It is necessary to measure the current of rotor for controlling the active and reactive power generated by the stator side of the doubly fed induction generator (DFIG) system. There are offset and scaling errors in the current measurement. The offset and scaling errors cause one and two times current ripples of slip frequency in the synchronous reference frame of vector control, respectively. This paper proposes a compensation method to reduce their ripples. The stator current is variable according to the wind force but the rotor current is almost constant. Therefore input of the rotor current is more useful for a compensation method. The proposed method adopts the synchronous daxis current of the rotor as the input signal for compensation. The ripples of the measurement errors can be calculated by integrating the synchronous daxis stator current. The calculated errors are added to the reference current of rotor as input of the current regulator, then the ripples are reduced. Experimental results show the effectiveness of the proposed method.
1. Introduction
A double fed induction generator (DFIG) is a popular wind turbine system due to its high energy efficiency, reduced mechanical stress on the wind turbine, and relatively low power rating of the connected power electronics converter of low costs
[1

4]
. The vector control of the rotor current is used to control the active and reactive power independently and stably using a rotating reference frame fixed on the gap flux
[5

7]
. Therefore, precise measurement of the rotor currents is very important in the vector control
[8
,
9]
.
The rotor and gridside currents are measured from the current sensors of the converter through low pass filters and A/D converters. In this process, current measurement errors can be generated due to the nonlinearity of the current sensors, quantization error of A/D converters, and the thermal drift of the analog electric elements. These errors cause the ripples in the produced power of the DFIG
[10
,
17]
. The errors can be classified as offset errors, scaling errors and nonlinearity errors.
In the rotor side control, the ripples by offset and scaling errors have one and two times component of the fundamental rotor current frequency, respectively. Then the ripples of the rotor side lead to the fluctuations of the stator side. The ripple frequency by the offset error is same as the difference between the grid frequency and the slip frequency, and it by the scaling error is same as the difference between the grid frequency and two times of the slip frequency
[18]
.
In
[19]
, a method was proposed in order to solve the problem of the offset and scaling errors in the DFIG system. The method obtains the two errors directly from the phase currents of the rotor side, and compensates the two errors on the current measurement path. It can improve the steady state performance of the DFIG by eliminating the effects of the offset and scaling error. However, this method cannot guarantee the complete compensation in the transient state because the phase currents of the stationary reference frame are used as inputs for the calculation of the errors.
This paper analyzes the error components of the offset and the scaling on the basis of the synchronous reference frame of the DFIG, and proposes a compensation method to reduce the effect of the errors. The proposed method adopts the synchronous daxis current of the rotor as the input signal for compensation due to the several advantages. This method can be simply implemented by calculating the several integral and subtracting operations. Also the method is well operated not only under the steady state but also under the transient state, and robust to the variation of the machine parameters. The validity of the proposed method is verified through the experiments.
2. Description of DFIG[17]
Fig. 1
illustrates the configuration of a DFIG system. As shown in
Fig. 1
, the stator magnetizing current is obtained from the grid.
Configuration of DFIG system
The voltage equations and the stator flux of the synchronous reference frame are given in (13) and (4).
where
ω_{e}
is the synchronous angular speed,
L_{s}
is the selfof stator and
L_{m}
is inductance the magnetizing inductance.
The voltage equations and the rotor flux of the synchronous reference frame are given in (57) and (8).
where
ω_{r}
is the angular speed of the rotor.
The produced active and the reactive powers of DFIG are given by (9) and (10).
By using (13), and (4), the active and reactive power equations of DFIG can be rewritten as follows:
As known in (11) and (12), the synchronous d and qaxis currents of the rotor are directly proportional to the reactive and active powers of a DFIG, respectively. In this paper, two rotor current sensors are used for the vector control of backtoback converter of a DFIG.
3. Effect of Measurement Error of Rotor Current[19,20]
Fig. 2
shows the measurement path of the rotor currents for DFIG control. Because of the nonlinearity of the hall sensors, the thermal drift of the analog elements, quantization error of the A/D converters, and unbalance of each element, the errors are generated from current measurement path and inevitable even if the control system is well designed and constructed.
 3.1 Effect of offset error
Fig. 3
shows the block diagram of the calculating process about the influence of rotor phase current offset error.
