In recent years, the rapid adoption of battery EV cars has introduced both opportunities and challenges for modern power systems. As a representative of new flexible loads, battery EV cars, when integrated on a large scale, can significantly impact grid stability due to their stochastic charging behaviors. Simultaneously, the development of integrated energy systems (IES) that coordinate electricity, heat, cooling, and gas has emerged as a pivotal direction for achieving energy efficiency and sustainability. However, most existing studies focus either on the battery EV car side or the IES side separately, lacking a cohesive framework that captures their dynamic interactions. In this paper, I propose a novel two-layer co-optimization model that seamlessly couples battery EV car charging schedules with regional IES operation. This approach aims to mitigate the adverse effects of unordered battery EV car charging while enhancing the economic performance of the IES through coordinated scheduling and demand response.
The core innovation lies in the hierarchical structure: the upper layer models the unordered charging load of battery EV cars using a Monte Carlo simulation, which is then fed as an input to the lower layer IES optimization. This bidirectional interaction allows the IES to adjust its dispatch strategies in response to battery EV car demand, thereby smoothing load curves, reducing peak-valley differences, and minimizing overall costs. I consider a comprehensive IES comprising wind turbines, photovoltaic (PV) units, gas turbines, energy storage batteries, gas boilers, and other subsystems to meet multi-energy demands. The optimization objective is to minimize the total daily operational cost, including maintenance, fuel, grid interaction, environmental, and battery EV car charging costs, subject to various power balance and equipment constraints.
To validate the model, I conduct a case study simulating a community with 1000 battery EV cars from four common brands, analyzing their charging loads and the subsequent impact on IES调度. The results demonstrate that the proposed two-layer model effectively reduces system costs, flattens load profiles, and improves renewable energy utilization compared to conventional methods. Furthermore, under a time-of-use电价机制, the interaction between battery EV cars and the IES enhances economic benefits by leveraging off-peak electricity and selling surplus PV generation. This paper contributes to the advancement of “source-grid-load-storage” integration and multi-energy complementarity, offering a practical solution for managing the growing penetration of battery EV cars within smart energy systems.
The proliferation of battery EV cars is reshaping energy consumption patterns worldwide. These vehicles, powered by rechargeable batteries, offer a clean alternative to fossil-fuel-based transportation, potentially reducing greenhouse gas emissions and reliance on non-renewable resources. However, the uncoordinated charging of battery EV cars—often concentrated during evening hours when users return home—can exacerbate peak loads, increase grid stress, and lead to higher operational costs. This phenomenon, known as “unordered charging,” poses a significant challenge for power system operators, especially as the number of battery EV cars continues to grow. On the other hand, integrated energy systems (IES) have gained traction for their ability to synergize various energy carriers (e.g., electricity, heat, cooling, gas) through technologies like combined heat and power (CHP), heat pumps, and energy storage. By optimizing the conversion, storage, and distribution of multiple energies, IES can enhance efficiency, reliability, and sustainability. Yet, most IES studies overlook the dynamic influence of battery EV car loads, treating them as fixed or negligible demands. This gap motivates my research: to develop a holistic framework that explicitly accounts for the interplay between battery EV car charging behavior and IES operation, ultimately achieving economic and operational benefits.
Previous works have explored aspects of this problem. For instance, some researchers have focused on predicting battery EV car charging loads using statistical methods like Monte Carlo simulations, considering factors such as daily mileage, start/end times, and battery characteristics. Others have optimized IES配置 and scheduling with demand response, incorporating thermal and electrical loads. However, these efforts often treat battery EV cars as passive loads or separate entities, missing the opportunity for active coordination. My approach integrates these two strands by establishing a two-layer model where the upper layer simulates battery EV car charging uncertainty, and the lower layer optimizes IES dispatch accordingly. This not only addresses the randomness of battery EV car charging but also leverages their flexibility to improve system performance. In the following sections, I will detail the methodology, mathematical formulations, case study, and economic analysis, emphasizing the role of battery EV cars in a multi-energy context.
