In this section, in order to test the optimization effect of ARC-EMS and the ability of the proposed MOO method to balance energy consumption and emissions, simulation and experimental bench will be used to validate the EMS described in Sect. 2.
MOO simulation model
AMEsim and MATLAB/Simulink software are used to build the vehicle dynamic model and the proposed EMS respectively, and the co-simulation of the two is realized through the S-function, as shown in Fig. 6.
Simulation platform of the R-EEV for the MOO problem: (a) Simulation platform of the R-EEV; (b) Control strategy model developed using MATLAB/Simulink.
The fundamental parameters of the target vehicle researched are shown in Table 2.
The algorithm design scheme employed in the study enhances computational efficiency through the optimization of data structures, reduction of unnecessary computational steps, and utilization of parallel computing techniques. This is reflected in multiple aspects including the simplified battery degradation model, the low-computational-cost fuzzy adaptive algorithm, and the implementation of rule-based strategy control logic using pre-stored rules. Regarding implementation difficulty, both algorithmic complexity and programming feasibility have been carefully considered. The implementation complexity has been reduced through rational module partitioning and well-structured code organization. Furthermore, comprehensive validation has been conducted through unit testing, integration testing, and performance testing to ensure algorithmic stability and reliability.
Parameter optimization results based on Pareto solution sets
An optimization model was built and integrated based on the AMEsim software mentioned above, and the optimization variable results was observed. As shown in Fig. 7, the variations in optimization variables throughout the iterative process, demonstrating the trend of these variables as the iteration count increases. After approximately 120 optimization iterations, the optimization variables converge to a constant value, and during the iteration process, the paths of convergence exhibit some discrepancies, which indicate the effectiveness of the algorithm.
In the initial phase of the convergence analysis for ne and Te, a relatively large fluctuation range of ne, spanning from 1000 to 1650, was observed. This indicates that, during the early stages of the optimization process, the algorithm was exploring a variety of potential velocity values in order to locate the optimal solution. After approximately 40 iterations had elapsed, the fluctuation range of ne began to diminish and stabilize. This indicates that the algorithm has commenced convergence and is progressively approaching the optimal velocity value. After undergoing 60 iterations, the fluctuation ranges of ne and Te stabilized within [1250, 1350] and [100, 120], respectively, and converged steadily to approximately 1280 and 115. These values are likely to be the optimized velocity and torque thresholds that achieve the optimization objectives under the given constraints. This reflects the efficiency characteristics of the hybrid power system across different power operating regions. In the low-power consumption region, the system efficiency is relatively low; therefore, the optimization results tend to be oriented towards increasing the power margin values to enhance efficiency. During the convergence analysis phase for SoCH_0 and SoCL_0, the fluctuation ranges of both SoCH_0 and SoCL_0 were initially large and exhibited a downward trend. After approximately 80 iterations had elapsed, the fluctuation ranges of SoCH_0 and SoCL_0 began to diminish and stabilize. This indicates that the algorithm has commenced convergence and is progressively approaching the optimal velocity values. After undergoing 120 iterations, the fluctuation ranges of SoCH_0 and SoCL_0 were stabilized within [0.65, 0.68] and [0.42, 0.44], respectively, and converged steadily to approximately 0.66 and 0.43. At the low SoC stage, the battery charging and discharging efficiency is relatively low; therefore, the optimization results tend to increase the proportion of charging conditions, maintaining a trend of sustaining the SoC within a higher efficiency range to enhance overall efficiency. The uniformity and rationality of the working mode distribution also demonstrate the effectiveness of the optimization algorithm. This allocation method can balance the required power range during operation, thereby ensuring the stable operation of the M-MPHV across different driving scenarios and loading conditions.
Optimization variables changes during the iterative process.
This section adopts the analysis method of Pareto optimal theory, which reflects the essential features of MOO problem directly. The contradictory relationship between the two goals is comparatively analyzed in relation to evaluation indicators such as Cfuel_ele, Qloss and Icom_ovp. Figure 8 shows the solution set of the optimal Icom_ovp, which is described at length later as the optimized decision result.
