# Model-Based Analysis and Improvement of Vehicle Radiation Emissions at Low Frequency
## 5 Application and Analysis
### Modeling of Radiation Emission  
Normally, the radiated emission at low frequency range is caused by the high voltage systems including PDU, compressor, battery, DC/DC, on board charger (OBC), positive temperature coefficient heater (PTC), battery heater, driver inverter and motor. The schematic of these systems is shown in Figure 5(a),b. It should be noted that the indexes in Figure 6 are defined for the convenience of modelling for this radiation problem and are different from those in Figure 2.  
Figure 5: Radiated emission test: (**a**) Test site; (**b**) Electric field.  
Figure 6: _Cont._  
According to the topological modelling approach introduced in Section 3 and the test requirement of SAE J551-5, a topological model composed of two networks is established as show by Figure 6c considering the following facts:  
1. The positive and negative wires are arranged in parallel and the loop area of the differential mode interferences is comparatively smaller than that of common ones. In the present modelling, only the common mode interferences are considered and the differential ones are neglected;
2. All mentioned power components in Figure 6a are packed in the metal shells, which are finely grounded;
3. PDU is a junction of all power cables and its internal schematic is shown by Figure 6b.  
In Figure 6c, the network V1,1 is to describe the propagation of electromagnetic field in/out the vehicle space and the other is for the coupling in PDU. When modelling the nodes, their equivalent impedances and voltages are assumed to be independent of the working state. To ensure the accuracy, the voltage \(U_{i}\) and the current \(I_{i}\) are by the oscilloscope and current probe under the same running condition as SAE J551-5. With the measured voltage and current, the equivalent voltages of nodes connected to the network are calculated by:  
\[V_{i}=U_{i}+Z_{\text{S};i}I_{i} \tag{12}\]  
where \(U_{i}\) and \(I_{i}\) are the measured voltage and current, \(Z_{\text{S};i}\) is the impedance measured by the network analyzer when power off. Some of the results are shown by Figure 7.  
Figure 6: Modelling process: (**a**) Schematic diagram of power system; (**b**) Schematic diagram of PDU; (**c**) Topological multi-port network diagram.  
The parameter of networks is calculated from the S-parameter, which is solved numerically by FEKO [24] as shown in Figure 8. For the feasibility and efficiency of computation, the model was simplified by deleting the nonmetal components of vehicle body, comparatively small metal structures and electric components, and the low voltage wiring harness. These two models are solved separately to reduce the consumption of time and computation resources. Moreover, several methods, such as experimental test, numerical calculation, etc., can also be used to acquire the data required by Equation (6).  
Some of the simulation results of the S-parameter and the calculated Z-parameter are shown in Figure 9, where the subscript of variables denotes the index of ports.  
Figure 8: Simulation model in FEKO: (**a**) EV model; (**b**) PDU model.  
Figure 7: Parameters of equivalent circuit nodes: (**a**) Equivalent internal impedance; (**b**) Interference current; (**c**) Equivalent interference voltage.  
The radiation emission predicted by the topological model is compared with the experimental one in Figure 10. Overall, they have the same trend and the frequency range where the electric field exceeds the limit is similar. Though the simulation result has some small peaks in the frequency range between 1 MHz and 3 MHz, the electric field in this frequency range is much lower than the limit. When using this model to diagnose the emission problem, we focus on the frequency range where the emission is over the limit. The comparative results show that this model can be used to find the main factor causing the emission problem.