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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 1

A Combined Vector and Direct Power

Control for DFIG-Based Wind Turbines
Jafar Mohammadi, Sadegh Vaez-Zadeh, Senior Member, IEEE, Saeed Afsharnia, and
Ehsan Daryabeigi

Abstract—In this paper, a combined vector and direct power I. INTRODUCTION

control (CVDPC) is proposed for the rotor side converter (RSC) of
N THE past decades, a great increase in electrical power
doubly fed induction generators (DFIGs). The control system is
based on a direct current control by selecting appropriate voltage
vectors from a switching table. In fact, the proposed CVDPC enjoys
I demand and depletion of natural resources have made
environmental and energy crises. These have led to an increased
the benefits of vector control (VC) and direct power control (DPC) in need for production of energy from renewable sources so that the
a compacted control system. Its benefits in comparison with VC
include fast dynamic response, robustness against the machine world wind energy production has grown significantly due to
parameters variation, lower computation, and simple implementa- cleanness and renewability. Wind power generation is estimated
tion. On the other hand, it has benefits in comparison with DPC, to be 10% of the world’s total electricity by the year 2020 and is
including less harmonic distortion and lower power ripple. An expected to be double or more by the year 2040 [1]. Wind
extensive simulation study, using MATLAB/Simulink, is conducted turbines (WTs), which play a main role in wind energy, are
on a 9-MW wind farm composed of six 1.5-MW DFIG-based wind
turbines. The performance of the proposed CVDPC method is basically divided into fixed and variable-speed technologies.
compared with both VC and DPC under steady-state and transient Variable-speed WTs have been increasingly employed
conditions. Simulation results confirm the superiority of the recently due to several advantages compared with the fixed-
CVDPC over either VC or DPC. speed technologies, including maximized power capture,
Index Terms—Direct power control (DPC), doubly fed induction decreased mechanical stresses imposed on the turbine, improved
generator (DFIG), vector control (VC), wind turbine (WT). power quality, and decreased acoustical noise [2]. The variable-
speed technologies can be further subdivided into two types:
synchronous generators with full-scale converters and doubly
NOMENCLATURE fed induction generators (DFIGs) with partial-scale converters.
Vector and Symbols The DFIG is particularly employed for high-power applications,
' Voltage, current, and flux vectors. due to the lower converters cost and lower power losses. The
Active and reactive power. DFIG control comprises both the rotor side converter (RSC) and
Resistance and inductance. grid side converter (GSC) controllers so that the RSC controls
Angular speed and angle. stator active and reactive powers and the GSC regulates dc-link
Angle between rotor flux and stator flux. voltage as well as generates an independent reactive power that is
Frequency and rotor slip. injected into the grid [3].
Leakage factor and error. Vector control (VC) is the most popular method used in the
Subscripts DFIG-based WTs [4], [5]. Some of the advantages are precise
Synchronous stator-voltage frame. steady-state performance, less power ripple, and lower converter
Stator, rotor, grid, and mutual. switching frequency. However, it has some disadvantages, such
Tangential and radial components. as its dependence on the machine parameters variation due to the
Number of inverter voltage vector. decoupling terms and high online computation owing to the
Supscripts pulsewidth modulation (PWM) procedure. Moreover, the coef-
Reference value for controllers. ficients of proportional–integral (PI) controllers, in the conven-
tional VC, must be optimally tuned to ensure the system stability
within the whole operating range and attain sufficient dynamic
response during the transient conditions [6]. This will deteriorate
the transient performance of VC and affect the system stability
within changing operation conditions. In order to overcome the
Manuscript received July 27, 2013; revised October 31, 2013 and December aforementioned problems, different nonlinear control methods
10, 2013; accepted January 14, 2014. such as direct torque control/direct power control (DTC/DPC)
The authors are with the School of Electrical and Computer Engineering,
College of Engineering, University of Tehran, Tehran 1439957131, Iran (e-mail: have been proposed [7], [8]. The main advantages of DTC/DPC
j.mohammady@ece.ut.ac.ir; safshar@ut.ac.ir; vaezs@ut.ac.ir; daryabeigi_e_e_e@ methods include fast dynamic response, robustness against the
yahoo.com). machine parameters variation, reduction in computation, and
Color versions of one or more of the figures in this paper are available online at
http://ieeexplore.ieee.org. simple implementation. However, they have some disadvantages
Digital Object Identifier 10.1109/TSTE.2014.2301675 including significant torque/power ripples due to the high