Multi objective optimization results based on Pareto and comparative analysis: (a) distribution of the Pareto optimal solution in objective space; (b)performance comparison.
The configuration of the powertrain operating modes, specifically the manner in which the internal combustion engine, electric motor, and battery collaborate, directly leads to differences in energy consumption and battery capacity degradation. These differences are profoundly influenced by the control strategies that are implemented. In order to minimize energy consumption, strategies are flexibly adjusted based on the state of the battery: When the battery’s SoC is low, the system tends to select the range-extended mode (M2), in which the internal combustion engine operates at its optimal efficiency point to charge the battery, thereby avoiding battery operation in low-efficiency ranges, reducing energy consumption, and protecting the battery. Conversely, when the battery’s SoC is high, there is a greater tendency to adopt the pure electric mode (M1), allowing the battery to operate in a high-efficiency state and maximizing the utilization efficiency of electrical energy. When confronted with high power demands (Preq), the system is switched to the internal combustion engine drive mode (M4), leveraging the advantage of the internal combustion engine operating in its high-efficiency range to further reduce energy consumption and enhance the battery’s lifespan. It is noteworthy that when the proportion of Preq is low, the system may face the challenge of increased energy consumption. Although frequent power switching in M4 mode may result in additional fuel consumption, this mode actually reduces the frequency of battery usage, thereby contributing to the extension of battery life. The inherent contradiction between these control objectives is an inevitable issue in powertrain optimization, highlighting the importance of optimizing relevant thresholds and key parameters to achieve an optimal balance between energy consumption and battery life.
Comparison results of parameter fixation and parameter adaptation
In this section, in order to verify the universality, the parameter optimization results with the optimal Icom_APU are selected for comparative study, and the RC-EMS with adaptive parameter adjustment module is referred to as a revise strategy (ARC-EMS). As a result, much more engine power transients can be observed within the entire CS phases. The comparison of simulation results before and after optimization is shown in Fig. 9.
The comparison of simulation results before and after optimization.
Figure 9 shows the significant differences in the switching results of the power system operating modes under RC-EMS and ARC-EMS. And the designed control logic was implemented when the power switching conditions were met, which demonstrates the excellent ability of the two comparison strategies. The addition of adaptive modules increases the working ratio of M1 and M4 under ARC-EMS. By running the ICE at its optimal efficiency point in M4, the battery is charged to avoid working in the low efficiency range, reduce energy consumption, and protect the battery; The M1 is relatively increased to drive vehicles with as much electricity as possible, while the M2 is relatively reduced to save fuel consumption. In M4 mode, ICE operation is optimized to maintain peak efficiency by the adaptive module, reducing energy waste. Dynamic adjustments to M1 and M2 modes are implemented, prioritizing electric propulsion to lower fuel consumption. ARC-EMS demonstrates superior SoC management, with smoother trajectory variations and reduced discharge depth, achieving significant improvements in both energy efficiency and battery lifespan. The SoC trajectory and battery charging and discharging current information under RC-EMS and ARC-EMS. The two SoC curves, which are considered roughly monotonic, slowly decrease to 0.631 and 0.622, respectively. Compared with RC-EMS, as expected, the SoC curve of ARC-EMS has reached a lower final SoC value, because the adaptive module will adjust the operating mode after curing according to the objective situation that the SoC value is too large, so that more battery energy can be used. According to the constraints set in the problem, the battery SoC varies within the range of [0.6, 0.7], with minimal variation during the driving cycle, achieving good tracking characteristics for SoC reference and thus extending battery life. The slight changes in SoC significantly reduce the depth of discharge, which is beneficial for achieving longer battery life and ensuring that the SoC trajectory does not exceed the lower limit, thereby avoiding damage to battery health.
