@misc{AlghamdiSchifferFridman, author = {Alghamdi, Sultan and Schiffer, Johannes and Fridman, Emilia}, title = {Synthesizing Sparse and Delay-Robust Distributed Secondary Frequency Controllers for Microgrids}, series = {IEEE Transactions on Control Systems Technology}, volume = {29}, journal = {IEEE Transactions on Control Systems Technology}, number = {2}, issn = {1558-0865}, doi = {10.1109/TCST.2020.2977300}, pages = {691 -- 703}, abstract = {Consensus-based control schemes experience increasing popularity in the context of secondary frequency control in microgrids. Fundamental aspects in their practical implementation are the design of the communication topology as well as robustness with respect to both time-varying communication delays and exogenous disturbances. Motivated by this, we propose a design procedure for a consensus-based secondary frequency controller that ensures robustness with respect to heterogeneous fast-varying communication delays and simultaneously provides the option to trade off the L₂-gain performance against the number of required communication links. Our design criterion is equilibrium-independent and based on the Lyapunov-Krasovskii method for interval time-varying delays together with the descriptor method. The efficacy of the proposed approach is demonstrated by using numerical experiments on the CIGRE benchmark medium-voltage distribution network.}, language = {en} } @misc{BobtsovOrtegaNikolaevetal., author = {Bobtsov, Alexey and Ortega, Romeo and Nikolaev, Nikolay and Schiffer, Johannes}, title = {A Globally Convergent State Observer for Multimachine Power Systems with Lossy Lines}, series = {21st IFAC World Congress, Berlin, Germany, Jul. 11-17, 2020}, journal = {21st IFAC World Congress, Berlin, Germany, Jul. 11-17, 2020}, pages = {6}, abstract = {We present the first solution to the problem of estimation of the state of multimachinepower systems with lossy transmission lines. We consider the classical three-dimensional "flux-decay" model of the power system and assume that the active and reactive power as wellas the rotor angle and excitation voltage at each generator is available for measurement—ascenario that is feasible with current technology. The design of the observer relies on two recentdevelopments proposed by the authors: a parameter estimation based approach to the problemof state estimation and the use of the dynamic regressor extension and mixing technique toestimate these parameters. Thanks to the combination of these techniques it is possible toovercome the problem of lack of persistent excitation that stymies the application of standardobserver designs. Simulation results illustrate the performance of the proposed observer.}, language = {en} } @misc{RuedaEscobedoTangSchiffer, author = {Rueda-Escobedo, Juan G. and Tang, Shiqing and Schiffer, Johannes}, title = {A Performance Comparison of PLL Algorithms in Low-Inertia Power Systems Using an Observer-Based Framework}, series = {21st IFAC World Congress, Berlin, Germany, Jul. 11-17, 2020}, journal = {21st IFAC World Congress, Berlin, Germany, Jul. 11-17, 2020}, pages = {7}, abstract = {Phase-locked loop (PLL) implementations are critical components for the control and operation of grid-connected converters. Hence, they have to exhibit a highly reliable behavior under a wide range of operating conditions. Available implementations and performance analyses mainly focus on the impact of unbalances and harmonics. However, in converter-dominated low-inertia power systems an additional important type of perturbation will arise from fast variations in the grid frequency. Motivated by this, we show that the structure of several popular PLL implementations is closely related to that of high-gain observers and, by using this framework, provide a tuning criterion for the PLL gains that mitigates the impact of the rate of change of the frequency (RoCoF) on the estimation performance. This criterion is then used to conduct a numerical comparison of four popular PLL implementations under three distorted conditions: unbalances, harmonics and frequency variations.