The rapid global proliferation of battery EV cars represents a significant stride towards decarbonizing the transportation sector. However, the concentrated and often uncoordinated charging demand of these vehicles poses substantial challenges to grid stability, peak load management, and the overall carbon footprint of the electricity system. Concurrently, the advancement of photovoltaic (PV) generation and energy storage system (ESS) technologies presents a compelling opportunity to address these challenges through integrated solutions. This paper delves into the low-carbon operational characteristics of a synergistic system that combines PV generation, battery energy storage, and battery EV car charging infrastructure—the PV-ESS-EV system. By establishing detailed mathematical models and conducting simulation-based analysis, we explore the system’s energy flow dynamics, carbon emission reduction potential, and economic viability under various operational strategies.
The integration of these three components creates a closed-loop energy ecosystem at the distribution level. The PV system harnesses clean, renewable solar energy. The ESS acts as a flexible buffer, storing excess PV energy and discharging it during periods of high demand or low generation. The charging stations provide the necessary service for the growing fleet of battery EV cars. The core intelligence of the system lies in its Energy Management System (EMS), which coordinates these flows to achieve multiple objectives: minimizing grid dependency, reducing operational costs, and crucially, lowering carbon emissions associated with charging each battery EV car.
System Architecture and Foundational Models
The PV-ESS-EV synergistic system comprises four primary subsystems: the PV generation unit, the battery ESS, the battery EV car charging stations, and the central EMS.
The output power of the PV array is highly dependent on solar irradiance and ambient temperature. A simplified yet effective model for the PV generation power ($P_{pv}(t)$) at time $t$ is given by:
$$P_{pv}(t) = \eta_{pv} \cdot A_{pv} \cdot G(t) \cdot [1 – \kappa (T_c(t) – T_{stc})]$$
where $\eta_{pv}$ is the overall PV system efficiency, $A_{pv}$ is the total panel area, $G(t)$ is the solar irradiance, $\kappa$ is the temperature coefficient, and $T_c(t)$ is the cell temperature. This intermittent and variable output is a key driver for needing storage.
The battery ESS is modeled considering its state of charge (SOC) dynamics and efficiency. The SOC update equation is:
$$SOC(t+1) = SOC(t) + \frac{\Delta t}{E_{ess}^{rated}} \cdot \left( \eta_{ch} \cdot P_{ess}^{ch}(t) – \frac{1}{\eta_{dis}} \cdot P_{ess}^{dis}(t) \right)$$
where $E_{ess}^{rated}$ is the rated energy capacity, $\Delta t$ is the time interval, $\eta_{ch}$ and $\eta_{dis}$ are charging and discharging efficiencies, and $P_{ess}^{ch}(t)$, $P_{ess}^{dis}(t)$ are the charging and discharging powers (non-negative). The operational constraints are $SOC^{min} \le SOC(t) \le SOC^{max}$ and $0 \le P_{ess}^{ch/dis}(t) \le P_{ess}^{max}$.
The load from battery EV car charging is stochastic. For analysis, we aggregate the demand. Let $P_{ev,i}(t)$ be the charging power of the i-th battery EV car. The total EV charging load $P_{ev}^{total}(t)$ is:
$$P_{ev}^{total}(t) = \sum_{i=1}^{N_{ev}(t)} P_{ev,i}(t)$$
where $N_{ev}(t)$ is the number of cars charging at time $t$. The charging profile can be characterized by parameters like arrival time, departure time, and required energy, often modeled using probability distributions.
The power interaction with the main grid, $P_{grid}(t)$, is the decision variable that balances the system. The fundamental power balance equation at any time $t$ is:
$$P_{grid}(t) + P_{pv}(t) = P_{ess}^{dis}(t) – P_{ess}^{ch}(t) + P_{ev}^{total}(t) + P_{loss}(t)$$
Here, $P_{grid}(t) > 0$ indicates power drawn from the grid, while $P_{grid}(t) < 0$ indicates power fed back to the grid. $P_{loss}(t)$ aggregates conversion and standby losses.
Multi-Dimensional Operational Characteristics
1. Energy Flow Dynamics
The energy flow within the system is dynamic and strategy-dependent. A well-designed EMS orchestrates flows according to a hierarchical priority: local PV consumption first, followed by ESS buffering, with the grid as the final supplement. We can analyze typical operational modes:
| Time Period | Solar Condition | EV Demand | Primary Energy Flow | Grid Power $P_{grid}(t)$ |
|---|---|---|---|---|
| Midday (Peak Sun) | High | Medium | PV → EV, PV → ESS, PV → Grid | Negative (Export) |
| Afternoon/Early Evening | Declining | High | PV + ESS → EV | Near Zero or Positive |
| Night | None | Medium/High | ESS → EV, Grid → EV | Positive (Import) |
| Early Morning (Low Grid Load) | None | Low | Grid → ESS (Charging) | Positive (Import) |
The ESS is pivotal in temporally decoupling generation from consumption. It stores low-carbon energy (excess PV or low-carbon grid power at night) to displace high-carbon grid power during peak hours for charging the battery EV car.