1949-3029 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.
See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
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2 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY

bandwidth of the hysteresis controllers, variable switching fre- As the SVOF is used for the controllers synchronization,
quency of the converters, and deterioration of the controller vanishes and the stator active and reactive power equations are
performance during the machine starting and low-speed opera- simplified to
tions. Although many modified methods have been presented to
overcome these problems [9]–[11], their drawback is complex
online computation.
In order to enjoy the benefits of VC and DTC, the combined
VC and DTC (CVDPC) method has been applied successfully to
induction motor [12]–[14] and permanent magnet synchronous According to the stator flux equations in the synchronous
motors [15], [16]. However, the CVDPC method has not been frame [3], in this condition, the stator currents can be written as
studied appropriately for the DFIG. In this paper, it is focused on
comparison of VC and DPC by looking for similarities between
their principles and searching for a fundamental common basis.
From this common basis, in order to enjoy the benefits of VC and
DPC and to avoid some of the implementation difficulties of
either of two methods, the CVDPC method is proposed for the Subtituting (5) and (6) into (3) and (4) yields
RSC of the DFIG. The proposed CVDPC has several advantages
in comparison with VC, including fast dynamic response, ro-
bustness against the machine parameter variations, lower com-
putation, and simple implementation. On the other hand, it has
benefits in comparison with DPC, including less harmonic
distortion and lower power ripple. The rest of this paper is
organized as follows. In Section II, the VC and DPC methods So, the stator active and reactive powers are controlled through
are described and the common basis of them is investigated. In and , respectively. The block diagram of the RSC-based
Section III, the proposed control system and its basic idea are VC is shown in Fig. 1.
discussed. In Section IV, simulation results are shown, and
finally, in Section V, the conclusion is presented. B. Direct Power Control
In the DPC method, the current control loop is eliminated and
the stator active and reactive powers are controlled directly.
II. COMBINED VECTOR AND DIRECT POWER CONTROL The principles of DPC can be explained by the following stator
active and reactive power equations [7]:
A. Vector Control
VC is the most popular method used in the DFIG-based ' '
WTs. In this method, the stator active and reactive powers are
controlled through the rotor current VC. The current vector is
' ' '
decomposed into the components of the stator active and
reactive power in synchronous reference frame. This decouples
the active power control from the reactive power control. The By assuming constant magnitude for the stator and rotor flux,
stator active and reactive power references are determined by the derivative of (9) can be represented approximately as
the maximum power point tracking (MPPT) strategy and the
grid requirements, respectively. The phase angle of the stator ' '
flux space vector is usually used for the controller synchroni-
zation. However, if the stator flux-oriented frame (SFOF) is
used, the overall performance of VC will be highly dependent Equation (11) shows that the stator active power dynamics
on the accurate estimation of the stator flux position. This can depends on the variation of . Therefore, the fast active power
be a critical problem under the distorted supply voltage control can be achieved by rapidly changing . By assuming
condition or varying machine parameters. Therefore, in this constant magnitude for the stator flux and , the derivative of (10)
paper, the stator-voltage-oriented frame (SVOF) is used for the can be represented approximately as
controller synchronization. In order to extract the synchroni-
zation signal from the stator voltage signal, a simple phase- '
'
locked-loop (PLL) system is used. The stator active and
reactive powers are expressed as [3]
Equation (12) shows that the stator reactive power dynamics
depend on the rotor flux magnitude variation. Therefore, the fast
reactive power control can be achieved by rapidly changing the
rotor flux magnitude. The variation in the rotor flux can be carried
out by applying the appropriate inverter voltage vectors to the
rotor windings to rotate the rotor flux linkage vector. The rotor
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MOHAMMADI et al.: CVDPC FOR DFIG-BASED WTs 3

Fig. 1. Block diagram of the vector-controlled RSC.

TABLE I
SWITCHING TABLE OF ROTOR VOLTAGE VECTOR IN DPC METHOD

Fig. 2. Block diagram of the direct power-controlled RSC.