}, language = {en} } @misc{MachadoSchiffer, author = {Machado, Juan Eduardo and Schiffer, Johannes}, title = {A Passivity-Inspired Design of Power-Voltage Droop for DC Microgrids with Electrical Network Dynamics}, series = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, journal = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, pages = {6}, abstract = {We propose a design procedure for a power-voltage droop controller in structure-preserving DC microgrids under explicit consideration of the electrical network dynamics. Differently from most related literature, the system's controlled output is taken as the power—not the current—injection at each generation unit, yielding a nonlinear closed-loop system. This makes the output regulation problem non-trivial, yet far more appealing in a practical setting than the usual linear current-voltage droop control. Our approach is inspired by passivity-based control design in the sense that we exploit the natural port-Hamiltonian representation of the system dynamics and its associated shifted Hamiltonian to derive a control law together with sufficient conditions on the tuning gains that guarantee global asymptotic stability. The analysis is illustrated via detailed simulations, where accurate power sharing is manifested among the distributed generation units in the presence of load variations.}, language = {en} } @misc{RuedaEscobedoSchiffer, author = {Rueda-Escobedo, Juan G. and Schiffer, Johannes}, title = {Data-Driven Internal Model Control of Second-Order Discrete Volterra Systems}, series = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, journal = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, pages = {8}, abstract = {The increase in system complexity paired with a growing availability of operational data has motivated a change in the traditional control design paradigm. Instead of modeling the system by first principles and then proceeding with a (model-based) control design, the data-driven control paradigm proposes to directly characterize the controller from data. By exploiting a fundamental result of Willems and collaborators, this approach has been successfully applied to linear systems, yielding data-based formulas for many classical linear controllers. In the present paper, the data-driven approach is extended to a class of nonlinear systems, namely second-order discrete Volterra systems. Two main contributions are made for this class of systems. At first, we show that - under a necessary and sufficient condition on the input data excitation - a data-based system representation can be derived from input-output data and used to replace an explicit system model. That is, the fundamental result of Willems et al.is extended to this class of systems. Subsequently a data-driven internal model control formula for output-tracking is derived. The approach is illustrated via two simulation examples}, language = {en} } @misc{RojasRuedaEscobedoEspinosaPerezetal., author = {Rojas, Michael and Rueda-Escobedo, Juan G. and Espinosa-P{\´e}rez, Gerardo and Schiffer, Johannes}, title = {Observer-Based Excitation Control for Transient Stabilization of the Single Machine Infinite Bus System}, series = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, journal = {59th IEEE Conference on Decision and Control (CDC), Jeju Island, Republic of Korea, Dec. 14-18, 2020}, pages = {6}, abstract = {The availability of excitation controllers to enhance transient stability has regained significant relevance in recent years, due to the unprecedented ongoing changes in power systems. Yet, the practical deployment of many reported control schemes is hampered by the fact that their implementation requires the measurement of the full state vector. Our main contribution is to address this fundamental obstacle by proposing an observer-based excitation controller using modern phasor measurement technology. For this purpose, a linear time-varying observer scheme for the generator frequency and the internal voltage is derived. This observer is then combined with a classical passivity-based excitation controller. Stability of the resulting nonlinear observer-based closed-loop system is shown by deriving an ISS-based separation principle. The performance of the proposed approach is demonstrated via simulation example.}, language = {en} } @misc{LorenzMeyerBobtsovOrtegaetal., author = {Lorenz-Meyer, Nicolai and Bobtsov, Alexey and Ortega, Romeo and Nikolaev, Nikolay and Schiffer, Johannes}, title = {PMU-Based Decentralized Mixed Algebraic and Dynamic State Observation in Multi-Machine Power Systems}, series = {IET Generation, Transmission \& Distribution}, volume = {14}, journal = {IET Generation, Transmission \& Distribution}, number = {25}, issn = {1751-8695}, doi = {10.1049/iet-gtd.2020.1275}, pages = {6267 -- 6275}, abstract = {We propose a novel decentralized mixed algebraic and dynamic state observation method for multi-machine power systems with unknown inputs and equipped with Phasor Measurement Units (PMUs). More specifically, we prove that for the third-order flux-decay model of a synchronous generator, the local PMU measurements give enough information to reconstruct algebraically the load angle and the quadrature-axis internal voltage. Due to the algebraic structure a high numerical efficiency is achieved, which makes the method applicable to large scale power systems. Also, we prove that the relative shaft speed can be globally estimated combining a classical Immersion and Invariance (I\&I) observer with—the recently introduced—dynamic regressor and mixing (DREM) parameter estimator. This adaptive observer ensures global convergence under weak excitation assumptions that are verified in applications. The proposed method does not require the measurement of exogenous inputs signals such as the field voltage and the mechanical torque nor the knowledge of mechanical subsystem parameters.