With the urgent global demand for carbon neutrality and sustainable energy, electric vehicles have become one of the most promising solutions for reducing greenhouse gas emissions and petroleum dependence. In my research, I focus on the coordinated operation of transportation networks and distribution networks through electric vehicle charging scheduling. The deep coupling between traffic flow and power flow introduces significant complexity. On one hand, the travel trajectory, speed, and charging-station selection of electric vehicles directly shape the spatiotemporal distribution of charging demand. On the other hand, the distribution network must reallocate power to maintain stability while absorbing the stochastic charging loads. This mutual dependency makes conventional isolated optimization methods insufficient.
I identify three major technical gaps in existing work. First, most energy-consumption estimation studies treat a whole road as a single unit and ignore the time-varying traffic states along the road, resulting in low estimation accuracy for electric vehicles. Second, charging navigation strategies seldom exploit the bidirectional information exchange between transport and power networks, so user charging cost, grid operational efficiency, and traffic-flow distribution cannot be jointly optimized. Third, the intermittent nature of renewable generation and the dynamic evolution of traffic flow make robust navigation and scheduling extremely challenging. To address these issues, I propose an energy-aware charging optimization and scheduling framework built on a high-fidelity dynamic energy-consumption estimation model. The core contributions of my dissertation are summarized as follows.
1. Research Background and Motivations
Electric vehicles are not merely passive loads. They can act as mobile energy-storage units and provide vehicle-to-grid (V2G) services when parked and connected. This additional flexibility enables the distribution network to mitigate renewable-energy intermittency, reduce peak load, and improve economic efficiency. However, the exploitation of this flexibility depends heavily on accurate knowledge of the energy required to reach a charging station and of the energy margin remaining at departure. If the energy consumption of an electric vehicle is overestimated, the driver may charge more often than necessary, increasing cost and congestion. If underestimated, the vehicle may run out of energy before reaching the charger. Therefore, energy-aware scheduling is essential for a practical electric vehicle charging navigation system.
My study is organized in three progressive layers. In the first step, I design a macroscopic–microscopic energy-consumption estimation method for electric vehicles. This method integrates graph-convolutional traffic-speed prediction with a vehicle-longitudinal-dynamics model. In the second step, I build a bi-level charging navigation model for a single electric vehicle. The upper level chooses the charging station and route, while the lower level optimizes V2G charging plans inside the station. In the third step, I extend the model to a three-layer cooperative scheduling framework for many electric vehicles. This framework explicitly models the aggregated charging flexibility of electric vehicles and solves the resulting large-scale optimization problem with a hybrid proximal-policy-optimization and alternating-direction-method-of-multipliers algorithm. The remainder of this article describes these contributions in detail.
2. Dynamic Energy-Consumption Estimation Based on Macro–Micro Traffic States
2.1 Macroscopic Traffic-Flow Speed Prediction
To estimate the energy consumption of an electric vehicle accurately, I first need to predict the speed profile that the vehicle will experience along the planned route. I model a city road not as one homogeneous link but as a series of road micro-segments. Each road micro-segment is 100 meters long. By discretizing roads into such micro-segments, I can describe the spatial and temporal evolution of traffic flow using fluid-dynamics conservation laws. Let \(m\) index the road micro-segment and \(t\) the time interval. The macroscopic velocity inside micro-segment \(m\) at time \(t\) is the arithmetic mean of all instantaneous vehicle speeds within that segment:
$$ V(m,t) = \frac{1}{N_{\mathrm{veh}}(m,t)} \sum_{i=1}^{N_{\mathrm{veh}}(m,t)} v_{i,t}, $$
where \(N_{\mathrm{veh}}(m,t)\) is the number of vehicles in road micro-segment \(m\) during the interval \([t\Delta T, (t+1)\Delta T]\), and \(v_{i,t}\) is the speed of vehicle \(i\). I decompose the macroscopic acceleration into a local component and a convective component:
$$ A = \frac{\mathrm{d}V}{\mathrm{d}t} = \underbrace{\frac{\partial V}{\partial t}}_{A_{\mathrm{local}}} + \underbrace{V \frac{\partial V}{\partial x}}_{A_{\mathrm{conv}}}. $$
These two terms are approximated by finite differences:
$$ A_{\mathrm{local}} = \frac{V(m,t+1)-V(m,t)}{\Delta T}, \qquad A_{\mathrm{conv}} = \frac{V(m+1,t+1)-V(m,t)}{\Delta T}. $$
The choice of \(\Delta x\) and \(\Delta T\) must satisfy the Courant–Friedrichs–Lewy condition:
$$ \Delta T \leq \frac{\Delta x}{c+\max_{v} |v_{\mathrm{desire}}| + \sigma_v}, $$
where \(v_{\mathrm{desire}}\) is the desired free-flow speed, \(\sigma_v\) is the speed deviation of individual vehicles, and \(c\) is the traffic-shockwave propagation speed. This condition guarantees that a vehicle cannot pass through more than one micro-segment within one time step.
