TY - GEN A1 - Schiffer, Johannes A1 - Alghamdi, Sultan A1 - Fridman, Emilia T1 - Distributed Secondary Frequency Control Design for Microgrids: Trading off L2-Gain Performance and Communication Efforts under Time-Varying Delays T2 - 2018 European Control Conference, (EEC) 12-15 Jun 2018, Limassol, Cyprus KW - Microgrids Y1 - 2018 UR - eprints.whiterose.ac.uk/128268/1/DAI_design_ecc18_final.pdf SN - 978-3-9524-2698-2 PB - IEEE CY - Piscataway, NJ ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis T1 - A new criterion for boundedness of solutions for a class of periodic systems T2 - 17th European Control Conference (ECC), Limassol, Cyprus, 2018 Y1 - 2018 UR - https://hal.inria.fr/hal-01755084/document ER - TY - GEN A1 - Zonetti, Daniele A1 - Ortega, Romeo A1 - Schiffer, Johannes T1 - A Tool for Stability and Power Sharing Analysis of a Generalized Class of Droop Controllers for High-Voltage Direct-Current Transmission Systems T2 - IEEE Transactions on Control of Network Systems N2 - The problem of primary control of high-voltage direct-current transmission systems is addressed in this paper, which contains four main contributions. First, a new nonlinear, more realistic model for the system suitable for primary control design, which takes into account nonlinearities introduced by conventional inner controllers, is proposed. Second, necessary conditions-dependent on some free controller tuning parameters-for the existence of equilibria is determined. Third, additional (necessary) conditions are formulated for these equilibria to satisfy the power-sharing constraints. Fourth, establish conditions for the stability of a given equilibrium point. The usefulness of the theoretical results is illustrated via numerical calculations on a four-terminal example. Y1 - 2018 U6 - https://doi.org/10.1109/TCNS.2017.2687080 SN - 2325-5870 VL - 5 IS - 3 SP - 1110 EP - 1119 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Ortega, Romeo T1 - Almost Global Synchronization in Multi-Machine Power Systems T2 - 57th IEEE Conference on Decision and Control, Miami Beach, FL, USA, December 17-19, 2018 Y1 - 2018 UR - https://ieeexplore.ieee.org/document/8619788 SN - 978-1-5386-1395-5 U6 - https://doi.org/10.1109/CDC.2018.8619788 SP - 800 EP - 805 PB - IEEE CY - Piscataway, NJ ER - TY - GEN A1 - Schiffer, Johannes A1 - Krishna, Ajay A1 - Raisch, Jörg T1 - A Consensus-Based Control Law for Accurate Frequency Restoration and Power Sharing in Microgrids in the Presence of Clock Drifts T2 - 2018 European Control Conference, (EEC) 12-15 Jun 2018, Limassol, Cyprus KW - Microgrids Y1 - 2018 SN - 978-3-9524-2698-2 U6 - https://doi.org/10.23919/ECC.2018.8550191 PB - IEEE CY - Piscataway, NJ ER - TY - GEN A1 - Alghamdi, Sultan A1 - Schiffer, Johannes A1 - Fridman, Emilia T1 - Conditions for Delay-Robust Consensus-Based Frequency Control in Power Systems with Second-Order Turbine-Governor Dynamics T2 - 57th IEEE Conference on Decision and Control, Miami Beach, FL, USA, December 17-19, 2018 N2 - Consensus-based distributed secondary frequency control schemes have the potential to simultaneously ensure real-time frequency restoration and economic dispatch in future power systems with large shares of renewable energy sources. Yet, due to their distributed nature these control schemes critically depend on communication between units and, thus, robustness with respect to communication uncertainties is crucial for their reliable operation. Furthermore, when applied in bulk power systems the control design and analysis should take higher-order turbine-governor dynamics of the generation units explicitly into account. Both aspects have not been addressed jointly in the existing literature. Motivated by this, we derive conditions for robust stability of a consensus-based distributed frequency control scheme applied to a power system model with second-order turbine-governor dynamics in the presence of heterogeneous time-varying communication delays and dynamic communication topology. The result is established by a novel coordinate transformation and reduction to eliminate the invariant subspace in the closed-loop dynamics and by constructing a strict common Lyapunov-Krasovskii functional. Y1 - 2018 UR - https://ieeexplore.ieee.org/document/8619709 SN - 978-1-5386-1395-5 SP - 786 EP - 793 PB - IEEE CY - Piscataway, NJ ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Barabanov, Nikita A1 - Ortega, Romeo T1 - A Relaxed Characterization of ISS for Periodic Systems with Multiple Invariant Sets T2 - European Journal of