As a researcher focusing on the integration of transportation and distribution networks, I have dedicated my work to the energy-aware optimization scheduling of electric car charging. The global push for carbon neutrality has accelerated the adoption of electric cars, and the associated charging behavior is no longer a simple point-to-point energy supply problem. Instead, it becomes a coupled decision problem that spans traffic dynamics, renewable energy availability, user convenience, and grid stability. In this article, I present a comprehensive framework that captures the macroscopic traffic flow characteristics, microscopic vehicle dynamics, and multi-level charging coordination for electric cars with vehicle-to-grid (V2G) capability.
My research begins with the observation that traditional charging scheduling models treat the traffic network and the power distribution network as two independent systems. This assumption leads to suboptimal decisions for electric car users, because the actual travel time and energy consumption of an electric car are strongly affected by real-time traffic flow, road gradients, and congestion levels. In turn, the charging demand is disturbed in both time and space, causing inefficiencies in renewable energy utilization and grid operation. The purpose of my study is therefore to design a systematic scheduling mechanism that is aware of the energy consumption of electric cars at every road segment and that coordinates the charging decisions from the perspective of distribution system operation.
In the subsequent parts of this article, I will first discuss the energy consumption estimation algorithm that combines macroscopic traffic flow prediction with microscopic electric car dynamics. Then I will present a bi-level charging navigation model for a single electric car, followed by a three-layer scheduling framework that leverages the temporal and spatial flexibility of aggregated electric cars. I will also introduce the joint optimization algorithms, including Generalized Benders Decomposition with Logarithmic Barrier Functions and a PPO-ADMM hybrid solver. Finally, I will summarize key experimental results, tables, and insights that demonstrate the effectiveness of my approach in reducing charging costs, improving renewable energy utilization, and alleviating traffic congestion.
Macroscopic and Microscopic State Estimation for Electric Car Energy Consumption
Accurate estimation of the energy consumption of an electric car is the foundation of any charging navigation strategy. The energy required to travel along a given path depends not only on the static features of the road, such as length and gradient, but also on the dynamic traffic state, which changes minute by minute. The traffic flow speed directly affects the driving cycle of an electric car, influencing acceleration and deceleration events, which are responsible for a considerable share of the energy usage. I therefore develop a two-layered modeling procedure: the first layer predicts the macroscopic traffic flow speed by treating the road network as a graph and using a graph convolutional network with multi-head attention; the second layer calculates the tractive force and energy consumption using a longitudinal dynamics model of the vehicle.
To capture the spatial variation inside a long corridor, I discretize each urban link into small road units of length \(\Delta x = 100\ \text{m}\). This allows me to apply fluid dynamics conservation laws and compute macroscopic acceleration from local and convective components. The total acceleration \(A\) at road unit \(m\) and time step \(t\) is given by:
$$
A = A_{\mathrm{local}} + A_{\mathrm{conv}} = \frac{\partial V}{\partial t} + V\frac{\partial V}{\partial x}
$$
where \(V\) is the space-mean speed. Using finite difference schemes, the local and convective components are computed as:
$$
A_{\mathrm{local}} = \frac{V(m,t+1) – V(m,t)}{\Delta T}
$$
$$
A_{\mathrm{conv}} = \frac{V(m+1,t+1) – V(m,t)}{\Delta T}
$$
The graph convolutional network is used to predict future macro traffic speeds. The road network is represented as a graph \(\mathcal{G}=(\mathcal{V},\mathcal{E},W)\) where each node is a road micro-unit. At each time step the node features include historical speeds, volume, and network position. The hidden spatial features are obtained by the K-th order Chebyshev graph convolution:
$$
H^{(l+1)} = \sigma\left(\sum_{k=0}^{K} \Theta_k T_k(\tilde{L}) H^{(l)}\right)
$$
Temporal dynamics are captured by a temporal convolutional network with dilated causal convolutions, and a multi-head attention mechanism is placed on the output to strengthen important connections between road units and time lags. The final speed prediction is denoted as \(\hat{V}_t(x, t_0 + m^*\Delta T)\). This predicted speed is then used as an input to a microscopic energy consumption model.
