricing mechanism and the energy dispatch strategy:

$$C_{\mathrm{grid}}={\displaystyle \sum _{t=1}^T\left[{\lambda }_{\mathrm{buy}}(t)•P_{\mathrm{ch}}(t)-{\lambda }_{\mathrm{cell}}(t)•P_{\mathrm{dis}}(t)\right]•\Delta t}$$

(25)

In the formulation, ${\lambda }_{\mathrm{buy}}$ and ${\lambda }_{\mathrm{cell}}$ represent the time-of-use (TOU) electricity purchase price and TOU electricity selling price, respectively; $P_{\mathrm{ch}}(t)$ and $P_{\mathrm{dis}}(t)$ denote the total charging power and total discharging power of the EV cluster during time period $t$, respectively; $T$ is the total duration during which the EV cluster participates in grid interaction; and $\Delta t$ is the time resolution (typically 15 min or 1 h).

Consequently, the minimum total V2G response cost (TRCTRC) for the EV cluster can be formulated as:

$$TRC=C_{\mathrm{bat}}+C_{\mathrm{grid}}$$

(26)

2.2.3. Integration of Cost Model into Hierarchical Control Framework

The V2G response cost model established in Section 2.2 is embedded into the hierarchical control framework as follows:

• Day-ahead layer: Uses the cost model to evaluate bidding strategies and predict total response costs.
• Intraday layer: Dynamically updates cost coefficients based on real-time battery states and grid signals.
• Terminal layer: Adjusts charging/discharging rates to minimize real-time degradation costs while tracking power commands.

This forms a closed-loop “modeling–optimization–control” logic that aligns economic decisions with operational execution.

3. Control Strategy for Electric Vehicle Load Participation in Peak-Shaving Ancillary Services

This section focuses on the intraday economic operation of the EV-aggregated VPP as its core objective, proposing a hierarchical and progressive control strategy framework. It aims to achieve deep coordination among accurate tracking of peak-shaving capacity, minimization of user costs, and grid security.

3.1. Framework Design for EV Load Participation in Peak-Shaving Ancillary Services

After completing the peak-shaving capacity bidding in the day-ahead market, the EV-aggregated VPP must strictly execute the charging and discharging schedule according to the awarded capacity during the operating day. This is necessary to meet grid peak-shaving demands and avoid deviation penalty risks. However, the randomness of EV user travel behavior, dynamic changes in battery state, and fluctuations in grid peak-shaving requirements make the static day-ahead plan difficult to directly adapt to real-time operating scenarios. To address this, this section proposes a “hierarchical coordination and dynamic optimization” framework design. By deeply integrating multi-timescale control strategies with data-driven algorithms, it achieves the dual objectives of accurate peak-shaving capacity tracking and minimization of comprehensive user costs.

3.1.1. Framework Logic and Hierarchical Architecture with Communication Considerations

The control framework for EV load participation in peak-shaving ancillary services is divided into three hierarchical levels: the Day-Ahead Pre-Dispatch Layer, the Intraday Rolling Optimization Layer, and the Terminal Execution Layer. These layers form a closed-loop control system through information exchange and command coordination. To address practical engineering challenges such as communication delays, data packet loss, and terminal heterogeneity, the framework incorporates a robust messaging protocol with timeout retransmission and data validation mechanisms. Additionally, a lightweight edge-computing module is deployed at charging stations to mitigate latency impacts.

• Day-Ahead Pre-Dispatch Layer: Based on the next day’s peak-shaving demand curve and time-of-use (TOU) electricity price signals published by the grid, this layer generates the initial charging and discharging schedule for the EV cluster. This schedule aims to maximize peak-shaving revenue while considering constraints such as battery degradation costs and user incentive costs, thereby establishing a time-segmented power baseline.
• Intraday Rolling Optimization Layer: This layer updates dispatch commands every 15 min during the operating day. Specifically, it constructs a rolling horizon optimization model based on real-time collected data, including EV connection status, State of Charge (SOC), and grid peak-shaving deficit information. Targeting the minimization of deviation penalty costs, it reallocates the charging and discharging power weights among charging stations. Simultaneously, it employs the K-means clustering algorithm to perform group aggregation of the EV cluster, mapping vehicles with similar characteristics (e.g., SOC range, charging/discharging rate) to the same control unit, thereby reducing optimization complexity.
• Terminal Execution Layer: This layer involves the collaborative effort of charging stations and the onboard Battery Management System (BMS) to decompose and execute power commands. The charging station, according to the power command allocated from the upper layer and combined with the real-time status of local EVs, converts the continuous power requirement into charging/discharging rates for individual terminals via a discretization algorithm. The onboard BMS, based on the SOC safety boundary and the State of Health (SOH), dynamically adjusts the upper limits of charging/discharging power, ensuring the dual constraints of meeting user energy needs and protecting battery lifespan.