Experimental test implementation and its results
Comparative study against benchmark control strategy to thoroughly evaluate the proposed ARC-EMS, the control strategies are introduced as comparison basis. The proposed ARC-EMS urges multiple energy sources to work towards more battery discharge conditions, and the robustness of its strategies is proven as the overall trend of statistical results remains similar even as working conditions become more. The developed control strategy exhibits excellent performance in terms of energy consumption, emissions, and battery life, with a particular highlight being the significant reduction in battery life attenuation that can substantially lower the overall vehicle’s service cost economically. Similar to the previous study, due to the different units and scales, before comparing the performance of the four strategies horizontally across different cycles, the normalization parameters of the performance indicators are calculated as follow:
$${\theta _{ik}}=\frac{{{\delta _{ij}} – \delta _{{ij}}^{{\hbox{min} }}}}{{\delta _{{ij}}^{{\hbox{max} }} – \delta _{{ij}}^{{\hbox{min} }}}}$$
(14)
Where ɵik is the normalized index of j-th evaluation index on i-strategy; δij is the index value; δminij and δmaxij are the index minimum and maximum value, respectively.
In addition to considering the results of the energy storage system, the simulation results of system fuel consumption, the comparison of 100 km equivalent fuel consumption (Ge) between six control strategies after the modification of terminal SoC (the SoC corrected fuel efficiencies) are shown in Fig. 10; Table 3. DP is utilized as an optimal off-line baseline under the test driving cycle, while optimal control is employed with Icom_ovp as the objective function. Eventually, the data domain used for normalization analysis is determined, which includes the simulation results under the above strategies and the result data under the single target based on Pareto solution set. Based on formula 15, the normalized statistical results are shown in Fig. 10.
Comparison of normalized evaluation indicators.
As shown in Fig. 10, the result of the proposed strategy is closest to the best performance that can be achieved. And the performance results under each strategy show different performance, which implies that the ARC-EMS considered in this study can achieve the better balance among the two objectives.
The total consumption of ARC-EMS slightly reduced by about 2.7% compared to M2, whereas the ARC-EMS is almost identical to M2 with a difference of only 1.3%, leading to the conclusion that ARC-EMS is slightly better than RC-EMS. Comparing with the results of RC-EMS and ARC-EMS with threshold parameter adjustable, there is not much difference in fuel consumption (Ge), which signifies that the proposed ARC-EMS performs well in terms of fuel economy. Based on the different operating characteristics of M-HEV in different modes, the optimized strategy will tend to operate ICE in the high-efficiency region. This mode adopts a power tracking control strategy to operate the engine at the optimal operating point corresponding to the required power. In terms of battery life, the Qloss under ARC-EMS is relatively small, reaching 10.2%, which is 32.5% lower than the 15.1% under M1. The comprehensive index Icom_ovp considering energy consumption and battery life reaches the maximum value of 0.91. In summary, ARC-EMS has shown good performance in energy consumption control, engine operating efficiency, battery life, and overall performance. These advantages make ARC-EMS an energy management strategy worth considering and applying in hybrid power systems. The results demonstrate that the proposed ARC-EMS achieves comparable optimization performance to DP-based strategies. Specifically, 4% improvement in energy efficiency and 3% reduction in battery capacity degradation are observed in ARC-EMS compared to the DP-based approach. However, the advantages of ARC-EMS extend beyond these metrics. Superior performance in real-world vehicle applications is demonstrated, with computational resource requirements being significantly lower than those of DP-based algorithms. This characteristic enhances the practicality and cost-effectiveness of ARC-EMS in actual vehicular environments. Therefore, it can be concluded that while ARC-EMS matches DP in optimization outcomes, its superior real-world applicability and reduced computational demands represent a breakthrough in energy management systems. ARC-EMS not only achieves optimization effects similar to DP but also exhibits significant advantages in practical implementation and computational efficiency, solidifying its potential for high utility and broad application prospects in energy management.
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