## 2 Integrated Power and Thermal Management in Electrified Propulsion Aircraft
### Electrified Propulsion Aircraft  
The definition of degree of hybridisation (DoH) developed by [PERSON] et al. [19] helps to categorise the types of aircraft (shown in Table 1) as follows:  
* DoH for power (\(H_{P}\))
* DoH for energy (\(H_{E}\))  
where \(P_{motor}\) = power of motor, \(P_{engine}\) = power of engine, \(P_{tot}\) = aircraft total power, \(E_{battery}\) = energy of battery, \(E_{engine}\) = energy of engine, and \(E_{tot}\) = aircraft total energy. Based on the DoH, the aircraft propulsion system can be electrified using motors (\(H_{P}>1\)) and without a battery (e.g., turboelectric aircraft). Figure 1 shows the simplified schematic of the propulsion system for EPA. Readers can refer to [20; 21; 22; 23] for more information on electrified aircraft propulsion. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Aircraft Type** & **DoH for Power** & **DoH for Energy** \\ \hline Conventional aircraft & 0 & 0 \\ Series HEA & 1 & \textless{}1 \\ Turboelectric & \textgreater{}0 & 0 \\ Parallel HEA & \textless{}1 & \textless{}1 \\ AEA & 1 & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification of aircraft. Generally, as Figure 1 shows, an electrical propulsion system (EPS) consists of electric machines (motors or generators), power distribution systems (DC or AC bus), and converters (rectifiers, inverters, or DC/DC converter). The motors have four main types of loss [24]: (1) ohmic losses, (2) core losses, (3) windage losses, and (4) other losses. The other losses are usually assumed to be constant as they are independent on the motor torque or rotational speed. Assuming the loss coefficients remain the same, the ohmic losses are dependent on the motor's torque, while the core losses and the windage losses are dependent on the motor's rotational speed. In this case, when the rotational speeds of the aircraft's propulsors are constant, the heat from the motors might not be reduced significantly even under low-power conditions, which increases the requirements of the TMS. Additionally, with the advancement of motor technology, motors are becoming smaller and lighter. However, a smaller size can limit the size of the motor's cold plate. Even though the efficiency of the motor may improve, under high-power conditions, the heat flux of the motor could increase, introducing challenges for the TMS. For the power distribution systems, the higher the system voltage, the less heat from the bus is generated. However, the higher system voltage might require a bigger size of battery or generator, which requires trade-off studies between the EPS and the TMS designs. Compared with other electrical components, the range of the operating temperature of the battery is narrower, usually within 15-45 \({}^{\circ}\)C [25]. While ensuring the battery temperature does not exceed the maximum temperature, an active temperature control might be required under low-temperature conditions to ensure the temperature is above the minimum temperature. Furthermore, the battery's state of charge should be above the minimum state of charge to prevent damage. Therefore, the IPTMS design should consider the power and thermal requirements of the battery. For series and parallel HEA, the battery power output can be determined by determining the DoH, or by determining the power of the gas turbine engines. For example, the DoH for each flight phase is determined, and then the battery is sized. Alternatively, the maximum power output of the gas turbine engines is determined so that during the take-off flight segment, the supplementary power is provided by the battery. Additionally, at the end of the mission (i.e., during the descent or landing flight phase), the battery could also provide power, or it could be charged by the engine-driven generators to save energy. For AEA, all the power, such as for cooling, propulsion, emergency, etc., are provided by the battery.