Modeling and control of power systems in microgrids

This thesis addresses several problems related to modeling and control of power systems in microgrids. First, a method is established to measure the effect of the addition of output impedances on the inductivity of a power network. We define a network inductivity measure, and compute it for homogeneous networks with RL output impedances. Second, we propose a master-slave architecture for microgrids, in which the source with the highest generation capacity acts as the master. In this scheme, power sharing can be achieved among the sources, without the need to any communication network. Third, we derive an improved swing model for synchronous generators which, compared to the swing equation, predicts better the behavior of the system, and yet it is easy to use. Incremental passivity properties of this model paves the path for a controller design. As a fourth problem, we look into the problem of lack of inertia in networks with dominant renewable energies. We model the power converters with large capacitors acting as inertia, and show stability and frequency regulation for a network of these converters. Fifth, we investigate the shifted passivity property of port-Hamiltonian systems with strictly convex Hamiltonian. We establish conditions under which the system is shifted passive, and guarantee stability of forced equilibria of pH systems. Finally, a subclass of port-Hamiltonian systems is developed, where the control input or disturbance is acting on the power entering the system. We investigate the shifted passivity of such pH systems, and characterize a region of attraction for stability of the equilibrium

On the Generation of Large Passive Macromodels for Complex Interconnect Structures

This paper addresses some issues related to the passivity of interconnect macromodels computed from measured or simulated port responses. The generation of such macromodels is usually performed via suitable least squares fitting algorithms. When the number of ports and the dynamic order of the macromodel is large, the inclusion of passivity constraints in the fitting process is cumbersome and results in excessive computational and storage requirements. Therefore, we consider in this work a post-processing approach for passivity enforcement, aimed at the detection and compensation of passivity violations without compromising the model accuracy. Two complementary issues are addressed. First, we consider the enforcement of asymptotic passivity at high frequencies based on the perturbation of the direct coupling term in the transfer matrix. We show how potential problems may arise when off-band poles are present in the model. Second, the enforcement of uniform passivity throughout the entire frequency axis is performed via an iterative perturbation scheme on the purely imaginary eigenvalues of associated Hamiltonian matrices. A special formulation of this spectral perturbation using possibly large but sparse matrices allows the passivity compensation to be performed at a cost which scales only linearly with the order of the system. This formulation involves a restarted Arnoldi iteration combined with a complex frequency hopping algorithm for the selective computation of the imaginary eigenvalues to be perturbed. Some examples of interconnect models are used to illustrate the performance of the proposed technique

Stabilization of structure-preserving power networks with market dynamics

This paper studies the problem of maximizing the social welfare while stabilizing both the physical power network as well as the market dynamics. For the physical power grid a third-order structure-preserving model is considered involving both frequency and voltage dynamics. By applying the primal-dual gradient method to the social welfare problem, a distributed dynamic pricing algorithm in port-Hamiltonian form is obtained. After interconnection with the physical system a closed-loop port-Hamiltonian system of differential-algebraic equations is obtained, whose properties are exploited to prove local asymptotic stability of the optimal points.Comment: IFAC World Congress 2017, accepted, 6 page

Efficient time-domain modeling and simulation of passive bandpass systems

In communication systems, the signals of interest are often amplitude and/or phase modulated ones. In this framework, the baseband equivalent signals and systems representation is usually adopted to simulate the digital parts of communication systems in an efficient manner. This contribution extends the applicability of such representation to RF/analog devices, leading to a common and efficient modeling and simulation framework. In particular, the proposed method can build half-size models compared to existing approaches, and allows one to choose the simulation time step according to the bandwidth of the modulating signals rather than the carrier frequency, thereby significantly speeding up the simulation procedure. The novel proposed method is validated via a suitable application example

Permanent Magnet Synchronous Motors are Globally Asymptotically Stabilizable with PI Current Control

This note shows that the industry standard desired equilibrium for permanent magnet synchronous motors (i.e., maximum torque per Ampere) can be globally asymptotically stabilized with a PI control around the current errors, provided some viscous friction (possibly small) is present in the rotor dynamics and the proportional gain of the PI is suitably chosen. Instrumental to establish this surprising result is the proof that the map from voltages to currents of the incremental model of the motor satisfies some passivity properties. The analysis relies on basic Lyapunov theory making the result available to a wide audience

Krasovskii's Passivity

In this paper we introduce a new notion of passivity which we call Krasovskii's passivity and provide a sufficient condition for a system to be Krasovskii's passive. Based on this condition, we investigate classes of port-Hamiltonian and gradient systems which are Krasovskii's passive. Moreover, we provide a new interconnection based control technique based on Krasovskii's passivity. Our proposed control technique can be used even in the case when it is not clear how to construct the standard passivity based controller, which is demonstrated by examples of a Boost converter and a parallel RLC circuit

A Parallel Hamiltonian Eigensolver for Passivity Characterization and Enforcement of Large Interconnect Macromodels

Best Paper Award Nominatio