Research on Intelligent Hierarchical Energy Management for Connected Automated Range-Extended Electric Vehicles Based on Speed Prediction

Abstract

To address energy management challenges for intelligent connected automated range-extended electric vehicles under vehicle-road cooperative environments, a hierarchical energy management strategy (EMS) based on speed prediction is proposed from the perspective of multi-objective optimization (MOO), with comprehensive system performance being significantly enhanced. Focusing on connected car-following scenarios, acceleration sequence prediction is performed based on Kalman filtering and preceding vehicle acceleration. A dual-layer optimization strategy is subsequently developed: in the upper layer, optimal speed curves are planned based on road network topology and preceding vehicle trajectories, while in the lower layer, coordinated multi-power source allocation is achieved through EMS_MPC-P, a Bayesian-optimized model predictive EMS based on Pontryagin’ s minimum principle (PMP). A MOO model is ultimately formulated to enhance comprehensive system performance. Simulation and bench test results demonstrate that with SoC₀ = 0.4, 7.69% and 5.13% improvement in fuel economy is achieved by EMS_MPC-P compared to the charge depleting-charge sustaining (CD-CS) method and the charge depleting-blend (CD-Blend) method. Travel time reductions of 62.2% and 58.7% are observed versus CD-CS and CD-Blend. Battery lifespan degradation is mitigated by 16.18% and 5.89% relative to CD-CS and CD-Blend, demonstrating the method’s marked advantages in improving traffic efficiency, safety, battery life maintenance, and fuel economy. This study not only establishes a technical paradigm with theoretical depth and engineering applicability for EMS, but also quantitatively reveals intrinsic mechanisms underlying long-term prediction accuracy enhancement through data analysis, providing critical guidance for future vehicle–road–cloud collaborative system development.

1. Introduction

Connected automated range-extended electric vehicle (CAR-EEV) energy management strategies (EMSs) are enhanced through the dynamic coordination of power source operational modes [1]. Although global optimization and real-time control advancements exist, their efficacy remains limited by operational uncertainty. Vehicle-to-everything (V2X) enables EMS optimization [2] but current strategies depend on full SPaT (signal phase and timing) data for green-wave passage, ignoring non-connected vehicle impacts. A real-time EMS is proposed for mixed traffic flows with limited information, balancing energy emissions, battery degradation, and traffic efficiency.

1.1. Literature Review

CAR-EEVs achieve energy savings through the coordinated operation of traction batteries and an auxiliary power unit (APU) [3], overcoming fixed state of charge (SoC) thresholds via external charging and enabling dynamic SoC regulation for flexible energy dispatch and range extension. The multi-power-source nonlinear coupling characteristics of CAR-EEVs render the fuel economy sensitive to engine efficiency, motor characteristics, drivetrain configurations, and dynamic conditions, positioning EMSs as core technologies for balancing performance and economy [4]. An EMS must consider the inputs for varying driving behaviors, road traffic, load, and environmental conditions to assure flexibility of EVs among different users across the globe [1]. Rule-based control strategies allocate power through preset thresholds (simple implementation and high reliability) but exhibit poor adaptability to operating conditions and lack global optimality. A rule-based fuel cell electric vehicle (FCEV) operating mode control strategy is presented and is validated through multiple tests with different driving cycles and battery SoC strategy points [5]. A real-time rule-based strategy is proposed to determine the torque distributions of the parallel electric-hydraulic hybrid powertrain, optimizing the electric motor operating points [6]. Global optimization strategies, such as dynamic programming (DP) and convex optimization, require complete driving cycle data to derive theoretical optimal solutions but are constrained by computational complexity and real-time feasibility [7]. DP is employed to solve the constrained optimal problem for travel time, distance, and speed limit by exploring all possible control options [8]. Instantaneous optimization strategies primarily include the equivalent consumption minimization strategy (ECMS) and Pontryagin’ s minimum principle (PMP). The disadvantage is that it is not possible to find a globally optimal solution. ECMS balances fuel and motor energy consumption through equivalence factors [9]. ECMS is combined to refine the algorithm to optimize fuel consumption and fuel cell lifespan, achieving high computation efficiency, lower power fluctuation of the fuel cell and optimal fuel economy of fuel cell hybrid electric vehicles (FCHEVs) [10]. A rolling convergent ECMS for energy management of plug-in hybrid electric vehicles (PHEVs) was proposed, gaining fuel economy better than that using a traditional adaptive ECMS under two real-world driving cycles, respectively [11]. An adaptive EMS is achieved by the selection of an optimal PMP co-state variable, utilizing the clustering driving patterns [12]. An adaptive co-state design approach was introduced aimed at improving the adaptability of PMP-based EMSs for real-time implementation in PHEVs, and its energy-saving effectiveness approaches that of DP solutions [13]. Model predictive control (MPC)-based EMSs balance real-time capability and quasi-global optimality through rolling optimization and short-term operational condition prediction [14]. A novel data-driven MPC-based EMS is proposed with a dual-model framework (DDMPC) for fuel cell electric vehicles (FCEVs) to substantially enhance economic performance while maintaining control robustness [15]. A switched model predictive control with a parametric weights-based mode transition strategy was proposed to significantly elevate the quality of mode transition for a specific parallel hybrid electric vehicle (HEV) configuration [16].