}, language = {en} } @misc{MetzkowRuedaEscobedoDoeringetal., author = {Metzkow, Ren{\`e} and Rueda-Escobedo, Juan G. and D{\"o}ring, Daniela and Schiffer, Johannes}, title = {An Internal Model Approach to Robust Current Control of IPMSM Drives with Respect to Unknown and Varying Inductances}, series = {IFAC PapersOnLine}, volume = {53}, journal = {IFAC PapersOnLine}, number = {2}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2020.12.1046}, pages = {14185 -- 14191}, abstract = {Interior permanent magnet synchronous machines (IPMSMs) are well-suited for high-performance applications, such as traction drives in hybrid and electric vehicles. Yet a major challenge to fully exploit their potential is the fact that their self and cross-coupling inductances vary significantly across the operation range. In addition, this variation is difficult to characterize and complicates the design of provably stabilizing and robust controls. Motivated by this, by using an IPMSM model with current dependant inductances together with the internal model principle, a nonlinear current control scheme is derived that renders the equilibrium point of the closed-loop system exponentially stable. Both the control and the stability result only require the knowledge of an upper bound of the gradient of the inductances as well as lower and upper bounds on the inductance values themselves, while their actual evolution can be completely unknown. This is a major advantage compared to existing (PI-based) current control approaches, as it makes costly practices to determine the inductance variations unnecessary. The efficacy of the proposed control scheme is demonstrated in a simulation example.}, language = {en} } @misc{BaiZhangCaietal., author = {Bai, Handong and Zhang, Hongwai and Cai, He and Schiffer, Johannes}, title = {Voltage regulation and current sharing for multi-bus DC microgrids: A compromised design approach}, series = {Automatica}, volume = {142}, journal = {Automatica}, issn = {0005-1098}, doi = {10.1016/j.automatica.2022.110340}, pages = {7}, abstract = {It is well known that accurate current sharing and voltage regulation are both important, yet conflicting control objectives in multi-bus DC microgrids. In this paper a distributed control scheme is proposed, which simultaneously considers these two control objectives via a trade-off factor. This factor permits to adjust the degree of compromise between accurate voltage regulation and current sharing. At the same time, the voltage of a critical node can be precisely regulated. A sufficient condition for closed-loop stability is given and it is shown that the control parameters can always be chosen, such that stability is guaranteed. In addition, the steady state voltage and current deviations relative to their rated values are quantified via suitable metrics. For a given topology and settings of a DC microgrid, a sufficient condition for the existence of the trade-off factor is provided. The results are illustrated by simulation examples.}, language = {en} } @misc{BobtsovOrtegaNikolaevetal., author = {Bobtsov, Alexey and Ortega, Romeo and Nikolaev, Nikolay and Lorenz-Meyer, Nicolai and Schiffer, Johannes}, title = {State Observation of Power Systems Equipped with Phasor Measurement Units: The Case of Fourth Order Flux-Decay Model}, series = {IEEE Transactions on Automatic Control}, volume = {67}, journal = {IEEE Transactions on Automatic Control}, number = {4}, issn = {0018-9286}, doi = {10.1109/TAC.2021.3073887}, pages = {2123 -- 2130}, abstract = {The problem of effective use of phasor measurement units (PMUs) to enhance power systems awareness and security is a topic of key interest. The central question to solve is how to use these new measurements to reconstruct the state of the system. In this article, we provide the first solution to the problem of (globally convergent) state estimation of multimachine power systems equipped with PMUs and described by the fourth-order flux-decay model. This article is a significant extension of our previous result, where this problem was solved for the simpler third-order model, for which it is possible to recover algebraically part of the unknown state. Unfortunately, this property is lost in the more accurate fourth-order model, and we are confronted with the problem of estimating the full state vector. The design of the observer relies on two recent developments proposed by the authors, a parameter estimation based approach to the problem of state estimation and the use of the dynamic regressor extension and mixing (DREM) technique to estimate these parameters. The use of DREM allows us to overcome the problem of lack of persistent excitation that stymies the application of standard parameter estimation designs. Simulation results illustrate the latter fact and show the improved performance of the proposed observer with respect to a locally stable gradient-descent-based observer.