Time-domain Transient Simulation Research Articles

Fast Detection of SSR for Wind Parks Connected to Series-Compensated Transmission Systems

The interactions between wind parks and the series-compensated transmission lines can bring about sub- or super-synchronous resonance (SSR) incidents which jeopardize the safe operation of the entire network. In practice, such incidents may emerge under various conditions as different types of wind turbines with various parameters can be deployed at several locations in the network. Hence, it is crucial to efficiently identify the conditions that lead to adverse interactions and their subsequent SSR incidents. This paper proposes a simulation-based method, namely disturb and scan (DaS), for fast and automated detection of SSR. The proposed technique uses small-scale disturbances in time-domain electromagnetic transient (EMT) simulations to perform spectral analysis along with positive-sequence impedance scans. Numerical results are presented and validated for benchmark systems that utilize type-III and type-IV wind turbines. The system operators can adopt the developed methodology to quickly assess the risks of SSR, evaluate conditions of instability, and improve their network protection and control schemes.

A Distribution Line Fault Location Estimation Algorithm Based on Electromagnetic Time-Reversal Method Calculated in the Finite Difference Time Domain

The distribution line is an important part of a power system. How to quickly eliminate faults is of great significance to improve the power supply reliability. Based on electromagnetic time-reversal (EMTR), this article proposes a fault location estimation algorithm calculated by the finite-difference time-domain (FDTD) method to solve two problems. One is the calculation efficiency of the fault current based method in the EMTR, and the other is the fault location accuracy of the EMTR-based method when the measurement device has a low sampling rate in the direct time. We first derived the FDTD updated equation of the node voltage, which is at the discontinuous point of the lossless single conductor transmission line. The algorithm obtains the fault current at any transverse branch of the distribution line through one-time simulation, which improves the calculation efficiency. Furthermore, considering the sampling rate of the transient signals, we analyzed the impact of the spectrum range of the transient signal, the interval of the guessed fault location, the length of the time-reversal window, the fault impedance, and the length of the line. The results showed that when the transient signal is measured at a high sampling rate (10 MHz), the proposed algorithm can be used to locate the fault with a minimum time-reversal window of 1 ms. When the sampling rate is as low as 100 kHz, the proposed algorithm can achieve accurate fault location estimation compared to the algorithm in the other time-domain electromagnetic transient simulation. The error of the proposed location algorithm is less than 100 m.

Fault Protection Considerations for MVDC Shipboard Power Systems Operating with Pulsed-Power Loads

Medium Voltage Direct Current (MVDC) power distribution architectures are of immense interest for various shipboard power applications due to their advantages over classical MVAC distribution systems with respect to power quality, power density, and efficiency. However, MVDC are far away from maturity when compared to MVAC with respect to fault detection and isolation. Currently, there are no standards available for applying MVDC protection systems in shipboard applications. Furthermore, due to the absence of zero crossings in DC waveforms and unique transient fault signatures, it is challenging to design effective protection system schemes to isolate faults via conventional protection systems. This paper investigates and analyses various types of shipboard MVDC dynamic fault behaviours and signatures under different DC bus disturbances such as: bus to ground, bus to bus to ground, and impact of Pulsed-Power Load (PPL) with and without faults on a shipboard MVDC distribution system. Furthermore, a communication-based fault detection and isolation system controller that improves upon a directional ac overcurrent relay protection system is proposed offering additional protection discrimination between faults and PPLs in MVDC systems. To validate the effectiveness of the proposed protection controller, different bus current disturbances are simulated within a time-domain electromagnetic transient simulation of a shipboard power system including a PPL system operating with different ramp rate profiles, pulse widths, peak powers, and fault locations

Stability Constraints on Practical Implementation of Parity-Time-Symmetric Electromagnetic Systems

Recently, several applications leveraging unconventional manipulation of electromagnetic radiation based on parity-time symmetry have been proposed in the literature. Typical examples include systems with unidirectional invisibility and asymmetric refraction. Such applications assume an inherent system stability and no occurrence of unbounded signal growth or unwanted self-oscillations. Here, a general instability issue of parity-time-symmetric systems is investigated, with particular emphasis on a recently proposed system based on resistive metasurfaces. Explicit closed-form stability criterion is derived, crosschecked and verified by both time-domain transient simulations and the measurements on an experimental demonstrator operating in a lower radiofrequency range. Results of this study lead to the conclusion that any parity-time-symmetric system is necessarily marginally stable. Finally, it is shown that such a marginally stable system may easily become unstable if not designed carefully.

