The large-scale integration of renewable energy sources, primarily wind and solar, into modern power grids has introduced significant challenges to maintaining system frequency stability. The inherent variability and uncertainty of these sources increase the net load fluctuations, thereby escalating the demand for fast and reliable frequency regulation resources. Traditional thermal power plants, the conventional backbone of frequency control via Automatic Generation Control (AGC), are often limited by their mechanical ramp rates. This constraint can hinder their ability to rapidly compensate for sudden power imbalances, especially in systems with high renewable penetration. Concurrently, the global fleet of Electric Vehicle Cars (EVs) is experiencing exponential growth. When aggregated, these distributed energy resources present a substantial, spatially dispersed pool of flexible capacity. Their power electronics-based charging infrastructure enables remarkably fast and precise charge/discharge responses, making them a theoretically ideal candidate for providing ancillary services, particularly frequency regulation. This synergy suggests a promising future for coordinated frequency regulation between thermal units and规模化 Electric Vehicle Cars.
Accurately quantifying the available regulation capacity from a fleet of Electric Vehicle Cars is the foundational step for their integration into system operations. A critical challenge lies in modeling the aggregate capabilities of thousands of individual EVs, each with unique constraints related to battery state-of-charge (SOC), connection/disconnection times, charging power limits, and user travel demands. Simplified methods, such as grouping or statistical approximations, often sacrifice precision. While advanced techniques like Minkowski sum aggregation offer accuracy, their computational complexity becomes prohibitive for large-scale scenarios. Therefore, this paper proposes a dynamic, block-aggregation method for evolving the feasible operating region of an EV fleet. By tracking the aggregate SOC and power boundaries of EVs in a “charge/regulation-ready” state over discrete time intervals, this approach enables a more precise, time-series evaluation of the total upward and downward frequency regulation capacity available from a heterogeneous Electric Vehicle Car fleet.
Evaluating the system’s overall frequency regulation capacity requirement in the context of规模化 Electric Vehicle Car participation necessitates a robust methodology. Existing approaches can be categorized as model-driven or data-driven. Model-driven methods use system frequency response (SFR) models to simulate frequency deviations based on input power disturbances. However, they often struggle to accurately incorporate the complex, time-coupled load dynamics introduced by a large fleet of participating Electric Vehicle Cars. Conversely, purely data-driven methods rely on historical correlations between regulation capacity, power imbalances, and performance metrics, but they lack the physical insight of dynamic system models, potentially reducing reliability. To address these limitations, this paper develops a hybrid data-and-model-driven assessment framework. High-resolution historical data for renewable generation and conventional load is used to generate typical day-ahead scenarios, capturing uncertainty. The dynamic load profile from the participating Electric Vehicle Car fleet is then integrated. These combined scenarios drive a detailed SFR model. Within a distributionally robust optimization (DRO) framework, this hybrid approach identifies the minimum regulation capacity required to meet frequency performance standards under the worst-case probability distribution of these scenarios.
A pivotal question for system operators is understanding how the participation of规模化 Electric Vehicle Cars, as a fast-responding resource, alters the total system regulation capacity need compared to a thermal-dominated system. Furthermore, it is essential to quantify the relative effectiveness of Electric Vehicle Car regulation capacity versus traditional thermal capacity. While existing research often focuses on optimally dispatching a given capacity mix between EVs and thermal units, the impact of varying the EV participation level on the total required capacity is less explored. This paper investigates this impact. The proposed assessment model is used to analyze how the total system regulation capacity requirement ($R^{res}$) changes as the proportion ($\alpha$) of this requirement met by Electric Vehicle Cars varies. Building on this, we define a Relative Frequency Regulation Effectiveness Coefficient ($\delta$) to quantitatively compare Electric Vehicle Car and thermal resources. The coefficient is derived from the change in total system need when shifting capacity between resource types. The analysis provides crucial insights for grid operators on optimally allocating regulation capacity between fast (Electric Vehicle Car) and slow (thermal) resources to achieve cost-effective and reliable frequency control.