In the microscopic view, I formulate the total longitudinal tractive force of an electric car as:
$$
F_{\mathrm{tot}} = F_{\mathrm{slope}} + F_{\mathrm{fric}} + F_{\mathrm{air}} + F_{\mathrm{acc}}
$$
In this formulation, \(F_{\mathrm{slope}} = M g \sin\beta\) accounts for the road gradient, \(F_{\mathrm{fric}} = M g f_r \cos\beta\) models tire rolling resistance, \(F_{\mathrm{air}} = \frac{1}{2} \rho C_D A_f V^2\) represents aerodynamic drag, and \(F_{\mathrm{acc}} = M \delta A\) is the inertial resistance associated with acceleration. Table 1 summarizes the major symbols used in this work.
| Symbol | Description | Typical value/unit |
|---|---|---|
| \(M\) | Mass of the electric car | 1600–1800 kg |
| \(C_D\) | Air drag coefficient | 0.284 |
| \(A_f\) | Frontal area | 1.7 m² |
| \(f_r\) | Rolling resistance coefficient | 1.2×10⁻² |
| \(\rho\) | Air density | 1.29 kg/m³ |
| \(\eta_m\) | Electric motor efficiency | 95% |
| \(\eta_e\) | Mechanical transmission efficiency | 96% |
| \(P_{aux}\) | Auxiliary power consumption | 1.5–3 kW |
The total energy consumed by an electric car traversing path \((o,d)\) is:
$$
E_{od} = \frac{1}{\eta_m \eta_e} \int F_{\mathrm{tot}}(t)\,v(t)\,dt + \frac{P_{aux}\,d}{v}
$$
During regenerative braking, the equation is modified with a recuperation factor, and the net energy becomes smaller. I apply the Sobol global sensitivity analysis to investigate which variables have the largest influence on the energy consumption of an electric car. Using 700,000 Monte Carlo samples, I obtain the first-order sensitivity indices \(S_i\) and total indices \(S_i^T\) reported in Table 2.
| Variable | \(S_i\) | \(S_i^T\) |
|---|---|---|
| SOC | 0.0009 | 0.0012 |
| Speed \(V\) | 0.0117 | 0.1393 |
| Acceleration \(A\) | 0.4377 | 0.7172 |
| Gradient \(\beta\) | 0.0163 | 0.1552 |
| Gear ratio \(\theta\) | 0.0446 | 0.2231 |
| Motor overload \(\lambda\) | 0.0026 | 0.0776 |
The acceleration \(A\) is clearly the most influential variable, with a total sensitivity index above 0.7. This confirms that predicting realistic driving cycles is more important than precisely modeling the battery state or the internal control parameters of the electric car. In my subsequent energy-aware scheduling algorithms, I always derive the speed and acceleration from the predicted macro traffic flow, so that the energy consumption estimate reflects the actual congestion dynamics rather than an average value.
To evaluate the energy consumption estimation method, I compare it with two conventional approaches, denoted as the Barth method and the Park method. The experiments are performed on a 5 km and an 8 km urban route in a simulated environment. The prediction results for a 16-minute horizon are shown to be highly consistent with measurements. Table 3 lists the mean absolute percentage errors observed.
| Method | Energy on 5 km (kWh) | Accuracy (5 km) | Energy on 8 km (kWh) | Accuracy (8 km) |
|---|---|---|---|---|
| Simulated ground truth | 0.665 | – | 1.085 | – |
| My method | 0.647 | 95.3% | 1.053 | 97.1% |
| Barth | 0.599 | 90.2% | 0.999 | 92.1% |
| Park | 0.589 | 88.6% | 0.972 | 89.6% |
The proposed method improves the estimation accuracy by about 5–7.5%, which leads to a considerable reduction in the conservative energy buffer that an electric car driver must reserve. With more accurate consumption knowledge, the charging scheduling algorithms can guide electric cars to charge at more suitable stations without provoking range anxiety.
