Companion Circuits Research Articles

Circuit Model for Nth-Order Filtering Wire Antenna, Parameter Extraction, and Radiation Prediction

This article proposes a general circuit model for a thin wire antenna and a generalized approach to design an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N$</tex-math> </inline-formula> th-order parallel coupled wire antenna with its companion circuit model. Frequency-variant <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$</tex-math> </inline-formula> -inverters are involved in the new equivalent circuit to describe the frequency-variant radiation effect of the antenna. The design procedure starts with an initial prototype developed from a synthesized arrow coupling matrix, and then, its companion circuit is constructed accordingly. All the circuit parameters associated with the prototype can be extracted from EM models using space mapping technology. Iterative tuning is employed in the EM and circuit model, such that the final response satisfies the given specifications. An analytic method based on the circuit model is proposed to predict the radiation performance of the antenna. It is the first time ever that this type of filtering antenna has been designed and predicted quantitatively by using its circuit model, and the tuning of the antenna structure can also be guided by its circuit model. The proposed method offers a deterministic way for optimally designing an arbitrary-order filtering wire antenna with proper frequency characteristics.

An Automatable Approach for Small-Signal Stability Analysis of Power Electronic-Based Power Systems Using EMT Companion Circuits

The increasing presence of power electronic (PE) controlled devices in power systems has widened the bandwidth of transients to be studied for grid stability. While these transients are normally studied using time-domain simulation (TDS), wide bandwidth linear time-invariant (LTI) state-space models are a useful complement to TDS for diagnostics, controller design and parametric analysis. A general automatable method to compute an LTI sampled-data model of a PE-based circuit is presented in this paper. The proposed method is based on the techniques employed in electro-magnetic-transient (EMT) programs to perform TDS of PE-based circuits. The method uses the building blocks of EMT nodal formulation such as conductance matrix of companion circuit and its LU factors computed during TDS, interpolation and chatter elimination corrections, and EMT model of the firing angle control system. The method yields a small-signal LTI sampled-data model which is amenable to eigenanalysis and is illustrated using simple PE-based circuits such as a buck converter and a grid-connected STATCOM with closed-loop control.

A Testing Tool for Converter-Dominated Power System: Stochastic Electromagnetic Transient Simulation

To investigate the impact of uncertain variability and provide a rigorous testing environment for converter-dominated power systems, this article develops a testing tool called stochastic electromagnetic transient simulation. The tool is derived from the stochastic differential equation (SDE) representing the stochastic process of parameter migration. By inheriting the principle of companion circuit, the dynamic companion circuits of the lumped elements with parameter migration are further established. Combined with the analysis of the numerical stability in discrete simulation as well as the stability of the continuous system with parameter migration, a numerical algorithm that is compatible with the electromagnetic transients program (EMTP) framework is designed, as well as a C program package. The verification results on a grid-connected three-phase two-level rectifier and a two-terminal dc distribution system demonstrate that the developed tool can simulate the parameter migrations and the stimulated system dynamic process simultaneously, which can also be used to efficiently reflect the real performance of various control subsystems and their coordination in extreme cases.

A Comparative Study of Electromagnetic Transient Simulations using Companion Circuits, and Descriptor State-space Equations

This paper investigates an alternative method for EMT simulation of power networks, which uses Descriptor State-space Equations (DSE) to represent the dynamical equations of the circuit. An automated procedure to formulate the DSEs directly from the circuit's netlist is presented. Once formulated, the DSEs can be discretized using the trapezoidal integration method, and subsequently used for EMT simulations. This approach is compared with the widely used Companion Circuit (CC) approach. Advantages and disadvantages of each approach are discussed. Finally, a procedure for interfacing a DSE-based formulation with a CC-based EMT simulator is also presented. This procedure enables interfacing of arbitrary power networks with a commercial CC-based EMT simulation package and can also be used to speed up the simulation using parallel processing.

A Method of Low-Cost Pure-Digital GPS Disciplined Clock for Improving Frequency Accuracy and Steering Frequency Through TAF-DPS Frequency Synthesizer

One of the key characteristics of modern devices is time-awareness, which demands frequency source of good accuracy, precision, and stability. Unfortunately, all high-quality sources are expensive and bulky. An alternative is to add a companion clocking circuit to the primary source for performing frequency compensation in real time, under the guidance of a good time or frequency reference. The companion circuit aims at counteracting the primary source's systematic error and environment-induced variations. In this work, a frequency synthesizer having the features of small frequency granularity and fast frequency switching is adopted as such companion circuit. It functions as a tuning tool for periodically adjusting device's output frequency under the supervision of 1 PPS signal locked to global positioning system (GPS). This clock disciplining method can also be used for steering output frequency away from the specified value and toward a user-defined target. The main focus of this method is on improving frequency accuracy. The key advantage of the proposed method is low-cost and high-accessibility. It provides a new perspective, or devises a new instrument, for dealing with the sophisticated task of real-time frequency compensation. Our primary goal is to significantly simplify the engineering effort of this task without sacrificing the quality of clock signal noticeably. An field-programmable gate array (FPGA)-based system is created to demonstrate its capability of frequency compensation and steering. Further, 20 such systems are used to study the precision of a multi-node organization, as an example of using this instrument as a syntonization tool. The handy implementation on FPGA illustrates the advantage of DIY (do it yourself), making this method conveniently applicable for a variety of user scenarios.