To predict future speed, I construct a graph whose nodes are road micro-segments. Each node carries historical velocity and flow features. I use a graph convolutional network (GCN) to capture spatial dependencies and a multi-head attention mechanism to weight the influence of neighboring micro-segments. A temporal convolutional network then captures multi-scale temporal patterns. The prediction of the future speed of micro-segment \(k\) at time \(t^{*}\) depends on its own history and on the history of its immediate upstream and downstream neighbors:
$$ V^{*}(x_k, t_0 + m^*\Delta T) = f\Big(V(x_k,t_0+m\Delta T), Q(x_k,t_0+m\Delta T), V(x_{k-1},t_0+m\Delta T), Q(x_{k+1},t_0+m\Delta T)\Big), $$
where \(m^*>m\) and \(f\) is the deep-learning model trained with historical traffic data. In my experiments the prediction horizon is 16 minutes. The predicted speed curves closely match real-world measurements, indicating that the joint GCN and attention mechanism can effectively capture dynamic traffic propagation.
2.2 Microscopic Electric Vehicle Propulsion Model
Once the speed profile is known, I calculate the traction force required by an electric vehicle. The total longitudinal force is the sum of four resistance components:
$$ F_{D}^{n,t} = F_{\mathrm{slop}}^{n,t} + F_{\mathrm{fric}}^{n,t} + F_{\mathrm{air}}^{n,t} + F_{\mathrm{acc}}^{n,t}. $$
The detailed expressions are:
$$ F_{D}^{n,t} = M_n g \cos \beta_t \, f_{r,n} + M_n g \sin \beta_t + \frac{1}{2} C_{D,n} A_{f,n} \rho_{\mathrm{air}} V_{n,t}^2 + M_n \delta_n A_{n,t}, $$
where \(M_n\) is the vehicle mass, \(g\) is gravity, \(\beta_t\) is the road grade, \(f_{r,n}\) is the rolling-resistance coefficient, \(C_{D,n}\) is the air-drag coefficient, \(A_{f,n}\) is the frontal area, \(\rho_{\mathrm{air}}\) is the air density, \(\delta_n\) is the rotational-mass factor, and \(A_{n,t}\) is the acceleration derived from the local and convective acceleration components. The total vehicle mass includes the curb weight, occupants, and battery:
$$ M_n = m_n + n_s n_p \frac{U_N Q_N}{\rho_e} + m_{\mathrm{extra}}, $$
where \(n_s\) and \(n_p\) are the series and parallel cell counts, \(U_N\) and \(Q_N\) are the nominal cell voltage and capacity, and \(\rho_e\) is the cell energy density.
The energy consumed on a route from origin \(o\) to destination \(d\) is expressed as:
$$ E_{od} = \sum_{(i,j) \in \Omega_A} \frac{a_{ij} \, F_{D}^{ij} \, L_{ij}}{3600}, \quad a_{ij} \in \{0,1\}, $$
where \(L_{ij}\) is the length of road segment \((i,j)\). During regenerative braking, part of the kinetic energy is recovered. The total energy consumption is therefore divided into positive traction energy and negative regenerative energy:
$$ E_{od}^{\mathrm{total}} = \begin{cases}
\dfrac{E_{od}^+}{\eta_{m,n} \eta_{e,n}} + P_{\mathrm{aux}} t, & \text{accelerating/cruising}, \\[6pt]
E_{od}^- \eta_{m,n} \eta_{e,n} + P_{\mathrm{aux}} t, & \text{decelerating},
\end{cases} $$
where \(\eta_{m,n}\) and \(\eta_{e,n}\) are the motor and mechanical efficiencies, and \(P_{\mathrm{aux}}\) represents auxiliary loads such as air conditioning.
