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In this article, we discuss the relationship between subcycle and instantaneous power metrics in polyphase ac systems. While both approaches have very low computational cost, which makes them suitable for real-time control of industrial processes, the two-sample subcycle scheme offers several distinct advantages over the purely-instantaneous approach. In particular, we show that: a) the level of steady-state fluctuation of subcycle power metrics that use only two time-domain samples is significantly lower than that of purely-instantaneous metrics, and b) the subcycle scheme generates several additional power metrics, which can be used to detect onset of faults, and accurately determine their duration. We illustrate our points using both synthetic and (real-life) industrial examples. In addition, we examine the connection between the two-sample subcycle scheme and other near-instantaneous approaches, based on derivatives of currents and voltages. We again observe a significantly lower numerical sensitivity for the two-sample subcycle quantities. Furthermore, two-sample quantities have a unique feature that they can naturally be extended to more samples, with concomitant reduction in fluctuations, better accuracy and with only moderate increase in computational cost. We posit that the subcycle approach has promise in detection, control, and classification applications.

This paper presents a procedure for estimating the systems state when considerable Information and Communication Technology (ICT) component outages occur, leaving entire system areas un-observable. For this task, a novel method for analyzing system observability is proposed based on the Manifold Boundary Ap-proximation Method (MBAM). By utilizing information geome-try, MBAM analyzes boundaries of models in data space, thus detecting unidentifiable system parameters and states based on available data. This approach extends local, matrix-based meth-ods to a global perspective, making it capable of detecting both structurally unidentifiable parameters as well as practically uni-dentifiable parameters (i.e., identifiable with low accuracy). Be-yond partitioning identifiable/unidentifiable states, MBAM also reduces the model to remove reference to the unidentifiable state variables. To test this procedure, cyber-physical system (CPS) simulation environments are constructed by co-simulating the physical and cyber system layers.

This paper deals with the estimation of parameters of a Thevenin equivalent in an AC grid. We consider the practically relevant case of measurements coming from a grid-connected inverter. Our focus is on non-intrusive measurements, as we postulate and later experimentally observe transients that occur in normal operation as the primary source of information. We notice that even during quiet, after work hours there are typically enough variations in the grid to enable successful convergence of our procedure. For completeness, we also consider the artificial case of no external variations and show that injection of very small current perturbations suffices for convergence. Our procedure is based on real-time monitoring of the estimated determinant of the regression matrix. Regression matrix properties are also used to evaluate the integrity of the estimates and to initiate a brief sequence of perturbation in rare cases of the exceptionally restful grid. The estimation algorithm is simple enough to be implementable on standard industrial controllers, yet robust and reliable in terms of speed of convergence.

The paper describes a manifold learning-based algorithm for big data classification and reduction, as well as parameter identification in real-time operation of a power system. Both black-box and gray-box settings for SCADA- and PMU-based measurements are examined. Data classification is based on diffusion maps, where an improved data-informed metric construction for partition trees is used. Data classification and reduction is demonstrated on the measurement tensor example of calculated transient dynamics between two SCADA refreshing scans. Interpolation/extension schemes for state extension of restriction (from data to reduced space) and lifting (from reduced to data space) operators are proposed. The method is illustrated on the single-phase Motor D example from a very detailed WECC load model, connected to the single bus of a real-world 441-bus power system.

We extend in several directions the study of our fast sparse alternative to the standard (FFT-based) evaluation of dynamic phasors. We present analysis for an arbitrary shift between the waveform samples used to construct sub-cycle dynamic phasors. Next, we show that the transient response of sub-cycle dynamic power metrics can be improved by using a small number of waveform samples and adjusting the uniform inter-sample shift. Our real-life examples demonstrate that reduction of the inter-sample shift can be quite effective in the presence of fast transients (wide-band in frequency). We use a synthetic example to demonstrate that a metric obtained from a sub-cycle scheme provides surprisingly accurate information about the duration and onset-time of a transient. We also identify a range of shift values for which the steady-state error remains near-optimal, and we derive conditions for a superior performance for slow transients. Finally, our results suggest that in practical real-time implementations it may be advantageous to calculate at least two sets of phasors to cover both slow and fast transients: the computational cost of such a scheme is still significantly lower than that of a standard full-cycle calculation.

