Doubly fed electric machine

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Doubly fed electric machines are electric motors or electric generators that have windings on both stationary and rotating parts, where both windings transfer significant active power between shaft and electrical system. Usually the stator winding is directly connected to the three-phase grid and the three-phase rotor winding is fed from the grid through a rotating or static frequency converter.

Doubly fed machines are typically used in applications that require varying speed of the machine's shaft in a limited range around the synchronous speed, for example ± 30%, because the power rating of the frequency converter is reduced similarly. Today doubly fed drives are the most common variable speed wind turbine concept.


The doubly fed machine has its origins in wound rotor induction motors with multiphase winding sets on the rotor and stator, respectively, with the rotor winding set connected to resistors via slip rings for starting. However, the slip power was lost in the resistors. Thus means to increase the efficiency in variable speed operation by recovering the slip power were developed. In Krämer (or Kraemer) drives the rotor was connected to an AC and DC machine set that fed a DC machine connected to the shaft of the slip ring machine.[1] Thus the slip power was returned as mechanical power and the drive could be controlled by the excitation currents of the DC machines. The drawback of the Krämer drive is that the machines need to be overdimensioned in order to cope with the extra circulating power. This drawback was corrected in the Scherbius drive where the slip power is fed back to the AC grid by motor generator sets.[2][3]

The rotating machinery used for the rotor supply was heavy and expensive. Improvement in this respect was the static Scherbius drive where the rotor was connected to a rectifier-inverter set constructed first by mercury arc based devices and later on with semiconductor diodes and thyristors. In the schemes using a rectifier the power flow was possible only out of the rotor because of the uncontrolled rectifier. Moreover, only sub-synchronous operation as a motor was possible.

Another concept using static frequency converter had a cycloconverter connected between the rotor and the AC grid. The cycloconverter can feed power in both directions and thus the machine can be run both sub- and oversynchronous speeds. Large cycloconverter controlled doubly fed machines have been used to run single phase generators feeding 16 2/3 Hz railway grid in Europe [4] and run the turbines in pumped storage plants.[5]

Today the frequency changer used in applications up to few tens of megawatts consists of two back to back connected IGBT inverters.

Several brushless concepts have also been developed in order to get rid of the slip rings that require maintenance.


Electric machines are either Singly Fed with one multiphase winding set that actively participates in the energy conversion process or Doubly Fed with two active winding sets. An active winding set has at least two AC phases with independent electrical ports for the production of a rotating or moving magnetic field that actively participation in the energy conversion process. Since both winding sets of a doubly-fed electric machine actively participate in the energy conversion process, a doubly-fed electric machine operates to twice synchronous speed or twice the constant torque range with a given frequency of excitation. Many confuse the singly-fed slip-energy recovery induction and the field-excited synchronous electric machines with two electrical ports as doubly-fed but only one port or winding set actively participates in the energy conversion process and as a result, these electric machines are not designed for operation to twice synchronous speed with a given frequency of excitation. A practical doubly-fed electric machine system must operate between sub-synchronous and super synchronous speed without control discontinuity.

Only practical with the evolution of control technology, there are now three varieties of doubly fed electric machine systems: 1) the Doubly Fed Induction Machine (DFIM), which is the conventional wound-rotor doubly fed electric machine with an active winding set on the rotor and stator, respectively, and flux vector controlled rotor excitation through a multiphase slip-ring assembly; 2) the Brushless Doubly-Fed Induction Machine (BDFIM), which is the brushless doubly fed induction (or reluctance) electric machine with cascaded active winding sets of unlike pole-pairs on the stator assembly of which one is flux vector controlled and a flux focusing rotor assembly; and 3) Synchro-Sym electric machine system, which is the only Brushless Doubly-Fed Synchronous Machine (BDFSM). Unlike the doubly-fed electric machine topologies that always rely on slip-induction for operation, the Synchro-Sym electric machine system has a brushless real time control method that eliminates reliance on slip-induction, multiphase slip ring assemblies, or any derivative of rotor flux vector controllers to provide twice synchronous speed for a given frequency of excitation with active rotor and stator winding sets.