Global positioning system (GPS) technologies have driven hybrid vehicle energy management innovations [17]. Connected energy management frameworks can be categorized into single-vehicle and dual-vehicle scenarios. For single-vehicle scenarios, EMSs based on speed route prediction preplan SoC trajectories by integrating driving distance, gradient, and speed limit information but exhibit limited adaptability to dynamic traffic. A combined prediction model is proposed to improve the prediction accuracy [18]. A data-driven hierarchical control strategy is developed to optimize SoC trajectories in real-time, demonstrating significant energy savings compared to non-connected systems [19]. Eco-driving-based EMSs generate eco-speed profiles through global optimization and integrate them into EMS controllers, with core challenges lying in real-time solutions for complex traffic scenarios. Hierarchical control architectures decompose driving tasks into acceleration, constant-speed, deceleration, and braking modules, with the upper layer optimizing switching timing and the lower layer executing energy-optimal control [20]. Traffic flow prediction-based energy management systems dynamically optimize power allocation robustness by integrating ITS-predicted disturbances but remain sensitive to prediction accuracy. A Monte Carlo method is used to handle traffic light timing uncertainty combined with ECMS to improve fuel economy [21]; SoC trajectories are trained via PMP and neural networks to achieve fuel savings [19]. EMSs for two vehicles, in terms of adaptive cruise control (ACC)-based energy management strategies, include a target-decoupled hierarchical control architecture that is proposed for multi-objective synergy [22]. A novel co-optimization method is developed based on PMP, which reduces fuel consumption in two different scenarios incorporating the SPaT strategy [23]. A novel efficiency model of an HEV powertrain is proposed and is used to define the economic index for evaluation [24]. For predictive cruise control (PCC) strategies, an AI-MPC framework is proposed to synchronously plan speed-SoC trajectories while optimizing power allocation and inter-vehicle distance control [25]. Stochastic preceding vehicle speed prediction models are established using radar and SPaT data to enhance following efficiency [26]. A method is developed for fitting energy consumption and universal characteristics specific to commercial vehicles based on multi-operating condition data. The resulting dataset can then be leveraged to design and implement the PCC control system [27]. Both strategies must address dynamic traffic randomness.

To address existing limitations in EMS research concerning stochastic adaptation to dynamic traffic information and global optimality inadequacies, the real-time EMS resolution problem in connected car-following scenarios is investigated. With dynamic traffic information considered, a dynamic traffic scenario model is constructed, and acceleration sequence prediction is implemented based on Kalman filtering and preceding vehicle acceleration. A dual-layer optimization strategy is proposed: optimal speed curves are planned based on road network topology and preceding vehicle trajectories in the upper layer, while coordinated multi-power source allocation is achieved through a Bayesian-optimized PMP-based model predictive EMS (EMS_MPC-P) in the lower layer. A multi-objective optimization model (MOO) is additionally formulated to achieve comprehensive system performance enhancement.

1.2. Motivation and Innovation

A multi-objective optimized control scheme integrating real-time traffic perception and hierarchical optimization is proposed to address energy management challenges in connected car-following scenarios for CAR-EEVs under vehicle-road cooperation. A dynamic traffic model with Kalman filtering-based acceleration prediction algorithms is established, involving a hierarchical framework where road topology-guided speed planning is executed in the upper layer and a Bayesian-optimized model predictive EMS based on the PMP (EMS_MPC-P) is proposed to enable multi-power coordination in the lower layer. Finally, a MOO model for system performance enhancement is formulated to achieve the optimization of vehicle operating parameters. Innovations include the following: (1) Establishment of vehicle-road cooperative dynamic scenario models featuring Kalman filtering-based acceleration sequence prediction algorithms that improve traffic efficiency through analysis of preceding vehicle states and traffic light information; (2) An intelligent hierarchical architecture integrating topology-based speed planning with EMS_MPC-P for power allocation; (3) A MOO model for comprehensive performance improvement. Through the deep integration of V2X perception and intelligent optimization technologies, enhancements of EMS in traffic efficiency, safety, and fuel economy are realized based on overcoming the limitations of conventional approaches, which provides a technical solution with both theoretical breakthroughs and engineering value for CAR-EEV.

2. Velocity Prediction Model Based on Acceleration Sequence

2.1. Acceleration Sequence Prediction Algorithm Based on Kalman Filtering

Under dynamic traffic conditions, CAR-EEV vehicles cannot rely solely on SPaT for speed planning to achieve green-wave passage. The timing of preceding vehicles passing through traffic signals is considered in the connected vehicle-following scenario. The traffic information framework of a CAR-EEV is shown in Figure 1a, while the velocity and acceleration selected as the testing set are shown in Figure 1b.

A Kalman filtering-based speed prediction algorithm utilizing preceding vehicle acceleration is developed for connected scenarios [28], where vehicle motion is assumed to remain almost unaffected by traffic variations. The optimal driving profile is selected from the maximum speed limit, acceleration profile, deceleration profile, and constant-speed profile, which are based on the acceleration magnitude, sign, and velocity values to plan instantaneous speed variations at time t. The instantaneous state x_t at time t is defined as:

$$x_t=\left[\begin{array}{c}{v}_t\\ a_t\end{array}\right]$$

(1)

where v_t is defined as the car-following speed at time t, and a_t is defined as the car-following acceleration at time t.

The state equation of the system is expressed as:

$$x_t=M{x}_{t-1}+N{a}_{t-1}+w_{t-1}$$

(2)

where a_t−1 denotes the preceding vehicle acceleration at time t − 1, with the state transition matrix $M=\left[\begin{array}{cc}1& \Delta t\\ 0& 1\end{array}\right]$, the control matrix $N=\left[\begin{array}{c}{\displaystyle \frac{1}{2}}\mathsf{\Delta }{t}^2\\ \mathsf{\Delta }t\end{array}\right]$. The process noise w_t−1 follows a zero-mean Gaussian distribution, which can be represented as w_t−1 ~ N (0, C).

The observation equation is defined as:

$$z_t=W{x}_t+v_t$$

(3)

where z_t represents the observed speed obtained from the wheel speed sensors at time t. W and v_t are the observation matrix and measurement noise, which can be represented as W = [1 0] and v_t ~ N (0, A), respectively.

The iterative updates for time and measurement states are subsequently performed as follows:

$${x_t}^{*}=M{x_{t-1}}^{*\prime }+N{a}_{t-1}$$

(4)

$$P_t=M{P_{t-1}}^{\prime }{F}^T+C$$

(5)

$$k_t={\displaystyle \frac{P_t{W}^T}{W{P}_t{W}^T+A}}$$

(6)

$${x_t}^{*\prime }={x_t}^{*}+k_t(z_t-W{x_t}^{*})$$

(7)

$${P_t}^{\prime }=(I-k_{t}W)P_t$$

(8)

where x_t−1*’ and x_t*’ denote the posterior state estimates at time steps t − 1 and t, respectively, with x_t* representing the prior state estimate at time t. While P_t−1’ and P_t’ are the posterior estimation covariance at time steps t − 1 and t, with P_t representing the prior estimation covariance at time t. C denotes the process noise covariance, k_t is the Kalman gain matrix, and A is the measurement noise covariance.

