Characteristic of cylindrical-rotor synchronous generator

It has been observed that the values of the magnetizing reactances in both d- and q-axis are reduced significantly from their corresponding unsaturated values as a result of nonlinearities introduced by saturation under both steady-state and transient operations. In the round rotor synchronous machine, q-axis magnetic circuit saturates appreciably more than that along the d-axis because of the presence of the rotor teeth. In the second section, a new method to calculate the q-axis saturation characteristic from the existing d-axis saturation characteristic has been presented. We have next calculated the saturated values of the d- and q-axis self magnetizing reactances and mutual cross magnetizing reactances between the two orthogonal axes under the steady-state operation. Finally, the effect of saturation, particularly the effect of q-axis saturation, on the power system transient stability has been presented     

Steady-state magnetic circuit analysis of salient-pole synchronous machines considering cross-magnetization

A simple magnetic circuit of salient-pole synchronous machines is presented. A method for calculating steady-state electrical performances using the circuit is described. Magnetic saturation including the cross-magnetizing phenomenon is considered in the method. The saturated reactances, field currents, and load angles are calculated easily from the method without much computational effort as compared with the finite element method. Despite the simplicity of the magnetic circuit, the calculated reactances at various load conditions using the method are close to the measured and FEM values.     

Effect of saturation on the steady-state stability of a synchronousmachine connected to an infinite bus system

A synchronous machine model that includes the effect of the saturated reactances the cross-magnetizing phenomenon is presented. This model is used to study the steady-state stability of a synchronous machine connected to an infinite bus system. These studies show that the effect of saturation is noticeably large and depends mainly on the cross-magnetizing effect. The results obtained by this model are found to be in good agreement with those obtained from the experimental results     

Methods for determining the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis characteristics

For the accurate analysis of salient-pole synchronous machines using the two-axis frame models, the direct- (d-) and quadrature-axis (q-axis) saturation characteristics are needed. Usually, the d-axis saturation characteristics can be obtained easily by the conventional open-circuit test with the machines excited from their field winding. On the other hand, the q-axis saturation characteristics of synchronous machines cannot be measured applying simple, conventional methods, and thus, they are usually not available. In this paper, four different methods for calculating the q-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics are explored. In these methods, the q-axis saturation characteristics can be calculated from the readily available test data, namely the d-axis saturation characteristics and the d- and q-axis unsaturated magnetizing reactances. Finally, a comparison between these methods is made.     

Modeling and analysis of six-phase synchronous generator for stand-alone renewable energy generation

This paper presents a mathematical model of six-phase synchronous generator (SPSG) for analysis of its transient and dynamic behavior for stand-alone renewable energy generation in conjunction with a hydro power plant. In the analytical model, effect of common mutual leakage reactance between the two three-phase winding sets, and the mutual leakage coupling between d- and q-axis of the two stator windings have been considered. Paper also discusses the applicability of SPSG for supplying two individual loads by presenting the results of analytical and experimental study of transient and steady-state behavior under various operating conditions. It is shown that it can be used to supply two independent three-phase loads. While the interaction between the two windings is inevitable and variation of load at one winding set changes the operating conditions at the other winding, the situation is still satisfactory for a wide range of rural resistive loads.     

Determination of the parameters representing the cross-magnetizingeffect in saturated synchronous machines

This paper introduces the concept of the cross-magnetizing phenomenon in saturated synchronous machines (the magnetic coupling between the direct and quadrature-axis). The parameters which represent this cross-magnetizing effect are defined and techniques for determining these parameters are proposed. In these techniques, there is no need for an auxiliary winding in the q-axis of the machine and, thus, they can be applied to conventional synchronous machines. Experimental results which verify the accuracy of these techniques are presented     

Methods for determining the intermediate-axis saturation Characteristics of salient-pole synchronous Machines from the measured D-axis Characteristics

In the analysis of the steady-state performances of saturated synchronous machines using the classical two-axis (d- and q-axis) frame model, the accurate calculation of the machine performances depends to a large extent on their saturation conditions. However, the effect of saturation depends not only on the saturation level in the axis of the resultant machine ampere-turns (intermediate-axis) but also on the phase angle between the resultant ampere-turns and the resultant magnetic flux. This work presents four analytical methods for determining the intermediate-axis saturation characteristics of salient-pole synchronous machines from the measured d-axis saturation characteristics. The accuracies of these four methods have been verified by comparing the measured field currents and load angles of two laboratory salient-pole synchronous machines of different designs with those calculated using an innovated approach which uses the intermediate-axis saturation characteristics directly in the modeling of the saturated synchronous machines. Moreover, the calculated intermediate-axis saturation characteristics have been compared with the measurable ones in the case of one of these machines.     

