Phasor Model Research Articles

Improved characterization of multi-stage voltage dips based on the space phasor model

This paper proposes a method for characterizing voltage dips based on the space phasor model of the three phase-to-neutral voltages, instead of the individual voltages. This has several advantages. Using a K-means clustering algorithm, a multi-stage dip is separated into its individual event segments directly instead of first detecting the transition segments. The logistic regression algorithm fits the best single-segment characteristics to every individual segment, instead of extreme values being used for this, as in earlier methods. The method is validated by applying it to synthetic and measured dips. It can be generalized for application to both single- and multi-stage dips.

Estimación de Sincrofasores en Redes Eléctricas Inteligentes: de Modelos a Restricciones de Diseño

Presentamos en primer lugar una reseña de dos populares clases de métodos de estimación de sincrofasores. Ellas son la clase de métodos basados en la transformada de Fourier discreta (DFT) y la transformada de Taylor-Fourier (TFT), que surgen de un modelo de fasor constante y polinómico, respectivamente. Se exponen las limitaciones de estos métodos, que surgen por los propios modelos asumidos, lo cual los hace poco apropiados en situaciones donde el fasor no puede representarse en términos tan simples. Este problema puede resolverse con los estimadores basados en optimización convexa semi-infinita (CSIP), un enfoque novedoso que también es descripto. En particular, enfatizamos las restricciones asociadas con las situaciones más críticas para los métodos basados en modelos, mostrando cómo controlar precisamente el desempeño de los estimadores en dichos casos. Finalmente, mostramos que los estimadores DFT y TFT son instancias particulares del estimador CSIP, de modo existe una conexión entre estos dos enfoques aparentemente diferentes. Esto abre la puerta para futuros análisis y desarrollos.

Impact of Inertia and Effective Short Circuit Ratio on Control of Frequency in Weak Grids Interfacing LCC-HVDC and DFIG-Based Wind Farms

Although virtually every overhead HVdc line is based on line commutated converter (LCC) technology, hardly any work has been reported on modeling and analysis of the impact of inertia and effective short circuit ratio on control of frequency in weak grids interfacing LCC-HVdc and onshore doubly fed induction generator (DFIG)-based wind farms. This paper develops a comprehensive modeling and stability analysis framework of a weak grid that interfaces an LCC-HVdc station and a DFIG-based wind farm. To that end, a nonlinear averaged phasor model of the system is derived, which is then benchmarked against a detailed switched model. The averaged model is linearized to design a frequency controller for the LCC-HVdc rectifier station. Participation factor and eigenvalue sensitivity measures indicate that the ac system electromechanical mode and the “HVdc PLL” mode are highly sensitive to changes in effective dc inertia constant and effective short circuit ratio, respectively. Root-locus analysis in a progressively weak grid validates these results. A systematic design process of the frequency controller parameters reveals a negative interaction between the “generator speed-HVdc PLL-frequency controller” mode and the “DFIG-GSC controller” mode.

Advanced Droop Control in Islanded Microgrids Using Dynamic Phasor Models

A dynamic phasor model for low- and medium-voltage distribution grids is presented. This model accurately represents the transient dynamics of this type of grid, and its low order makes it well suited for control design. A novel fixed-structure, robust control design method based on convex optimization is then used to design a decentralized low-order controller that shows a significantly improved transient performance compared to classical droop controllers. The performance of the designed controller is then validated in a simulation example for voltage and frequency control of an islanded medium-voltage distribution grid.

Dynamic Phasor Modeling of Line-Commutated Rectifiers With Harmonics Using Analytical and Parametric Approaches

Line-commutated rectifiers (LCRs) are widely used in various industrial applications, wherein they are also known to be a significant source of harmonics. The dynamic phasor (DP) modeling approaches have been well studied in the literature to simulate the dynamics of power systems and their components including harmonics. In this paper, the state-of-the-art analytical DP (ADP) models of LCRs, which relate the ac and dc subsystems through complicated switch functions, are first investigated. Then, a new parametric DP (PDP) model of LCRs is proposed, wherein the DP dynamics of rectifier/dc-link are represented using a set of explicit algebraic functions that are numerically established. Rigorous computer studies demonstrate that the proposed PDP methodology is capable of accurately predicting the steady-state and transient responses of LCR systems under a wide range of loading conditions, while providing significant computational advantages over the conventional detailed model and the established ADP models.

