In the context of global energy transition and carbon neutrality goals, the integration of distributed resources, particularly battery electric vehicle (EV) cars, into virtual power plants (VPPs) presents both opportunities and challenges. The rapid proliferation of battery EV cars has intensified the demand for electricity, which, if not managed properly, can lead to increased carbon emissions and grid instability due to the spatiotemporal randomness of charging loads. Traditional VPP scheduling methods often rely on simplified global carbon emission constraints or static pricing mechanisms, which fail to capture the heterogeneous carbon footprint across grid nodes and thus cannot effectively guide user behavior toward low-carbon outcomes. This limitation hinders the synergistic optimization of economic and environmental benefits in VPP operations. To address this, I propose a novel dynamic pricing method for battery EV car charging stations based on carbon flow tracing, which establishes a quantitative link between node carbon potential and electricity prices, thereby incentivizing battery EV car users to shift their charging activities to low-carbon nodes. This approach not only enhances grid efficiency but also contributes significantly to carbon reduction, offering a practical pathway for VPPs to achieve sustainable energy management.
The core innovation lies in a hierarchical optimization framework that integrates road network planning, power flow analysis, and carbon flow tracing into a closed-loop feedback system. By leveraging node carbon potential—a metric that quantifies the carbon intensity associated with electricity consumption at specific grid nodes—the method dynamically adjusts charging prices for battery EV car stations. This price signal influences the charging decisions of battery EV car users, whose aggregated behavior, in turn, affects grid load distribution and carbon emissions. Through iterative optimization, the framework achieves a balance between maximizing VPP operational revenue and minimizing overall carbon footprint. The methodology is designed to be computationally efficient and adaptable to real-world scenarios, making it a viable tool for grid operators and policymakers aiming to promote the adoption of battery EV cars while ensuring grid stability and environmental sustainability.
The proposed framework consists of three layers: an outer layer for multi-objective optimization, a middle layer for iterative coordination, and an inner layer for physical modeling. Each layer addresses specific aspects of the problem, from high-level decision-making to detailed technical calculations. Key components include a road network planning model that simulates battery EV car user behavior, an optimal power flow module for grid analysis, and a carbon flow tracing module for carbon accounting. The dynamic pricing mechanism is expressed as:
$$P_{\text{CS},z} = P_0 + k e_z$$
where \(P_{\text{CS},z}\) is the charging price at station \(z\), \(P_0\) is the base electricity price, \(k\) is the carbon-electricity conversion coefficient, and \(e_z\) is the node carbon potential at the grid node connected to station \(z\). This formula embeds carbon costs directly into the price, encouraging battery EV car users to prefer stations with lower carbon potential. The coefficient \(k\) serves as a tunable parameter that reflects the emphasis on carbon reduction; a higher \(k\) prioritizes low-carbon outcomes, while a lower \(k\) favors economic gains. This flexibility allows VPP operators to tailor strategies based on regional policies and market conditions, ensuring that the integration of battery EV car charging aligns with broader carbon reduction targets.
To quantify the impact, the optimization objectives are defined as maximizing VPP operational revenue and minimizing total carbon emissions. The revenue function accounts for generation costs and income from battery EV car charging, while the emission function sums carbon outputs from various generation sources. Mathematically, these are expressed as:
$$\max F_1 = -\sum_{i=1}^{N} C_i + \sum_{z \in Z} p_{\text{CS},z} P_{\text{CS},z}$$
$$\min F_2 = \sum_{i=1}^{N} e_{i,\text{gen}} p_{i,\text{gen}}$$
where \(C_i\) is the generation cost at node \(i\), \(p_{\text{CS},z}\) is the load power at charging station \(z\), \(e_{i,\text{gen}}\) is the carbon emission factor of the generator at node \(i\), and \(p_{i,\text{gen}}\) is the active power injection from the generator. The generation cost varies by source, such as wind, solar, gas turbines, and thermal plants, modeled with quadratic or linear functions to capture operational characteristics. For instance, the cost for thermal plants includes startup and shutdown expenses, which are crucial for accurate economic dispatch in systems with high penetration of intermittent renewable energy and battery EV car charging loads.
