Wound Rotor Doubly Fed Induction Machine with Radial Rotary Transformer

This paper shows a wound rotor doubly fed induction machine in which the typical brushes and slip-rings are substituted by rotary transformers. The advantages of rotary transformer usage, the doubly fed induction machine operation and the dimensioning of a radial rotary transformer are the main aspects presented in this study. The use of analytical equations is a very interesting resource for the development of industrial software for the calculation of this kind of device. Comparison between simulated and measured results shows the good approximation of the steady-state model with the reality of this equipment.


I. INTRODUCTION
The doubly fed induction machine is a useful motor for industrial application and a largely adopted generator in wind energy farms.Its speed and torque can be controlled by rheostats or frequency converter connected to the rotor winding, what allows the reduction of converter power just to a fraction of induction machine mechanical power, saving installation costs [1] - [7].
In this context, the benefits of the use of doubly fed induction machines are undeniable; nevertheless, to take advantages of them it is mandatory to provide electrical connection between the rotor winding and the rheostat or the frequency converter [1] - [8].
The most common way to access the rotor winding is by brushes and slip-rings.However, the mechanical contact between moving slip-rings and static brushes wears these components and involves high rate of maintenance.Powder generated by brushes wearing can be also prejudicial for motor insulation.Additionally, any fault on electrical contact can generate sparks, limiting this machine installation only to non-explosive environments [1] - [3].
The development of brushless technologies is very interesting for reducing maintenance costs and expanding the use of doubly fed induction machines to explosive atmospheres [1] - [8].
Many studies consider the use of two induction machines connected in cascade for obtaining Wound Rotor Doubly Fed Induction Machine with Radial Rotary Transformer Maurício Ruviaro, Fredemar Rüncos WEG Equipamentos Elétricos S.A. -Energia, Jaraguá do Sul -SC, Brazil mauricior@weg.net,fredemar@weg.netbrushless devices [4] - [8].This solution is effective from the point of view of eliminating brushes and slip-rings, but introduces the superposition of two different torque curve behaviors.The result is a device with anomalous torque vs. speed curve in which synchronous speed is determined by the combination of the number of poles of each machine [4], [5].Only the join of the induction machine with a device incapable to offer any resistance torque avoids any change on the typical shape of torque vs. speed curve [1].
Since the seventies, there are several studies with the aim of substituting brushes and slip-rings by contactless energy transfer systems, like, e.g., rotary transformers [9] - [18].Initially, these devices were developed concerning spacecrafts applications, where the lack of reliability and high rate of maintenance of brushes and slip-rings are totally undesirable [9].In [11], Papastergiou and Macpherson propose the rotary transformer as an alternative solution for contactless transfer of energy across the revolving frame of airborne electronic-scanning radar.In [17], Legranger et al. propose the replacement of gliding contacts of a wound rotor synchronous machine by a radial rotary transformer operating like a contactless transmission power system.Despite of some particularities, the majority of studies for rotary transformer involve applications where the transformer is submitted to frequencies of hundreds of Hz [9] - [18].
In  The rotary transformer allows the access to rotor circuit without any mechanical contact.By using an appropriate drive, it is possible to control the induction machine operation as motor or generator at almost any speed, except at synchronous rotation.
The solution presented in [1] - [3] is very convenient for systems that must generate voltages with constant frequency through variable speed devices, like wind turbines [4] - [8].

II. DOUBLY FED INDUCTION MACHINE OPERATION
The electrical connections for the use of converter in doubly fed induction machine operation are shown in Figure 2.This configuration allows controlling torque, speed, power factor and current of induction machine by a converter connected to the stator winding of the rotary transformer.Frequency converter controls the machine acting on amplitude, frequency and phase of the voltage applied in stator winding of rotary transformer [1] - [5].
and rotary transformer parameters mean: V t1 : stator winding single-phase voltage (in volts).
R ext : external resistance (in ohms).
The equivalent circuit permits the steady-state analysis of the equipment operating as motor or generator.In the built prototype, all electrical connections were made in Y, but the configuration of circuits with delta (D) connection is also possible.

III. ROTARY TRANSFORMER DESIGN
One of the most effective methods for rotary transformer designing is the use of analytical equations, what makes possible the obtaining of faster results.

A. General constructive features
The apparent power of three-phase rotary transformer (S t ) is determined trough the induction machine rotor voltage (V lm2 or V m2 ) and current (I m2 ), as follow: where V lm2 : rotor winding line voltage (in volts).
From these conditions, the general constructive features of rotary transformer can be determined, i.e., its core cross-section (S tm ), the number of turns (N t1 and N t2 ) and the conductor cross-section (S cond1 and S cond2 ).
Transformer core-cross section S tm (in square meters) can be calculated by: where K core : core usage factor.
f en : rated electric frequency (in hertz).
In this context, it is important to observe that K core represents a useful variable for optimization studies.
The number of rotor winding turns (N t2 ) is calculated by: where B tmáx : maximum magnetic flux density (in tesla).
The number of stator winding turns (N t1 ) is defined according the desired stator voltage (V t1 ): The electrical connection between the induction machine and the rotary transformer establishes the same rotor current for both circuits: In this way, rotary transformer stator current (I t1 ) is calculated by: Conductors' cross-sections (S cond1 and S cond2 ) depend of the nominal current values (I t1 and I t2 ) and current density (J cond ): where S cond1 : stator conductor cross-section (in square meters).
The total stator and rotor winding cross-sections (S tcu1 and S tcu2 ) are defined by: where S tcu1 : stator winding cross-section (in square meters).
Taking account the winding fill factor (f tfill ), slots cross-sections (S tslot1 and S tslot2 ) are defined by: where S tslot1 : stator slot cross-section (in square meters).S tslot2 : rotor slot cross-section (in square meters).