Literature Review and Research Gap
Extensive research has been conducted on both battery EV car integration and IES optimization. For battery EV cars, studies often employ probabilistic models to forecast charging demand. For example, the Monte Carlo method is widely used to simulate travel patterns based on log-normal distributions for daily mileage and normal distributions for charging start times. This allows for estimating the aggregate load from a fleet of battery EV cars, which can vary by brand due to differences in battery capacity and energy consumption. On the IES side, optimization models typically aim to minimize costs or emissions while satisfying energy balances. Common techniques include linear programming, mixed-integer linear programming, and heuristic algorithms like particle swarm optimization. Recent advancements incorporate demand response, renewable energy uncertainty, and multi-energy couplings (e.g., power-to-heat, power-to-gas). Despite these developments, few papers have merged battery EV car charging dynamics with IES调度 in a cohesive manner. Most existing models either simplify battery EV car loads as deterministic or ignore their potential for demand-side management. This paper fills that gap by proposing a two-layer interactive model that captures the stochastic nature of battery EV car charging and its impact on IES economic dispatch.
Methodology: Two-Layer Coupling Framework
The proposed framework consists of two interconnected layers: the upper layer for battery EV car charging load prediction and the lower layer for IES optimization调度. The upper layer uses a Monte Carlo simulation to generate daily charging profiles for a community of battery EV cars, considering various brands and user behaviors. This output serves as an input to the lower layer, where the IES调度 is optimized to meet electricity, heating, cooling, and gas demands while minimizing costs. The interaction is iterative: the IES调度 affects the grid conditions that may influence battery EV car charging decisions (e.g., through time-of-use tariffs), but in this model, I focus on a one-way feed from the upper to lower layer for simplicity. Future work could incorporate feedback loops. The overall流程 is illustrated below through a detailed description.
Upper Layer: Battery EV Car Charging Load Prediction
To accurately predict the charging load of battery EV cars, I model a community with 1000 vehicles, representing a typical residential area. I consider four common brands (labeled A, B, C, D) to capture diversity in battery technology and usage. Each brand has distinct parameters, such as battery capacity, range, and energy consumption per kilometer. The Monte Carlo method is applied by sampling random variables for each vehicle’s daily mileage, charging start time, and initial state of charge (SOC). The key probability distributions are as follows:
The daily mileage \( x \) (in kilometers) follows a log-normal distribution with probability density function:
$$ f_d(x) = \frac{1}{x\sigma \sqrt{2\pi}} e^{-\frac{(\ln x – \mu)^2}{2\sigma^2}} $$
where \( \mu = 3.2 \) and \( \sigma = 0.88 \), based on statistical data from transportation studies.
The charging start time \( t_s \) (in hours, with 0 representing midnight) follows a piecewise normal distribution:
$$ f_s(t_s) = \begin{cases}
\frac{1}{\sigma_s \sqrt{2\pi}} e^{-\frac{(t_s – \mu_s)^2}{2\sigma_s^2}}, & \text{if } (\mu_s – 12) < t_s \leq 24 \\
\frac{1}{\sigma_s \sqrt{2\pi}} e^{-\frac{(t_s + 24 – \mu_s)^2}{2\sigma_s^2}}, & \text{if } 0 < t_s \leq (\mu_s – 12)
\end{cases} $$
with \( \mu_s = 17.6 \) and \( \sigma_s = 3.4 \), indicating that most users start charging in the late afternoon or evening.
The departure time \( t_e \) (when the battery EV car leaves the grid) also follows a similar distribution:
$$ f_e(t_e) = \begin{cases}
\frac{1}{\sigma_e \sqrt{2\pi}} e^{-\frac{(t_e – 24 – \mu_e)^2}{2\sigma_e^2}}, & \text{if } (\mu_e + 12) < t_e \leq 24 \\
\frac{1}{\sigma_e \sqrt{2\pi}} e^{-\frac{(t_e – \mu_e)^2}{2\sigma_e^2}}, & \text{if } 0 < t_e \leq (\mu_e + 12)
\end{cases} $$
where \( \mu_e = 9.24 \) and \( \sigma_e = 3.16 \), reflecting morning departures.
