Effect of DC Link Capacitor on the Performance of Wind-Driven
Double-Fed Induction Generator
SANAA M I AMER, MONA N ESKANDER
Department of Power Electronics and Energy Conversion,
Electronics Research Institute,
Cairo,
EGYPT
Abstract: - In this paper, the starting performance of a double-fed induction generator (DFIG) operating at
super-synchronous speed is investigated when varying the values of the DC link capacitor. The starting
transients, the settling time, and the harmonics of the stator and rotor currents and voltages are investigated as a
function of the DC link capacitor Cd. Curve fitting is applied to derive mathematical equations (polynomial)
relating the variation of the stator current THD with the value of the DC capacitor. Similarly, polynomials are
deduced to relate the THD of the rotor current and rotor voltage with the value of the DC link capacitor. These
polynomials help to design the DC link parameters that lead to minimum current and voltage harmonics of the
grid-connected DFIG. The minimum THD values of the stator current, rotor current, and rotor voltage are
presented. These results are repeated at different rotor speeds to deduce the optimum Cd value within a wide
speed range. Also, the effect of Cd on the DC link current and voltage ripples is demonstrated at different
speeds.
Key-Words: - double-fed induction generator, super-synchronous speed, DC link capacitor, THD, DC ripples,
starting transients, settling time, stator harmonics, rotor harmonics.
Received: February 25, 2023. Revised: December 11, 2023. Accepted: December 21, 2023. Published: March 12, 2024.
1 Introduction
Power generation from wind energy, as a renewable
non-polluting energy source, is preferably done with
DFIG (Doubly Fed Induction Generator) due to the
low ratings of the rotor converters leading to an
economic generation system, [1], [2], [3], [4], [5].
The rotor of the DFIG is mechanically coupled to
the wind turbine, while the stator windings of the
DFIG are directly connected to the grid. The rotor
windings are connected to the grid via slip rings and
an AC/DC/AC converter (rectifier and inverter with
a common DC link). The maximum power that the
rotor converters of the DFIG have to handle under
steady-state conditions is a fraction of the DFIG
machine-rated power. This fraction is approximately
equal to the 30% of the rated power, [6].
Recent studies showed that faults in the power
electronic converters account for a great share of the
overall wind turbine systems faults, [7], [8], [9]. The
DC link capacitors are regarded as one of the
weakest parts in back-to-back power converters,
[10], [11]. The DC link capacitor ripple current
causes thermal stress, leading to a high percentage
of the overall capacitor losses, [12]. Hence, it is
clear that the DC link capacitor impacts the
performance of the DFIG, not only during its steady
state operation but also at starting and during grid
voltage fluctuations. It also affects the total
harmonic distortion THD of the DFIG voltages and
currents. Hence the DC link filter must be carefully
designed to attain optimum DFIG performance at
starting, at steady state, and during grid voltage sags
and swells.
In this paper, the effect of the DC link capacitor
on the starting transients, the settling time, and the
harmonics of the stator and rotor currents, and stator
and rotor voltages, are being investigated.
Moreover, the DC voltage and current ripples are
calculated at different values of Cd. The THD of the
stator current, the rotor current, and rotor voltage at
different values of the DC capacitor; are also
deduced. Mathematical equations relating the
variation of the stator current, rotor current, and
rotor voltage THD with the value of the DC
capacitor are deduced. These results help in
designing the DC link filter components to attain
minimum transients’ settling time and minimum
harmonics for better performance of the DFIG. The
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Sanaa M. I. Amer, Mona N. Eskander
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ripples of the DC link voltage and current are
deduced and plotted versus Cd.
The contribution achieved in this paper can be
summarized as follows:
i. demonstrating the effect of the DC link
capacitor on the magnitude of starting current and
voltage transients and on their settling time, which
leads to safe starting
ii. deducing mathematical equations to relate the
value of the DC link capacitor with the harmonics of
stator current and rotor voltage and rotor current,
which helps in designing the DC link components to
minimize the current and voltage harmonics.
Fig. 1: The DFIG with back-to-back converters
2 Mathematical model of DFIG
Figure 1 shows the configuration of the DFIG with
back-to-back converters and the DC link. The DFIG
dynamic equations in the d-q synchronously rotating
frame are given as, [13]:
(1)
The electric torque equation is:
Where, , v, i, ω, Te denote flux, voltage, current,
angular speed, and electromagnetic torque
respectively. Suffixes d and q denote the d-axis
component and q-axis component in the
synchronously rotating d-q reference frame,
respectively. r and L denote resistance and
inductance, respectively. Suffixes s, r, and m
denote stator, rotor, and mutual parameters
respectively; P is the number of pole pairs
The power balance equation in the DC link, [14]:
(11)
(12)
Where Pin is power given by inverter I, shown in
Figure 1, Pout is power output from DC link, Pl is DC
link losses.
Substituting equation (11) in equation (12) gives:
(13)
(14)
(15)
Where Vdc is the instantaneous voltage and Wbus
is the instantaneous energy stored in a capacitor.