Methodology: Modeling and Assessment Framework
1. Dynamic Aggregation of Electric Vehicle Car Fleet Capability
The scheduling horizon is divided into discrete intervals (e.g., 15 minutes). Each Electric Vehicle Car $i$ is characterized by its parameters: battery capacity $C_i^{Bat}$, maximum charge/discharge power $P_i^{max}/P_i^{min}$, charging efficiency $\eta^c$, discharging efficiency $\eta^{dis}$, initial SOC $SOC_i^{con}$, desired departure SOC $SOC_i^{exp}$, and connection window $[t_i^c, t_i^{dis}]$. The feasible operating region for a single Electric Vehicle Car, considering user demand and battery limits ($SOC^{min}$, $SOC^{max}$), can be constructed. For aggregation, we focus on EVs in the “charge/regulation-ready” state.
The aggregate power limits for $N^{FR}$ ready Electric Vehicle Cars at time $t$ are:
$$P_t^{max} = \sum_{i=1}^{N^{FR}} P_i^{max}, \quad P_t^{min} = \sum_{i=1}^{N^{FR}} P_i^{min}$$
The aggregate SOC feasible region bounds are calculated by summing the individual SOC boundaries, weighted by battery capacity:
$$SOC_{t,J}^{dn/up} = \frac{\sum_{i=1}^{N^{FR}} SOC_{i,t,J}^{dn/up} \cdot C_i^{Bat}}{\sum_{i=1}^{N^{FR}} C_i^{Bat}}$$
where $J$ denotes the time interval. Transitions between intervals account for Electric Vehicle Cars entering or leaving the ready pool, causing step changes in the aggregate SOC.
To quantify the maximum available regulation capacity within an interval $J_n$, an optimization is formulated. The objective is to maximize the aggregate upward ($R_{t,J_n}^{up}$) and downward ($R_{t,J_n}^{dn}$) regulation capacity, subject to aggregate power and SOC constraints derived from the feasible region:
$$\max (R_{t,J_n}^{dn} + R_{t,J_n}^{up})$$
subject to:
$$P_t^{min} \le P_{t,J_n}^{EV} \le P_t^{max}$$
$$P_{t,J_n}^{EV} = P_{t,J_n}^{base} + \delta_{t,J_n}^{dn}R_{t,J_n}^{dn} – \delta_{t,J_n}^{up}R_{t,J_n}^{up}$$
$$SOC_{t+1,J_n} = SOC_{t,J_n} + \frac{P_{t,J_n}^{EV} \cdot \Delta t \cdot \eta}{C_J^{Bat}}$$
$$SOC_{t,J_n}^{dn} \le SOC_{t,J_n} \le SOC_{t,J_n}^{up}$$
$$0 \le R_{t,J_n}^{dn} \le \min\left( P_t^{max} – P_{t,J_n}^{base}, \frac{(SOC_{t,J_n} – SOC_{t,J_n}^{dn}) \cdot C_J^{Bat}}{\eta^{dis} \cdot \Delta t} \right)$$
$$0 \le R_{t,J_n}^{up} \le \min\left( P_{t,J_n}^{base} – P_t^{min}, \frac{(SOC_{t,J_n}^{up} – SOC_{t,J_n}) \cdot C_J^{Bat}}{\eta^{c} \cdot \Delta t} \right)$$
Here, $P_{t,J_n}^{base}$ is the baseline charging power, and $\delta$ are binary signals indicating regulation direction.