Although the algorithm exhibits performance limitations under emergency conditions, during regular driving when system noise approximates a Gaussian distribution and vehicle dynamic models can be considered quasi-linear, it achieves high-precision prediction of preceding vehicle acceleration and velocity through iterative updates of state and observation equations. With low computational complexity, rapid prediction completion enables real-time response to vehicle state changes, delivering precise information for intelligent driving assistance systems. During continuous driving, the algorithm performance remains stable without degradation over time or mileage. Furthermore, the algorithm’s underlying assumptions generally hold approximately in real-world road environments, enabling adaptation to urban roads, highways, and various traffic flow scenarios.

Through the aforementioned Kalman filtering process, the state estimate xt at each time step can be obtained. This methodology enables long temporal interval prediction of vehicle arrival times at traffic signals based on current acceleration profiles. The pseudo-code of the speed prediction algorithm based on the acceleration of the front vehicle is shown in Algorithm 1.

Algorithm 1: Vehicle speed prediction based on Kalman filtering

Input: Sensor measurement sequence {z1, z2, …, zN}, control input sequence {a1, a2, …, aN}, sampling interval dt Output: Followed vehicle speed estimation sequence 1: // Initialization parameters 2: Initialize x_t_minus_1 = [0; 0]               // Initial state [Vehicle speed; Acceleration] 3: Initialize P_t_minus_1 = eye(2)              // Initial covariance matrix 4: Define F = [1, dt; 0, 1], B = [0.5*dt^2; dt], H = [1, 0] // State transfer matrix, control matrix, observation matrix 5: Define Q = q_var * eye(2), R = r_var      // Noise covariance 6: for t = 1 to N do                       // Time-based iteration 7:     // Forecasting phase 8:     u_t = a_t                // The acceleration of the preceding vehicle at the current moment is used as a control input 9:     x_t_hat_minus = F * x_t_minus_1 + B * u_t          // Priori state estimation 10:     P_t_minus = F * P_t_minus_1 * F′ + Q            // Priori Estimated covariance 11:    // Update phase 12:    z_t = Get Wheel Speed Measurement(t)  // Get the wheel speed sensor measurement value at the current moment 13:    K_t = P_t_minus * H′ * inv(H * P_t_minus * H′ + R)  // Filter gain matrix 14:    x_t_hat = x_t_hat_minus + K_t * (z_t - H * x_t_hat_minus)  // Posteriori estimated state update 15:    P_t = (eye(2) - K_t * H) * P_t_minus              // Posteriori estimated covariance update 16:    x_t_minus_1 = x_t_hat, P_t_minus_1 = P_t        // Save the result of the current moment for the next iteration 17:    // Output current speed estimate 18:    Output Or Record (x_t_hat(1))                    // Following speed 19: end for 20: Function Output Or Record (value)              // Output or record the estimated speed of the following vehicle (for plotting or subsequent processing) 21: end Function

Based on this state estimation, the arrival time of vehicles can be predicted through combination with the location of traffic signals. This algorithm can comprehensively utilize the dynamic changes in acceleration and the uncertainty of observation data to achieve accurate prediction over a long time interval. By integrating dynamic acceleration information with observation data, effective reduction in noise interference and real-time prediction adjustment according to different acceleration changes can be achieved, which shows high adaptability to complex traffic scenarios and thus has strong fault tolerance for observation errors and model uncertainties. In summary, the velocity prediction results generated by the Kalman filtering are input to the EMS_MPC-P through a rolling optimization mechanism. The predicted velocity profile v_ego(t_k ~ t_k + l) within the prediction horizon serves as an input for lower-layer energy management, combined with the cost function in Equation (30) to guide multi-objective weight allocation. Bayesian optimization dynamically adjusts the reference SoC curve, maps it to power allocation strategies, and employs MPC to update control variables for achieving optimal coordination.

2.2. Speed Predictions Results Based on the Acceleration Sequence

The speed prediction algorithm based on the acceleration sequence is simulated to compare the predicted speeds when the prediction domain is 8 s and 4 s. The fitting effect with the actual speed and simulation results are shown in Figure 2.

It can be observed that during the initial simulation phase, velocity predictions in the 8 s prediction domain exhibited larger errors compared to that with a 4 s domain, where prediction deviations were reduced with alterations in the temporal window, demonstrating favorable tracking accuracy. Superior tracking performance of the 4 s domain velocity prediction curve was demonstrated compared to the 8 s domain implementation. Based on this prediction domain configuration, temporal predictions of the preceding vehicle’s arrival timing at traffic signals are generated, establishing informational foundations for subsequent eco-vehicle speed optimization.

Preceding vehicles are not equipped with vehicle-to-infrastructure (V2I) technology, so their operational information is transmitted to eco-vehicles (equipped with V2I technology) through vehicle-to-vehicle (V2V) communication, enabling prediction and computation within eco-vehicles. Using an acceleration sequence-based velocity prediction algorithm and signal/speed data, the arrival times of a preceding vehicle at two adjacent traffic signals are predicted in different time domains and time points.

The distance between the preceding vehicle and the signal is used to calculate the time t_1-pre when it reaches the first approaching signal and to determine its corresponding signal phase (green or red). For the current instantaneous state, x_t is in the acceleration case:

$$d_{1\text{-}pre}={\displaystyle {\int }_{t_k}^{t_{1\text{-}pre}}{v}_{pre}}dt,a>0$$

(9)

$$d_{2\text{-}pre}={{\displaystyle \int }}_{t_k}^{t_{2\text{-}pre}}{v}_{pre}dt,a>0$$

(10)

where t_k is the current moment, t_1-pre is the time at which the preceding vehicle arrives at Signal 1, t_2-pre is the time at which the preceding vehicle arrives at signal 2, v_pre is the predicted speed of the preceding vehicle, d_1-pre is the distance from the preceding vehicle to Signal 1, and d_2-pre is the distance from the preceding vehicle to Signal 2, which can be solved by the distance from the eco-vehicle to the signal and its following distance.

