## 2 Modeling and Simulation of an Aircraft Electrical Power System (EPS)
### Fault Injection in the EPS Digital Twin  
The EPS supplies power to required LRUs of the aircraft systems through a series of switches and circuit breakers that protect the electrical circuits from events like overcurrent surge. These circuit breakers are modeled to trip on their own when the current exceeds the defined limit, as shown in Figure 2a. These circuit breakers can also be tripped at the beginning of the simulation, on purpose, by providing a fault signal as input to these components. In Figure 2b, DC_TRU_B, AC_Lamp_B, and FS_ACMotor_B are the fault input signals that would induce circuit breaker tripping in the distribution node that supplies AC Power to TRU, AC lamps, and FS motor, respectively. Injecting faults in the circuit breakers will stop the current flow to the respective node that supplies power to the LRU connecting to a particular aircraft system like the engine, the fuel system, or the ECS. Similarly, faults can be injected via the integrated gate bipolar transistor (IGBT) switches that connect to the valves and nozzles within the DC circuit (as seen in Figure 3), as well as through the switches in AC lamp circuits (not shown in the figure). The faults in the DC circuits from Figure 3 emulate the stuck open scenarios by opening the IGBT switches to a partial degree. For testing purposes, FS_valve switch is stuck at 80%, FS_Nozzle switch is stuck at 70%, Eng_BleedValve is stuck at 60%, and the ECS_TCValve is stuck at 50%. Figure 3 also shows the noise signals added to voltage measurements. Similar noise is added to voltage measurements in AC lamp circuits. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Monitored Parameters** & **Healthy Measurements** & **Unit** \\ \hline Power\_ACLoad & 4182.908 & VA \\ Power\_FSPump & 4001.362 & VA \\ Power\_ACLamp & 73.349 & VA \\ Power\_TRU & 111.102 & VA \\ FS\_Motor\_Speed & 311.813 & rad/sec \\ FS\_Motor\_Stator\_I & 4.822 & A \\ FS\_Motor\_Torque & 5.612 & Nm \\ FS\_Nozzle\_I & 0.908 & A \\ FS\_Valve\_I & 0.889 & A \\ Eng\_BleedValve\_I & 0.901 & A \\ ECS\_TCValve\_I & 0.890 & A \\ AC\_Fluro\_I & 0.259 & A \\ AC\_Instru\_I & 4.892 & A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Measured values during the Healthy Run. Figure 2: Fault injection in circuit breakers connecting generators to other aircraft systems: (**a**) User input current limits set for circuit breakers; (**b**) Manual tripping input inside the AC power distribution mask. Figure 3: Fault injection to DC loads via integrated gate bipolar transistor (GBT) switches and noise signal added to voltage measurements. In the case of the FSPump AC induction motor, there are several methods to inject faults that would result in the reduction of its rotor speed output. For this paper, the variation of the supply voltage method is chosen [29]. This is carried out by inserting a step-down transformer in the motor circuit, as shown in Figure 4. Through this, the supply voltage to the pump motor is reduced to induce the fault. Considering only abrupt faults, as either intermittent or constant over time, faults chosen for diagnosis in the EPS digital twin are listed in Table 2. As discussed above, the faults are chosen in such a way that, when injected, their effects can be observed in the overall power generated by the generator and the overall power consumed by their corresponding LRUs. These faults are also the most common electrical faults explored in the aircraft industry. For demonstration purposes and to avoid a lengthier presentation, all faults listed in Table 2 (F1, F2,..., F9) are injected for a duration of 0.25 s each, instead of injecting individual faults per simulation run. Fault F10 is simulated separately. The effects of the faults on the systems and their components and how they affect other systems are observed and compared with the healthy case simulation from Table 1. The faults either affect the power supply to the entire system along with their subsystems or only the LRUs based on the location of the fault injection.