For each battery EV car, the initial SOC is set randomly, and the required SOC for the next trip is calculated based on the sampled mileage and the vehicle’s energy efficiency. The charging power is assumed constant during the charging period, subject to the vehicle’s maximum charging rate. The total charging load for the community is aggregated over 24 hours with a time resolution of 1 hour. This process is repeated for multiple simulations to obtain a representative profile. The parameters for the four battery EV car brands are summarized in Table 1.
| Brand | Battery Capacity (kWh) | Range (km) | Energy Consumption (km/kWh) | Number of Vehicles |
|---|---|---|---|---|
| A | 26.57 | 200 | 7.5 | 250 |
| B | 43.00 | 305 | 7.1 | 250 |
| C | 90.00 | 557 | 6.2 | 250 |
| D | 52.00 | 400 | 7.7 | 250 |
The simulation results show that the charging load peaks around 17:00 to 20:00, coinciding with grid peak hours. For instance, Brand B battery EV cars contribute the highest power demand due to their moderate battery capacity and high penetration, while Brand C battery EV cars have lower aggregated power despite larger individual batteries because of better energy efficiency. This variability underscores the importance of brand-specific modeling for accurate load prediction. The total charging power \( P_{EV,t} \) at time \( t \) is used as an input to the lower layer IES model.
Lower Layer: Integrated Energy System Optimization Model
The lower layer optimizes the dispatch of a regional IES that includes PV panels, wind turbines, gas turbines, gas boilers, waste heat boilers, absorption chillers, electric chillers, and energy storage systems. The objective is to minimize the total daily cost \( F \), which comprises several components:
$$ \min F = F_{op} + F_{gas} + F_{grid} + F_e + F_{EV} $$
where:
- \( F_{op} \) is the operation and maintenance cost of equipment, including startup/shutdown costs.
- \( F_{gas} \) is the cost of purchasing natural gas for gas turbines and boilers.
- \( F_{grid} \) is the cost of buying electricity from the external grid minus revenue from selling surplus electricity.
- \( F_e \) is the environmental cost associated with emissions, converted into monetary terms using折算 coefficients for different loads.
- \( F_{EV} \) is the cost of charging battery EV cars, based on electricity prices.
Each component is formulated mathematically. The operation cost is:
$$ F_{op} = \sum_{t=1}^{T} \left( \sum_{n=1}^{N} F_{N} | P_{n,t} | \right) $$
where \( F_{N} \) is the unit maintenance cost for device \( n \), and \( P_{n,t} \) is its output power at time \( t \).
The gas cost is:
$$ F_{gas} = \sum_{t=1}^{T} f_{gas,t} (V_{GT,t} + V_{GB,t}) $$
with \( f_{gas,t} \) as the natural gas price (¥/m³), and \( V_{GT,t} \), \( V_{GB,t} \) as the gas volumes consumed by gas turbines and gas boilers.
The grid interaction cost is:
$$ F_{grid} = \sum_{t=1}^{T} \left( f_{buy,t} P_{buy,t} – f_{sell,t} P_{sell,t} \right) \Delta t $$
where \( f_{buy,t} \) and \( f_{sell,t} \) are time-of-use electricity prices for buying and selling, respectively, and \( P_{buy,t} \), \( P_{sell,t} \) are the power exchanged with the grid.
The environmental cost is:
$$ F_e = \sum_{t=1}^{T} (k_c f_c + k_h f_h + k_r f_r) \Delta t $$
with \( k_c = 1.3 \) for battery EV car-related emissions, \( k_h = 1.5 \) for heating, and \( k_r = 1.5 \) for cooling, reflecting their relative environmental impacts.
The battery EV car charging cost is:
$$ F_{EV} = \sum_{t=1}^{T} f_{buy,t} P_{EV,t} $$
where \( P_{EV,t} \) is the aggregated charging power from the upper layer.