B. General dimensions
Determined the constructive features of the rotary transformer, it is possible to calculate the general dimensions indicated in Figures 4 and 5. Considering that l tb , l te , l tg1 and l tg2 are pre-defined values, l tf1 and l tf2 are defined by: where l tf1 : stator winding depth (in meters).
l te : air-gap length (in meters).
The main rotary transformer diameters are presented in Figure 5. Considering that transformer core is constituted by lamination placed longitudinal to the shaft, all diameters are calculated as following: where D t1a-d : stator diameters (in meters).
The core width l ta (in meters) corresponds to: Determined all transformer diameters, the winding average length (l tcu1 and l tcu2 ) and air-gap (l te12 ) can also be calculated: where l tcu1 : stator winding average length (in meters).l tcu2 : rotor winding average length (in meters).
The definition of average lengths is very important for the calculation of equivalent circuit parameters.

C. Magnetic lengths
The calculation of magnetic lengths is important for the determination of reluctance and magnetizing reactance.Magnetic lengths observed in Figure 6 are defined by: where l tj1 : stator radial magnetic length (in meters).
l th : axial magnetic length (in meters).

D. Equivalent circuit parameters
Knowing transformer general dimensions and magnetic lengths, it is possible to calculate the equivalent circuit parameters.Resistances R t1 and R t2 correspond to: where  : electric resistivity (in ohms.meter).
Leakage reactance X t1 and X t2 are calculated trough: where u 0 : magnetic permeability of air (in henrys per meter).
The reluctance of magnetic circuit corresponds to: where S tm1 : stator leg core cross-section (in square meters).
S te : air-gap cross-section (in square meters).
Stator leg cross-section (S tm1 ) and air-gap cross-section (S te ) are determined by: The magnetizing reactance (X tm ) can be obtained through: To calculate the iron resistance, it is necessary to know the iron or core losses, which can be calculated by [3]: where w core : iron losses (in watts per kilogram).
p f : eddy current losses (in watts per kilogram).
p h : hysteresis losses (in watts per kilogram).
m core : iron mass (in kilograms).
p core : iron losses (in watts).
The iron resistance (R tc ) corresponds to: IV. MANUFACTURED PROTOTYPE According to the previous definitions, a rotary transformer was manufactured to be installed in a 90kW prototype with the characteristics presented in Table I.P shaft : mechanical power on shaft (in watts).
To achieve the requirements established by prototype data, dimensions of the rotary transformer are according to Table II.The equivalent circuit parameters reflected to induction machine stator expressed in ohms are presented on table III.Tables VI and VII present measurement results for 25% to 125% load for motor and generator regime.In both cases, rotary transformer stator winding is short-circuited.Power factor verified for this prototype is smaller than standard values for conventional 6 poles induction machines.Obviously, this reduction on power factor is explained by the inductive nature of rotary transformer [1].

VI. CONCLUSION
Rotary transformers are an interesting alternative to substitute brushes and slip-rings on wound rotor induction machines.Avoiding mechanical contact between rotating circuits, motors and generators maintenance can be drastically reduced.
The development of analytical equations for rotary transformer calculation is a good way for obtaining fast results, consisting in important resource for the development of industrial software for designing this device.
The realization of laboratory tests under the equipment shows concordance between steady-state simulation and measurement results.
[1] -[3] Ruviaro et al. present the use of a radial three-phase rotary transformer electrically connected to an induction machine rotor circuit as can be seen at Figure 1.

Figure 1 -
Figure 1 -Doubly fed three-phase induction machine with rotary transformer

Figure 2 -
Figure 2 -Grid connection of the doubly fed three-phase induction machine with rotary transformer

Figure 3
Figure 3 presents the equivalent single-phase circuit that represents the connection between the induction machine and the rotary transformer.

Figure 3 -
Figure 3 -Equivalent circuit of doubly fed induction machine with rotary transformer

Figure 7
Figure 7 presents the rotor and stator of the manufactured transformer.

Figure 8
Figure 8 exhibits the behavior of torque and current vs. speed curves for different values of external resistance.

Figure 8 -
Figure 8 -Torque and current vs. speed curve for different external resistance values

Fig. 10 -
Fig. 10 -Torque and current vs. speed for transformer stator winding in short-circuit

Fig. 11 -
Fig. 11 -Torque and current vs. speed for transformer stator winding connected to external resistance of 0.23Ω

Fig. 12 -
Fig. 12 -Electromagnetic torques for transformer stator winding connected to external resistance of 0.41Ω Journal of Microwaves, Optoelectronics and Electromagnetic Applications, Vol.12, No. 2, December 2013 Brazilian Microwave and Optoelectronics Society-SBMO received 21 Oct 2012; for review 7 Dec 2012; accepted 3 July 2013 Brazilian Society of Electromagnetism-SBMag © 2013 SBMO/SBMag ISSN 2179-1074 419 Applying the values presented at Table III on the equivalent circuit of Figure3, it is possible to evaluate the steady-state performance of this prototype.

TABLE VI INDUCTION
MACHINE WITH ROTOR CONNECTED TO ROTARY TRANSFORMER (MOTOR OPERATION)

TABLE VII INDUCTION
MACHINE WITH ROTOR CONNECTED TO ROTARY TRANSFORMER (GENERATOR OPERATION)