}, language = {en} } @misc{OrtegaBobtsovNikolaevetal., author = {Ortega, Romeo and Bobtsov, Alexey and Nikolaev, Nikolay and Schiffer, Johannes and Dochain, Denis}, title = {Generalized parameter estimation-based observers: Application to power systems and chemical-biological reactors}, series = {Automatica}, journal = {Automatica}, number = {129}, issn = {0005-1098}, doi = {10.1016/j.automatica.2021.109635}, abstract = {In this paper we propose a new state observer design technique for nonlinear systems. It consists of an extension of the recently introduced parameter estimation-based observer, which is applicable for systems verifying a particular algebraic constraint. In contrast to the previous observer, the new one avoids the need of implementing an open loop integration that may stymie its practical application. We give two versions of this observer, one that ensures asymptotic convergence and the second one that achieves convergence in finite time. In both cases, the required excitation conditions are strictly weaker than the classical persistent of excitation assumption. It is shown that the proposed technique is applicable to the practically important examples of multimachine power systems and chemical-biological reactors.}, language = {en} } @misc{RuedaEscobedoFridmanSchiffer, author = {Rueda-Escobedo, Juan G. and Fridman, Emilia and Schiffer, Johannes}, title = {Data-Driven Control for Linear Discrete-Time Delay Systems}, series = {IEEE Transactions on Automatic Control}, volume = {67}, journal = {IEEE Transactions on Automatic Control}, number = {7}, issn = {1558-2523}, doi = {10.1109/TAC.2021.3096896}, pages = {3321 -- 3336}, abstract = {The increasing ease of obtaining and processing data together with the growth in system complexity has sparked the interest in moving from conventional model-based control design toward data-driven concepts. Since in many engineering applications time delays naturally arise and are often a source of instability, we contribute to the data-driven control field by introducing data-based formulas for state feedback control design in linear discrete-time time-delay systems with uncertain delays. With the proposed approach, the problems of system stabilization as well as of guaranteed cost and H∞ control design are treated in a unified manner. Extensions to determine the system delays and to ensure robustness in the event of noisy data are also provided}, language = {en} } @misc{KrishnaSchiffer, author = {Krishna, Ajay and Schiffer, Johannes}, title = {A Port-Hamiltonian Approach to Modeling and Control of an Electro-Thermal Microgrid}, series = {IFAC-PapersOnLine}, volume = {54}, journal = {IFAC-PapersOnLine}, number = {19}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2021.11.092}, pages = {287 -- 293}, abstract = {We address the problems of modeling and controlling multi-energy microgrids (meMGs) composed of an electrical and a thermal system, which are connected via heat pumps (HPs). At first, we model the individual subsystems in a port-Hamiltonian (pH) framework. Then, by exploiting the structural properties of pH systems, we interconnect the subsystems in a passive manner and show that the overall meMG is shifted passive with respect to the control input-output mapping. We then use this property to propose a distributed passivity based-control (PBC) that addresses frequency and temperature regulation by utilizing the resources in the meMG in a proportional fashion and renders the closed-loop equilibrium asymptotically stable.}, language = {en} } @misc{RuedaEscobedoMorenoSchiffer, author = {Rueda-Escobedo, Juan G. and Moreno, Jaime A. and Schiffer, Johannes}, title = {L2-Gain Tuning for the Gradient Descent Algorithm in the Presence of Disturbances}, series = {2022 European Control Conference (ECC)}, journal = {2022 European Control Conference (ECC)}, publisher = {IEEE}, address = {Piscataway}, isbn = {978-3-9071-4407-7}, doi = {10.23919/ECC55457.2022.9838051}, pages = {1610 -- 1616}, abstract = {Due to its simplicity and inexpensive computation, the gradient descent algorithm is one of the most used tools in adaptive control and system identification. Although it has been studied for decades, little has been achieved in terms of tuning methods in the presence of disturbances. One of the main difficulties in its analysis is the time-varying nature of the algorithm. In this work, we contribute in such direction by providing LMI tools for tuning the gradient descent algorithm gain such that a guaranteed upper bound on the L2 -gain with respect to parameter variations and measurement noise is achieved. Two academic examples are provided to illustrate the efficient application of the method.