This study proposes a novel flexible hybrid state estimation (SE) algorithm when a realistic communication system with its irregularities is taken into account. This system is modelled by the Network Simulator 2 software tool, which is also used to calculate communication delays and packet drop probabilities. Within this setup, the system observability can be predicted, and the proposed SE can decide between using the static SE (SSE) or the discrete Kalman filter plus SSE-based measurements and time alignment (Forecasting-aided SE). Flexible hybrid SE (FHSE) incorporates both phasor measurement units and supervisory control and data acquisition-based measurements, with different time stamps. The proposed FHSE with detailed modelling of the communication system is motivated by: (i) well-known issues in SSE (time alignment of the measurements, frequent un-observability for fixed SE time stamps etc.); and (ii) the need to model a realistic communication system (calculated communication delays and packet drop probabilities are a part of the proposed FHSE). Application of the proposed algorithm is illustrated for examples with time-varying bus load/generation on two IEEE test cases: 14-bus and 300-bus.

Renewable energy integration and control in microgrid demands computationaly efficient model along with effective control methodology for switched converters. The dual active bridge (DAB) being an integral part of the microgrid suffers from the stability issues. This research proposes dynamic phasor (DP) based higher index model of DAB and demonstrates the effect of appropriate selection of model on performance. To evaluate the system stability for performance objectives of voltage regulation, suppression of measurement noise, sinusoidal disturbances and robustness, a robust control strategy based on loop shaping technique for DP model of DAB is proposed. Comparison of the responses of the higher index model with existing DP model with dc and index 1 terms makes apparent the benefits of the proposed model. The Hardware-in-Loop (HIL) simulation using Opal-RT and dSPACE simulators is carried out for validation of the proposed control scheme.

This paper presents an application of interconnection and damping assignment passivity-based control (IDA-PBC) principle to the port-controlled phasor Hamiltonian (PCPH) model of solid-state transformer (SST) (comprising of three stages, namely, ac/dc rectifier, dual active bridge converter, and dc/ac inverter). A PCPH model of SST is established for each individual stages using dynamic phasor concept. In comparison with other PBC approaches, IDA-PBC offers an additional degree of freedom to solve the partial differential equations. According to the target of the controller design at each stage, the desired equilibrium point of the system is obtained. The closed-loop system performance achieves regulation of constant output dc-bus voltage and unity input power factor. Large-signal simulation results for the full system validate the simplifications introduced to obtain the controller and verify the proposed controller. Robustness of the controller is demonstrated with 20% load disturbance and 10% input disturbance. For validation of the proposed approach and its effectiveness, hardware-in-loop simulation is carried out using Opal-RT and dSPACE simulators.

Since the publication of the original paper on power system stability definitions in 2004, the dynamic behavior of power systems has gradually changed due to the increasing penetration of converter interfaced generation technologies, loads, and transmission devices. In recognition of this change, a Task Force was established in 2016 to re-examine and extend, where appropriate, the classic definitions and classifications of the basic stability terms to incorporate the effects of fast-response power electronic devices. This paper based on an IEEE PES report summarizes the major results of the work of the Task Force and presents extended definitions and classification of power system stability.

This paper addresses signal processing aspects of dynamic power quality monitoring in ac energy systems. The widespread use of high-bandwidth sensors enables a characterization of both steady-state and transient operation. However, the volume of so generated data is such that it necessitates extensive preprocessing and extraction of events of interest in estimation and control. We review approaches based on single (vector) samples, and compare them with methods that require full-period information, such as standard dynamic phasors. In this paper, we propose a sparse alternative to the standard (fast Fourier transform based) evaluation of dynamic phasors, thus bridging the gap between the two classes of techniques. We also outline the computational cost tradeoffs among different variants of sparse Fourier transform customized for electric energy system data.

We analyze the performance of a networked multisensor continuous-discrete Kalman filter in the presence of random observation delay and irregular sampling. The primary cause for irregular intersample intervals is the occasional loss of information packets. Additional causes include lack of synchrony between sensors, difference in their sampling rates, and the superposition of multiple sampling patterns. We rely on time stamping of all sensor packets to accurately determine, at the estimation hub, both transmission delay and sensor sampling instants. We relate the average (steady-state) error covariance to two moment-generating functions: 1) we provide lower and upper bounds on the average error covariance in the presence of irregular sampling, expressed in terms of the moment-generating function of the sampling intervals; 2) we obtain a stability condition that depends on the region of convergence of this moment-generating function; and 3) we derive an expression for the added error caused by transmission delay, which depends on the moment-generating function of the delay. We also demonstrate that the average error covariance depends primarily on the average sampling interval, with a very minor dependence on the variance and higher order moments of the multisensor intersample interval.

