In the face of the global energy crisis and increasingly stringent environmental regulations, achieving sustainable development in the automotive sector has become an urgent priority. Hybrid electric vehicles (HEVs), particularly parallel configurations, are pivotal in this green transition due to their superior fuel economy and reduced emissions. The core technological challenge lies in the intelligent and efficient management of energy flow between the internal combustion engine and the electric motor to maximize system efficiency. Traditional rule-based strategies, while robust, often fail to achieve global optimality across diverse driving conditions. This study proposes a novel Adaptive Equivalent Consumption Minimization Strategy (A-ECMS) optimized by an Improved Sand Cat Swarm Optimization (SCSO) algorithm. The strategy dynamically adjusts critical equivalence factors in real-time, ensuring optimal power split under varying operational scenarios. The proposed method is implemented and validated through co-simulation using AVL CRUISE for vehicle modeling and MATLAB/Simulink for control strategy development, demonstrating significant improvements in fuel economy and battery state-of-charge (SOC) maintenance.
The architecture of a parallel hybrid car, especially the P2 configuration where the electric motor is positioned between the engine and the transmission, offers great flexibility. This configuration allows for multiple operational modes, including pure electric driving, engine-only driving, combined power assist, regenerative braking, and on-the-fly battery charging. The effective coordination of these modes is the primary task of the Energy Management Strategy (EMS). For the P2 hybrid car under study, key vehicle parameters are summarized in the table below.
| Component | Parameter | Value |
|---|---|---|
| Vehicle | Curb Weight (kg) | 1700 |
| Gross Vehicle Mass (kg) | 1930 | |
| Frontal Area (m²) | 1.88 | |
| Air Drag Coefficient | 0.32 | |
| Engine | Type | Gasoline, Inline 4-Cylinder |
| Peak Power (kW) | 127 @ 6000 rpm | |
| Displacement (L) | 2.478 | |
| Electric Motor | Type | Permanent Magnet Synchronous |
| Peak Power (kW) | 21.6 | |
| Peak Torque (Nm) | 110 | |
| Battery Pack | Type | Li-ion |
| Nominal Voltage (V) | 320 | |
| Capacity (Ah) | 20.1 |
The foundation of our energy management approach begins with a rule-based strategy known as Charge Depleting-Charge Sustaining (CD-CS). This strategy is intuitive and ensures safe operation. It divides the battery’s State of Charge (SOC) into two primary zones. In the Charge Depleting (CD) zone (high SOC), the hybrid car prioritizes electric driving to utilize the cheaper and cleaner grid electricity stored in the battery. The electric motor meets the driver’s torque demand whenever possible. Only when the demanded power exceeds the motor’s capability or during high-speed cruising does the engine engage. In the Charge Sustaining (CS) zone (low SOC), the primary goal shifts to maintaining the battery SOC within a narrow band. The engine becomes the primary power source, operating more frequently and often at a higher load to simultaneously propel the vehicle and recharge the battery via the motor acting as a generator. The engine operating points are chosen based on its optimal Brake Specific Fuel Consumption (BSFC) map to improve efficiency. The mode switching logic can be described by the following pseudo-code rules, where $T_{req}$ is the requested wheel torque, $T_{em,max}$ is the maximum motor torque, and $SOC_{low}$/$SOC_{high}$ are the CS zone boundaries.