The offset errors may be caused by an imbalance of current sensors and the measurement path or other problems as mentioned above. The offset errors are calculated as:
Path of rotor phase current measurement
Effect of rotor phase current offset error
where
i_{ar}, i_{br}
are ideal a and bphase rotor currents and
ΔI_{ar} , ΔI_{br}
are offsets of a and bphase, respectively.
From (13), the synchronous dq axis ripple currents of the rotor are expressed as:
where
sω_{e}
is the slip angular speed of the rotor,
I^{e}_{dr_offset}
and
I^{e}_{qr_offset}
are the ripple components of the rotor currents due to the offset error, respectively. As known from (14) and (15), the synchronous d and q axis currents of the rotor have the fundamental components of the slip frequency.
The synchronous d and q axis current ripples by the offset in the stator can be derived in (16) and (17), respectively.
The current ripples of the 3phase reference frame can be an be obtained in (18, 19) and (20).
where
,
and
are the offset errors of 3phase current. As known from (18, 19) and (20), the frequency component of the stator has (1–
s
) due to the offset effect of the rotor side.
 3.2 Effect of scaling error
Fig. 4
shows the block diagram of the calculating process about the influence of rotor phase current scaling error.
If the rotor currents contain scaling errors without offsets, they can be expressed as follows:
where,
I
is the real value of the phase current without offset and scaling errors,
K_{a}
and
K_{b}
denote the scale factor of a, and b phase currents, respectively.
From (21), the synchronous dq axis ripple currents of the rotor can be derived as:
The synchronous d and q axis current ripples by the scaling error in the stator can be derived in (24) and (25), respectively.
The current ripples of the 3phase reference frame can be obtained in (26, 27) and (28).
Effect of rotor phase current scaling error
where
,
and
are the scale errors of 3phase current. As known from (26), (27) and (28), the frequency component of the stator has (1 – 2
s
) due to the scaling error of the rotor side.
4. Detection and Compensation of Current Errors
 4.1 Input signal adoption for compensation
Among previous equations, the synchronous d and qaxis currents of the rotor and stator can be selected for the input signal of the compensator. The qaxis of the stator current is not suitable for the input signal of the proposed compensator because the synchronous qaxis current of the stator is always fluctuating according to the intensity of the wind. The offset errors of the rotor and stator are given in (14) and (16), respectively. The scaling errors of the rotor and stator are given in (22) and (24), respectively. As known from (14, 16, 22) and (24), the amplitude of the stator current is lower than that of the rotor current. Moreover, the synchronous daxis current of the rotor is nearly zero or constant for the vector control. Therefore, the input signal of the proposed compensator uses the synchronous daxis current of the rotor in this paper as shown in
Table 1
.
 4.2 Compensation of current measurement errors
The offset and scaling errors (
ΔI_{ar} , ΔI_{ar} , K_{a} – K_{b}
) can be obtained from the selected (14) and (22) according to the specific rotor slip angle as shown in
Table 2
and
3
.
Due to the proportional integral (PI) current regulator of the synchronous dand qaxis, DC components of (22) and (23) are compensated automatically, respectively. Therefore, the front sine term can be only considered regardless of the rear DC term in (22) and (23).
Input signal adoption for compensation
Input signal adoption for compensation
This compensation method using the
Table 2
and
3
is very simple but difficult to bring the reliable error values due to the effects of inaccurate sampling point and the switching noise of IGBT.
However, the proposed compensation method can have high accuracy and reliability due to the use of the average values through continuous integrals.
In order to compensate the measurement errors, two parts of the integrating operation are needed. The first is the integral of detecting the offset error, and the second is detecting the scaling error.
The first parts are divided into two steps as shown in
Figs. 5
, and
Fig. 6
. The first step is the integral of the synchronous daxis current of the rotor according to the slip angle
θ_{sl}
from 1/2π to 3/2π as shown in the sector I of
Fig. 5
. As shown in (29), the calculation makes the cancellation of the sine term of (14), and can obtain the offseta,
ΔI_{ar}
.
Detection of offset error on a specific slip angle
Detection of offset error on a specific slip angle
Detection of scale error on a specific slip angle
Detection of scale error on a specific slip angle
Detection of offseta (ΔI_{ar})
After acquiring the offseta (
ΔI_{ar}
), the second step is the integral of the current of (14) from 0 to π according to the slip angle as shown in the sector II of
Fig. 6
. In this integral calculation, the cosine term of (14) is removed, and the offsetb (
ΔI_{br}
) can be obtained as shown in (30).