2. Hybrid Data-Model Driven System Regulation Capacity Requirement Assessment
The system frequency response to a power imbalance $\Delta P_{sy}$ is modeled using a standard linearized model for a single control area:
$$2H \frac{d\Delta f(t)}{dt} + D\Delta f(t) = \Delta P_{sy} – \Delta P_M(t) – \Delta P_L(t)$$
$$T_G \frac{d\Delta P_M(t)}{dt} + \Delta P_M(t) = \Delta P_V(t)$$
$$T_T \frac{d\Delta P_V(t)}{dt} + \Delta P_V(t) = -\frac{1}{R}\Delta f(t) + \Delta P_{AGC}(t)$$
where $\Delta f$ is frequency deviation, $H$ is inertia, $D$ is load damping, $\Delta P_M$ is mechanical power change, $\Delta P_V$ is governor valve position, $T_G, T_T$ are time constants, $R$ is droop, and $\Delta P_{AGC} = -K \int \Delta f dt$ is the AGC response. $\Delta P_L = K_L \Delta f$ is the load frequency response. Solving these equations yields the time-domain expression for $\Delta f(t)$ after a disturbance.
The system power imbalance $\Delta P_{sy,t}$ is the difference between scheduled generation (thermal + renewable) and total load, which now includes the net demand from the Electric Vehicle Car fleet:
$$\Delta P_{sy,t} = \sum_k \lambda_k (P_{G,k,t} + P_{W,k,t} + P_{S,k,t}) – \sum_k \lambda_k P_{L,k,t}^{con} – P_t^{EV}$$
where $\lambda_k$ are probabilities for typical renewable/load scenarios $k$ generated from historical data, and $P_t^{EV}$ is the aggregate Electric Vehicle Car power (baseline + regulation).
The system’s regulation performance is measured by the standard deviation of frequency deviation over a compliance period (e.g., 30 seconds):
$$\sigma_{\Delta f} = \sqrt{\frac{1}{\Delta T} \sum_{t=1}^{\Delta T} (\Delta f_t – \mu_{\Delta f})^2}$$
The Control Performance Standard 1 (CPS1) is also calculated based on the Area Control Error (ACE).
The total system regulation capacity requirement $R^{res}$ is defined as the minimum capacity needed to ensure $\sigma_{\Delta f} \le \sigma_{\Delta f}^{lim}$ and CPS1 $\in [100\%, 200\%]$ under all plausible scenarios. This is formulated as a two-layer distributionally robust optimization (DRO) problem:
$$\min_{R^{res}} \max_{\lambda \in \Psi} \sum_{k=1}^{K} \lambda_k R^{res}_k$$
subject to:
$$\sigma_{\Delta f}(R^{res}_k, \Delta P_{sy,k}) \le \sigma_{\Delta f}^{lim}, \quad \forall k$$
$$R^{res}_k \le \mathbb{E}[\Delta P_{sy,k}]$$
$$CPS1(R^{res}_k, \Delta P_{sy,k}) \in [100\%, 200\%]$$
Here, $\Psi$ is an ambiguity set for scenario probabilities $\lambda_k$ constructed using 1-norm and $\infty$-norm constraints around a nominal distribution (e.g., from historical data or forecast). The inner maximization finds the worst-case probability distribution that maximizes the needed capacity, while the outer minimization finds the smallest capacity that satisfies constraints under that worst case. $R^{res}$ is shared between thermal ($R^G$) and Electric Vehicle Car ($R^{EV}$) resources: $R^{res} = R^G + R^{EV}$.
3. Evaluating the Relative Effectiveness of Electric Vehicle Car Regulation
Let $\alpha$ denote the fraction of the total system regulation capacity requirement $R^{res}$ provided by the Electric Vehicle Car fleet: $R^{EV} = \alpha R^{res}$, and $R^{G} = (1-\alpha) R^{res}$. As $\alpha$ changes, the input $P_t^{EV}$ to the model changes, affecting the calculated $R^{res}$.