Analytical Approach for Fast Frequency Response Control of VSC HVDC

The importance of the auxiliary control of power electronic devices such as HVDC and FACTs is growing owing to the increase in the generation capacity of renewable energy sources. This paper presents a temporary frequency support strategy using the electrostatic energy in voltage-sourced converter-type high-voltage direct current systems. An analytical derivation for selecting the optimal droop constant to improve the frequency nadir was established. The optimal droop constant was derived via system frequency response analysis by using the support termination time. Furthermore, the optimality of the support was computed using numerical equations. Modified outer control loops were implemented in the master controller to utilize the proposed method in voltage-sourced converter control. The effect of the fast frequency support control strategy was verified via a time-domain electromagnetic transient program simulation based on case studies. To examine the practical applicability of the proposed strategy, the parameter robustness was investigated by performing deviated system parameter simulations. The results validated the proposed strategy.

Resonance Stability Analysis of Large-Scale Wind Power Bases with Type-IV Wind Generators

To guarantee the reliable and efficient development of wind power generation, oscillation problems in large-scale wind power bases with Type-IV generators are investigated from the view of resonance stability in this paper. Firstly, the transfer characteristics of disturbances in Type-IV wind generators are analyzed to establish their impedance model, based on the balance principle of frequency components. Subsequently, considering the dynamic characteristics of the transmission network and the interaction among several wind farms, the resonance structure of a practical wind power base is analyzed based on the s-domain nodal admittance matrix method. Furthermore, the unstable mechanism of the resonance mode is further illustrated by the negative-resistance effect theory. Finally, the established impedance model of the Type-IV wind generator and the resonance structure analysis results of the wind power bases are verified through the time-domain electro-magnetic transient simulation in PSCAD/EMTDC. Case studies indicate that there is a certain resonance instability risk in large-scale wind power bases in a frequency range of 1–100 Hz, and the unstable resonance mode is strongly related to the negative-resistance effect and the capacitive effect of Type-IV wind generators.

Behavioral Modeling of Complex Magnetic Permeability With High-Order Debye Model and Equivalent Circuits

In this article, a systematic procedure to derive equivalent circuit networks accurately reproducing the frequency response of the input impedance of magnetic cores in a broad frequency range is presented. The proposed procedure foresees to represent the effective complex permeability spectra of a magnetic core (i.e., the permeability resulting from the superposition of intrinsic material properties and effects due to structural features of the core) by a high-order Debye series expansion, which is subsequently synthesized into suitable Foster and Cauer networks. Such networks can be implemented in any circuit simulator, and are particularly favorable for time-domain transient simulation since they can be easily combined with hysteresis models. Two nanocrystalline tape-wound cores and a commercial bulk current injection probe are used as test cases to prove the effectiveness of the proposed method both in terms of accuracy and ease of implementation.

Design and tests of a super real‐time simulation‐based power system real‐time decision‐making emergency control system

In many China's enterprise-owned power grids (EPGs), the frequently changing operation state and the poor reliability of some outdated facilities may lead to inaccuracy or even malfunctions of the traditional pre-decision-making emergency control systems, which have already caused several blackouts in EPGs. To solve this problem, a real-time decision-making emergency control system based on the detailed time-domain transient stability simulation is designed. Based on the trajectory characteristics of the stability restoration process of EPGs, the stability restoration criteria are proposed to significantly shorten the simulation time needed to judge the elimination of a certain stability problem. Fast decision-making algorithms for frequency instability, rotor angle instability and branch overload with relatively low computational cost are introduced. Control strategies can be determined within a specific time after faults are detected. The corresponding countermeasures are directly executed when the strategy is obtained. The system configuration is designed to be capable of dealing with complicated and unanticipated faults, such as cascading outages and unexpected grid splitting. The test results of a 31-node practical EPG show that the proposed algorithms and the system configuration are practical and efficient. This work is a meaningful exploration of the real-time decision-making emergency control system.

Optimized Frequency Scanning of Nonlinear Devices Applied to Subsynchronous Resonance Screening

Frequency scanning is a powerful and versatile approach for subsynchronous resonance (SSR) screening in power grids. Among different numerical and analytical frequency scanning techniques, the harmonic injection method is well suited for the scan of black-box models with active elements, such as in wind farms and solar plants. The results can be used for SSR risk assessment, in which accuracy performs a decisive role. The ideal situation for this method, which leads to the most accurate results, is to perform one simulation per single-frequency injection. However, for SSR studies with a wide range of frequencies and simulations with very small time steps (scale of μs), this comes at the expense of increased simulation time. This article proposes a technique to improve the accuracy of the harmonic injection method through the optimization of the crest factor while injecting all frequencies at one shot, therefore also reducing simulation time. The proposed technique was tested on a wind farm connected to a radial test case and on a portion of a Texas synthetic grid with multiple active elements, including two wind farms and a VSC-based STATCOM. The frequency scan results were benchmarked with both time-domain transient simulations and the ideal multiple single-frequency injection case and compared with other techniques. The results show that the proposed method is superior in accuracy when compared to the other techniques and is 11.71 times faster when compared to multiple single-frequency injections.