This study describes a new class of system identification procedures, tailored to electric power systems with renewable resources. The procedure described here builds on computational advances in differential geometry, and offers a new, global, and intrinsic characterisation of challenges in data-derived identification of electric power systems. The approach benefits from increased availability of high-quality measurements. The procedure is illustrated on the multi-machine benchmark example of IEEE 14-bus system with renewable resources, but it is equally applicable to identification of other components and systems (e.g. dynamic loads). The authors consider doubly-fed induction generators (DFIG) operating in a wind farm with system level proportional-integral controllers.

This paper describes a new class of system identification procedures that are tailored to electric power systems, in particular to synchronous generators (SGs) and other dynamic components. Our procedure builds on computational advances in differential geometry, and offers a new, global characterization of challenges frequently encountered in system identification of electric power systems. The approach also benefits from increasing availability of high-quality measurements. While the proposed procedure is illustrated on SG example in a multimachine benchmark (IEEE 14-bus and real-world 441-bus power systems), it is equally applicable to identification of other system components, such as loads.

The paper describes a new model reduction procedure tailored to power systems. It uses measurement data to devise a family of reduced order nonlinear models while retaining physical interpretability of parameters and equations. The manifold boundary approximation method (MBAM) uses the Fisher information matrix calculated from measurements to identify the least relevant parameter combination in the original model. Next, it numerically constructs a geodesic on the corresponding statistical manifold originating from the initial parameters in the least relevant parameter direction until a manifold boundary is found. MBAM then identifies a limiting approximation in the mathematical form of the model and removes one parameter combination. The simplified model is recalibrated by fitting its behavior to that of the original model, and the process is repeated as appropriate. MBAM is demonstrated on the example of a synchronous generator (SG), which has been treated extensively in the literature. Implications of the proposed model reduction procedure on large power system models are illustrated on a 441-bus, 72-SG dynamical model.

International audience; Microgrids have been identified as key components of modern electrical systems to facilitate the integration of renewable distributed generation units. Their analysis and controller design require the development of advanced (typically model-based) techniques naturally posing an interesting challenge to the control community. Although there are widely accepted reduced order models to describe the dynamic behavior of microgrids, they are typically presented without details about the reduction procedure—hampering the understanding of the physical phenomena behind them. Preceded by an introduction to basic notions and definitions in power systems, the present survey reviews key characteristics and main components of a microgrid. We introduce the reader to the basic functionality of DC/AC inverters, as well as to standard operating modes and control schemes of inverter-interfaced power sources in microgrid applications. Based on this exposition and starting from fundamental physics, we present detailed dynamical models of the main microgrid components. Furthermore, we clearly state the underlying assumptions which lead to the standard reduced model with inverters represented by controllable voltage sources, as well as static network and load representations, hence, providing a complete modular model derivation of a three-phase inverter-based microgrid.

We describe a method for simultaneously identifying and reducing dynamic power systems models in the form of differential-algebraic equations. Often, these models are large and complex, containing more parameters than can be identified from the available system measurements. We demonstrate our method on transient stability models, using the IEEE 14-bus test system. Our approach uses techniques of information geometry to remove unidentifiable parameters from the model. We examine the case of a networked system with 58 parameters using full observations throughout the network. We show that greater reduction can be achieved when only partial observations are available, Including reduction of the network itself.

A high frequency solid-state transformer (SST) proposed by FREEDM centre is an interesting alternative to conventional distribution transformer in microgrids as it supports additional functionalities such as active-reactive power flow control, fault current limitation and voltage regulation. This paper proposes a dynamic phasor based robust control of SST through the modular control of each stage. The control problem is formulated in frequency domain by representing the system states with time varying Fourier coefficients or dynamic phasors (DP). This formulation transforms the oscillating waveforms of ac circuits to constant or slowly varying variables, hence allow the use of PI controller to track the sinusoidal references. For rectifier and inverter stages of SST, dq transformation is applied on DP which facilitates the design of PI controller to smoothen out the ripples in the output voltage waveform. The controller gains are tuned to reject input and load disturbances and attenuate measurement noise using loop shaping and pole assignment technique. The robustness of the controller is assured analytically against parametric uncertainties using small gain theorem. Simulation results are provided to support the proposed control scheme. Hardware-in-Loop (HIL) simulation is carried out on critical stages using Opal-RT and dSPACE simulators to confirm the effectiveness of the proposed scheme.

