Quadrature-axis Reactance Research Articles

Performance analysis of a permanent magnet synchronous motor with dual stator windings

This paper presents the modelling and performance analysis of a line-start three-phase interior permanent magnet synchronous motor (IPMSM) with dual stator windings. The machine has two sets of windings, main and auxiliary windings. The main winding is connected to the supply while the auxiliary is connected to a balanced capacitor. The dynamic model equations are derived in the d-q rotor reference frame using the concept of winding function theory. The machine input impedance was construed from the steady-state equations, where the effects of capacitance on the performance of the motor were studied. An improved torque was obtained when a suitable capacitance was connected to the auxiliary winding. A point of good performance was established by enhancing its direct axis reactance and the quadrature axis reactance which depend on the size of the capacitor. It is shown that thenew configuration has better performance characteristics when compared with those of the traditional configuration in terms of output power, torque density and efficiency.

Dynamic Performance of a Hybrid Synchronous Machine with Ultra-High XD/XQ Ratio

This paper presents a hybrid synchronous machine with ultra-high XD/XQ ratio. A conventional synchronous machine has two components of output power; the excitation and the reluctance component. The reluctance power which depends on the saliency ratio (XD/XQ ) is negligible when compared with the excitation component. A hybrid machine with variable XD/XQ ratio has the capability of raising the reluctance component of the power to infinity theoretically. The stator frame of the hybrid machine is stacked with two identical cylindrical cores (A, B) that are magnetically isolated. A hybridised rotor; salient cum cylindrical is used. There are two windings on the stator core stacks identifiable as the main and control windings respectively which are electrically isolated but magnetically coupled. The main windings are connected in series across the two stacks (A and B) and the terminals connected to the utility supply for motor operation while for generator, the terminals feed the load busbar. The control windings are transposed in passing from one stack to the other and terminated across a balanced adjustable capacitor bank. It is shown that the quadrature axis reactance (XQ) of the hybrid machine can be adjusted from zero to infinity (0<=XQ<=inf.) theoretically by varying the balanced adjustable capacitor bank. The reluctance component of the output power of the machine which depends on the reactance ratio (XD/XQ ) is also seen to theoretically increase to infinity. The reluctance power is shown to be twice the excitation power when the capacitor of 800uf is connected to the control winding. Depending on the value of the capacitive reactance, the reluctance power can be made even ten times the excitation power.

Virtual laboratory to conduct slip test of synchronous machine

The educational system is presently undergoing a substantial change to improve the teaching-learning process of all engineering domains. This includes the utilization of user-friendly simulation tools as part of the laboratory for an enhanced practical experience on a virtual platform. Owing to the advantages of virtual experimentation, engineering laboratories are now preferably integrated with suitable simulation tools. This paper deals with the integration of simulation tools with undergraduate courses of electrical machinery. For this purpose, a simulation model was developed to conduct the slip test on a three phase synchronous machine on a virtual platform using MATLAB or Simulink for the determination of direct axis reactance Xd and quadrature axis reactance Xq . From the test results, a close relationship between the calculated value of synchronous reactance and rated parameters of the machine is observed, showing the acceptability and suitability of conducted test for the integration of virtual platform with laboratory session. Concept of virtual laboratory may be extended to undergraduate course of electrical machinery during teaching-learning process.

Steady – State Performance of Induction and Transfer Field Motors – A Comparison

This paper presents the steady–state performance comparison between polyphase induction motor and polyphase TF motor operating in the asynchronous mode. It is shown graphically that a p-pole TF motor in operation is similar to an induction motor with 2p poles and hence its synchronous speed is limited to one-half (ω/2) of that of an induction motor. Additionally the pull-out torque of TF motor is inferior to that of an induction motor of the same dimensions, being less than ¼ of that of an equivalent induction motor on account of its higher leakage reqactance and in particular, the quadrature axis reactance. http://dx.doi.org/10.4314/njt.v34i2.24

10.5937/zeint24-6717 = Method for indirect determination of turbogenerator parameters under operating condition

