Transient Simulation Algorithm Research Articles

Electromagnetic Transient Simulation Algorithm for Nonlinear Elements Based on Rosenbrock Numerical Integration Method

Electromagnetic Transient Simulation Algorithm for Nonlinear Elements Based on Rosenbrock Numerical Integration Method

A Waveform Relaxation Solver for Transient Simulation of Large-Scale Nonlinearly Loaded Shielding Structures

This article introduces an algorithm for transient simulation of electromagnetic structures loaded by lumped nonlinear devices. The reference application is energy-selective shielding, which adopts clipping devices uniformly spread along shield apertures to achieve a shielding effectiveness that increases with the power of the incident field, thereby blocking high-power interference while allowing low-power communication. Transient simulation of such structures poses a number of challenges, related to their large-scale and low-loss nature. In this work, we propose a waveform relaxation (WR) scheme based on decoupling the linear electromagnetic structure from its nonlinear terminations. In a preprocessing stage, the electromagnetic subsystem is characterized in the frequency domain and converted into a behavioral rational macromodel. Transient simulation is performed by refining estimates of the port signals through iterations. The proposed scheme combines a time partitioning approach with an inexact Newton–Krylov solver. This combination provides fast convergence also in those cases where standard WR schemes fail due to a strong mismatch at the decoupling sections. Numerical results on several test cases of increasing complexity with up to 1024 ports show that the proposed approach proves as reliable as HSPICE in terms of accuracy, with a speedup ranging from one to three orders of magnitude.

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Multiscale modeling and simulation methods for electromagnetic and multiphysics problems

Efficient transient thermal analysis based on spectral element time domain method with curvilinear hexahedrons

AbstractIn this paper, a three‐dimensional transient thermal simulation algorithm based on spectral element method is proposed. This algorithm uses distorted hexahedron for mesh generation, which not only keeps the high efficiency of hexahedron element calculation, but also improves the flexibility of mesh generation. It supports efficient forward difference and unconditionally stable backward difference in time step. Through practical examples and comparison with commercial software, the reliability and stability of the algorithm are verified, and it has obvious advantages in memory consumption and computing efficiency.

Fast emergency control strategy calculation based on dynamic equivalence and integral sensitivity

To simplify the transient stability analysis of a large-scale power system and realize real-time emergency control, a fast transient stability simulation algorithm based on real-time dynamic equivalence is proposed. Generator models are grouped and aggregated according to a fast numerical integration. A fast calculation method of the admittance matrix is then proposed to calculate the parameters of an equivalent system, and numerical integration is performed using the obtained equivalent system. Then, based on integral sensitivity, a new fast emergency control strategy is proposed for the equivalent system. The final emergency control strategy is obtained by mapping the control strategy for the equivalent system back to the original system. The results of a simulation on an East China Power System that includes 496 generators and 5075 buses show that the suggested algorithm can output an accurate transient stability simulation result and form an effective emergency control strategy. The proposed algorithm is much faster than the existing solutions and has the potential to be used for online pre-decision.

Stability of Algorithms for Electro-Magnetic-Transient Simulation of Networks With Switches and Non-Linear Inductors

This paper extends the analysis of the stability of electromagnetic transient simulation algorithms to non-linear systems with switching elements and non-linear inductor branches. A theoretical analysis based on common quadratic Lyapunov function theory is used to investigate the stability of numerical algorithms for the simulation of lumped strictly passive switched circuits (LSPSC). It is proved that only when certain fundamental physical properties, i.e., passivity and invariance of Lyapunov energy function, are satisfied, the widely used trapezoidal method results in stable simulations of such networks for any time-step size. This is different from the simulation of linear time invariant systems where any real-world stable system has a stable simulation if an A-stable integration method (e.g., trapezoidal rule) is used. Subsequently, it is shown that the problem of simulating a piecewise linear inductor can be equivalent to simulating a LSPSC; and ergo its simulation with the trapezoidal rule is also stable.

