| 1. |
- Jouini, Taouba, et al.
(författare)
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Distributed learning for optimal allocation of synchronous and converter-based generation
- 2021
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Ingår i: 29th Mediterranean Conference on Control and Automation. - 9781665422581 ; , s. 386-391
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Konferensbidrag (refereegranskat)abstract
- 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 a power network with six generation units.
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| 2. |
- Jouini, Taouba, et al.
(författare)
-
Frequency synchronization of a high-order multi-converter system
- 2021
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Ingår i: IEEE Transactions on Control of Network Systems. - 2325-5870.
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 3. |
- Jouini, Taouba, et al.
(författare)
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Frequency Synchronization of a High-Order Multiconverter System
- 2022
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Ingår i: IEEE Transactions on Control of Network Systems. - 2325-5870. ; 9:2, s. 1006-1016
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the frequency stability of a high-order multi-converter system. For this, we identify its symmetry (i.e., rotational invariance) generated by a static angle shift and rotation of ac signals. We characterize the synchronous 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 frequency synchronous steady-state set by applying the center manifold theory. We guarantee the Jacobian's eigenvalue condition via an explicit approach that requires sufficient damping on the dc and ac side. Finally, we demonstrate our results based on a numerical example involving a network of dc/ac converters.
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| 4. |
- Jouini, Taouba, et al.
(författare)
-
Fully decentralized conditions for local convergence of DC/AC converter network based on matching control
- 2020
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Ingår i: Proceedings on the Conference on Decision and Control, CDC 2020.
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Konferensbidrag (refereegranskat)abstract
- 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, as well as their region of contraction. We provide ways to satisfy these conditions and initialize each converter on the contraction region. We illustrate our results based on numerical simulations of a two-converter benchmark.
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| 5. |
- Jouini, Taouba, et al.
(författare)
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Inverse optimal control for angle stabilization in converter-based generation
- 2022
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Ingår i: Proceedings of the American Control Conference 2022. ; , s. 4945-4950
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Konferensbidrag (refereegranskat)abstract
- In inverse optimal control, an optimal controller is synthesized with respect to a meaningful, a posteriori defined, cost functional. 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 {\em 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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| 6. |
- Jouini, Taouba Kaouther, et al.
(författare)
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Input and state constrained inverse optimal control with application to power networks
- 2023. - 2
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Ingår i: IFAC-PapersOnLine. - 9781713872344 ; , s. 5451-5456
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Konferensbidrag (refereegranskat)abstract
- We study input and state constrained inverse optimal control problems starting from a stabilizing controller with a control Lyapunov function, where the goal is to make the controller an explicit solution of the resulting constrained optimal control problem. For an appropriate cost design and initial states for which a sublevel set of the Lyapunov function is contained in the state constraint set and the initial input lies on an ellipsoid inside the input constraint set, we show that the stabilizing controller solves the constrained optimal control problem. Compared to the state-of-the-art, we avoid solving nonlinear optimization problems evaluated pointwise, i.e., for every state, or in a repetitive fashion, i.e., at each time step. We apply our theoretical results to study the angular droop control studied in (Jouini et al., 2022) of an inverter-based power network. For this, we accommodate the constraints on the angle and power generation and exemplify our approach through a two-inverter case study.
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| 7. |
- Jouini, Taouba, et al.
(författare)
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Local Synchronization of Two DC/AC Converters Via Matching Control
- 2019
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Ingår i: 18th European Control Conference, ECC 2019. ; , s. 2996-3001
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Konferensbidrag (refereegranskat)abstract
- We address the problem of local synchronization of two DC/AC converters connected via a RL line in closed-loop with machine matching control by pursuing a novel approach for the assessment of small-signal stability. Our method is defined using an oblique projection. We use this Lyapunov function to obtain a local stability certificate in the neighborhood of a well-defined set of equilibria characterized by frequency synchronization. To this end, we first reduce the fifth-order DC/AC converter model to a third-order one. Then, we investigate local stability based on Lyapunov's method performed on the linearized and reduced-order model. Moreover, we certify stability via sufficient and fully decentralized conditions that can be satisfied by choosing an appropriate operating point and control gains. Finally, we demonstrate our results using numerical simulations.
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| 8. |
- Jouini, Taouba
(författare)
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Network Synchronization and Control Based on Inverse Optimality : A Study of Inverter-Based Power Generation
- 2021
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- This thesis dwells upon the synthesis of system-theoretical tools to understand and control the behavior of nonlinear networked systems. This work is at the crossroads of three topics: synchronization in coupled high-order oscillators, inverse optimal control and the application of inverter-based power systems. The control and stability of power systems leverages the theoretical results obtained for synchronization in coupled high-order oscillators and inverse optimal control.First, we study the dynamics of coupled high-order nonlinear oscillators. These are characterized by their rotational invariance, meaning that their dynamics remain unchanged following a static shift of their angles. We provide sufficient conditions for local frequency synchronization based on both direct, indirect Lyapunov methods and center manifold theory. Second, we study inverse optimal control problems, embedded in networked settings. In this framework, we depart from a given stabilizing control law, with an associated control Lyapunov function and reverse engineer the cost functional to guarantee the optimality of the controller. In this way, inverse optimal control generates a whole family of optimal controllers corresponding to different cost functions. This provides analytically explicit and numerically feasible solutions in closed-form. This approach circumvents the complexity of solving partial differential equations descending from dynamic programming and Bellman's principle of optimality. We show this to be the case also in the presence of disturbances in the dynamics and the cost. In networks, the controller obtained from inverse optimal control has a topological structure (e.g., it is distributed) and thus feasible for implementation. The tuning is analogous to that of linear quadratic regulators.Third, motivated by the pressing changes witnessed by the electrical grid toward renewable energy generation, we consider power system stability and control as the main application of this thesis. In particular, we apply our theoretical findings to study a network of power electronic inverters. We first propose a controller we term the matching controller, a control strategy that, based on DC voltage measurements, endows the inverters with an oscillatory behavior at a common desired frequency. In closed-loop with the matching control, inverters can be considered as nonlinear oscillators. Our study of the dynamics of nonlinear oscillator network provides feasible physical conditions that ask for damping on DC- and AC-side of each converter, that are sufficient for system-wide frequency synchronization.Furthermore, we showcase the usefulness of inverse optimal control for inverter-based generation at two different settings to synthesize robust angle controllers with respect to common disturbances in the grid and provable stability guarantees. All the controllers proposed in this thesis, provide the electrical grid with important services, namely power support whenever needed, as well as power sharing among all inverters.
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| 9. |
- Jouini, Taouba, et al.
(författare)
-
On cost design in applications of optimal control
- 2021
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Ingår i: IEEE Control Systems Letters. - 2475-1456. ; 6, s. 452-457
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Tidskriftsartikel (refereegranskat)abstract
- 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 the 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 H_\infty control and optimal control of coupled oscillators.
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| 10. |
- Jouini, Taouba, et al.
(författare)
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Parametric local stability condition of a multi-converter system
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286.
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Tidskriftsartikel (refereegranskat)abstract
- We study local (also referred to as small-signal) stability of a network of identical DC/AC converters having a rotating degree of freedom by closing the loop with the matching control at each converter. 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 but improves upon them. We find stability conditions descending from a particular Lyapunov function involving an oblique projection into the invariant set of synchronous steady states 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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