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Drones can be connected as a swarm to precisely monitor large agricultural areas and manage them more sustainable. They test sensor technology in real environments and solve complex tasks faster. Key aspects include accurate localization, reliable communication, and dynamic flight control. The localization accuracy of RTK-GNSS-enabled system, which includes GPS, GLONASS, GALILEO positioning systems is compared with Ultra-Wideband (UWB) one. The UPWARDS communication hub is presented as a processing and connection point across swarm agents. This controller also incorporates collision avoidance features and testing of evasion strategies.
Dynamic state and parameter estimation (DSE) plays a key role for reliably monitoring and operating future, power-electronics-dominated power systems. While DSE is a very active research field, experimental applications of proposed algorithms to real-world systems remain scarce. This motivates the present paper, in which we demonstrate the effectiveness of a DSE algorithm previously presented by parts of the authors with real-world data collected by a Phasor Measurement Unit (PMU) at a substation close to a power plant within the extra-high voltage grid of Germany. To this end, at first we derive a suitable mapping of the real-world PMU-measurements recorded at a substation close to the power plant to the terminal bus of the power plants’ synchronous generator. This mapping considers the high-voltage transmission line, the tap-changing transformer and the auxiliary system of the power plant. Next, we introduce several practically motivated extensions to the estimation algorithm, which significantly improve its practical performance with real-world measurements. Finally, we successfully validate the algorithm experimentally in an auto- as well as a cross-validation.
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.
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.
Design of controls for ISS and Integral ISS Stabilization of Multistable State Periodic Systems
(2023)
We propose an optimal operation controller for an electro-thermal microgrid. Compared to existing work, our approach increases flexibility by operating the thermal network with variable flow temperatures and in that way explicitly exploits its inherent storage capacities. To this end, the microgrid is represented by a multi-layer network composed of an electrical and a thermal layer. We show that the system behavior can be represented by a discrete-time state model derived from DC power flow approximations and 1d Euler equations. Both layers are interconnected via heat pumps. By combining this model with desired operating objectives and constraints, we obtain a constrained convex optimization problem. This is used to derive a model predictive control scheme for the optimal operation of electro-thermal microgrids. The performance of the proposed operation control algorithm is demonstrated in a case study.
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.
Small Unmanned Aerial Vehicles (UAVs) have vast application potential from industrial logistics and disaster monitoring to smart farming, for example, to create maps with Normalized Difference Vegetation Index (NDVI) cameras and AI-based image classification or the precision spot application of fertilizers. Operating multiple UAVs in parallel, including those with different specializations, enables efficient coverage of large areas. While existing research focused mainly on predefined flight formations for swarms or autonomous missions for single UAVs, the focus of this work is on multiple UAVs with individually adaptable missions. We derive communication system requirements from swarm coordination algorithms and present a respective design. The resulting modular architecture enables future research on autonomous adaptive UAV swarms and their use as flying sensor platforms.
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.
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.
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
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.
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.
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.
Robust State and Input Estimation with Enhanced Convergence Rate for Monitoring Anaerobic Digestion
(2022)
In this study, an observer for estimating the state and unknown inputs is proposed for monitoring anaerobic digestion processes. This estimator is based on a dynamic model considering acidogenesis and methanogenesis, and consists of three sub-observers: (a) a gramian-based fixed-time convergent observer for the inlet chemical oxygen demand (COD) and the acidogenic bacteria population, (b) an asymptotic observer for the methanogenic bacteria population, and (c) a super-twisting observer for systems with time-varying parameters to estimate the inlet volatile fatty acid (VFA) concentration. These sub-observers can be designed independently, which greatly simplifies the tuning process. Proofs of convergence are developed and simulation tests show the performance of the estimation scheme as compared to classical extended Kalman filtering.
Voltage regulation and current sharing for multi-bus DC microgrids: A compromised design approach
(2022)
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.
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.
This work proposes a control strategy for revoluta joints manipulators using an equivalent manipulator composed of a revoluta joint and a prismatic joint. The equivalent model allows a better characterization of the interaction between a manipulator and a mobile base, for example in an aerial manipulator. The equivalence conditions presented, allows to design the control strategy under the equivalent model representation and implement it on the real model. Through numerical simulations, the effectiveness of the proposed control system is evaluated.
Strong Lyapunov functions for two classical problems in adaptive control and parameter identification are presented. These Lyapunov functions incorporate in their structure the classical persistency of excitation conditions, allowing to show global uniform asymptotic stability of the associated adaptive systems under sufficient and necessary conditions.
