Six-phase electrical machines are often found in special purpose applications, such as vehicular, ship, and aircraft power systems, and are now becoming considered in renewable energy generation. For design and analysis of such power systems, accurate and numerically efficient models are required for various transient simulation programs. Recently, a constant-parameter voltage-behind-reactance (CPVBR) model has been developed for magnetically linear six-phase synchronous machines as an alternative to the conventional qd0 and VBR machine models. In this paper, a saturable CPVBR model is presented for six-phase machines, which includes the main flux saturation and achieves magnetically decoupled and constant RL interfacing branches. The new magnetically decoupled CPVBR (DCPVBR) model has many advantages for implementation in commonly available simulation programs where it can be easily interfaced with inductive andor power-electronic circuit elements. The proposed DCPVBR model is demonstrated to have improved computational performance compared to the conventional qd0 and VBR models.

This paper presents a methodology based on the Discrete Time Fourier Series (DTFS) to solve electromagnetic transients in power systems with multiconductor transmission lines. The proposed methodology is based on the correct specification of the time and frequency windows. The time window is chosen with sufficient width to allow the time constants of the transients to decay to a small value and the frequency window width is determined by the maximum frequency of the transient. The proposed DTFS method is simpler to use than the numerical Laplace transform (NLT), which has been traditionally used for frequency-domain solutions of power system transients, and can achieve similar levels of accuracy without requiring user intervention to specify the value of the damping factor and filtering windows required in the NLT. The results from the DTFS are compared with results from the most-accepted frequencydependent transmission line models in the Electro-Magnetic Transients Program (EMTP): the fdLINE (JMARTI) model and the Universal Line Model (ULM) for asymmetrical double-circuit line configurations under unbalanced faults conditions.

Six-phase electrical machines have received significant attention in the literature due to their use in special purpose applications (e.g., aircraft, naval, and vehicular systems). Recently, such machines have also been considered for renewable energy systems including wind generators. Modeling of such machines in commonly available transient simulation programs is not straightforward, especially when the machine model is interfaced with external inductive network and/or power electronic converters. The available modeling approaches include the classical qd 0 model, the coupled-circuit-phase-domain and the voltage-behind-reactance (VBR) models (each having its interfacing challenges). This paper extends the prior research in this area and proposes a constant-parameter VBR model that has a very convenient constant RL-branch interfacing circuit (even for salient pole machines), which makes it simple to implement in most state-variable-based simulations programs. The presented computer studies demonstrate significant numerical advantages of the new model over the existing alternative models.

Six-phase synchronous machines are utilized in special applications, such as naval and aircraft power systems, due to lower power per-phase, less mechanical stress, and higher reliability compared to three-phase machines. The voltage behind-reactance (VBR) machine models offer advantages in transient simulation programs such as capability of interfacing with arbitrary networks without snubber circuits and reduced system matrix size, compared to conventional qd0 model and coupled circuit phase-domain model (CCPD). This paper presents a VBR model of a six-phase synchronous machine that considers stator mutual inductances and main flux saturation. Performance of the proposed saturable VBR model is investigated in a hybrid ac-dc generation system. Simulation results verify numerical advantages of the proposed model in terms of accuracy and simulation speed over the conventional CCPD and qd0 models.

Large electric networks typically exhibit variables that behave on differing time scales. However, most of the software used to simulate the dynamics of these systems uses the same integration step for the entire network, which is often a waste of computational time. The multirate implementation of the Multiarea Thévenin Equivalent (MATE) framework, that we will call MATE-MR, addresses this problem by dividing a system into subsystems and solving each subsystem with a different time step. MATE-MR is presented in this work with particular attention to the effect of combining different integration rules for representing the slow and fast subsystems and the coupling links. To show the effectiveness of the methodology, a simple HVDC system is tested using the MATE-MR solver. The errors introduced by the interaction among subsystems solved with different integration rules are assessed for convergence and stability. The paper concludes with specific recommendations in the application of MATE-MR for the interfacing of power system converters with the main transmission system network.

