# An Overview of Modelling and Energy Management Strategies for Hybrid Electric Vehicles
## 3 Research and Current Status of Energy Management Strategies for HEVs
### Optimization-Based Energy Management Strategies
#### 3.2.1 Equivalent Consumption Minimization Strategies
After the successful identification of the driving style level, the obtained driving style level and the correction function associated with SOC are exploited to adjust the EF and establish an adaptive ECMS strategy. The framework was divided into two parts, which is shown in Figure 8.  
Reference [120] developed an adaptive EMS for PHEB by using a clustering algorithm. Road types were classified and the corresponding categories were assigned to actual roads. Using a trained neural network model, the different road categories were combined to optimize the equivalent fuel consumption coefficient in the ECMS. This was achieved by calculating and planning the SOC reference trajectory. The torque distribution of the strategy under WLTC and UDDS conditions can be seen in Figure 9. The simulation  
Figure 8: Framework of a proposed strategy (source [119]). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**ECMS**} & \multicolumn{3}{c}{**Adaptive ECMS**} \\ \hline Type & 1 & 2 & 3 & 1 & 2 & 3 \\ Fuel (L/100 km) & 10.56 & 9.39 & 8.95 & 9.42 & 8.66 & 8.52 \\ \(\Delta\)Fuel (\%) & & & \(-\)10.76 & \(-\)7.79 & \(-\)4.78 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of the fuel economy for three road segments (Data from the source [118]). results showed that the fuel economy was improved while guaranteeing a reduction in computational effort. The approach can be practically applied in specific urban conditions provided that sufficient road information is collected. For HEVs with dual-motor powertrains, wang et al. propose an EMS that takes into account the mode transition constraints [121]. This EMS could balance the fuel economy of a hybrid vehicle with the mode-switching frequency of a dual motor. A multi-criterion cost function \(J_{\textit{EMS-MTC}}\) was established as:  
\[J_{\textit{core}} =J_{\textit{coo}}+J_{\textit{com}}+J_{t} \tag{4}\] \[=\int_{t_{0}}^{t_{f}}\left[\dot{m}_{f}(x(t),u(t),t)+\dot{m}_{ \textit{ress}}(x(t),u(t),t)\right]\,dt+\alpha\left(\delta v+\overline{\Delta v^ {2}}\right)+\beta^{e^{-\frac{1}{1-|\frac{t-t_{0}}{t_{e}}|}}}\]  
where \(t_{0}\) and \(t_{f}\) are the initial time and the final time. \(J_{\textit{coo}}\), \(J_{\textit{com}}\), and \(J_{t}\) represent the cost of fuel economy, driving comfort, and mode transitions, respectively. \(t_{e}\) and \(\beta\) represent the effect time and amplitude of the penalty function. Usually, the extra penalty function can be restricted by adjusting these two parameters. \(t_{l}\) is the moment when the latest change happened. Experiments and tests have shown that this adaptive ECMS could reduce mode switching by more than 60% and achieve a trade-off between mode switching frequency and fuel economy. At the cost of a slight increase in fuel consumption, its practical application potential was demonstrated. Similar observations were studied by [PERSON] et al. [122] and [PERSON] et al. [123]. ECMS is a mathematical model and optimization algorithm that transforms the control strategy of a vehicle powertrain into a mathematical optimization problem in order to minimize the objective cost function and obtain the optimal control sequence [124]. With the development of hybrid technology in recent years, ECMS is gradually being used increasingly in HEVs. In global terms, the algorithm's fuel economy optimization results are closer to those of the global optimum, but compared to the global optimum control, the algorithm does not require prior knowledge of the full operating conditions, greatly reducing the amount of computation required to calculate the optimum power distribution and making the application of ECMS to real vehicles more possible [125; 126; 127].