The symmetrical circuit topology and operational relationships of the wound-rotor doubly-fed synchronous electric machine core with active winding sets on the rotor and stator, respectively, become the classic study for all other electric machines by de-optimizing their symmetry with asymmetry; for instance, by replacing the symmetrical circuit topology provided by the rotor active winding set with the asymmetrical circuit topology provided by a passive permanent magnet assembly, which has no active power port and as a result, cannot actively participate in the energy conversion process. A true doubly-fed electric machine must have two active winding sets (ports) excited with bi-directional power for practical operation from sub-synchronous to super-synchronous speed without regions of discontinuity, such as about synchronous speed.

The DFIM and BDFIM rely on speed-based asynchronism (or slip) between the rotor and stator windings to induce speed-synchronized current onto the rotor winding set. However at the low slip experienced about synchronous speed, the time critical measurement or excitation synthesis of shallow time-differential signals makes stability increasingly elusive. The BDFIM has eliminated the multiphase slip-ring assembly and partially improved stability by sacrificing size, cost, and efficiency. In contrast, the BDFSM as only provided by the Synchro-Sym electric machine system brushlessly propagates instantaneously derived speed-synchronized multiphase excitation to the rotor winding set without discontinuity and without relying on slip-induction as in synchronous electric machines, although slip-induction may be experienced as in all singly-fed and doubly-fed induction electric machines.

Features of doubly fed machines[edit]

The wound rotor doubly fed synchronous electric machine as only provided by the Synchro-Sym electric machine system is the only electric machine that operates with rated torque to twice synchronous speed for a given frequency of excitation and without control discontinuity at synchronous speed where slip-induction ceases to exist (i.e., 7,200 rpm with one pole-pair doubly fed machine when both stator and rotor are fed with 60 Hz versus 3,600 rpm for otherwise similar singly fed electric machine). In high power applications two or three pole-pair machines are common. Higher speed with rated torque means that doubly fed machines have lower cost per kW, higher efficiency, and higher power density.

In concept, any multiphase electric machine can be converted to a wound-rotor doubly fed electric motor or generator by changing the rotor assembly to a multiphase wound rotor winding set. If the rotor winding set can transfer bi-directional active or working power to the electrical system, the conversion result is a wound-rotor doubly fed electric motor or generator with higher speed and power rating than the original singly fed electric machine. These advantages can be achieved without core saturation, all by electronically controlling half or less of the total motor power for full variable speed control.[6]

As do all electromagnetic electric machines, doubly fed machines need torque current and magnetic flux to produce torque. Because there are no permanent magnets in the doubly fed machine, magnetizing current is needed to produce magnetic flux. Magnetizing current and torque current are orthogonal vectors and do not add directly. Since the magnetizing current is much smaller than the torque current, it is only significant in the efficiency of the machine at very low torque. Furthermore, magnetizing current of the wound rotor doubly fed electric machine can be shared between the stator and rotor windings. If all magnetizing current is supplied by the rotor windings, the stator will only have torque current and so unity power factor. However, by optimal current sharing the total I2R loss can be minimized.

At synchronous speed the rotor current has to be DC, as in ordinary synchronous machines. If the shaft speed is above or below synchronous speed, the rotor current must be AC at the slip frequency. Thus the rotor winding requires reactive power when it is used to magnetize the machine in non-synchronous operation.

Torque production requires that rotor current also has a torque producing component in addition to magnetization. Thus active power is present in the rotor in addition to reactive power.

The frequency and the magnitude of the rotor voltage is proportional to the difference between the speed of the machine and the synchronous speed (the slip). At standstill, the frequency will be the same as the frequency in the stator; the voltage magnitude is determined by the ratio of the stator and rotor winding turns. Thus if the number of turns is equal, the rotor has the same voltage as the stator. The doubly fed machine is a transformer at standstill. The transformer-like characteristics are also present when it is rotating, manifesting itself especially during transients in the grid.