FPGA-Based Submicrosecond-Level Real-Time Simulation of Solid-State Transformer With a Switching Frequency of 50 kHz

The switching frequency of power electronic devices has become much higher than before, which brings great challenges to real-time simulators. The small time step in high switching frequency simulations remarkably increases the difficulty to satisfy the real-time requirement. This article realizes the accurate real-time simulation of a solid-state transformer (SST) with a switching frequency of 50 kHz at the time step of 250 ns on a field-programmable gate array (FPGA)-based platform. The hybrid companion circuit modeling method and the compact-electromagnetic transient program (EMTP) algorithm are proposed in this article to make sure that the simulation loop can complete in less than 1 μs. The hybrid companion circuit modeling method can avoid too many digits used in representing simulation variables. The compact-EMTP algorithm is designed by combining the sequential computation tasks of the traditional EMTP to fully utilize the parallelized hardware structure of the FPGA. Besides, a circuit partition method is adopted to further parallelize the circuit solution of the SST circuit. In these ways, the simulation loop of the SST can be completed in 38 clock cycles (about 237.5 ns). The simulation results show that the real-time simulation waveforms are almost consistent with those of the off-line simulation software. Besides, the hardware-in-the-loop (HIL) simulation can also be performed on this platform to test the control functions of the SST.

Efficient Estimation and Characteristic Analysis of Short-Circuit Currents for MMC-MTDC Grids

Short-circuit current calculation and its characteristic analysis are the foundation of selecting circuit breakers and designing protection systems. First, a companion circuit-based method is presented to fast calculate the short-circuit current of asymmetric bipolar modular multilevel converter-based multiterminal direct current (MMC-MTDC) grids. With the reduction of the whole MTDC grid into an equivalent RLC circuit, the short-circuit current of the grid is efficiently and accurately solved by companion circuit method instead of the numerical integration. In addition to the efficiency, the proposed method can readily adapt to various types of MTDC grids and all kinds of dc faults. Second, unique short-circuit current characteristics of a bipolar MTDC grid following different types of dc faults are theoretically analyzed. A fault type discrimination method is then proposed for bipolar MMC-MTDC grids with dedicated metallic return. Finally, intensive numerical results of two MTDC grids validate the accuracy, adaptability, and efficiency of the presented dc grid short-circuit current calculation method as well as the correctness of the short-circuit current characteristic analyses.

Accurate and Efficient Estimation of Short-Circuit Current for MTDC Grids Considering MMC Control

DC short-circuit current calculation for the modular multilevel converter based multi-terminal direct current (MMC-MTDC) grid is critical and fundamental in equipment selection and protection setting. The existing MTDC grid short-circuit current calculation methods suffer from low efficiency, poor adaptability, and inflexibility. To address these issues, this paper proposes an efficient and general companion circuit-based method to estimate the short-circuit currents of asymmetric bipolar MTDC grids. First, an MMC is equivalent to an RLC series circuit in parallel with a time-dependent controlled current source. The equivalent model considers not only the discharge currents of the sub-module capacitors but also the ac in-feed current determined by MMC controllers. Then, the equivalent model for a bipolar MTDC grid with the dedicated metallic return is established by combing the equivalent MMC model with the lumped model of the dc transmission lines. Next, the companion circuit method is employed to efficiently and readily solve the equivalent model of the dc grid to obtain post-fault branch currents and node voltages. Both theoretical analyses and intensive tests on the CIGRE benchmark MTDC grid and Zhangbei bipolar MTDC grid verify the improved accuracy, efficiency, adaptability, and flexibility of the presented method.

Modeling and simulation of large power system with inclusion of bipolar MTDC grid

This paper presents an electromechanical transient modeling and simulation method for large power system with inclusion of bipolar multi-terminal direct current (MTDC) grid. First, the dynamic model of a modular multilevel converter (MMC) is presented. The dynamic model of the bipolar DC grid is then established by using the companion circuit method. In particular, the inductances of DC lines are carefully modeled to ensure the simulation accuracy when a DC fault occurs. Second, the electromechanical transient simulation procedure for a power system with inclusion of an MTDC grid is presented. The AC and DC grids are solved alternately. Due to the difference between time constants of AC and DC grids, the multi-rate scheme is used to ensure the simulation efficiency. Third, the proposed method is employed to simulate a real-life large power system with inclusion of a bipolar MTDC grid. The simulation results validate the correctness and the effectiveness of the proposed method. Unique interaction characteristics between AC and DC grids are also revealed by the results.