When the preceding vehicle decelerates to stop due to a red light, its final crossing time at the signal must account for the red-light waiting duration. Moreover, preceding vehicles do not accelerate immediately upon green light activation but exhibit a delayed response, potentially due to queued vehicles at the intersection. Thus, a Gaussian distribution model is established between the distance from the vehicle’s deceleration stop position (under a red light) to the traffic signal and the specific startup timing after green light activation. Consequently, the preceding vehicle’s arrival time at Signal 1 and 2 under deceleration conditions is calculated as:

$$t_{1\text{-}\mathrm{int}er}=G(d_{1\text{-}pre}-{\displaystyle {\int }_{t_k}^{t_1}{v}_{pre}}dt)$$

(11)

$${t_{1\text{-}pre}}^{\prime }=t_1+t_{1\text{-}\mathrm{int}er}$$

(12)

$$t_{2\text{-}\mathrm{int}er}=G(d_{2\text{-}pre}-{\displaystyle {\int }_{{t_{1\text{-}pre}}^{\prime }}^{t_2}{v}_{pre}}dt)$$

(13)

$${t_{2\text{-}pre}}^{\prime }=t_2+t_{2\text{-}\mathrm{int}er}$$

(14)

where t_1-inter is the red-light waiting duration at Signal 1, t_2-inter is the red-light waiting duration at Signal 2, t₁ is the moment when the preceding car slows down and stops at Signal 1, t₂ is the moment when the preceding car slows down and stops at Signal 2, G is the Gaussian function equation, t_1-pre’ is the final crossing time at signal 1, and t_2-pre’ is the final crossing time at Signal 2.

SoC planning in the no-gradient scenario often uses an equidistant distribution method, where the total distance traveled is obtained by GPS. The SoC consumption is linearly correlated with the mileage and uniformly distributed over the whole road segment. The distance traveled in its prediction domain [t_k, t_f] at time t_k is:

$$S_p={{\displaystyle \int }}_{t_k}^{t_f}{v}_p(t)dt$$

(15)

Then, its corresponding predicted optimal SoC value can be set by the scaling equation as follows:

$$So{C}_{opt}=So{C}_k-(So{C}_k-So{C}_{final})\cdot {\displaystyle \frac{S_p}{S_{total}-S_k}}$$

(16)

S_total is the total distance, S_k is the distance already traveled, SoC_final is the final SoC after the total distance traveled, and SoC_k is the SoC at the current t_k time.

A Bayesian optimization-based dynamic SoC allocation strategy is proposed to reconstruct the SoC reference curve in the prediction domain. Bayesian optimization consists of a probabilistic agent model and an acquisition function. The acquisition function used in this paper is:

$$\begin{array}{l}\alpha (m,D_{1:t})=(\mu (m^{\ast })-\xi -\mu (m))\mathsf{\Phi }({\displaystyle \frac{\mu (m^{\ast })-\xi -\mu (m)}{\sigma (m)}})\\ +\sigma (m)\mathsf{\Phi }({\displaystyle \frac{\mu (m^{\ast })-\xi -\mu (m)}{\sigma (m)}})\hspace{1em},\sigma (m)>0\\ \alpha (m,D_{1:\mathrm{t}})=0\hspace{1em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{0.33em}\hspace{1em}\hspace{1em}\hspace{1em},\sigma (m)=0\end{array}$$

(17)

where x is the parameter to be updated, D_1:t = {(m₁, n₁), (m₂, n₂), …, (m_t, n_t)} denotes the set of observations of the control variable m_t and the corresponding state variable n_t, μ(m*) denotes the optimal value in the current state set, Φ() denotes the standard normal distribution function, ξ is the balance parameter between global and local search, and σ(m) denotes the posterior standard deviation. The formula for the next evaluation point is:

$$m_{t+1}={\max }_{m\in \chi }{a}_t(m;D_{1:t})$$

(18)

The equation for the reference SoC under Bayesian optimization is updated as:

$$So{C}_{opt}=So{C}_k-(So{C}_k-So{C}_{final})\cdot {\displaystyle \frac{S_p}{S_{toal}-S_k}}-m$$

(19)

3. Hierarchical EMS Based on Speed Prediction

3.1. EMS for Eco-Vehicles in a Connected Scenario

The coexistence of connected and non-connected vehicles in mixed traffic flows is identified as a defining characteristic of early-stage intelligent connected driving environments. In connected car-following scenarios, preceding vehicle dynamics are perturbed by non-connected agent interactions and traffic signal variations, inducing operational complexities, including congestion-induced stationary states, emergency braking-triggered abrupt deceleration, and signal phase misinterpretation-driven red light violations. Such stochastic disturbances substantially escalate uncertainties in eco-vehicle velocity optimization. To address CAR-EEV control demands under dynamic traffic conditions, coordinated speed-energy management strategies are prioritized, integrating the MOO of traffic flow efficiency, safety distance compliance, and fuel economy enhancement. The implemented dual-layer energy management framework is architecturally shown in Figure 3.

The upper layer of the architecture generates globally optimal speed trajectories through dynamic tracking of a preset optimal constant speed benchmark, with the objective of maximizing the stable cruising time window. In the lower-layer energy management module, a Bayesian-optimized model predictive EMS based on the PMP (EMS_MPC-P) is proposed to solve MOO problems, achieving optimal allocation of the torque parameters and rotational speed operating points in the powertrain system. Numerical validation and algorithm performance evaluation are ultimately conducted through a MATLAB R2020a/Simulink co-simulation platform.

Cooperative passing strategies are proposed. The front vehicle is allowed to pass through Signal 1 quickly (and then wait at Signal 2), and the eco-vehicle is delayed to pass at Signal 1 until the next green period to achieve synchronization at Signal 2. By restricting the time deviation threshold for the two vehicles to reach the key nodes, the risk of cascading delays caused by a continuous green light for the front vehicle and a continuous red light for the rear vehicle can be effectively avoided. According to the above constraint principle of the following car scenario, the interval time Δt_s does not affect the pre-speed planning.

$$t_{pre\_end}<t_{ego\_end}\le t_{pre\_end}+\Delta t_s$$

(20)

where t_{pre_end} denotes the time used by the front vehicle to reach the end, and t_{ego_end} denotes the time used by the eco-vehicle to reach the end. This paper is based on the concept of MPC scrolling to improve the efficiency of the passage, so as to ensure in real-time that both vehicles arrive at the second signal from the target vehicle as simultaneously as possible.

$${t_{2\text{-}ego}}^{\min }=t_{2\text{-}pre}$$

(21)

where t_2-ego^min is defined as the eco-vehicle’s minimum arrival time at the second downstream signal, with t_2-pre representing the preceding vehicle’s estimated arrival time at the same signal. Temporal traffic efficiency is ensured through rolling updates of the eco-vehicle’s real-time position calculations.