We define the Relative Frequency Regulation Effectiveness Coefficient $\delta$ to compare the resources. Suppose when the Electric Vehicle Car share increases from $\alpha_1$ to $\alpha_2$, the total system requirement changes from $R^{res}_1$ to $R^{res}_2$. The coefficient $\delta$ is the ratio of the increase in Electric Vehicle Car capacity to the decrease in thermal capacity:
$$\delta = \frac{\alpha_2 R^{res}_2 – \alpha_1 R^{res}_1}{(1-\alpha_1) R^{res}_1 – (1-\alpha_2) R^{res}_2}$$
The physical interpretation: If $\delta < 1$, it means that 1 MW of thermal regulation capacity can be replaced by less than 1 MW of Electric Vehicle Car capacity to achieve the same frequency performance, indicating Electric Vehicle Cars are more effective. If $\delta > 1$, Electric Vehicle Cars are less effective than thermal units on a capacity-equivalent basis. The value of $\delta$ as a function of $\alpha$ reveals how the marginal effectiveness of Electric Vehicle Car resources changes with their penetration level in the regulation service.
Case Study and Simulation Analysis
1. Electric Vehicle Car Fleet and System Setup
The Electric Vehicle Car fleet is categorized into three types: Home-Based Work (HBW), Home-Based Other (HBO), and Non-Home-Based (NHB), with parameters listed in Table 1. Their connection/disconnection times follow normal distributions. A time-of-use electricity price is used to derive a cost-minimizing baseline charging profile. The available upward and downward regulation capacity from an aggregated fleet of 2,250 Electric Vehicle Cars (1000 HBW, 1000 HBO, 250 NHB) is calculated using the dynamic aggregation method.
The power system model uses real renewable and load data from the Belgian grid. Thermal unit parameters and system frequency response parameters are listed in Table 2 and 3, respectively.
| Parameter | HBW | HBO | NHB |
|---|---|---|---|
| $C^{Bat}$ (kWh) | 50 | 50 | 245 |
| $P^{max}$ (kW) | 15 | 15 | 60 |
| $\eta^c / \eta^{dis}$ | 0.9 | 0.9 | 0.85 |
| $t^c$ (hour, $\sigma$) | 8, 1.2 | 20, 1.2 | 23, 1.2 |
| Count | 1000 | 1000 | 250 |
Table 1: Electric Vehicle Car Parameter Settings.
| Parameter | Value |
|---|---|
| System Inertia Constant $H$ (s) | 4.44 |
| Governor Time Constant $T_G$ (s) | 0.50 |
| Turbine Time Constant $T_T$ (s) | 0.25 |
| Droop $R$ (pu) | 0.05 |
| Load Damping $D$ (pu) | 1.00 |
Table 2: System Frequency Response Parameters.
2. Assessment of System Regulation Capacity Requirement
Applying the proposed DRO-based assessment model, the system regulation capacity requirement $R^{res}$ and its decomposition between thermal units ($R^G$) and the Electric Vehicle Car fleet ($R^{EV}$) are calculated for a 24-hour period. Results for selected hours are summarized in Table 3. During early morning (1-6h) and night (22-24h) hours, low load and high wind variability create a need for significant downward regulation. Thermal units, limited by their minimum output and ramp rates, cannot provide all required capacity, necessitating Electric Vehicle Car contribution ($R^{EV}>0$). During midday and evening peaks (e.g., hours 12-18), large load and renewable swings create upward regulation needs where thermal units hit maximum output limits, again requiring Electric Vehicle Car support.
| Time Interval | $R^{res}$ (MW) | $R^{G}$ (MW) | $R^{EV}$ (MW) | Primary Limiting Factor |
|---|---|---|---|---|
| 02:00-03:00 | 85 | 52 | 33 | Thermal min output / ramp rate |
| 12:00-13:00 | 128 | 98 | 30 | Thermal max output / ramp rate |
| 18:00-19:00 | 142 | 109 | 33 | Thermal max output / ramp rate |
| 23:00-24:00 | 78 | 45 | 33 | Thermal min output / ramp rate |
Table 3: Decomposition of Regulation Capacity Requirement in Sample Hours.