Six-phase synchronous machines have been used in special-purpose applications such naval and aircraft power systems, and are now being considered in renewable energy systems due to their advantages such as lower power per phase, less mechanical' stress, and higher reliability compared to three-phase machines. This paper is focused on techniques for modeling six-phase synchronous machines in transient simulation programs. Firstly, the qd0 model is presented, and a method for incorporating the main flux saturation is proposed. However, since in simulation programs, the qd0 model is interfaced as a current source, it creates interfacing challenges with power electronics devices and inductive networks. To alleviate the interfacing challenge, the already available coupled-circuit phase domain (CCPD) model is also considered. This paper presents a new voltage-behind-reactance (VBR) formulation that includes the stator mutual inductances and main flux saturation, while achieving direct interface with external circuit. The presented VBR model is verified in a single-phase to ground fault scenario while connected to an arbitrary six-phase network. The computer studies demonstrate the numerical advantages of the new model including simulation time and accuracy over the CCPD and the conventional qd0 models. (C) 2016 Elsevier B.V. All rights reserved.

The objective of this paper is to provide a clear derivation of the Multi-Area Thévenin Equivalent Concept (MATE) including current- and voltage-dependent sources. The links concept in MATE is advantageous in representing branches connecting subsystems. MATE deviates from Diakoptics and from the Modified Nodal Analysis (MNA) methods in the way it is solved, by manipulating the submatrices in a form that preserves the individuality of the internal subsystems while solving their interdependences at the level of Thévenin Equivalents. The generalization presented in this paper expands the link branch equations to dependent, coupled, linear or nonlinear relations, thus resulting in unsymmetrical matrices. Its significance occurs when complex control systems and power system equations are simultaneously solved in an Electromagnetic Transients Program (EMTP). In this case, exact results can be achieved with less computational effort for power system dynamics studies. A test case with simulation results illustrates the main modelling concepts.

Wind power generation with permanent magnet synchronous machines (PMs) has been made possible using power electronic converters. With the increasing use of such systems, the numerically efficient modeling and simulation are of critical importance. As an alternative to traditional qd models, the coupled-circuit phase-domain (CCPD) and voltage-behind-reactance (VBR) models have been recently proposed to achieve advantageous numerical properties. Constant parameter VBR (CPVBR) models has also been presented to avoid having the variable inductance matrix that is present in CCPD and VBR models in case of salient rotor machines. This paper improves the CPVBR model using the auxiliary rotor winding to achieve better accuracy when the machine in connected to power electronic converters. The new model is shown to possess very good accuracy and advantages over alternative existing models.

Six-phase machines and the challenge of interfacing them with power electronics devices and inductive networks have always been an interesting topic of research. Coupled Circuit Phase Domain (CCPD) model of the machine has been an alternative to the conventional qd0 equivalent circuit to address the machine interfacing issue. This paper presents another suitable alternative in the form of a Voltage-Behind-Reactance (VBR) model of the machine. Similar to the CCPD model, the VBR model can also be interfaced with any kind of network without using any snubber circuits. At the same time The VBR model achieves better numerical efficiency compared with the CCPD model due to reduced size of the system matrices. The machine model is simulated in a single-phase to ground fault scenario while being connected to a 6 phase grid. The presented model also considers machine mutual leakage inductances which are shown to have considerable effects on the simulation results.

-This paper presents comparative solutions of different algorithms to the problem of numerical oscillations, which are caused by the trapezoidal integration rule, used by EMTP-based programs. These numerical oscillations emerge mostly from the abrupt variation of the voltage between the terminals of a capacitor, or from the abrupt current change in inductors, or even when non-linear elements, with piece-wise linearized models swap among linear regions. The importance of this review work stands on the exact understanding of the numerical oscillations problem and the evaluation of different methods proposed to solve this problem. Indeed, several approaches have been developed, but not all of them are really effective and only someones have been implemented in public or commercial software to eliminate numerical oscillations.

