Through researching the instantaneous control strategy and Elman neural network, the paper established equivalent fuel consumption functions under the charging and discharging conditions of power batteries, deduced the optimal control objective function of instantaneous equivalent consumption, established the instantaneous optimal control model, and designs the Elman neural network controller. Based on the ADVISOR 2002 platform, the instantaneous optimal control strategy and the Elman neural network control strategy were simulated on a parallel HEV. The simulation results were analyzed in the end. The contribution of the paper is that the trained Elman neural network control strategy can reduce the simulation time by 96% and improve the realtime performance of energy control, which also ensures the good performance of power and fuel economy.
Under the dual pressure of environmental pollution and energy crisis, hybrid vehicles have advantages of both conventional vehicles and electric vehicles, which have characteristics of energy conservation, environmental protection, diverse shapes, and strong implementation. Hybrid vehicles have become an effective way to solve the problem of energy crisis and environmental protection and also have been one of the most perspective vehicle models.
According to different connective ways of power system, hybrid electric vehicle (HEV) can be mainly divided into four styles: series, parallel, seriesparallel, and complex. The dynamic structure diagram is shown in Figure
Classification of hybrid electric vehicles.
Engine output energy of series HEV is transformed two times and the efficiency of the motor and generator is relatively low, so series HEV loses more energy and leads to lower efficiency than vehicles of internal combustion engine. Parallel HEV (PHEV) is equipped with series and parallel power systems, and their structures and control systems are more complex and have higher cost. Complex HEV structures and control systems are most complex and have highest cost. However, parallel hybrid power system can adapt to various road conditions and is widely used by enterprises [
As the core of multiple energy control system, the energy control strategy determines performances of PHEV. Based on vehicle’s torque, energy control strategies of PHEV are mainly divided into four types [
The basic principle of instantaneous optimal control strategy is based on the model of the optimal curve of engines; the object function of the whole power system was optimized on the specific operating points of parallel HEV. On the basis of the instantaneous optimal operating points, it makes power of variable states redistributed and make the loss of energy minimized in the energy flow process at any time (see Figure
Energy flow diagram of parallel hybrid electric vehicles.
The hybrid vehicles possess good power performance and fuel economy and obtain rapid allocation energy by finding a new energy control strategy. Elman neural network is a feedback neural network and has a very strong computing ability and stability [
Based on the research of the instantaneous optimal control strategy, the strategy possesses good fuel economy and makes energy distributed reasonably. However, its realtime performance is poor. In order to solve bad realtime defects of instantaneous control strategy, instantaneous optimal control rules are used to train the Elman neural network control strategy and improve the realtime performance of the trained Elman energy control strategy on the premise that it can guarantee advantages of the instantaneous optimal control strategy. The results show that the trained Elman neural network control strategy can replace the instantaneous optimal control strategy, optimize power distribution, and make the simulation time reduced by 60%.
Instantaneous optimal control strategy is defined as follows. In order to achieve the minimum fuel consumption of HEV, the optimal output power of the engine and electric motor is calculated in each control cycle of hybrid power system. Working conditions of HEV and calculation expressions of the equivalent fuel consumption are different in every time. So an optimal objective function should be established [
Here, the full line represents the circulation and transformation of fuel chemical energy in the hybrid power system. The dotted line represents electric current circulation and transformation in the hybrid power system.
When the power battery takes part in driving hybrid cars, its SOC value will reduce and deviate from the target of SOC value. In order to compensate for the used electricity and restore SOC value of power batteries, the engine drives the motor to charge power batteries in the future time [
The relationship between the motor power (
When the motor drives the vehicle, the energy consumption of power batteries can be converted into the engine fuel consumption. The equivalent fuel consumption rate of the motor is
Let
Merge (
When the motor drives the vehicle after a period of
When the power battery is charged by the engine, its SOC value will rise and even exceed the target of the SOC value. In order to maintain SOC values, power battery energy will be consumed in future [
In a certain period of discharging time, the relationship between motor power (
When the motor drives the vehicle, the relationship between the motor power battery energy consumption and the fuel consumption rate is
Let
Simplify the (
When the motor charges power batteries after a period of
Set two new variables:
The instantaneous control objective function of the lowest fuel consumption is
SOC value change of batteries and braking energy recovery both have a certain effect on energy control. The optimal function of the working point needs to be improved.
Set
The value table between
SOC  0.11  0.14  0.2  0.25  0.3  0.35 