Practical detailed model for generators

The Parks equation is currently used for mathematical expressions of the state of synchronous generators connected to power systems. The calculation results using the Parks equation, however, differ greatly from the results of measurement on the real generator when the Parks equation is applied to an event where the flux linking the generator undergoes a very large change as when the generator is suddenly disconnected from a load during normal operation. The difference between the field test result and the calculation result is larger for a turbogenerator with a solid iron rotor than for a salient synchronous machine. To deal with this problem, this paper introduces a mathematical expression of generating machines, which is an extension of the Parks equation and which is practically applicable to an event in which the flux within the generating unit changes sharply as when it experiences a load rejection. The newly introduced expression takes the following considerations: (1) a magnetic flux saturation coefficient k is applied to d- and q-axis; and (2) T'_q0 that corresponds to T'_d0 of d-axis is introduced to q-axis. A generator model incorporating the magnetic flux saturation coefficient k and another parameter T'_q0 has proved capable of providing a good simulation representing a load rejection whose calculation results coincide satisfactorily with the measurements of actual generators     

Finite-element calculation of leakage inductances of a saturated salient-pole synchronous machine with damper circuits

It is important to understand the relationship between leakage flux distributions and machine characteristics for better design of synchronous machines. This paper presents a calculation method for leakage inductances of saturated salient-pole machines with damper circuits. All leakage inductances are divided into the self-leakage, gap leakage, and winding-differential leakage inductances. The leakage inductances correspond directly to the leakage flux distributions in the machines. Cross-magnetizing inductances are also calculated. The method is applied to a 300-MVA class generator. The relationship between the winding distributions, flux distributions, saturation, and inductances is discussed. Weak magnetic influence of the damper circuits on the armature in the d-axis is quantitatively illustrated through values of the winding-differential leakage inductances. The cross-magnetizing inductances, except for the d-axis damper circuits, are relatively large. Variations of the armature self-leakage inductances with saturation are small, and variations of the field and damper self-leakage inductances are larger.     

IPM synchronous machine drive response to symmetrical and asymmetrical short circuit faults

A closed-form solution is presented for the steady-state response of interior permanent magnet (IPM) synchronous machines to symmetrical short circuits including the effects of q-axis magnetic saturation. Machine response to single-phase asymmetrical short circuits is also investigated. Experimental data are presented to verify predicted behavior for both types of short circuits. It is shown that single-phase asymmetrical short circuit faults produce more severe fault responses with high pulsating torque and a significant threat of rotor demagnetization. A control strategy that purposely transitions such faults into symmetrical three-phase short circuits can minimize the fault severity and associated demagnetization risks. Implications for the design of IPM machines with improved fault tolerance are discussed.     

Experimental study of the saturation and the cross-magnetizingphenomenon in saturated synchronous machines

The cross-magnetizing effect in both the d- and q-axis in a small salient-pole machine was measured. Two simple equations describing the cross-magnetizing effect in both axis directions are derived. An accurate saturation representation that includes the effect of both the machine-saturated reactances and the cross-magnetizing phenomena is also given. In addition to this, the modified phasor diagram and power/load angle relationship are obtained. The results of the machine output power obtained by this technique show a good agreement with those obtained from test. The saturation effect in changing the power/load angle curves is seen to be noticeably large and depends mainly upon the cross-magnetizing effect     

A finite element technique for calculating the magnet sizes andinductances 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     

Impact of dynamic cross-saturation on accuracy of saturatedsynchronous machine models

Cross-saturation effect in synchronous machines has been a subject of considerable attention. Inclusion of the cross-saturation in the machine model has two consequences. The first one, called here “steady-state cross-saturation”, consists of dependence of the steady-state d-q axis magnetizing inductances on the currents in both axes. The second one, termed here “dynamic cross-saturation”, is the existence of nonzero elements in the system matrix, that describe cross coupling between d- and q-axis. Dynamic cross-saturation appears in all the saturated machine models, regardless of the selected set of state-space variables, with the exception of the winding flux linkage state-space model. The aim of this paper is to compare behavior of various models when dynamic cross-saturation is neglected. It is shown that the impact of dynamic cross-saturation on accuracy depends on the selected set of state-space variables. In the majority of cases omission of dynamic cross-saturation leads to very inaccurate results. However, it is found that for one particular class of models, omission of dynamic cross-saturation has practically no impact on accuracy. These models therefore fully describe the complete saturation effect by means of only continuous variation of the d-q axis magnetizing inductances     

Analysis of leakage flux distributions in a salient-pole synchronous machine using finite elements

It is important to understand the relationship between iron core configurations and leakage flux distributions to get a better design of synchronous machines. This paper presents a method for calculating the steadyand transient-state leakage flux distributions in salient-pole synchronous machines. The method provides information on leakage flux distributions that cannot be obtained by terminal quantities. The method analyzes the leakage inductances that properly represent the corresponding leakage fluxes. They are calculated using the gap flux distributions by finite elements with magnetic saturation. The calculated leakage inductances of a synchronous machine under various loads are also shown and the relationship between the inductances and magnetic saturation is discussed.     