Grounding grids in electro-magnetic transient simulations with frequency-dependent equivalent circuit

The frequency behaviour of a grounding grid cannot be neglected in insulation coordination studies. This paper proposes a new approach, which consists of calculating the frequency behaviour of a grounding grid by means of a software which implements the electromagnetic theory, building a two-port component, whose internal admittances are defined as rational functions in the Laplace domain, and finally using this two-port component for time-domain fast transient simulations.

Frequency-Dependent Resistances and Inductances in Time-Domain Transient Simulations of Power Transformers

This paper presents the methodology and validation of high-frequency (HF) transformer simulations, which take into account the frequency dependence of the winding resistances and inductances. The parameters’ frequency dependence is approximated by curve fitting of the values computed by the finite element method (FEM) simulations in the frequency domain. After inverse Fourier transformation into the time domain, the convolution integrals are solved efficiently by the trapezoidal integration rule. The simulation results are validated using measurement data.

Crosstalk modeling in high-speed transmission lines by multilayer perceptron neural networks

Signal degradation due to crosstalk-related issues has become increasingly important particularly in high-speed signal transmissions. Conventional analysis of crosstalk requires a full electromagnetic modeling of the signal transmission path along with a time-domain transient simulation which is computationally demanding. In this work, we apply a multilayer perceptron neural network for crosstalk prediction in coupled transmission lines. The well-trained neural networks can be used to predict the time-domain crosstalk directly, thereby replacing complex circuit simulations. Numerical results show a high degree of generalization of the neural networks, which are able to produce accurate results and can be trained to include effects such as reflections and input mismatches.

Efficiently computing the electrical parameters of cables with arbitrary cross-sections using the method-of-moments

In a recent work, a proximity- and skin-effect aware formulation known as the surface-volume-surface electric field integral equation discretized with 2-D method-of-moments (MoM) was optimized to efficiently extract the frequency dependent series impedance matrix of cables with arbitrary shapes. However, it was only applied to sector-shaped and coaxial cables due to the constraints on computing the shunt admittance matrix using closed-form approximations. This work presents formulation, discretization, and optimization techniques, for fast computation of the shunt admittance matrix of arbitrary-shaped cables by discretizing the problem of the quasi-electrostatics using 2-D MoM. With the proposed MoM techniques and optimization strategies, it is possible to accurately compute all the electrical parameters of arbitrary-shaped cables required in electromagnetic transient programs (EMTP) using today's typical computer power and with reasonable computational times. This provides an efficient modeling tool for any desired cable design. Frequency domain solutions of the proposed technique are compared against the finite-element method as well as the classical approximate formulas available for pertinent cable models. The resulting time domain transient simulations in EMTP are also investigated.

Front-End Isolated Quasi-Z-Source DC–DC Converter Modules in Series for High-Power Photovoltaic Systems—Part II: Control, Dynamic Model, and Downscaled Verification

This paper is the continuation of Part I in which a quasi-Z-source modular cascaded converter (qZS-MCC), comprising front-end isolated qZS half-bridge dc–dc converter submodules (SMs), for dc integration of high-power photovoltaic (PV) systems is proposed. The qZS-MCC-based PV system features modular structure, high-voltage dc collection of PV power, simple control with a unified and constant duty cycle for the front-end isolation converter of all SMs, and low qZS impedance due to no double-line-frequency pulsating power. Here, control scheme of the qZS-MCC PV system integrated into the dc collection grid is investigated. Dynamic model of the system is established for controllers design and time-domain transient simulation. Experimental tests are carried out on the downscaled prototype as a proof-of-concept of the proposed control and modeling, demonstrating the validity of the proposed approaches.

Transient stability based dynamic security assessment indices

AbstractAs power systems become increasingly stability constrained, the need for dynamic security assessment (DSA) becomes important. However, the resources and technology required to achieve on-line DSA at reasonable cost for utility companies are not easily come by. Therefore, an offline method is needed to examine and screen all likely contingencies to determine those that may lead to instability. Some indices and techniques have been proposed to tackle this problem but are mostly for small disturbances which are not really threats when timely cleared. Some methods are based on evolutionary computation which comes with a lot of drawbacks as there is no guarantee of finding optimal solutions within a finite time and parameter tuning are mostly by trial-and-error. In this paper, a simpler approach to power system DSA indices is proposed using time domain transient stability analysis simulations. A conventional power system which synchronous machines are modeled with two-axis dynamic model, and modeled by...