In the VC method, at constant stator voltage, (7) and (8) imply

voltage equation can be represented and approximated in a short that
interval of as
'
'

The six inverter voltage vectors can be appropriately used to On the other hand, considering the principles of DPC, Fig. 3
control the position and value of the rotor flux ' by knowing the shows the rotation of the rotor flux vector ' to ' in an inverter
sector in which ' is located. The block diagram of the direct switching period, while ' remains intact at the stator time
power controlled RSC is shown in Fig. 2. The hysteresis con- constant which is much longer than the inverter switching period.
trollers generate flags ( and ) via the stator active and Here, ' is decomposed into its radial component ' and its
reactive power errors to choose the best voltage vector from the tangential component ' , where the former contributes to the
switching table presented in Table I [3]. flux magnitude and the latter provides the flux angle rotation.
According to Fig. 3, (9) and (10), the stator active and reactive
C. Mathematical Similarities Between VC and DPC power variations are obtained as
In this section, the mathematical similarities between VC and
' ' '
DPC are presented to prove that these methods have a common
basis despite their implementation differences. ' ' '
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4 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY

methods provide the same performance if the number of inverter

voltage vectors is not limited.

III. PROPOSED CONTROL SYSTEM

A. The Basic Idea
As shown in Section II, there is a direct relationship between
the hysteresis control of the stator active power in DPC and the
rotor direct axis current control in VC. On the other hand, it is
illustrated that the hysteresis control of the stator reactive power
Fig. 3. Flux linkage vector variation during a switching period in DPC. in DPC closely corresponds to the rotor quadrature axis current
control in VC. Owing to these facts, it is possible to propose a
where the constant values of , , and are given in new control system based on the common fundamentals of both
Appendix A. According to the small value of , with a good methods by combining the merits of DPC and VC. This way, it
approximation of may be possible to provide a control system with a desirable
performance and a rather simpler implementation. Equivalently,
it may be regarded as a new system without some of the
difficulties associated with either DPC or VC.
and As was proven, by faster selection of the power electronic
'
switches status, DPC can provide faster torque/power response.
'
This, in turn, is due to the use of a predetermined switching table
' ' ' instead of a much more time consuming PWM procedure. Also,
the use of hysteresis controllers, which provide inputs to the
Substituting (17)–(19) into (15) and (16) yields switching table, contributes to the fast dynamics of DPC. There-
fore, the hysteresis controllers and switching table are good
' '
' ' ' candidates for the construction of the new control system. In the
indirect VC system, the direct and quadrature axis components of
the rotor current are controlled instead of the stator active and
' ' reactive power.

B. The Control System Structure

In (20), the second term in the bracket is created due to the
limited inverter voltage vectors and inverter failure to separate The proposed control system in Fig. 4 is divided into a VC part
the radial and tangential flux components. This term becomes and a DPC part that are shown on the left side and the right side of
extremely small by decreasing the bandwidth of the hysteresis the figure, respectively. As seen, the system uses the - and -axis
controllers. Also, the third term in the bracket contains multipli- hysteresis current controllers similar to those in VC and the
cation of small terms, such that a good approximation of the switching table like the one in DPC. The - and -axis current
stator active power variations is obtained as commands are conventionally generated by the PI power con-
trollers and compared with their actual values. Of course, the
' '
reference frame transformation is required as in VC. The - and
Thus, -axis flags as inputs to the switching table are produced from the
' rotor current errors by the hysteresis controllers. The third input
' to the switching table determines the sector through which the
rotor flux vector is passing. It is produced by measuring the stator
From (23) and (24), the stator active and reactive power and rotor currents and the rotor position. The switching table
variations are negatively proportional to the tangential and radial provides the proper voltage vectors by selecting the status of the
components variation in the rotor flux respectively. By compar- inverter switches, the same as in DPC. The switching table is
ing (23) and (24) with (14), the following results are obtained: shown in Table I, which produces all eight voltage vectors
including zero voltages. The system lacks PI current controllers,
' a PWM, and feed-forward terms that are usually available in the
' VC systems. In fact, the system is a current VC system by means
of a voltage vector selection of the DPC type.
It means that the variations in the tangential and radial
components of the rotor flux in DPC are proportional to the
IV. SIMULATION RESULTS
variations in the direct and quadrature axis components of the
rotor current vector in VC, respectively. Therefore, there is an In this section, an extensive simulation study, using MATLAB/
obvious analogy between VC and DPC methods, so that two Simulink, is conducted on a 9-MW wind farm consisting of
perpendicular variables are responsible for controlling the stator six 1.5-MW DFIG-based WTs to compare the performance of
active and reactive powers independently. Indeed, two control the proposed CVDPC method with both VC and DPC. Fig. 5
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MOHAMMADI et al.: CVDPC FOR DFIG-BASED WTs 5

Fig. 4. Proposed control system.

