In recent years, the rapid development of electric vehicles (EVs) has positioned them as a critical component in modern power systems, particularly in China, where policies strongly support the adoption of EVs. The integration of EVs into the grid offers a unique opportunity to leverage their “source-load” characteristics for auxiliary frequency regulation. This paper addresses the challenge of ensuring economic feasibility while maintaining system performance when large-scale electric vehicle charging stations participate in grid ancillary services. Specifically, we focus on load frequency control (LFC) in multi-area interconnected power grids, proposing a distributed economic model predictive control (DEMPC) approach. This method optimizes both economic costs and control performance in a single-layer structure, enabling collaborative control across regions. Through convex relaxation of economic cost functions and terminal cost functions to ensure asymptotic stability, the DEMPC method demonstrates superior effectiveness in simulations.
The power grid is evolving towards higher penetration of renewable energy sources, which introduces intermittency and frequency fluctuations. In China, the push for carbon neutrality by 2060 has accelerated the deployment of EVs, making them a flexible load that can act as both a consumer and generator when connected to the grid via vehicle-to-grid (V2G) technology. Electric vehicles can rapidly respond to frequency deviations, providing a fast-acting resource for LFC. However, coordinating large-scale EV participation economically remains a complex issue. Traditional LFC methods often rely on hierarchical control, which may not optimize transient economic performance. Our approach integrates economic optimization and frequency control into a unified framework using DEMPC, which handles multi-area systems efficiently.
To model the system, we consider a multi-area interconnected grid where each area includes thermal power units and aggregated electric vehicle charging stations. The state-space representation for each area i is given by:
$$ \dot{x}_i(t) = A_{ii} x_i(t) + B_{ii} u_i(t) + F_{ii} d_i(t) + \sum_{i \neq j} A_{ij} x_j(t) $$
$$ y_i = C_{ii} x_i(t) $$
where \( x_i \) represents the state vector including frequency deviation, generator power, governor output, EV power, state of charge (SOC), and tie-line power. The matrices \( A_{ii} \), \( B_{ii} \), \( F_{ii} \), and \( C_{ii} \) are derived from the system dynamics. For instance, the generator dynamics are modeled as:
$$ \Delta \dot{X}_{gi} = -\frac{1}{T_{gi} R_i} \Delta f_i – \frac{1}{T_{gi}} \Delta X_{gi} + \frac{1}{T_{gi}} \Delta u_i $$
and the EV dynamics for an equivalent aggregated model are:
$$ \Delta \dot{P}_{Ek} = \frac{1}{T_e} \Delta u_{Ek} – \frac{1}{T_e} \Delta P_{Ek} $$
with constraints on EV power and SOC:
$$ -\mu_{ek} \leq \Delta P_{Ek}(t) \leq \mu_{ek}, \quad -\delta_{ek} \leq \Delta \dot{P}_{Ek}(t) \leq \delta_{ek} $$
$$ SOC_{i,min} \leq SOC_i \leq SOC_{i,max} $$
The economic cost function for the system combines generation costs, frequency control penalties, tie-line power control, and EV regulation costs. For area i, the stage cost is:
$$ l_i(x_i(k), u_i(k)) = F_{pi}(k) + F_{ci}(k) + F_{di}(k) + F_{ei}(k) $$
where:
$$ F_{pi}(k) = \frac{1}{2} a_i \Delta P_{gi}^2(k) + b_i \Delta P_{gi}(k) + c_i $$
$$ F_{ci}(k) = \Delta f_i(k) Q_{ci} \Delta f_i(k) $$
$$ F_{di}(k) = \Delta P_{tie,i}(k) Q_{di} \Delta P_{tie,i}(k) $$
$$ F_{ei}(k) = a_{ei} \Delta P_{EVi}^2(k) + b_{ei} \Delta P_{EVi}(k) $$
These functions ensure that the control strategy minimizes costs while maintaining frequency stability. The DEMPC approach optimizes a collaborative cost function across areas:
$$ V(x, u^{*p}_i) = \min_{u_i} \left[ \alpha_i \phi_i(x, u_i) + \sum_{j \neq i} \alpha_j \phi_j(x, u^{p-1}_j) \right] $$
where \( \phi_i(x, u_i) = \sum_{t=0}^{N-1} l_i(x_i(t|k), u_i(t|k)) + V_{fi}(x_i(N|k)) \), and \( V_{fi} \) is the terminal cost. The optimization is subject to constraints on state and input variables, ensuring feasibility.
Stability analysis is conducted using Lyapunov methods. We assume strict dissipativity, which holds for the convex cost functions. The rotated stage cost is defined as:
$$ \tilde{l}_i(x_i, u_i) = l_i(x_i, u_i) – l_i(x_{si}, u_{si}) + \lambda_i(x_i) – \lambda_i(x_i^+) $$
and the terminal cost satisfies:
$$ V_{fi}(x_i^+) – V_{fi}(x_i) \leq -l_i(x_i, u_i) + l_i(x_{si}, u_{si}) $$
This ensures asymptotic stability of the closed-loop system. The terminal set and cost are computed using linear matrix inequalities (LMI) or discrete linear quadratic regulator (DLQR) methods to guarantee constraint satisfaction.