Control N2 - A necessary and sufficient criterion to establish input-to-state stability (ISS) of nonlinear dynamical systems, the dynamics of which are periodic with respect to certain state variables and which possess multiple invariant solutions (equilibria, limit cycles, etc.), is provided. Unlike standard Lyapunov approaches, the condition is relaxed and formulated via a sign-indefinite function with sign-definite derivative, and by taking the system’s periodicity explicitly into account. The new result is established by using the framework of cell structure and it complements the ISS theory of multistable dynamics for periodic systems. The efficiency of the proposed approach is illustrated via the global analysis of a nonlinear pendulum with constant persistent input. Y1 - 2017 U6 - https://doi.org/10.1016/j.ejcon.2017.04.002 SN - 1435-5671 VL - Vol. 37 SP - 1 EP - 7 ER - TY - GEN A1 - Schiffer, Johannes A1 - Barabanov, Nikita A1 - Ortega, Romeo A1 - Efimov, Denis T1 - Conditions for Almost Global Attractivity of a Synchronous Generator Connected to an Infinite Bus T2 - Transactions on Automatic Control N2 - Conditions for existence and global attractivity of the equilibria of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. First, necessary and sufficient conditions for existence and uniqueness of equilibrium points are provided. Then, sufficient conditions for local asymptotic stability and almost global attractivity of one of these equilibria are given. The analysis is carried out by employing a new Lyapunov-like function to establish convergence of bounded trajectories, while the latter is proven using the powerful theoretical framework of cell structures pioneered by Leonov and Noldus. The efficiency of the derived sufficient conditions is illustrated via extensive numerical experiments based on two benchmark examples taken from the literature. Y1 - 2017 UR - https://ieeexplore.ieee.org/document/7858643 U6 - https://doi.org/10.1109/TAC.2017.2671026 SN - 1558-2523 SN - 0018-9286 VL - 62 IS - 10 SP - 4905 EP - 4916 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Ortega, Romeo A1 - Barabanov, Nikita T1 - An Input-to-State Stability Approach to Verify Almost Global Stability of a Synchronous-Machine-Infinite-Bus System T2 - Philosophical transactions of the Royal Society. Series A, Mathematical, physical and engineering sciences N2 - Conditions for almost global stability of an operating point of a realistic model of a synchronous generator with constant field current connected to an infinite bus are derived. The analysis is conducted by employing the recently proposed concept of input-to-state stability (ISS)–Leonov functions, which is an extension of the powerful cell structure principle developed by Leonov and Noldus to the ISS framework. Compared with the original ideas of Leonov and Noldus, the ISS–Leonov approach has the advantage of providing additional robustness guarantees. The efficiency of the derived sufficient conditions is illustrated via numerical experiments. Y1 - 2017 U6 - https://doi.org/10.1098/rsta.2016.0304 SN - 1364-503X SN - 1471-2962 VL - 375 IS - 2100 ER - TY - GEN A1 - Schiffer, Johannes A1 - Dörfler, Florian A1 - Fridman, Emilia T1 - Robustness of Distributed Averaging Control in Power Systems: Time Delays & Dynamic Communication Topology T2 - Automatica N2 - Distributed averaging-based integral (DAI) controllers are becoming increasingly popular in power system applications. The literature has thus far primarily focused on disturbance rejection, steady-state optimality and adaption to complex physical system models without considering uncertainties on the cyber and communication layer nor their effect on robustness and performance. In this paper, we derive sufficient delay-dependent conditions for robust stability of a secondary-frequency-DAI-controlled power system with respect to heterogeneous communication delays, link failures and packet losses. Our analysis takes into account both constant as well as fast-varying delays, and it is based on a common strictly decreasing Lyapunov–Krasovskii functional. The conditions illustrate an inherent trade-off between robustness and performance of DAI controllers. The effectiveness and tightness of our stability certificates are illustrated via a numerical example based on Kundur’s four-machine-two-area test system. Y1 - 2017 UR - https://www.sciencedirect.com/science/article/pii/S0005109817301140?via%3Dihub U6 - https://doi.org/10.1016/j.automatica.2017.02.040 SN - 0005-1098 VL - 80 SP - 261 