Optimization with Time and Frequency Constraints Using Automatic Differentiation: Application to an Aircraft Electrical Power Channel

The ordinary differential equations used to model a dynamic system can evolve during the simulation in circumstances where unpredictable events occur, more specifically, in regard to the domain of power electronics, for example, static converters will exhibit natural switching. Optimal sizing, on top of developing such a model, is a significant challenge for designers, particularly due to the complexity of incorporating efficiently both time-domain and frequency-domain constraints and objectives. This paper presents a methodology and tool to address this issue, leveraging a ‘white-box’ modeling approach, with automatic gradient computation. An efficient optimizer is coupled with a differential equation solver, capable of leveraging automatic differentiation and symbolic derivation, leading to both faster and more accurate outcomes than alternative methods. Furthermore, the developed solver incorporates original functionalities that are crucial for optimization, such as the ability to automatically detect the steady state and extract time-domain and frequency-domain features from the simulations to be optimized or constrained. The methodology is demonstrated through its application in regard to the optimal design of an aircraft electrical power channel.