The effectiveness of the hybrid assessment method (S2) is validated against a pure model-driven method (S0) and a pure data-driven method (S1). The comparison metric is the total regulation capacity required over a period and the achieved CPS1 compliance rate. Results in Table 4 show that the model-driven method (S0) is overly conservative, procuring excess capacity. The data-driven method (S1) underestimates requirements, leading to poor CPS1 compliance. The proposed hybrid method (S2) finds a balance, meeting reliability standards without excessive conservatism.
| Method | Total $R^{res}$ (MW) | CPS1 Compliance Rate |
|---|---|---|
| S0 (Model-Driven) | 13,080 | 87.8% |
| S1 (Data-Driven) | 7,090 | 40.8% |
| S2 (Proposed Hybrid) | 12,910 | 100% |
Table 4: Comparison of Assessment Methods.
3. Impact of Electric Vehicle Car Scale and Regulation Effectiveness
The analysis is extended to understand how the total system requirement $R^{res}$ changes with the scale of the participating Electric Vehicle Car fleet. Five scales (N1 to N5) are simulated, with N5 having sufficient aggregate capacity to meet all regulation needs. Figure 1 shows the trend of the average $R^{res}$ for upward regulation periods as the Electric Vehicle Car scale increases, comparing ordered (price-responsive) and uncoordinated charging. With ordered charging, $R^{res}$ initially decreases as more Electric Vehicle Cars help flatten the net load, reducing imbalances. Beyond a certain point (scale N3-N4), $R^{res}$ begins to rise because a very high $\alpha$ leads to frequent saturation of the Electric Vehicle Car fleet’s energy capacity, requiring more total capacity to maintain reliability. Uncoordinated charging monotonically increases $R^{res}$ due to added volatility.
The relationship between the total system requirement $R^{res}$ and the Electric Vehicle Car share $\alpha$ is analyzed for different frequency deviation limits ($\sigma_{\Delta f}^{lim}$). Results are plotted in Figure 2. For all performance standards, $R^{res}$ exhibits a “U-shaped” curve versus $\alpha$. There exists an optimal $\alpha^*$ (approximately 30% in this case) that minimizes the total system regulation capacity requirement. Stricter frequency standards (smaller $\sigma_{\Delta f}^{lim}$) raise the overall curve but do not drastically shift $\alpha^*$.
Finally, the Relative Effectiveness Coefficient $\delta$ is calculated from the $R^{res}$ vs. $\alpha$ curves. Figure 3 plots $\delta$ against $\alpha$ for different $\sigma_{\Delta f}^{lim}$. Key observations:
- For small $\alpha$ (e.g., <10%), $\delta < 1$, often around 0.7. This confirms that初期参与的 Electric Vehicle Car capacity is more effective than thermal capacity; 1 MW of thermal capacity can be substituted by ~0.7 MW of Electric Vehicle Car capacity.
- The advantage is more pronounced under stricter frequency standards ($\delta$ is lower for smaller $\sigma_{\Delta f}^{lim}$), highlighting the value of fast response.
- As $\alpha$ increases, $\delta$ rises sharply. The crossover point ($\delta=1$) occurs around $\alpha \approx 30\%$. Beyond this, further increases in Electric Vehicle Car share require more than 1 MW of Electric Vehicle Car capacity to replace 1 MW of thermal capacity, indicating diminishing marginal effectiveness and eventually inferiority on a capacity-equivalent basis.
Discussion and Implications
The case study results yield several important insights for system operators and policymakers. First, they empirically demonstrate that thermal power plants alone are often insufficient to meet the frequency regulation demands of a renewable-rich system due to physical ramp and output limits. The complementary use of a规模化 Electric Vehicle Car fleet is not just beneficial but necessary to fill these gaps, confirming the need for market or control structures to unlock this resource.