Due to the voltage and current behavior described above the rotor will either require, or generate, active power depending on the speed and torque. If the machine is producing torque and operating as a motor, the rotor will generate power if the speed is below synchronous speed (subsynchronous operation). At standstill all active power fed in the stator (excluding losses) is returned via the rotor. If the motor has rated torque, rated active power is circulating through the stator, rotor and frequency converter and only losses are taken from the grid. The mechanical power being the angular speed multiplied by the torque of the motor is zero at standstill. Thus like all electric machines, the efficiency of the machine is not very good at low speeds because losses depend on the current that is required to produce torque but little or no mechanical power is produced.

If the machine is operating as a motor at speeds over the synchronous speed (supersynchronous operation), the mechanical power is fed in both through the stator and rotor. As a consequence the efficiency is now better than with singly fed motors. For example, the doubly fed electric machine with equal stator and rotor turns produces same torque at double speed (and thus twice the power) as a singly fed electric machine. The losses, being roughly proportional to the torque, are quite the same. Thus efficiency, which is the power taken divided by the total power produced, is better than singly fed electric machines. Naturally one has to take into account the loss of the power electronic control equipment. However, the frequency converter of the doubly fed machine has to control only 50% or less of the power of the machine, and thus has about half of the loss of the singly fed machines' frequency converter that has to pass through 100% of the power.

Since efficiency is the ratio between the output power to the input power, the magnetic core efficiency of a wound rotor doubly fed machine, which has just two winding sets of loss but shows twice the power for a given frequency and voltage of operation, is comparable to the magnetic core efficiency of permanent magnet machines with just one winding but without magnetizing current. Coupled with the low power electronic controller, the wound-rotor doubly fed electric machine system would be more efficient than permanent magnet machine systems without magnetizing current.

For operation as a generator a similar situation exists. At subsynchronous speeds the stator is generating the power but part of it has to be fed back to rotor. At supersynchronous speeds both the rotor and stator are producing power to the grid.

Thus the current rating of the rotor converter is defined by the maximum active current required by the torque production and the maximum reactive current required to magnetize the machine.

Doubly fed electric machines outperform the others in supersynchronous speeds. They can operate at constant torque to twice synchronous speed if each active winding is rated at half the total power of the machine and can provide continuous operation between sub-synchronous through supersynchronous speed range.

Doubly fed machines do not produce more continuous rated torque per volume than singly fed machines. The bigger power rating is due to the higher speed attainable without weakening the magnetic flux. The short time maximum torque of a wound rotor doubly fed electric machine is, however, much higher than all other electric machines, including induction or permanent magnet machines, because increasing torque current does not directly increase air-gap flux, which leads to core saturation. In practice, torque current increase is only limited by the temperature of the windings and the maximum current capability of the rotor frequency converter.

With one of the two armature winding sets residing on the rotor and stator body, respectively, the rotor real estate of the wound-rotor doubly fed machine actively participates in the energy conversion process, which is different from all other electric machines, including permanent magnet synchronous machines. As a result, the magnetic core of the wound-rotor doubly fed electric machine shows highest power density.

Changing of the direction of the rotation requires the swap of two stator phases near zero speed if symmetrical speed range in both directions is required.

It is common to dimension the doubly fed machine to operate only at a narrow speed range around synchronous speed and thus further decrease the power rating (and cost) of the frequency converter in the rotor circuit.

Typical applications of doubly fed machines have been high power pumps and fans, hydro and wind generators, shaft generators for ships etc. where operating speed range has been quite narrow, less than ±30% of the synchronous speed and only small power is required in the subsynchronous range.