The minimum safety distance must consider rear-end collision risks and road access efficiency, where endpoint arrival time synchronization is already ensured by prior access efficiency constraints. Minimum safe spacing is determined via a time headway model, with the inter-vehicle safety distance defined as:

$$s_{pre}-s_{ego}\ge s_{min}+h\cdot v_{ego}$$

(22)

where s_pre is the real-time distance between the preceding vehicle and the starting point, s_ego is the real-time distance between the eco-vehicle and the starting point, s_min indicates the minimum spacing between the vehicles, and h indicates the driver’s reaction time, whose specific value has less influence on the whole speed planning. The minimum spacing is set to 3 m, the reaction time is set to 0.5 s, and v_ego represents the speed of the eco-vehicle.

Optimal constant speeds of 5–15 m/s are set in this paper. The economy is optimized by maximizing the constant speed travel time of the eco-vehicle. For the optimal speed curve of the eco-vehicle, the planning steps are as follows:

(1)

The optimal constant-speed profile v_opt is established as a stationary horizontal line. Derived from preceding vehicle historical driving data, the canonical acceleration profile v_acc (standstill → maximum speed limit) and deceleration profile v_dec (maximum speed limit → standstill) are extracted. These are systematically integrated with the emergency braking profile v_bre to synthesize the optimal velocity trajectory.

$$v_{ego}={\zeta }_1{v}_{acc}+{\zeta }_2{v}_{dec}+{\zeta }_3{v}_{opt}+{\zeta }_4{v}_{bre}$$

(23)

$$[{\zeta }_1,{\zeta }_2,{\zeta }_3,{\zeta }_4]\in [0,1]$$

(24)

For the optimal constant speed curve, the influence of 11 constant speed plans in the interval of 5–15 m/s is considered in this paper. The emergency braking curve is dynamically generated based on the real-time acceleration demand to ensure that the distance from the front vehicle after braking satisfies the constraints of Equation (22).

(2)

The preceding vehicle’s speed prediction is based on its current speed v_pre and SPaT information (remaining time t_remain). An acceleration sequence model generates the speed sequence, which is combined with position data (d_1-pre, d_2-pre) to estimate its arrival times t_1-pre and t_2-pre at traffic signals (implemented in Section 2).

(3)

The temporal information from two adjacent signals and the predicted preceding vehicle arrival time is utilized to calculate the minimum allowable time and maximum allowable time for the eco-vehicle’s arrival at the first and second signal:

$$\mathrm{int}1=fix((t_{1\text{-}ego}-t_{1\text{-}remain})/t_{cir})$$

(25)

$$\mathrm{int}2=fix((t_{2\text{-}ego}-t_{2\text{-}remain})/t_{cir})$$

(26)

where fix() is a rounding function, t_1-remain indicates the remaining time of the current Signal 1 phase, t_2-remain indicates the remaining time of the current Signal 2 phase, and t_cir indicates the fixed cycle time of the signal.

(4)

The eco-vehicle’s arrival times (t_1-acc/t_1-opt/t_1-dec for Signal 1, t_2-acc/t_2-opt/t_2-dec for Signal 2) under three speed profiles (v_acc, v_opt, v_dec) are computed. Prioritizing sustained travel duration maximization within the prediction horizon, the optimal speed profile v_opt serves as the baseline velocity, formulated as:

$$J=\arg \max {{\displaystyle \int }}_{t_k}^{t_{2\text{-}pre}}{v}_{opt}dt$$

(27)

The specific method of solving and analyzing can be followed in the following steps: eco-speed decision logic: If the eco-vehicle’s arrival time t₂^max at Signal 2 under speed v_acc satisfies t₂^max < up_t₂ + t_b (up_t₂ is the minimum allowable time to arrive at Signal 2, buffer threshold t_b = 1 s), then v_ego = v_opt; otherwise, v_ego = v_acc. A secondary validation sets v_ego = v_opt if t_1-max < up_t₁ + t_b (up_t₁ is the minimum allowable time to arrive at Signal 1), which compensates for the prediction error in the arrival time of the preceding vehicle to ensure near-synchronized passage through Signal 2. Speed control logic: if the eco-vehicle is stationary and can reach Signal 1 earlier via v_opt, standstill is maintained; if it is in motion, it decides to accelerate or decelerate based on whether the following distance exceeds the safety threshold. The new speed v_ego is planned by validating if the v_opt-based arrival time t_1-opt falls within the window [up_t₁, down_t₁] (down_t₁ is the maximum allowable time to arrive at Signal 1) at the signal. Then, under safety constraints, v_ego is iteratively updated, taking into account the dynamic parameters of the preceding vehicle (v_pre, a_pre, d_pre) and the stop line position. Finally, the optimal speed v_ego is updated again based on the last time down_t₁ at which the eco-vehicle can cross the signal, ensuring that the eco-vehicle can cross the signal within the specified interval.

