Electromagnetic Transients Research Articles

Sparse solver application for parallel real-time electromagnetic transient simulations

The main purpose of this research is to speed up real-time simulations of electromagnetic transients (EMTs) using sparse linear solver techniques. This paper presents the integration of a direct sparse linear solver (KLU) into a real-time software for EMT simulation. This solver is combined with parallelization of network solution. Fill-in reduction techniques are investigated as well as partial refactorization to speed up computations. The pivoting technique during refactorization is asserted in terms of simulation stability as compared to existing sparse solver based on code generation without pivoting. Performance and validation are studied on practical power system cases with real-time Hardware-In-the-Loop (HIL) simulation. Substantial performance gains, up to 50%, are obtained using fill-in reduction and partial refactorization. Pivoting is necessary to maintain numerical stability.

Adaptive fault ride through control of VSM Grid-forming converters

Recently, many high voltage direct current (HVdc) transmission lines are being constructed with the intention of becoming “backbones” of future power grids. Grid-forming (GFM) controlled Voltage Source Converters (VSCs) are anticipated to provide significant stability advantages compared with Grid-following (GFL) VSCs in HVdc converters connected to weak ac grids or to grids with high penetration of renewable inverter-based resources (IBRs). This paper proposes an adaptive fault ride through controller for Virtual Synchronous Machine (VSM) GFM control, which has significantly improved fault ride through capability over the more conventional GFM control with cascaded or switchable current limiting. The performance of the proposed adaptive control is investigated using Electromagnetic Transient (EMT) simulation. The results show that the proposed adaptive control has superior post disturbance recovery from ac faults as well as phase angle shifts, and overcomes the instability reported in GFM converters connected to strong ac networks.

Passivity enforcement of wideband model through a new and full perturbation formulation

Passive component models are necessary to ensure numerical stability in the simulation of electromagnetic transients in power systems. However, it is challenging to represent transmission lines and cables with frequency-dependent wideband models that are accurate, efficient, and passive. This paper proposes a new method for the passivity enforcement of wideband line and cable models. The wideband models rely on pole-residue identification of characteristic admittance and propagation function in rational forms. In case the resulting models are not passive, the proposed method simultaneously applies perturbation to the residue matrices of characteristic admittance and propagation function. The set of equations related to passivity enforcement through the residues of propagation function in phase domain is complex and presented for the first time in this paper. The proposed approach minimizes the overall perturbation for maintaining passivity as opposed to the existing simplified approaches that rely on the perturbation of the residues of either characteristic admittance or diagonal elements of propagation function. The performance of the method is validated with application cases, and it is shown that it outperforms the existing methods that seek simplification in problem formulation.

An improved high-accuracy interpolation method for switching devices in EMT simulation programs

This paper presents an interpolation with Backward Euler (BE) method that enhances the switching simulations accuracy in an electromagnetic transient (EMT) simulation with a fixed time-step. Because of the switching operations on discrete instants, the simulations can show artificial voltage spikes and numerical oscillations (chatter), compromising the accuracy and producing misleading results. We thus present a method that eliminates the spurious switching losses and improves the accuracy by combining interpolation and extrapolation with a half-time-step BE solution over existing interpolation-based approaches to resolve the issues above. In addition, this improved method requires the same calculation steps as the industry-accepted instantaneous interpolation. Analytical discussion reinforced by the simulation studies for a simple and complex power electronic circuits demonstrates the accuracy and efficacy of the proposed interpolation with BE method.

Equivalent grid-following inverter-based generator model for ATP/ATPDraw simulations

This paper presents an equivalent time-domain grid-following inverter-based generator model, which can be used in Electromagnetic Transients Programs (EMTP). It is developed in the Alternative Transients Program (ATP) using the ATPDraw graphical interface. A complete benchmark photovoltaic model available in ATP/ATPDraw environment is taken as reference to evaluate the proposed model under steady-state and fault scenarios. The obtained results showed that the proposed model is simpler and less time-consuming than the complete model, being capable of easily consider the implementation of different components/controls of Inverter-Based Resources (IBR) in EMTP. The settings used in the implemented control schemes proved to be effective, resulting in an average error of about 2.33% during fault conditions. Also, a reduction of about 70 % in the execution time was achieved when compared to the analyzed benchmark one, attesting its usefulness for power system studies with high presence of grid-following IBRs.

