Dynamic Phasor Model Research Articles

A Dynamic Phasor Model of an MMC With Extended Frequency Range for EMT Simulations

This paper presents a new dynamic phasor (DP) model of a modular multilevel converter (MMC) with extended frequency range for direct interfacing to an electromagnetic transient (EMT) simulator. The internal dynamics of the MMC are modeled considering dominant harmonic components of each variable. To model the external dynamics of the converter, a novel construct referred to as a base-frequency DP is employed, which allows to capture and model any number of frequency components of external variables without a significant increase in computational burden. The proposed model is validated against detailed EMT models by comparing its results for an inverter system, a back-to-back high-voltage direct current system, and a 12-bus power system built in PSCAD/EMTDC simulator. Simulation results prove that the new model is significantly more computationally efficient than existing models and is capable of maintaining a high level of accuracy. Experimental verification on a scaled-down laboratory setup is also included.

Damping Subsynchronous Resonance in Dynamic Phasor and dq0 model using Thyristor Controlled Reactor

Damping Subsynchronous Resonance in Dynamic Phasor and dq0 model using Thyristor Controlled Reactor

Transient Response Analysis of Inverter-Based Microgrids Under Unbalanced Conditions Using a Dynamic Phasor Model

Microgrids (MGs) are often unbalanced due to the integration of single-phase generators, unbalanced loads, and asymmetrical faults. To better analyze such MGs, this paper presents an approach to analyze the transient response for an inverter-based MG under the unbalanced condition. The dynamic phasor (DP) concept is used for the MG modeling under the stationary abc reference frame. First, the DP model of the inverter-based distributed generation (DG) is developed. The influence of unbalanced conditions on the inverter including oscillations on the dc side is considered in this paper. Then, the model of the network and loads is developed. Finally, all the submodules are combined on a time-variable system frequency to obtain the complete DP model of the unbalanced MG. To validate the proposed approach, the DP method is applied to an MG test system with three-phase and single-phase DGs. Small-signal analysis is carried out to derive the dominant modes and their influence on the system response. Simulation results from the DP model are compared against the detailed model built in MATLAB/SimPowerSystem. The results from load disturbances and asymmetrical faults are used to verify the DP model.

Frequency-Dependent Model for Transient Stability Analysis

This letter proposes a precise frequency-dependent model for power systems that takes into account spatial variations of the frequency in the network during a transient. In the proposed approach, boundary conditions are synchronous machine rotor speeds and the variation of the frequency is based on the concept of frequency divider recently proposed by the authors. The proposed model leads to a more accurate simulation of transient conditions than conventional models for angle and voltage stability analysis. This letter discusses the theoretical background of the proposed model and compares it with the standard transient stability model, as well as with a fully-fledged dynamic phasor model through a 1479-bus dynamic model of the all-island Irish transmission system.

Dynamic Phasor Modeling of LCC-HVDC Systems: Unbalanced Operation and Commutation Failure

This paper develops a dynamic phasor model of a line-commutated converter high-voltage direct current (LCC-HVDC) system that includes unbalanced operation and commutation failure. This model is beneficial in studying the behavior of the HVDC systems under asymmetrical faults, and it complements the conventional transient simulation-based methods. Equally, importantly, the model includes the representation of commutation failure that may arise as a result of severe faults. Due to its selectivity of the considered harmonics, the developed model has markedly less computational intensity than an electromagnetic transient (EMT) simulation model. This gives the model a distinct advantage in the study of large-signal transients of the LCC-HVDC systems, particularly where repetitive simulations are required. Validation of the proposed model is done using a detailed EMT model of the CIGRE monopolar LCC-HVDC benchmark.

Decentralized and Distributed Transient Control for Microgrids

This paper presents a comprehensive approach toward the design of primary and secondary controllers in low-inertia power grids with mixed lines and a large amount of inverter-interfaced generation. First, a complete dynamic phasor model is developed that represents the electromagnetic and electromechanic dynamics of lines, inverters, synchronous machines, and constant power loads. The model offers a straightforward way to combine white-, gray- and black-box models, and its structure lends itself well to control design. In a second step, it is shown how a recently developed robust fixed-structure control design method can be applied to the challenging and relevant problem of primary and secondary control in medium-and low-voltage grids. A comprehensive three-part simulation example demonstrates how frequency and voltage transient stability and performance can be achieved through a methodical design process. It is also shown how nonstandard performance specifications such as proportional power sharing can be directly incorporated in the design. Finally, a distributed secondary controller from the literature is reformulated and designed using the presented framework, and all results are validated in nonlinear simulation.