The road network planning module simulates the decision-making process of battery EV car users, who choose charging stations based on a generalized cost that includes travel time, queueing time, and charging price. This is formulated as a non-cooperative game, where each battery EV car user minimizes their individual cost:
$$\min f_{\text{EV},i,j} = \omega \left( t_{w,z} + \sum_{r \in R(i,z)} t_r \right) + P_{\text{CS},z}$$
Here, \(f_{\text{EV},i,j}\) is the cost for battery EV car \(j\) starting from road node \(i\), \(\omega\) is a conversion factor from time to economic cost, \(t_{w,z}\) is the waiting time at station \(z\), and \(t_r\) is the travel time on path \(r\). The road network model incorporates congestion effects, where travel and waiting times increase with traffic flow, as described by:
$$t_r = t_{r,0} \left[ 1 + \alpha \left( \frac{s_r}{c_r} \right)^2 + \frac{\beta}{1 – s_r / c_r} \right]$$
$$t_{w,z} = t_{w,0} \frac{s_z^2}{1 + \theta s_z}$$
where \(s_r\) and \(s_z\) are the traffic flow on path \(r\) and the throughput at station \(z\), respectively, and \(c_r\) is the path capacity. Parameters \(\alpha\), \(\beta\), and \(\theta\) capture nonlinear congestion dynamics, ensuring that the model reflects real-world bottlenecks that battery EV car users face. The charging power of each battery EV car is also price-sensitive, decreasing as costs rise, which models demand elasticity:
$$p_{\text{EV},i,j} = p_0 + \frac{p_{\text{max}} – p_0}{1 + \gamma (f_{\text{EV},i,j} / f_{\text{EV},0})^2}$$
This elasticity is vital for accurately predicting how battery EV car charging loads respond to dynamic pricing signals, ultimately affecting grid stability and carbon emissions.
The optimal power flow module ensures efficient grid operation by minimizing network losses while satisfying physical constraints. Using second-order cone programming (SOCP) relaxation, the problem is convexified for reliable solution. The objective is:
$$\min F_E = \sum_{(i,j) \in G_E} I_{ij} r_{ij}$$
where \(I_{ij}\) is the square of the current magnitude on branch \((i,j)\), and \(r_{ij}\) is the resistance. Constraints include power balance, voltage limits, and generation capacity, all essential for maintaining grid reliability amidst fluctuating battery EV car charging loads. The SOCP relaxation is valid for radial distribution networks, common in urban areas where battery EV car charging stations are deployed, and it guarantees global optimality under typical conditions.
Carbon flow tracing is the cornerstone of the pricing mechanism. It calculates node carbon potential by tracking the flow of carbon emissions through the grid, attributing emissions to specific loads like battery EV car charging. Based on the carbon emission flow theory, the node carbon potential \(e_j\) at node \(j\) is derived from:
$$\sum_{i \in \mu(j)} e_i p_{ij} + e_{j,\text{gen}} p_{j,\text{gen}} = e_j \left( p_{j,\text{load}} + \sum_{k \in \nu(j)} p_{jk} \right)$$
where \(\mu(j)\) and \(\nu(j)\) are sets of parent and child nodes in terms of active power flow. This equation ensures that carbon emissions are allocated proportionally to the power consumed, providing a fair and transparent basis for pricing. In matrix form, the system solves for carbon potentials as:
$$\mathbf{e} = (\mathbf{S} + \mathbf{L} – \mathbf{F})^{-1} \mathbf{G}$$
where \(\mathbf{S}\), \(\mathbf{L}\), \(\mathbf{F}\), and \(\mathbf{G}\) are matrices representing child flows, loads, parent flows, and generation emissions, respectively. This linear solution enables rapid computation, making it feasible for real-time or near-real-time pricing updates in response to changing grid conditions and battery EV car charging patterns.
The iterative coordination layer bridges the pricing parameters and carbon potentials, resolving circular dependencies. A variable-step self-approximation algorithm updates the carbon potentials until convergence, ensuring consistency between pricing signals and grid states. The update rule is:
$$e_i^{(n+1)} = \lambda e_i^{(n)} + (1-\lambda) \hat{e}_i^{(n)}$$
with \(\lambda\) adjusted dynamically based on the error between estimated and calculated potentials. This algorithm guarantees convergence to a unique equilibrium, where the pricing strategy aligns with actual carbon outcomes, thereby effectively guiding battery EV car users toward low-carbon behavior without compromising grid efficiency.
To validate the method, I conduct simulations on a coupled road-power network, as summarized in Table 1. The test system includes a simplified urban road network with 31 nodes and 42 paths, five battery EV car charging stations, and a standard IEEE 33-node grid with diverse generation sources (thermal, gas, wind, and solar). Key parameters for battery EV car behavior, such as time-cost conversion and charging elasticity, are derived from real-world data to ensure realism.
| Component | Parameters | Values |
|---|---|---|
| Road Network | Nodes, Paths, Stations | 31, 42, 5 (CS1–CS5) |
| Battery EV Cars | Vehicles per Node, Time-Cost Factor | 10–20 (uniform), 0.1 ¥/s |
| Charging Stations | Base Queue Time, Saturation Coefficient | 400–1000 s, 6–10 |
| Grid (IEEE 33) | Generators, Capacities, Carbon Factors | Thermal: 0.855 tCO₂/MWh, Gas: 0.392, Wind: 0.002, Solar: 0.005 |
Four dispatch modes are compared: Mode 1 (traditional economic dispatch, \(k=0\)), Mode 2 (fixed carbon price, \(k=5\) ¥/kgCO₂), Mode 3 (proposed dynamic optimization), and Mode 4 (ideal low-carbon mode). The carbon-electricity conversion coefficient \(k\) in Mode 3 is optimized via the NSGA-II algorithm, which generates a Pareto frontier trading off revenue and emissions. Results show that Mode 3 outperforms others, achieving a 16.7% carbon reduction at the same revenue level as Mode 1, and a 30.4% revenue increase at the same emission level as Mode 2. This demonstrates the efficacy of carbon flow tracing in enhancing the economic-environmental synergy for battery EV car charging management.