The principles of a new line surge arrester's transient current measurement system

Power systems are exposed to different types of electromagnetic transients, which involve a large spectrum of signals whose duration can range from several nanoseconds to several milliseconds, and whose peak values can also cover a wide range of values. Therefore, measuring electromagnetic transients in power systems is a challenging task. Fast front transients caused by lightning events are especially dangerous, and improved knowledge about them is essential for better protection design. The development of measuring systems for such phenomenon is important. This paper is dedicated to the development of a measuring system for lightning and line surge arrester currents. Modern electronic tools and equipment, as well as cutting-edge communication and information technologies, constitute the foundation of the proposed system. This includes the most recent models of acquisition units and GPS devices that are now available on the market, as well as communication networks including 4 G, 5 G, and WiFi. Software and hardware components of the system are described. The paper presents laboratory tests conceived to prove that the system operates correctly and provides accurate results. The measurements are compared to EMTP and MATLAB simulations. Both are in agreement.

Mitigation of Lightning-Induced Transient Effects on a Hybrid Photovoltaic–Wind System Based on Lightning Protection Standards

Installing surge protection devices in a hybrid photovoltaic (PV)–wind system is essential to guarantee the survival of the system’s components. If the surge arresters are connected without taking into account the recommendations given by standards, the equipment to be protected might be damaged despite the energy coordination of the arresters. In this study, nonlinear surge protective devices (SPDs) are designed for a multi-MW hybrid system based on lightning protection standards with optimised threat level ratings to investigate the mitigation of lightning transients to an acceptable level. The system is implemented using Power System Computer-Aided Design for Electromagnetic Transients including Direct Current (PSCAD/EMTDC) software. It comprises a 2 MW PV farm, a 2 MW wind farm, and a backup energy storage system (ESS), which are all connected to a 132 kV grid via a step-up transformer and a transmission line. The results were obtained at critical system nodes for two standard lightning current surges, i.e., 1/10 µs and 10/350 µs, considering two lightning strike point scenarios with and without a lightning protection system (LPS). The simulation results showed that the connected SPDs could successfully limit the transient overvoltage in the system to an acceptable level. The analysis in this work is crucial for designing, operating, and maintaining a hybrid PV–wind system. It can help to find the potential vulnerability areas within such a system and implement appropriate protection measures since there is no available lightning standard for such systems. Additionally, it assists the system operators in increasing the uptime and dependability of their RE systems, limiting expensive downtime and environmental effects while optimising energy output. Based on the results obtained, recommendations were made for lightning protection developers.

MANA Formulation Based Load Flow Solution for DC Distribution Networks

This paper presents an efficient load-flow (LF) solution method for direct current distribution networks (DC-DNs). The principles of this method are based on the modified-augmented-nodal-analysis (MANA) formulation and Newton-Raphson (NR) algorithm. The guaranteed convergence and quadratic convergence conditions are also formulated using Kantorovich’s theorem. The modified IEEE 33 bus test feeder is simulated to test the proposed method and compare its performance with Laplacian Matrix based LF methods, Holomorphic Embedding LF method (HE-LFM) and classical Gauss-Seidel (GS) solution. Apart from the comparisons with these numerical methods the accuracy of the proposed method is also validated with Electromagnetic Transients (EMT) results. The proposed method offers much better convergence properties with a faster simulation speed.

Small Signal Stability of Phase Locked Loop Based Current-Controlled Inverter in 100% Inverter-Based System

Present-day inverter control mainly employs phase locked loop (PLL) based current-controlled strategies. With growing penetration of inverter-based resources in power systems, stability issues associated with inverter control have been reported in weak grid scenarios. A natural and fundamental question to answer is whether this instability is inherent to PLL based current-controlled strategies or it can be resolved with proper frequency and voltage control loop design. This paper addresses this question by analyzing the small signal stability of the current-controlled inverter in island and weak grid operation scenarios. Torque analysis, which is well known for synchronous machine stability analysis, is adapted to uncover the stability enhancement effect of properly designed and parameterized outer-loop controls. Different types of loads are considered and investigated in the study. Electromagnetic transient (EMT) simulations are conducted on a test network to validate the analytical results. The results from this study indicate that with appropriate outer-loop voltage and frequency control design, the PLL based current-controlled inverter can be small signal stable with high inverter penetration, even in a 100% inverter-based system.