EP - 271 ER - TY - GEN A1 - Schiffer, Johannes A1 - Hans, Christian A. A1 - Kral, Thomas A1 - Ortega, Romeo A1 - Raisch, Jörg T1 - Modelling, Analysis and Experimental Validation of Clock Drift Effects in Low-Inertia Power Systems T2 - IEEE Transactions on Industrial Electronics N2 - Clock drift in digital controllers is of great relevance in many applications. Since almost all real clocks exhibit drifts, this applies in particular to networks composed of several individual units, each of which being operated with its individual clock. In the present paper, we demonstrate via extensive experiments on a microgrid in the megawatt range that clock drifts may impair frequency synchronization in low-inertia power systems. The experiments also show that-in the absence of a common clock-the standard model of an inverter as an ideal voltage source does not capture this phenomenon. As a consequence, we derive a suitably modified model of an inverter-interfaced unit that incorporates the phenomenon of clock drifts. By using the derived model, we investigate the effects of clock drifts on the performance of droop-controlled grid-forming inverters with regard to frequency synchronization and active power sharing. The modeling and analysis is validated via extensive experiments on a microgrid in the megawatt range. Y1 - 2017 UR - https://ieeexplore.ieee.org/document/7781662 U6 - https://doi.org/10.1109/TIE.2016.2638805 SN - 1557-9948 SN - 0278-0046 VL - 64 IS - 7 SP - 5942 EP - 5951 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Barabanov, Nikita A1 - Ortega, Romeo T1 - Relaxing the Conditions of ISS for Multistable Periodic Systems T2 - IFAC-PapersOnLine N2 - The input-to-state stability property of nonlinear dynamical systems with multiple invariant solutions is analyzed under the assumption that the system equations are periodic with respect to certain state variables. It is shown that stability can be concluded via a sign-indefinite function, which explicitly takes the systems' periodicity into account. The presented approach leverages some of the difficulties encountered in the analysis of periodic systems via positive definite Lyapunov functions proposed in Angeli and Efimov (2013, 2015). The new result is established based on the framework of cell structure introduced in Leonov (1974) and illustrated via the global analysis of a nonlinear pendulum with a constant persistent input. Y1 - 2017 UR - https://hal.inria.fr/hal-01508766 U6 - https://doi.org/10.1016/j.ifacol.2017.08.1365 VL - 50 IS - 1 SP - 7217 EP - 7222 ER - TY - GEN A1 - Schiffer, Johannes A1 - Krishna, Ajay A1 - Hans, Christian A. A1 - Raisch, Jörg A1 - Kral, Thomas T1 - Steady State Evaluation of Distributed Secondary Frequency Control Strategies for Microgrids in the Presence of Clock Drifts T2 - 25th Mediterranean Conference on Control and Automation N2 - Secondary frequency control, i.e., the task of restoring the network frequency to its nominal value following a disturbance, is an important control objective in microgrids. In the present paper, we compare distributed secondary control strategies with regard to their behaviour under the explicit consideration of clock drifts. In particular we show that, if not considered in the tuning procedure, the presence of clock drifts may impair an accurate frequency restoration and power sharing. As a consequence, we derive tuning criteria such that zero steady state frequency deviation and power sharing is achieved even in the presence of clock drifts. Furthermore, the effects of clock drifts of the individual inverters on the different control strategies are discussed analytically and in a numerical case study. Y1 - 2017 UR - http://eprints.whiterose.ac.uk/115991/ U6 - https://doi.org/10.1109/MED.2017.7984168 SN - 2473-3504 SP - 508 EP - 515 ER - TY - GEN A1 - Schiffer, Johannes A1 - Ojo, Yemi T1 - Towards a Time-Domain Modeling Framework for Small-Signal Analysis of Unbalanced Microgrids T2 - IEEE PowerTech 2017, Manchester, UK, 2017 N2 - Small-signal analysis is one of the most frequently used techniques to assess the operating conditions of power systems. Typically, this analysis is conducted by employing a phasor-based model of the power network derived under the assumption of balanced operating conditions. However, distribution networks and, amongst these, microgrids are often unbalanced. Hence, their analysis requires the development of tools and methods valid under such conditions. Motivated by this, we propose a modeling approach for generic nonlinear and