This paper addresses the problem of powered descent control of a lunar lander during its final landing phase, where soft and precise landing at the target cite is required. In the literature, this problem has been solved considering a fully actuated lunar lander. Recently, landers are designed as complex systems with several onboard payloads and subsystems for completing demanding mission tasks. There are increasing constraints on mass budget and space availability onboard a
lander. In order to meet these requirements, a novel controller using a single thruster is proposed. The proposed controller has three control inputs (thrust and two gimbaled angles) to control the six degrees of motion of a lander; these control inputs are non-affine. The proposed controller is designed based on variable structure control technique augmented with a high order filter, an immersion and invariance-based mass estimator and a sliding mode angular velocity observer. The stability analysis using Lyapunov theory and the results of the numerical simulations along with Monte Carlo simulations of the system show that the precise landing of the lunar lander using a single thruster is feasible.
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.
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.
Wide-Area Control (WAC) can be efficiently used for oscillation damping in power systems. However, to implement a WAC, a communication network is required to transmit signals between the generation units and the control center. In turn, this makes WAC vulnerable to time-varying communication delays that, if not appropriately considered in the control design, can destabilize the system. Moreover, with the increasing integration of renewable energy resources into the grid, usually interfaced via power electronics, power system dynamics are becoming drastically faster and making WAC more vulnerable to communication delays. In this paper, we propose a design procedure for a delay-robust wide-area oscillation damping controller for low-inertia systems. Its performance is illustrated on the well-known Kundur two-area system. The results indicate that the obtained WAC successfully improves the oscillation damping while ensuring robustness against time-varying communication delays.
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.
Synthesizing Sparse and Delay-Robust Distributed Secondary Frequency Controllers for Microgrids
(2020)
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.
In this work, an observer for a linear time-varying system with delayed measurements is developed. The delay is assumed to be unknown, bounded, and it can be time-varying with no restriction on its rate of change. The observer uses auxiliary signals related to the constructibility Gramian of the system and it contains nonlinearities that provide a uniform fixed-time convergence to a bounded region in the estimation error coordinates. This means that the convergence time can be bounded by a positive constant which is independent from the initial conditions and the initial time. This property is new for the addressed class of systems. The ultimate bound of the estimation error depends on the maximum difference between the nominal output and the delayed one, and not directly on the delay size or its time derivative. These properties are illustrated in a numerical simulation.
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
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.
PMU-Based Decentralized Mixed Algebraic and Dynamic State Observation in Multi-Machine Power Systems
(2020)
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.
It is well known that constant power loads in power systems have a destabilizing effect. Their growing presence in modern installations significantly aggravates this issue, hence, motivating the development of new methods to analyze their effect in ac and dc power systems. Formally, this problem can be cast as the analysis of solutions of a set of nonlinear algebraic equations of the form f(x) = 0, where f : R n → R n , to which we associate the differential equation x = f(x). By invoking advanced concepts of dynamical systems theory and effectively exploiting its monotonicity, the following properties are established: First, prove that, if there are equilibria, there is a distinguished one that is stable and attractive, and give conditions such that it is unique. Second, give a simple online procedure to decide whether equilibria exist or not and to compute the distinguished one. Third, prove that the method is also applicable for the case when the parameters of the system are not exactly known. It is shown how the proposed tool can be applied to the analysis of long-term voltage stability in ac power systems, and to the study of existence of equilibria of multiterminal high-voltage dc systems and dc microgrids.
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.
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.
In the present paper, a lumped parameter model for the novel Silicon Granulate Crucible (SiGC) method is proposed, which is the basis for a future model-based control system for the process. The model is analytically deduced based on the hydromechanical, geometrical, and thermal conditions of the process. Experiments are conducted to identify unknown model parameters and to validate the model. The physical consistency of the model is verified using simulation studies and a prediction error of below 2% is reached.
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.
Wide-Area Control (WAC) can be efficiently used for oscillation damping in power systems. However, to implement a WAC, a communication network is required to transmit signals between the generation units and the control center. In turn, this makes WAC vulnerable to time-varying communication delays that, if not appropriately considered in the control design, can destabilize the system. Moreover, with the increasing integration of renewable energy resources into the grid, usually interfaced via power electronics, the power system dynamics becoming drastically faster and making WAC more vulnerable to communication delays. In this paper, we propose a design procedure for a delay-robust wide-area oscillation damping controller for low-inertia systems. Its performance is illustrated on the well-known Kundur two-area system. The results indicate that the obtained WAC successfully improves the oscillation damping while ensuring robustness against time-varying communication delays.
The increasing penetration of power-electronic-interfaced devices is expected to have a significant effect on the overall system inertia and a crucial impact on the system dynamics. In future, the reduction of inertia will have drastic consequences on protection and real-time control and will play a crucial role in the system operation. Therefore, in a highly deregulated and uncertain environment, it is necessary for transmission system operators to be able to monitor the system inertia in real time. We address this problem by developing and validating an online inertia estimation algorithm. The estimator is derived using the recently proposed dynamic regressor and mixing procedure. The performance of the estimator is demonstrated via several test cases using the 1013-machine ENTSO-E dynamic model.
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.
On boundedness of solutions of state periodic systems: a multivariable cell structure approach
(2019)
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.
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.
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.
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.
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.