Modeling of MMC-based STATCOM with embedded energy storage for the simulation of electromagnetic transients

Modeling of MMC-based STATCOM with embedded energy storage for the simulation of electromagnetic transients

Protection against sub-synchronous oscillations, a relay model

With increased integration of renewable energy resources, FACTs devices and series compensation, sub-synchronous oscillations (SSO) have become more common in electrical power systems in recent years. Specially designed relaying devices are often employed to detect and isolate harmful SSO conditions as when unconstrained, they can lead to widespread equipment damage and system instability. This paper presents design and implementation of a SSO relay model that can effectively extract sub-synchronous components in system measurements to quickly detect SSO conditions. Dependability and security of the developed relay model are validated using electro-magnetic transient (EMT) type simulations. In addition, performance of the developed relay model is compared against a commercial (physical) SSO relay. Obtained results demonstrate the effectiveness of the implemented relay model in detecting SSO and protecting electrical power systems against SSO conditions.

An investigation of electromagnetic transient characteristics on a practical 500 kV submarine cable system

This paper performs an investigation on electromagnetic transients for a practical 500 kV cable system. The system consists of 500 kV overhead lines, submarine and underground cables. In order to study the insulation coordination of the cable system, the transient simulations are performed using EMTP. The modal propagation constants of submarine cable are also investigated. Moreover, the cable series and shunt parameters are calculated using the newly developed Line/Cable Data Module in EMTP. The voltage and current characteristics of the cable system in steady-state, and for switching, fault and lightning transients, are studied. The transient overvoltage levels are also compared with requirements of insulation coordination in local standards. The work shown in this paper could provide a reference for the insulation design of 500 kV cable system.

High-frequency transformer winding model with adequate protection

High local electric field intensity in transformer windings originating from transient signals is one of the reasons for transformer failures. Due to the integration of renewable energy sources into the power grids and the increased number of transients, the likelihood of transformer catastrophic failure increases accordingly. Therefore, to ensure the reliable performance of transformers and associated power networks studying their behavior during these events is required. Accordingly, there is a need for accurate modeling of transformer windings capable of simulating electromagnetic transients. Using these models, it is possible to identify frequencies that can be dangerous to the transformer windings and to study different protection schemes. This paper aims to find an accurate analytical model of transformer winding validated by experimental measurements and to study the performance of the R-L protection device during the transient phenomena. The protection device is designed based on the winding model to introduce an impedance comparable to that of the transformer winding at critical frequencies where voltage amplification in the winding is significant. This approach ensures enhanced protection against potential transformer damage to the transformer. By using this protection scheme, the high inter-turn voltage originating from transient signals may be mitigated. At the same time, it does not affect the grid's performance during normal conditions.

Modeling of a capacitive voltage transformer for evaluation of transient response in conformity with the IEC 61869-5 Standard

This paper presents the implementation of a nonlinear model of a Capacitive Voltage Transformer (CVT) to evaluate the transient response in conformity with the international standard IEC 61869-5. The work is divided into three main steps: electrical tests to measure the CVT parameters and frequency response; implementation of linear mathematical modeling and an optimization algorithm to estimate unmeasured parameters; and implementation of nonlinear modeling in a simulation program for electromagnetic transients. First, the requirements of the IEC standard about the transient response of CVT are presented. Then, some important aspects of CVT modeling are discussed. Afterward, a linear model of a CVT is used to estimate the parameter not measured in the laboratory. Then, a nonlinear model is implemented in ATP. The model is validated in the time domain by comparing the simulation results with some signals measured in the laboratory. Finally, simulations of the transient response tests are made following the IEC 61869-5. The results show that the model developed in this work is reliable and can be used for the simulation of ferroresonance and transient response tests following the IEC 61869-5 when no laboratory structure is available.

Small signal analysis of a grid-forming modular multilevel converter with a novel virtual synchronous generator control

This paper introduces a grid forming (GFM) control method – detailed synchronous machine emulation virtual synchronous generator (VSG). The proposed method makes a voltage source converter exactly emulate a synchronous generator (SG), using a current source interface. The precise emulation of an SG gives tighter control over overcurrent and improved transient damping. Electromagnetic Transients (EMT) simulation is used to demonstrate the operation, and small signal model is used to assess the stability performance. Small signal analysis shows that the resulting VSG operates stably, and oscillatory modes can be damped by appropriate optimization of the virtual damping windings resistances.

Performance evaluation of communication fabrics for offline parallel electromagnetic transient simulation based on MPI

Offline electromagnetic transient (EMT) simulation is a very time-consuming activity for large-scale and complex power systems. Hydro-Québec (HQ) is involved in the development of EMT simulation tools, one of which can operate both in real-time (RT) and offline. This software heavily relies on parallel processing to achieve high-level performance. However, the offline mode is currently limited as it targets only single system image computers. As the offline mode uses the Message Passing Interface (MPI) standard to implement its parallel processing, porting the offline mode to PC clusters is the logical step to increase the offline simulation capabilities of HQ EMT simulation software.This paper evaluates the performance of different communication fabrics for the execution of offline EMT simulation operating in parallel with MPI. The performance metrics used for this evaluation are first discussed. The evaluated communication fabrics are then presented and tested with an offline simulation of the HQ power transmission system.