3.2. Multi-Objective Optimization Model

This study establishes a V2I-based car-following control framework employing an MPC rolling optimization mechanism. The speed prediction horizon is defined as [t_k, t_2-ego], where t_k denotes the current timestep and t_2-ego represents the predicted arrival time of the eco-vehicle at Signal 2. The initial segment [t_k, t_k + l] defines the prediction horizon with length l. Within this horizon, the traffic flow efficiency, fuel economy, and SoC are optimized simultaneously to generate the velocity prediction profile. The initial speed prediction segment is fed into the lower-layer EMS, where the optimal control variable for the next second is executed as the powertrain command, with real-time state updates and rolling solution enabled. The velocity trajectory optimization is formulated as a maximization problem:

$$d_{pre}-d_{ego}\ge s_{\min }+h\cdot v_{ego}$$

(28)

The velocity in the prediction horizon is:

$$v_{\mathrm{ego}}^{*}=v_{\mathrm{ego}}(t_k\sim t_k+l)$$

(29)

The predicted velocity profile within the prediction horizon is integrated into the lower-layer EMS, where the EMS_MPC-P method presented solves the fuel consumption minimization problem. The lower-layer objective function is formulated as:

$$J={{\displaystyle \int }}_{t_k}^{t_k+l}{\omega }_C\cdot C_{fuel\_ele}(n_{APU},T_{APU})+{\omega }_B\cdot P_{batt}(SoC,I_{batt})+{\omega }_Q\cdot Q_{loss}+{\omega }_T\cdot T_{pass}dt$$

(30)

where J is the cost function, ω_C is the unit fuel parameter, ω_B is the unit battery parameter, ω_Q is the unit battery life degradation parameter, ω_T is the unit pass time parameter, n_APU is the APU system speed, T_APU is the APU system torque, I_batt is the instantaneous battery current, C_{fuel_ele} is the oil-to-electric conversion loss rate, Q_loss is the battery life degradation, P_batt is the battery output power, and T_pass is the average pass time (sec) through traffic lights.

The Hamiltonian function is constructed as:

$$\begin{array}{l}H(SoC(t),u(t),\lambda (t),t)={\omega }_C\cdot C_{fuel\_ele}(n_{APU},T_{APU})\\ +{\omega }_B\cdot P_{batt}(SoC,I_{batt})+{\omega }_Q\cdot Q_{loss}+{\omega }_T\cdot T_{pass}+{\lambda }_1(t)\cdot {\displaystyle \frac{dSoC}{dt}}+{\lambda }_2(t)\cdot {\displaystyle \frac{d{n}_{APU}}{dt}}\end{array}$$

(31)

where λ₁ is the covariate of the battery SoC, and λ₂ is the covariate of the APU system speed.

The optimal EMS is transformed into a minimization problem:

$$u^{*}(t)=(n_{APU}^{*}(t),T_{APU}^{*}(t),P_{batt}^{*}(t))=\arg \min H(SoC(t),u(t),\lambda (t),t)$$

(32)

In the CAR-EEV architecture, the internal combustion engine (ICE) serves as a vital energy conversion component, with fuel consumption being thoroughly evaluated. Fuel consumption assessment criteria and battery capacity degradation metrics are delineated. It demonstrates that battery longevity can be extended by stabilized SoC trajectories, which, in turn, improves the efficiency of energy exchange between the battery and engine. Functional synergy between the APU and batteries is achieved through hybrid energy storage system implementation, forming an effective strategy for battery service life extension. Electric motor efficiency considerations are integrated, with C_{fuel_ele} and Q_loss being mathematically defined through Equation (33).

$$\left\{\begin{array}{l}{C}_{fuel\_ele}=1-{\displaystyle \frac{360\cdot {\eta }_{ele}}{{\eta }_{fuel}\cdot \rho }}\\ Q_{loss}={\displaystyle {\int }_0^{T_{cyc}}0.495\times \frac{d{I}_{batt}\left(t\right)}{dt}\times \exp \left(0.379\frac{I_{batt}\left(t\right)}{A{h}_{cell}}\right)\times N_{cyc}\times DODdt}\\ T_{pass}={\displaystyle \frac{{\displaystyle \sum _{j=1}^{n_{tot}}(t_{j\_pass})}}{n_{tot}}}\\ I_{com\_ovp}={\displaystyle \frac{1}{{\omega }_c{C}_{fuel\_ele}+{\omega }_Q{Q}_{loss}+{\omega }_T{T}_{pass}}}\end{array}\right.$$

(33)

The power generation efficiency of the generator is represented by η_ele, with η_fuel characterizing the fuel-to-effective power conversion efficiency of the engine. The gasoline calorific value (ρ) is quantified as 4.6 × 10⁷ J/kg. The total cycle duration is designated as T_cyc. The depth of charge/discharge (DOD) is specified as 0.7, with N_cyc quantifying the total life cycles and Ah_cell corresponding to the battery’s cumulative capacity. t_{j_pass} is the passing time at the j-th traffic light, n_tot is the number of traffic lights and I_{com_ovp} is the comprehensive performance evaluation index of the APU, taking into account the energy consumption and battery life. In practical considerations, the transit time weight coefficient is relatively lower than the energy consumption emission factors, being significantly influenced by external factors, such as road traffic conditions and traffic participant behaviors, that exhibit strong uncertainty and uncontrollability, while system control over the transit time remains limited. Furthermore, optimizing energy consumption emissions may involve sacrificing partial transit time but achieves enhanced energy efficiency and cost reduction. Comprehensively balancing the system control objectives with the controllability and importance of various factors, the weight parameters are adjusted to [ω_C, ω_Q, ω_T]^T = [0.4, 0.3, 0.3]^T based on the developers’ understanding of the control requirements.

4. Verification and Results Analysis

4.1. Simulation Results and Analysis of Vehicle Speed Prediction of Eco-Vehicles

CAR-EEV is characterized as an electromechanical hybrid power system jointly driven by multiple energy sources, where precise modeling of its powertrain system and components is established as the fundamental basis for EMS research. Detailed component-level modeling of CAR-EEV powertrains is conducted utilizing AVL, encompassing dynamic system architectures, APU configurations, battery modules, DC/DC converters, and drive motor characteristics. The degradation mechanisms of the battery systems are analytically examined with corresponding lifespan deterioration models formulated. Traffic simulation scenario frameworks are constructed to enable subsequent traffic information-driven vehicle speed prediction studies. The topological structure of the powertrain system for a CAR-EEV is shown in Figure 4.

To validate the performance of the intelligent EMS proposed in terms of energy consumption economy and mitigating battery capacity degradation in a CAR-EEV, a traffic simulation framework based on SUMO with a co-simulation platform interfaced to MATLAB via Traci is utilized to obtain vehicle driving condition information, which is then applied to the EMS_MPC-P within a continuous action space. Car-following and lane-changing behavioral models are implemented across all vehicular agents to enable route optimization for destination convergence. Real-world vehicular datasets are utilized to construct a SUMO traffic network model, ensuring full-scale roadway simulation across all segments.

