As a graduate researcher focusing on the integration of transport electrification with power system operation, I have dedicated my master’s thesis to investigating how large-scale electric vehicle (electric vehicle) clusters can actively participate in regional grid frequency regulation (FR). The transition toward renewable-dominated power systems significantly reduces the system inertia and weakens frequency stability, while the stochastic nature of renewable generation intensifies the requirement for fast-response FR resources. Compared to conventional thermal power units that are constrained by ramp-rate limits, electric vehicle fleets possess unique advantages including rapid response, bidirectional energy capability, and distributed siting characteristics. My research centers on establishing an operational framework that effectively coordinates multiple FR participants, quantifies the regulation potential of heterogeneous electric vehicle users, and optimally decomposes dispatch commands from the grid operator through the EV aggregator (EVA) down to individual electric vehicles.
1. Introduction and Problem Formulation
The installed capacity of renewable energy in China has experienced a continuous increase, reaching approximately 56% of total generation capacity by the end of 2024. Wind and solar photovoltaic generation expanded to 520 GW and 890 GW respectively, while total renewable generation surpassed 3.46 trillion kWh, accounting for 35% of the national electricity production. Although such an evolution significantly contributes to decarbonization, the inherent intermittency of renewable sources and the widespread deployment of power-electronic interfaces have jointly weakened the frequency support capability of conventional generators, such that the frequency regulation of the system is increasingly challenging. On the other hand, the ownership of electric vehicles has witnessed dramatic expansion. By the end of 2024, the total number of new energy vehicles in China reached 31.4 million, of which pure electric vehicles accounted for approximately 70%, representing 22.09 million units. The fast-growing electric vehicle population forms a distributed energy resource whose aggregate regulation capability should not be neglected.
From a technical point of view, electric vehicle clusters can accomplish bidirectional power exchange through vehicle-to-grid technology, which enables the cluster to act as an efficient frequency regulation provider. Market regulations in several Chinese provinces including Anhui, Zhejiang, Hubei and Chongqing have announced that load aggregators, virtual power plants and charging-pile operators are entitled to participate in FR ancillary service markets after proper aggregation. Despite such encouraging progress, the uncertainty of electric vehicle charging behaviors and the reliability limitations of the estimated regulation capability remain significant barriers. Moreover, the compensation price mechanism for electric vehicle FR services has not been sufficiently investigated, especially considering the heterogeneous willingness among electric vehicle owners. Additionally, the intra-EVA decomposition of an FR command to each electric vehicle is complicated by individual state-of-charge, charging demand, risk attitudes and the market compensation signal.
Therefore, my research aims to resolve three key problems: (1) how to design a reasonable FR mileage price that accounts for heterogeneous user risk preferences in an interactive game framework; (2) how to accurately model the stochastic dispatchable capability of an electric vehicle fleet considering multidimensional random variables and their dependence structures; and (3) how to implement the hierarchical optimal dispatch to allocate the FR signal dynamically between thermal units and EVA, and then from EVA to each electric vehicle, while balancing economy and system stability.
2. Market Mechanism and Control Framework for Large-Scale Electric Vehicle Participation in Frequency Regulation
2.1 Organization and Clearing Mechanism
Based on the typical provincial FR ancillary service market in China, the market process is organized through three stages: day-ahead quotation, day-ahead pre-clearing, and intraday real-time deployment. Each participating unit submits its available FR capacity together with mileage price information before the day-ahead operation. Frequency regulation mileage refers to the absolute power difference between pre-regulation and post-regulation outputs. The clearing rule sequences the participants according to the ratio of mileage price to composite performance index. The compensation consists of two components:
$$C_{M,t} = k \cdot M_t \cdot \lambda_{M,t}$$
$$C_{E,t} = E_t \cdot \lambda_{E,t}$$
where CM,t denotes the mileage compensation, CE,t represents the capacity compensation, while Mt and Et correspond to the FR mileage and reserved capacity in time interval t; λM,t and λE,t are the corresponding price signals and k is the composite FR performance factor defined as:
$$k = \omega_1 k_1 + \omega_2 k_2 + \omega_3 k_3$$
with k1 the regulation-rate coefficient, k2 the regulation-accuracy coefficient and k3 the response-time coefficient. The weight coefficients used in this thesis are ω1=0.4, ω2=0.3 and ω3=0.3 following an operational rule of a provincial FR market. Each performance coefficient is formulated as:
$$k_1 = \frac{v_R}{v_N} \qquad (k_1 \le 5)$$
$$k_2 = 1 – \frac{\Delta P_R}{\Delta P_N}$$
$$k_3 = 1 – \frac{T_D}{T_N}$$
where vR and vN denote the actual and standard regulation rate, ΔPR is the deviation between the actual output and the dispatch command, ΔPN is the allowable tolerance, TD represents the delay time of response, and TN is the permitted delay.