Table 2 presents key performance indicators at typical operating points. Mode 3 balances revenue and emissions, whereas Mode 1 prioritizes economics at high carbon cost, and Mode 2 overemphasizes low-carbon outcomes at the expense of revenue. The dynamic pricing in Mode 3 successfully shifts battery EV car loads from high-carbon to low-carbon nodes, as evidenced by changes in charging station utilization. For instance, under Mode 3, stations connected to nodes with lower carbon potential see increased usage, directly reducing the system’s carbon intensity.
| Dispatch Mode | VPP Revenue (¥) | Total Carbon Emissions (kgCO₂) | Carbon Reduction vs. Mode 1 | Revenue Gain vs. Mode 2 |
|---|---|---|---|---|
| Mode 1 (Economic) | 462 | 67.6 | — | — |
| Mode 2 (Fixed Carbon Price) | 368 | 60.3 | 10.8% | — |
| Mode 3 (Proposed) | 462 | 56.3 | 16.7% | 30.4% |
| Mode 4 (Ideal Low-Carbon) | 1.7 | 0.1 | 99.9% | — |
The node carbon potential distribution, illustrated through simulations, reveals spatial heterogeneity: nodes near thermal generators exhibit higher carbon potential, while those near renewables are lower. Under Mode 3, pricing signals effectively guide battery EV car users to avoid high-potential nodes, flattening the carbon profile across the grid. For example, when base price is set at 2.18 ¥/kWh, Mode 3 yields station prices ranging from 2.39 to 3.97 ¥/kWh, compared to a uniform 2.18 ¥/kWh in Mode 1. This differential drives a 77% reduction in carbon emissions relative to Mode 1, with only a 49% drop in revenue, highlighting the trade-off optimization. The behavior of battery EV car users is detailed in Table 3, showing how charging choices evolve with pricing strategies.
| Dispatch Mode | Battery EV Cars at CS1–CS5 | Total Charging Power (kW) | Average Cost per Battery EV Car (¥) |
|---|---|---|---|
| Mode 1 | 63, 67, 59, 59, 54 | 370.0 | 2.18 |
| Mode 2 | 0, 17, 0, 50, 13 | 55.5 | 3.16–6.47 |
| Mode 3 | 24, 70, 4, 64, 21 | 152.1 | 2.39–3.97 |
| Mode 4 | 0, 0, 0, 0, 10 | 16.6 | 3.07–9.80 |
Algorithm efficiency is critical for real-world deployment. The proposed hierarchical framework with iterative coordination reduces computational complexity compared to monolithic optimization. As shown in Table 4, the method achieves a hypervolume (HV) metric of 189 ¥·tCO₂ in Pareto frontier coverage, with a runtime of 3610 seconds, outperforming high-precision alternatives that require 16010 seconds for similar results. This efficiency stems from decoupling the multi-objective optimization into layers, each handling a subset of variables—such as pricing parameters and carbon potentials—thereby accelerating convergence while maintaining solution quality for battery EV car charging scenarios.
| Algorithm | Decision Variables | Constraints | Runtime (s) | HV (¥·tCO₂) | Pareto Coverage (%) |
|---|---|---|---|---|---|
| Proposed Method | 2 | 0 | 3610 | 189 | 100 |
| Low-Precision Baseline | 6 | 4 | 1289 | 178 | 82 |
| High-Precision Baseline | 6 | 4 | 16010 | 188 | 100 |
In conclusion, the carbon flow tracing-based pricing method for battery EV car charging stations offers a robust framework for VPPs to harmonize economic and environmental objectives. By dynamically linking node carbon potential to electricity prices, it provides a transparent and effective mechanism to guide battery EV car users toward low-carbon charging behaviors. The three-layer optimization architecture ensures computational tractability and practical applicability, enabling real-time adjustments in response to grid conditions and user patterns. Simulations confirm that the approach can reduce carbon emissions by 16.7% without sacrificing revenue, or boost revenue by 30.4% at constant emissions, outperforming traditional fixed-price or carbon-agnostic strategies. This underscores the potential of carbon-aware pricing to accelerate the adoption of battery EV cars while supporting grid decarbonization.
Future work should focus on integrating the method with electricity market mechanisms, such as real-time bidding and carbon trading, to enhance its economic viability. Additionally, adaptive calibration of the carbon-electricity coefficient \(k\) using machine learning could improve responsiveness to fluctuating renewable generation and battery EV car demand. Extending the user behavior model to incorporate bounded rationality and long-term learning would further refine predictions of battery EV car charging patterns. Overall, this research paves the way for smarter, greener grid management, where battery EV car charging becomes a lever for sustainable energy transition, leveraging carbon flow tracing as a key enabler for a low-carbon future.