# An Online Energy Management Control for Hybrid Electric Vehicles Based on Neuro-Dynamic Programming
## 4 Results and Discussion  
In the simulation test of the proposed NDP-based EMS, the detailed model of the parallel HEV is built in ADVISOR2002 (Advanced Vehicles Simulator) to accurately reflect the vehicle performance, which is based on Simulink. The simulation was carried out on a computer with Intel Core 2 Duo 3.10 GHZ CPU and 32G memory. We have compared the proposed NDP method with the NDP method in [14] to test the proposed NDP based on CWNN and MRWNN. We have also compared the NDP EMS with a SDP method proposed in [6], which is an optimal method, in driving cycles of CYC_UDDS, CYC_1015 and a composite driving cycle, which is composed of a CYC_1015, a CYC_UDDS, and a CYC_WVUCITY driving cycle, to test the optimality of the proposed NDP method.  
According to Section 2.2, the orientation of the EMS is to maximize the fuel economy and to satisfy SOC constraint. In simulations, we evaluate fuel economy with miles per gallon (mpg) gasoline equivalent. The SOC constraint is to ensure battery SOC \(\in[0.3,0.8]\). Meanwhile, we evaluate the component efficiency of the parallel HEV with engine average efficiency, average motoring efficiency, and average generating efficiency.  
Table 2 shows the fuel economy and HEV component efficiency of the proposed NDP and NDP EMS in [14] in driving cycles of CYC_UDDS. From Table 2, we can see that the proposed NDP improves fuel economy by about 5.4%, average generating efficiency by about 7.6%, and average motoring efficiency by about 1.2% compared with the NDP in [14]. The two NDP methods keep SOC in nearly the same range of 0.55-0.7. These indicate that the proposed NDP with CWNN and MRWNN has better control results in the UDDS driving cycle than the NDP with RBFNN in [14]. In the NDP in [14], they are 25 and 20. This may be due to the CWNN and MRWNN enjoying better approximation and learning ability in handling nonlinear problems than a RBFNN. To further improve the performance of the proposed NDP EMS, we can increase the maximum training time of the action and critic network, or decrease the training error of the two networks.  
Tables 3-5 show the fuel economy and component efficiency of SDP, and the proposed NDP-based EMS in driving cycles of CYC_UDDS, CYC_1015, and the composite driving cycle. We can conclude that, compared with the SDP in [6], the proposed NDP EMS improves fuel economy by about 25.9%, 6.2%, and 25.6%, respectively, under CYC_UDDS, CYC_1025, and the composite driving cycle. In the three driving cycles, the proposed NDP and SDP all keep SOC in nearly the same range. The proposed NDP EMS also improves the average generating efficiency by about 6.7%, 5.2%, and 4%, respectively, under CYC_UDDS, CYC_1025, and the composite driving cycle. This shows that the proposed NDP is better than the SDP method. There are three reasons for the simulation results. The first is that the state space and action space are all discretized in SDP and successive in NDP, which reduces the error induced by low discretization resolution. The second reason is that the NDP-based method has generalization ability and  
the engine is in a higher torque output mode most of the time, and the motor provides energy in peak and engine starting times. Battery SOC is constrained in the region of 0.55-0.7, which ensures safe battery usage.  
Figure 7 shows the engine operation efficiency in NDP EMS. We can see that, in most situations, the engine is in an efficiency region larger than 0.35.  
Figure 6: NDP EMS simulation results under CYC_UDDS driving cycle.  
Figure 7: Engine efficiency in NDP EMS under the CYC_UDDS driving cycle.  
Figure 8 shows the motor operation efficiency in NDP EMS. We can see that, in most situations, the motor is in an efficiency region larger than 0.8. The operation points in the lower efficiency region are distributed uniformly, which coincides with the actual operational points of the motor in real applications.