Fig. 5. Schematic diagram of the simulated system.

shows the schematic diagram of the simulated system with

parameters given in Appendix B. Generally, in order to evaluate
the CVDPC method, the evaluation is divided into two parts: the
first part is related to the steady-state conditions and the second
part is regarding the transient conditions. The bandwidth of
hysteresis current controllers are set to in
this study. By selecting these values, a tradeoff between the rotor
current tracking accuracy and the maximum switching frequency
(MSF) of the RSC is obtained. An optimal tuning of the PI Fig. 6. Converge of the cost function in GA.
controller gains is necessary to achieve a fair comparison be-
tween the three methods. Therefore, an optimal conventional Fig. 7 shows the system simulation results in the steady-state
controller (OCC) of the PI type is used. The controller parar- conditions for . The assumed constant wind speed
meters are optimized by using the standard optimization genetic is 15 m/s when the generators rotate at based on
algorithm (GA). The control loops of the stator active and the simulated optimal power–speed curve. As so, the active
reactive powers and rotor currents have been optimized under power of 9 MW is generated in the wind farm. As the DFIGs
the constant conditions of rotor speed and stator reactive power at rotate at supersynchronous speed with , the active
and simultaneously. The cost func- power is delivered to the grid through both stator and rotor
tion of the optimization algorithm is defined as windings ( and ). According to
the maximum use of the RSC current capability for producing
active power, the stator reactive power production is zero.
Considering the results given in Fig. 7, it can be concluded that
the CVDPC has power ripple as low as that of VC, which is equal
The convergence of the cost function in each optimization step to 0.55%. Also, it operates the machine significantly softer than
is shown in Fig. 6. DPC with a ripple of 2.22%.
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6 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY

Fig. 8. (a) Stator output current in steady-state conditions and (b)–(d) THD of
VC, DPC, and CVDPC.

Fig. 7. System simulation results in steady state conditions.

harmonic distortion (THD) is equal to 1.28% and the switching
Moreover, the steady-state performance of the CVDPC is frequency specified by the carrier waveform, e.g., 2.5 kHz. Also,
compared with both VC and DPC in terms of the harmonic in case of the DPC, the THD is equal to 4.64%, and the MSF is
distortions of the stator output current and the MSF of the RSC by limited to 7.5 kHz. However, by using CVDPC, the THD of the
a fast Fourier transform (FFT) analysis. Fig. 8 shows the stator stator current is equal to 2.10% and the MSF is limited to 7.5 kHz.
three-phase currents and harmonic spectra. For VC, the total So, the THD level and the amplitudes of the individual harmonic
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MOHAMMADI et al.: CVDPC FOR DFIG-BASED WTs 7

Fig. 10. System simulation results when is changed.

step changes from 15 to 10 m/s at , the rotor speed

Fig. 9. Simulation results when the wind speed varies from 15 to 10 m/s.
changes from 1.2 to 0.8 p.u. and the stator active power produc-
tion decreases from 7.58 to 2.81 MW. When the DFIGs rotate at
subsynchronous speed with , 20% of the stator active
components are lower than the permitted distortion limits sug- power is fed back to the machine through the converters
gested in IEEE Standard 1547 [17]. Therefore, it can be con- ( ). Note that the stator active power changes
cluded that the CVDPC has a suitable THD as low as that of VC, are obtained by decreasing from 0.79 to 0.3 p.u., while is
which is less than that of DPC. kept constant. This matter illustrates the independent control of
The second part of the evaluation includes the transient the stator active and reactive powers. Note that during the
conditions under the variable wind speed. Fig. 9 shows the synchronous operation around , no active power is
simulation results in these conditions. While the wind speed transferred from the back-to-back converters connected to the
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8 IEEE TRANSACTIONS ON SUSTAINABLE ENERGY

