In the context of global efforts to achieve carbon neutrality, the integration of electric cars and distributed energy resources into power systems has become a critical focus. The rapid growth of China EV adoption presents both opportunities and challenges for grid stability and economic efficiency. However, existing scheduling strategies often overlook the segmental regulation capability of electric car charging, which limits the optimization of charging prices and the flexible coordination with distributed resources. This paper addresses these gaps by proposing a master-slave game-based scheduling framework that incorporates segmental charging power regulation and dynamic pricing mechanisms, considering carbon trading to enhance low-carbon benefits.
The proposed framework involves multiple actors: a microgrid operator as the leader, and electric car aggregators and distributed resource aggregators as followers. The microgrid operator sets dynamic charging prices for electric cars and electricity sale prices for distributed resources based on time-of-use tariffs and carbon market information. The electric car aggregators manage the charging of numerous electric cars using a segmental power regulation strategy, allowing adjustable charging power and duration within the grid connection period. This strategy ensures that charging demands are met while optimizing costs and reducing peak load impacts. The distributed resource aggregators control photovoltaic (PV) systems and energy storage, adjusting their output based on sale prices to minimize operational costs. Carbon trading is integrated to incentivize low-carbon operations, with emissions from electric car charging and conventional generation accounted for in the cost functions.
The segmental charging power regulation for electric cars is formulated to allow flexible power levels between minimum and maximum values. For each electric car, the charging power \( P_{i,t}^{\text{EV}} \) can be selected from a set of discrete values, such as \( P^{\text{EV}}_k \in [P^{\text{EV}}_0, P^{\text{EV}}_1, \dots, P^{\text{EV}}_{\text{max}}] \), where \( P^{\text{EV}}_{\text{max}} \) is the maximum allowable power. The charging delay time \( t^l_i \) and charging duration \( T_i \) are determined based on the state of charge (SOC) requirements. The SOC at connection \( S^{\text{con}}_i \), minimum SOC \( S^{\text{min}}_i \), and maximum SOC \( S^{\text{max}}_i \) are modeled as random variables to reflect real-world variability. The charging power and time are optimized to satisfy the energy needs while minimizing costs, as expressed in the following constraints:
$$ t_i = t^d_i – t^c_i $$
$$ D^l_i = \eta (t_i – t^l_i) P^{\text{EV}}_{k,i} – (S^{\text{min}}_i – S^{\text{con}}_i) C^{\text{EV}} $$
$$ t^{\text{end}}_i = t^c_i + t^l_i + \min \left( t^d_i – t^c_i – t^l_i, \frac{(S^{\text{max}}_i – S^{\text{con}}_i) C^{\text{EV}}}{\eta P^{\text{EV}}_{i,t} \Delta t} \right) $$
Here, \( \eta \) is the charging efficiency, \( C^{\text{EV}} \) is the battery capacity, and \( \Delta t \) is the time interval. The dynamic charging price \( \pi^{\text{EV}}_t \) for electric cars is constrained by upper and lower limits to protect user interests, and it is derived from the weighted average of prices from the microgrid operator and distributed resource aggregators:
$$ \pi^{\text{EV}}_{\text{ave}} = \frac{1}{T} \sum_{t=1}^T \pi^{\text{EV}}_t $$
$$ \sum_{t=1}^T \pi^{\text{EV}}_t P^{\text{EV}}_t = \sum_{t=1}^T \pi^{\text{DA}}_t P^{\text{DA}}_t + \sum_{t=1}^T \pi^{\text{MG}}_t P^{\text{MG}}_t $$
$$ \pi^{\text{min}}_t \leq \pi^{\text{EV}}_t \leq \pi^{\text{max}}_t $$
The electric car aggregator’s objective is to minimize the total charging cost, which includes electricity costs and carbon trading costs. The carbon emissions from electric car charging are calculated based on the fossil fuel proportion in the power supply, and the reduction compared to conventional vehicles is credited:
$$ J^{\text{EV}} = \sum_{t=1}^T \left( \pi^{\text{EV}}_t P^{\text{EV}}_t – C^{\text{EV}}_t \right) $$
$$ E^{\text{EV}}_t = \beta_t P^{\text{EV}}_t \Delta t q^{\text{EV}} $$
$$ R^{\text{EV}}_t = E^{\text{OV}}_t – E^{\text{EV}}_t $$
$$ C^{\text{EV}}_t = k R^{\text{EV}}_t $$
In these equations, \( \beta_t \) is the fossil energy ratio, \( q^{\text{EV}} \) is the emission factor for electric cars, \( E^{\text{OV}}_t \) is the emissions from equivalent oil vehicles, and \( k \) is the carbon price. The growth of China EV market necessitates such models to ensure sustainability.
