## 2 Integrated Power and Thermal Management in Electrified Propulsion Aircraft
### Power Management Optimisation  
Figure 2 shows a control architecture for EPA. The control for EPA is generally recognised as two levels: supervisory control and component control [46]. The EPA has a supervisory controller to manage the commands for the conventional and the electrified propulsion systems. Usually, in some papers, \"control system design\" or \"controller design\" refers to the component (lower)-level design, and the supervisor control approach refers to \"power (energy) management strategy\". In the IPTMS, based on the thermal requirements, the TMS components, such as the coolant pumps and the cooling fans, require power for cooling, which can be provided by the engine-driven generators or the battery. In the electrical propulsion system, the battery needs to provide power for the motors to drive propulsors. In this case, the supervisory controller should balance the energy flows, satisfying the power and thermal requirements, and obtain an optimal solution to minimise the energy consumption. Therefore, the power management optimisation strategies are researched for the supervisory controller.  
PM strategies have been studied widely for hybrid-electric ground-based vehicles (HEVs) and have been integrated with TMSs to manage energy flows at the vehicle level [47; 48]. However, the general technologies developed for HEVs are not available for implementation in aircraft as aircraft have different considerations. Aircraft manage energy flows based on mission profiles. An aircraft mission has several segments in the following sequence: taxi-out, takeoff, climb, cruise, descent, landing, and taxi-in, and the propulsion requirements per mission segment (e.g., balancing thrust and drag) are different. In HEA, the PM strategy is more complicated, minimising fuel consumption with electric power, providing sufficient power for TMS and other electric components, and ensuring the state of charge (SOC) of the battery is above the minimum value to avoid damage [49].  
PM strategies can be generally categorised into two types: causal and non-causal. Researchers apply non-causal ones when future conditions are known [50; 51; 52; 53] and apply causal PM strategies for unknown-future conditions [54; 55; 56; 57; 58]. Both methods can be implemented for real-time applications, depending on if the mission profile is known beforehand or not. For aircraft, the decision of the type of PM strategy depends on the objective, optimising for the entire flight mission or a single moment. If the optimisation is non-causal, the overall fuel consumption is assessed and minimised. A non-causal cost function can be described by Equation (1). If the optimisation is causal, the fuel consumption for each time step is assessed and minimised. A causal cost function can be described by Equation (2).  
\[\text{J}=\int_{t_{i}}^{t_{end}}Wt_{fuel}(t_{k})dt,\ t_{k}\in[t_{i},\ t_{end}] \tag{1}\]  
\[\text{J}=W_{fuel}(t_{k}),\ t_{k}\in[t_{i},\ t_{end}] \tag{2}\]  
where J = objective function, \(t\) = time, \(t_{i}\) = initial time, \(t_{end}\) = end time, \(Wt_{fuel}\) = fuel weight, and \(W_{fuel}\) = fuel flow rate.