Phase Variable Model Research Articles

FE-based physical phase variable model of PM synchronous machines under stator winding short circuit faults

An FE-based physical phase variable model is proposed for PM machines under stator short-circuit faults. The parameters of the proposed model, inductances and back EMFs are determined using the FE-circuit coupled computation of the machine under the same type of fault. The parameters obtained include information on the fault location and the number of turns involved, in addition to the space harmonics and the effects of stator saturation. The FE-based phase variable model that has been developed is verified through comparison with the FE model. The significance of the work is that it introduces a feasible procedure to build a physically accurate and computationally fast phase variable model for PM machines under stator short-circuit fault conditions. Such a model is useful for the study of fault diagnosis and prognosis.

Finite-element-based nonlinear physical model of iron-core transformers for dynamic simulations

A finite-element (FE)-based transformer physical phase variable model is proposed. In this model, the effects of nonlinear magnetization on inductances are included by considering the inductance variations with the amplitude of the ac flux as well as its phase angle during a complete ac cycle. Such a consideration is represented by 2-D inductance tables. The magnetizing currents at various magnetization levels are used to calculate the inductances then build the table. The magnetizing currents are determined using circuit-coupled FE analysis of the transformer with sinusoidal voltage supplies. The structure of the inductance table is given and the procedure of inductance table lookup during dynamic simulation is provided. Simulink implementation of the FE-based transformer phase variable model is performed. The validity of the presented technique is verified through comparing the magnetizing current waveforms obtained from the FE-based phase variable model and those from an FE model. The significance of the proposed FE-based phase variable model is in its accuracy and its applicability for dynamic simulation of interconnected components in a power system

High frequency PM synchronous motor model determined by FE analysis

A high frequency phase variable model for PM synchronous motor is proposed. It is composed of a low frequency phase variable model with a high frequency winding branch connected in parallel. The winding branch considers the high frequency effects on the machine winding parameters namely resistance, inductance and capacitance. The resistance and inductance of each individual winding turn were calculated by time harmonic FE analysis. The self capacitance of each turn and the mutual capacitances between turns were evaluated by electrostatic FE analysis. Using these circuit parameters, a distributed-parameter winding circuit is formed. The Kron reduction technique is applied to the distributed-parameter winding circuit to obtain a lumped high frequency branch. The implementation is performed on a 2-hp PM synchronous motor and the simulation results show the validity of the proposed model. The originality of this work is that it provides a numerical tool for examining the machine design instead of experiments

Electric machine operational modeling utilizing coupled electromagnetic and electric drives simulations

PurposeThe purpose of this research is to develop new techniques for component physical modeling for the dynamic simulation of integrated power systems.Design/methodology/approachA FE‐based phase variable model is proposed so as to achieve fast and accurate simulation. Such a model is established based on the nonlinear transient FE analysis, in order to take into consideration the harmonic effects due to the nonlinear magnetization property, magnetic circuit geometry as well as other design variations.FindingsIn the FE‐based phase variable model, the inductances are described as functions of the phase angle and the magnitude of winding currents, the rotor position and other operational parameters. They are obtained from the transient FE solutions, stored in tables, and retrieved during the simulation. The FE‐based phase variable model is implemented in Simulink in two ways. The first is the equation‐based block and the second is the circuit component‐based block. The FE‐based phase variable models of various electrical components in the power system were studied. This includes various types of rotating machines and transformers. Examination and application examples show the correctness and effectiveness of the proposed operational modeling procedures.Originality/valueThe developed FE‐based physical phase variable model is as accurate as the full FE model with much faster simulation speed. It will benefit the dynamic simulation of integrated power system. This combination of physical modeling and integrated dynamic simulation is original and represents an added value to the state‐of‐the‐art in this field.

A phase variable model of brushless dc motors based on finite element analysis and its coupling with external circuits

This paper presents a fast and accurate brushless dc motor (BLDC) phase variable model for drive system simulations. The developed model was built based on nonlinear transient finite-element analysis to obtain the inductances, back electromotive force as well as the cogging torque. The model was implemented in a Simulink environment through the creation of an adjustable inductance component to account for the dependence of inductances on rotor position. Since no dq model for BLDC actually exists, the significance of this work is that it provides an accurate equivalent circuit model of BLDC motors for utilization in simulation environments. Using the developed model, the sensorless control and the torque ripple control issues were investigated and the simulation results show its practical effectiveness.