$$
\begin{aligned}
&\text{If } SOC > SOC_{high} \quad \text{(CD Zone):} \\
&\quad \text{If } |T_{req}| \leq T_{em,max} \text{ and } T_{req} > 0 \rightarrow \text{Pure Electric Mode} \\
&\quad \text{If } T_{req} > T_{em,max} \rightarrow \text{Engine-On, Motor Assist Mode} \\
&\quad \text{If } T_{req} < 0 \rightarrow \text{Regenerative Braking Mode} \\
&\text{If } SOC \leq SOC_{high} \quad \text{(CS Zone):} \\
&\quad \text{Target: Maintain SOC near } SOC_{low} \\
&\quad \text{Engine operates near optimal BSFC curve} \\
&\quad \text{Motor used for load leveling and regenerative braking}
\end{aligned}
$$
While the CD-CS strategy provides a reliable baseline, its heuristic nature limits the overall fuel economy potential of the hybrid car. To overcome this, we employ the Equivalent Consumption Minimization Strategy (ECMS) as our core optimization framework. ECMS is an instantaneous optimization method that equates electrical energy usage to an equivalent amount of fuel consumption at each time step. The total cost to minimize is the sum of the actual engine fuel consumption and the equivalent fuel consumption from battery use. The equivalence is governed by a factor, $s(t)$, which acts as a virtual “price” for electricity. The fundamental ECMS problem for the hybrid car at each instant $t$ is formulated as:
$$
J(t) = \min_{T_e(t), T_m(t)} \left[ \dot{m}_{fuel}(T_e(t), \omega_e(t)) + s(t) \cdot \frac{P_{batt}(T_m(t), \omega_m(t))}{Q_{lhv}} \right]
$$
Subject to the following constraints that define the operational limits of the hybrid car powertrain:
$$
\begin{aligned}
& T_{req}(t) = T_e(t) + T_m(t) \\
& \omega_e(t) = \omega_m(t) = \omega_{wh}(t) \cdot \text{GR} \quad \text{(for P2 configuration)} \\
& T_{e,min}(\omega_e) \leq T_e(t) \leq T_{e,max}(\omega_e) \\
& T_{m,min}(\omega_m) \leq T_m(t) \leq T_{m,max}(\omega_m) \\
& SOC_{min} \leq SOC(t) \leq SOC_{max}
\end{aligned}
$$
Here, $P_{batt}$ is the battery power (positive for discharge, negative for charge), $Q_{lhv}$ is the lower heating value of the fuel, and $T_e$, $T_m$, $\omega_e$, $\omega_m$ are the torques and speeds of the engine and motor, respectively. The critical element $s(t)$ is the equivalence factor. A constant $s(t)$ value is suboptimal as it cannot adapt to changing driving cycles or battery SOC. Therefore, an adaptive law for $s(t)$ is essential. A common approach links $s(t)$ to the battery SOC using a PI controller to maintain SOC around a reference value $SOC_{ref}$:
$$
s(t) = s_0 + K_p (SOC_{ref} – SOC(t)) + K_i \int_0^t (SOC_{ref} – SOC(\tau)) d\tau
$$
However, tuning the parameters $s_0$, $K_p$, and $K_i$ for optimal performance across all conditions is a complex optimization problem itself. This is where we introduce the Improved Sand Cat Swarm Optimization (SCSO) algorithm to find the optimal parameters for the A-ECMS law.
The standard SCSO algorithm is a metaheuristic inspired by the hunting behavior of sand cats. These animals use sensitive hearing to detect low-frequency prey noises and exhibit both exploratory (searching) and exploitative (attacking) behaviors. In the algorithm, each “sand cat” represents a candidate solution vector $\vec{X}_i = [s_0, K_p, K_i]$. The population navigates the search space by adjusting positions based on the best-found solution and a controlled auditory sensitivity range $r_G$. The position update for the searching phase is:
$$
\vec{X}_i(t+1) = r_G \cdot (\vec{X}_{best}(t) – \text{rand}(0,1) \cdot \vec{X}_i(t))
$$
For the attacking phase, it is:
$$
\vec{X}_i(t+1) = \vec{X}_{best}(t) – r_G \cdot \vec{X}_{rnd} \cdot \cos(\theta)
$$
where $\vec{X}_{rnd} = \text{rand}(0,1) \cdot (\vec{X}_{best} – \vec{X}_i(t))$ and $\theta$ is a random angle. The parameter $r_G$ decreases linearly from an initial sensitivity $s_M$ to zero over iterations, balancing global exploration and local exploitation.
To enhance the standard SCSO for the hybrid car energy management problem, we propose three key improvements:
1. Chaotic Perturbation for Population Diversity: To prevent premature convergence, we introduce a chaotic map (Logistic Map) to periodically perturb a selected individual. Every $N$ generations, one sand cat’s position is modified using:
$$x_{new} = 4 \cdot x_{old} \cdot (1 – x_{old})$$
This injection of chaos helps the algorithm escape local optima in the parameter space.
2. Dynamic Learning Factor: Instead of a linearly decreasing $r_G$, we employ a non-linear decay based on a temperature-like parameter $T$ that cools down over iterations:
$$T(iter) = T_{max} \cdot \exp(-\lambda \cdot iter)$$
$$r_G(iter) = s_M \cdot \frac{T(iter)}{T_{max}}$$
This allows for a more gradual transition from exploration to exploitation, yielding a more thorough search.
