The rapid global proliferation of electric cars represents a significant dual challenge for modern power systems: a substantial new source of electrical load and a potentially vast, distributed energy storage resource. As the penetration of electric cars accelerates annually, urban distribution networks face unprecedented strain during peak hours while simultaneously holding a key to a more flexible and resilient grid. The paradigm of Vehicle-to-Grid (V2G) technology, which enables bidirectional power flow between the electric car battery and the grid, transforms these vehicles from passive loads into active, controllable grid assets. This capability is crucial for supporting the integration of intermittent renewable energy sources, such as rooftop photovoltaic (PV) systems, and for optimizing the economic and technical operation of localized energy areas, like commercial or residential building complexes.
The core opportunity lies in leveraging the inherent flexibility and storage capacity of electric car batteries. When aggregated, a fleet of electric cars can provide significant demand response services, shifting their charging load away from peak periods and even injecting stored energy back into the grid during times of high demand or low renewable generation. To fully unlock this potential, sophisticated coordination strategies are required. This article, from my research perspective, proposes a multi-objective optimization framework for scheduling electric cars within a V2G-operated area. The goal is to create a dispatch strategy that can intelligently balance competing objectives—primarily minimizing operational costs and maximizing the smoothness of the net load profile—by dynamically adjusting the charging and discharging behavior of electric cars and supporting stationary storage.
The operational area under consideration is a semi-autonomous microgrid-like environment, typically a building complex. It comprises the following entities:
- The Building Load: The conventional, largely inflexible electricity demand from the premises.
- Rooftop Photovoltaic (PV) Generation: A local renewable energy source whose output is stochastic and time-dependent.
- Stationary Battery Energy Storage System (BESS): A dedicated storage device for additional flexibility.
- A Fleet of Electric Cars: The primary flexible resource, each equipped with V2G capability.
- The External Grid: Provides backup power and establishes energy prices through a Time-of-Use (ToU) tariff.
The central challenge is to coordinate the energy flows among these entities over a scheduling horizon (e.g., 24 hours) to achieve optimal performance according to defined goals.
1. Modeling the V2G Operation Area
Accurate mathematical models for each component are the foundation of any effective optimization strategy.
1.1 Electric Car Aggregation Model
The behavior of each individual electric car is modeled stochastically to reflect real-world usage patterns. The arrival time \( t_{arr} \) and departure time \( t_{dep} \) for an electric car are assumed to follow normal distributions:
$$f(t_x) = \frac{1}{\sigma\sqrt{2\pi}} \exp\left(-\frac{(t_x – \mu)^2}{2\sigma^2}\right)$$
where \( t_x \) represents either \( t_{arr} \) or \( t_{dep} \), \( \mu \) is the mean arrival/departure time, and \( \sigma^2 \) is the variance. The initial State of Charge (SOC) of the battery upon arrival, \( SOC_{init} \), is modeled using an exponential distribution, reflecting the likelihood of drivers arriving with a partially depleted battery:
$$f(SOC_{init}) = \lambda \exp(-\lambda \cdot SOC_{init})$$
Each electric car \( i \) during time interval \( t \) can be in one of three states: charging (\( P^{EV}_{CHG} \)), discharging (\( P^{EV}_{DIS} \)), or idle (\( P^{EV}_{NO}=0 \)). This is enforced using binary variables:
$$P^{EV}_{i,t} = \alpha^{EV}_{i,t} P^{EV}_{DIS} + \beta^{EV}_{i,t} P^{EV}_{CHG} + \gamma^{EV}_{i,t} P^{EV}_{NO}$$
$$P^{EV}_{DIS} = – P^{EV}_{CHG}$$
$$ \alpha^{EV}_{i,t} + \beta^{EV}_{i,t} + \gamma^{EV}_{i,t} = 1; \quad \alpha^{EV}_{i,t}, \beta^{EV}_{i,t}, \gamma^{EV}_{i,t} \in \{0,1\}$$
The dynamics of the battery’s State of Charge (SOC) are governed by:
$$SOC^{EV}_{i,t} = SOC^{EV}_{i,t-1} + \frac{P^{EV}_{i,t} \cdot \eta^{EV}_{i} \cdot \Delta t}{E^{EV}_{i,rated}}$$
where \( \eta^{EV}_{i} \) is the charging/discharging efficiency (accounting for losses), \( \Delta t \) is the time interval length, and \( E^{EV}_{i,rated} \) is the battery’s rated capacity. The electric car must meet the driver’s mobility requirement, expressed as a target SOC at departure:
$$SOC^{EV}_{i,departure} \geq SOC^{EV}_{i, target}$$
Furthermore, the SOC is constrained within safe operational limits: \( SOC^{EV}_{min} \leq SOC^{EV}_{i,t} \leq SOC^{EV}_{max} \).