The distributed resource aggregator manages PV and energy storage systems, with the goal of minimizing operational costs. The sale price \( \pi^{\text{DA}}_t \) is bounded to encourage participation, and the cost function includes revenue from electricity sales and carbon benefits from PV generation:
$$ J^{\text{DA}} = \sum_{t=1}^T \left( \pi^{\text{DA}}_t P^{\text{DA}}_t – C^{\text{E}}_t + C^{\text{PV}}_t \right) $$
$$ C^{\text{E}}_t = \lambda^{\text{ESS}}_t P^{\text{ESS}}_t $$
$$ C^{\text{PV}}_t = k \epsilon_1 P^{\text{PV}}_t $$
Energy storage constraints include charging and discharging limits, efficiency, and state of charge boundaries:
$$ 0 \leq P^{\text{ESS,c}}_t \leq u_t P^{\text{ESS,max}}_t $$
$$ – (1 – u_t) P^{\text{ESS,max}}_t \leq P^{\text{ESS,d}}_t \leq 0 $$
$$ S^{\text{ESS}}_t = S^{\text{ESS}}_{t-1} + \left( \eta^{\text{ESS}}_c P^{\text{ESS,c}}_t – \frac{P^{\text{ESS,d}}_t}{\eta^{\text{ESS}}_d} \right) \Delta t $$
$$ \mu_{\text{min}} S^{\text{ESS}}_{\text{max}} \leq S^{\text{ESS}}_t \leq \mu_{\text{max}} S^{\text{ESS}}_{\text{max}} $$
The microgrid operator aims to minimize operational costs and load variance, formulated as a multi-objective problem. The cost includes expenses from gas turbine operation, power purchases, and carbon trading, while the load variance objective promotes grid stability:
$$ J_1 = \sum_{t=1}^T \left( \pi^{\text{MG}}_t P^{\text{MG}}_t – \pi^{\text{EV}}_t P^{\text{EV}}_t – \pi^{\text{DA}}_t P^{\text{DA}}_t + \lambda^{\text{MT}}_t P^{\text{MT}}_t + C^{\text{MT}}_t + C^{\text{C}}_t \right) $$
$$ J_2 = \sum_{t=1}^T \left( P^{\text{L}}_t – P^{\text{PV}}_t + P^{\text{EV}}_t – P_{\text{ave}} \right)^2 $$
$$ J^{\text{MG}} = \omega_1 J_1 + \omega_2 J_2 $$
Carbon trading costs for the microgrid operator are derived from gas turbine and purchased power emissions:
$$ Q^{\text{MT}}_t = E^{\text{MT}} P^{\text{MT}}_t – \epsilon_2 P^{\text{MT}}_t $$
$$ C^{\text{MT}}_t = k Q^{\text{MT}}_t $$
$$ Q^{\text{C}}_t = a_1 (P^{\text{C}}_t)^2 + b_1 P^{\text{C}}_t + c_1 – \lambda_c P^{\text{C}}_t $$
$$ C^{\text{C}}_t = k Q^{\text{C}}_t $$
Power balance is maintained through the following constraint:
$$ P^{\text{EV}}_t + P^{\text{L}}_t = P^{\text{MT}}_t + P^{\text{C}}_t + P^{\text{PV}}_t + P^{\text{ESS}}_t $$
The master-slave game is solved using an improved Kriging metamodel to handle the increased complexity from segmental regulation. This approach reduces computational load by approximating the lower-level responses, with particle swarm optimization refining the solution. The game reaches a Nash equilibrium where no participant can improve their outcome by changing strategies unilaterally.
Simulations are conducted with 2,000 electric cars under different scenarios to evaluate the proposed method. Key parameters include time-of-use tariffs from Jiangsu Province, China, and carbon trading prices. The scenarios compare unordered charging, segmental regulation with fixed prices, dynamic pricing with interruptible charging, and the full proposed approach. Results demonstrate that the segmental regulation combined with dynamic pricing reduces charging costs by 15.1% and peak-to-valley load difference by 11.6% compared to unordered charging. The table below summarizes cost comparisons across scenarios:
| Scenario | EV Aggregator Cost ($) | Distributed Resource Aggregator Cost ($) | Microgrid Operator Cost ($) |
|---|---|---|---|
| Unordered Charging | 21,899 | -21,619 | 82,590 |
| Segmental with Fixed Price | 21,280 | -31,818 | 85,669 |
| Dynamic with Interruptible | 19,130 | -31,699 | 85,620 |
| Proposed Method | 18,589 | -31,410 | 82,499 |
Carbon emissions are significantly reduced in scenarios incorporating carbon trading, with electric car charging shifting to periods of high PV output. The algorithm comparison shows that the Kriging metamodel converges faster than genetic algorithms, with an average of 66 iterations versus 267, and achieves lower costs. The flexibility of segmental power regulation allows electric cars to charge at optimal times, enhancing the integration of distributed resources and supporting the growth of China EV infrastructure.
In conclusion, the proposed master-slave game framework with segmental charging power regulation and dynamic pricing effectively optimizes electric car charging in microgrids. It reduces costs, lowers carbon emissions, and improves load profile smoothness. Future work could explore larger-scale implementations and real-time adjustments for electric car fleets, further advancing the role of China EV in sustainable energy systems.