The speed optimization analysis is carried out for the research scenario of this paper. The optimized simulated traffic trip is shown in Figure 5 (Where the red parts represent the red light time and the green parts represent the green light time):

It can be observed that during the car-following process, the trajectory curve of the eco-vehicle is maintained along the green line with synchronized arrival time relative to the preceding vehicle at 3400 s, satisfying trafficability requirements. At intersections, the trajectory of the preceding vehicle is precisely followed by the eco-vehicle, and no red light violations are observed throughout the process. When the preceding vehicle is halted by a red light, coordinated stopping is achieved with the eco-vehicle maintaining proximity to the preceding vehicle, where smooth traffic flow is ensured and the effectiveness of the speed planning strategy in maintaining following performance and traffic efficiency is validated.

4.2. Comparative Analysis and Verification of Experimental Results

A comparative analysis is performed to evaluate the energy consumption optimization and battery capacity degradation mitigation across four EMS for CAR-EEVs: Dynamic programming (DP)-based EMS, charge depleting-charge sustaining (CD-CS), charge depleting-blend (CD-Blend), and the proposed multi-objective intelligent EMS (EMS_MPC-P). The effectiveness of EMS_MPC-P in coordinated energy-battery optimization is verified through systematic benchmarking. The CD-CS strategy triggers APU activation at SoC = 30%, emulating conventional threshold control, whereas CD-Blend employs dynamic PI-controlled electric-oil power coupling. Comparative metrics reveal CD-CS reduces battery cycling by 42%, while CD-Blend decreases the APU start-stop frequency by 38%. Algorithmically, EMS_MPC-P and DP share Q-value function frameworks but diverge in state-space treatment. DP utilizes 40 × 80 discretized grids versus EMS_MPC-P’s four-layer fully connected network for continuous mapping, both maintaining a 0.95 discount factor. Experimental rigor is ensured through 100 Monte Carlo trials with 95% confidence intervals.

The energy storage system’s performance and fuel consumption were jointly assessed through simulation. The passage time T_pass and battery degradation metrics are tabulated in

Table 1. Test results of simulation test.

Strategy	Cfuel_ele	∆Cfuel_ele	Tpass	∆Tpass	Qloss	∆Qloss	Icom_ovp
CD-CS	0.76	−	35.5	−	11.6%	−	0.76
CD-Blend	0.75	−1.32%	34.6	−2.5%	10.2%	−13.79%	0.88
DP	0.70	−7.89%	11.6	−67.3%	9.5%	−18.1%	0.94
EMSMPC-P	0.71	−6.58%	12.3	−65.4%	9.6%	−17.2%	0.93

, with comparative results provided against DP-based EMS benchmarks. DP’s reliance on a priori information and its computationally intensive nature limits its applicability to real-time energy management, restricting its utilization to benchmark validation purposes.

The C_{fuel_ele} energy consumption values are measured as 0.76 and 0.71 for CD-CS-based EMSs and EMS_MPC-P, respectively. Compared to CD-CS, a 6.58% reduction in equivalent energy consumption is achieved by the EMS_MPC-P strategy, accompanied by a 7.89% deviation reduction from DP and energy efficiency reaching 80% of DP levels. In computational timeliness, CD-CS demonstrates optimal real-time performance with 0.15 s processing time, while EMS_MPC-P requires 0.18 s, remaining feasible for online applications. With respect to reduction in pass time, the EMS_MPC-P strategy has a ∆T_pass of −65.4%, which is close to the DP strategy’s −67.3%. Battery lifespan analysis reveals CD-Blend reduces degradation by 13.79% relative to CD-CS, with the DP strategy achieving 18.1% improvement. DP’s superiority is attributed to high-efficiency battery operation range maintenance, effectively mitigating degradation. EMS_MPC-P exhibits 17.2% lower degradation than CD-CS, confirming its battery management efficacy. EMS_MPC-P approaches optimality in degradation regulation and reduction in pass time.

The EMS_MPC-P achieves energy consumption economy comparable to DP-based global optimization while demonstrating superior equilibrium in battery capacity degradation mitigation relative to DP and CD-CS strategies. This approach synergistically optimizes battery longevity and system economics through operational condition simulations, validating EMS_MPC-P advantages in energy cost reduction, lifespan regulation, and control robustness across diverse driving scenarios (Figure 6). As the primary energy supply unit for hybrid electric vehicles, the APU system satisfies fundamental power demands. Battery-integrated APU configurations attenuate load power fluctuations through responsive energy buffering, thereby extending APU service life. The EMS_MPC-P incorporates a battery SoC preservation coefficient within its reward function to explicitly address lifespan considerations. The EMS_MPC-P framework defines four operational modes: (1) CD-EV Mode: Electric propulsion dominates, with the CD strategy managing battery charging during power surplus. (2) CD-Blend Mode: APU engagement balances dual-energy utilization, progressively increasing power contribution as reserves diminish while maintaining a certain percentage of power. (3) CS-Blend Mode: CS strategy stabilizes battery SoC via engine-dominant propulsion with concurrent charging. (4) DC Mode: Predictive congestion-triggered battery replenishment through dynamic charging during motion.

The CD-CS strategy exhibits maximal SoC volatility, correlating with accelerated lifespan degradation. Battery current/power distributions under three EMS reveal EMS_MPC-P’s operational point concentration in high-efficiency regions per strategic specifications, contrasting with fuel minimization-driven clustering in lower-efficiency zones. Comparative analysis demonstrates EMS_MPC-P’s superiority in energy economy and lifespan preservation. The CD-CS strategy is characterized by the highest total equivalent energy consumption and maximal battery lifespan degradation, indicative of battery operation within minimally efficient ranges. A balance between energy consumption economy and capacity fade mitigation is achieved by the EMS_MPC-P, where the global energy consumption economy is approximated, battery lifespan degradation is suppressed, and operational longevity is enhanced.

