## 2 Modeling and Simulation of an Aircraft Electrical Power System (EPS)
### The EPS Digital Twin  
The EPS digital twin consists of a constant speed source from the engine shaft that is fed to a generator of 40 kVA capacity. This generator is defined by a simplified synchronous machine in MATLAB Simulink, which produces 115/200 V AC power at 400 Hz. For the given frequency f, the synchronous speed N\({}_{\text{s}}\) at which the required voltage is produced by the synchronous machine is calculated using the following formula:  
\[\text{N}_{\text{s}}=\text{f(2/P)}\times 60=400\ \text{Hz}\times\text{(120/4)}=12,000\ \text{rpm} \tag{1}\]  
where P is the number of poles in the generator. With this result, all the simulations of the EPS digital twin will be run at a constant speed of 12,000 rpm [18]. The synchronized machine also takes regulated field voltage as an input, which is fed from the IEEE type 1 voltage regulator combined excitation system. Considering the dissipation losses in the circuit, the total apparent power generated by this synchronous machine is calculated using the following formula [21]:  
\[\text{Apparent Power, }p=3\text{V}_{\text{rms}}\ \text{I}_{\text{rms}}(\text{kVA}) \tag{2}\]  
where rms = root mean square.  
As mentioned in Section 1, with the growing demand for more electrification of advanced aircraft, the EPS is designed to distribute power to several aircraft systems through its constituent LRUs. For this EPS digital twin, the following LRUs in the aircraft systems are considered for this simulation, with the necessary parameters taken from their respective technical specification sheets provided by their commercial suppliers [25; 26; 27; 28]. Figure 1 shows the defined MATLAB Simulink model developed for the EPS representative discussed in this paper.  
The 115/200 V AC power is provided to the fuel pump AC induction motor. The induction motor is defined by an asynchronous machine rated at 9 KW power and 8000 rpm, with a squirrel cage rotor that results in the rotor speed required to run the fuel pump. The paper refers to the power distributed to this LRU as Power_FSPump; the motor's speed, torque, and stator current are referred to as FS_Motor_Speed, FS_Motor_Torque, and FS_Motor_Stator_I, respectively.  
The AC power is distributed to the Transformer Rectifier Unit (Power_TRU) and is converted to 28 V DC. This DC power is then supplied to a valve and a nozzle in the fuel system, to a bleed air system high-pressure shut-off valve in the engine, and a temperature control valve in the ECS. This paper refers to these LRUs as FS_Valve, FS_Nozzle, Eng_BleedValve, and ECS_TCValve, respectively.  
Figure 1: MATLAB-Simulink model for the aircraft Electrical Power System (EPS).  
The AC power distributed to the AC Lamps (Power_ACLamp) is directly provided for the cabin window fluorescent lights (AC_Fluro) and stepped down to 5 V AC for the cockpit instrument panel lights (AC_Instru).  
The AC power generated is referred to as Power_ACLoad and is distributed at each node representing the aircraft systems, and is also calculated using Equation (2). Random noise is added in the measurement devices, in order to avoid replicating an ideal condition for the EPS.  
Table 1 presents the performance of the EPS digital twin at a constant speed of 12,000 rpm, considering a steady state as the operating condition. This simulated condition is considered as the healthy state condition or the baseline for the EPS digital twin. Following the simulation with the healthy scenario, the next section discusses the faults induced in the EPS digital twin.