Transverse feedback passivation in control of multi-machine and multi-converter power networks

This thesis investigates the coordinated stabilization for two important classes of power conversion systems in electrical networks: the synchronous generator and the three-phase DC/AC converter. Starting from first-principles, we cast a geometric treatment and arrive at the problem of stabilizing a particular log-polar configuration, corresponding to the optimal network flow in an electrical circuit. The approach is, on the one hand, based on constructing a feedback-equivalent system which naturally decomposes into dynamics on the ray and on the circle. These spaces can be seen as mutual quotients of the Euclidean plane. Upon augmenting the appropriate amplitude-coupling component, the so-called phase-coupled oscillator system is no longer constrained to evolve on the n-torus. On the other hand, a model-matching procedure is proposed to induce dominant dynamics for the radial and the angular coordinates. As in mechanical systems, these simple integrators act as generalized coordinates and are associated with a special potential energy construction. From a power systems perspective, the potential energy function encodes the canonical network objective of inductor current minimization and capacitor voltage maximization. As the rest of the system is naturally damped, a harmonic steady-state behavior emerges, allowing a zero-dynamics refinement procedure. We then explore ways of shaping the energy in the aim of achieving higher-level objectives, such as tracking given active and reactive power set points. Finally, we pose a problem of transverse stabilization, and arrive at a constructive energy function and a feedback law for the synchronous machine and the inverter alike. This unified design methodology further allow us to study the dynamic properties of the most significant circuit elements in power systems