The developed control strategy demonstrates optimized energy consumption and battery longevity performance. DP is established as the offline optimal benchmark. Normalization parameters are computed for cross-strategy performance comparison due to dimensional heterogeneity among evaluation metrics, calculated as:

$${\eta }_{ik}={\displaystyle \frac{{\lambda }_{ij}-{\lambda }_{ij}^{\min }}{{\lambda }_{ij}^{\max }-{\lambda }_{ij}^{\min }}}$$

(34)

where η_ik is defined as the normalized value of the j-th evaluation metric under the i-th strategy, and λ_ij denotes the raw metric value, with λ^min_ij and λ^max_ij representing its theoretical minimum and maximum bounds.

Normalization analysis incorporates simulation outcomes from the implemented strategies, with the statistical results shown in Figure 7.

From the comparison of the normalization parameters, it can be seen that the CD-Blend strategy outperforms the CD-CS strategy in terms of Q_loss and SoC, and the proposed EMS_MPC-P is the closest to the DP-optimal solution in all the parameters.

4.3. Experimental Test Implementation and Its Results

EMS_MPC-P was formulated and simulated offline, with adaptive control model recalibration required for real-world deployment to ensure real-time functionality. The experimental protocol comprises: (1) vehicle parameters and driving cycles conditions being loaded into road load simulation software; (2) AVL system emulation of road loads via closed-loop control of speed and torque of the motor/dynamometer; (3) real-time electric power calculation through DC bus voltage-current monitoring; (4) battery SoC-driven EMS execution generating engine/generator speed-torque commands; (5) APU power coordination determination. Four-strategy validation experiments were conducted with calculated APU power as tracking targets. The structure of the experimental platform is shown in Figure 8.

The parameters of the components are provided in

Table 2. Parameters of the vehicle components of the experimental platform (Changchun, China).

Components	Parameters	Value	Components	Parameters	Value
Engine	Maximum power (kW)	65	Battery	Continuous discharge capacity (C)	2
	Minimum speed (r/min)	950		Nominal voltage (V)	320
	Maximum speed (r/min)	6500		Capacity (A·h)	25
Generator	Maximum power (kW)	60	Motor	Peak power (kW)	75
	Maximum speed (r/min)	9000		Maximum speed (r/min)	9000

.

The energy consumption economy outcomes from the simulations and bench tests are tabulated in

Table 3. Test results of experimental test.

Strategy		SoC0 = 0.4
	Cfuel_ele	∆Cfuel_ele	Tpass	∆Tpass	Qloss	∆Qloss	Icom_ovp
CD-CS	0.78	−	36.5	−	13.6%	−	0.72
CD-Blend	0.76	−2.56%	35.2	−3.5%	12.2%	−10.29%	0.83
DP	0.72	−7.69%	13.1	−64.1%	10.9%	−19.85%	0.91
EMSMPC-P	0.72	−7.69%	13.8	−62.2%	11.4%	−16.18%	0.90
Strategy		SoC0 = 0.8
	Cfuel_ele	∆Cfuel_ele	Tpass	∆Tpass	Qloss	∆Qloss	Icom_ovp
CD-CS	0.75	−	36.4	−	12.1%	−	0.78
CD-Blend	0.74	−1.33%	34.7	−4.6%	11.8%	−2.48%	0.85
DP	0.71	−5.33%	12.6	−65.4%	9.8%	−19.01%	0.94
EMSMPC-P	0.71	−5.33%	13.1	−64.0%	10.2%	−15.70%	0.93

. The consistency between the offline simulations and the bench testing results is demonstrated, confirming effective power tracking and dynamic performance compliance. A marginal increase in energy consumption is observed during bench testing compared to the simulations, with deviations remaining within acceptable thresholds. The proposed EMS_MPC-P achieves real-time speed tracking with minimal errors, validating control precision. Simulation–experimental consistency is maintained despite minor discrepancies caused by signal accuracy and transmission latency, confirming EMS functional integrity.

Analysis of Table 3 reveals three conclusions: At SoC₀ = 0.4, EMS_MPC-P achieves the SoC control target, while CD-CS and CD-Blend exhibit poor performance. Fuel economy superiority is demonstrated by EMS_MPC-P with C_{fuel_ele} = 0.72 (7.69% reduction vs. CD-CS, 5.13% reduction vs. CD-Blend). The pass time is reduced by EMS_MPC-P with T_pass = 13.8 s (62.2% and 58.7% reduction vs. CD-CS and CD-Blend). The battery degradation is minimized under EMS_MPC-P (16.18% and 5.89% reductions vs. CD-CS and CD-Blend). At SoC₀ = 0.8, the energy consumption, pass time, and battery lifespan loss are also reduced. An enhancement in battery operating efficiency is demonstrated with the increase in SoC, accompanied by reductions in overall energy consumption and mitigation of battery lifespan degradation. Bench testing confirms the feasibility and effectiveness of the proposed EMS_MPC-P.

5. Conclusions

To address energy management challenges for intelligent CAR-EEVs under vehicle-road cooperative environments, a hierarchical EMS based on speed prediction is proposed from the perspective of MOO, with comprehensive system performance being significantly enhanced. Focused on connected car-following scenarios, acceleration sequence prediction is performed based on Kalman filtering and preceding vehicle acceleration. A dual-layer architecture is designed: the upper layer plans optimal speed curves based on the road topology and preceding trajectories, while the lower layer enables coordinated multi-power allocation through EMS_MPC-P. Finally, a MOO model for system performance enhancement is formulated to achieve the optimization of vehicle operating parameters. Simulations and bench tests validate the effectiveness of the proposed hierarchical energy management strategy. A vehicle-road cooperative dynamic scenario model was constructed, providing an extensible technical framework for real-time energy management of intelligent connected vehicles. The proposed EMS_MPC-P achieves deep integration between MOO models and V2X perception, enhancing traffic efficiency and safety while reducing battery lifespan maintenance costs by over 16%. The research outcomes can be applied to on-board controller development in intelligent transportation systems, offering a theoretical foundation for standardized protocol design in vehicle–road–cloud cooperative systems. Considering the inherent robustness of Kalman filtering, future improvements could involve introducing extended Kalman filtering to handle nonlinear dynamics, integrating real-time sensor data (e.g., radar or camera) to enhance the environmental perception capabilities, and designing adaptive noise covariance update modules to improve the algorithm’s effectiveness and reliability in complex traffic scenarios.