# 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  
ECMS is a strategy for optimizing the powertrain control method to minimize the equivalent fuel consumed by the vehicle's powertrain while achieving a specific driving objective [101; 102; 103]. For the vehicle system, the internal energy flow can be divided into the following two states: When the battery output power is positive, the motor is in the traction motor state and the motor outputs positive torque outwards. At this point, the mechanical energy provided by the electrical energy consumed by the motor will equivalently replace some of that provided by the engine [104; 105; 106; 107]. When the battery output is negative, the motor is in generator mode and the motor outputs negative torque outwards. The electrical energy obtained from this regenerative energy recovery can replace part of the fuel energy in the future, and this replacement power is also determined by the operating state of the engine at this time [108; 109]. Based on this, the basic principle of the ECMS is to allocate part of the consumed energy to the battery so that the consumption or storage of this electrical energy is equivalent to the use or saving of a certain amount of fuel [110; 111]. To obtain the control strategy that minimizes the instantaneous equivalent fuel consumption, a cost function for equivalent fuel consumption is defined, and the traversal of each instantaneous state quantity is solved [112]. For HEVs, the energy path of the ECMS is shown in Figure 7.  
For the ECMS, the key is to associate electrical energy with the equivalent fuel consumption during the charging and discharging of the battery [113]. The instantaneous fuel consumption can be divided by the source into actual and virtual fuel consumption, the expression of which can be described as:  
\[\dot{m}_{f,exp}(t)=\dot{m}_{f}(t)+\dot{m}_{\text{{ress}}}(t) \tag{1}\]  
where \(\dot{m}_{f,exp}(t)\) is the instantaneous equivalent fuel consumption, \(\dot{m}_{f}(t)\) and \(\dot{m}_{\text{{ress}}}(t)\) are the instantaneous actual fuel consumption and the instantaneous equivalent fuel consumption, respectively [114]. Meanwhile, \(\dot{m}_{f}(t)\) can be formulated as:  
\[\dot{m}_{f}(t)=\frac{P_{eng}(t)}{\eta_{eng}(t)Q_{\textit{thr}}} \tag{2}\]  
where \(Q_{\textit{thr}}\) is the low calorific value of the fuel, which is the available energy per unit mass of fuel. \(P_{eng}\) represents the power generated when the engine is in operation. Also, \(\dot{m}_{\text{{ress}}}(t)\) should be calculated as:  
\[\dot{m}_{\text{{ress}}}(t)=\frac{EF}{Q_{\textit{thr}}}P_{\textit{batt}}(t) \tag{3}\]  
where \(EF\) is the equivalence factor for the oil-to-electric conversion and \(P_{\textit{batt}}(t)\) is the power generated by the battery. A number of studies have reported changes in ECMS optimization  
Figure 7: Schematic diagram of the energy flow path of ECMS, (**a**) in the discharge state, (**b**) in the charge state. strategies. These include adaptive ECMS and telemetric ECMS, which adjust _EF_ based on past driving data and future predictions [115; 116; 117]. In [118], an adaptive EMS based on ECMS was proposed, incorporating real-time traffic information such as average speed, average acceleration, and the standard deviations of speed for different road sections. Markov speed prediction models were then established to predict velocity and applied to the energy management of a PHEB. The adoption of adaptive ECMS (AECMS) overcame the limitations of fixed ECMS, which cannot change in real time. Finally, the method was evaluated using three real road sections, and the fuel consumption rates were notably reduced when compared to traditional ECMS, as shown in Table 3.  
[PERSON] et al. improved the fuel economy of HEVs through driving style recognition in synergy with ECMS [119]. To accurately identify the driving style of the driver in real-time, a hybrid recognition algorithm based on feature samples was presented.