A new method for determining the operational saturated synchronous reactances (Xd,sat and Xq,sat) and the rotor angle (δ), under the normal operating condition, was presented in this paper. At the power station the voltages (U), active (P) and reactive power (Q) are recorded. It is necessary to fit the no load generator saturation curve with appropriate analytical function. The output results obtained by corresponding calculations includes values of Xd,sat, Xq,sat and power angle δ, that reflect the level of generator saturation. Procedure by proposed method is following: - first the synchronous reactance Xd,sat value is determined by no load saturation curve using the voltage behind from leakage reactance (Xℓ) value or the voltage behind Potier reactance (XP), then - quadrature-axis reactance (Xq,sat) and load angle (δ) are determined by corresponding per-unit equations that connects generator parameters and characteristics d-axis and q-axis. The proposed method was verified using reported case study of 500 MW generator [1], where are used, besides U, P, Q and E(if) curve, the recorded rotor load angle value δ at rated load. Obtained results by new method differ up to 1-2 % from results in [1] obtained by more complex procedure, i.e. (i) by method with direct measurement of power angle δ, and corresponding Xd,sat, Xq,sat values determined by indirect method, i.e. on the base by corresponding per-unit equations, and (ii) by the finite-element method, when Xd,sat, Xq,sat and power angle (δ) values are calculated. Obtained results proved that synchronous reactance Xd,sat values can be as much as 30% below unsaturated vales (Xd,unsat), and measured values Xq,sat can be up to 20 % below Xd,sat values. Based on obtained results the proposed method is verified for indirect measurement of synchronous turbine-generator parameters and characteristics under load condition.

Analysis for Impacts of Internal Impedance on the Load Characteristic of a Permanent Magnet Synchronous Generator

The load characteristic analysis of permanent magnet synchronous generator is presented. An internal impedance mathematic model of the generator was built with phasor analysis method for analyzing the relationship between exterior voltage characteristic or voltage regulation rate, active power and armature reactance. The research results demonstrated that the internal impedance of generator has both current and power factor angle negative feedback characteristic, which makes the voltage regulation rate be improved to a certain extent and the improved effect lying on both the direct-axis armature reactance under condition of an inductive load and the quadrature-axis armature reactance under resistive load. Additionally, an optimal range of the armature reactance being of less voltage regulation rate was determined according to numerical calculation and analysis. An experimental result based on the experimental measurement and data analysis of exterior voltage characteristic corresponds to the theoretical calculation demonstrated the correctness of the research model based upon the armature reaction analysis. Those can provide the theoretically guidance to the electromagnetic design of permanent magnet generator.

AC/DC Permanent Magnet Synchronous Generator Design and Research

This paper has designed and produced an ac/dc permanent magnet synchronous generator which used in ac/dc power system independent. The design of the motor and the basic properties of the motor is discussed in this paper. In order to reduce the voltage regulation of the permanent magnet generator, installation of a soft magnetic material in the generator permanent magnetic pole tail, by increasing the motor load quadrature axis reactance drop improves motor voltage regulation. A prototype is made and test analysis, the generator voltage regulation rate of small, high efficiency, and the simulation result is consistent with the basic design to achieve the requirements.

Steady-state performance of a line-start synchronous reluctance motor with capacitive assistance

This paper sets forth the steady-state performance analysis of a connection scheme that improves the power factor and torque with a lower magnetizing current for a line-start synchronous reluctance motor. The machine stator winding is split into two equal halves, one connected to the mains and the other connected to a balanced capacitor. Performance of the machine is improved if the capacitor value is such that the winding to which it connected operate at or very close to resonance in the d-axis. Current in both windings contributes positively to torque production and external control circuitry is not required. Steady-state equations arising from the d– q model gives a direct insight on the operating limits and how this capacitance aids the machines torque and power factor by boosting its direct axis reactance while the quadrature axis reactance remains fairly constant. An equivalent circuit is also deduced from the steady-state equations from which an explicit expression for input impedance of the new machine can be derived. Conditions for unity-power factor at varying load conditions are also examined. A comparison with conventional single-winding synchronous reluctance motor is given. Such comparison is fair because both machines have the same amount of copper and iron. Experimental results are provided to validate the analytical results.

Thermal Equivalent Short-Time Currents in Three-Phase Balanced Short Circuits

This letter presents the analytical calculation of the thermal equivalent currents occurring in three-phase balanced near-to-generator short circuits and having decaying ac components. The thermal equivalent currents are the squared root of the integral of the squared armature currents, whose equations are calculated considering a sudden symmetrical short circuit of an unloaded synchronous generator rotating at fixed speed. The relative differential equations have been simplified by omitting the terms containing the squared armature resistance and neglecting the resistances of the field and of the dampers windings. These expressions used for the currents depend on the angle /spl lambda/ between the axis of the phase A and the direct-axis in the instant of the short circuit and are valid also for salient pole generators, which have quadrature-axis and direct-axis subtransient reactances with different values.

