# Analysis and Synthesis of Architectures for Automotive Battery Management Systems
## 6 Exemplary Synthesis of a Powertrain Domain Focusing Start-Up and Shut-Down of the HV-System
### Detailed Function and Interaction Analysis
In the following, those three systems are presented in detail. All schematics allow one to pre-charge and active discharge the HV-capacitor with a single resistor (resistor 1). Further, the voltage drop at the two main contactors (HV+ contactor and HV- contactor) is measured at the positions K1, K2, K3 and K4. With this setup, the states of the HV+ contactor and the HV- contactor can be observed and determined. Therefore, a cross-measurement (CM) module is included in the upcoming Figures. Figure 10 shows four switches and two resistors (4S2R) setup. Resistor 1 is the pre- and discharge resistor. Resistor 2 is a high value discharge resistor and switch 1 shifts resistor 1 from a series to a parallel connection. In state 1, the resistor is disconnected. Switch 2 is bridging resistor 1 under operation. The second schematic in Figure 11 is the first of two schematics, which only consists of three switches and two resistors (3S2R1). The resistor function is the same as in the presented 4S2R system. Moreover, switch 1 has the same function as in the 4S2R system. The HV+ contactor is now also bridging resistor 1 under operation. Figure 11: Three switches/contactors and two resistors (3S2R1) setup. Figure 10: Four switches/contactors and two resistors (4S2R) setup. The third schematic is slightly different compared to the second (3S2R1) and is presented in Figure 12. In comparison to the 3S2R1-system, this 3S2R2-system is able to actively discharge the capacitor without the need to close the HV+ contactor. The switch S1 must face the same requirements regarding safety and service life as the main Contactors (HV+ and HV-) of the HV-system. It is discussed to use semiconductor switches such as IGBTs, super-junction or silicon carbide (SiC) MOSFETs for those Contactors already [57; 58]. Using semiconductors, the problem of arousing arcs no longer exists, since semiconductors do not switch in a mechanical way. This leads to a reduction of size and more service life. However, no galvanic isolation can be provided, on the other hand. The next Section 6.2 presents possible failure modes based on simulation results. Those real-time simulations are carried out with a Typhoon HiL system. To verify the simulation models, a first calculation helps, which is presented in the following. The presented equations are also used for the design of the relevant components. This example assumes a 400 V battery system. A DC-capacitor charging time of 1.5 s should be achieved. The DC-capacitor has a capacity of 400 \(\upmu F\). The charge and discharge time is calculated with the help of the time constant \(\tau\), the resistance \(R\) and the capacity \(C\). \[\tau=R\cdot C \tag{1}\]  
It is assumed that the capacitor is almost charged after a time of \(5\cdot\tau\). This results in Equation (2) and a resistance of \(R_{1}=750\;\Omega\) for resistor 1. \[R_{1}=\frac{1.5\;s}{5\cdot 400\;\upmu F}=750\;\Omega \tag{2}\]  
The maximum current in this example is also dependent from the battery voltage \(U_{0}\). \[I_{\text{max}}=\frac{U_{0}}{R_{1}}=0.53\;A \tag{3}\]  
In addition, the present current while starting-up the system can be calculated as a function of time \(t\). Figure 12: Three switches/contactors and two resistors (3S2R2) setup. \[i(t)=\frac{U_{0}}{R_{1}}*e^{-\frac{t}{R_{1}}*\frac{t}{R_{1}}*\frac{t}{R_{1}}} \tag{4}\]  
The influence of the second high-value resistor connected in parallel is neglected in these calculations. This is taken into account in the simulation, which is why the values differ slightly from the first design. Figure 13 shows the schematic of the simulation of the 3S2R2 system. In the schematic, \(R_{2}\) represents the high-value resistor and \(R_{1}\) represents resistor 1. Since Typhoon HiL does not provide multiple-state-switches yet, two switches (S1 and S2) are used to simulate S1 from Figure 12.  
Figure 14 shows the current and the voltage for capacitor \(C_{1}\) of 3S2R2 as a function of time (scale of x-axis: \(1\frac{s}{dtv}\)).