arXiv subjects

Taouba Jouini

Publications and source records attributed to Taouba Jouini.

14 recordsLinked to original sources

arXiv2026

Hardware test and validation of the angular droop control: Analysis and experiments

We present a hardware-based validation of angular droop control for grid-forming DC/AC converters, a control strategy that establishes active power-to-angle droop. Angular droop control enables exact frequency regulation at steady state, thereby combining primary and secondary control into a single layer. We provide traceable analysis and suggest solutions to the main implementation challenges with angular droop control, specifically addressing the challenges concerning discretization and clock drift in hardware experiments. This is illustrated in two different scenarios. Experimental results from the single converter to load scenario demonstrate black start capability and power-to-angle droop behavior for two different implementation schemes. A multi-converter setup validates frequency synchronization and power-sharing properties, proving the ancillary services that angular droop control provides in the real-world experimental setup.

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arXiv2024

Disturbance feedback-based model predictive control in uncertain dynamic environments

This paper presents a robust MPC scheme for linear systems subject to time-varying, uncertain constraints that arise from uncertain environments. The predicted input sequence is parameterized over future environment states to guarantee constraint satisfaction despite an imprecise environment prediction and unknown evolution of the future constraints. We provide theoretical guarantees for recursive feasibility and asymptotic convergence. Finally, a brief simulation example showcases our results.

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arXiv2022

Leveraging second-order information for tuning of inverse optimal controllers

We leverage second-order information for tuning of inverse optimal controllers for a class of discrete-time nonlinear input-affine systems. For this, we select the input penalty matrix, representing a tuning knob, to yield the Hessian of the Lyapunov function of the closed-loop dynamics. This draws a link between second-order methods known for their high speed of convergence and the tuning of inverse optimal stabilizing controllers to achieve a fast decay of the closed-loop trajectories towards a steady state. In particular, we ensure quadratic convergence, a feat that is otherwise not achieved with a constant input penalty matrix. To balance trade-offs, we suggest a practical implementation of the Hessian and validate this numerically on a network of phase-coupled oscillators that represent voltage source controlled power inverters.

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arXiv2022

Inverse optimal control for angle stabilization in converters-based generation

In inverse optimal control, the optimality of a given feedback stabilizing controller is a byproduct of the choice of a meaningful, a posteriori defined, cost functional. This allows for a simple tuning comparable to linear quadratic control, also for nonlinear controllers. Our work illustrates the usefulness of this approach in the control of converter-based power systems and networked systems in general, and thereby in finding controllers with topological structure and known optimality properties. In particular, we design an inverse optimal feedback controller that stabilizes the phase angles of voltage-source controlled DC/AC converters at an induced steady state with zero frequency error. The distributed angular droop controller yields active power to angle droop behavior at steady state. Moreover, we suggest a practical implementation of the controller and corroborate our results through simulations on a three-converter system and a numerical comparison with standard frequency droop control.

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arXiv2022

Grid-friendly Matching Control of Synchronous Machines by DC/AC Converters in Bulk Power Networks

An islanded inverter-based microgrid is a collection of heterogeneous DC energy resources, e.g., photovoltaic arrays, fuel cells, and energy-storage devices, interfaced to an AC distribution network and operated independently from the bulk power system. Energy conversion is typically managed by power electronics in voltage source inverters. Drawing from the control of synchronous machines in bulk power systems, different control schemes have been recently adopted in order to achieve a stable network operation. The vast majority of academic and industrial efforts opt for these strategies during real-time operation. Starting with a dynamical averaged DC/AC converter model, we review different controllers by presenting their main scope analytically and through simulations. Next, we explore a new alternative of controlling DC/AC converters in bulk power systems by matching traditional synchronous machines with emphasis on the role that DC-circuit can play in control architecture, usually neglected in conventional strategies. Compared to standard emulation methods, our controller relies solely on readily available DC-side measurements and takes into account the natural DC and AC storage elements. As a result, our controller is generally faster and less vulnerable to delays and measurement inaccuracies. We additionally provide insightful interpretations of the suggested control, various plug-and-play properties of the closed-loop, such as steady-state power flow analysis, passivity with respect to the DC and AC ports, stability proof as well as high-level control architectures contributing to enhancing the controller performance and attaining further control goals, which we illustrate in both analysis and simulation.

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arXiv2021

On cost design in applications of optimal control

A new approach to feedback control design based on optimal control is proposed. Instead of expensive computations of the value function for different penalties on the states and inputs, we use a control Lyapunov function that amounts to be a value function of an optimal control problem with suitable cost design and then study combinations of input and state penalty that are compatible with this value function. This drastically simplifies the role of the Hamilton-Jacobi-Bellman equation, since it is no longer a partial differential equation to be solved, but an algebraic relationship between different terms of the cost. The paper illustrates this idea in different examples, including $\mathcal{H}_{\infty}$ control and optimal control of coupled oscillators.

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arXiv2021

Steady state characterization and frequency synchronization of a multi-converter power system on high-order manifolds

We investigate the stability properties of a multi-converter power system model, defined on a high-order manifold. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of AC signals. We characterize the steady state set, primarily determined by the steady state angles and DC power input. Based on eigenvalue conditions of its Jacobian matrix, we show asymptotic stability of the multi-converter system in a neighborhood of the synchronous steady state set by applying the center manifold theory. We guarantee the eigenvalue conditions via an explicit approach. Finally, we demonstrate our results based on a numerical example involving a network of identical DC/AC converter systems.