Several heuristic procedures to estimate the rotor position of interior permanent magnet synchronous motors via signal injection have been reported in the applications literature, and are widely used in practice. These methods, based on the use linear time invariant high-pass/low-pass filters, are instrumental for sensorless controllers. To the best of our knowledge, no theoretical analysis has been carried out for them. The objectives of this note, are (i) to invoke some recent work on the application of averaging techniques for injection-based observer design to develop a theoretical framework to analyze the sensorless methods, and (ii) to propose a new method that, on one hand, ensures an improved accuracy and, on the other hand, can be related with the current filtering technique. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments.

This paper describes a manifold learning algorithm for big data classification and parameter identification in real-time operation of power systems. We assume a black-box setting, where only SCADA-based measurements at the point of interest are available. Data classification is based on diffusion maps, where an improved data-informed metric construction for partition trees is used. Data reduction is demonstrated on an hourly measurement tensor example, collected from the power flow solutions calculated for daily load/generation profiles. Parameter identification is performed on the same example, generated via randomly selected input parameters. The proposed method is illustrated on the case of the static part (ZIP) of a detailed WECC load model, connected to a single bus of a real-world 441-bus power system.

International audience; Several heuristic procedures to estimate the rotor position of interior permanent magnet synchronous motors (IPMSM) via signal injection have been reported in the application literature, and are widely used in practice. These methods, based on the use of linear time-invariant (LTI) high-pass/low-pass filtering, are instrumental for the development of sensorless controllers. To the best of authors’ knowledge, no theoretical analysis of these methods has been carried out. The objectives of this note are (i) to invoke some recent work on the application of averaging techniques for injection-based observer design to develop a theoretical framework to analyse the LTI filtering used in sensorless methods and (ii) to propose a new method that on the one hand ensures improved accuracy and on the other hand can be related to the current filtering technique. An additional advantage of the new method is that it relies on the use of linear operators, implementable with simple computations. The effectiveness of the proposed scheme is assessed by experiments on an IPMSM platform driven by a 521 V DC bus with a 5-kHz pulse-width modulation.

The paper explores interleaved and coordinated refinement of physics- and data-driven models in describing transient phenomena in large-scale power systems. We develop and study an integrated analytical and computational data-driven gray box environment needed to achieve this aim. Main ingredients include computational differential geometry-based model reduction, optimization-based compressed sensing, and a finite approximation of the Koopman operator. The proposed two-step procedure (the model reduction by differential geometric (information geometry) tools, and data refinement by the compressed sensing and Koopman theory based dynamics prediction) is illustrated on the multi-machine benchmark example of IEEE 14-bus system with renewable sources, where the results are shown for doubly-fed induction generator (DFIG) with local measurements in the connection point. The algorithm is directly applicable to identification of other dynamic components (for example, dynamic loads).

This paper proposes a tractable and scalable algorithm to identify and analyze bifurcation points of a large-scale power system model, which are directly related to dynamic voltage instability problems. Different types of bifurcations are analyzed, including: saddle-node (fold), Hopf, singularity-induced and limit-induced. An algorithm that combines optimization and predictor-corrector procedure is proposed for equilibrium tracing. The algorithm is based on calculation of only critical (rightmost and closest-to-zero) eigenvalues. The proposed algorithm is extended to the case of dynamic voltage stability assessment for power systems with optimized topology (simultaneously subjected to the topology control changes and generation re-dispatch). The proposed approach is illustrated on two (medium- and large-scale real-world) test power systems.

This paper proposes a probabilistic extension to flexible hybrid state estimation (FHSE) for cyber-physical systems (CPSs). The main goal of the algorithm is improvement of the system state tracking when realistic communications are taken into account, by optimizing information and communication technology (ICT) usage. These advancements result in: 1) coping with ICT outages and inevitable irregularities (delay, packet drop and bad measurements); 2) determining the optimized state estimation execution frequencies based on expected measurement refresh times. Additionally, information about CPSs is gathered from both the phasor measurement units (PMU) and SCADA-based measurements. This measurement transfer introduces two network observability types, which split the system into observable (White) and unobservable (Grey) areas, based on 1) deployed measuring instruments (MIs) and 2) received measurements. A two-step bad data detection (BDD) method is introduced for ICT irregularities and outages. The proposed algorithm benefits are shown on two IEEE test cases with time-varying load/generation: 14-bus and 300-bus.