unbalanced three-phase microgrids, which allows to derive a small-signal model in a standard fashion. The approach is based on a time-domain decomposition of the electrical waveforms in positive and negative synchronous reference frames. The efficacy of the approach is demonstrated via application to an exemplary unbalanced microgrid. Y1 - 2017 UR - http://eprints.whiterose.ac.uk/114880/ U6 - https://doi.org/https://doi.org/10.1109/PTC.2017.7981013 ER - TY - GEN A1 - Gustavo-Escobedo, Juan A1 - Moreno, Jaime A. A1 - Schiffer, Johannes T1 - Finite-Time Estimation of Time-Varying Frequency Signals in Low-Inertia Power Systems T2 - 8th European Control Conference (ECC) N2 - The ongoing and unprecedented transformation of power systems leads to a reduction in the number of conventional power plants, which are the classical actuators of the grid. In addition, this development results in a decreasing system inertia, which is expected to yield faster frequency dynamics. Therefore power-electronics-interfaced units have to take over system control tasks and, in particular, frequency control. For this purpose, accurate and fast estimation algorithms for time-varying frequency signals are needed. Motivated by this fact, we propose a time-varying parameter estimator and a tuning criterion, which for sufficiently small initial estimation errors allows to reconstruct the time-varying frequency signal of a symmetric three-phase waveform in finite time. The proposed estimator is derived by using a time-varying version of the super twisting algorithm and its performance is illustrated via numerical examples. KW - Power Systems, Frequency Signals, Finite-Time Estimation Y1 - 2019 U6 - https://doi.org/10.23919/ECC.2019.8795926 SP - 2108 EP - 2114 ER - TY - GEN A1 - Schiffer, Johannes A1 - Efimov, Denis A1 - Ortega, Romeo T1 - Global synchronization analysis of droop-controlled microgrids—A multivariable cell structure approach T2 - Automatica N2 - The microgrid concept represents a promising approach to facilitate the large-scale integration of renewable energy sources. Motivated by this, the problem of global synchronization in droop-controlled microgrids with radial topology is considered. To this end, at first a necessary and sufficient condition for existence of equilibria is established in terms of the droop gains and the network parameters. Then, the local stability properties of the equilibria are characterized. Subsequently, sufficient conditions for almost global synchronization are derived by means of the multivariable cell structure approach recently proposed in Efimov and Schiffer (2019). The latter is an extension of the powerful cell structure principle developed by Leonov and Noldus to nonlinear systems that are periodic with respect to several state variables and possess multiple invariant solutions. The analysis is illustrated via numerical examples. KW - Global synchronization KW - controlled microgrids Y1 - 2019 UR - https://www.sciencedirect.com/science/article/pii/S000510981930411X U6 - https://doi.org/10.1016/j.automatica.2019.108550 SN - 0005-1098 IS - 109 ER - TY - GEN A1 - Krishna, Ajay A1 - Schiffer, Johannes A1 - Monshizadeh, Nima A1 - Raisch, Jörg T1 - A consensus-based voltage control for reactive power sharing and PCC voltage regulation in microgrids with parallel-connected inverters T2 - European Control Conference 2019, Naples, Italy N2 - We consider small-scale power systems consisting of several inverter-interfaced units connected in parallel to a common bus, the point of common coupling (PCC), and sharing a joint load. This is a frequently encountered configuration in microgrid applications. In such a setting, two important control objectives are reactive power sharing and voltage regulation at the PCC. In this paper, we first show that the nonlinear equilibrium equations corresponding to the aforementioned objectives admit a unique positive solution. Then, we propose a consensus-based distributed voltage controller which renders this desired unique solution locally asymptotically stable. Finally, control performance is illustrated via a simulation example. Y1 - 2019 SN - 978-3-907144-00-8 SN - 978-3-907144-01-5 SN - 978-1-7281-1314-2 U6 - https://doi.org/10.23919/ECC.2019.8795924 CY - Neapel ER - TY - GEN A1 - Alghamdi, Sultan A1 - Smith, Nathan A1 - Aristidou, Petros A1 - Schiffer, Johannes T1 - Delay-Robust Distributed Secondary Frequency Control: A Case Study T2 - IEEE PES PowerTech Conference 2019, Milano, Italy N2 - With the purpose of enabling a low-carbon