Representation of synchronous machines using constant-parameter voltage-behind-reactance (VBR) formulations improves accuracy and numerical efficiency of power systems transient simulation programs. This paper extends the VBR representation to the rotor circuit and presents two new formulations that achieve direct constant-parameter interfacing of the rotor and stator terminals with arbitrary external networks. In the first model, the entire machine is represented by constant RL branches that have algebraic coupling among the circuit variables. In the second model, all damper windings are implemented in state-space form to increase the numerical efficiency, while the stator and field windings are provided as constant-parameter circuits. The proposed models are validated against the commonly used and some state-of-the-art alternative models using a single machine with a simplified ac excitation system. Computer studies demonstrate the improved accuracy and efficiency of the proposed models when external rotor circuitry is considered.

This paper presents a general algorithm to calculate an optimal time step size and a maximum simulation time for EMTP-based programs. This is of particular importance for new users of EMTP-based programs, since the user is responsible for setting up these parameters before running a simulation case. The selection of the time step size affects the precision of the simulation. The time step size depends on the maximum frequency expected in the phenomena, which is normally unknown, a priori. A robust algorithm is presented here based on all the input data given for the circuit under simulation. The proposed calculation process is based on single- or multi-phase uncoupled or coupled circuits, with lumped or distributed parameters. Simulations are given demonstrating the effectiveness of the proposed rules. A future challenge will be the creation of a methodology capable of adapting the time step size dynamically.

The possibility of leveraging the data provided by smart meters to understand the load characteristics is studied in this paper. The loads are modeled as voltage-dependent elements to increase the accuracy of volt-VAR optimization (VVO) techniques for distribution systems. VVO techniques are part of the distribution management system and may be used for purposes such as loss reduction, voltage profile improvement, and conservation voltage reduction. A deterministic framework is proposed that formulates the VVO problem as a mixed-integer quadratically constrained programming problem, which is solved efficiently using advanced branch-and-cut techniques. The proposed framework is capable of optimally controlling capacitor banks, voltage regulators, and under-load tap changers (ULTCs) for day-ahead operation planning. The results indicate that loss reductions of up to 40% and a total demand reduction of up to 4.8% are achievable under some loading conditions in a radial test system. The effect of the load voltage dependence is also demonstrated through analytical simulations.

This paper focuses on the backup generation units of the telecommunication power systems and presents a fast and accurate model of the alternators used in such systems. The presented model is faster and more accurate as compared to the models existing in the libraries of commonly-used simulation programs. The model is based on a recently developed constant-parameter voltage-behind-reactance (CP-VBR) formulation whose application with power electronic elements is verified in this paper. The formulation of this model is presented for implementation in different simulation programs. The simulation results show that the presented new model is very accurate (about 1% numerical error) for studies of dc backup generation system and is an order-of-magnitude faster than existing classical models. The new model can facilitate the design of ac-dc power systems.

This paper presents fundamental concepts associated with the method of Shifted Frequency Analysis (SFA) for modelling electric circuit transients at frequencies close to the fundamental rated power frequency (50Hz or 60Hz). In a Smart Grids scenario, where the inertia of the generating sources is much less than at the transmission system level, electric transients simulation tools like the Electromagnetic Transients Program - EMTP become particularly important to assess the impact of distributed generation and voltage and frequency dynamics. With SFA implemented in the EMTP, very accurate results can be achieved with relatively large time steps that can trace the envelopes of transient voltages and currents around the fundamental frequency. If required, instantaneous values can be obtained directly from the "dynamic phasor solution" obtained with SFA. This paper presents a rigorous mathematical derivation of SFA based on the Hilbert transform. Error analysis is performed in terms of the integration time step size and the width of the frequency band around the fundamental frequency. A test case illustrates the main modelling concepts.