Development of dynamic phasor based higher index model for performance enhancement of dual active bridge

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.

<italic>Fast</italic>-TFM—Multifrequency Phasor Measurement for Distribution Networks

To effectively manage the growing number of distributed energy resources, more extensive monitoring is needed at distribution network levels, where a challenging combination of constraints and cost-effectiveness requirements must be taken into account. In this paper, we consider the idea of combining accurate phasor measurement with the capability to analyze harmonic and interharmonic phasors. This creates the need to deal with multiple phasor components having different amplitudes, including interharmonics with unknown frequency locations. For this purpose, we propose an enhanced compressive sensing-based algorithm for the estimation of Taylor–Fourier coefficients in a multifrequency dynamic phasor model. We characterize its accuracy in harmonic and interharmonic phasor measurement and discuss reporting rate and latency performance. We show that very good accuracy can also be achieved as a standard phasor measurement unit, allowing to combine multiple functions into a promising new-generation measurement, monitoring, and diagnostic device.

Analysis, Design and Implementation of Droop-Controlled Parallel-Inverters Using Dynamic Phasor Model and SOGI-FLL in Microgrid Applications

The droop control strategy is widely used in islanded microgrids to control power flows according to the load condition, with the absence of a critical communication line, interfacing distributed energy sources to provide for the active and reactive power demand of loads. In this case, the system modeling for both steady-state and transient time is one of the key issues of a droop-controlled system for an inverter-based microgrid (MG). With the rapid development of microgrids, it is essential to identify the system stability and optimize the control parameters, taking into account the network and control dynamics caused by multiple tasks such as electric signal filtering, network synchronization, and so on. Therefore, in order to improve model accuracy and determine control coefficients, this paper analyzes and extends a dynamic phasor-based model to the droop-controlled parallel-inverters, considering network and control dynamics such as a low-pass filter, a second-order generalized integrator frequency-locked-loop (SOGI-FLL), and a system operating sequence. Moreover, discussed in this paper are both the design approaches for and the implementation of a droop-controlled parallel-inverter, which enables the system to be stable and reliable. To demonstrate the effectiveness and validity of this paper, PSIM simulation was performed and two parallel-inverters were combined as the proposed design procedure for the 4-kVA prototypes.

System‐level dynamic phasor models of hybrid AC/DC microgrids suitable for real‐time simulation and small signal analysis

This study develops a system-level dynamic phasor (DP) model of a hybrid AC/DC microgrid. A new definition of DP, based on the multiple frequency shift transformation, is proposed to extend the models of a variety of AC/DC and DC/DC converters. The comprehensive control system is considered in developing the DP model of microgrid. Furthermore, a computational framework for applying this DP model into system-level simulation and small signal analysis (SSA) is given. The DP-based simulation is tested under conditions of environmental disturbances and unbalanced supply voltages. The SSA is performed on the developed DP model to evaluate the voltage stability and harmonic modes of the microgrid. Besides, this DP model shows high potential when implemented in the real-time simulation with larger scale system.

Generalised extended‐frequency dynamic phasor model of LCC‐HVDC systems for electromagnetic transient simulations

This study introduces a new model for line-commutated converter high-voltage direct current (LCC-HVDC) systems based upon the concept of extended-frequency dynamic phasors (DPs). The proposed model is able to represent LCC-HVDC converters during normal as well as abnormal operating modes such as system imbalances and commutation failure by automatically adjusting its parameters based upon converter terminal quantity measurements. The model offers a high level of accuracy with reduced computational burden, and is suitable as a replacement for conventional switch-based models of LCC in electromagnetic transient (EMT) simulation platforms. The proposed model is thoroughly evaluated against detailed EMT simulations of the CIGRE HVDC benchmark and the IEEE 12-bus systems with an embedded LCC-HVDC link. Simulation results confirm that the proposed DP-based model retains EMT-grade accuracy even at large simulations steps. Significant acceleration ratios reaching up to an order of magnitude are observed in the simulations using the proposed model compared with conventional EMT models.