Energy-Aware Bi-Level Navigation Model for Single Electric Car
After establishing the dynamic energy consumption estimation algorithm, I construct a bi-level charging navigation model that coordinates the routing decisions and the charging plan of a single electric car in the coupled transportation and distribution network. The overall architecture comprises an upper layer, which selects the optimal charging station and path for the electric car user, and a lower layer, which optimizes the V2G charging/discharging schedule within the selected charging station. Information is exchanged iteratively between the two layers through a smart city management platform.
I model the transportation network as a directed graph \(\mathcal{G}_{TN}=(\Omega_N,\Omega_A)\), where the nodes represent intersections and charging stations, while edges represent the urban roads joining them. For any road segment \((a,b)\), I compute the travel time from the macro traffic speed prediction:
$$
t_{od} = \sum_{(i,j)\in \Omega_{od}} \frac{\Delta x}{V(i,j)}
$$
The total transportation cost \(C_{TN}\) is the sum of an energy-based cost and a time-based cost:
$$
C_{TN} = \sum_{(i,j)\in \Omega_{od}} \left(C_{Energy} \cdot E_{ij} + C_{Hour} \cdot t_{ij}\right)
$$
where \(E_{ij}\) is the energy consumed by the electric car on road segment \((i,j)\), estimated according to the model discussed earlier. The charging cost is based on a dynamic pricing mechanism, which depends on the total load at the charging station and the charging power of electric cars. The dynamic price \(C_t^{DP}\) is defined as:
$$
C_t^{DP} = C_t^{DP0} + \sum_{i=1}^{N} \frac{P_{ev,i,t}}{ \eta_{ev,i}} \cdot 0.1593
$$
Thus, the upper-level objective for the electric car user is:
$$
F_{upper} = C_{TN} + C_{ch}, \quad C_{ch} = \sum_{t=t_a}^{t_d} C_t^{DP} P_{ev,t}\eta_{ev}
$$
In the lower level, the objective is to minimize the interaction power between the charging station and the main grid, so that local distributed generation and storage are used as much as possible. The lower-level objective is:
$$
\min \sum_{t=0}^{T} \left( \sum_{i=1}^{N} P_{ev,i,t} + P_{ess,t} – P_{pv,t} \right)^2
$$
subject to power balance constraints, state-of-charge dynamics of the energy storage system, charging/discharging power limits, and the minimum charging energy required by the electric car user. To handle the presence of intermittent photovoltaic power \(P_{pv}\), I use a budget of uncertainty set, denoted as:
$$
\Omega_{pv} = \left\{ P_{pv,t}: \hat{P}_{pv,t} – \Gamma_t \widehat{P}_{pv,t} \leq P_{pv,t} \leq \hat{P}_{pv,t} + \Gamma_t \widehat{P}_{pv,t},\ \sum_{t} |\xi_{t,n}| \leq \Gamma_t \right\}
$$
The parameter \(\Gamma_t\) controls the conservativeness of the robust solution. I choose \(\xi_{t,n}\in[0,1]\) and the robust counterpart enables the charging station to operate safely even when PV output deviates from its forecast by up to a desired confidence level.
The joint bi-level optimization problem is solved using a combination of Generalized Benders Decomposition and Logarithmic Barrier Function. GBD splits the problem into a master problem that contains the discrete routing variables, and a subproblem that handles continuous power variables. The master problem is initialized with an upper bound from a feasible route. At each iteration, the subproblem returns dual information that is used to generate Benders cuts. Because the subproblem includes nonlinear power flow constraints, I apply the logarithmic barrier method to convert inequalities into smooth logarithmic penalized terms. The barrier subproblem is:
$$
\min \ c_c^T X_c – \mu \sum_i \log(-g_i(X_c))
$$
with decreasing \(\mu\). By iterating the master and subproblem, the algorithm converges to a solution that minimizes the total cost for the electric car while ensuring grid-aware charging operation.