rotor. Considering the results, it can be concluded that the Grid filter impedance:
CVDPC responds to the wind speed variations approximately
2) Transmission line parameters:
as fast as that of DPC, which outperform the VC in terms of
Length: 30 km;
dynamic response.
Positive and zero sequence resistances: 0.1153,
In order to compare the proposed CVDPC with VC in terms of
Positive and zero sequence inductances: 1.05, 3.32 mH/km
robustness and decoupled performance, changing is sug-
Positive and zero sequence capacitances: 11.33, 5.01 nF/km
gested. Fig. 10 shows the simulation results in this condition. So,
at , is increased to four times the current value. As a 3) Transformer parameters:
result, the total active power expriences the transient state before : 12 MVA, 585 V/25 KV, impedance:
returning to the steady-state operation. The stator active power : 47 MVA, 25 KV/120 KV, impedance:
increases from 7.58 to 8 MW and the rotor active power
decreases from 1.42 to 1 MW, whereas the stator reactive
4) Network impedance:
power remains unchanged. As it is noticed in Fig. 10, when is
changed, the CVDPC-like DPC operates more robustly in com-
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MOHAMMADI et al.: CVDPC FOR DFIG-BASED WTs 9

Jafar Mohammadi received the B.Sc. degree in Saeed Afsharnia received the B.Sc. and M.Sc. de-
electrical engineering from the University of grees in electrical engineering from the University of
Mazandaran, Babolsar, Iran, in 2009, and the M.Sc. Amirkabir, Tehran, Iran, in 1987 and 1990, respec-
degree in electrical engineering from the University of tively, and the Ph.D. degree in electrical engineering
Tehran, Tehran, Iran, in 2012. from the Institute National Polytechnique de Lorraine
He is currently working as a Research Assistant at (INPL), Lorraine, France, in 1995.
the University of Tehran. His current research inter- Currently, he is an Associate Professor in the
ests include motor drives and application of power School of Electrical and Computer Engineering, Uni-
electronics in renewable energy conversion, especial- versity of Tehran, Tehran, Iran. His research interests
ly control and operation of doubly fed induction are the application of power electronics to power-
generator for wind power generation. quality problems and distributed generation.

Ehsan Daryabeigi received the B.Sc. degree in elec-

trical engineering from the Islamic Azad University
Sadegh Vaez-Zadeh (S’95–M’03–SM’05) received (IAU), Yazd, Iran, in 2005 and the M.Sc. degree in
the B.Sc. degree from Iran University of Science and electrical engineering from the IAU, Najafabad, Iran,
Technology, Tehran, Iran, in 1985, and the M.Sc. and in 2009.
Ph.D. degrees from Queen’s University, Kingston, He has been an Associate Researcher with the
ON, Canada, in 1993 and 1997, respectively, all in Advanced Motion Systems Research Laboratory,
electrical engineering. University of Tehran, Tehran, Iran, since 2011. His
Currently, he is a Professor and the Director of research interests include applications of advanced
Advanced Motion Systems Research Laboratory in control and optimization techniques in electric drive
the School of Electrical and Computer Engineering, control, power electronics, and power systems.
University of Tehran. His research interests include Mr. Daryabeigi has been a Student Member of Young Researchers and Elite
advanced rotary and linear electric machines and Club, since 2008, and a member of the American Association for the Advance-
drives, magnetic levitation, electric vehicles, and power system control and ment of Science, since 2012. Furthermore, he has been a reviewer for the Journal
policy issues. He has authored or coauthored about 60 journal papers in these of Intelligent and Fuzzy Systems, since 2013.
areas and holds a U.S. patent.
Prof. Vaez-Zadeh is an Editor of IEEE TRANSACTIONS ON ENERGY CONVERSION
and a member of editorial boards of International Journal of Power System
Optimization and Iranian Journal of Electrical and Computer Engineering. He
has been a Coeditor of the Journal of Asian Electric Vehicles. He is the president
of Power Electronics Society of Iran and a member of IEEE PES Motor Sub-
Committee and Power System Stability Control Sub-Committee. He has received
a best paper award from the Iran Ministry of Science, Research and Technology in
2001 and a best research award from the University of Tehran in 2004. He has also
been awarded an International Khwarizmi Award and the first prize of The
Commission on Science and Technology for Sustainable Development in the
South (COMSATS) in 2011.