Simulations were performed on a four-area interconnected grid with a total capacity of 100 MW per area. Parameters for thermal plants and EVs are summarized in Tables 1 and 2. Each area includes two aggregated electric vehicle stations, and the load demand changes at t=3 s. The results show that the DEMPC method effectively regulates frequency deviations and optimizes economic performance.
| Area | \( T_{gi} \) (s) | \( T_{ti} \) (s) | \( M^a_i \) | \( D_i \) | \( R_i \) | \( a_i \) | \( b_i \) | \( c_i \) | \( P_{di} \) (p.u.) | \( \Delta P_{di} \) (p.u.) |
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 0.081 | 0.28 | 3.50 | 2.75 | 2.6 | 3.31 | 0.13 | 1.32 | 0.012 | 0.005 |
| 2 | 0.072 | 0.30 | 3.70 | 3.20 | 2.8 | 2.75 | 0.11 | 1.05 | 0.013 | 0.005 |
| 3 | 0.083 | 0.32 | 4.00 | 2.80 | 2.7 | 3.15 | 0.14 | 1.50 | 0.015 | 0.005 |
| 4 | 0.075 | 0.35 | 3.75 | 2.50 | 2.4 | 3.78 | 0.12 | 1.74 | 0.011 | 0.005 |
| EV Station | \( T_{ei} \) (s) | \( \delta_{ei} \) (p.u.) | \( \mu_{ei} \) (p.u.) | \( E_{max,i} \) | \( E_{min,i} \) |
|---|---|---|---|---|---|
| EV1 | 1 | 0.02 | 0.01 | 0.95 | 0.80 |
| EV2 | 1 | 0.02 | 0.015 | 0.90 | 0.75 |
The frequency deviations under load demand changes are depicted in the simulations, showing that all areas converge to zero deviation quickly. The output power of thermal plants and EVs adjusts to balance the system, with EVs providing rapid response. The tie-line power exchange between areas is also regulated effectively. Compared to centralized and decentralized EMPC, the DEMPC method offers better performance with reduced computational burden, making it suitable for large-scale applications.
In conclusion, the integration of electric vehicle charging stations into grid frequency regulation via DEMPC provides an economically efficient and stable solution. This approach is particularly relevant for China’s evolving energy landscape, where electric vehicles are becoming ubiquitous. Future work could explore real-time implementation and scalability to larger networks.
The economic model predictive control framework directly optimizes the stage cost function, which includes terms for generation, frequency deviation, tie-line power, and EV usage. For a multi-area system, the collaborative cost function ensures that each subsystem considers its neighbors’ states. The optimization problem at each time step k for area i is:
$$ \min_{u_i} \sum_{t=0}^{N-1} l_i(x_i(t|k), u_i(t|k)) + V_{fi}(x_i(N|k)) $$
subject to:
$$ x_i(t+1|k) = A_{ii} x_i(t|k) + B_{ii} u_i(t|k) + F_{ii} d_i(t|k) + \sum_{j \neq i} A_{ij} x_j(t|k) $$
$$ x_i(0|k) = x_i(k), \quad x_i(N|k) \in X_f $$
The terminal cost \( V_{fi} \) is chosen as a quadratic function:
$$ V_{fi}(x_i) = x_i^T P_{fi} x_i + x_i^T p_{fi} $$
and the terminal set \( X_f \) is defined by power balance constraints:
$$ \| P_{gi} – P_{di} – P_{tie,i} + P_{EV1,i} + P_{EV2,i} \| \leq \epsilon $$
This ensures that the system reaches a steady state where frequency is stabilized. The dissipativity condition guarantees that the rotated cost is positive definite, leading to asymptotic stability.
In simulations, the DEMPC method was tested against centralized and decentralized EMPC. The results demonstrate that DEMPC achieves faster convergence and better economic performance. For instance, the frequency deviation in area 1 under a load change of 0.005 p.u. at t=3 s is reduced to zero within seconds, with EVs contributing to the rapid response. The output power of thermal plants shows a slight overshoot to accelerate frequency recovery, but it settles to the optimal steady state quickly.
The use of electric vehicles in China for grid services is a promising avenue to enhance renewable integration. By employing DEMPC, we can ensure that large-scale EV participation is both cost-effective and reliable. The method’s distributed nature allows for scalability, while the economic optimization reduces operational costs. This aligns with global trends in smart grid development and the growing importance of electric vehicles in energy systems.
Further analysis could involve robustness to uncertainties in EV availability or renewable generation. However, the current framework provides a solid foundation for implementing EV-based frequency regulation in multi-area power grids. The continuous advancement of electric vehicle technology in China will likely expand these opportunities, making DEMPC an essential tool for future grid management.