Harmonic Modelling of the Wind Turbine Induction Generator for Dynamic Analysis of Power Quality

Given the increasing integration of wind-based generation systems into the electric grid, efforts have been made to deal with the problem of power quality associated with the intermittent nature of these systems. This paper presents a new modelling approach oriented towards harmonic distortion analysis of the induction machine for wind power applications. The model is developed using companion harmonic circuit modelling, which is a natural approach for analysis of the adverse effects of harmonic distortion in electric power systems, and represents an easier solution method than the well known dynamic harmonic domain, since it solves algebraic equations instead of state-space differential equations. The structure of the companion circuits simplifies both the formulation and solution for power systems with wind-based generation systems. This approach is especially useful for analysis of the harmonic interaction in transient and steady states between the wind power generator and the power system, whose interconnection is made through electronic converters. The proposed model allows us to compute the dynamics of the wind turbine, which are influenced by disturbances such as changes in the wind velocity, voltage fluctuations, electric waveform distortion, and mechanical vibrations, among other factors. Moreover, the cross-coupling between harmonic components at different frequencies is considered. The proposed model represents an integral framework of the electrical and mechanical subsystems of a wind turbine, allowing for analysis of the interactions between them, and understanding power quality degradation behaviour as well as causes and consequences, while also giving useful information on the field of simulation and control. To test the performance of the proposed model, a test power system is used to obtain the behaviour of a wind turbine induction generator in response to typical power quality disturbances, i.e., harmonic distortion, and voltage sags and swells. Then, the dynamics of the variables considering their harmonic interactions are analysed.

Companion harmonic circuit models for transient studies

This paper presents a methodology that combines the dynamic harmonic domain analysis and discrete companion circuit modeling resulting in a powerful analytic technique, called companion harmonic circuit modeling. This new approach provides a complete method for dynamic harmonic analysis of electric circuits, preserving the advantages of discrete companion circuit models and harmonic analysis, resulting in an accurate steady state initialization and transient analysis method. An illustrative electric system will be used to show power of the proposed technique.

Dynamic Harmonic Analysis of Transformers

This paper presents a methodology for steady-state and transient harmonic analysis in electrical networks, the methodology is applied to transformer harmonic analysis. The method is based on the use of dynamic harmonic domain (DHD) and companion circuit models. The dynamic harmonic domain is a natural approach for conducting dynamic and steady-state studies of the evolution of harmonics in electrical networks. On the other hand, the companion circuit models facilitate the transient analysis of large electrical networks. The model presented in this paper is developed to be used on transient harmonic studies of power systems.

Dynamic companion harmonic circuit models for analysis of power systems with embedded power electronics devices

In this paper a methodology that extends the dynamic harmonic domain (DHD) analysis of large networks is presented. The method combines DHD analysis and discrete companion circuit modeling resulting in a powerful analytic technique called dynamic companion harmonic circuit modeling. It provides for a complete dynamic harmonic analysis of the system while preserving the advantages of discrete companion circuit models. The methodology is illustrated by its application to a three-node power system, where reactive power compensation is achieved using a fixed-capacitor, thyristor-controlled reactor (FC-TCR) and its control system.

NUMERICAL STEADY-STATE ANALYSIS OF NONLINEAR ANALOG CIRCUITS DRIVEN BY MULTITONE SIGNALS

Widely-separated time scales appear in many electronic circuits, making traditional analysis difficult, even impossible, if the circuits are highly nonlinear. This paper presents a new version of the modified nodal method in two time variables for the analysis of the circuit with widely separated time scales. By applying this approach the differential algebraic equations (DAE) describing the nonlinear analog circuits driven by multitone signals are transformed into multitime partial differential equations (MPDEs). In order to solve MPDEs, associated resistive discrete equivalent circuits (companion circuits) for the dynamic circuit elements are used. The boundary conditions are detailed and simulation results are presented.

A COMPANION CIRCUIT MODEL OF INDUCTION MOTORS

ABSTRACT The theory of a companion circuit model of the induction motor is presented. The model comprises an independent current source in parallel with a constant resistance. Accuracy of problem solutions is the same as that obtained from conventional models, but the time of solution is much shorter. This stems from the combined consideration given to the problem formulation and its solution. A companion circuit model can include extra sets of machine coils such as those needed to represent deep-bar effects. Conventional motor models are adequate for single-machine, transient studies. It is for multi-machine studies that the companion circuit concept provides advantages for formulation and solution.