Experiment Results of the Bi-Level Model on a Single Electric Car
I set up the simulation on a regional traffic network consisting of 96 roads and 56 nodes. Four charging stations are placed at different locations, each equipped with PV generation, battery storage, and V2G-capable chargers. For the single electric car navigation experiment, I compare my bi-level approach against four baseline strategies:
- Case 1: shortest-distance path selection.
- Case 2: shortest-time dynamic routing.
- Case 3: minimum-energy path using a static energy map.
- Case 4: lowest-charging-price charging station selection without traffic awareness.
Table 4 presents the optimal route and cost details under each strategy for the same starting point and destination point.
| Method | Route | Energy cost ($) | Time cost ($) | Charging cost ($) | Total cost ($) |
|---|---|---|---|---|---|
| Case 1 | 1-13-12-26-31-51 | 13.10 | 74.28 | 7.01 | 94.39 |
| Case 2 | 1-13-12-26-27-28 | 22.49 | 37.30 | 12.44 | 72.23 |
| Case 3 | 1-13-14-15-16-50 | 12.16 | 56.40 | 6.91 | 77.43 |
| Case 4 | 1-13-14-24-34-45-44-49 | 14.64 | 64.32 | 3.88 | 82.89 |
| My method | 1-13-14-15-16-17-18-21 | 14.69 | 39.36 | 4.91 | 58.96 |
These results show that minimizing only one component of the total cost cannot guarantee an economical solution for the electric car user. The shortest path in Case 1 is cheap in energy but extremely time-consuming because congestion is not considered. The immediate-time routing in Case 2 greatly reduces time but forces the electric car to pass through a longer corridor with high energy consumption and increased charging demand. The dynamic pricing in Case 4 reduces the charging price alone, but the resulting route is longer, leading to higher transportation costs. My coordinated framework achieves the lowest integrated cost by balancing energy, time, and electricity price while considering the local renewable generation condition at the charging station.
To analyze the impact on the traffic network, I simulate 100 electric cars that trigger charging requests at different nodes. After each navigation method is applied, I calculate the average traffic load per road segment. Figure 1 in the original presentation shows the spatial traffic distribution; in summary, my method reduces the average number of electric cars assigned to each road from 26.0–30.5 (in Cases 1–3) to 20.6. This corresponds to a reduction of 5.4 to 9.9 electric cars per road segment, which significantly mitigates congestion probability.
The grid operation analysis is performed at one charging station with 6 electric cars that arrive at different times. Compared to uncoordinated charging (where electric cars immediately draw maximum power) and ordered charging without discharging, the V2G scheduling in my model is more effective in flattening net load fluctuation. The energy exchange between the charging station and the main grid is reported in Table 5 for four charging stations.
| Charging station | V2G method (kW) | Ordered charging (kW) | Unordered charging (kW) |
|---|---|---|---|
| CS1 | 17.69 | 26.57 | 94.03 |
| CS2 | 22.96 | 235.21 | 126.71 |
| CS3 | 19.16 | 29.65 | 106.10 |
| CS4 | 16.61 | 26.06 | 83.79 |
The results show that the V2G operation reduces the grid interaction by a substantial factor. At charging station 2, the difference is particularly notable, since the high penetration of electric cars and the presence of photovoltaic generation make the ordered charging strategy prone to large surplus or deficit spikes. My method successfully absorbs these fluctuations by using the electric car battery as an elastic energy buffer.
