On H2 and H-infinity Optimal Control of Mass-Spring Networks with Power System Applications
Sammanfattning: Electric power systems are undergoing huge changes due to the shift from conventional power production to more renewable-based generation like solar and wind. This is primarily driven by the need to mitigate climate change by reducing CO2 emissions. The shift to more generation from solar and wind will affect the dynamical behaviour of power systems, and consequently how they should be controlled. This thesis explores optimal control with respect to disturbance rejection. The systems that are investigated are damped mass-spring systems. The dynamics of AC frequency in power systems can be captured through such models. Further, the implications of the derived optimal control laws are investigated. In the first paper of this thesis, undamped mass-spring systems (and more generally lossless systems) are investigated. The optimal controllers that achieve the lowest ?2-gain and ?∞-gain from disturbances to performance outputs are derived analytically for a standard setup. An analytical expression of the optimal gains are also presented. Finally, the results are interpreted in the context of electrical power systems. The results show the detrimental effect low inertia, typically associated with renewable generation like solar and wind, can have on ?2 performance. However, it is further shown numerically that under the optimal controller, these effects are mostly isolated to the low inertia regions of the grid. The second paper of this thesis considers ?2 optimal control for disturbance rejection for a damped mass-spring system with uniform damping. The main contribution is to show that the optimal controller that achieves the smallest gain from disturbances to performance outputs is itself a damped mass-spring system. The optimal controller works both for stable and unstable systems. In the unstable case the ?2-gain becomes larger than the undamped system in the first paper, while for positively damped systems it becomes smaller. Together the results presented in this thesis offer optimal controllers for un-damped and uniformly damped mass-spring systems. These have been applied to simple models of electrical power transmission. Finally, future work detailing how to extend the techniques to cover a broader range of power system control problems is outlined.
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