Parallel Algorithm for Transient Stability Simulation Based on Sherman-Morrison Formula

Parallel computing is an effective approach to transient stability real-time simulation of large-scale power system. In this paper, a new parallel algorithm for power system transient stability simulation is proposed by combining Gauss method and the Sherman-Morrison formula. The algorithm adopts the Gauss method to convert the differential-algebraic equations into a set of nonlinear algebraic equations by multi-stages discretization, while the algebraic system is solved using rigorous Newton method. On this basis, the whole Jacobian matrix involved in Newton method is split to a block diagonal matrix and a block constant coefficients matrix according to s time points, and then based on the block diagonal matrix, the computing tasks at s time points are fully decoupled through the extended Sherman-Morrison matrix inverse formula. The proposed algorithm preserves the good convergence of rigorous Newton method and meanwhile has a high degree of parallelism both in time and in space.

Parallel Simulation of Power Systems Transient Stability Based on Implicit Runge–Kutta Methods and W-transformation

This paper presents a novel parallel algorithm for power systems transient stability simulation based on fully implicit Runge–Kutta (IRK) method. The s-stage IRK method is used to convert the differential-algebraic system simultaneously at s different time points into a set of non-linear algebraic equations, and the algebraic system is then solved by Newton's method. By the use of the matrix factorization technique, the solution of the linear equations involved in Newton's process is divided into two parts: the first part is decoupled at s different time points, thus it is fully parallelizable in time, and the second part is solved by preconditioned generalized minimal residual method (GMRES) method, while a new preconditioning method has been proposed by using the W-transformation and double-parameters method. For test, the proposed algorithm is implemented on multiple-graphics processing units (GPUs) computing platform. The results show that the proposed algorithm is accurate and has good convergence. Moreover, the parallel algorithm implemented on multiple-GPUs computing platform achieves high parallel efficiency.

Power System Transient Stability Analysis Using Hybrid Model Based on the Finite Element Method

This paper presents a simple, but very powerful, numerical algorithm for the power system transient stability simulation. The aim of this paper is to fill the gap between the Transient Stability Programs (TSP) and the Electromagnetic Transient Programs (EMTP) by developing a new simulation tool based on the finite element (FE) representation of the power system element. The proposed hybrid model based on the Finite Element Method (FEM) allows us to avoid disadvantages of TSP comparing to EMTP that leads to the simulation of the electromechanical transients in a more accurate and efficient way. In order to show the principles of the proposed method in details, the proposed numerical method has been tested and compared to the solutions obtained by the well known and established EMTP simulation tool where a very good correlation has been demonstrated.

Interfacing an EMT‐type modular multilevel converter HVDC model in transient stability simulation

This study proposes a hybrid electromechanical and electro-magnetic transient (EMT) simulation algorithm, which interfaces the EMT-type modular multilevel converter (MMC) high-voltage direction current (HVDC) model into transient stability simulation. The proposed hybrid simulation algorithm offers high fidelity simulation results for the fast transient phenomenon of the MMC HVDC using the EMT program (EMTP). At the same time, the hybrid simulation algorithm utilises the transient stability program (TSP) to represent a large external AC network connected to the MMC HVDC. Thus, the proposed hybrid simulator combines the advantages of the TSP and EMTP simulations and offers accurate and efficient solutions for the integrated AC and HVDC systems. A case study of MMC HVDC system connected to 10-generator 39-bus New England AC System is simulated using hybrid and full-EMTP simulations in PSCAD/EMTDC. The simulation results demonstrate the proposed hybrid simulator produces accurate simulation results compared to the full-EMTP solutions.

