On some dynamic properties of electrical power systems : sobre algunas propiedades dinámicas de los sistemas eléctricos de potencia

This thesis treats some dynamic properties of power system models. An extension of the classical concept of dissipativity is formulated to deal with these systems described by differential-algebraic equations on phasor variables. A class of models of these systems the same that is known to admit an energy function is shown to be dissipative in the sense mentioned above, to later be extended to include realistic models of synchronous machines and other devices. The small signal models are shown to satisfy a convex constraint in the frequency domain that is later articulated with Integral Quadratic Constraints, a well-known stability analysis tool. Specific features of realistic power system models, as the effect of voltage regulation and damping injection, are precisely captured and incorporated into the analysis. It is shown that a trade-off between the mentioned control actions and the voltage sensitivity is a sufficient condition to establish the robustness of the electromechanical modes. This result and others mentioned above are validated through several examples.Esta tesis trata algunas propiedades dinámicas de los sistemas eléctricos de potencia. Se formula una extensión del concepto clásico de disipatividad compatible con estos sistemas, descritos por ecuaciones algebraico-diferenciales sobre variables fasoriales. Se muestra que una clase de modelos de estos sistemas satisface este concepto de disipatividad y se muestra que también lo hacen modelos detallados de máquinas síncronas y otros dispositivos de potencia. Se demuestra que los modelos en pequeña señal satisfacen una restricción convexa en el dominio de la frecuencia, capaz de ser articulada con herramientas bien conocidas de análisis de estabilidad. Características específicas de los sistemas eléctricos reales, tales como la acción de la regulación de tensión y las señales estabilizadoras, son precisamente definidas e incorporadas al análisis. Se demuestra que un adecuado balance entre las acciones de control mencionadas y la sensibilidad a variaciones de tensión es una condición suficiente para la robustez de los modos electromecánicos del sistema. Este resultado y otros mencionados anteriormente son validados mediante el análisis de varios ejemplos

Application of frequential properties of power systems to robustness analysis

Abstract-This paper studies the application of certain frequency domain properties of a class of power systems to the robustness analysis. The small signal models of a significant class of power systems-namely, systems without resistive losses nor excitation control-was recently shown to meet passivitylike, convex conditions in the frequency domain. A classical benchmark is considered and it is shown that the presence of excitation control and resistive elements does not completely destroy the above-mentioned property, which remains valid in the frequency band associated to the electromechanical modes. The example includes a detailed robustness analysis showing the importance of the a priori knowledge of the frequential properties of these models in the frequency band of interest

A Lyapunov Approach to Control of Microgrids with a Network-Preserved Differential-Algebraic Model

We provide sufficient conditions for asymptotic stability and optimal resource allocation for a networkpreserved microgrid model with active and reactive power loads. The model considers explicitly the presence of constantpower loads as well as the coupling between the phase angle and voltage dynamics. The analysis of the resulting nonlinear differential algebraic equation (DAE) system is conducted by leveraging incremental Lyapunov functions, definiteness of the load flow Jacobian and the implicit function theorem

Efficient Control Approaches for Guaranteed Frequency Performance in Power Systems

Due to high penetration of renewable energy, converter-interfaced sources are increasing in power systems and degrading the grid frequency response. Synthetic inertia emulation and guaranteed primary frequency response is a challenging task. Still, there is high potential for application of highly controllable converter-interfaced devices to help performance. Renewable energy sources and demand side smart devices also need to be equipped with innovative frequency control approaches that contribute to frequency regulation operations. First, the wind turbine generator is chosen to represent an example of a converter- interfaced source. An augmented system frequency response model is derived, including the system frequency response model and a reduced-order model of the wind turbine generator representing the supportive active power due to supplementary inputs. An output feedback observer-based control is designed to provide guaranteed frequency performance. System performance is analyzed for different short circuit ratio scenarios where a lower bound to guarantee the performance is obtained. Second, the load side control for frequency regulation with its challenges is introduced. 5G technology and its potential application in smart grids are analyzed. The effect of communication delays and packet losses on inertia emulation are investigated to show the need of using improved communication infrastructure. Third, a robust delay compensation for primary frequency control using fast demand response is proposed. Possible system structured uncertainties and communication delays are considered to limit frequency variations using the proposed control approach. An uncertain governor dead-band model is introduced to capture frequency response characteristics. Guaranteed inertial response is achieved and compared with a PI-based Smith predictor controller to show the effectiveness of the proposed method. Fourth, set theoretic methods for safety verification to provide guaranteed frequency response are introduced. The Barrier certificate approach using a linear programming relaxation by Handelman’s representation is proposed with its application to power systems. Finally, the Handelman’s based barrier certificate approach for adequate frequency performance is studied. The computational algorithm is provided for the proposed method and validated using power system benchmark case studies with a discussion on a safety supervisory control (SSC)

Asynchronous Networks and Event Driven Dynamics

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks

Stability of Stochastic Differential Equations with Jumps by the Coupling Method

The topic of this thesis is the study of R^d-valued stochastic processes defined as solutions to stochastic differential equations (SDEs) driven by a noise with a jump component. Our main focus are SDEs driven by pure jump Levy processes and, more generally, by Poisson random measures, but our framework includes also cases in which the noise has a diffusion component. We present proofs of results guaranteeing existence of solutions and invariant measures for a broad class of such SDEs. Next we introduce a probabilistic technique known as the coupling method. We present an original construction of a coupling of solutions to SDEs with jumps, which we subsequently apply to study various stability properties of these solutions. We investigate the rates of their convergence to invariant measures, bounds on their Malliavin derivatives (both in the jump and the diffusion case) and transportation inequalities, which characterize concentration of their distributions. In all these cases the use of the coupling method allows us to significantly strengthen results that have been available in the literature so far. We conclude by discussing potential extensions of our techniques to deal with SDEs with jump noise which is inhomogeneous in time and space