Due to the high rotor to stator winding turns ratio that is typical in these applications and the high voltage thus induced in the rotor at standstill, the starting of this kind of restricted operating speed range motor drive is usually done with rotor resistors in induction motor mode. When speed is in the operating speed range, the resistors are disconnected and the frequency converter is connected to the rotor. If the starting torque is low enough it is also possible to short circuit the stator and use the frequency converter in the induction motor control mode to accelerate the motor to the operating speed range. Generators, naturally, don't usually need any additional starting means because wind or water is used to accelerate the machine to the operating speed range.

Electronic control[edit]

The controller, a frequency converter, conditions bi-directional (four quadrant), speed synchronized, and multiphase electrical power to at least one of the winding sets (generally, the rotor winding set). Due to the lack of damper windings used in synchronous machines, the wound-rotor doubly fed electric machines are susceptible to instability without stabilizing control because torque is a function of position.[7][8][9] Pioneering work of Drs. Albertson, Long, Novotny, and Schmitz.[10][11] from the engineering department of the University of Wisconsin realized this must be overcome with instantaneous control. Like any synchronous machine, losing synchronism will result in alternating torque pulsation and other related consequences.

Doubly fed electric machines require electronic control for practical operation and should be considered an electric machine system or more appropriately, a variable-frequency drive.[12]

Wound-rotor doubly fed electric machine[edit]


Two multiphase winding sets with similar pole-pairs are placed on the rotor and stator bodies, respectively. Since the rotor winding set actively participates in the energy conversion process with the stator winding set, utilization of the magnetic core real estate is optimized in contrast to all other electric machine types.

The doubly fed machine operation at unity stator power factor requires higher flux in the air-gap of the machine than when the machine is used as wound rotor induction machine. It is quite common that wound rotor machines not designed to doubly fed operation saturate heavily if doubly fed operation at rated stator voltage is attempted. Thus a special design for doubly fed operation is necessary.

A multiphase slip ring assembly is traditionally used to transfer power to the rotating winding set and to allow independent control of the rotor winding set. The slip ring assembly requires maintenance and compromises system reliability, cost and efficiency. Attempts to avoid the slip ring assembly are constantly being researched with limited success (see Brushless doubly fed induction electric machines).


Although the multiphase slip ring assembly reduces reliability and requires regular maintenance, it allows easy control of the rotor (moving) winding set so both multiphase winding sets actively participate in the energy conversion process with the electronic controller controlling half (or less) of the power capacity of the electric machine for full control of the machine.

This is especially important when operating at synchronous speed, because then the rotor current will be DC current. Without slip rings the production of DC current in the rotor winding is only possible when the frequency converter is at least partly located in the rotor and rotating with it. This kind of rotor converter naturally requires its own winding system (preferably using high frequency in the 10 kHz range for compact size) for power transfer out of or into the rotor. Furthermore, there are thermal and mechanical constraints (for example centrifugal forces) of the power electronic assembly in the rotor. However,high speed alternators have had electronics incorporated on the rotor for many years. Furthermore, high frequency wireless power transfer is used in many applications because of improvements in efficiency and cost over low frequency alternatives.


Neglecting the slip ring assembly, the theoretical electrical loss of the wound-rotor doubly fed machine core in supersynchronous operation is comparable to the most efficient electric machine systems available (the synchronous electric machine with permanent magnet assembly) under similar operating metrics. The efficiency is similar because the total current is split between the rotor and stator winding sets while the electrical loss is proportional to the square of the current flowing through the winding set. Further considering that the electronic controller handles less than 50% of the power of the machine, the wound-rotor doubly fed machine theoretically shows nearly half the electrical loss of other machines of similar rating.

Power density[edit]

Neglecting the slip ring assembly and considering similar air-gap flux density, the physical size of the magnetic core of the wound-rotor doubly fed electric machine is smaller than other electric machines because the two active winding sets are individually placed on the rotor and stator bodies, respectively, with virtually no real-estate penalty. In all other electric machines, the rotor assembly is passive real estate that does not actively contribute to power production. The potential of higher speed for a given frequency of excitation, alone, is an indication of higher power density potential. The continuous constant-torque speed range is up to 7200 rpm @ 60 Hz with 2 poles compared to 3600 rpm @ 60 Hz with 2 poles for other electric machines. In theory, the core volume is nearly half the physical size compared to other machines of similar rating.