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arXiv2021

Distributed learning for optimal allocation of synchronous and converter-based generation

Motivated by the penetration of converter-based generation into the electrical grid, we revisit the classical log-linear learning algorithm for optimal allocation {of synchronous machines and converters} for mixed power generation. The objective is to assign to each generator unit a type (either synchronous machine or DC/AC converter in closed-loop with droop control), while minimizing the steady state angle deviation relative to an optimum induced by unknown optimal configuration of synchronous and DC/AC converter-based generation. Additionally, we study the robustness of the learning algorithm against a uniform drop in the line susceptances and with respect to a well-defined feasibility region describing admissible power deviations. We show guaranteed probabilistic convergence to maximizers of the perturbed potential function with feasible power flows and demonstrate our theoretical findings via simulative examples of power network with six generation units.

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arXiv2020

Grid-forming lambda-omega virtual oscillator control in converter-based power systems

Inspired by the kinetics of wave phenomena in reaction-diffusion models of biological systems, we propose a novel grid-forming control strategy for control of three-phase DC/AC converters in power systems. The ($λ-ω$) virtual oscillator control or (lambda-omega) VOC is a natural increment on ideas from virtual oscillator dynamics rotating at a fixed nominal frequency to adaptive, angle-based frequency function. We study a network of identical three-phase DC/AC converters interconnected via $Π$ transmission lines. For this, we prove almost global asymptotic stability for a reduced (time-scale separated) version of the model, associated to a well-defined set of controller gains and system parameters. Additionally, we link the (λ-ω) VOC to well-studied controllers in the literature, e.g. droop control. Finally, we validate our results on an example three DC/AC converter network.

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arXiv2020

Fully decentralized conditions for local convergence of DC/AC converter network based on matching control

We investigate local convergence of identical DC/AC converters interconnected via identical resistive and inductive lines towards a synchronous equilibrium manifold. We exploit the symmetry of the resulting vector field and develop a Lyapunov-based framework, in which we measure the distance of the solutions of the nonlinear power system model to the equilibrium manifold by analyzing the evolution of their tangent vectors. We derive sufficient and fully decentralized conditions to characterize the equilibria of interest, and provide an estimate of their region of contraction. We provide ways to satisfy these conditions and illustrate our results based on numerical simulations of a two-converter benchmark.

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arXiv2020

Performance analysis and optimization of power systems with spatially correlated noise

Based on stochastic differential equations (SDEs), we analyse the overall performance of heterogeneous power systems network, subject to spatially distributed and correlated noise with random initial conditions. We determine bounds on the H_2 norm of the heterogeneous system based on a closed-form of the norm of the homogeneous power system. Then, we formulate possible scenarios for performance optimization and link these to applications for network design and control problems in power systems. Our results are corroborated by numerical simulations from Kundur's four-machine two-area network after adaption to our setup.

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arXiv2019

Parametric local stability condition of a multi-converter system

We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom. We develop a stability theory for a class of partitioned linear systems with symmetries that has natural links to classical stability theories of interconnected systems. We find stability conditions descending from a particular Lyapunov function involving an oblique projection onto the complement of the synchronous steady state set and enjoying insightful structural properties. Our sufficient and explicit stability conditions can be evaluated in a fully decentralized fashion, reflect a parametric dependence on the converter's steady-state variables, and can be one-to-one generalized to other types of systems exhibiting the same behavior, such as synchronous machines. Our conditions demand for sufficient reactive power support and resistive damping. These requirements are well aligned with practitioners' insights.

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arXiv2018

Grid-forming Control for Power Converters based on Matching of Synchronous Machines

We consider the problem of grid-forming control of power converters in low-inertia power systems. Starting from an average-switch three-phase inverter model, we draw parallels to a synchronous machine (SM) model and propose a novel grid-forming converter control strategy which dwells upon the main characteristic of a SM: the presence of an internal rotating magnetic field. In particular, we augment the converter system with a virtual oscillator whose frequency is driven by the DC-side voltage measurement and which sets the converter pulse-width-modulation signal, thereby achieving exact matching between the converter in closed-loop and the SM dynamics. We then provide a sufficient condition assuring existence, uniqueness, and global asymptotic stability of equilibria in a coordinate frame attached to the virtual oscillator angle. By actuating the DC-side input of the converter we are able to enforce this sufficient condition. In the same setting, we highlight strict incremental passivity, droop, and power-sharing properties of the proposed framework, which are compatible with conventional requirements of power system operation. We subsequently adopt disturbance decoupling techniques to design additional control loops that regulate the DC-side voltage, as well as AC-side frequency and amplitude, while in the end validating them with numerical experiments.

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arXiv2014

Generalization of the construction method for multistability-equivalent gene regulatory networks to systems with multi-input multi-output loopbreaking

The problem of equivalence in terms of multistability properties between gene regulatory network models of different dimensionality has been recently addressed by Schittler et al. (2013). The authors in that work proposed construction rules for a high-dimensional dynamical system, when given a low-dimensional dynamical system and the high-dimensional network structure. However, the proof therein was restricted to the class of systems for which all internal feedback loops can be broken by a loopbreaking approach yielding a single-input single-output (SISO) system. In this report, we present the generalization of the proof to systems with any number of internal feedback loops, which will be broken by a generalized loopbreaking approach resulting in a multi-input multi-output (MIMO) system. This generalization of the method renders the construction method applicable to a broad class of gene regulatory network models, thus promoting the transfer of results from core motif models to more realistic, high-dimensional models of gene regulation. We demonstrate the potential and value of our method by applying it to an example of a gene regulatory network in mesenchymal stem cell differentiation.

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