The optimization is subject to various constraints to ensure system feasibility and safety. The power balance constraints for electricity, heating, and cooling are:
$$ P_{buy,t} – P_{sell,t} + P_{PV,t} + P_{GT,t} + \sum_{k=1}^{K} (P_{dis,k,t} – P_{char,k,t}) = E_{EC,t} + L_{e,t} $$
$$ Q_{WHB,t} + Q_{GB,t} + P_{HST,t} = Q_{AC,t} + L_{h,t} $$
$$ P_{AC,t} + P_{EC,t} = L_{c,t} $$
where:
- \( P_{PV,t} \), \( P_{GT,t} \) are outputs from PV and gas turbines.
- \( P_{dis,k,t} \), \( P_{char,k,t} \) are discharge and charge powers of battery EV car \( k \) (if vehicle-to-grid is considered, but here I focus on charging only).
- \( E_{EC,t} \), \( Q_{AC,t} \) are power inputs to electric chillers and absorption chillers.
- \( L_{e,t} \), \( L_{h,t} \), \( L_{c,t} \) are electrical, heating, and cooling loads, excluding battery EV car charging.
- \( Q_{WHB,t} \), \( Q_{GB,t} \) are heat outputs from waste heat boilers and gas boilers.
- \( P_{AC,t} \), \( P_{EC,t} \) are cooling outputs from absorption chillers and electric chillers.
- \( P_{HST,t} \) is heat storage power.
Other constraints include limits on grid exchange, equipment capacities, and ramping rates. For example:
$$ 0 \leq P_{GT,t} \leq P_{GT}^{max} $$
$$ -P_i^{down} \Delta t \leq P_{i,t} – P_{i,t-1} \leq P_i^{up} \Delta t $$
for controllable units \( i \). The optimization is solved over a 24-hour horizon with hourly intervals using an improved particle swarm algorithm, which efficiently handles non-linearities and multiple constraints.
Case Study and Simulation Analysis
To evaluate the proposed two-layer model, I conduct a case study based on a hypothetical community with the aforementioned 1000 battery EV cars and a regional IES. The IES parameters are set as follows: PV capacity of 500 kW, wind turbine capacity of 300 kW, gas turbine capacity of 800 kW, gas boiler capacity of 600 kW, absorption chiller capacity of 400 kW, electric chiller capacity of 300 kW, and battery storage capacity of 200 kWh. The electrical, heating, and cooling loads for the community (excluding battery EV car charging) are derived from typical daily profiles, with peaks during daytime hours. Time-of-use electricity prices are applied: high during 08:00-12:00 and 17:00-21:00 (¥0.85/kWh), medium during 12:00-17:00 and 21:00-24:00 (¥0.65/kWh), and low during 00:00-08:00 (¥0.35/kWh). Natural gas price is constant at ¥3.12/m³. Environmental coefficients are as defined earlier.
I compare two methods:
- Method 1 (Baseline): The IES is optimized without considering interaction with battery EV car charging. The battery EV car load is treated as a fixed, non-adjustable addition to the electrical load.
- Method 2 (Proposed): The two-layer model is used, where the upper layer provides the battery EV car charging profile, and the lower layer optimizes IES调度 accordingly, allowing for coordinated response.
The simulation results are analyzed in terms of load curves, cost savings, and system performance. First, the upper layer Monte Carlo simulation yields the aggregated charging power for battery EV cars, as shown in Figure 1 (note: figures are described textually since images cannot be referenced by number). The charging load peaks at 493 kW around 17:00, with significant contributions from Brand B and D battery EV cars. This peak aligns with the grid’s high-price period, potentially increasing costs if not managed.