After that, the scaling error of the rotor currents can be obtained from the second part. As shown in
Fig. 7
, the error is acquired by integrating the current (18) from π/3 to 5π/6 as shown in (31).
Detection of offsetb (ΔI_{br})
Detection of scale error (K_{a} , K_{b})
Fig. 8
shows the block diagram of the proposed compensation scheme. The synchronous daxis current of the rotor side is used for an input signal of the integrators as shown in
Fig. 8
. The offset regulator consists of two steps. One is for compensating the aphase offset error, and the other is for the bphase offset error. These two have integral type regulators (
K_{offset}/s
). These integral regulators force
ε_{1}
and
ε_{2}
to be zero as shown in
Fig. 8
. The controller for compensating the scaling error also has the same regulator of the offset error, and forces
ε_{3}
to be zero. These integral controllers have a memory function to store the compensated values of the offset and scaling, respectively. The proposed algorithm automatically compensates the offset and scaling errors by using the integral type regulators as shown in
Fig. 8
.
The gains (
K_{offset }
and
K_{scale}
) of the compensators can be set between 0 and 1, respectively. The smaller the gain is given, the slower the response and more accurate the compensating performance can be obtained. The final compensating equations are achieved as in (32) from the output (
Offset_a, Offset_b, Scale_a,b
) of the integral regulators as shown in
Fig. 8
.
Block diagram of proposed compensation scheme
5. Experimental Results
Fig. 9
shows the experimental setup. Experimental tests were performed in a 3.3kW DFIG test rig. The DFIG is coupled to the permanent magnet synchronous motor (PMSM) of 3kW controlled by a variable speed driver providing torque and speed regulation. The rotor of DFIG and PMSM are controlled separately by microprocessor. The switching frequency of both converters is 5 kHz. Space vector PWM is used for switching pulse generation with a sampling frequency of 10 kHz. The parameters of the experimental system are shown in
Table 4
.
Fig. 10
shows the stator phase currents, the synchronous daxis rotor current and their FFT results under the following conditions;
ΔI_{ar}
= 0.5,
ΔI_{br}
= 0.5,
K_{a}
= 0.99, and
K_{b}
=1.05. The rotor is rotating at 50Hz and the synchronous speed of this induction generator is 60 Hz. Hence, the slip frequency is 10 Hz.
Fig. 10(b)
is the daxis current of the rotor side and its FFT result. The daxis current has one and two times ripples of the slip frequency,
f_{sl}
, by the offset and scaling error, respectively. As the result, the a and bphase current of the stator side in
Fig. 10(a)
have (1 –
s
) and (1 – 2
_{s}
) times ripples of the synchronous frequency,
f_{e}
, respectively as shown in Figs. 10(c) and (d).
Configuration of experimental system
The Experimental Parameters
The Experimental Parameters
Fig. 11
shows the synchronous daxis rotor current and its FFT result before the compensation of two errors. The experimental results were obtained under these error conditions;
ΔI_{ar}
= 0.1,
ΔI_{br}
= 0.3,
K_{a}
= 0.99, and
K_{b}
= 1.05. The conditions are the maximum tolerable errors of the worst case based on their datasheets of the current sensors, low pass filter, matching circuit, and A/D converter. As shown in FFT result of
Fig.11
, the synchronous daxis current has one and two times of the slip frequency of the rotor. If the FFT result is compared with the previous waveform, the two times ripple by scaling error has the same amplitude and the one times ripple by the offset error is decreased due to the reduced offset.
Fig. 12
shows three output values of the compensator in the block diagram of
Fig 8
. At first, the offseta and b values are calculated by the two integrators, respectively. After that, the third integrator obtains the scaling error by integrating the two times ripple component until it is nearly zero. In this paper,
K_{offset}
= 0.1 and
K_{scale }
= 0.05 are chosen for stable and precise operation.
Stator phase currents, synchronous daxis rotor current and their FFT result
Synchronous daxis rotor current before compensating operation
Characteristics of compensation
Daxis current after compensating offset error
Daxis current after compensating scaling error
Fig. 13
shows the compensation result removed the offset error of
Fig. 11
. As shown in the FFT result, the ripple of the slip frequency is eliminated, and the synchronous daxis current has only two times of the slip frequency of the rotor. Then the scaling error compensator becomes active. As the result, the ripple components by both the offset and scaling errors are nearly compensated in the synchronous daxis current of the rotor as shown in
Fig.14
. Therefore, power quality is improved and the vibrations of the generator by low frequency ripples are reduced because the stator phase currents do not have the low frequency ripples by offset and scaling errors.
5. Conclusion
This paper proposed a compensation method to solve the offset and scaling problem by the measurement errors of the current sensors in a DFIG. The principal feature of the proposed method is using the synchronous daxis current of the rotor as an input signal of the compensator. Therefore, the proposed method has the several attractive features: robustness with regard to the variation of the machine variables, application to the steady and transient states, easy implementation. The feasibility and effectiveness of the proposed compensating method were verified through experimentation.
Acknowledgements
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government. (No.2012026153)
BIO
YungDeug Son He was born in Busan, Korea, in 1971. He received the B.S. degrees in Control and Instrumentation Engineering from Korea Maritime University in 1997. He was a student researcher with Tokyo Institute of Technology, Japan, in 1998, and received the M.S. degrees in from Kobe University of Mercantile Ocean ElectroMechanical, Japan, in 2001. From 2001 to 2009, he was a Senior Research Engineer with Hyundai Heavy Industries Co., Ltd. He is currently working toward the Ph.D. degrees in Electrical Engineering from Pusan National University, Korea. He is a Professional Engineer Building Electrical Facilities and a Professional Engineer Electric Application. His research interests include power conversion, electric machine drives, electrical facilities and renewable power system.
WonSang Im He was born in Busan, Korea, in 1981. He received the B.S., M.S. and Ph.D. degrees in Electrical Engineering from Pusan National University, Busan, Korea, in 2007, 2009 and 2013, respectively. He is currently a Postdoctoral Researcher with Klipsch school of Electrical and Computer Engineering in New Mexico State University, Las Cruces. His research interests include power conversion, electric machine drives, and their diagnosis and faulttolerance.
HanSeok Park He received his B.S. and M.S. degrees in Electrical Engineering from ChungAng University, Seoul, Korea, in 1981, 1983, and Ph.D. degrees from the department of Electrical Engineering, from Korea Maritime University, Busan, Korea, in 1996, respectively. Since 1986, he has been with the School of Electrical Engineering, Pukyong National University (PKNU), where he is currently a professor. His current interests include the control of electric machines, energy conversion and research interests include the electric machine design & control, renewable energy system.
JangMok Kim He received his B.S. from Pusan National University (PNU), Korea, in 1988, and the M.S. and Ph.D. degrees from the department of Electrical Engineering, Seoul National University, Seoul, Korea, in 1991 and 1996, respectively. From 1997 to 2000, he was a Senior Research Engineer with the Korea Electrical Power Research Institute (KEPRI). Since 2001, he has been with the School of Electrical Engineering, PNU, where he is currently a Research Member of the Research Institute of Computer Information and Communication, a Faculty Member, and a head of LG electronics Smart Control Center. As a Visiting Scholar, he joined the Center for Advanced Power Systems (CAPS), Florida State University, in 2007. His current interests include the control of electric machines, electric vehicle propulsion, and power quality.
Lihui Yang
,
Zhao Xu
,
Zhao Yang Dong
2012
“Advanced Control Strategy of DFIG Wind Turbines for Power System Fault Ride Through,”
IEEE Trans. Power Systems
27
(2)
713 
722
DOI : 10.1109/TPWRS.2011.2174387
Muller S.
,
Deicke M.
,
De Doncker R. W.
2002
“Doubly fed inductioin generator systems for wind turbines,”
IEEE Industry Applications Magazine
8
(3)
26 
33
Kiani. M
,
Lee W.J.
2008
“Effects of Voltage Unbalance and System harmonics on the Performance of Doubly Fed Induction Wind Generators,”
Industry Application Society Annual Meeting
1 
7
Choy YoungDo
,
Han ByungMoon
,
Lee JunYoung
,
Jang Gilsoo
2011
“RealTime Hardware Simulator for GridTied PMSG Wind Power System,”
Journal of Electrical Engineering & Technology
6
(3)
375 
383
DOI : 10.5370/JEET.2011.6.3.375
Yamamoto M.
,
Motoyoshi O.
1991
“Active and Reactive Power Control for DoublyFed Wound Rotor Induction Generator,”
IEEE Trans. Power Electronics
6
(4)
624 
629
DOI : 10.1109/63.97761
Pena R.