Comparison of time-varying phasor and dq0 dynamic models for large transmission networks

In recent years, with increasing penetration of small distributed generators and fast power electronics based devices, the assumption of quasi-static phasors is becoming increasingly inaccurate. In order to describe fast dynamic behavior and rapid amplitude and phase variations, more accurate dynamic models based on the dq0 transformation are used. To better understand the differences between these two models, in this work we compare their relative accuracy when applied to large-scale transmission networks. In this light, the present work describes the two types of models using similar terminology, which is based on dq0 quantities. Based on this result, we show that quasi-static models may be obtained from dq0 models at low frequencies, and that there exists a frequency range in which quasi-static model approximates the dq0 model well. The obtained results allow to estimate the frequency after which the quasi-static model cannot accurately describe the system dynamics, and dq0 models should be used instead.

Open‐source python‐OpenDSS interface for hybrid simulation of PV impact studies

This study introduces an open-source Python-OpenDSS simulation tool where the phasor simulation software OpenDSS is interfaced with an electromagnetic transient (EMT) program-type simulation tool implemented in Python environment. The tool is designed to perform impact study of photovoltaic (PV) integration in distribution systems. It is composed of an EMT model of a grid-tied PV system interfaced with a phasor model of the distribution network. The proposed tool provides an add-on that expands OpenDSS capabilities in order to perform various PV impact studies that cannot be performed inherently by OpenDSS since they require detailed modelling. This study describes the methodology and theory behind the interfacing of the EMT model with OpenDSS. The tool is tested with various case studies using the IEEE 37-bus system with multiple interconnected PV systems. The tool is validated by comparing its results with those of a full EMT model of the IEEE 37-bus system simulated using SimPowerSystems. The results indicate that the hybrid tool offers significant advantages over single-rate simulations that use either full phasor or full EMT simulation approach. It provides faster simulation time and less computational intensity, and the accuracy is remarkably close to the full blown, more complex and slower, EMT simulation.

Phasor Estimation and Modelling Techniques of PMU- A Review

Abstract The values of voltage / current signal at various places in a power network are measured by Phasor Measurement Unit(PMU). The PMU's work on the phasor values of the data collected using Phasor estimation technique. This mechanism is essential for analysis and interpretation of collected data in a correct manner. Therefore, a Phasor estimation process has a lot of importance in design of control mechanism and various protection systems to be implemented. Numbers of PMUs are being installed across the world for different applications such as post fault analysis, state estimation and protection of power system. Since the cost of PMUs is very high, they are placed optimally in the power system such that complete power system is observable. In this study, PMU along with techniques used for phasor measurement has been reviewed. Some of the used phasor estimation techniques viz. zero crossing, DFT and SDFT are described to compute magnitude and phase value of input signal.

Phasor model simulation of a grid integrated variable speed pumped storage system

This study presents a phasor model simulation of a grid integrated variable speed pumped storage (VSPS) system focusing on generating mode. The VSPS is configured by the voltage sourced converter doubly-fed induction machine (DFIM) scheme. A wound rotor induction machine dynamic mathematical model and generalised averaging theory are adopted to derive the phasor model technique of the system. Based on the dq -axis synchronous reference frame concept, the direct power control strategy of the system is designed. The steady-state and transient stability responses of the proposed system are analysed in MATLAB/Simulink platform by considering a 300 MW/18 kV/50 Hz DFIM-based VSPS system and a grid consisting of two hydropower plants with synchronous generator, a diesel power plant with synchronous generator, a solar photovoltaic farm and fixed loads. A comparison of phasor model and detailed model simulations of the system is also conducted. The results show that the grid integrated VSPS system is stable without significant deviation in grid voltages, DC voltage and rotor speed of the DFIM unit under the designed control strategy. Moreover, the phasor model simulation achieves results with good accuracy as the detailed model, but with faster speed. Hence, the phasor model simulation is very effective for analysis and control design of large grid integrated VSPS systems.