An automatic grid partitioning technique of large grids based on CloudPSS

The rapid development of power electronics technology makes the traditional grid power generation, transmission, and consumption gradually show the trend of “power electronics”. With the increase in the number of power electronic converters, the accurate electromagnetic transient (EMT) simulation of model power electronic networks is under tremendous computational pressure. Aiming at solving the problem of slow calculation of large-scale power electronics simulation, scientists have widely used parallel computation of sub-networks to accelerate EMT simulation. This paper proposes an automatic grid partitioning algorithm for large power grids based on merging neighbor nodes with the basic principle of the transmission line decoupling (TLD) method. The algorithm can effectively reduce the communication time and the waiting time due to the uneven computational load during parallel simulation. Finally, the method is implemented in the CloudPSS platform with various scales of grids, and the test results show that the algorithm can realize the EMT simulation efficiently and accurately.

Dynamic Interactions between Parallel Grid-Forming Inverters in a Microgrid

The potential instability issues caused by the dynamic interactions between parallel grid-forming inverters are examined. The approach adopted for analysis is s-domain admittance-based eigenvalue and mode shape analysis. This admittance is based on a five-node circuit diagram after the conversion of each electric circuit element and inverter control unit into impedance models. Eigenvalue analysis results show that unstable resonance modes may exist due to the interactions of two parallel inverters. Impacts of transmission line length, the converter control’s virtual impedance unit, and the voltage feed-forward unit are examined via the eigenvalue and mode shape analysis. The results show that the virtual impedance control has a negligible influence on the resonance while the voltage feed-forward unit stabilizes the resonance. Finally, the stability analysis is validated using electromagnetic transient (EMT) simulations.

DC grid load flow solution incorporating generic DC/DC converter topologies

This research proposes a load flow (LF) solver with DC/DC converter models for DC distribution. The solver is based on modified-augmented-nodal-analysis (MANA) formulation and is implemented with the Newton–Raphson (NR) algorithm. The conditions to guarantee the convergence range of the MANA are demonstrated with Kantorovich’s theorem. The proposed formulation is generic and flexible, allowing it to accommodate any arbitrary DC grid configuration. In addition, the formulation is extendable due to MANA’s modular structure, which enables the incorporation of any device without changing the prior formulation. Instead of bus power injections, the summation of line flows and their associated derivatives are used when considering connections with various kinds of buses equipped with various converters. The proposed method is implemented in MATLAB and tested on the modified IEEE 33 bus distribution test feeder. Electromagnetic Transient (EMT) simulations confirmed the accuracy of the proposed method. Moreover, the results are also compared with the recently proposed efficient Laplacian Matrix (eLM) based method. Results suggest that the proposed method is robust and offers superior convergence characteristics with a faster simulation speed.

A new stationary frame multi-input multi-output EMT-level frequency scanning method for inverter based resources

Impedance-based stability analysis (IBSA) is an effective method to identify subsynchronous interaction (SSI) problem between the inverter-based resources (IBRs) and series compensated or weakly tied AC grids. The electromagnetic transient (EMT) level positive sequence and dq-frame frequency scanning methods (p-scan and dq-scan, respectively) are used to obtain the sequence single-input single-output (SISO) and dq multi-input multi-output (MIMO) impedance of IBRs, respectively. The dq MIMO impedance usage in IBSA provides more accurate results compared to the sequence SISO impedance. This paper proposes an EMT-level αβ-frame frequency scanning method (αβ-scan) to obtain the αβ MIMO impedance and its usage in IBSA. The αβ-scan requires significantly less time compared to dq-scan for the convergence of MIMO IBR impedance representation and offers similar accuracy with dq-scan in IBSA. The accuracy of the proposed αβ MIMO IBSA is validated by comparing with dq MIMO IBSA and EMT simulations on series capacitor SSI cases with different type IBRs (Doubly-fed induction generator (DFIG)-based wind park (WP) and full-scale converter (FSC)-based WP). This paper also uses a multivariable structure function(MSF)-based method for the first time in IBSA of SSI to achieve Bode plot-based analysis for providing better visualized presentation of resonance frequency and stability margins compared to generalized Nyquist criterion.