Delay-robust distributed secondary frequency control for next-generation power systems: Stability analysis and controller synthesis

Power systems worldwide are undergoing major transformation to enable a low-carbon future. These developments require new procedures for advanced control to ensure a stable and efficient system operation. Consensus-based distributed secondary frequency control schemes have the potential to ensure real-time frequency restoration and economic dispatch simultaneously in future power systems with significant contribution of renewable energy sources. However, owing to their distributed nature, these control schemes critically depend on communication between different controlled units. Thus, robustness against communication uncertainty is crucial for their reliable operation. In this work, control design and stability analysis of delay-robust secondary frequency control in next-generation power systems are studied. The main contributions of the present thesis can be summarised as follows: (i) A design procedure for a consensus-based secondary frequency controller in microgrids is proposed that ensures robustness with respect to heterogeneous fast-varying communication delays and simultaneously provides the option to trade off the L2-gain performance against the number of required communication links; (ii) The conditions for robust stability of a consensus-based frequency control scheme applied to a power system model with second-order turbine-governor dynamics in the presence of heterogeneous time-varying communication delays and dynamic communication topology are derived; (iii) The performance of the proposed consensus-based secondary frequency controller is analysed in a detailed model capturing the dynamic behaviour of a real system. The results provide insights to the robustness of the closed-loop system with respect to unmodelled (voltage and higher-order generator) dynamics as well as communication delays

H∞ Control of Nonlinear Systems: A Class of Controllers

The standard state space solutions to the H∞ control problem for linear time invariant systems are generalized to nonlinear time-invariant systems. A class of nonlinear H∞-controllers are parameterized as nonlinear fractional transformations on contractive, stable free nonlinear parameters. As in the linear case, the H∞ control problem is solved by its reduction to four simpler special state space problems, together with a separation argument. Another byproduct of this approach is that the sufficient conditions for H∞ control problem to be solved are also derived with this machinery. The solvability for nonlinear H∞-control problem requires positive definite solutions to two parallel decoupled Hamilton-Jacobi inequalities and these two solutions satisfy an additional coupling condition. An illustrative example, which deals with a passive plant, is given at the end

Distributed Secondary Frequency Control Design for Microgrids: Trading Off L2-Gain Performance and Communication Efforts under Time-Varying Delays

Consensus algorithms are promising control schemes for secondary control tasks in microgrids. Since consensus algorithms are distributed protocols, communication efforts and time delays are significant factors for the control design and performance. Moreover, both the electrical and the communication layer in a microgrid are continuously exposed to exogenous disturbances. Motivated by this, we derive a synthesis for a consensus-based secondary frequency controller that guarantees robustness with respect to time-varying delays and in addition provides the option to trade off L2 disturbance attenuation against the number of required communication links. The efficacy of the proposed approach is illustrated via simulations based on the CIGRE benchmark medium voltage distribution network

Regelungstheorie

The workshop “Regelungstheorie” (control theory) covered a broad variety of topics that were either concerned with fundamental mathematical aspects of control or with its strong impact in various fields of engineering

Manifold turnpikes, trims, and symmetries

Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler–Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings