Marcello Colombino

In this article, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of the dynamics is influenced only by the slower dynamics and the successive fastest one. The proposed approach explicitly considers more than two time scales, it does not require modeling multiple time scales via scalar time constants, and provides analytic bounds that make ad-hoc time-scale separation arguments rigorous. Motivated by the technical results, we develop a novel control strategy for a grid-forming power converter that consists of an inner cascaded two-degree-of-freedom controller and dispatchable virtual oscillator control as a reference model. The resulting closed-loop converter-based ac power system is in the form of a nested system with multiple time scales. We apply our technical results to obtain explicit bounds on the controller set points, branch powers, and control gains that guarantee almost global asymptotic stability of the multiconverter ac power system with respect to a prespecified solution of the ac power flow equations. Finally, we validate the performance of the proposed control structure in a case study using a high-fidelity simulation with detailed hardware validated converter models.

In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system – a problem known as sample complexity analysis in computer science. Motivated by the increasing adoption of distributed energy resources into the distribution-level grids, it becomes imperative to estimate the state of distribution grids in order to ensure stable operation. Traditional power system state estimation techniques mainly focus on the transmission network which involve solving an overdetermined system and eliminating bad data. However, distribution networks are typically underdetermined due to the large number of connection points and high cost of pervasive installation of measurement devices. In this paper, we consider the recently proposed state-estimation method for underdetermined systems that is based on matrix completion. In particular, a constrained matrix completion algorithm was proposed, wherein the standard matrix completion problem is augmented with additional equality constraints representing the physics (namely power-flow constraints). We analyze the sample complexity of this general method by proving an upper bound on the sample complexity that depends directly on the properties of these constraints that can lower number of needed samples as compared to the unconstrained problem. To demonstrate the improvement that the constraints add to state estimation, we test the method on a 141-bus distribution network case study and compare it to the traditional least squares minimization state estimation method.

In this paper, we propose an analytical framework to quantify the amount of data samples needed to obtain accurate state estimation in a power system - a problem known as sample complexity analysis in computer science. Motivated by the increasing adoption of distributed energy resources into the distribution-level grids, it becomes imperative to estimate the state of distribution grids in order to ensure stable operation. Traditional power system state estimation techniques mainly focus on the transmission network which involve solving an overdetermined system and eliminating bad data. However, distribution networks are typically underdetermined due to the large number of connection points and high cost of pervasive installation of measurement devices. In this paper, we consider the recently proposed state-estimation method for underdetermined systems that is based on matrix completion. In particular, a constrained matrix completion algorithm was proposed, wherein the standard matrix completion problem is augmented with additional equality constraints representing the physics (namely power-flow constraints). We analyze the sample complexity of this general method by proving an upper bound on the sample complexity that depends directly on the properties of these constraints that can lower number of needed samples as compared to the unconstrained problem. To demonstrate the improvement that the constraints add to distribution state estimation, we test the method on a 141-bus distribution network case study and compare it to the traditional least squares minimization state estimation method.

In this work, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based AC power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, i.e., if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of AC power inverters with respect to a pre-specified solution of the AC power-flow equations. While this approximation is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system. In this work, we establish explicit bounds on the controller set-points, branch powers, and control gains that guarantee almost global asymptotic stability of dVOC in combination with a dynamic model of the transmission network.

In this work, we analyze the effect of transmission line dynamics on grid-forming control for inverter-based AC power systems. In particular, we investigate a dispatchable virtual oscillator control (dVOC) strategy that was recently proposed in the literature. When the dynamics of the transmission lines are neglected, i.e., if an algebraic model of the transmission network is used, dVOC ensures almost global asymptotic stability of a network of AC power inverters with respect to a pre-specified solution of the AC power-flow equations. While this approximation is typically justified for conventional power systems, the electromagnetic transients of the transmission lines can compromise the stability of an inverter-based power system. In this work, we establish explicit bounds on the controller setpoints, branch powers, and control gains that guarantee almost global asymptotic stability of dVOC in combination with a dynamic model of the transmission network.

This paper develops a distributed saddle-flow algorithm to regulate the output of a networked system – modeled as static linear map – to the solution of a constrained convex optimization problem. The algorithm is “feedback-based”, in the sense that measurements of the network output are leveraged in the saddle-flow updates to avoid a complete (oracle-based) knowledge of the network map. In the distributed architecture, each actuator has access to only a subset of measurements; nevertheless, supported by a connected communication graph, a distributed protocol is implemented to achieve consensus on pertinent dual variables associated with network-level output constraints and, therefore, on the solution of the constrained problem. Using a LaSalle argument, we show that under an easily satisfiable Linear Matrix Inequality condition the proposed algorithm converges to an optimal primal-dual solution. We demonstrate the effectiveness of the proposed method in a voltage regulation problem for power systems with high penetration of renewable generation.

This paper develops and analyzes feedback-based online optimization methods to regulate the output of a linear time-invariant (LTI) dynamical system to the optimal solution of a time-varying convex optimization problem. The design of the algorithm is based on continuous-time primal-dual dynamics, properly modified to incorporate feedback from the LTI dynamical system, applied to a proximal augmented Lagrangian function. The resultant closed-loop algorithm tracks the solution of the time-varying optimization problem without requiring knowledge of (time-varying) disturbances in the dynamical system. The analysis leverages integral quadratic constraints to provide linear matrix inequality (LMI) conditions that guarantee global exponential stability and bounded tracking error. Analytical results show that, under a sufficient time-scale separation between the dynamics of the LTI dynamical system and the algorithm, the LMI conditions can be always satisfied. The paper further proposes a modified algorithm that can track an approximate solution trajectory of the constrained optimization problem under less restrictive assumptions. As an illustrative example, the proposed algorithms are showcased for power transmission systems, to compress the time scales between secondary and tertiary control, and allow to simultaneously power re-balancing and tracking of DC optimal power flow points.

In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback based on relative state information and local measurements that induces consensus-like dynamics. We show that, under a mild stability condition, the combination of the synchronizing feedback with a decentralized magnitude control law renders the oscillators' almost globally asymptotically stable with respect to set-points for the phase shift, frequency, and magnitude. We apply these result to rigorously solve an open problem in control of inverter-based AC power systems. In this context, the proposed control strategy can be implemented using purely local information, induces a grid-forming behavior, and ensures that a network of AC power inverters is almost globally asymptotically stable with respect to a pre-specified solution of the AC power-flow equations. Moreover, we show that the controller exhibits a droop-like behavior around the standard operating point thus making it backward-compatible with the existing power system operation.

In this work, we explore a new approach to synchronization of coupled oscillators. In contrast to the celebrated Kuramoto model we do not work in polar coordinates and do not consider oscillations of fixed magnitude. We propose a synchronizing feedback based on relative state information and local measurements that induces consensus-like dynamics. We show that, under a mild stability condition, the combination of the synchronizing feedback with a decentralized magnitude control law renders the oscillators' almost globally asymptotically stable with respect to set-points for the phase shift, frequency, and magnitude. We apply these result to rigorously solve an open problem in control of inverter-based AC power systems. In this context, the proposed control strategy can be implemented using purely local information, induces a grid-forming behavior, and ensures that a network of AC power inverters is almost globally asymptotically stable with respect to a pre-specified solution of the AC power-flow equations. Moreover, we show that the controller exhibits a droop-like behavior around the standard operating point thus making it backward-compatible with the existing power system operation.

This paper presents an analysis and experimental validation of dispatchable virtual oscillator control (dVOC) for inverter-dominated power systems. dVOC is a promising decentralized control strategy that requires only local measurements to induce grid-forming behavior with programmable droop characteristics. It is dispatchable i.e., the inverters can vary their power generation via user-defined power set-points and guarantees strong stability. To verify its feasibility, a testbed comprising multiple dVOC-programmed inverters with transmission line impedances is designed. With an embedded synchronization strategy, the dVOC inverters are capable of dynamic synchronization, black start operation, and transient grid voltage regulation with dynamic load sharing, and real-time-programmable droop characteristics for backward compatibility. All these features are experimentally verified.