Second, the “U-shaped” relationship between total regulation capacity need and Electric Vehicle Car participation share ($\alpha$) has significant economic implications. Initially, adding fast-responding Electric Vehicle Car resources reduces the total quantity of regulation capacity the system needs to procure—a pure cost saving. However, there is an optimal participation level ($\alpha^*$). Beyond this point, procuring more regulation capacity from Electric Vehicle Cars becomes counterproductive, increasing the total system need. This non-monotonic relationship arises from the energy constraints of Electric Vehicle Car batteries. At high $\alpha$, the fleet is more frequently deployed, leading to faster depletion or saturation of its aggregate state-of-charge. When the fleet cannot respond due to energy limits, the system effectively has less available capacity, requiring a larger nominal procurement to ensure reliability. This underscores that Electric Vehicle Cars are energy-limited resources, unlike traditional generators which are primarily power-limited.
The Relative Effectiveness Coefficient $\delta$ provides a crucial metric for resource allocation and procurement strategy. The finding that $\delta < 1$ for low $\alpha$ justifies paying a premium for Electric Vehicle Car regulation services, as they provide greater “bang for the buck” in terms of frequency control performance. This could inform market-clearing rules or performance payment structures. The crossover point ($\delta=1$) near $\alpha=30\%$ suggests a natural equilibrium or target for the mix of fast and slow regulation resources. System operators could use such an analysis to guide long-term procurement targets or to design incentives that maintain a near-optimal mix, maximizing system efficiency and minimizing overall consumer cost.
Furthermore, the analysis distinguishes between ordered (price-responsive or centrally coordinated) and uncoordinated Electric Vehicle Car charging. The results clearly show that uncoordinated integration increases system volatility and regulation needs, while ordered participation as a flexible resource can reduce them. This strongly advocates for the implementation of smart charging infrastructure, supportive tariffs, and aggregation platforms to harness the flexibility of the Electric Vehicle Car car fleet effectively.
Limitations of this study include the use of a single-area frequency response model, which neglects inter-area oscillations and tie-line power effects. Future work could extend the framework to multi-area systems. Additionally, the model assumes perfect communication and control response from the Electric Vehicle Car aggregator. Incorporating realistic response delays, communication failures, and individual driver compliance uncertainties would enhance the practical relevance of the assessment.
Conclusion
This paper addresses the critical challenge of evaluating frequency regulation capacity requirements in power systems with大规模 Electric Vehicle Car participation. A comprehensive methodology was developed, integrating: 1) a dynamic, block-aggregation model for精确刻画 the time-varying regulation capacity of a heterogeneous Electric Vehicle Car fleet, 2) a hybrid data-and-model-driven distributionally robust optimization framework to assess the minimum system regulation capacity needed to meet frequency performance standards, and 3) a novel metric—the Relative Frequency Regulation Effectiveness Coefficient ($\delta$)—to quantitatively compare the performance of Electric Vehicle Car and thermal regulation resources.
The key findings from the case study are:
- Thermal power plants frequently cannot meet the total regulation requirement alone due to ramp and output limits, necessitating supplemental capacity from规模化 Electric Vehicle Cars.
- Ordered participation of Electric Vehicle Cars (responding to price or control signals) can reduce the total system regulation capacity requirement, whereas uncoordinated charging increases it.
- The total system regulation capacity requirement ($R^{res}$) as a function of the Electric Vehicle Car share ($\alpha$) follows a U-shaped curve, with an optimal point (around $\alpha^*=30\%$ in our case) that minimizes the required capacity.
- The relative effectiveness of Electric Vehicle Car capacity is high ($\delta < 1$) at low penetration levels, demonstrating their superiority for fast frequency control. However, this effectiveness diminishes as $\alpha$ increases, with Electric Vehicle Cars becoming less effective than thermal units ($\delta > 1$) beyond the optimal mix point, primarily due to their energy constraints.
These conclusions provide valuable guidance for grid operators and market designers. They underscore the economic and reliability benefits of integrating a controlled规模化 Electric Vehicle Car fleet into frequency regulation markets but also caution against over-reliance. An optimal mix of fast (Electric Vehicle Car) and slow (thermal) regulation resources should be targeted to minimize total system cost while maintaining stringent frequency standards. The proposed assessment framework and effectiveness metric offer practical tools to inform this crucial resource planning and procurement process as the global transition towards electrified transportation and renewable energy accelerates.