2.2 Evolutionary Game Formulation for FR Mileage Price
In the market integration of electric vehicles, the compensation price strongly influences their willingness to respond to dispatch. To determine an appropriate price interval for different electric vehicle users, I developed an evolutionary game model between the grid operator and electric vehicle owners. The adaptation functions of the grid and the electric vehicle when choosing the cooperative strategy can be written as follows:
$$f_{EV}(r_1,s_1) = qR_{EV} – (1-q)L_{EV}$$
$$f_{grid}(r_1,s_1) = pR_{grid} – (1-p)L_{grid}$$
where p and q are the interaction willingness of electric vehicle population and grid respectively, REV and Rgrid are the revenues of the electric vehicle and grid, and LEV and Lgrid are the loss functions. The revenue of the grid is intended to reflect the reduced spinning-reserve costs due to the substitution effect of electric vehicle resources:
$$R_{grid} = (1-\alpha)E_{ev}\lambda_G – M_{ev}\lambda_M$$
Similarly, the electric vehicle revenue function accounts for the regulation gain minus the time-based loss from being utilized:
$$R_{EV} = \lambda_M P_{FR,t}\Delta t / T – \gamma_1 \Delta t$$
The replicator dynamic equations of the EV population and grid operator can be expressed by:
$$\dot{p} = p(1-p)[qR_{EV} – L_{EV}]$$
$$\dot{q} = q(1-q)[pR_{grid} – L_{grid}]$$
Setting the replicator equations to zero and requiring non-negative utilities for both parties, I obtained the feasible domain for the FR mileage price. From the numerical study, the FR mileage price interval was identified as [1.45, 3.61] Yuan/MW, while the feasible dispatchable power range was [8.87, 12.40] MW within the balanced evolution equilibrium (1,1). Further analysis accounting for different preference types showed that more proactive (aggressive) electric vehicle users accept a wider price range as shown in Table 2.1.
| EV preference type | Dispatchable power (MW) | Mileage price interval (Yuan/MW) |
|---|---|---|
| Conservative | [8.57, 8.87] | [2.04, 2.22] |
| Neutral | [8.57, 12.45] | [1.45, 3.61] |
| Aggressive | [8.57, 21.95] | [1, 5] |
3. Probability Assessment Model of Electric Vehicle Dispatchable Power
3.1 Individual dispatchable power model
For an individual electric vehicle, the FR capability during a dispatch interval can be described by the charging power adjustment from its baseline power Pbase. The upward and downward regulation capability limits are subject to:
$$0 \le \Delta P_{up} \le P_{max} – P_{base}$$
$$-P_{base} \le \Delta P_{down} \le 0$$
Moreover, maintaining the battery SOC within safe boundaries and considering the time-coupling of the charging process, the actual regulation capability is constrained by:
$$\Delta P_{up} \le \frac{SOC_{max} – SOC_t}{\Delta t} P_{base}$$
3.2 Risk-preference-based differentiated control strategy
In practice, electric vehicle owners exhibit substantially different sensitivities to the FR mileage price. Some owners prefer to satisfy their charging demand at all costs, while others are more willing to flexibly adjust their charging power to obtain economic benefits. I categorized electric vehicle users into three risk-preference representative types: conservative, neutral and aggressive. Control strategies were designed for each type to reflect their attitudes toward FR interactions.