Experimental determination of synchronous machine reactances from DC decay at standstill

Measurement of parameters of high-power synchronous machines from steady-state or transient AC operational tests requires a great deal of electrical power. This paper presents a new application of a floating-point analog-to-digital converter which is employed in a microcomputer-embedded system that implements a standstill time response method to measure synchronous machine parameters. Floating-point quantization of the stator current response of a locked-rotor synchronous machine to a step signal is used to find the direct-axis and quadrature-axis reactances. Compared to previous solutions, this testing technique is characterized by higher precision, while still reducing the required power and minimizing the testing time. Simulated and experimental results are finally presented to compare the precision of this system with current state-of-the-art solutions.

Predicting the performance of a permanent magnet synchronous motor by analytical and numerical methods

The performance of a permanent magnet (PM) motor is predicted by using both analytical and numerical methods. From the simple analytical calculations, the initial machine dimensions for more accurate numerical analysis can be obtained easily. The resulting expressions can also be used for calculating different machine parameters, such as direct and quadrature axis reactances or generated voltage. The numerical calculations are performed by the finite element method. The field equation and the circuit equations of the winding are combined and solved together. By utilizing the procedure presented, the performance of a designed PM motor can be predicted with good accuracy. >

A finite element technique for calculating the magnet sizes and inductances of permanent magnet machines

A method for calculating the magnet size, and the direct and quadrature axis reactances of permanent magnet synchronous machines, using the finite-element method is presented. In this method the machine is modeled by its equivalent d-q representation of armature MMF and the appropriate reactances are calculated from the magnetic energy in the magnetic field. This is in contrast to the conventional approach of using an abc phase current model, solving the model and then converting the resulting quantities to respective d-q-o quantities. The method is applied to a permanent magnet motor design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Analytical models for interior-type permanent magnet synchronous motors

Keen interest in the design of Permanent Magnet (P.M.) synchronous motors is being fuelled by continuing developments in permanent magnet material technology. The most recent of these developments has been in the introduction of Neodymium-Boron-Iron (N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</inf> BF <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</inf> ) with residual flux density of 1.23 T and energy product (BH <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</inf> ) of 320 kJ/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . However a continuing difficulty with the analysis of permanent magnet motors, irrespective of their magnet composition, is the prediction of the direct and quadrature axis reactances. This is particularly the case with motors having permanent magnets imbedded in the rotor iron below the cage winding. The purpose of this paper is to present equivalent circuit models for such interior-type P.M. motors and develop simple analytical expressions for the calculation of axis reactances. Computed reactances including saturation effects are presented along with experimental values for verification.

Iron saturation effects in PM AC motors

Iron saturation causes the lumped circuit parameters to vary with the point of operation. Experimental evidence shows that the field excitation voltage and the direct axis reactance are not affected significantly by the armature reaction. This can be attributed to the presence in the direct axis of the magnets whose thickness represents a large effective air gap. In the quadrature axis, instead, the contribution of the air gap to the reluctance is small. Therefore, the quadrature axis reactance depends strongly on both the quadrature and direct axis components of armature magnetomotive force. This suggests a simple, albeit approximate, approach for predicting the parameter variation with operating point. As a result, both the design and analysis of synchronous motors excited by permanent magnets (PM's) are facilitated.

Parameters and performance of a high-field permanent-magnet synchronous motor for variable-frequency operation

The paper studies the application of conventional two-axis machine theory to the performance analysis of modern permanent-magnet synchronous motors. A representative motor with radially-oriented samarium-cobalt magnets in a rotor of interior type is considered as an example. Full performance data are measured for the full 360° range of load angles at various supply frequencies. Performance computations using constant motor parameters show significant discrepancies when compared with measurements, particularly at low supply frequency. Detailed determinations of parameter values reveal an important variation of quadrature-axis reactance as a function of quadrature-axis current, owing to magnetic saturation on this axis. When this variation is included within the analysis, together with temperature variation of stator resistance, excellent correlation is shown in all respects.