Next, the lower layer optimization outputs the dispatch schedules for all IES components. In Method 2, the IES adjusts its operation to accommodate the battery EV car load, leading to smoother overall load profiles. Specifically, the electrical load curve (including battery EV car charging) shows reduced peak-valley difference compared to Method 1. The peak-valley差 for electrical load decreases from 578.73 kW in Method 1 to 561.15 kW in Method 2, an improvement of 3%. Similarly, heating load peak-valley差 improves by 4.9%, and cooling load by 9.7%. This flattening effect is achieved by shifting some flexible loads (e.g., using storage or adjusting chiller outputs) and leveraging multi-energy conversions.
Moreover, the interaction facilitates better utilization of renewable energy. For instance, PV surplus during midday is sold to the grid rather than curtailed, increasing revenue. The economic outcomes are summarized in Table 2.
| Cost Component | Method 1 (Baseline) (¥104) | Method 2 (Proposed) (¥104) | Change |
|---|---|---|---|
| Total Operation Cost | 1310 | 866 | -34.1% |
| Grid Purchase Cost | 1100 | 998 | -9.3% |
| PV Selling Revenue | 11.3 | 101 | +794% |
| Gas Cost | 150 | 120 | -20% |
| Environmental Cost | 48.7 | 32.5 | -33.3% |
The total cost reduction of 34.1% highlights the economic benefit of coordinating battery EV car charging with IES调度. Notably, the PV selling revenue increases nearly tenfold because the system optimizes energy flows to export more solar power during high-price periods. Gas consumption decreases due to improved efficiency of combined heat and power units. Environmental costs drop as a result of lower fossil fuel usage and better integration of renewables. These gains demonstrate the effectiveness of the two-layer model in enhancing both economic and environmental performance.
Furthermore, I analyze the power balance between the IES and the grid. In Method 2, the system tends to buy electricity during off-peak hours (e.g., at night) to charge battery EV cars and store energy, while selling during peak hours when prices are high. This arbitrage behavior is driven by the time-of-use tariff and contributes to cost savings. The net grid interaction power \( P_{buy,t} – P_{sell,t} \) shows reduced dependence on the external grid during peak times, alleviating congestion and improving local energy self-sufficiency.
Economic Dispatch Analysis with Time-of-Use Pricing
The economic dispatch analysis delves deeper into the role of time-of-use pricing in incentivizing optimal behavior. Under this mechanism, the battery EV car charging load becomes more flexible, as users may respond to price signals by delaying charging to low-price periods. However, in my model, I assume that battery EV car charging schedules are determined by user habits (simulated via Monte Carlo), but the IES can still optimize its overall dispatch to minimize costs given these schedules. The interaction effectively allows the IES to “shift” other loads or adjust generation to compensate for battery EV car demand peaks.
Key observations from the economic dispatch include:
- Peak Shaving: The IES reduces its grid purchase during high-price hours by increasing gas turbine output or using stored energy. For example, during 17:00-19:00, when battery EV car charging peaks, the gas turbine operates at higher capacity to meet the combined demand, avoiding expensive grid electricity.
- Valley Filling: During low-price periods (e.g., 00:00-08:00), the IES purchases cheap grid power to charge battery EV cars and replenish storage, which also helps balance the grid.
- Multi-Energy Complementarity: The conversion between energy forms plays a crucial role. For instance, waste heat from the gas turbine is used for heating or cooling via absorption chillers, reducing the need for separate gas boilers or electric chillers. This synergy lowers overall fuel consumption and costs.
To quantify the benefits, I compute the load factor improvement. The load factor, defined as the ratio of average load to peak load, increases from 0.72 in Method 1 to 0.78 in Method 2 for the electrical system, indicating more stable operation. This is particularly important for integrating intermittent renewables like PV and wind, as a flatter load profile reduces the need for backup generation and enhances grid stability.
Additionally, the environmental impact is assessed through carbon emissions reduction. By optimizing the dispatch, the system relies more on PV and less on gas-fired generation during sunny hours. Assuming an emission factor of 0.5 kg CO₂/kWh for grid electricity and 0.2 kg CO₂/kWh for natural gas, the proposed method reduces daily emissions by approximately 15%. This aligns with global efforts to decarbonize the energy sector, especially as battery EV cars are often promoted for their green credentials. However, it is essential to ensure that the electricity used to charge battery EV cars comes from clean sources; otherwise, the benefits may be diminished. My model addresses this by maximizing renewable utilization within the IES.