,
Clare J.C.
,
Asher G.M.
1996
“A doublyfed induction generator using two backtoback PWM converters and its application to variable speed wind energy system,”
IEE Proc
143
(3)
231 
241
DOI : 10.1049/ipcom:19960613
Hofman. W
,
Okafor. F
2001
“Optimal control doubly fed full controlled induction wind generator with high efficiency,”
IECON '01, 27th annual Conference of the IEEE
3
1213 
1218
Saccomando G.
,
Svensson J.
,
Sannino A.
2002
“Improving Voltage Disturbance Rejection for Variablesspeed Wind Turbines,”
IEEE Trans. Energy Conversion
17
(3)
422 
428
DOI : 10.1109/TEC.2002.801989
Kim GwangSeob
,
Lee KyoBeum
,
Lee DongChoon
,
Kim JangMok
2014
“Fault Diagnosis and Fault Tolerant Control of DClink Voltage Sensor for Twostage ThreePhase GridConnected PV Inverters,”
Journal of Electrical Engineering & Technology
8
(4)
752 
759
DOI : 10.5370/JEET.2013.8.4.752
Dehkordi Behzad Mirzaeian
,
Payam Amir Farrokh
,
Hashemnia Mohammad Naser
,
Sul SeungKi
2009
“Design of an Adaptive Backstepping Controller for DoublyFed Induction Machine Drives,”
Journal of Power Electronics
9
(3)
343 
353
Jung HanSu
,
Hwang SeonHwan
,
Kim JangMok
,
Kim CheulU
,
Choi Cheol
2006
“Diminution of CurrentMeasurement Error for VectorControlled AC Motor Drives,”
IEEE Trans. Industry Applications
42
(5)
1249 
1256
DOI : 10.1109/TIA.2006.880904
Chung DaeWoong
,
Sul SeungKi
1998
“Analysis and Compensation of Current Measurement Error in VectorControlled AC Motor Drivers,”
IEEE Trans. Industry Applications
34
(2)
340 
345
DOI : 10.1109/28.663477
Lam B. H.
,
Panda S. K.
,
Xu J. X.
,
Lim K. W.
1999
“Torque ripple minimization in PM synchronous motor using iterative learning control,”
in proceedings of the 1999 Industrial Electronics Society Annual Conference of the IEEE
3
1458 
1463
Barro Roberto
,
Hsu Ping
1997
“Torque ripple compensation of induction motors under field oriented control,”
IEEE APEC Conference
1
527 
533
Qian Weizhe
,
Panda S. K.
,
Xu J. X.
2002
“Reduction of periodic torque ripple in PM synchronous motors using learning variable structure control,”
IEEE IECON Conf.
2
1032 
1037
Choi JongWoo
,
Lee SangSup
,
Yu SangYeop
,
Kang SeokJoo
1998
“Novel periodic torque ripple compensation scheme in vector controlled AC motor drives,”
IEEE APEC Conference
1
81 
85
Lee SolBin
,
Lee KyoBeum
,
Lee DongChoon
,
Kim JangMok
2010
“An Improved Control Method for a DFIG in a Wind Turbine under an Unbalanced Grid Voltage Condition,”
Journal of Electrical Engineering & Technology
5
(4)
614 
622
DOI : 10.5370/JEET.2010.5.4.614
Kim YoungIl
,
Hwang SeonHwan
,
Kim JangMok
,
Song SeungHo
,
Kim ChanKi
,
Choy YoungDo
2008
“Reduction of current ripples due to current measurement errors in a doubly fed induction generator,”
IEEE Applied Power Electronics Conference and Exposition(APEC) 2008
756 
760
Park GuiGeun
,
Hwang SeonHwan
,
Kim JangMok
,
Lee KyoBeum
,
Lee DongChoon
2008
“Reduction of Current Ripples due to Current Measurement Errors in a Doubly Fed Induction Generator,”
Journal of Power Electronics
10
(3)
313 
319
DOI : 10.6113/JPE.2010.10.3.313
Im WonSang
,
Hwang SeonHwan
,
Kim JangMok
,
Choi Jeaho
2009
“Analysis and compensation of current measurement errors in a doubly fed induction generator,”
IEEE Energy conversion congress and Exposition(ECCE) 2009
1713 
1719