Three-Layer Cooperative Scheduling Framework with Aggregated Electric Car Flexibility
When the number of electric cars increases, solving a centralized optimization problem for every individual user becomes computationally prohibitive. Therefore, I extend the bi-level model to a three-layer charging cooperative scheduling framework that aggregates the temporal and spatial flexibility of electric cars. The framework consists of three layers that are solved sequentially and iteratively:
Layer 1 – Power allocation among aggregated electric cars: The charging station receives the requests from many electric cars and computes the total charging/discharging power trajectory \(P_{all,t}\) that minimizes the power exchange with the main grid. The decision is based on the aggregate energy and power boundaries of all electric cars, as well as the predicted PV and wind power and the base load. The objective is:
$$
\min_{P_{all}} \sum_{t=0}^{T} \left( P_{all,t} + P_{ess,t} – P_{pv,t} – P_{wind,t} \right)^2
$$
subject to the aggregate boundaries \(\underline{E}_{ev,t} \leq E_{ev,t} \leq \overline{E}_{ev,t}\) and \(\underline{P}_{ev,t} \leq P_{all,t} \leq \overline{P}_{ev,t}\). These boundaries are derived from the energy and flexibility modeling of electric cars.
Layer 2 – Individual electric car charging plan: Given \(P_{all,t}\) as the total power reference, the second layer decomposes it into specific charging profiles for each electric car. The objective for each electric car \(n\) is the sum of charging cost and battery degradation cost:
$$
\min \sum_{t=t_{a,n}}^{t_{d,n}} \left( C_t^{DP} P_{ev,n,t} + \Pi_n(P_{ev,n,t}) \right)
$$
where the battery degradation cost is expressed as:
$$
\Pi_n(P_{ev,n,t}) = \pi_1 \left(\frac{P_{ev,n,t}}{Cap_n}\right)^2 + \pi_2 \frac{P_{ev,n,t}}{Cap_n} + \pi_3
$$
This quadratic penalty takes into account that high C-rates increase battery aging. The layer-2 model respects each electric car’s arrival time, departure time, initial SOC, final SOC requirement, and the maximum/minimum power limits.
Layer 3 – Economic navigation planning: The third layer uses the previously described energy consumption estimation model to calculate the path from the electric car’s current location to each feasible charging station, and computes the total navigation cost, which includes the transportation cost and the charging cost. The navigation objective is:
$$
\min_{c\in \Omega_{cs}} \left\{ \psi_E \sum_{n} E_{od,n} + \psi_T \sum_{n} t_{od,n} + C_{ch}(c) \right\}
$$
where \(\Omega_{cs}\) is the set of charging stations accessible by the electric car. The routing decision is constrained by the battery charge requirement: the electric car must be able to reach the selected charging station with a non-negative SOC margin:
$$
SOC_{ini,n} Cap_n \ge E_{od,n}^{total}
$$
Since the traffic state changes over time, my third layer recomputes the route when the electric car receives updated traffic information from the intelligent transportation platform.
Flexibility Modeling of Electric Cars
The aggregated flexibility of electric cars is the key enabler of layer 1. For each electric car, I distinguish three typical user types:
Type 1: Electric cars with no flexibility. They must charge at rated power from the moment they arrive until they fulfill the requested energy, because their plug-in duration is too short to allow any shift.
Type 2: Electric cars that have time flexibility but cannot discharge immediately, since their initial SOC is below the minimum acceptable limit. These cars must charge first for a while before participating in V2G.
Type 3: Fully flexible electric cars that can charge or discharge throughout the whole parking period, as long as their SOC remains within allowable boundaries.
Let \(e_{ev,n,t}^{+}\) and \(e_{ev,n,t}^{-}\) be the upper and lower bounds of stored energy for electric car \(n\) at time interval \(t\). Similarly, \(p_{ev,n,t}^{+}\) and \(p_{ev,n,t}^{-}\) denote the charging and discharging power limits. The aggregate energy bound is:
$$
E_{ev,t}^{+} = \sum_{n} e_{ev,n,t}^{+}, \quad E_{ev,t}^{-} = \sum_{n} e_{ev,n,t}^{-}
$$
and the aggregate power bound is:
$$
P_{ev,t}^{+} = \sum_{n} p_{ev,n,t}^{+}, \quad P_{ev,t}^{-} = \sum_{n} p_{ev,n,t}^{-}
$$
Using these bounds, layer 1 can decide \(P_{all,t}\) without knowing the identity or individual constraints of each electric car. This reduces the dimensionality of the grid-side optimization while preserving the feasibility of the later disaggregation. My simulation results for 100 electric cars at charging station 1 show that the aggregate total charging power curve closely follows the net renewable power curve (\(P_{pv}+P_{wind}-P_{load}\)) whenever possible. During the night, when PV output is zero and wind output cannot cover the base load, my model schedules V2G discharging from electric cars to feed the station load, thus reducing the power drawn from the upper grid.