Measurement of the saturation characteristics in the quadrature axis of synchronous machines

For the accurate prediction of the performances of saturated synchronous machines, the saturation characteristics in both the direct and quadrature axes are needed. The d-axis saturation characteristic of a synchronous machine can be measured easily by the open-circuit test with the machine excited from its field winding. On the other hand, the q-axis saturation characteristic of a synchronous machine cannot be measured applying a similar easy, simple method and, as a result, these characteristics are usually not experimentally measured and are not available. In this paper, three possible experimental methods for determining the q-axis saturation characteristics of both cylindrical-rotor and salient-pole synchronous machines are presented. The merits and demerits of these experimental methods are discussed from the point of view of their complexity and their accuracy. Comparisons between the measured q-axis saturation characteristics obtained by these experimental methods are made for a cylindrical-rotor machine and two salient-pole machines. Moreover, the various sources of errors, which may affect the accuracy of determining the q-axis saturation characteristics by these methods, are investigated.     

On-line evaluation of a round rotor synchronous machine parameterset estimated from standstill time-domain data

This paper presents a method for identifying the best linear circuit model parameters of a three-phase, round rotor synchronous machine. Standstill time-domain test data and the maximum likelihood estimator are used to identify the values for the equivalent circuit models. The estimated models are validated against standstill data and an online test. A steady-state error adjustment procedure is introduced and the results are analyzed. The final dand q-axis model selections are based on the minimization of the cost function, the concept of parsimony and how well the models predict the online dynamics of the machine. Issues related to the necessity of the L_fld differential leakage inductance and the necessity of the Z_fe eddy current branch are also discussed     

Identification of synchronous machines parameters using broadbandexcitations

This paper describes a newly developed measurement and identification technique for synchronous machine parameters. The first part presents a technique to generate periodic broadband power signals with a controllable amplitude spectrum using a classic rectifier bridge. These signals are well suited to measure the frequency response function of large power systems using the fast Fourier transform. The broadband measurements are compared with the classical mono frequency measurements. The second part presents a frequency domain identification method taking into account the uncertainty on all the current and voltage measurements, and giving a confidence interval on the estimated synchronous machine parameters. As an illustration the d- and q-axis model of a 1.905 kVA/220 V micro-machine is identified     

Adaptive Dead-Time Compensation Strategy for Permanent Magnet Synchronous Motor Drive

This paper presents an adaptive dead-time compensation strategy to obtain fundamental phase voltage for inverter-fed vector-controlled permanent magnet synchronous motor drives. A phase dead-time compensation voltage (DTCV) to compensate the disturbance voltage due to undesirable characteristics of inverter, such as dead time, turn on/off time of switching devices, and on-voltages of switching devices and diode, is transformed into q-axis DTCV in the rotor reference frame. The relationship between q-axis DTCV and a dead-time compensation time (DTCT) is investigated. DTCT is identified online by using q-axis disturbance voltage, which is estimated by a disturbance observer. The amplitude of phase DTCV is adaptively determined according to the identified DTCT. The accuracy of identified DTCT is experimentally confirmed by calculating the mean absolute percentage error (MAPE) between calculated active power and measured one. MAPE for adaptive DTCT is within 5% at any operating point and is less than that for the fixed DTCT.     

Neural network based saturation model for round rotor synchronousgenerator

This paper presents an artificial neural network (ANN) based technique to model saturation for a round rotor synchronous generator. The effects of excitation level, rotor angle, and real power generation on generator saturation are included in the modeling process. To illustrate the technique, small excitation disturbance tests are conducted on a 7.5 kVA, 240 V, 60 Hz round rotor synchronous generator at various levels of excitation and loading. The small excitation disturbance responses are processed by a recursive maximum likelihood algorithm to yield estimates of mutual inductances L_ad and L _aq at each operating condition. By developing a suitable training pattern, variables representative of generator operating condition are mapped to mutual inductances L_ad and L_aq . The developed models are validated with measurements not used in the training process and with large disturbance responses     

A new method for determining the armature leakage reactance ofsynchronous machines

A method for determining the armature leakage reactance of synchronous machines is presented. In this method, the terminal voltage/armature current characteristic with the machine unloaded and unexcited is needed, together with the open-circuit characteristic of the machine. The armature leakage reactance is derived from these two curves using an iterative technique. The armature leakage reactances of five synchronous machines of different designs are obtained using this method. Their values are compared with those of the Potier reactance of these machines measured at various terminal voltages