2.3 Sensitivity Analysis of Energy-Consumption Variables
Many factors affect the energy consumption of an electric vehicle. To identify the variables that most influence consumption and to simplify the subsequent optimization, I applied Sobol global sensitivity analysis. The output variance is decomposed as:
$$ \mathrm{Var}(Y) = \sum_i V_i + \sum_{i<j} $$="" +=""
where \(V_i\) is the variance contribution of input \(X_i\). The first-order and total sensitivity indices are:
$$ S_i = \frac{V_i}{\mathrm{Var}(Y)}, \qquad S_i^T = \frac{V_i + \sum_{j\neq i} V_{ij}}{\mathrm{Var}(Y)}. $$
I sampled 700,000 input vectors using Monte Carlo methods. The variables include average speed \(V\), acceleration \(A\), road grade \(\beta\), state of charge (SOC), battery pack configuration, motor rated power, and gearbox parameters. The results are summarized in the table below.
| Variable | \(S_i\) | \(S_i^T\) |
|---|---|---|
| SOC | 0.0009 | 0.0012 |
| Speed \(V\) | 0.0117 | 0.1393 |
| Acceleration \(A\) | 0.4377 | 0.7172 |
| Road grade \(\beta\) | 0.0163 | 0.1552 |
| Battery parallel cells \(n_p\) | 0.0056 | 0.0725 |
| Gearbox total ratio \(\theta\) | 0.0446 | 0.2231 |
| Motor overload factor \(\lambda\) | 0.0026 | 0.0776 |
| Motor rated power \(N_P\) | 0.0116 | 0.1693 |
| Battery series cells \(n_s\) | 0.0018 | 0.0437 |
The sensitivity analysis clearly shows that acceleration \(A\) has both the largest first-order index and the largest total index. Therefore, the accuracy of the predicted vehicle operating profile—especially acceleration—determines the accuracy of energy-consumption estimation. This insight motivated my later use of high-resolution macroscopic speed prediction in charging navigation.
2.4 Simulation Results of Energy Estimation
I compared my proposed macro–micro energy-consumption model with two earlier methods: one based on average-speed lookup tables and another based on random spatiotemporal speed sampling. The tests were performed on routes of 5 km and 8 km. The table below reports the estimated energy, accuracy, and gap from the reference simulation.
| Route length | Method | Energy (kWh) | Accuracy | Gap |
|---|---|---|---|---|
| 5 km | Reference simulation | 0.665 | — | — |
| My method | 0.647 | 95.3% | 4.7% | |
| Average-speed method | 0.599 | 90.2% | 9.8% | |
| Random-speed method | 0.589 | 88.6% | 11.4% | |
| 8 km | Reference simulation | 1.085 | — | — |
| My method | 1.053 | 97.1% | 2.9% | |
| Average-speed method | 0.999 | 92.1% | 7.9% | |
| Random-speed method | 0.972 | 89.6% | 10.4% |
The proposed method improves the estimation accuracy by 5.1% and 6.7% for the 5-km route and by 5.0% and 7.5% for the 8-km route when compared with the two benchmark approaches. These results confirm that combining macroscopic traffic-flow trend information with microscopic vehicle dynamics produces a highly reliable energy-consumption model for electric vehicles.
3. Energy-Aware Charging Navigation for a Single Electric Vehicle
3.1 Bi-Level System Architecture
Using the dynamic energy-consumption estimation as a basis, I developed a bi-level coordinated charging navigation model. The upper model is responsible for charging-station selection and route guidance. It gathers map data, real-time traffic-flow information, and vehicle parameters. The lower model represents the distribution-network side. It optimizes the charging and discharging plan of each charging station, with photovoltaic (PV) generation, energy-storage systems, and V2G-capable electric vehicles. The two levels exchange information iteratively until the total charging and navigation cost is minimized.