For a conservative electric vehicle, the dispatchable power PFR,t is formulated as:
$$P_{FR,t}^b = \begin{cases} -\Delta P_{down}^{max} \cdot (1 – SOC^2) & \Delta f < 0 \\ \Delta P_{up}^{max} \cdot (SOC^2 – 1) & \Delta f > 0 \end{cases}$$
For a neutral electric vehicle:
$$P_{FR,t}^b = \begin{cases} -\Delta P_{down}^{max} \cdot (SOC – 0.1) & \Delta f < 0 \\ \Delta P_{up}^{max} \cdot (0.9 – SOC) & \Delta f > 0 \end{cases}$$
And for an aggressive electric vehicle:
$$P_{FR,t}^b = \begin{cases} -\Delta P_{down}^{max} \left[ 1 – \left(\frac{SOC – SOC_{min}}{SOC_{high} – SOC_{min}}\right)^2 \right] & \Delta f < 0 \\ \Delta P_{up}^{max} \left[ 1 – \left(\frac{SOC_{max} – SOC}{SOC_{max} – SOC_{low}}\right)^2 \right] & \Delta f > 0 \end{cases}$$
3.3 Multivariate Gaussian Copula-based EVSP evaluation model
The dispatchable power of an electric vehicle cluster PEVA,j can be accumulated from each individual electric vehicle as:
$$P_{j,up}^{EVA} = \sum_{n=1}^{N_{ev}} \Delta P_{up,n}$$
$$P_{j,down}^{EVA} = \sum_{n=1}^{N_{ev}} \Delta P_{down,n}$$
Rather than merely describing each variable according to marginal distributions, the EV scheduling potential is influenced by the joint effect of SOC, FR mileage price and user risk preference. Considering the nonlinear dependence and the tail-correlation properties between these variables, I adopted the multivariate Gaussian Copula to establish a joint probability distribution model. The Gaussian Copula is expressed as:
$$C_{\Sigma}^{Gauss}(u_1, \dots, u_N) = \Phi_{\Sigma}(\Phi^{-1}(u_1), \dots, \Phi^{-1}(u_N))$$
and its probability density function is:
$$C_{\Sigma}^{Gauss}(u) = \frac{1}{(2\pi)^{N/2}|\Sigma|^{1/2}} \exp\left(-\frac{1}{2} x^T \Sigma^{-1} x\right)$$
where xi = Φ−1(ui), and Σ is the covariance matrix. Through the inverse distribution function, samples of the dispatchable power with a prescribed marginal distribution are generated, providing a three-dimensional landscape that links the electric vehicle dispatchable power with the FR mileage price and the SOC. Table 3.1 provides the marginal distributions fitted from the sample data for each preference type.
| EV type | Dispatchable power distribution |
|---|---|
| Conservative | Gamma(4, 0.35) |
| Neutral | N(2.75, 0.7) |
| Aggressive | Beta(10, 2.5) |
I compared the Gaussian Copula with the T-Copula in terms of the rank correlation matrix. The Gaussian Copula produced a smaller fitting error and better captured the dependence structure. The graph inserted below illustrates the trend of electric vehicle development in China from 2015 to 2024, which reinforces the practical relevance of the proposed approach.
To validate the differentiated control strategy relative to the conventional SOC-based group control, I simulated a fleet of 5000 electric vehicles with a ratio of 0.3:0.4:0.3 among conservative, neutral and aggressive users. The comparison results are presented in Table 3.2.
| Strategy type | Upward regulation power (MW) | Downward regulation power (MW) |
|---|---|---|
| SOC-based group control | 13.79 | 13.08 |
| Proposed model | 14.71 | 14.22 |
The results show that the upward regulation power improved by 11.1% and the downward regulation power improved by 3.72% when compared to the traditional group control method. This confirms that the differentiated control strategy can quantify the heterogeneous requirements of electric vehicle users and exploit the dispatchable potential as much as possible.