Turbine-generator steady-state reactances

The variation of the steady-state axis reactances of a 500 MW generator with load and power factor has been obtained from measured load points. At rated power, the direct axis reactance can be as much as 30% below the unsaturated value, and measured values of quadrature-axis reactance can vary by 20% over a range of power factors. The finite-element method has been used successfully to simulate the same load points. In these calculations, the absence of experimental error, and the ability of the method to show distributions of flux and saturation, have allowed a clearer insight into the complex phenomena that cause reactance variation. On load, the rotor body carries field leakage flux on the d-axis, and mutual flux displaced from it. These fluxes act together to give a saturation pattern about an intermediate axis. Thus, when current acts on one axis (d or q), flux is produced on both axes, although the cross-axis effect is only about one-tenth of the self effect. Each operating point may be described by effective values for the three conventional reactances (xd, xq and xa) used in a normal phasor diagram, or by six more basic reactances (three self- and three cross-axis reactances), each of which is load dependent. The variation of these reactances with load angle, at 100% and 50% of rated power, has been calculated, and its significance is discussed.

Slotless-disc alternator with AC-side excitation

The paper examines a version of the double-disc alternator with AC-side excitation that uses a slotless stator. It is an interesting form of slotless machine because Gramme ring windings can be wound automatically on the strip-wound circular core and produce a mechanically secure unit. A basis for the design of this form of machine is described, and the main considerations which influence the choice of a suitable geometry are discussed. Experimental results demonstrate that the performance of the machine is satisfactory. Predictions of direct- and quadrature-axis reactances and full-load field current by standard synchronous machine methods are also adequate. A particular feature of the machine, the absence of stray loss in the solid rotor due to stator-slot permeance variations, is seen to be particularly beneficial. Eddy-current losses in the stator windings exposed to the main airgap field are examined and are shown to be relatively small but measurable. Methods of predicting these losses for round and rectangular conductors in both sinusoidal and uniform airgap fields are presented.

Disc-geometry homopolar synchronous machine

The paper presents the results of an experimental and theoretical investigation of a disc-geometry homopolar synchronous machine with field excitation on the primary side. The unlaminated mild-steel rotor contained no windings and was brushless. The prototype machine produced approximately 75 kW of mechanical output at 3000 rev/min, with a product of power factor and efficiency greater than 0.7. The construction of the stator core was unusual and incorporated both laminated and unlaminated portions. The magnetic circuit was also arranged to minimise the axial force between the stator and rotor. A novel rotor design which achieved a reduced quadrature-axis reactance is shown experimentally to be superior to the conventional homopolar rotor. A three-dimensional magnetostatic computer program `GFUN? is shown to predict closely the flux densities prevailing in the machine. The quadrature-axis reactances calculated from these results also agreed well with measurements. An analytical method of calculating the axial force in the machine is validated by comparison with experimental data. The method uses the principle of Maxwell's stresses, and is based on the two-axis model of the machine. Prediction of the steady-state synchronous performance of the machine is also shown to be possible, using the two-axis model, provided that the assumptions implicit in that model are valid for the operating conditions of the machine. However, it was found that the output of the machine could be improved by a substantial amount by producing a degree of saturation in the magnetic circuit by means of the field winding. Under these conditions, the output of the machine exceeded predictions.

Segmented-rotor disc motor

The steady-state synchronous behaviour of a large-airgap, single-sided segmented-rotor disc machine is investigated theoretically and experimentally. Two methods of calculating normal forces using Maxwell&apos;s stresses are described. Their predictions are compared with measured results. A two-axis model is shown to give acceptable results for large-airgap machines but the use of the harmonic airgap flux density is preferred for small airgaps. Equivalence is drawn between Maxwell stress and energy methods in an Appendix. Prediction of the synchronous performance of a prototype motor by existing methods of analysis is shown to be possible provided that an airgap fringe factor is included in calculation of the direct and quadrature axis reactances. Experimental and theoretical results for torque, current, power factor and efficiency are presented and compared. The pull-in capability of a reluctance motor was found to deteriorate when operated with a large airgap, and ways of overcoming this problem are suggested.

Concerning the design of inductor synchronous motors fed by current source inverters

An approach to the design of the inductor synchronous motor is presented based on two assumptions: The first is that iron saturation, rather than thermal stress, is the basic limitation on this machine. The second is that when fed by a current-source inverter, and under closed loop operation, selection of the operating angle Ψ (between the direct axis and the armature current maximum) is feasible. Under these conditions, it is shown that the near-equality of the direct and quadrature axis reactances, a special property of this machine despite its variable reluctance construction, makes it a simple matter to select an optimum value for Ψ for unity power factor designs. This choice is characterized by a sizeable reduction of the additive effects of the armature reaction on the air-gap flux density under the pole faces. In turn, this reduces saturation in the armature teeth, the most stressed part of the iron. In addition, at the same time, this choice of Ψ maximizes the thrust-per-unit-area, and hence, for a specified power output, tends to lead to a machine of minimum size.