The transportation network is represented as a directed graph \(\mathcal{G}_{TN} = (\Omega_N, \Omega_A)\), where \(\Omega_N\) is the set of intersections and charging stations and \(\Omega_A\) is the set of directed roads. The distribution network contains multiple charging stations that are connected to the main grid. Each charging station is composed of PV panels, energy storage, base loads, and charging units. The energy flow within a charging station is balanced by:
$$ I_{\mathrm{buy},t} P_{\mathrm{buy},t} – I_{\mathrm{sell},t}P_{\mathrm{sell},t} + P_{\mathrm{pv},t} + I_{\mathrm{dch},t}P_{\mathrm{dch},t}\eta_{\mathrm{ess}} – I_{\mathrm{ch},t}P_{\mathrm{ch},t}/\eta_{\mathrm{ess}} = \sum_{i=1}^{N} \frac{I_{\mathrm{evsdc},i,t}P_{\mathrm{evsdc},i,t}}{\eta_{\mathrm{ev},i}} + I_{\mathrm{evsc},i,t}P_{\mathrm{evsc},i,t}\eta_{\mathrm{ev},i} + P_{\mathrm{load},t}, $$
where the binary variables ensure that buying and selling, charging and discharging, do not happen simultaneously in a single time step.
3.2 Upper-Level Navigation Objective
The upper-level objective minimizes the sum of traffic cost and charging cost:
$$ \min C_{od} = C_{od}^{TN} + C_{od}^{DN}. $$
The traffic cost contains energy cost and time cost:
$$ C_{od}^{TN} = \sum_{(a,b)} \left( C_{\mathrm{Energy}} E_{od}^{\mathrm{total}} + C_{\mathrm{Hour}} t_{od} \right), \quad t_{od} = \sum_{\mathrm{segments}} \frac{\Delta x}{V(m,t)}. $$
The charging cost uses a dynamic pricing mechanism. The dynamic price at time \(t\) is defined as:
$$ C_{t}^{DP} = C_{t}^{DP,0} + 0.1593 \sum_{i=1}^{N_{\mathrm{ev}}} \frac{P_{\mathrm{ev},i,t}}{\eta_{\mathrm{ev},i}}, $$
where \(C_{t}^{DP,0}\) is the base electricity price and \(P_{\mathrm{ev},i,t}\) is the charging power of electric vehicle \(i\). Thus, the charging cost for an electric vehicle that arrives at time \(t_{a}\) and departs at \(t_{d}\) is:
$$ C_{od}^{DN} = \sum_{t=t_{a}}^{t_{d}} C_{t}^{DP} P_{\mathrm{ev},t} \eta_{\mathrm{ev}} \Delta t. $$
3.3 Lower-Level Distribution-Network Operation
The lower-level model aims at minimizing the power exchange between the charging station and the main grid:
$$ \min \sum_{t=0}^{T-1} \sum_{i=1}^{N} \left( P_{\mathrm{ev},i,t} + P_{\mathrm{ess},t} – P_{\mathrm{pv},t} \right)^2. $$
I model PV generation uncertainty using a budget-based uncertainty set:
$$ \mathcal{P}_{pv,t} = \left\{ P_{pv,t} \middle| \underline{P}_{pv,t} \leq P_{pv,t} \leq \overline{P}_{pv,t}, \sum_t \frac{|P_{pv,t}-\hat{P}_{pv,t}|}{\hat{P}_{pv,t}} \leq \Gamma_t \right\}. $$
The robust parameter \(\Gamma_t\) controls the conservativeness of the solution. A larger \(\Gamma_t\) leads to higher robustness against PV forecast errors but may increase operating cost. This trade-off is evaluated in the experiments.
Important constraints include the storage state transition:
$$ ESS_{t+1} = ESS_t + I_{\mathrm{ch},t}P_{\mathrm{ch},t} \eta_{\mathrm{ess}} \Delta t – I_{\mathrm{dch},t}P_{\mathrm{dch},t} / \eta_{\mathrm{ess}} \Delta t, $$
and the electric vehicle state-of-charge constraints:
$$ SOC_{ev}^{\min} \leq SOC_{ev,\mathrm{ini}} + \frac{E_{ev}}{Cap_{ev}} \leq SOC_{ev}^{\max}, \qquad SOC_{ev,\mathrm{end}} \geq SOC_{ev}^{\min}. $$
3.4 GBD-LBF Combined Solution Algorithm
The bi-level optimization problem is a mixed-integer nonlinear program. To solve it efficiently, I combined generalized Benders decomposition (GBD) with a logarithmic barrier function (LBF) method. GBD separates discrete decisions, such as charging-station selection and road choice, from continuous variables, such as charging power and battery state. The master problem contains only discrete variables and an auxiliary variable \(\vartheta\), while the subproblem is solved for the continuous variables. The subproblem objective is:
$$ \min_{X_c} c_c^T X_c + \vartheta, $$
with coupling constraints \(A_d Z_d + A_c X_c \leq b_a\), where \(Z_d\) is fixed by the master problem. If the subproblem is feasible, I compute optimality cuts; if infeasible, I solve a feasibility subproblem using slack variables \(S_a\) and \(S_b\) and generate feasibility cuts.