A novel sensorless control strategy of doubly fed induction motor and its examination with the physical modeling of machines

Available sensorless speed control strategy of doubly fed induction machines based on rotor flux linkage fails around the synchronous speed due to the inaccurate estimation of the rotor flux linkage. In order to solve this problem, an excitation-current-based speed/position estimation strategy is proposed. The corresponding speed regulation system is constructed. Using the nonlinear transient finite element solutions of the doubly fed induction machine, a physical phase variable motor model is developed. The speed regulation system is verified using the proposed machine model. Simulation results show that the novel sensorless speed control strategy works properly in the whole speed zone and provides good speed regulation performance.

Physical modeling of PM synchronous motors for integrated coupling with Machine drives

A physical phase variable model for permanent magnet synchronous motors is proposed. This model is initiated to pursue an accurate and fast motor model for integrated motor drive simulation. Since the full finite element (FE) model may be time consuming and the direct- and quadratic-axis (dq)-model is inaccurate, the proposed physical phase variable model eliminates these deficiencies. The proposed model is a circuit model with inductance, back electromotive force (EMF), and cogging torque calculated from nonliner transient FE solutions. The main characteristics of this model are that it is as accurate as the full FE model while giving fast computational results. The Simulink implementation of the proposed model is studied. Comparisons of the proposed model with the full FE model and the dq-model are performed. The results verify the validity of the proposed model and show its practical superiority in drives applications.

Phase-variable model of PM synchronous machines for integrated motor drives

In a phase-variable model of PM synchronous motors and its implementation in integrated motor drive simulations the stator winding inductances and the three-phase flux linkages contributed by permanent magnets are considered as rotor-position dependent. The first-mentioned is calculated by an energy perturbation method using FE solutions, the second is obtained through FE analysis without applying excitation currents. The cogging torque due to slotting is taken into account and is evaluated through FE analysis as well. The proposed phase-variable model is implemented in Simulink in two ways. One is component based, another is equation based. The rotor-position dependence of inductance, the flux linkage due to permanent magnets, and the cogging torque are utilised using a look-up table function. A 2-HP PM synchronous motor is used as an example to examine the model as well as the developed Simulink block. For comparison and verification, the d–q model and the full FE model of the same machine were built to verify the proposed model. The behaviour of these three models is investigated with a vector-control speed regulation system. Simulation results show that the phase-variable model provides the same performance as the full utilisation of FE models but with much faster simulation speed.

Analysis Of Heating And Losses In Generator Field Discharge Resistors And Generator Rotors Following Severe Disturbances On The Electrical Supply System

ABSTRACT The paper examines heating and losses in generator field discharge resistors and generator rotors following sustained stator-terminal and HV busbar L-L short circuits at full-load and no-load. Losses in generator rotors following L-L-L short-circuits on a weak line which is connected to the HV generator transformer busbar with clearance at fault current zeros where the generator either remains in synchronism or falls from synchronism, and following worst case malsynchronisation are also reviewed. Comparisons are made with negative sequence losses in solid generator rotors following these disturbances given by I2 2t computed from detailed analysis for both loaded and unloaded machines. The analysis uses a phase-variable model of a synchronous-generator with detailed and reduced damper representations to compute stator and rotor current following a severe electrical disturbance at either the machine terminals or at the HV unit transformer busbar. Simulations at full-load and no-load for a variety of assumptions and approximations, with connection of the field discharge resistor on tripping the main generator breaker are performed. The investigations are undertaken using data for a 660MW, 3000 rpm and a 500MW, 3600 rpm Machine.