Neglecting the slip ring assembly, the theoretical system cost is nearly 50% less compared to other machines of similar rating because the power rating of the electronic controller, which is the significant cost of any electric machine system, is 50% (or less) than other electric motor or generator systems of similar rating.

Peak Torque[edit]

With the symmetrical or dual-ported transformer topology of two active winding sets on the rotor and stator, respectively, the wound-rotor doubly fed electric machine core produces nearly twice the peak torque of any electric machine by similarly increasing torque current without affecting air-gap flux density or saturating the magnetic core because the torque currents (and flux production) on each side of the air-gap are neutralized. For all electric machines, peak torque current increases dissipation while reducing efficiency.

Double fed induction generator[edit]

DFIG for Double Fed Induction Generator, a generating principle widely used in wind turbines. It is based on an induction generator with a multiphase wound rotor and a multiphase slip ring assembly with brushes for access to the rotor windings. It is possible to avoid the multiphase slip ring assembly (see brushless doubly fed electric machines), but there are problems with efficiency, cost and size. A better alternative is a brushless wound-rotor doubly fed electric machine.

Principle of a Double Fed Induction Generator connected to a wind turbine

The principle of the DFIG is that rotor windings are connected to the grid via slip rings and back-to-back voltage source converter that controls both the rotor and the grid currents. Thus rotor frequency can freely differ from the grid frequency (50 or 60 Hz). By using the converter to control the rotor currents, it is possible to adjust the active and reactive power fed to the grid from the stator independently of the generator's turning speed. The control principle used is either the two-axis current vector control or direct torque control (DTC).[13] DTC has turned out to have better stability than current vector control especially when high reactive currents are required from the generator.[14]

The doubly fed generator rotors are typically wound with 2 to 3 times the number of turns of the stator. This means that the rotor voltages will be higher and currents respectively lower. Thus in the typical ± 30% operational speed range around the synchronous speed, the rated current of the converter is accordingly lower which leads to a lower cost of the converter. The drawback is that controlled operation outside the operational speed range is impossible because of the higher than rated rotor voltage. Further, the voltage transients due to the grid disturbances (three- and two-phase voltage dips, especially) will also be magnified. In order to prevent high rotor voltages - and high currents resulting from these voltages - from destroying the IGBTs and diodes of the converter, a protection circuit (called crowbar) is used.

The crowbar will short-circuit the rotor windings through a small resistance when excessive currents or voltages are detected. In order to be able to continue the operation as quickly as possible an active crowbar[15] has to be used. The active crowbar can remove the rotor short in a controlled way and thus the rotor side converter can be started only after 20-60 ms from the start of the grid disturbance when the remaining voltage stays above 15% of the nominal voltage. Thus it is possible to generate reactive current to the grid during the rest of the voltage dip and in this way help the grid to recover from the fault. For zero voltage ride through it is common to wait until the dip ends because with zero voltage it is not possible to know the phase angle where the reactive current should be injected.[16]

As a summary, a doubly fed induction machine is a wound-rotor doubly fed electric machine and has several advantages over a conventional induction machine in wind power applications. First, as the rotor circuit is controlled by a power electronics converter, the induction generator is able to both import and export reactive power. This has important consequences for power system stability and allows the machine to support the grid during severe voltage disturbances (low voltage ride through, LVRT). Second, the control of the rotor voltages and currents enables the induction machine to remain synchronized with the grid while the wind turbine speed varies. A variable speed wind turbine utilizes the available wind resource more efficiently than a fixed speed wind turbine, especially during light wind conditions. Third, the cost of the converter is low when compared with other variable speed solutions because only a fraction of the mechanical power, typically 25-30%, is fed to the grid through the converter, the rest being fed to grid directly from the stator. The efficiency of the DFIG is very good for the same reason.

