## 4 Results
### Coupled Operation  
The coupled operation is validated by comparing the torques and speeds of the two test benches. An evaluation can be made on the basis of the difference between the reference value specification inputs and the actual measured values. Both the time difference (Equation (1)) and the value difference (Equation (2)) must be considered.  
\[\Delta t(y)=t_{2}(y)-t_{1}(y), \tag{1}\]  
\[\Delta y(t)=y_{2}(t)-y_{1}(t). \tag{2}\]  
The reference values are calculated in the simulation, as described in Section 3.1. In the case of the EM, the values must also be sent from the ICE test bench--where the simulation host is located, see Figure 4--to the EM test bench.  
For the analysis of the coupled operation, a measurement was performed with the Worldwide harmonized Light-duty vehicles Test Cycle (WLTC) as speed specification. The following parameters were predefined:  
* Start SoC = 20%
* Start temperature of the EM \(T_{EM}\) = 30 \({}^{\circ}\)C  
Validation of EM  
For a better visualization, a dynamic section of the WLTC was selected. In Figure 8, the reference speed \(n_{EM,REF}\) (green) and the actual speed set at the EM test bench \(n_{EM,ACT}\) (blue dashed) are shown next to the vehicle velocity \(v\) (red). Both the time shift and the value difference are small in this dynamic case. Due to the latency caused by the data transfer required for the virtual coupling, as well as measurement noise or measurement inaccuracies at the test bench, the small deviations can be neglected. The mapping of dynamic speed change demands from the simulation software to the EM due to shifting operations during acceleration or braking is also possible, see speed changes at \(t\approx 1040\) s while increasing vehicle velocity \(v\), although this functionality is typically not used in normal EM test bench operation.  
When analyzing the torque in Figure 9, particular attention must be paid to compliance with the maximum dynamic torque of the EM \(M_{EM,MAX}\) (red). This is neither exceeded by  
Figure 8: Reference \(n_{EM,REF}\) and actual speed \(n_{EM,ACT}\) of the EM in a WLTC compared to the virtual vehicle velocity \(v_{ACT}\).  
the reference torque \(M_{EM,REF}\) (green), nor by the torque actually set at the EM test bench \(M_{EM,ACT}\) (blue dashed). A value difference between the reference and actual torque is only apparent in the case of torque peaks, but can also be neglected due to measurement noise or measurement inaccuracies at the test bench.  
Validation of ICE and Hybrid Controller  
The validation of the ICE is closely linked to the validation of the hybrid controller (HC), since the EM is primarily used for torque generation when the SoC is high. As defined in the hybrid controller, the ICE is only used for support at low SoC, for example. For this reason, a start SoC of 20% was chosen to begin in charge sustaining mode.  
To validate this purpose, another section of the WLTC was selected (Figure 10). If the pedal position \(\alpha_{HC}\) (brown dash-dotted) set by the driver exceeds the limit of the maximum possible throttle position \(\alpha_{ICE}\) (green) at the ICE test bench of 50%, the resulting difference is covered by the torque \(M_{EM,ACT}\) (blue dashed) set by the EM. If the required pedal position is smaller than the limit value of the ICE, the torque of the EM is zero or negative, depending on the operating mode. For the last case, the reference value for the ICE \(\alpha_{ICE}\) is larger than the pedal position \(\alpha_{HC}\) set by the driver, because the operation mode load point lifting is executed.