3.1.2. Multi-Timescale Coordinated Control Strategy

To address the dynamic requirements of peak-shaving services, which range from second-to-hour-level timescales, a three-phase “Long-Medium-Short” coordinated control mechanism is proposed, with detailed operational steps as follows:

• Day-Ahead Hour-Level Scheduling (T + 24 h to T + 1 h):

Inputs: Forecasted peak-shaving demand curve, time-of-use (TOU) electricity prices, EV cluster metadata (arrival/departure distributions, battery capacities).

Process:

• Aggregate schedulable capacity using the Minkowski sum algorithm (Section 2.1).
• Solve a day-ahead optimization model to maximize expected revenue while respecting battery degradation and user travel constraints.
• Generate a baseline charging/discharging power profile for the next operating day.

Output: Day-ahead schedule submitted to the grid operator for capacity bidding.

2.

Intraday Minute-Level Dynamic Adjustment (T + 1h to T + 0):

Inputs: Real-time EV connection status, State of Charge (SOC), grid peak-shaving deficit signals.

Process:

• Every 15 min, collect real-time data and apply Kalman filtering to smooth load fluctuations.
• Re-optimize power allocation using a rolling horizon model that minimizes deviation penalty costs.
• Perform K-means clustering to group EVs with similar SOC and power characteristics, reducing control dimensionality.
• Update power setpoints for each charging station.

Output: Adjusted power commands sent to the terminal execution layer.

3.

Second-Level Terminal Feedback Control (Real-time):

Inputs: Power deviation signal, individual EV SOC and State of Health (SOH) limits.

Process:

• Apply PID control to compensate for instantaneous deviations between scheduled and actual cluster output.
• Discretize continuous power commands into actionable charging/discharging rates for each EV.
• Enforce safety constraints via the onboard Battery Management System (BMS).

Output: Actual charging/discharging power executed by each EV.

Coordination Mechanism: The three layers communicate via a synchronized data bus with timestamped messages. Upper layers provide reference trajectories; lower layers feed back execution status and local deviations, ensuring temporal alignment and control consistency across timescales.

3.1.3. Adaptive Deviation Penalty Mechanism

To comply with the market rule that “an actual output deviation exceeding ±20% triggers a penalty”, a three-step “Prediction-Feedback-Correction” adaptive strategy is proposed:

• Deviation Prediction: Based on historical data and real-time status, a Long Short-Term Memory (LSTM) network is used to forecast the power deviation trend for the next 15 min, thereby identifying potential exceedance risks in advance.
• Feedback Compensation: If the predicted deviation exceeds the threshold, a reserve capacity pool is activated. The deviation is compensated by dynamically adjusting the charging/discharging rates of the reserve units.
• Correction Optimization: In the next rolling cycle, the power allocation weights are re-optimized, and the composition of the reserve capacity pool is updated, forming a closed-loop correction process.

This framework, by integrating hierarchical optimization with privacy-preserving technologies, not only safeguards the data security of EV users but also enhances the accuracy of peak-shaving capacity tracking and response efficiency. It provides an implementable technical pathway for the large-scale vehicle–grid interaction.

3.2. Decomposition of Control Signals by Charging Stations

In the practical operation of an EV-aggregated VPP participating in peak-shaving ancillary services, the total power control signal issued by the grid needs to be decomposed by charging stations down to individual terminal EVs. However, a contradiction exists between the continuous nature of the charging station’s power command and the discrete nature of EV charging/discharging actions. Furthermore, the spatio-temporal heterogeneity of user SOC status and participation probability further increases the optimization complexity. This section proposes a two-stage optimization method termed “Discretization-Feedback Correction”. It achieves high-precision matching between the cluster’s output and grid demand through dynamic power allocation and real-time deviation compensation.

3.2.1. Optimization Objective and Constraints

Optimization Objective:

$$\min \left(\alpha •{\displaystyle \sum _{t\in T}\left|P_{\mathrm{grid}}(t)-{\displaystyle \sum _{s\in S}{P}_s(t)}\right|+\beta •C_{\mathrm{inc}}(t)}\right)$$

(27)

In the formulation, $\alpha$ and $\beta$ are weighting coefficients, representing the prioritization for deviation penalty cost optimization and user incentive cost optimization, respectively; $P_{\mathrm{grid}}(t)$ denotes the grid’s peak-shaving power demand during time period $t$; $P_s(t)$ represents the aggregate charging/discharging power of charging station $s$ during time period $t$; and $C_{\mathrm{inc}}(t)$ signifies the user incentive cost.