Brushless doubly fed versions[edit]

Brushless doubly fed induction electric machine[edit]

Brushless doubly fed induction electric machine is constructed by adjacently placing two multiphase winding sets with unlike pole-pairs on the stator body. With unlike pole-pairs between the two winding sets, low frequency magnetic induction is assured over the speed range. One of the stator winding sets (power winding) is connected to the grid and the other winding set (control winding) is supplied from a frequency converter. The shaft speed is adjusted by varying the frequency of the control winding. As a doubly fed electric machine, the rating of the frequency converter need only be fraction of the machine rating.

The brushless doubly fed electric machine does not utilize core real-estate efficiently and the dual winding set stator assembly is physically larger than other electric machines of comparable power rating. In addition, a specially designed rotor assembly tries to focus most of the mutual magnetic field to follow an indirect path across the air-gap and through the rotor assembly for inductive coupling (i.e., brushless) between the two adjacent winding sets. As a result, the adjacent winding sets are excited independently and actively participate in the electro-mechanical energy conversion process, which is a criterion of doubly fed electric machines.

The type of rotor assembly determines if the machine is a reluctance or induction doubly fed electric machine. The constant torque speed range is always less than 1800 rpm @ 60 Hz because the effective pole count is the average of the unlike pole-pairs of the two active winding sets. Brushless doubly fed electric machines incorporate a poor electromagnetic design that compromises physical size, cost, and electrical efficiency, to chiefly avoid a multiphase slip ring assembly. Although brushless doubly fed electric machines have not seen commercial success since their conception in the early 1970s, the promise of a low cost, highly efficient electronic controller keeps the concept under perpetual study, research, and development.

Brushless wound-rotor doubly fed electric machine[edit]

The brushless wound-rotor [synchronous] doubly-fed electric machine incorporates the electromagnetic structure of the wound-rotor doubly fed electric machine, but replaces the traditional multiphase slip ring assembly with a brushless instantaneous control means to independently power the rotor winding set with multiphase AC power as hypothesized by electric machine experts since the 1960's.[17][18] Since it does not rely on induction as a result of slip (i.e.., slip-induction) for practical operation, it differs from the brushless doubly fed induction electric machines that relies on very different principles of unlike pole-pair induction for operation or the wound-rotor doubly fed induction electric generators or motors.

With an independent means of brushlessly exciting the rotor multiphase AC winding set under brushless real time control, the torque of the wound-rotor doubly-fed electric machine is independent of slip-induction or the precise position alignment of the free moving shaft, which were the classic instability conditions of the brushless doubly fed induction electric machines or the wound-rotor doubly fed induction electric machines, and as a result, torque can even be produced at synchronous speed, which is the operating point of the synchronous electric machines where slip-induction ceases to exist. For stable synchronous operation, the excitation frequency and phase of the multiphase AC rotor armature relative to the speed and position of the shaft must be instantaneously synchronized to the excitation frequency and phase of the stator armature, which is not trivial at any speed but particularly difficult about synchronous speed where slip-induction no longer exists. Experts have known that if these conditions were met as only provided by the patented synchro-sym electric machine system, then all the attractive attributes of the synchronous wound-rotor doubly fed electric machine would be realized, such as ultra high power density, ultra low cost, ultra-high efficiency, and ultra-high torque potential, as the result of showing twice the continuous constant-torque speed range for a given frequency of excitation as known by expert research since at least 1960, which is a certain indication of power density and efficiency.[19] By eliminating the need for extraneous permanent magnets, reluctance saliencies, or squirrel cage windings components that consume real-estate without contributing to electromechanical work, the patented Synchro-Sym electric machine system makes ongoing research to improve the cost-size-performance of extraneous electric machine components less relevant.[20]

See also[edit]