To handle nonlinear constraints such as the power-flow equation \(G(X_c)\), I use a logarithmic barrier function. For an inequality constraint \(g(x) \leq 0\), the barrier term is \(-\mu \log(-g(x))\), where \(\mu\) is the barrier parameter. The augmented Lagrangian is then formed, and the variables are updated by interior-point iterations. The barrier parameter follows an exponential decay \(\mu^{(k+1)} = \sigma \mu^{(k)}\) with \(\sigma \in (0,1)\). The algorithm stops when the duality gap is smaller than a specified tolerance. In my experiments, this GBD-LBF method converges within one minute for typical single-electric-vehicle navigation instances, providing timely guidance.
3.5 Performance Evaluation of the Bi-Level Navigation Model
I evaluated the model on a realistic urban transportation network in China with 96 roads and 56 nodes. The network contains several charging stations, each equipped with PV panels, battery storage, and V2G chargers. I compared my method with four benchmark navigation strategies: (1) shortest-distance routing, (2) fastest-time routing, (3) lowest-energy routing, and (4) cheapest-charging routing. The table lists the resulting route costs.
| Strategy | Energy cost ($) | Time cost ($) | Charging cost ($) | Total cost ($) |
|---|---|---|---|---|
| Shortest distance | 13.10 | 74.28 | 7.01 | 94.39 |
| Fastest time | 22.49 | 37.30 | 12.44 | 72.23 |
| Lowest energy | 12.16 | 56.40 | 6.91 | 77.43 |
| Cheapest charging | 14.64 | 64.32 | 3.88 | 82.89 |
| My bi-level method | 14.69 | 39.36 | 4.91 | 58.96 |
My method achieves the lowest total cost because it trades off energy consumption, travel time, and charging price simultaneously. It does not minimize each component individually, but the combined navigation cost is reduced by 17.3% to 37.6% compared with the four benchmark strategies.
I further simulated 100 electric vehicles starting from different nodes to evaluate the impact on traffic flow. The benchmark approaches create uneven traffic distributions, resulting in congested corridors. My method distributes electric vehicles more uniformly across the network. The average number of vehicles per selected road path is shown below.
| Navigation method | Average number of selected electric vehicles per road |
|---|---|
| Shortest distance | 26.0 |
| Fastest time | 29.3 |
| Lowest energy | 30.5 |
| My method | 20.6 |
The proposed navigation model reduces the average per-road electric-vehicle count by 5.4 to 9.9 vehicles, significantly alleviating congestion pressure. On the distribution-network side, my V2G charging pattern is compared with orderly charging and uncontrolled charging. The results show that V2G operation reduces the power exchange between charging stations and the main grid. For four charging stations, the average exchange powers are summarized below.
| Charging pattern | Charging station 1 (kW) | Charging station 2 (kW) | Charging station 3 (kW) | Charging station 4 (kW) |
|---|---|---|---|---|
| Uncontrolled charging | 94.03 | 126.71 | 106.10 | 83.79 |
| Orderly charging | 26.57 | 235.21 | 29.65 | 26.06 |
| V2G charging (my method) | 17.69 | 22.96 | 19.16 | 16.61 |
The lower exchange power reduces grid load fluctuation and ensures a more secure and energy-saving distribution network. The dynamic charging schedule also satisfies users’ departure requirements. In the PV uncertainty tests, I considered four forecast-error scenarios. With the budget parameter \(\Gamma_t=1\), the model is most conservative, and the operating cost increases modestly while maintaining feasibility. This confirms that the robust formulation can effectively handle renewable-generation uncertainty.