1.2 Stationary Storage (BESS) Model
The BESS provides complementary flexibility. Its SOC update equation is:
$$SOC^{BESS}_{t} = SOC^{BESS}_{t-1} + \frac{P^{BESS}_{t} \cdot \eta^{BESS} \cdot \Delta t}{E^{BESS}_{rated}}$$
Its power output is bounded by its rated charge and discharge power: \( P^{BESS}_{disch, max} \leq P^{BESS}_{t} \leq P^{BESS}_{ch, max} \). Similar to the electric car, its SOC is kept within limits, and it may have a target SOC at the end of the scheduling period for cyclical operation.
1.3 Rooftop PV Generation Model
The power output of the rooftop PV system at time \( t \) is calculated based on solar irradiance:
$$P^{PV}_{t} = \eta_{PV} \cdot A_{PV} \cdot f_{shading} \cdot f_{temp} \cdot G_{t}$$
where \( \eta_{PV} \) is the panel efficiency, \( A_{PV} \) is the total area, \( f_{shading} \) and \( f_{temp} \) are loss factors, and \( G_{t} \) is the solar irradiance. The output is naturally constrained by \( 0 \leq P^{PV}_{t} \leq P^{PV}_{rated} \).
1.4 System Power Balance
The fundamental constraint ensuring stable operation is the real-time power balance within the area. The net power \( P^{net}_{t} \) that must be imported from (or exported to) the external grid is:
$$P^{net}_{t} = P^{Building}_{t} – P^{PV}_{t} + \sum_{i=1}^{N_{EV}} P^{EV}_{i,t} + P^{BESS}_{t}$$
A positive \( P^{net}_{t} \) indicates power import, while a negative value indicates power export back to the grid.
2. Multi-Objective Optimization Framework
The innovation of the proposed strategy lies in its explicit multi-objective formulation. We aim not for a single “best” solution, but for a strategy that can navigate the trade-off between economic efficiency and grid-supportive “responsiveness.” This is achieved by defining three cost components.
2.1 Definition of Cost Objectives
Objective 1: Total Operational Cost (\( F_1 \)). This represents the direct, tangible costs of operating the V2G area. It includes the cost of purchasing electricity from the grid and the degradation cost incurred by electric car batteries due to V2G cycling.
$$F_1 = \sum_{t=1}^{T} \left( C^{grid}_{t} + \sum_{i=1}^{N_{EV}} C^{deg}_{i,t} \right)$$
where \( C^{grid}_{t} = p^{ToU}_{t} \cdot P^{net}_{t} \cdot \Delta t \) for \( P^{net}_{t} > 0 \), with \( p^{ToU}_{t} \) being the Time-of-Use price. The battery degradation cost for electric car \( i \) in period \( t \) is modeled as proportional to the absolute energy throughput and the unit replacement cost:
$$C^{deg}_{i,t} = \frac{c^{EV}_{coeff}}{100} \cdot \frac{|SOC^{EV}_{i,t} – SOC^{EV}_{i,t-1}| \cdot E^{EV}_{i,rated}}{E^{EV}_{i,rated}} \cdot C^{replace}_{i}$$
Objective 2: Load Profile Variance Cost (\( F_2 \)). This objective aims to “flatten” the net load profile \( P^{net}_{t} \) seen by the external grid. A flatter profile reduces stress on distribution infrastructure and improves overall system stability. It is quantified as the variance of the net load around its mean \( \overline{P^{net}} \):
$$F_2 = \sum_{t=1}^{T} \left( P^{net}_{t} – \overline{P^{net}} \right)^2$$
Objective 3: Peak-to-Valley Difference Cost (\( F_3 \)). This is a more aggressive form of load smoothing, directly targeting the reduction of the difference between the maximum and minimum net load during the scheduling period. This is crucial for peak shaving.
$$F_3 = \max_{t}(P^{net}_{t}) – \min_{t}(P^{net}_{t})$$
While \( F_1 \) is a monetary cost, \( F_2 \) and \( F_3 \) are technical performance metrics expressed in cost-equivalent units to enable a unified optimization.