7  2  1.05  1.05  1.03  1.04 
SOC  0.4  0.45  0.5  0.55  0.59  0.64 

1.02  1.02  1  0.99  0.98  0.96 
SOC  0.7  0.74  0.81  0.85  0.9  

0.96  0.94  0. 94  0.8  0.2 
Based on the Matlab platform and Table
SOC and
Polynomial function of the fitting curve is
Considering the influence of power battery SOC, the formula of instantaneous equivalent fuel consumption of HEV can be expressed as
The statistical time range is divided into
When power batteries discharge, the objective function of instantaneous equivalent fuel consumption is
In summary, taking the influence of power battery SOC and brake energy recovery into consideration, the final objective function of instantaneous optimal control strategy is
Elman neural network is put forward by Jeffrey L. Elman in 1990 and is a typical local recessionary grid, as shown in Figure
Elman neural network model.
The inputs of structure diagram of Elman neural network is the required torque, speed, and SOC value of power battery and its output is motor torque. The structure diagram of Elman neural network is shown in Figure
Structure diagram of Elman neural network.
The structure diagram of Elman neural network contains input layer, hidden layer, undertaken layer, and output layer. Let the input vector of the input layer be threedimensional vector
Define two functions:
The input and output functions of the
The input and output functions of the
The input and output functions of the output layer’s neuron are
The neuron number is determined by following formula [
The excitation function of Elman neural network of the feedback layer selects the Tansig function [
Elman neural network is trained by LevenbergMarquardt algorithm. The error index function of LevenbergMarquardt arithmetic is
The formula of the adjusting weight is
The computing formula of the increment weight is
Neural network weight is adjusted by the LevenbergMarquardt algorithm, and the adjusting process is shown in Figure
Process map of the adjusting network weight.
On the platform of Matlab/simulink, the instantaneous control model is established and mainly includes two parts: the calculation model of average braking energy of recovered power and the calculative model of optimal working point [
First, the calculation model of average braking energy of the recovery power is established as shown in Figure
Flow diagram of average recovery power of braking energy.
Second, the calculation model of the revised SOC value of power battery is established, as shown in Figure
Flow diagram of the revised SOC value of power batteries.
Third, the calculation model of the optimal operating point is established, as shown in Figure
Flow diagram of the optimal operating point.
Finally, the whole simulation diagram of the instantaneous control strategy is established, as shown in Figure
Total simulation diagram of the instantaneous control strategy.
Elman neural network is gradually learning to do something by imitating human brain. Its essence is to improve the learned knowledge and the neurons weight [
The training flow diagram of the trained Elman neural network.
The basic vehicle parameters are shown in Table
Parallel hybrid electric vehicle parameters.
Vehicle  
Curb weight  1605 kg 
Face area  2.65 m² 
Wheel base  2.775 m 
Height of the center of mass  0.5 m 
Front axle load distribution ratio  0.51 
Coefficient drag  0.32 
Engine  
Peak power  118 kW 
Displacement  2.5 L 
Power battery pack  
Voltage  244.8/650 V 
Style  NIMH 
Volume  6.5 Ah 
Mold number  34 
Motor  
Peak power  105 kW 
Style  PMSM 
Traffic parameters of simulation experiments are described in Table
Traffic parameters of simulation experiments.
Parameter  NEDC  HWFET 

Idle time (s)  298  6 
Top speed (km/h)  10.93  16.51 
Cycle time (s)  1184  765 
Average speed (km/h)  33.21  77.58 
Maximum acceleration (m/s^{2})  1.06  1.43 
Maximum deceleration (m/s^{2})  −1.39  −1.48 
Park time (time)  13  1 
Traveling distance (km)  120  96.4 
The original control model is replaced by the instantaneous optimal control model in ADVISOR 2002. Then the trained Elman neural network controller is imported to the software [
Simulation results are shown in Figure
Simulation model of the parallel hybrid electric vehicle.
Contrast power battery SOC.
NEDC working condition
HWFET working condition
Compared with the instantaneous optimal control strategy, the Elman neural network strategy can slow down the decline of SOC value and maintain SOC value at high efficient range on the NEDC working condition in Figure
As shown in Figure
As seen in Figure
As shown in Table
Fuel consumption of 100 km (L/100 km).
Strategy  Road  

NEDC  HWFEF  
Instantaneous optimal control  9.4  6.5 
Elman neural network  9.8  7 
Simulation time (s).
Strategy  Road  

NEDC  HWFEF  
Instantaneous optimal control  471.3  315.8 
Elman neural network  15.6  10.2 
In conclusion, as seen in Figures
Contrast engine torque.
NEDC working condition
HWFET working condition
Contrast the motor torque.
NEDC working condition
HWFET working condition
Through the research on the instantaneous optimal strategy and Elman neural network control strategy, we deduce the objective functions of instantaneous optimal control and establish the instantaneous control model and design the Elman controller. Based on the ADVISOR 2002 platform, two control strategies were simulated on a hybrid electric vehicle.
It is seen from the simulation results that the trained Elman neural network strategy shows similar control ability on the vehicle energy distribution compared with the instantaneous optimal control strategy, which ensures good performances of power and fuel economy of HEV, reduces the control reaction time greatly, and overcomes the disadvantage of poor realtime performance of the instantaneous optimal control strategy. The research significance of the paper is that the simulation time of energy control is reduced by 96%.
Future works are listed as below.
Simulation and experiment should be improved by adding more design parameters, such as vehicle emission.
It is necessary to do lots of experiments to enrich simulation results.
Actual road condition is more complex than the simulation road condition, so control strategies need to be tested in the actual road conditions.
The authors declare that there is no conflict of interests regarding the publication of this paper.