PPO-ADMM Joint Solver
To efficiently solve the layer-1 quadratic optimization problem with many constraints, I employ the Alternating Direction Method of Multipliers (ADMM). The augmented Lagrangian of the layer-1 problem is:
$$
L(x,z,u) = F_1(x) + \frac{\rho}{2} \left\| z – x + u \right\|^2_2
$$
where \(x\) represents the total charging power of electric cars, \(z\) represents the auxiliary variable that aligns with the net renewable power boundary, and \(u\) is the scaled dual variable. The ADMM iteration updates \(x\) and \(z\) alternately, followed by a gradient-ascent step for \(u\).
The convergence speed of ADMM depends heavily on the penalty parameter \(\rho\). In traditional ADMM, \(\rho\) is fixed manually. I improve this by training a near-end policy optimization (PPO) agent that observes the current iteration gap and adjusts \(\rho\) in real time. The state at iteration \(k\) is defined as \(s_k = [k, r_k, \rho_k]\), and the action \(a_k\) is the increment to modify \(\rho_{k+1} = \rho_k + a_k\). The reward is the negative number of iterations required to reach convergence. Through many episodes, the agent learns a robust step-size adjustment policy. Table 6 compares the number of iterations required for different solvers under four charging station problem sizes (50, 100, 200, and 500 electric cars).
| Solver | Charging station 1 | Charging station 2 | Charging station 3 | Charging station 4 |
|---|---|---|---|---|
| SQP | 121 | 133 | 147 | 181 |
| ADMM | 76 | 93 | 113 | 137 |
| Manual tuning | 58 | 82 | 87 | 106 |
| Adaptive ADMM | 42 | 53 | 78 | 89 |
| PPO-ADMM (my method) | 18 | 31 | 50 | 72 |
The PPO-ADMM solver outperforms all considered benchmarks in terms of required iterations. In addition, the average wall-clock time of PPO-ADMM is about 3.5 seconds, whereas SQP requires about 13 seconds for the largest case. This improvement is valuable for real-time electric car charging scheduling, especially when hundreds of electric cars appear simultaneously.
Experimental comparison of charging modes
I compare the three-layer framework against three charging modes:
- Mode 1: ordered charging, in which electric cars charge at constant nominal power in a queue order.
- Mode 2: uncontrolled charging, where electric cars begin charging immediately without any coordination.
- Mode 3: minimum charging-station operating cost scheduling, which does not manage renewable intermittency.
- Mode 4: my proposed three-layer framework that uses V2G and aggregate flexibility.
Table 7 reports the grid interaction and renewable utilization metrics under these four modes for a complete day.
| Metric | Mode 1 | Mode 2 | Mode 3 | Mode 4 |
|---|---|---|---|---|
| Exchanged power (kWh) | 1765 | 5286 | 1532 | 948 |
| Renewable energy utilization | 67.6% | 35.9% | 60.8% | 72.1% |
| Base load supply rate | 0% | 0% | 30.2% | 79.6% |
Mode 4 reduces the exchanged energy from 1765 kWh to 948 kWh, which corresponds to a reduction of 46% compared with ordered charging. The renewable penetration rises from 67.6 to 72.1%, which is a modest improvement. More importantly, my framework successfully uses the V2G capacity of electric cars to supply 79.6% of the station base load during the periods when renewable generation is insufficient. This is not possible in Mode 1 or Mode 2, since they do not support discharging.