Alleviation SSR and Low Frequency Power Oscillations in Series Compensated Transmission Line using SVC Supplementary Controllers

In this work, supplementary sub-synchronous damping controllers (SSDC) are proposed for damping sub-synchronous oscillations in power systems with series compensated transmission lines. Series compensation have extensively been used as effective means of increasing the power transfer capability of a transmission lines and improving transient stability limits of power systems. Series compensation with transmission lines may cause sub-synchronous resonance (SSR). The eigenvalue investigation tool is used to ascertain the existence of SSR. It is shown that the addition of supplementary controller is able to stabilize all unstable modes for T-network model. Eigenvalue investigation and time domain transient simulation of detailed nonlinear system are considered to investigate the performance of the controllers. The efficacies of the suggested supplementary controllers are compared on the IEEE first benchmark model for computer simulations of SSR by means of time domain simulation in Matlab/Simulink environment. Supplementary SSDC are considered in order to compare effectiveness of SSDC during higher loading in alleviating the small signal stability problem.

Unstable force analysis for induction motor eccentricity

The increasing popularity of motors in machinery trains has led to an intensified interest in the forces they produce that may influence machinery vibration. Motor design typically assumes a uniform air gap, however in practice all motors operate with the rotor slightly displaced from the motor centerline in what is referred to as an eccentric position. Rotor center eccentricity can cause a radially unbalanced magnetic field when the motor is operating. This will results in both a radial force pulling the motor further away from the center, and a tangential force which can induce a vibration stability problem. In this paper, a magnetic equivalent circuit MEC modeling method is proposed to calculate both the radial and tangential motor eccentric force. The treatment of tangential force determination is rarely addressed, but it is very important for rotordynamic vibration stability evaluation. The proposed model is also coupled with the motor electric circuit model to provide capability for transient vibration simulations. FEM is used to verify the MEC model. A parametric study is performed on the motor radial and tangential eccentric forces. Also a Jeffcott rotor model is used to study the influence of the motor eccentric force on mechanical vibration stability and nonlinear behavior. Furthermore, a stability criteria for the bearing damping is provided. The motor radial and tangential eccentric forces are both curved fitted to include their nonlinearity in time domain transient simulation for both a Jeffcott rotor model and a geared machinery train with coupled torsional-lateral motion. Nonlinear motions are observed, including limit cycles and bifurcation induced vibration amplitude jumps.

Piecewise Average-Value Model of PWM Converters With Applications to Large-Signal Transient Simulations

State-space average-value models (AVMs) of pulse width modulation converters are widely used in both small-signal frequency-domain analysis and large-signal time-domain transient simulations. This paper is focused on the latter category. The limitations of the traditional state-space AVM (T-AVM) are discussed. A piecewise state-space AVM, P-AVM, is proposed, which uses the actual duty ratio as the control input instead of the continuous duty ratio used by the T-AVM. In order to consider the effect of switching ripples, an approximate ripple function is obtained. An iterative algorithm is proposed for utilization of P-AVM and ripple function for large-signal time-domain transient simulations. A boost converter and a two-level three-phase ac–dc converter are used to validate the performance of the P-AVM in comparison with the T-AVM under large ripple and large disturbance conditions. The detailed models developed in PSCAD/EMTDC are used as benchmarks. Improvement in accuracy is demonstrated. The efficiency of the iterative algorithm is discussed. Experiments on a 50-kVA three-phase ac–dc converter are conducted to validate the proposed method.

A Fast Method for Generating Time-Varying Magnetic Field Patterns of Mid-Range Wireless Power Transfer Systems

Visualizing the magnetic flux paths for wireless power transfer systems enables researchers and engineers to understand the operations and design the geometrical dimensions of the practical systems. However, time-domain transient simulations of 3-D electromagnetic fields of complex wireless power transfer systems with multiple coil-resonators are extremely time-consuming. This paper describes a fast hybrid approach that combines the time-domain coupled circuit modeling and the magnetostatic analysis to form a fast time-domain analytical tool for studying complex wireless power transfer systems. The proposed methodology has been successfully applied to several wireless domino-resonator systems. For the first time, the time-varying magnetic flux variations of wireless power domino-resonator systems can be visualized in computer simulations.

Type-III Wind Power Plant Harmonic Emissions: Field Measurements and Aggregation Guidelines for Adequate Representation of Harmonics

Large wind power plants (WPPs) based on variable speed turbines produce harmonics and interharmonics of voltage and current. This paper presents some generic guidelines about resulting harmonics and interharmonics at the high voltage point of interconnection (POI) of a type-III WPP. These guidelines are supported by both field measurements and time-domain electromagnetic transient (EMT) simulations. Specific focus is placed on how these harmonics and interharmonics can be represented in EMT simulation using detailed and aggregated models of a WPP. First, a theoretical explanation of the origin of all frequencies produced by a type-III wind generator (WG) is presented. The results of field measurements from a large WPP are then reported and analyzed confirming the theory. Subsequently, the field measurements are compared to simulation results of a detailed EMT model of the entire WPP and differences are explained. Finally, aggregated models of the same WPP are established and the accuracy of these aggregated models is discussed in light of the specific need of time-domain EMT studies that require adequate representation of harmonics.