A New Three-Phase Three-Winding Transformer Electromagnetic Transient Model

This paper firstly points out a defect of the damping trapezoidal method in electromagnetic transient simulation algorithm. The backward Euler method is recommended to use. Then, a new three-phase three-winding transformer model which could consider ratio and connection group feature is put forward. Compared with PSCAD, it is obtained the proposed model is accurate and reliable. In view of the implicit trapezoidal method with considerable accuracy and good numerical stability, the electromagnetic transient program mostly uses this method. But when the grid topology changes, non- state variables abrupt at same time, the implicit trapezoidal method calculates the equivalent current source of the abrupt time which is based on the abrupt non-state variable's value; this will result in numerical oscillation (1, 2). Obviously this oscillation is unreasonable. There are always two ways to eliminate this numerical oscillation which are backward Euler method (3-5) and the damping trapezoidal method (6). The former is that the implicit trapezoidal method has been using when the network topology remains unchanged; and the backward Euler method is used when the network changes, then cut back to the implicit trapezoidal method. As this method avoids the abrupt non-state variable values, and only uses non-abrupt state variable's value, it could solve the problem of numerical oscillation, but its programming is slightly more complex. The damping trapezoidal method takes the numerical calculation by mixing the implicit trapezoidal method and backward Euler method together from start to end, which is regardless of the grid topology whether changed, so it is easy to program. As to three-phase three-winding transformer model, paper (2) considered the three-winding transformer magnetizing slip alone, so it can not consider the transformer connection group. The transformer model of paper (7) is based on the controlled current source model which could consider the connection group feature and the ratio. This paper presents a new kind three-phase three-winding transformer electromagnetic transient model which takes into account the ratio and connection group feature. The transformer is taken as a coupling circuit of multi-slip series resistance and inductance. The connection group feature is achieved by the relationship of transformer's winding connection, and the ratio is simulated by the matrix of relationship of winding voltage/current and terminal voltage/current. This paper firstly points out a serious defect of damping trapezoidal method in the electromagnetic transient simulation algorithm, and the backward Euler method is recommended. Then a new three-phase three-winding transformer model is proposed which could consider the ratio and connection group feature.

Real-time electromagnetic transient simulation algorithm for integrated power systems based on network level and component level parallelism

The analysis and simulation of power system are becoming more and more challenging as the complexity of system topology and components has been increased. In this paper, a hybrid parallel algorithm is proposed for the real-time electromagnetic transient simulation (EMTS) of integrated power systems containing multiphase machines. The proposed algorithm is composed of a novel network partition method called component level parallelization and the Multi-Area Thevenin Equivalent (MATE) method, which extends the flexibility of the network partition in parallel simulation. Moreover, several methods are developed to enhance the efficiency of the communication and computation. Power systems with up to 410 single-phase electrical nodes and 336 switches are simulated in a time step of 50 μs to validate the proposed algorithm.

Feasibility Study on Online DSA Through Distributed Time Domain Simulations in WAN

As power systems become more closely interconnected and are deregulated, multi-area united online dynamic security assessment (DSA) is highly demanded. In this paper, a distributed framework for carrying out multi-area united online DSA over a wide area network (WAN) is proposed. In this framework, different control centers take part in the computation in a distributed processing manner with only boundary conditions being exchanged. To make the distributed DSA feasible for online use, a high performance distributed transient simulation algorithm is presented. Moreover, the overall time cost of the multi-case distributed simulations is modeled by analogizing the influence of different computation and communication resources. Based on the theoretic model obtained, the optimal task scheduling strategy is studied for scanning multiple contingencies. A distributed simulation platform which can emulate the WAN communication environment is built up, and the standard IEEE 39-bus system and a real Chinese power system with 5422 buses are used as test systems. Results demonstrate that with current computing and communication techniques, distributed DSA can fully satisfy the requirements of online use.

Parallel and Scalable Transient Simulator for Power Grids via Waveform Relaxation (PTS-PWR)

This paper presents a fast algorithm for transient simulation of power grids in very large scale integration systems using waveform relaxation (WR) techniques. Novel partitioning methods and convergence accelerators are developed for fast convergence of WR iterations when applied to power grid networks. Unlike the direct solvers, the new method is highly parallelizable and scales well with the increasing number of CPUs, leading to significant speed-ups. Numerical examples are presented to demonstrate the validity and efficiency of the proposed method.