In terms of traffic effects, I evaluate four navigation methods (Nm 1–4) for 100 electric cars distributed over the map. The navigation methods are equivalent to the Case 1–4 strategies described in the bi-level experiment, while my method is labeled “proposed”. The maximum traffic flow on the most congested road segment is reduced from about 125 to 70 vehicles per hour when using my method, and the number of congestion events over 60 representative road segments falls from 20 to only 12 congestion events. This happens because my routing algorithm shifts some electric cars to less used alternative paths, thereby smoothing the traffic load distribution.
Finally, I analyze the total cost breakdown for ten electric cars traveling from a common starting point. Table 8 summarizes the average costs per electric car under different navigation modes.
| Cost component | Nm 1 (shortest distance) | Nm 2 (lowest time) | Nm 3 (lowest energy) | Nm 4 (lowest charging cost) | Proposed method |
|---|---|---|---|---|---|
| Energy cost ($) | 12.1 | 20.3 | 11.6 | 14.1 | 13.8 |
| Time cost ($) | 65.4 | 30.2 | 52.9 | 61.3 | 36.4 |
| Charging cost ($) | 6.8 | 11.8 | 6.5 | 3.7 | 4.7 |
| Battery degradation cost ($) | 0.7 | 1.3 | 0.6 | 0.8 | 0.9 |
| Total cost ($) | 85.0 | 63.6 | 71.6 | 79.9 | 55.8 |
Even though Nm 3 achieves the lowest energy cost and Nm 4 the lowest charging price, the proposed method yields the lowest total cost for the electric car owner. This reinforces the importance of a holistic scheduling approach. The modest increase in battery degradation cost in my method is far outweighed by the reduction in time and charging costs.
Conclusion
In this article, I presented a comprehensive study on energy-aware V2G charging scheduling for electric cars in coupled transportation and distribution systems. My first contribution is the advanced energy consumption estimation method that fuses macro traffic speed prediction with longitudinal dynamics. The second contribution is the bi-level navigation model that fully coordinates the route and charging plan of a single electric car, which I demonstrated to minimize the integrated user cost while reducing grid load fluctuation. The third contribution is the three-layer cooperative scheduling framework that aggregates the temporal and spatial flexibility of electric cars, thereby dramatically reducing the dimensional complexity of large-scale charging optimization. The PPO-ADMM solver emerged as a robust and fast algorithm that learns to tune the step size automatically.
Through extensive simulation experiments, I confirmed that the proposed algorithms achieve the following objectives:
- The dynamic energy consumption estimator improves the prediction accuracy by 5 to 7.5 percentage points compared to conventional baselines.
- The bi-level charging navigation reduces the total trip and charging cost of a single electric car to 58.96 dollars, while the best baseline reaches 72.23 dollars.
- The aggregated V2G scheduling reduces energy exchange with the main grid by about 46.3% relative to ordered charging and by 82.1% relative to uncontrolled charging.
- The renewable energy utilization is increased from 35.9% (uncontrolled charging) to 72.1%, and the base load supply rate from the storage pool of electric cars reaches 79.6%.
- The PPO-ADMM solver needs only 18–72 iterations to converge for problem sizes from 50 to 500 electric cars, and its computation time is roughly one quarter of a traditional nonlinear solver.
In future work, I plan to extend the proposed methodology to a joint uncertainty model that simultaneously handles traffic perturbations, solar irradiance fluctuations, and wind speed variability. I also aim to incorporate the uncertainty-aware sensitivity principle from my Sobol analysis into a real-time control loop, so that the charging scheduler can adjust the level of conservatism as actual traffic and weather data are received. Further exploration of multi-agent reinforcement learning for decentralized electric car charging coordination is another promising direction.
My overall conclusion is that the integration of accurate energy-consumption awareness and a hierarchical charging coordination architecture offers a powerful path toward the sustainable deployment of electric cars. The synergies among the traffic layer, the individual electric car, and the distribution grid can unlock a new level of economic and environmental efficiency. I expect that the methods presented in this article will provide a solid foundation for future intelligent charging ecosystems and future smart cities.