Comparison of losses and heating in generator rotors following severe supply system disturbances

Losses and heating in rotors of large synchronous generators are examined following sustained stator-terminal and HV busbar line-to-line short-circuits at full load and no load, three-phase (L-L-L) short-circuits on a weak line connected to the HV generator transformer busbar with clearance at fault current zeros where the generator either remains in synchronism or falls from synchronism, and worst-case malsynchronization. Comparisons are made with negative sequence losses in solid generator rotors following these disturbances. The analysis uses a phase-variable model of a synchronous generator with detailed and reduced damper representations to compute stator and rotor current following a severe electrical disturbance at either the machine terminals or the HV unit transformer busbar. Simulations at full load and no load for a variety of assumptions and approximations, with connection of a field discharge resistor on tripping the main generator breaker, are performed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modeling, simulation, and analysis of permanent-magnet motor drives. II. The brushless DC motor drive

For pt.I see ibid., vol.25, no.2, p.265-73 (1989). The authors develop a phase variable model of the BDCM (brushless DC motor) and use it to examine the performance of a BDCM speed servo drive system when fed by hysteresis and pulsewidth-modulated (PWM) current controllers. Particular attention was paid to the motor large-signal and small-signal dynamics and motor torque pulsations. The simulation included the state-space model of the motor and speed controller and real-time model of the inverter switches. Every instance of a power device turning on or off was simulated to calculate the current oscillations and resulting torque pulsations. The results indicate that the small- and large-signal responses are very similar. This result is only true when the timing of the input phase currents with the back EMF (electromotive force) is correct. The large-signal and small-signal speed response is the same whether PWM or hysteresis current controllers are used. This is because, even though the torque pulsations may be different due to the use of different current controllers, the average value which determines the overall speed response is the same.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect of Load and Damper Modelling on Evaluation of Negative Sequence Capability of Large Generators

The paper examines negative sequence losses in solid generator rotors following sustained stator-terminal and HV system L-L short-circuits at full-load and no load with or without a connection to the grid supply. Components of stator current which give rise to rotor heating over the period of the transient are identified and effective intrinsic values ot I22 t for a range of system and machine parameters are discussed. The analysis uses a phase-variable model of a synchronous-generator with detailed and reduced damper representations to compute stator current following rated-voltage line-to-line disturbances on the supply. Simulations from full-load for a variety of system parameters with and without connection of a field discharge resistor on tripping of the generator breaker are performed. From the responses, components of stator current which give rise to rotor heating are isolated by Fourier analysis combined with symmetrical component analysis. These components are integrated over the period of the transient to give effective values of I22 t. Maximum supply-frequency components of stator current taking into account d.c. components have been assumed. Effective values of I22 t using detailed and reduced damper models in simulations with and without voltage regulator action are compared with values predicted by simpler calculations where no allowance is made for generator load or for the connection to the grid supply. A 500 MW, 3600 rpm and a 660 MW, 3000 rpm Machine are analysed.

Effect of Fault Clearing and Damper Modelling on Excitation and Decay of Vibrations in Generator Shafts Following Severe Disturbances on the System Supply

The paper examines the effect damper circuit modelling and the current interruption process has on amplitude and decay of torsional vibrations in turbine-generator shafts following severe supply network disturbances. A phase-variable model of a synchronous-generator with up to 2 direct-axis and 3 quadrature-axis dampers where fault current is cleared at fault current zeros is employed to calculate generator airgap torque which results from a severe disturbance on the electrical supply. Using airgap torque, effective amplitude of torque excitation acting on the generator rotor for each eigenfrequency is determined by Fourier analysis. Amplitude of torsional vibration at each shaft section for each modal frequency is then calculated. Shaft torque at each shaft location for each modal frequency is thereby deduced. These components, together with the steady-state component (and that due to rotor swing), are summed as absolute values for all modal frequencies to yield approximate peak torque at critical locations along the shaft following each disturbance. Approximate peak shaft torque estimated by frequency domain analysis is compared in some instances with peak torque predicted by solution of exact differential equations. Presented results illustrate amplitude of torque excitation and shaft torques as a function of fault clearing time for L-L-L and L-L high-voltage system short-circuits, and effect reactive power and system resistance has on damping predominant torsional vibrations in the shaft.