}, language = {en} } @misc{JaramilloCajicaSchiffer, author = {Jaramillo-Cajica, Ismael and Schiffer, Johannes}, title = {A Dwell-Time Approach for Grid-Aware Operation of a Distributed Generator in an Islanded DC Microgrid}, series = {2022 European Control Conference (ECC)}, journal = {2022 European Control Conference (ECC)}, publisher = {IEEE}, address = {Piscataway}, isbn = {978-3-9071-4407-7}, doi = {10.23919/ECC55457.2022.9838354}, pages = {1079 -- 1084}, abstract = {We propose a switched control law for a DC-DC Buck converter that enables a grid-aware operation of a distributed generator (DG) in a low-voltage islanded DC microgrid (MG). The qualifier grid-aware means that the DG adjusts its operation mode in dependency of the MG status. The resulting closed-loop system is a switched system, in which the subsystems possess different equilibrium points. By means of a time- and state-dependent switching logic together with dwell-time stability analysis methods, we derive sufficient stability criteria that ensure the existence of a unique and globally exponentially stable equilibrium point of the resulting closed-loop switched system. The performance of the proposed control is illustrated via a numerical example.}, language = {en} } @misc{MendozaAvilaEfimovMercadoUribeetal., author = {Mendoza-Avila, Jesus and Efimov, Denis and Mercado-Uribe, Angel and Schiffer, Johannes}, title = {On Relaxed Conditions of Integral ISS for Multistable Periodic Systems}, series = {Proceedings of the 2021 61st IEEE Conference on Decision and Control (CDC)}, journal = {Proceedings of the 2021 61st IEEE Conference on Decision and Control (CDC)}, pages = {6}, abstract = {A novel characterization of the integral Inputto- State Stability (iISS) property is introduced for multistable systems whose dynamics are periodic with respect to a part of the state. First, the concepts of iISS-Leonov functions and output smooth dissipativity are introduced, then their equivalence to the properties of bounded-energy-bounded-state and global attractiveness of solutions in the absence of disturbances are proven. The proposed approach permits to relax the usual requirements of positive definiteness and periodicity of the iISSLyapunov functions. Moreover, the usefulness of the theoretical results is illustrated by a robustness analysis of a nonlinear pendulum with a constant bias input and an unbounded statedependent input coefficient.}, language = {en} } @misc{RuedaEscobedoMorenoSchiffer, author = {Rueda-Escobedo, Juan G. and Moreno, Jaime A. and Schiffer, Johannes}, title = {Design and Tuning of the Super-Twisting-Based Synchronous Reference Frame Phase-Locked-Loop}, series = {2022 IEEE 61st Conference on Decision and Control (CDC) ; December 6-9, 2022, Cancun, Mexico}, journal = {2022 IEEE 61st Conference on Decision and Control (CDC) ; December 6-9, 2022, Cancun, Mexico}, abstract = {The worldwide transition to climate-friendly energy systems entails the substitution of conventional energy generation based on synchronous generators by renewable energy sources based on power electronics. As a consequence, the overall inertia of the grid decreases, resulting in high volatility of the frequency and posing new challenges for the estimation of the latter quantity. To address this problematic, in the present paper a phase-locked-loop (PLL) based on the super-twisting algorithm is considered for the estimation of the phase angle and time-varying frequency of a symmetric three-phase signal. A rigorous proof of the algorithm's exact convergence in the presence of a fast-varying frequency together with tuning rules for its gains are derived by means of Lyapunov theory. Additionally, an estimate of the region of attraction is provided. The effectiveness of the proposed tuning method is illustrated in numerical simulations, while comparing its performance against a standard synchronous reference frame PLL.