Interfacing of ac electrical machine models in power system transient simulation programs is receiving increasing attention in the literature. Models based on the voltage-behind-reactance (VBR) formulation have been recently proposed to achieve a direct interface with external power networks. However, the rotor-position-dependent interfacing inductances due to dynamic saliency in synchronous machine models increase the computational cost of the overall system solution and limit the application of most VBR formulations. This paper presents new methods for elimination of dynamic saliency using continuous- and discrete-time approximation techniques to achieve explicit formulations. The proposed models have simple interfacing circuit consisting of decoupled constant-parameter RL branches. The new models are implemented in MATLAB/Simulink and the PLECS toolbox, and are shown to offer simple and easy-to-use interface, high accuracy, and numerical efficiency as compared to the existing models. The proposed models can find wide application in common state-variable-based transient simulation programs.

This paper presents the implementation of a constant-parameter voltage-behind-reactance (CP-VBR) synchronous machines model that can be directly interfaced in most state-variable-based transient simulation programs. The stator is interfaced using constant and decoupled RL branches, and the rotor equations are expressed in state-space form to facilitate their implementation. The proposed model accommodates salient or round rotor machines, and its implementation is shown in three popular MATLAB/Simulink toolboxes: SimPowerSystems, ASMG, and PLECS. The presented studies compare the efficiency and accuracy of the CP-VBR models with the classical qd0 model. It is demonstrated that the CP-VBR models are faster, have higher accuracy, and are easy to implement. Additionally, the limitations of each toolbox for the simulation of different scenarios are discussed. It is also noted that the built-in toolbox models do not include zero-sequence, which may limit their application and make them invalid for some studies.

Transient simulation programs, either nodal analysis-based (EMTP-like) or state-variable-based, are used very extensively for modeling and simulation of various power and energy systems with electrical machines. It has been shown in the literature that the method of interfacing machine models with the external electrical network plays an important role in numerical accuracy and computational performance of the overall simulation. This paper considers the state-variable-based simulation packages, and provides a constant parameter decoupled RL-branch equivalent circuit for interfacing the ac induction and synchronous machine models with the external electrical network. The proposed interfacing circuit is based on the voltage-behind-reactance (VBR) formulation which has been shown to have advantageous properties. For the synchronous machines, this paper describes both implicit and explicit (approximate) interfacing methods. The presented case studies demonstrate the advantages of using the proposed interfacing method over the traditional qd-models that are conventionally used in many simulation packages.

Traditional power-system dynamic simulation tools make a number of simplifying assumptions to speed up computations; thus, they can only capture snapshots of the system operation, ignoring the dynamics between states. This paper applies the shifted-frequency-analysis (SFA) theory to the Electromagnetic Transients Program (EMTP) simulator in order to efficiently obtain the time-domain simulation results in the neighborhood of the fundamental frequency without making quasi-steady-state or other simplifying assumptions. The SFA-based EMTP simulator can provide dynamic-phasor results that accurately trace the evolution of the system state in three-phase power systems. Dynamic phasors provide envelopes of the time-domain waveforms and can be accurately transformed back to instantaneous time values. Test cases have verified the usefulness of the SFA-based dynamic simulation method.

The electromagnetic transient programs (EMTP-like tools) are based on the nodal (or modified nodal) equations that enable an efficient numerical solution and, subsequently, fast time-domain simulations. The state-variable-based simulation programs, such as Simulink, are also used for studying the dynamics of electrical systems. Both the offline and real-time versions of these two types of simulation tools are widely used by the researchers and engineers in industry and academia to study the transient phenomena and dynamics in power systems with rotating electrical machines. This paper provides a summary of the interfacing techniques that are utilized to integrate the general-purpose models of electrical machines with the rest of the power system network for these studies. The interfacing methods are broadly classified as indirect and direct approaches. The paper also describes the numerical properties as well as limita- tions imposed by the interfacing of the commonly used machine models that should be considered when selecting the simulation parameters and assessing the final results.