Design of a dynamic phasors-based droop controller for PV-based islanded microgrids

This paper presents a novel autonomous droop-based power sharing scheme for parallel inverter-connected photovoltaic (PV)–based islanded microgrids, in which both resistive and inductive distribution lines are taken into account. The proposed control strategy contains a compensating approach with a view to adding a power offset to the real power owing to the fact of balancing the inverter output power during the variation in the output of solar energy. A derivative term is also included in the designed controller, which damps the oscillatory modes of the controller so that better dynamic performance is ensured. Proportional power sharing among inverter-interfaced PV generators is maintained by including a novel voltage control law in the control algorithm, in which the reference values of the voltage sources are kept the same. The stable range of droop-based control parameters are determined by the extended dynamic phasors model analysis. Finally, the performance of the designed controller is verified on a PV-based islanded test microgrid, and superior dynamic performance is obtained compared with the generalized droop-based controller.

Linearized DC-MMC Models for Control Design Accounting for Multifrequency Power Transfer Mechanisms

The dc-modular multilevel converter (DC-MMC) is one of a new class of single-stage modular multilevel dc-dc converters that has recently emerged for high-voltage dc applications. This paper presents the first small-signal state-space model for the DC-MMC that is able to account for the multifrequency power transfer mechanisms within the converter. Derived from a dynamic phasor model representation of the DC-MMC, the developed model is linear time-invariant (LTI), allowing for the application of conventional LTI tools for both analysis and design. The small-signal dynamics are validated by simulation results from a full switched model demonstrating its accuracy. A simplified model derived from the full LTI system is presented that readers can utilize to develop dynamic controls for the DC-MMC. As a case study, this benchmark model is leveraged to propose a dynamic controller that regulates dc power transfer between networks and balances the capacitor voltages. Control block diagrams are also provided that enable systematic control design of the DC-MMC via standard linear methods. Case study simulations verify the efficacy of the developed controls for dc network applications. The presented small-signal modeling and control design methodology can be readily applied to any MMC-based topology.

Parametric Dynamic Phasor Modeling of Thyristor-Controlled Rectifier Systems Including Harmonics for Various Operating Modes

A parametric dynamic phasor (PDP) model of diode rectifiers has been recently proposed, which uses a computer-aided approach to effectively represent the rectifier dynamics including ac-side harmonics that change with system conditions. This letter extends the PDP methodology to thyristor-controlled rectifier systems where the dc-link voltage is regulated via the thyristor firing control. Steady state and large-signal transient studies demonstrate that the new/extended model is accurate even for prediction of harmonics for various operating modes.

Dynamic phasor based frequency scanning for grid-connected power electronic systems

Frequency scanning is a method of obtaining the frequency response of a system by injecting a small-amplitude wide-band signal as an input in a time domain simulation of the system. This is an alternative to analytical derivation of small-signal models, especially for complex grid-connected power electronic systems (PESs). These models are required for the study of adverse interaction of PES with lightly damped oscillatory modes in a power system. The use of the frequency scans for conventional small-signal stability analysis is predicated upon the time-invariance of the underlying model. Since PES are generally time-periodic, time-invariance may be achieved in some transformed variables. Although the DQ transformation is suitable in many situations, it is not so for systems with low-order harmonics, individual-phase schemes, unbalanced or single-phase systems, and PES with negative-sequence controllers. This paper proposes the use of dynamic phasor variables in such situations since the underlying model in these variables is time-invariant. The procedure for dynamic phasor based scanning is, however, intricate because wide-band signal injection results in the simultaneous presence of harmonic dynamic phasor components. The paper outlines this procedure and presents illustrative case studies of Thyristor Controlled Series Compensator (TCSC) and STATCOM. For the TCSC, a comparison of the frequency response obtained from the scanning method and the one obtained from an approximate analytical dynamic phasor model is also presented .

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.

Three‐phase dynamic phasor model of HVDC systems

Three‐phase dynamic phasor model of HVDC systems

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.

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.