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Time-optimal Control and Switching Surface of the Swing Equation


J. Seitz

Master Thesis, SS16

The question of how to ensure rotor-angle stability of power systems has been addressed for several decades. The main purpose of this task is to keep the network in synchrony for which the swing equation has been employed as the basic tool. Traditional approaches often exploit Lyapunov theory and try to find sublevel sets of energy functions for which stability can be guaranteed. However, these sublevel sets generally do not share the shape of the true stable region and, thus, are quite conservative. Alternatively, the system behavior is tested for a set of worst case contingencies which leads to the well-known N 1 criterion. More recently, other methods have been developed that pose the maximization of the backwards reachable set of the stable equilibrium point as an optimization problem, which is solved numerically. The approach presented in this thesis follows a similar spirit and introduces a simplified model of a High Voltage Direct Current (HVDC) control scheme to the system in order to find a time-optimal control strategy for the swing equation. It can be shown that this naturally also maximizes the reachable sets. The switching surface for the resulting bang-bang control is characterized analytically as a function of the states of the linearized power system. This allows a fast and easy calculation of the surface but at the same time is restricted to one- and two-area power networks due to the rising complexity in higher dimensions. In order to guarantee a well-behaved control, conditions for controllability that allow to exclude singular arcs are provided and it is shown that the bang-bang property holds for every HVDC line separately.

Supervisors: Maryam Kamgarpour, Alexander Fuchs


Type of Publication:

(12)Diploma/Master Thesis

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% Autogenerated BibTeX entry
@PhdThesis { Xxx:2017:IFA_5592
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