3. Simulated Annealing Acceptance Criterion: When updating the global best solution, we occasionally accept a worse candidate solution with a probability $P$ to further avoid local traps:
$$P = \exp\left( -\frac{\Delta J}{T(iter)} \right)$$
where $\Delta J$ is the increase in the objective function (total fuel consumption over a driving cycle).
The objective function for the Improved SCSO algorithm is to minimize the total equivalent fuel consumption of the hybrid car over a standard driving cycle (e.g., NEDC):
$$
\text{Minimize: } F_{total} = \int_{0}^{t_{cycle}} \dot{m}_{fuel}(t) dt + \frac{\gamma}{Q_{lhv}} \cdot |E_{batt, final} – E_{batt, initial}|
$$
The second term penalizes any net change in battery energy over the cycle to enforce charge sustainability. The algorithm searches for the parameter set $\vec{X} = [s_0, K_p, K_i]$ that minimizes $F_{total}$ when used within the A-ECMS controller.
The entire simulation framework is built using AVL CRUISE for high-fidelity vehicle dynamics and powertrain modeling, coupled with MATLAB/Simulink where the control strategies (CD-CS, ECMS, SCSO-A-ECMS) are implemented. The NEDC driving cycle is used for both optimization and final performance validation. The simulation process is as follows:
- The Improved SCSO algorithm generates a population of parameter sets.
- For each parameter set, the A-ECMS controller is simulated over the NEDC cycle in the CRUISE-Simulink co-simulation environment.
- The total equivalent fuel consumption $F_{total}$ is calculated and returned as the fitness value to the SCSO algorithm.
- SCSO updates the population and repeats until the maximum number of iterations is reached.
- The best parameter set found is then used in a final validation simulation.
The results demonstrate the clear advantage of the optimized strategy for the hybrid car. First, we compare the performance of the baseline CD-CS strategy and a standard ECMS with a fixed, manually tuned equivalence factor.
| Energy Management Strategy | Fuel Consumption (L/100km) | Electrical Consumption (kWh/100km) | Equivalent Fuel Consumption* (L/100km) |
|---|---|---|---|
| Baseline CD-CS | 4.02 | 8.83 | 6.96 |
| Standard ECMS (Fixed s) | 3.74 | 5.74 | 5.65 |
| Proposed SCSO-A-ECMS | 3.51 | 4.92 | 5.15 |
*Equivalent fuel calculated as: Fuel + (Electrical Consumption / 3), assuming 1 kWh ≈ 0.3L fuel energy equivalent.
The SCSO-optimized A-ECMS strategy achieves the lowest fuel and electrical consumption. Compared to the baseline CD-CS, it reduces equivalent fuel consumption by approximately 26%. More importantly, compared to the standard ECMS with a fixed factor, it achieves a further 8.8% reduction in equivalent fuel use, highlighting the benefit of adaptive, optimized equivalence factors. The SOC trajectory also shows superior regulation, ending the cycle very close to the initial SOC with minimal fluctuation, which is crucial for battery longevity and consistent performance of the hybrid car.
The engine operating point distribution provides visual evidence of the optimization. Under the SCSO-A-ECMS strategy, a higher density of engine operating points falls within the region of lowest Brake Specific Fuel Consumption (BSFC), indicating more efficient engine utilization. The motor is more actively used for load leveling, keeping the engine operating in its sweet spot, and for regenerative braking. The torque split at any given moment is determined by the instantaneous minimization of the equivalent cost function with the dynamically adjusted factor $s(t)$.
In conclusion, this study successfully developed and validated an intelligent energy management strategy for a parallel hybrid car. By integrating an Improved Sand Cat Swarm Optimization algorithm with the Adaptive Equivalent Consumption Minimization Strategy, we created a system that dynamically tailors the power-split decision to the driving conditions and battery state. The co-simulation results confirm significant improvements in fuel economy and charge-sustaining capability over conventional rule-based and static ECMS approaches. The proposed SCSO-A-ECMS framework demonstrates strong potential for real-world application, offering a path to unlock the full efficiency potential of hybrid cars. Future work will focus on implementing this strategy on a real-time hardware platform and testing it under more stochastic, real-world driving cycles to further prove its robustness and adaptability for the next generation of intelligent hybrid vehicles.