}, language = {en} } @misc{SyedMachadoSchiffer, author = {Syed, Wasif H. and Machado, Juan E. and Schiffer, Johannes}, title = {Distributed Adaptive Control for a DC Power Distribution System of a Series-Hybrid-Electric Propulsion System of a Commuter Aircraft}, series = {2024 American Control Conference (ACC)}, journal = {2024 American Control Conference (ACC)}, publisher = {IEEE}, doi = {10.23919/ACC60939.2024.10644618}, pages = {2598 -- 2603}, language = {en} } @misc{RuedaEscobedoMetzkowSchiffer, author = {Rueda-Escobedo, Juan G. and Metzkow, Ren{\´e} and Schiffer, Johannes}, title = {Robust current control of IPMSM drives under uncertain and varying inductances}, series = {Automatica}, volume = {152}, journal = {Automatica}, issn = {0005-1098}, doi = {10.1016/j.automatica.2023.110998}, abstract = {Interior permanent magnet synchronous machines (IPMSMs) are gaining popularity in e-mobility applications due to their wide constant power speed range when compared with other electric motors. The high-performance of IPMSMs is due to the pronounced degree of magnetic saliency, which originates from embedding their magnets inside the rotor. Yet, this feature complicates their control since it increases nonlinear phenomena such as cross-magnetization and saturation. This results in pronounced variations of the machine inductances, which are highly dependent on the machine current. This behaviour is of particular relevance in e-mobility applications, where a highly dynamic operation of the machine is required. In contrast to most existing current control approaches, where precise inductance knowledge is required, we address this challenge by deriving a controller that exploits the machine dynamics to achieve exponential current tracking in the presence of unknown and varying inductances. By interpreting the flux linkage as a modelled disturbance, we propose a dynamic compensator based on the internal model principle. As a by-product, the method provides an estimate of the flux linkage. The gain in performance compared to the standard PI controller is illustrated in simulation.}, language = {en} } @misc{SchifferEfimov, author = {Schiffer, Johannes and Efimov, Denis}, title = {Strong and Weak Leonov Functions for Global Boundedness of State Periodic Systems}, series = {IEEE Transactions on Automatic Control}, volume = {68}, journal = {IEEE Transactions on Automatic Control}, number = {12}, issn = {0018-9286}, doi = {10.1109/TAC.2023.3251903}, pages = {7958 -- 7965}, abstract = {We present new results for the analysis of global boundedness of state periodic systems. Thereby, we address both the case of systems, whose dynamics is periodic with respect to a part of the state vector, and the case of systems, whose dynamics is periodic with respect to all state variables. To derive the results, the notion of strong Leonov functions is introduced. The main results are complemented by a number of relaxations based on the concept of weak Leonov functions.}, language = {en} } @misc{MercadoUribeMendozaAvilaEfimovetal., author = {Mercado-Uribe, Angel and Mendoza-{\´A}vila, Jes{\´u}s and Efimov, Denis and Schiffer, Johannes}, title = {A Leonov Function for Almost Global Synchronization Conditions in Acyclic Networks of Heterogeneous Kuramoto Oscillators}, series = {IFAC-PapersOnLine}, volume = {56}, journal = {IFAC-PapersOnLine}, number = {2}, issn = {2405-8963}, doi = {10.1016/j.ifacol.2023.10.248}, pages = {9505 -- 9510}, abstract = {Sufficient conditions for almost global synchronization in acyclic networks of Kuramoto oscillators with heterogeneous coupling strengths and natural frequencies are presented. The result is established by employing the recently developed Leonov function framework for systems whose dynamics are periodic for all state variables. The synchronization property is accompanied by necessary and sufficient conditions to guarantee the existence of equilibria. The implications of these conditions on the network topology, the oscillator's coupling strengths and natural frequencies are discussed. Finally, the results are illustrated via a numerical example.}, language = {en} } @misc{MendozaAvilaMercadoUribeEfimovetal., author = {Mendoza-Avila, Jesus and Mercado-Uribe, Angel and Efimov, Denis and Schiffer, Johannes}, title = {Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems}, series = {IFAC-PapersOnLine}, volume = {56}, journal = {IFAC-PapersOnLine}, number = {2}, doi = {https://doi.org/10.1016/j.ifacol.2023.10.936}, pages = {4472 -- 4477}, language = {en} } @misc{WuerfelLorenzMeyerSchiffer, author = {W{\"u}rfel, Hans and Lorenz-Meyer, Nicolai and Schiffer, Johannes}, title = {Experimentally Validated Reduced-Order Models for Grid-Connected Inverters Using Balanced Residualization}, series = {2023 8th IEEE Workshop on the Electronic Grid (eGRID), Karlsruhe, Germany, 16-18 October 2023}, journal = {2023 8th IEEE Workshop on the Electronic Grid (eGRID), Karlsruhe, Germany, 16-18 October 2023}, address = {Karlsruhe}, isbn = {979-8-3503-2700-7}, doi = {10.1109/eGrid58358.2023.10380931}, pages = {6}, language = {en} }