4. Bi-layer Optimization Dispatch for EVA Participation in the Intraday FR Market
4.1 Upper layer: Chance-constrained economic dispatch model
To balance the economy and the stability of the FR process in each 15-minute intraday dispatch interval, I formulate the upper-layer decision problem as a chance-constrained programming (CCP) model. The optimization objective is set as the overall FR cost of the market, which includes both the mileage compensation CM and the capacity compensation CE:
$$\min F = C_M + C_E$$
$$C_M = \sum_{t=1}^{T}\sum_{i=1}^{N_g} k_{i,t}^g \lambda_{M,i,t}^{gen} M_{i,t}^{gen} + \sum_{t=1}^{T}\sum_{j=1}^{N_a} k_{j,t}^a \lambda_{M,j,t}^{EVA} M_{j,t}^{EVA}$$
$$C_E = \sum_{t=1}^{T}\sum_{i=1}^{N_g} \lambda_{C,i,t}^{gen} E_{i,t}^{gen} + \sum_{t=1}^{T}\sum_{j=1}^{N_a} \lambda_{C,j,t}^{EVA} E_{j,t}^{EVA}$$
subject to deterministic constraints including thermal generator output limits, ramping constraints, EVA power limitations, tie-line transmission constraints, and the frequency control requirement:
$$\sum M_t \le P_{AGC,t}$$
$$0 < E_{i,t}^{gen} \le 0.1 E_{FR,t}$$
$$0 < E_{j,t}^{EVA} \le 0.05 E_{FR,t}, \quad \sum_{j=1}^{N_a} E_{j,t}^{EVA} \le 0.3 E_{FR,t}$$
Instead of treating the FR capacity requirement as a deterministic value, I model the actual FR power demand as a random variable following a zero-mean normal distribution. The frequency deviation after regulation should remain inside the allowed band with a certain confidence level β, which is expressed by the probabilistic constraint:
$$Prob\left\{ \Delta f \le \Delta f_0 \right\} \ge \beta$$
$$Prob\left\{ \sum_{i=1}^{N_g} \Delta P_{i,t}^{gen} + \sum_{j=1}^{N_a} \Delta P_{j,t}^{EVA} + B\Delta f_0 \ge P_{AGC,t} \right\} \ge \beta$$
The random variable PAGC,t is discretized into Nk scenario intervals with prescribed probabilities qk. A binary variable yk indicates whether the frequency deviation after adjustment satisfies the safety constraint under scenario k. The probability constraint is then transformed into an equivalent mixed-integer linear constraint using the big-M method:
$$\sum_{i=1}^{N_g} \Delta P_{i,t}^{gen} + \sum_{j=1}^{N_a} \Delta P_{j,t}^{EVA} + B\Delta f_0 \ge P_{AGC,k} – M(1-y_k)$$
$$\sum_{k=1}^{N_k} q_k y_k \ge \beta$$
4.2 Confidence-level selection
The appropriate confidence level is selected by performing optimization under a series of preset β values and calculating a satisfaction index μk for each target:
$$\mu_k = \frac{f_{k,max} – f_k(c)}{f_{k,max} – f_{k,min}}$$
In order to obtain a balanced solution, I maximize the minimum satisfaction among the objectives:
$$\max_{c=1:21} \left( \min_{k=1:2} \mu_k \right)$$
Simulations for different confidence values were carried out and the satisfaction comparison indicated that choosing β = 0.90 provides a stable balance between economic efficiency and frequency security.
4.3 Lower layer: differentiated power decomposition based on EVSP
When the total FR command PI,t is received from the upper layer, the lower layer decomposes it to individual electric vehicles according to their current dispatchable power PFR,t:
$$\Delta P_{EV,t} = \begin{cases} \frac{P_{FR,t}}{M_{j,down}^{EVA}} P_{I,t} & \Delta f < 0 \\ \frac{P_{FR,t}}{M_{j,up}^{EVA}} P_{I,t} & \Delta f > 0 \end{cases}$$
This decomposition ensures that electric vehicles with a larger dispatchable capability will be assigned more regulation power, whereas those with smaller margins contribute less, thereby achieving fair allocation and full utilization of the regulation capacity.
4.4 Result analysis
I compared the regulation effects of thermal power alone versus combined thermal and electric vehicle regulation under a confidence level of 90%. Table 4.1 summarizes the cost comparison.
| Scheme | Capacity cost (Yuan) | Mileage cost (Yuan) | Total cost (Yuan) |
|---|---|---|---|
| Thermal only | 2100.00 | 3167.85 | 5267.85 |
| Thermal plus EV | 1768.71 | 2255.93 | 4024.64 |
From Table 4.1, the introduction of electric vehicles reduced the total regulation cost by 23.6%. This is realized because the EV is prioritized during the FR dispatch due to its lower regulation cost, while thermal units compensate the remaining need.