Three‐phase dynamic phasor model of HVDC systems

Three‐phase dynamic phasor model of HVDC systems

Phasor model of full scale converter wind turbine for small‐signal stability analysis

Phasor model of full scale converter wind turbine for small‐signal stability analysis

Design and tuning of wind power plant voltage controller with embedded application of wind turbines and STATCOMs

This study addresses a detailed design and tuning of a wind power plant voltage control with reactive power contribution of wind turbines and static synchronous compensators (STATCOMs). First, small-signal models of a single wind turbine and STATCOM are derived by using the state-space approach. A complete phasor model of the entire wind power plant is constructed, being appropriate for voltage control assessment. An exemplary wind power plant located in the United Kingdom and the corresponding grid code requirements are used as a base case. The final design and tuning process of the voltage controller results in a guidance, proposed for this particular control architecture. It provides qualitative outcomes regarding the parametrisation of each individual control loop and how to adjust the voltage controller depending on different grid stiffnesses of the wind power plant connection. The performance of the voltage controller is analysed by means of a real-time digital simulation system. The impact of discretising the controller being initially developed in continuous-time domain is shown by various study cases.

Modeling Techniques for Dynamic and Steady-State Analysis of Modular Multilevel DC/DC Converters

A new class of modular multilevel dc/dc converters has recently emerged that eliminates the traditional full-rated intermediate ac stage inherent to two-stage dc/dc converter structures, that is, two cascaded dc/ac modular multilevel converters (MMCs). This paper introduces the first averaged dynamic state-space model for this new class of single-stage dc/dc converter, called the DC-MMC, which captures all input and output terminal dynamics as well as internal capacitor dynamics. Based on the developed analytical model, a dynamic phasor model is derived to accommodate the multifrequency components that exist at steady state. The phasor model enables: 1) solving for the full steady-state solution of the DC-MMC under arbitrary loading and 2) evaluation of DC-MMC open-loop stability via eigenvalue analysis. These analyses are not possible with existing DC-MMC models. Simulations of a comprehensive switched model verify the accuracy of the presented analytical models, which represent valuable study tools for the analysis of emerging modular multilevel dc/dc converters containing multiple frequency components.

Co-Simulation of Electromagnetic Transients and Phasor Models: A Relaxation Approach

Co-simulation opens new opportunities to combine mature electromagnetic transients (EMT) and phasor-mode (PM) solvers, and takes advantage of their respective high accuracy and execution speed. In this paper, a relaxation approach is presented, iterating between an EMT and a PM solver. This entails interpolating over time the phasors of the PM simulation, extracting phasors from the time evolutions of the EMT simulation, and representing each subsystem with a proper multiport equivalent when simulating the other subsystem. Various equivalents are reviewed and compared in terms of convergence of the PM-EMT iterations. The paper also considers the update with frequency of the Thevenin impedances involved in the EMT simulation, the possibility to compute the EMT solution only once per time step, and the acceleration of convergence through a prediction over time of the boundary variables. Results are presented on a 74-bus, 23-machine test system, split into one EMT and one PM subsystem with several interface buses.

Regularization and decimation pseudolikelihood approaches to statistical inference inXYspin models

We implement a pseudolikelyhood approach with l2-regularization as well as the recently introduced pseudolikelihood with decimation procedure to the inverse problem in continuous spin models on arbitrary networks, with arbitrarily disordered couplings. Performances of the approaches are tested against data produced by Monte Carlo numerical simulations and compared also from previously studied fully-connected mean-field-based inference techniques. The results clearly show that the best network reconstruction is obtained through the decimation scheme, that also allows to dwell the inference down to lower temperature regimes. Possible applications to phasor models for light propagation in random media are proposed and discussed.

