Optimal Architecture Synthesis for Aircraft Electrical Power Systems

Aircraft Electrical Power Systems (EPS) are becoming complex cyber-physical systems, consisting of a physical plant (generators, AC-Buses, rectifiers, DC-Buses, switches and loads) and a cyber component, namely the Bus Power Control Units (BPCU). To deal with the increasing complexity of EPS while guaranteeing the satisfaction of tight reliability and safety constraints, automated design tools for the synthesis of the topology (interconnection of components) are developed. These tools can significantly reduce the design time aiming to generate correct-by-construction systems. In this thesis, we propose two optimization oriented design methodologies to synthesize a reliable-by-construction EPS topology with minimal cost and complexity. The two methodologies differently deal with the non linear reliability constraint, that arise in the mathematical formulation of the synthesis problem. The first methodology uses a Mixed Integer Linear Programming Modulo Reliability (MILPMR) approach to generate minimal cost topologies, given a set of a connectivity and power flow constraints. The optimizer is placed in a loop with a reliability analysis algorithm, which evaluates the failure probability of the critical loads and implements several strategies that provide suggestions to the optimizer to improve the reliability of the topology, in case the requirements are not met. In the second methodology, we automatically generate a symbolic expression of the reliability analysis, linearize it and use it directly in a plain MILP optimizer. We successfully implement the two methodologies and compare them with respect to their runtime, scalability with the number of components and accuracy. The obtained results show that the MILPMR can result in a less efficient implementation because of the number of iterations needed to converge to the final solution, whereas the plain MILP normally converges in one iterations, but it relies on an approximate reliability algebra to improve on scalability.