future, power systems worldwide are undergoing major transformations. These developments require new advanced control and operation approaches to ensure a stable and efficient system operation. Distributed consensus-based algorithms are a promising option to provide the necessary flexibility and scalability to cope with these challenges and have, thus, been widely investigated in the literature. Yet, most available results are limited to scenarios with reduced-order models and ideal communication. Motivated by this, we perform a case study using a detailed dynamic model of the well-known Nordic test system equipped with a consensus-based distributed secondary frequency controller. Our main objectives are to analyse the robustness of the closed-loop system with respect to unmodelled (voltage and higher-order generator) dynamics as well as communication delays. To facilitate the later property, we employ robust-stability conditions in the control design. Then, the performance of the proposed controller is assessed through detailed dynamic simulations covering several disturbances leading to large frequency and voltage excursions. Y1 - 2019 SN - 978-1-5386-4722-6 SN - 978-1-5386-4723-3 U6 - https://doi.org/10.1109/PTC.2019.8810821 CY - Milano ER - TY - GEN A1 - Efimov, Denis A1 - Schiffer, Johannes T1 - On boundedness of solutions of state periodic systems: a multivariable cell structure approach T2 - IEEE Transactions on Automatic Control N2 - Many dynamical systems are periodic with respect to several state variables. This periodicity typically leads to the coexistence of multiple invariant solutions (equilibria or limit cycles). As a consequence, while there are many classical techniques for analysis of boundedness and stability of such systems, most of these only permit to establish local properties. Motivated by this, a new sufficient criterion for global boundedness of solutions of such a class of nonlinear systems is presented. The proposed method is inspired by the cell structure approach developed by Leonov and Noldus and characterized by two main advances. First, the conventional cell structure framework is extended to the case of dynamics, which are periodic with respect to multiple states. Second, by introducing the notion of a Leonov function, the usual definiteness requirements of standard Lyapunov functions are relaxed to sign-indefinite functions. Furthermore, it is shown that under (mild) additional conditions the existence of a Leonov function also ensures input-to-state stability, i.e., robustness with respect to exogenous perturbations. The performance of the proposed approach is demonstrated via the global analysis of boundedness of trajectories for a nonlinear system. Y1 - 2019 U6 - https://doi.org/10.1109/TAC.2019.2892395 SN - 0018-9286 SN - 1558-2523 VL - 64 IS - 10 SP - 4094 EP - 4104 ER - TY - GEN A1 - Krishna, Ajay A1 - Schiffer, Johannes A1 - Raisch, Jörg T1 - Distributed Secondary Frequency Control in Microgrids: Robustness and Steady-State Performance in the Presence of Clock Drifts T2 - European Journal of Control N2 - Microgrids are distributed systems with high share of inverter-interfaced renewable energy sources where stable and reliable system operation is realized by suitably controlling the inverters. In this work, we focus on secondary frequency control, which is an important ancillary service provided by the inverters. In the literature on secondary frequency control, the effect of clock drifts has often been neglected. However, clock drifts are practically unavoidable parameter uncertainties in inverter-based microgrids and we show that the most commonly employed distributed secondary frequency controllers exhibit performance deteriorations when taking clock drifts explicitly into consideration. Motivated by this, we propose a novel alternative control law called generalized distributed averaging integral (GDAI) control, which achieves the secondary control objectives of steady-state accurate frequency restoration and proportional power sharing in the presence of clock drifts. In addition, we derive a sufficient tuning criterion in the form of a set of linear matrix inequalities (LMIs) which guarantees robust stability of the closed-loop equilibrium point in the presence of uncertain clock drifts. Finally, our analysis is validated extensively via simulation with comprehensive comparisons to other related distributed control approaches. Y1 - 2020 U6 - https://doi.org/10.1016/j.ejcon.2019.08.003 SN - 0947-3580 VL - 51 SP - 135 EP - 145 ER -