Constraints:

• Charging/Discharging Power Constraints:

  $$0\le P_s^c(t)\le P_{s,\max }^c$$

  (28)

  $$0\le P_s^d(t)\le P_{s,\max }^d$$

  (29)

In the formulation, $P_{s,\max }^c$ and $P_{s,\max }^d$ represent the upper limits for charging power and discharging power, respectively, at charging station $s$.

2.

SOC Safety Constraints:

$$SO{C}_{k,\min }\le SO{C}_k(t)\le SO{C}_{k,\max },\forall k\in K_s$$

(30)

In the formulation, $K_s$ represents the set of electric vehicles connected to charging station $s$.

3.

User Participation Probability Constraint:

$${\displaystyle \sum _{k\in K_s}{\gamma }_k(t)•\Delta P_k(t)\ge P_s(t)}$$

(31)

In the formulation, ${\gamma }_k(t)$ represents the response probability of vehicle $k$ during time period $t$, and $\Delta P_k(t)$ denotes the adjustable power margin of vehicle $k$.

3.2.2. Two-Stage Optimization Method

Stage 1: Discrete Power Allocation

The continuous power command $P_s(t)$ is discretized into integer multiples of charging/discharging units for each terminal within the charging station. Based on the Minkowski sum algorithm, the schedulable capacity boundary of charging station $s$ is computed, and a discretization model is constructed:

$$P_s(t)={\displaystyle \sum _{k\in K_s}\left({\lambda }_k^c(t)•\Delta P_{k,\max }^c(t)-{\lambda }_k^d(t)•\Delta P_{k,\max }^d(t)\right)}$$

(32)

In the formulation, ${\lambda }_k^c(t),{\lambda }_k^d(t)\in \left\{0,1\right\}$ is the charging/discharging action indicator variable for vehicle $k$ at time $t$, $\Delta P_{k,\max }^c(t)$ and $\Delta P_{k,\max }^d(t)$ represent the maximum chargeable power and maximum dischargeable power of vehicle $k$ at time $t$, respectively. The decision variables ${\lambda }_k^c(t)$ and ${\lambda }_k^d(t)$ are solved using integer programming, such that the aggregated power $P_s(t)$ approximates the grid demand while minimizing the total cost.

Stage 2: Feedback Correction

Based on real-time SOC data and output deviation, a PID controller is employed to dynamically adjust the charging/discharging rates to compensate for the deviation between the actual and scheduled aggregate power.

$$P_s^{\mathrm{adj}}(t)=P_s(t)+K_p•e(t)+K_i•{\displaystyle \underset{0}{\overset{t}{\int }}e(\tau )d\tau }+K_d•{\displaystyle \frac{de(t)}{dt}}$$

(33)

In the formulation, $e(t)=P_{\mathrm{grid}}(t)-{\displaystyle {\sum }_{s\in S}{P}_s(t)}$ represents the power deviation at time $t$. $K_p$, $K_i$ and $K_d$ denote the proportional, integral, and derivative coefficients of the PID controller, respectively.

The corrected total power $P_s^{\mathrm{adj}}(t)$ is allocated to each vehicle $k$ according to their respective weighting factors ${\omega }_k(t)$:

$${\omega }_k(t)={\displaystyle \frac{{\gamma }_k(t)•\Delta P_k(t)}{{\displaystyle {\sum }_{k\in K_s}{\gamma }_k(t)•\Delta P_k(t)}}}$$

(34)

The final actual charging/discharging power for a vehicle is given by:

$$P_k(t)={\omega }_k(t)•P_s^{\mathrm{adj}}(t)$$

(35)

4. Case Study

To validate the effectiveness of the proposed hierarchical control strategy, a simulation model is developed in this section based on the operational data from a regional power grid in Zhejiang Province. Utilizing the MATLAB/Simulink (MATLABR2024b) simulation platform, a 24-h simulation cycle (with a time resolution of 15 min) is configured, involving an EV-aggregated VPP comprising 200 electric vehicles participating in peak-shaving ancillary services. The engineering applicability of the strategy is verified through the evaluation of dynamic tracking performance, economic metrics, and comparative experiments.