  1. ^ Leonhard, W.: Control of Electrical Drives. 2nd Ed. Springer 1996, 420 pages. ISBN 3-540-59380-2.
  2. ^ Shively, E. K.; Whitlow, Geo. S.: Automatic Control for Variable Ratio Frequency Converters. Transactions of the American Institute of Electrical Engineers, Volume: 51 Issue: 1 Date: March 1932 , Page(s): 121 - 127.
  3. ^ Liwschitz, M. M., Kilgore, L. A.: A Study of the Modified Kramer or Asynchronous-Synchronous Cascade Variable-Speed Drive. Transactions of the American Institute of Electrical Engineers, Volume: 61, Issue: 5, May 1942, Page(s): 255 - 260.
  4. ^ Pfeiffer, A.; Scheidl, W.; Eitzmann, M.; Larsen, E.: Modern rotary converters for railway applications. Proceedings of the 1997 IEEE/ASME Joint Railroad Conference, March 18–20, 2007, Boston, MA, Pages: 29-33.
  5. ^ A. Bocquel, J. Janning: 4*300 MW variable speed drive for pump-storage plant application. EPE Conference 2003, Toulouse.
  6. ^ FAQ: advanced brushless wound-rotor synchronous doubly fed electric motor or generator
  7. ^ Liwschitz, M. M.: Damping and Synchronizing Torque of the Double-Fed Asynchronous Machine. Transactions of the American Institute of Electrical Engineers, Volume: 60 Issue: 10 Oct. 1941, Page(s): 923 - 924
  8. ^ Prescott, J.C.; Raju, B.P.: The inherent instability of induction motors under conditions of double supply. Proceedings of the IEE - Part C: Monographs, Volume: 105 Issue: 7 Date: March 1958, Page(s): 319 - 329
  9. ^ Bird, B.M.; McCloy, K.; Chalmers, B.J.: New methods of stabilising doubly fed slip-ring machines. Proceedings of the Institution of Electrical Engineers, Volume: 114 Issue: 6, June 1967, Page(s): 791 - 796
  10. ^ Schmitz, N. L.; Albertson, V. D.: The Stabilized Doubly Fed Synchronous-Induction Machine: Test Results and Computer Solutions Transactions of the Power Apparatus and Systems, Volume: 83 Issue: 8 Date: Aug. 1964, Page(s): 858 - 864.
  11. ^ Long, W. F.; Schmitz, N. L.: Cycloconverter Control of the Doubly Fed Induction Motor Transactions of the Industry and General Applications, Volume: IGA-7 Issue: 1 Date: Jan. 1971, Page(s): 95 - 100.
  12. ^ Alberto Ortega Fraile: Die doppeltgespeiste Asynchronmaschine: Untersuchung als Generator für eine Windkraftanlage. Vdm Verlag Dr. Müller (August 2008), ISBN 978-3-639-03244-4
  13. ^ U.S. Patent 6,448,735
  14. ^ J. Niiranen: About the active and reactive power measurements in unsymmetrical voltage dip ride-through testing Wind Energy 2008; 11:121-131.
  15. ^ an active crowbar: for example U.S. Patent 7,164,562
  16. ^ Seman, S.; Niiranen, J.; Virtanen, R.; Matsinen, J.-P.: Low voltage ride-through analysis of 2 MW DFIG wind turbine - grid code compliance validations. Proceedings of the 2008 IEEE Power and Energy Society General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century, 20–24 July 2008, Pittsburgh, PA, 6 pages.
  17. ^ Klatt, F. W.:Qualitative analysis of the Brushless Wound-rotor [Synchronous] Doubly-fed Electric Machine stabilized by real-time control. Electric Machines & Drives Conference (IEMDC, 2013 IEEE International), pages 640-647.
  18. ^ Frederick W. Klatt, Best Electric Machines. Electric Machines & Drives Conference (IEMDC, 2013 IEEE International), pages 640-647.
  19. ^ [1]
  20. ^

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