Nonlinear Steady State Solution for a Thermoelastic Sliding System Using Finite Element Method

ABSTRACT A two-dimensional finite element model is developed for determining the non-linear steady-state configuration of a two-dimensional thermoelastic system involving sliding in the plane with frictional heat generation. Above a certain critical speed, this causes the uniform pressure solution to be unstable and the final steady-state configuration involves regions of separation at the interface and associated temperature and displacement fields that migrate over the contacting bodies in the direction of sliding. A major challenge in the development of a suitable algorithm is to determine this migration speed by iteration to be able to use a reference frame in which the fields are stationary. The results of the algorithm were validated by comparison with the long-time behaviour of a previously published (but very time consuming) transient simulation algorithm.

Hybrid-model transient stability simulation using dynamic phasors based HVDC system model

A novel hybrid-model transient stability simulation algorithm for ac/dc power systems is suggested in this paper, where dynamic phasors theory is applied for HVDC transmission system modeling, and traditional electromechanical transient models are used for ac system. A detailed dynamic-phasors-based HVDC system model is derived first, and the algorithm for interface of the dc dynamic phasors model to ac network is proposed next. Computer simulation results show that the HVDC dynamic phasors model has very good accuracy as compared with its electromagnetic transient model; the test results from a 2-area ac/dc power system and a multi-infeed HVDC power system show clearly that the suggested interface algorithm works effectively in system transient stability analysis. The proposed hybrid-model simulation algorithm provides a new approach for dynamic simulation of large-scale ac/dc power systems.

A Fast Algorithm and Practical Considerations for Passive Macromodeling of Measured/Simulated Data

Passive macromodeling of high-speed package and interconnect modules characterized by measured/simulated data has generated immense interest during the recent years. This paper presents an efficient algorithm for transient simulation of interconnect networks characterized by measured/simulated data in the presence of other linear and nonlinear devices. A new set of linear constraints are proposed, which help in preserving the passivity of resulting macromodels. Examples are presented to demonstrate the validity and efficiency of the proposed algorithm.

The power grid transient simulation in linear time based on 3-D alternating-direction-implicit method

The rising power consumption and clock frequency of very large scale integration technology demand robust and stable power delivery. Extensive transient simulations on large-scale power delivery structures are required to analyze power delivery fluctuation caused by dynamic IR drop and Ldi/dt drop as well as package and on-chip resonance. In this paper, we develop a novel and efficient transient simulation algorithm for the power distribution networks. Our algorithm, three-dimensional (3-D) transmission-line-modeling alternating-direction-implicit (TLM-ADI) method, first models the power delivery structure as 3-D transmission line shunt-node structure and transfers those equations to the telegraph equation. Finally, we solve it by the alternating direction implicit method. The 3-D TLM-ADI method, with linear runtime and memory requirement, is also unconditionally stable, which ensures that the time steps are not limited by any stability requirement. Extensive numerical simulation results show that the proposed algorithm is not only over 300 000 times faster than SPICE but also extremely memory saving and accurate.

Power grid transient simulation in linear time based on transmission-line-modeling alternating-direction-implicit method

The soaring clocking frequency and integration density demand robust and stable power delivery to support tens of millions of transistors switching. To ensure the design quality of power delivery, extensive transient power grid simulations need to be performed during the design process. However, the traditional circuit simulation engines are not scaled well for the complexity of power delivery. As a result, it often takes a long runtime and huge memory requirement to simulate a medium-sized power grid circuit. In this paper, the authors develop and present a new efficient transient simulation algorithm for power distribution. The proposed. algorithm, transmission-line-modeling alternating-direction-implicit (TLM-ADI), first models the power delivery structure as transmission line mesh structure, then solves the transient modified nodal analysis matrices by the alternating-direction-implicit method. The proposed algorithm, with linear runtime and memory requirement, is also unconditionally stable which ensures that the time-step is not limited by any stability requirement. Extensive experimental, results show that the proposed algorithm is not only orders of magnitude faster than SPICE but also extremely memory saving and accurate.

Accurate transient simulation algorithm for high-speed interconnections

In this letter, we present a new accurate transient simulation algorithm for high-speed interconnection structures consisting of general uniform dispersive and lossy multiconductor transmission lines terminated in arbitrary loads. All ports of the interconnection structure are modeled as extended Thevenin models.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>