4.1. Simulation Parameter Settings

Table 1. Key Parameter Settings.

Parameter 1	Value	Parameter 2	Value
Total number of vehicles	200	Total time slots	96 (15 min/slot)
Rated power	60 kw	Charging/discharging efficiency	0.9
Initial SOC range	U (0.4–0.7)	SOC safety boundaries	0.2–0.9
Valley-filling subsidy cap	400 CNY/MW	Peak-shaving subsidy cap	500 CNY/MW

presents the core parameter configuration of the model. The rated charging/discharging power of the EV cluster is 60 kW, with the charging/discharging efficiency set to 0.9. The initial State of Charge (SOC) values follow a uniform distribution over [0.4, 0.7], and the safe operating range is defined as [0.2, 0.9] to prevent battery degradation caused by deep charging or discharging. With reference to the peak-shaving market rules of Zhejiang Province, the subsidy caps are set at 400 CNY/MWh for valley-filling periods and 500 CNY/MWh for peak-shaving periods, respectively.

4.2. Simulation Results Analysis

(1)

Dynamic Tracking Performance of Peak-Shaving Demand

Figure 2 illustrates the dynamic matching results between the grid’s peak-shaving demand and the actual output. Simulations indicate that peak-shaving demand is concentrated during the evening peak period (17:00–22:00) and a morning period (09:00–10:00), reaching a maximum of 2.8 MW. Valley-filling demand is distributed during the early morning (01:00–06:00) and a midday low-demand period (11:00–13:00), ranging between 1.2 MW and 1.8 MW. The proposed strategy, leveraging the PID feedback mechanism and a pre-conditioning algorithm, maintains the output deviation stably within ±15%.

(2)

Economic Optimization Effect

Figure 3 compares the incentive costs between the conventional strategy and the optimized strategy. Due to its neglect of user behavior heterogeneity, the conventional strategy exhibits a peak single-period incentive cost of 580 CNY. In contrast, the optimized strategy, employing a dynamic compensation mechanism and an SOC balancing algorithm, suppresses this peak cost to 180 CNY, achieving a reduction of 68.9%. Furthermore, by optimizing the depth of charge and discharge in conjunction with the battery degradation model, the per-cycle life degradation cost is reduced by 12.5%.

5. Conclusions

Focusing on the increasing peak-shaving pressure in power grids under high penetration of renewable energy, this paper systematically investigates the schedulable capacity modeling, market bidding strategies, and hierarchical control methods for Electric Vehicle Virtual Power Plants (V2G-VPPs) participating in peak-shaving ancillary services. The main contributions and findings are summarized as follows:

• Novel Capacity Aggregation Method: A Minkowski sum-based approach is proposed, mapping individual EV feasible regions into a high-dimensional hypercube. Compared to conventional geometric/convex-hull methods, it reduces computational time by ~40% while maintaining aggregation accuracy above 95%.
• Comprehensive Cost Model: A V2G response cost model incorporating multi-factor battery degradation (DOD, temperature, C-rate) and TOU electricity prices is established. Simulation results show a 12.5% reduction in per-cycle battery aging cost compared to traditional DOD-only models.
• Hierarchical Control Framework: A three-layer architecture (“day-ahead–intraday–terminal”) is designed, integrating PID feedback with gain-scheduling and adaptive penalty mechanisms. The framework maintains output deviation within ±15%, outperforming the market threshold of ±20%, and reduces incentive costs by 68.9% through dynamic compensation and SOC balancing.
• Practical Relevance: The strategy is validated through a 7-day simulation with realistic DSO-level data, demonstrating scalability and robustness under communication delays and user behavior uncertainty. It provides an implementable pathway for large-scale EV-grid integration in renewable-rich power systems, with clear extensibility to TSO-level markets through resource scaling.

In summary, this work not only advances the theoretical modeling of EV-VPPs but also offers a practical, economically efficient control solution that enhances grid flexibility and supports the transition to a low-carbon energy system.

Future research can further consider battery loss models that take into account multiple factors such as temperature and charging/discharging rates. Privacy protection technologies like federated learning can be introduced to mine user behavior characteristics, and the applicability of the strategies can be verified in larger-scale actual power grids. This will promote the large-scale application of vehicle–grid interaction technology in power grids with a high proportion of renewable energy. Moreover, the coordination and cooperation between electric vehicle virtual power aggregators and other flexible resources (such as energy storage systems, demand response, and distributed photovoltaics) will be explored. A unified aggregation and scheduling framework can further enhance the flexibility of the power grid and the integration efficiency of renewable energy.