Furthermore, the lower layer results in a differentiated distribution of the FR signal. The average dispatchable power of aggressive, neutral and conservative electric vehicles was found to be 4.39 kW, 2.74 kW and 1.41 kW respectively. Aggressive electric vehicle users receive the largest share of the regulation tasks because their regulation ability is stronger and their willingness to respond is higher. To further validate the computational efficiency, the CCP model was compared with a multi-objective genetic algorithm. The results are provided in Table 4.2.
| Method | Cost (Yuan) | Optimization time (s) |
|---|---|---|
| CCP model (β=0.90) | 2255.93 | 0.37 |
| Multi-objective genetic algorithm | 3659.42 | 64.31 |
The proposed CCP model not only produces lower regulation costs but also reduces the computational time considerably, which is crucial for the intraday 15-min-level secondary frequency regulation.
5. Comprehensive Simulation Platform and Experimental Validation
5.1 Platform architecture and LabVIEW-based dispatch control
To bridge the gap between algorithm development and hardware-in-the-loop testing, I designed a real-time simulation platform consisting of three functional modules: a dispatch control system based on LabVIEW, a MATLAB algorithm optimization module performing the CCP model, and an RTDS-based real-time simulation module. The platform enables real-time data acquisition, visualization of the frequency regulation process and execution of the decision-making algorithm. The communication between the LabVIEW system and the RTDS simulator uses the UDP protocol through the GTNET-SKT interface. The optimization result from MATLAB is embedded into LabVIEW using the MATLAB script node, thus forming a closed-loop chain from data monitoring, optimization decision, command dispatch through the power control of thermal generators and electric vehicle charging stations.
5.2 Single-area simulation on the IEEE39-bus system
I established a modified IEEE39-bus system within the RTDS environment, where the conventional generating units G1 to G10 are installed at nodes 30 to 39, and node 31 was selected as the slack bus. The electric vehicle charging stations are integrated at nodes 20, 28 and 39 through step-down transformers so that they can respond to EVA dispatch signals. The thermal generating units follow their standard speed-governor models, while the charging piles adopt an equivalent frequency control model. In the single-area studies, I first investigated the effect of different EV penetrations by varying the level of charging power that is allowed to participate in the FR. The simulation window is 30 seconds with a time step of 50 microseconds. The load disturbance is introduced at a selected bus, and the secondary frequency regulation is triggered by adjusting the load reference of the thermal units and the power reference of the electric vehicle charging stations.
| Parameter | Value |
|---|---|
| Rated voltage | 10 kV |
| Rated power | 0.5 MW |
| Nominal frequency | 50 Hz |
| Charging station time constant | 0.015 |
| Proportional gain | 50 |
| Integral gain | 0.01 |
| Parameter | Value |
|---|---|
| Battery capacity | 60 kWh |
| Maximum charging power | 11 kW |
| Maximum discharging power | −11 kW |
| Initial SOC distribution | N(0.5, 0.1) |
| SOC lower / upper limits | 0.1 / 0.9 |
| Control mode | Manual (V2G) |
| Charging efficiency | 0.85 |
From the frequency regulation responses, when the load perturbation occurs, the thermal governor reacts within approximately 6 s, while the electric vehicle cluster starts responding as soon as the command is received. Without the EV, the frequency recovers to 50.05 Hz after around 11 seconds; with the EV, the necessary time is reduced to approximately 5 seconds. As the penetration of electric vehicle power increases, the recovery time becomes even shorter. The comparison presented in Table 5.3 evaluates the regulation performance in terms of the FR performance indices defined in Chapter 2.
| Scenario | Regulation rate coefficient | Regulation accuracy coefficient | Response time coefficient |
|---|---|---|---|
| Thermal alone | 0.92 | 0.60 | 0.80 |
| Thermal plus EV | 1.57 | 0.69 | 0.85 |
The overall FR performance indicator improved from 0.79 to 1.09, representing an increase of 36.34%. Moreover, the regulation rate coefficient increased by 70.65%, the accuracy coefficient increased by 15%, and the response time coefficient increased by 6.37%. These experimental outcomes strongly support the effectiveness of the proposed dispatch architecture in improving both dynamic response and steady-state behavior of the system frequency regulation.