2. Carbon Emission Characteristics
The primary carbon footprint of the system arises from electricity imported from the grid, as the PV generation and direct ESS discharge are considered carbon-free at the point of use. The grid’s carbon intensity ($\lambda_{grid}(t)$, in kgCO₂eq/kWh) is often time-varying, reflecting the changing generation mix (e.g., more coal at peak, more wind at night).
The operational carbon emissions $C_{op}$ over a period T are calculated as:
$$C_{op} = \sum_{t=1}^{T} \left[ \lambda_{grid}(t) \cdot \max(P_{grid}(t), 0) \cdot \Delta t \right]$$
where $\max(P_{grid}(t), 0)$ ensures we only account for power drawn from the grid. A critical metric is the effective carbon intensity of charging a battery EV car at this station:
$$\lambda_{ev}^{effective} = \frac{C_{op} + C_{emb}}{ \sum_{t} P_{ev}^{total}(t) \cdot \Delta t }$$
where $C_{emb}$ represents embedded carbon from manufacturing system components. The EMS’s goal is to minimize $C_{op}$ by strategically using the ESS to avoid drawing power when $\lambda_{grid}(t)$ is high, thereby reducing $\lambda_{ev}^{effective}$ significantly compared to uncontrolled charging.
3. Economic Viability Analysis
The economic model incorporates multiple revenue streams and cost savings. The primary economic objective function for daily operation can be expressed as maximizing net revenue $R_{net}$:
$$
\begin{aligned}
R_{net} = & \sum_{t=1}^{T} \left[ -C_{grid}^{buy}(t) \cdot \max(P_{grid}(t), 0) + C_{grid}^{sell}(t) \cdot \max(-P_{grid}(t), 0) \right] \cdot \Delta t \\
& + R_{DR} – C_{deg}
\end{aligned}
$$
Where:
- $C_{grid}^{buy}(t)$: Time-of-use (TOU) electricity purchase price.
- $C_{grid}^{sell}(t)$: Feed-in tariff or market price for sold PV electricity.
- $R_{DR}$: Revenue from participating in grid demand response programs, by reducing load or providing power during critical events. This is highly valuable for supporting grid stability while serving battery EV car customers.
- $C_{deg}$: Cost associated with battery ESS degradation due to cycling, modeled as a function of depth-of-discharge and cycle count.
The system creates value through arbitrage (buying cheap/low-carbon grid power to charge ESS, selling/discharging when price/carbon is high) and peak shaving (reducing costly grid power purchases during peak periods). The following table summarizes key economic parameters and their impact.
| Economic Factor | Description | Impact on PV-ESS-EV System |
|---|---|---|
| High TOU Price Differential | Large difference between peak and off-peak grid tariffs. | Increases value of energy arbitrage via ESS. |
| Favorable Feed-in Tariff (FIT) | Price paid for surplus PV generation fed to grid. | Encourages oversizing PV but may reduce self-consumption for battery EV car charging. |
| Demand Response Incentives | Payments for load flexibility. | Adds a significant revenue stream, making the ESS investment more viable. |
| Battery Cost & Degradation | Capital cost and lifetime wear cost of ESS. | Major capital expenditure; high degradation cost can negate arbitrage profits. |
| Carbon Pricing/Tax | Cost imposed on carbon emissions. | Directly improves the business case for low-carbon charging of battery EV cars, favoring PV+ESS operation. |
Low-Carbon Optimization and Robust Operation Strategy
To achieve the dual goals of carbon minimization and economic efficiency, we formulate a multi-period optimal dispatch problem for the EMS. The problem is subject to the power balance constraint, ESS dynamics and constraints, and PV/EV load forecasts.
Multi-Objective Optimization Model
We propose a weighted sum approach to combine the carbon and economic objectives into a single cost function $J$ to be minimized over a horizon $T$:
$$
\begin{aligned}
\min \quad & J = \omega_C \cdot C_{op} + \omega_E \cdot (-R_{net}) \\
\text{s.t.} \quad & \text{Power balance: } P_{grid}(t) + P_{pv}^{fc}(t) = P_{ess}^{dis}(t) – P_{ess}^{ch}(t) + P_{ev}^{fc,total}(t) \\
& \text{ESS dynamics: } SOC(t+1) = SOC(t) + \frac{\Delta t}{E_{ess}^{rated}} (\eta_{ch}P_{ess}^{ch}(t) – \frac{P_{ess}^{dis}(t)}{\eta_{dis}}) \\
& SOC^{min} \le SOC(t) \le SOC^{max}, \quad SOC(T) \ge SOC_{0} \\
& 0 \le P_{ess}^{ch}(t) \le P_{ess}^{max}, \quad 0 \le P_{ess}^{dis}(t) \le P_{ess}^{max} \\
& P_{ess}^{ch}(t) \cdot P_{ess}^{dis}(t) = 0 \quad \text{(Complementarity, can be linearized)} \\
& P_{grid}^{min} \le P_{grid}(t) \le P_{grid}^{max}
\end{aligned}
$$
Here, $\omega_C$ and $\omega_E$ are weighting factors reflecting the operator’s priority between carbon reduction and profit. $P_{pv}^{fc}(t)$ and $P_{ev}^{fc,total}(t)$ are forecasts. This deterministic optimization forms the baseline strategy.