4. Three-Layer Cooperative Scheduling Based on Aggregated Electric Vehicle Flexibility
4.1 Extending to Large-Scale Electric Vehicle Scheduling
The bi-level navigation model works well for a single electric vehicle or a small group. When hundreds of electric vehicles arrive at multiple charging stations, centralized optimization becomes intractable because the number of decision variables grows rapidly. Moreover, electric vehicles have both spatial flexibility, because the driver can choose different charging stations, and temporal charging flexibility, because the charging power can be shifted within the connection interval. To exploit these resources, I developed a three-layer cooperative scheduling framework that decomposes the problem into tractable subproblems.
4.2 Aggregated Charging Flexibility of Electric Vehicles
I classify electric-vehicle users into three categories. The first category has no charging flexibility: their required charging energy is so large that they must charge at rated power for the whole connection period. The second category can shift charging power but cannot perform V2G discharge until they reach a minimum energy level. The third category has full charging and discharging flexibility. For each electric vehicle \(n\), I define the charging energy boundary \(e_{ev,n,t}^{+}\) and the discharging energy boundary \(e_{ev,n,t}^{-}\), along with the corresponding power boundaries \(p_{ev,n,t}^{+}\) and \(p_{ev,n,t}^{-}\). The boundaries for a flexible vehicle are updated recursively:
$$ e_{ev,n,t+1}^{+} = \min\left(e_{ev,n}^{\max},\; e_{ev,n,t}^{+} + p_{ev,n,c}\eta_{ev,c}\Delta t\right), $$
$$ e_{ev,n,t+1}^{-} = \max\left(e_{ev,n}^{\min},\; e_{ev,n,t}^{-} + \frac{p_{ev,n,d}}{\eta_{ev,d}}\Delta t – e_{ev,n}^{req}\right). $$
The aggregated energy and power flexibility of all electric vehicles at a charging station are:
$$ E_{ev,t}^{+} = \sum_n e_{ev,n,t}^{+}, \qquad E_{ev,t}^{-} = \sum_n e_{ev,n,t}^{-}, $$
$$ P_{ev,t}^{+} = \sum_n p_{ev,n,t}^{+}, \qquad P_{ev,t}^{-} = \sum_n p_{ev,n,t}^{-}. $$
These aggregate quantities define the admissible region of the total charging power \(P_{all,t}\) that the station can absorb from or inject to the main grid.
4.3 Layer 1: Distribution-Level Power Allocation
The first layer optimizes the operation of the charging station from the perspective of the distribution network. The objective is to minimize the deviation between the total electric-vehicle charging power, renewable generation, wind generation, and base load:
$$ \min f_{1} = \sum_{t=0}^{T-1} \left( P_{all,t} – P_{pv,t} – P_{wind,t} + P_{load,t} \right)^2, $$
subject to the aggregate flexibility constraints:
$$ E_{ev,t}^{-} \leq E_{ev,t} \leq E_{ev,t}^{+}, \qquad P_{ev,t}^{-} \leq P_{all,t} \leq P_{ev,t}^{+}. $$
This layer determines the total charging power profile for the whole station, not for each electric vehicle. By doing so, it avoids the “curse of dimensionality” caused by thousands of vehicles.
4.4 Layer 2: Per-Electric-Vehicle Charging Plan
The second layer receives \(P_{all,t}\) from the first layer and allocates it among individual electric vehicles. The objective is to minimize the user charging cost and battery-degradation cost:
$$ \min f_{2} + f_{3} = \sum_{n=1}^{N_{ev}} \sum_{t=t_{a,n}}^{t_{d,n}} \left( C_t^{DP} P_{ev,n,t} \Delta t + \Pi_n(P_{ev,n,t}) \right), $$
where the battery-degradation function is modeled as a quadratic function of charging power and battery capacity:
$$ \Pi_n(P_{ev,n,t}) = \pi_1 \left(\frac{P_{ev,n,t}}{Cap_{ev,n}}\right)^2 + \pi_2 \frac{P_{ev,n,t}}{Cap_{ev,n}} + \pi_3. $$
The power balance is enforced by:
$$ P_{all,t} = \sum_{n=1}^{N_{ev}} P_{ev,n,t} + P_{ess,t}. $$
Additional constraints guarantee that each electric vehicle reaches the desired state of charge before departure and that the battery operates within safe voltage and temperature limits.