Developments in phase-variable modelling for thyristor-controlled reactive-power compensators

Of the different control objectives of reactive-power compensators based on thyristor-controlled reactors, the advances in modelling methods and computer simulation of the paper relate specifically to the mode of voltage-magnitude control in which each phase is controlled individually. For this control objective, a comprehensive analysis formulation is developed in phase-variable notation in a form which can directly be incorporated into Newton-Raphson network analysis in which each phase retains its separate identity. The main context of the development is that of the supply from transmission networks of loads of substantial imbalance between the separate phases. The analysis and evaluation facilities to which the developments of the paper can lead, provide means by which the response of compensators with individual phase-voltage-magnitude control functions can be investigated for the conditions of pronounced imbalance in steady-state primary system operation. Following the analysis derivations and the developments in phase-variable modelling for thyristor-controlled compensators, a representative design investigation is given in the paper in which phase-to-phase loads are supplied from a section of a 220 kV network. In this particular application, the effectiveness of individual phase-voltage-magnitude control in lowering operating imbalance is quantified.

SCR controlled induction machines: Transients and regeneration

An efficient method of transient performance analysis of three-phase SCR voltage controlled induction machines is presented based on phase-variable modelling. The induction machine is modelled in a three-phase stationary frame. Consideration is given to transition from motor to generator operation with the in-line thyristors present. Examples illustrate applications of the proposed method and the results obtained.

Phase-variable modelling of saturated reactor compensators with particular reference to long-distance transmission

Phase-variable modelling of saturated reactor compensators with particular reference to long-distance transmission

A New Approach to Dynamic Modeling and Transisent Analysis of SCR-Controlled Induction Motors

A dynamic model based on instantaneous symmetrical components theory is presented for purposes of transient analysis of thyristor-controlled three-phase induction motors. The distinct advantages of this model over the phase-variable model have been highlighted. In-line switching constraints are incorporated and the simulation of all operating modes is accomplished without reference to rotor position. Typical transient response patterns are presented using the new model and comparisons are made with similar results obtained by earlier methods.

Phase-variable primary-system modelling and solution methods in dynamic-response assessments of high-speed protection

Dynamic-response evaluations of high-speed primary-protection systems are assuming an increasing importance as protection measuring times are progressively reduced, and these require very considerable detail of representation, not only for protection systems, but for the primary transducers from which they operate, and for the section of the primary system protected. Within this composite simulation, it is the latter area, that of the primary system for which the protection system under investigation provides coverage, to which the paper is devoted. In particular, the paper develops a phase-variable analysis scheme for synchronous generation in a form that allows it to be used directly in conjunction with electromagnetic transient analysis for the network system interconnecting generation. This provides a rational and unified scheme of analysis which combines fast-solution properties with considerable flexibility in application.

Steady-state phase-variable model of the synchronous machine for use in 3-phase load-flow studies

The derivation of a steady-state phase-variable model of the synchronous machine is considered for the purpose of investigating the influence of machine saliency on the unbalanced behaviour of powersystem networks. The model is particularly relevant as a means of representing the salient-pole generators of important hydroelectric stations feeding large and remote load centres. Application of the model is also considered so that corresponding blocks of the system Jacobian matrix are formulated and used in a previously described Newton — Raphson algorithm to obtain 3-phase load flows. The results of computation illustrate that saliency is not an insignificant parameter amongst those which determine the extent and distribution of system unbalance.

Information pattern for linear discrete-time models with stochastic coefficients

A linear discrete-time system with constant coefficients has an information pattern that does not grow in complexity with time, an information state. This paper shows that a particular canonical form for such systems, the phase-variable model, retains this property when coefficients vary as Gaussian time series with rational spectra. The distribution of the output conditional on past data is normal, and its parameters, being functions of the information state, can be calculated in real time in a simple way. The property is fundamental for effective optimal control. A priori characteristics for the Gaussian time series must be specified, but a maximum likelihood method is proposed for estimating any unknown characteristics from a long sample of input-output data. Also, a parameter-free statistic is found for testing the validity of the phase-variable model in actual cases.