2.2 Forming the Multi-Objective Function
The three objectives are combined into a single, scalar objective function using the weighted sum method. This requires normalization of each objective to a comparable scale (e.g., 0 to 1) to prevent dominance by one objective due to its magnitude. The composite objective function is:
$$F = \omega_1 \cdot \widetilde{F_1} + \omega_2 \cdot \widetilde{F_2} + \omega_3 \cdot \widetilde{F_3}$$
where \( \widetilde{F_1}, \widetilde{F_2}, \widetilde{F_3} \) are the normalized values of the original objectives, and \( \omega_1, \omega_2, \omega_3 \) are their respective weighting coefficients, with \( \omega_1 + \omega_2 + \omega_3 = 1 \).
The key to the proposed strategy is the dynamic interpretation of these weights. They are not fixed but are determined to reflect a desired operational “mode” or priority:
- Economy-Priority Mode: \( \omega_1 \) is set significantly higher than \( \omega_2 \) and \( \omega_3 \). The scheduler primarily seeks to minimize electricity costs and battery wear for the electric car fleet, with load smoothing as a secondary concern.
- Response-Priority Mode: \( \omega_2 \) and \( \omega_3 \) are given higher weights. The scheduler aggressively uses the electric car and BESS resources to flatten the net load, accepting potentially higher operational costs to provide greater grid support.
2.3 Determining Weights via the Analytic Hierarchy Process (AHP)
To systematically determine the weight vectors for different operational modes, the Analytic Hierarchy Process (AHP) is employed. AHP translates expert judgment on the relative importance of the three objectives into a consistent set of weights.
Step 1: Experts compare the objectives pairwise using a standard 1-9 scale (e.g., 1=equally important, 9=extremely more important) to form a judgment matrix \( \mathbf{A} \).
Step 2: Consistency Check. The consistency of each expert’s judgment matrix is verified. The Consistency Index (CI) is calculated:
$$CI = \frac{\lambda_{max} – n}{n – 1}$$
where \( \lambda_{max} \) is the principal eigenvalue of matrix \( \mathbf{A} \) and \( n=3 \) is the number of objectives. A CI value less than 0.1 indicates acceptable consistency. Matrices failing this check are discarded or revised.
Step 3: Weight Calculation. For each consistent judgment matrix, the weights are derived by normalizing the geometric mean of each row:
$$M_p = \left( \prod_{q=1}^{n} A_{pq} \right)^{1/n}, \quad \omega_p = \frac{M_p}{\sum_{p=1}^{n} M_p}$$
Step 4: Aggregation. The final weight vector for a specific mode (Economy or Response) is obtained by averaging the weights from all consistent experts who evaluated that particular priority.
The resulting weights for two distinct operational modes might be as shown in the table below.
| Operational Mode | ω₁ (Economic Cost) | ω₂ (Load Variance) | ω₃ (Peak-Valley Diff.) |
|---|---|---|---|
| Economy-Priority | 0.70 | 0.20 | 0.10 |
| Response-Priority | 0.40 | 0.40 | 0.20 |
3. Case Study and Simulation Analysis
To validate the proposed multi-objective strategy, a simulation case study is conducted for a V2G-operated commercial building area over a 24-hour scheduling horizon.