4.5 Layer 3: Economic Charging Navigation for Electric Vehicle Users
After receiving the charging plan from a candidate station, the electric-vehicle user must still decide to which station to drive. The third layer evaluates the total driving cost using the macro–micro energy-consumption model. The objective is:
$$ \min F_{3} = \sum_{n=1}^{N_{ev}} \left( \psi_{E} E_{od,n}^{\mathrm{total}} + \psi_{H} t_{od,n} \right) + F_2, $$
where \(F_2\) is the charging cost obtained from the second layer. Thus, the three-layer model outputs both the optimal route and the optimal charging profile for every electric vehicle. The user is directed to the charging station that yields the lowest sum of driving energy cost, travel-time cost, charging cost, and battery-degradation cost.
4.6 PPO-ADMM Hybrid Algorithm
The first-layer optimization is a quadratic program with dynamic constraints. To improve convergence, I apply the alternating direction method of multipliers (ADMM). The augmented Lagrangian is:
$$ \mathcal{L}_{\rho}(P_{all}, z, u) = f_1 + \sum_t \left( \frac{\rho_t}{2} \| P_{all,t} – z_t + u_t \|^2 \right). $$
ADMM updates \(P_{all}\), \(z\), and the dual variable \(u\) iteratively. The step-size parameter \(\rho_t\) largely determines the convergence speed. Conventional ADMM uses a fixed \(\rho\). Instead, I model the selection of \(\rho_t\) as a Markov decision process. The state contains the current iteration index, residual, and current step size. The action adjusts \(\rho_t\). The reward is the negative of the iteration count. I use the proximal policy optimization (PPO) algorithm to learn an adaptive policy \(\pi_{\theta}(a|s)\). The PPO clipped objective is:
$$ L^{CLIP}(\theta) = \mathbb{E}_t \left[ \min\left( r_t(\theta) A_t,\; \operatorname{clip}(r_t(\theta), 1-\epsilon, 1+\epsilon) A_t \right) \right], $$
where \(r_t(\theta)\) is the probability ratio and \(A_t\) is the advantage estimate. The learned policy adjusts the ADMM step size dynamically, accelerating convergence without manual parameter tuning.
4.7 Simulation Setup and Performance Comparison
I tested the three-layer framework with charging stations of different sizes: station 1 with 50 electric vehicles, station 2 with 100, station 3 with 200, and station 4 with 500. The renewable generation profiles include both PV and wind power, so that the combined renewable output is available during both daytime and nighttime. I compared my method with three charging modes: orderly charging without discharge, uncontrolled charging, and charging-station-cost-minimization mode with V2G. The key performance indicators are displayed in the next table.
| Charging mode | Main-grid exchange power (kW) | Renewable utilization | Base-load supply ratio |
|---|---|---|---|
| Orderly charging | 1765 | 67.6% | 0% |
| Uncontrolled charging | 5286 | 35.9% | 0% |
| Station-cost-minimization charging | 1532 | 60.8% | 30.2% |
| My three-layer framework | 948 | 72.1% | 79.6% |
Compared with uncontrollable charging, the proposed framework reduces main-grid exchange power by more than 80% and increases renewable utilization by 36.2 percentage points. Compared with orderly charging, renewable utilization is improved by 4.5 percentage points. The high base-load supply ratio indicates that electric vehicles and storage effectively support the local loads during periods of high energy demand.
I also measured the impact of navigation on traffic congestion. I simulated 100 electric vehicles distributed over different origins. Four navigation strategies were compared: shortest distance, fastest time, lowest energy, and minimum charging cost. The following table reports the maximum vehicle flow and the number of congested roads.
| Navigation strategy | Peak vehicle flow on a single road (vehicles per period) | Number of congested roads |
|---|---|---|
| Shortest distance | 120 | 18 |
| Fastest time | 125 | 21 |
| Lowest energy | 100 | 17 |
| Minimum charging cost | 88 | 12 |
| My three-layer framework | 70 | 6 |
The navigation layer of my framework disperses electric-vehicle trips more evenly and reduces both peak flow and the number of congested roads. This behavior is particularly beneficial during rush hours, when the path-choice decisions of many electric vehicles strongly affect the whole traffic network.