Fuzzy based damping controller for TCSC using local measurements to enhance transient stability of power systems

This paper proposes a local fuzzy based damping controller (LFDC) for thyristor controlled series capacitor (TCSC) to improve transient stability of power systems. In order to implement the proposed scheme, detailed model of TCSC, based on actual behavior of thyristor valves, is adopted. The LFDC uses the frequency at the TCSC bus as a local feedback signal, to control the firing angle. The parameters of fuzzy controller are tuned using an off-line method through chaotic optimization algorithm (COA). To verify the proposed LFDC, numerical simulations are carried out in Matlab/Simpower toolbox for the following case studies: two-area two-machine (TATM), WSCC three-machine nine-bus and Kundur’s two-area four-machine (TAFM) systems under various faults types. In this regard, to more evaluate the effectiveness of the proposed method, the simulation results are compared with the wide-area fuzzy based damping controller (WFDC). Moreover, the transient behavior of the detailed and phasor models of the TCSC is discussed in the TATM power system. The simulation results confirm that the proposed LFDC is an efficient tool for transient stability improvement since it utilizes only local signals, which are easily available.

Transient Stability Enhancement Using Phasor Model of Superconducting Magnetic Energy Storage

Superconducting Magnetic Energy Storage (SMES) is one of most important device attracting researchers for enhancing the transient stability of power systems. To facilitate the use of this device in different simulations and studied, a phasor model is established and used to analyse the impact of this device using matlab/Simulink software. The phasor model has enough advantages like using the SMES without need detailed model that contains the electronic power converter and therefore minimize the simulation time. The Western Systems Council Coordinating (WSCC) 3 machine-9 bus system is taken as a power system test. Simulation results show that the phasor model of SMES unit is very effective to study their impact for enhancing the transient stability in large scale time.

Using Frequency Coupling Matrix Techniques for the Analysis of Harmonic Interactions

This paper develops a simplified phasor model for predicting harmonics present at the point of common coupling between a voltage-source power converter and the utility network. It employs the frequency coupling matrix (FCM) modeling technique. The FCM is experimentally determined without requiring access to converter internal details, such as control and output filter parameters, which are generally not available for converters used in distributed generation systems. Experimental measurements are conducted on a commercially available two-stage, three phase, grid-tied photovoltaic inverter to assess the accuracy of experimentally determined FCMs to predict the harmonic behavior of grid-connected converters. This paper considers two grid conditions for the experimental analysis: 1) when the grid is stiff and contains only background voltage harmonics and 2) when the grid contains harmonic grid impedances as well as background voltage harmonics. In all cases, a close match between the results predicted by the FCM approach and experimental measurements is achieved, thus demonstrating the practical viability of using experimentally determined FCM models for harmonic predictions.

A detailed designed model for UPFC in PSCAD

Generally, there are two models for every flexible AC transmission system (FACTS) devices, detailed and phasor models. Detailed model is exact simulation of real one which is used multi level converters with switches and diodes, capacitor for DC link, transformers and loop controllers. On the other hand, there is phasor model which is based on algebraic complex equations. Since detailed model is a complete and exact model that represents all transients, this model is considered as a perfect model. In this paper, process of detailed modelling of unified power flow controller (UPFC) is presented in PSCAD software. PSCAD software is one of the best power system simulators which can present transients of power system completely. In order to validate simulation results, simulated UPFC in PSCAD is compared to available UPFC in MATLAB. Simulation results show that the simulated UPFC in PSCAD is completely accurate and the results are very similar to MATLAB.

Dynamic Phasor Modeling of Multi-Generator Variable Frequency Electrical Power Systems

The dynamic phasor (DP) concept has been widely used in modeling electrical power systems. So far, the DP concept has been restricted to modeling systems with one single electrical source at a fixed fundamental frequency, either one generator or an ideal three-phase AC source. This paper aims to extend the DP modeling methodology to a wider application area. Two major achievements have been introduced: 1) application of DPs for multi-source, multi-frequency systems; 2) modeling of systems with time-varying frequencies. These two techniques enable the use of DPs to study nearly all types of electrical power systems (EPS). The developed theory is validated using a twin-generator system from the More Open Electrical Technologies (MOET) project. The accuracy and effectiveness of the developed models is confirmed by comparing the simulation results of detailed switching models and DP models under both balanced and unbalanced conditions.