3.1 System Configuration and Parameters
The simulation scenario includes a building load profile, a 100 kW rooftop PV system, a 200 kWh / 100 kW BESS, and a fleet of 50 electric cars. The electric car parameters, including arrival/departure distributions and battery specifications, are based on typical statistical data. A Time-of-Use electricity price with distinct peak, off-peak, and valley periods is applied.
| Component | Key Parameter | Value / Distribution |
|---|---|---|
| Electric Car | Arrival Time | Normal(μ=8:00, σ=1.5h) |
| Departure Time | Normal(μ=18:00, σ=1.5h) | |
| Initial SOC | Exponential(λ=0.3) | |
| BESS | Capacity / Power | 200 kWh / 100 kW |
| PV System | Peak Capacity | 100 kW |
3.2 Simulation Results and Comparative Analysis
The optimization model is implemented as a Mixed-Integer Linear Programming (MILP) problem and solved using the CPLEX solver. Three scenarios are compared:
- Uncoordinated Charging (Baseline): Electric cars charge at maximum power immediately upon arrival.
- Proposed Strategy – Economy Mode: Uses the Economy-Priority weight vector.
- Proposed Strategy – Response Mode: Uses the Response-Priority weight vector.
Net Load Profile Analysis: The primary visual result is the 24-hour net load profile \( P^{net}_{t} \). Compared to the Uncoordinated baseline, which shows sharp peaks coinciding with electric car arrivals, both optimized modes achieve significant load flattening. The Response-Priority mode produces the flattest profile, actively using electric car discharge during the evening peak. The Economy-Priority mode also reduces peaks but shows more sensitivity to electricity prices, shifting load to the cheapest periods.
Quantitative Performance Metrics: The effectiveness is quantified using key indicators.
| Performance Metric | Uncoordinated | Economy Mode | Response Mode |
|---|---|---|---|
| Total Electricity Cost | $1,850 | $1,520 | $1,610 |
| Electric Car Degradation Cost | $0 | $45 | $85 |
| Total Op. Cost (F₁) | $1,850 | $1,565 | $1,695 |
| Net Load Std. Deviation | 125 kW | 78 kW | 52 kW |
| Peak-to-Valley Difference | 410 kW | 255 kW | 180 kW |
The results clearly demonstrate the trade-off managed by the multi-objective strategy:
- Economy-Priority Mode achieves the lowest total operational cost ($1,565), saving over 15% compared to the baseline. It reduces load variance and peak-to-valley difference substantially but not as aggressively as the other mode.
- Response-Priority Mode achieves the best technical performance, minimizing the standard deviation (52 kW) and peak-to-valley difference (180 kW) of the net load by over 50% compared to the baseline. This comes at the expense of a higher operational cost ($1,695) due to increased battery cycling costs for the electric car fleet, though it is still more economical than uncoordinated charging.
Electric Car SOC Trajectories: Examining the aggregate SOC of the electric car fleet reveals the different behaviors. In Economy Mode, charging is concentrated during low-price valley periods. In Response Mode, charging is more distributed, and deliberate discharging occurs during the price and grid load peak, clearly demonstrating the V2G capability being leveraged for grid support.
4. Conclusion and Discussion
The simulation results conclusively validate the proposed multi-objective demand response scheduling strategy for electric cars in V2G-operated areas. The framework successfully coordinates electric cars, stationary storage, and local PV generation to transform a cluster of electric cars from a grid challenge into a manageable, valuable asset. The core achievement is the strategy’s ability to flexibly navigate the inherent trade-off between economic efficiency and grid-supportive responsiveness by simply adjusting the weight coefficients in the objective function.
Key findings are:
- The V2G capability of the electric car is essential for achieving high levels of load flattening and peak shaving, as evidenced by the superior performance of the Response-Priority mode.
- A purely economic dispatch (implicit in Economy Mode) yields significant cost savings but leaves some grid-support potential untapped.
- The multi-objective approach, parameterized via a systematic method like AHP, allows the system operator or aggregator to select an operating point on the spectrum between these two poles based on real-time grid needs, electricity market conditions, or predefined contracts.
A critical factor for real-world adoption is the compensation mechanism for electric car owners. The degradation cost model incorporated here is a proxy for battery wear. For sustainable V2G participation, a pricing or incentive scheme must be designed so that the revenue from providing grid services outweighs this degradation cost and provides a net benefit to the owner. Future work will integrate such market mechanisms into the optimization framework and explore robust or stochastic methods to handle the uncertainty in PV generation and electric car user behavior more explicitly, further enhancing the practicality and resilience of the scheduling strategy for the ever-growing fleet of electric cars.