4.8 Algorithm Efficiency of PPO-ADMM
I compared the iteration count of PPO-ADMM with standard ADMM, sequential quadratic programming (SQP), manual tuning, and adaptive ADMM in the four-charging-station test cases. The table below lists the required number of iterations.
| Algorithm | Charging station 1 (50 EVs) | Charging station 2 (100 EVs) | Charging station 3 (200 EVs) | Charging station 4 (500 EVs) |
|---|---|---|---|---|
| SQP | 121 | 133 | 147 | 181 |
| ADMM (fixed step size) | 76 | 93 | 113 | 137 |
| Manual tuning | 58 | 82 | 87 | 106 |
| Self-adaptive ADMM | 42 | 53 | 78 | 89 |
| PPO-ADMM | 18 | 31 | 50 | 72 |
PPO-ADMM requires the fewest iterations in all scenarios. The average solving time is about 3.5 seconds, which is significantly shorter than SQP and standard ADMM. The PPO-based learning strategy is particularly effective when problem size increases, demonstrating robust scalability for large-scale electric-vehicle charging dispatch.
5. Conclusions and Future Work
5.1 Summary of Contributions
My dissertation develops an energy-aware scheduling framework for electric vehicle charging in coupled transportation and distribution networks. The first contribution is a macro–micro traffic-state energy-consumption estimation model. This model combines graph-convolutional speed prediction and longitudinal vehicle dynamics to capture both deterministic traffic trends and random vehicle behaviors. Sobol sensitivity analysis reveals that acceleration is the dominant factor of energy use, which validates the value of high-resolution traffic-speed prediction. Experiments show that my model improves estimation accuracy by 5%–7.5% compared with conventional approaches, thereby reducing the range anxiety of electric-vehicle users.
The second contribution is a bi-level charging navigation model. The upper level selects charging stations and routes by minimizing the sum of energy cost, time cost, and charging cost. The lower level operates the charging station in a V2G mode and minimizes power exchange with the main grid. A GBD-LBF algorithm solves the mixed-integer nonlinear program efficiently. Simulation results confirm that the method reduces the total navigation cost by 17%–37% compared with four single-objective benchmark strategies. It also balances traffic flow and mitigates grid load fluctuation.
The third contribution is a three-layer cooperative scheduling framework for large-scale electric vehicles. The first layer aggregates charging flexibility and determines the total power profile; the second layer computes a minimum-cost charging plan for each electric vehicle; and the third layer provides economic navigation directions. I combine PPO and ADMM to accelerate convergence. The framework reduces main-grid exchange power by 948 kW compared with 5286 kW under uncontrolled charging and increases renewable utilization by up to 36.2 percentage points. At the same time, electric-vehicle users achieve lower total costs, and the traffic network experiences less congestion.
5.2 Future Research Directions
There are several promising directions for future work. First, the current uncertainty model focuses on photovoltaic generation. Wind power, traffic-flow randomness, and driving-behavior variability should be jointly represented in a unified stochastic-robust optimization framework. Second, smart-city data such as real-time parking availability, weather forecasts, and crowd-density information could be used to further improve the precision of energy estimation and route guidance. Third, more sophisticated multi-objective algorithms, such as multi-agent deep reinforcement learning with hierarchical reward shaping, might better handle conflicts among charging-station profits, user convenience, and grid security. Fourth, the proposed framework should be validated in field trials with real charging stations and connected electric vehicles. This could reveal operational issues such as communication latency, charging-protocol heterogeneity, and battery-management-system limitations. Fifth, the integration of electric-vehicle scheduling with dynamic electricity markets and carbon-trading mechanisms would be a valuable extension.
In conclusion, my research demonstrates that energy-aware scheduling is an essential enabler for large-scale electric-vehicle integration. By accurately estimating the energy requirements of electric vehicles and exploiting their charging flexibility, it is possible to harmonize transportation and energy systems. This not only reduces the operational cost for electric vehicle users but also improves the resilience and efficiency of the power grid. With continued advances in artificial intelligence, smart communication, and power electronics, I believe that the cooperative scheduling framework introduced here can be further improved and deployed in real-world smart cities.