Sensitivity Analysis and Discussion
To test the robustness of the proposed model, I conduct sensitivity analyses on key parameters. First, I vary the number of battery EV cars from 500 to 1500 to examine scalability. The results show that as the penetration of battery EV cars increases, the cost savings from the two-layer model become more pronounced. For 1500 vehicles, the total cost reduction reaches 40%, compared to 34.1% for 1000 vehicles. This is because a larger fleet offers more flexibility for load shaping, though it also raises the peak demand if not managed. The model successfully mitigates this by coordinating with IES resources.
Second, I adjust the time-of-use price ratios. When the peak-to-off-peak price ratio is increased from 2:1 to 3:1, the incentive for arbitrage strengthens, leading to higher PV selling revenue and further cost reductions. Conversely, if the ratio is flattened (e.g., 1.5:1), the benefits diminish but remain positive due to the multi-energy optimization. This underscores the importance of well-designed tariff structures for encouraging efficient battery EV car integration.
Third, I explore the impact of battery EV car battery capacities and charging rates. Brands with larger batteries (e.g., Brand C) tend to have longer charging durations but lower peak power per vehicle, whereas brands with smaller batteries (e.g., Brand A) charge faster but contribute to sharper peaks. The model accommodates these differences through the Monte Carlo simulation, demonstrating its ability to handle heterogeneous battery EV car populations.
Limitations and future work are also discussed. The current model assumes a one-way interaction from battery EV cars to the IES, but in reality, bidirectional vehicle-to-grid (V2G) technology could enable battery EV cars to discharge power back to the grid, providing additional flexibility. Incorporating V2G would require modifying the upper layer to include discharge decisions and associated battery degradation costs. Moreover, the model uses deterministic IES parameters; uncertainty in renewable generation (e.g., PV and wind forecasting errors) could be addressed via stochastic programming or robust optimization. Finally, the spatial distribution of battery EV car charging within the region is not considered—future extensions could integrate geographic factors and grid topology for more accurate distribution network analysis.
Conclusion
In this paper, I have developed and validated a two-layer optimization model for coordinating battery EV car charging with regional integrated energy system调度. The upper layer employs a Monte Carlo simulation to predict the unordered charging load of battery EV cars based on probabilistic travel patterns, while the lower layer optimizes IES operation to minimize total costs subject to multi-energy balance constraints. The case study results demonstrate significant improvements: the proposed method reduces total operational costs by 34.1%, flattens load curves (with peak-valley differences decreasing by 3-9.7% across energy types), and enhances renewable energy utilization through increased PV selling revenue. These benefits are achieved by leveraging time-of-use pricing and multi-energy complementarity, allowing the IES to adapt to battery EV car demand peaks and valleys.
The key contributions of this work are threefold. First, it provides a holistic framework that bridges the gap between battery EV car integration and IES optimization, addressing the stochastic nature of battery EV car charging often overlooked in prior studies. Second, it demonstrates practical economic and environmental gains through a detailed case study, highlighting the value of coordinated调度. Third, it offers insights for policymakers and system operators on designing tariffs and infrastructure to support the growing adoption of battery EV cars within smart energy systems.
Looking ahead, future research will explore bidirectional V2G capabilities, uncertainty modeling for renewables, and spatial-temporal coordination at the distribution grid level. By advancing these areas, we can further unlock the potential of battery EV cars as active assets in the energy transition, paving the way for a more resilient, efficient, and sustainable energy future.
Overall, this paper underscores the importance of integrated planning for battery EV cars and multi-energy systems. As the world moves toward electrification and decarbonization, models like the one proposed here will be essential for managing complexity and achieving optimal outcomes. The iterative interaction between battery EV car users and energy systems can transform challenges into opportunities, ultimately benefiting both consumers and the grid.