# 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
### Failure Modes and Comparison of the Presented Topologies  
In order to consider all faults systematically, the number of switching states must first be known. All three topologies (Figures 10-12) can have \(2^{n}\) different switching-states in theory, where \(n\) is the number of switches. S1 has three switching states but only one state can be active. This is why 24 different switching-states remain for the 4S2R topology instead of 64. The 24 different states of the 4S2R topology are listed in Table 1. The table describes the different switching states and the corresponding voltage and current measurements. Figure 14: Current (**left**) and voltage (**right**) at the capacitor \(C_{1}\), with start up and active discharge of the HV-system of the 3S2R2 topology as a function of time. Figure 15: Current (**left**) and voltage (**right**) at the capacitor \(C_{1}\), with start up while start-up and passive discharge of the HV-system of the 3S2R2 topology as a function of time. HV+ and HV- stands for the voltage drop over the HV+ or HV- contactor. K1/K4 and K2/K3 describes the potential difference between measurement point K1 and K4 or K2 and K3. This measurement-method is described as cross measurement CM in this paper. The abbreviation \"n.d.\" stands for a not defined state, which can be neglected. Since the simulations of the different states were taken separately, and the SoC of the battery was refreshed for each simulation, the voltage-measurement-values are equal in every cycle. The 4S2R topology shows two critical (red lined) states. These failure modes occur if resistor 1 is switched in parallel (position 2) to the HV-battery, while the HV+ and the HV- contactor is closed. In this case, the HV-battery is discharged through the low-value resistor 1. The current is relatively low with 0.6 A, but constant. Resistor 1 can stand such currents over a short time period. The typical constant power limit of around 50 W is exceeded in this state by a factor of more than five. This state may cause a destruction of resistor 1 after a certain time period. To prevent the system from such a critical state, one of the HV-contactors must disconnect the circuit. This includes that the switching states must be known by the system. With the state-of-the-art CM alone, the critical state cannot be detected. Table 2 shows the different switching states according to the 3S2R1 topology from Figure 11. The 3S2R1 system shows the same critical states as the 4S2R system when both HV-contactors are closed and the S1 is in switching position 2. If S1 is in state 2 and the HV-contactor is closed, the failure still occurs in this system, although the HV+ contactor is open. For this reason, it must be avoided that HV- gets closed whenever S1 is in switching state 2. If the HV- contactor cannot be opened, the error cannot be fixed. Table 3 shows the different switching states of the 3S2R2 topology from Figure 12. The 3S2R2 circuit shows only one switching state that is critical if both HV-contactors are closed and S1 is in state 2. A constant current of 0.6 A floods resistor 1. \begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline
**State** & **HV+ [V]** & **HV- [V]** & **K1/K4 [V]** & **K2/K3 [V]** & **HV+** & **HV-** & **S2** & **S1** & & & \\  & & & &  
In terms of the critical discharge states, the 3S2R2 schematic is the best of all three, since it only has one critical switching state. This state can be observed and prevented by opening one of the HV-contactors. Further, only three instead of four switches are used in that system. This reduces the complexity of the system and lowers the number of possible failing components. Less switches need to be provided, observed and controlled. In addition, the same resistor could be used for pre- and discharging the HV capacitor. In the example calculation and simulation above, the 750 \(\Omega\) resistor would lead to a maximal current of 0.6 A. Nevertheless, the 4S3R-schematic comes with the ability to disconnect the system even in the case when the HV+ contactor can not be opened.