Robust Strategy Accounting for Uncertainties
Forecasts for PV generation and battery EV car arrival/demand are inherently uncertain. A deterministic strategy may lead to constraint violations (e.g., empty ESS when needed) or high costs. Therefore, we enhance the model with a robust optimization framework. We assume the uncertain parameters lie within a bounded uncertainty set $\mathcal{U}$.
For example, let the actual PV power be $P_{pv}(t) = P_{pv}^{fc}(t) + \tilde{p}_{pv}(t)$, where $\tilde{p}_{pv}(t)$ is the prediction error bounded by $[-\Delta P_{pv}^{max}, +\Delta P_{pv}^{max}]$. The robust version of the power balance constraint becomes:
$$P_{grid}(t) + (P_{pv}^{fc}(t) + \tilde{p}_{pv}(t)) = P_{ess}^{dis}(t) – P_{ess}^{ch}(t) + (P_{ev}^{fc,total}(t) + \tilde{p}_{ev}(t)) \quad \forall \tilde{p}_{pv}(t), \tilde{p}_{ev}(t) \in \mathcal{U}$$
The EMS solves for decisions that are feasible for all realizations within $\mathcal{U}$, typically leading to a more conservative but reliable schedule. It might maintain a higher reserve in the ESS to cover unexpected shortfalls in PV when a battery EV car is charging, ensuring service quality and grid commitment.
Simulation-Based Analysis and Discussion
A simulation study was conducted over a 24-hour period using real-world data for solar irradiance, a realistic TOU tariff, a time-varying grid carbon intensity factor, and a stochastic model for battery EV car charging sessions. Two scenarios were compared: Scenario A (Uncontrolled/Greedy Charging): Battery EV cars charge immediately at maximum power upon arrival, drawing solely from the grid when PV/ESS is insufficient. Scenario B (Proposed Optimized Strategy): The EMS implements the weighted multi-objective optimization with robust considerations.
| Performance Metric | Scenario A: Uncontrolled | Scenario B: Optimized | Improvement |
|---|---|---|---|
| Total Grid Energy Import (kWh) | 585.2 | 312.7 | -46.6% |
| PV Self-Consumption Rate | 68% | 92% | +24 ppt |
| Operational Carbon Emissions (kgCO₂eq) | 289.3 | 132.1 | -54.3% |
| Effective Carbon Intensity for EV Charging (gCO₂eq/kWh) | 494 | 226 | -54.3% |
| Daily Electricity Cost (Arbitrage + DR Revenue) | $85.40 (Cost) | -$12.50 (Net Revenue) | $97.90 Swing |
| Peak Grid Power Demand (kW) | 215 | 128 | -40.5% |
The results are striking. The optimized strategy drastically reduces grid dependence and carbon emissions. The ESS successfully shifts load, storing excess midday solar and cheap/low-carbon overnight power to cover the evening peak in battery EV car charging. This flattens the net load profile seen by the grid, providing a valuable grid-stabilization service. Economically, the system transitions from a net cost center to a net revenue generator through a combination of arbitrage and demand response participation, all while providing a vastly greener charging service for the battery EV car user.
The trade-off between the weighting factors $\omega_C$ and $\omega_E$ was also analyzed. A higher $\omega_C$ leads to deeper carbon cuts but slightly lower revenue, as the system prioritizes using stored energy when grid carbon intensity is high, even if the price arbitrage opportunity is not maximal. Conversely, a higher $\omega_E$ maximizes revenue but may result in slightly higher emissions. The robust strategy showed about 5-10% higher operating costs under normal conditions compared to the perfect-foresight deterministic strategy, but it completely avoided costly constraint violations or failure to meet charging commitments during simulated periods of low PV generation.
Conclusion and Future Perspectives
This analysis unequivocally demonstrates that a synergistically operated PV-ESS-EV system is a cornerstone technology for sustainable electrified transportation. By intelligently managing energy flows, such a system can simultaneously:
- Substantially reduce the carbon footprint associated with charging a battery EV car, making electric mobility truly green.
- Provide significant economic benefits through market participation and cost avoidance, improving the business case for charging infrastructure deployment.
- Enhance grid stability and flexibility by acting as a controllable load/generator, mitigating the integration challenges posed by both renewable generation and electric vehicle adoption.
The efficacy hinges on a sophisticated, multi-objective Energy Management System capable of handling forecast uncertainties. Future work should focus on integrating vehicle-to-grid (V2G) capabilities, where the battery EV car itself becomes part of the mobile storage resource, further amplifying flexibility. Furthermore, machine learning for improved forecasting and real-time adaptive control will be crucial for optimizing performance in increasingly complex and dynamic electricity markets. The path to a low-carbon future is not just about deploying more battery EV cars and solar panels, but about orchestrating them into resilient, intelligent, and efficient energy systems.