The paper describes a global identification procedure for dynamic power system models in the form of differential and algebraic equations. Power system models have a number of features that makes their improvement challenging – they are multi-level, multi-user and multi-physics. Not surprisingly, they are nonlinear and time varying, both in terms of states (memory variables) and parameters, and discrete structures, such as graphs, are strongly blended with continuous dynamics, resulting in network dynamics. The transient stability models are used as a prototypical example. Our method is based on information geometry, and uses advances in computational differential geometry to characterize high-dimensional manifolds in the space of measurements. In the case of network parameters, a comparison is presented with circuit-theoretic techniques. The results are illustrated on the case of IEEE 14-bus test system with 58 parameters in our realization.

This paper is devoted to extensions and experimental investigations of a recently proposed robust, nonlinear and globally convergent position observer for surface-mounted or non-salient permanent magnet synchronous motors (SPMSMs). A key feature of the robust observer is that estimation of the rotor position θ requires only the knowledge of stator resistance R and inductance L. In this study, the performance of SPMSM sensorless (self-sensing) control is verified for the case when the estimated position signal is used to control the motor and with DC link voltage measurement only. The closed-loop control system combined with the nonlinear observer is also compared with the state-of-the-art industrial controller. It is demonstrated that the nonlinear observer achieves a significant improvement of the closed-loop performance in both low- and high-speed operation. At the same time, the availability of a complete theoretical analysis allows for portability of results to other platforms and drives. Proposed approach can be useful in fault detection and self-diagnosis of the cyber-physical systems with embedded PMSM.

In this paper we propose approximate bisimulation relations and functions for reduction of power system dynamic models in differential-algebraic (descriptor) form. The full-size dynamic model is obtained by linearization of the nonlinear transient stability model. We generalize theoretical results on approximate bisimulation relations and bisimulation functions, originally derived for a class of constrained linear systems, to linear systems in descriptor form. An algorithm for transient stability assessment is proposed and used to determine whether the power system is able to maintain the synchronism after a large disturbance. Two benchmark power systems are used to illustrate the proposed algorithm and to evaluate the applicability of approximate bisimulation relations and bisimulation functions for reduction of the power system dynamic models.

The paper proposes a scalable and tractable algorithm for dynamic topology optimization of power systems involving changes in branch on/off status, while respecting small-signal stability (SSS) constraints. A procedure for fast updates of the system matrices (in descriptor form) and without additional full matrix inversions is proposed. To additionally reduce the computation time, only critical eigenvalues (right-most or those in a specified damping ratio and frequency range) are calculated. A quadratic optimization approach is proposed for optimized generation re-dispatch to satisfy SSS constraints. The approach is applied to two (medium- and large-scale) real-world test power systems.

The paper proposes a power system state estimation algorithm in the presence of irregular sensor sampling and random communication delays. Our state estimator incorporates Phasor Measurement Units (PMU) and SCADA measurements. We use an Extended Kalman filter based algorithm for time alignment of measurements and state variables. Time stamps are assumed for PMU, SCADA and state estimation. Application of the proposed algorithm is illustrated for hourly/daily load/generation variations on two test examples: 14-bus and 118-bus.

Load modeling has been extensively studied in power systems. The problem is intrinsically hard, as a simple description is sought for a large collection of heterogeneous physical devices. One aspect of model simplification has to do with the number of parameters needed to describe a dynamic load. With the rich tapestry of methods proposed in the literature as a backdrop, this paper introduces a new approach to simplify the load models and estimate the parameters. Our method is based on information geometry which combines information theory with computational differential geometry to derive global estimation results and shed a new light on difficulties commonly encountered when fitting widely used models to the measurement data. The results are compared with the literature using simulations on the IEEE 14 bus benchmark system.

In contemporary power system practice, the stability limits are typically computed off-line and stored in databases to be monitored by system operators (dispatchers) in the real-time environment. Several sources of uncertainty affect such computations and consequently reasonable stability margins must be taken into account when determining operation limits. Despite these precautions, unplanned outages and planned switching actions (such as topology control [TC] actions) may cause operational conditions not considered at operation planning stages, and consequently system operators are left with no pertinent stability information. Online stability assessment has been proposed as an additional line of defense in which stability limits are computed based on the actual power system condition, which decreases the uncertainty, thus providing more accurate stability operation limits. The online stability assessment can be performed for the (real-time) operating point only, or additionally for a region around this condition [1].

The paper describes a REI-based procedure for estimating parameters of a dynamic model from measurements in the boundary buses/branches. Parameter identification of equivalent synchronous generators in fictitious buses is performed by Weighted Least Square (WLS) nonlinear optimization to minimize the difference between online measurements and transient responses of reduced power system.