In addition, from the sampling analysis of each EV type according to the real-time charging power, the SOC evolution and the estimated remaining charging time, the dispatch results confirm that aggressive electric vehicles possess the widest regulation margin; their SOC changed more visibly and their charging completion time was delayed more noticeably. Conservative electric vehicles showed the least impact, while neutral electric vehicles were located in between. This indicates that the proposed strategy explicitly respects the preferences of electric vehicle owners and reflects the trade-off between providing regulation service and fulfilling individual charging needs.
5.3 Interconnected two-area four-generator system
In the second case study, a two-area four-generator power system is employed to investigate the influence of large-scale electric vehicle participation at an interregional level. Each area comprises two thermal generators and its local load, while area A and area B are connected through a tie-line so that power exchanges and frequency coordination can be simulated. The EV charging station aggregators are connected to node 7 of area A. Three renewable penetration scenarios were examined: no renewables, 10% penetration and 20% penetration. Under higher renewable penetration, the grid suffers from larger frequency excursions. I further compared the operation with and without EV resources under the 20% renewable scenario. In the scenario where the load at node 6 of area A was reduced by 200 MW, the frequency initially rose to 50.28 Hz. With only the thermal governor actions, the frequency was stabilized at 50.14 Hz and the tie-line power settled at approximately 499.84 MW. When the EV charging cluster increased its aggregate charging power by 40 MW, the tie-line power deviation was significantly reduced while the frequency restoration to 50.04 Hz was accelerated through the joint action of thermal units and electric vehicles.
| Regulation scenario | Tie-line power deviation (MW) |
|---|---|
| Thermal only | 33.66 |
| Thermal plus EV | 28.72 |
The tie-line power fluctuation was reduced by 14.68% when the EV participated, which indicates that the proposed architecture effectively avoids unnecessary power flow variations on the interconnections and allows for a more balanced utilization of regulating resources across the system.
6. Conclusions and Future Perspectives
In this thesis, a systematic investigation was carried out to enable large-scale electric vehicle participation in the regional grid frequency regulation market considering heterogeneous user preferences. My main findings can be summarized as follows:
(1) Market-oriented FR price mechanism. The evolutionary game framework offered a quantitative method to establish the feasible range of FR mileage prices that encourages interactions between the grid and electric vehicles. In the considered case, the feasible price interval for the neutral-type electric vehicle was determined as [1.45, 3.61] Yuan/MW and the dispatchable power range was [8.87, 12.40] MW. Users with more aggressive risk attitudes possess wider acceptable price intervals, since their greater regulation power brings more benefits to the grid.
(2) Probabilistic evaluation of EVSP. The multivariate Gaussian Copula model was effective in capturing the nonlinear correlation between the electric vehicle dispatchable power, the SOC and the compensation price. Compared with the conventional cluster-level control, the differentiated control strategy increased the upward regulation power by 11.1% and the downward regulation power by 3.72% under the given test scenario. This not only utilizes the full dispatchable capacity of electric vehicles but also provides a useful tool for balance settlement in a market environment.
(3) Hierarchical optimization control. The proposed upper-layer CCP model provides a practical solution to allocate the FR command between thermal units and EVA, achieving a total regulation cost reduction of 23.6% in comparison with thermal-only regulation. The lower-layer power decomposition mechanism precisely reflects the differences among conservative, neutral and aggressive electric vehicle users, and realizes fair and efficient distribution of the FR signal across the fleet.
(4) Real-time validation. The comprehensive simulation platform combining LabVIEW, MATLAB and RTDS has proven to be an appropriate test bed for large-scale electric vehicle participation in FR. In both single-area and interconnected-area simulation cases, the electric vehicle cluster-based regulation significantly reduces the frequency restoration time, improves the composite FR performance by 36.34%, and reduces the tie-line power fluctuations by 14.68%. These results reveal the practical value of electric vehicles as promising frequency regulation resources in future renewable-rich power grids.
Several future research directions are worth exploring. First, the current study assumes that all participating electric vehicles are privately owned passenger cars. In reality, buses, taxis, and logistic electric vehicles have different usage patterns and opportunity costs when responding to frequency regulation. Extending the proposed methodology to a multi-class electric vehicle population with diverse traveling constraints will enhance its applicability. Second, my model sets the baseline charging power as constant within each 15-minute interval. In a more realistic setting, the baseline itself varies with the state of each electric vehicle and the market price. Thus, integrating a predictive model of the time-varying baseline and of the corresponding dispatchable power is an important direction for future work.