3 Results and Discussion
Equations (1-15) describing the grid-connected
DFIG at starting and during steady-state operation
are simulated using Matlab/Simulink software. The
system performance is investigated at two super-
synchronous speeds namely; 1850 rpm and 1900
rpm. The DC capacitor is varied at each speed to
study its influence on the DFIG performance. The
following results are obtained.
3.1 The Settling Time after Starting
Figure 2 shows the profiles of the stator voltage,
stator current, rotor voltage, and rotor current at
starting when the reference speed is 1850 rpm with
Cd=0.025F. Figure 3, Figure 4 and Figure 5 show
the starting profiles at Cd= 0.01F, Cd=.0075F, and
Cd=0.005F respectively. It is worth noticing that the
stator voltage is not affected by Cd. These results
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clarify the effect of the dc link capacitor on the
settling time, showing the decrease in starting
transients settling time with the increase in value of
Cd. It is noted that the magnitudes of the currents
and voltages starting transients are nearly equal, i.e.
not affected by the dc link capacitor.
Fig. 2: Voltage and current profiles at Cd=0.025F,
1850 rpm
Fig. 3: Voltage and current profiles at Cd=0.01F,
1850 rpm
Fig. 4: Voltage and current profiles at Cd=.0075F,
1850 rpm
Fig. 5: Voltage and current profiles at Cd=.005F,
1850 rpm
To prove the effect of Cd on starting transients,
the stator current, the rotor current, and the rotor
voltage at starting are calculated with the same
values of the DC link capacitor at 1900 rpm
reference speed. Figure 6, Figure 7, Figure 8 and
Figure 9 show the stator current, rotor voltage, and
rotor current at Cd=0.025F, 0.01F, 0.0075F, and
0.005F respectively.
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Fig. 6: Voltage and current profiles at Cd=0.025F,
1900 rpm
Fig. 7: voltage and current profiles at Cd=0.01F,
1900 rpm
Fig. 8: Voltage and current profiles at Cd=0.0075F,
1900 rpm
Fig. 9: voltage and current profiles at Cd=.005F,
1900 rpm
From these figures, it is clear that the settling
times of the stator and rotor currents and rotor
voltage are affected by Cd value while the
magnitude of these transients are not affected. To
clarify the effect of Cd on the starting transient
settling time, the settling time (ts) is plotted as a
function of the DC link capacitor as shown in Figure
10. The starting transient settling time decreases
drastically as Cd increases, revealing the influence
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of the dc link capacitor on the stator as well as on
the rotor currents and voltages.
It is noted from Figures 2, Figure 3, Figure 4,
Figure 5, Figure 6, Figure 7, Figure 8 and Figure 9
that settling time ts differs for each variable, i.e. ts of
stator current lower than ts of rotor current. In Figure
10, the longest ts (that of ir) is plotted versus Cd. An
exponential decrease in the settling time occurs as
Cd increases.
Fig. 10: Variation of rotor current starting transient
settling time with DC link capacitor
3.2 Effect of Cd on Current and Voltage
Harmonics
Suppressing current harmonics is essential for the
grid-tied doubly-fed induction generator (DFIG) to
prevent grid distortion, especially in weak grids or
grids with a large number of connected wind energy
sources. Sources of DFIG harmonics include
switching of the two back-to-back rotor converters,
as well as wind speed fluctuations. In this section,
the variation of currents’ and voltages' harmonics
(THD) with Cd is investigated and the results are
plotted. These results are then interpolated in the
form of mathematical equations relating the THD of
each variable with the value of Cd. These equations
help in determining the dc link capacitor value to
minimize the harmonics of each variable.
3.2.1 Variation of Stator Current Harmonics
with Cd
In Figure 11, the THD of the stator current is plotted
versus Cd showing minimum harmonics distortion
at Cd= 0.01F.
Fig. 11: Variation of stator current THD with Dc
link capacitor
Interpolating the THD versus Cd curve led to the
following polynomial.
General model:
(16)
where x stands for Cd and the coefficients are given
by:
p1= 2.675e4 p2= 3e4 p3= 3.086e4
q1=215.2 q2= 1854 q3= 2423 q4= 3020
Goodness of fit:
SSE (sum squared error): 0.1952
Figures 12a and 12b show the minimum THD of the
stator current. A 10.01% THD occurred at
Cd=0.01F for both reference speeds: 1850 rpm and
1900 rpm.
(a) at 1850 rpm
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(b) at 1900 rpm
Fig. 12: Stator current THD
3.2.2 Variation of Rotor Current Harmonics with
Cd
In Figure 13, the THD of the rotor current is plotted
versus Cd showing minimum harmonics distortion
at Cd= 0.005F.
Fig. 13: Variation of rotor current THD with DC
link capacitor at 1850 rpm
3.2.3 Variation of Rotor Voltage Harmonics with
Cd
In Figure 14, the THD of the rotor voltage is plotted
versus Cd showing minimum harmonics distortion
at Cd= 0.065F
Fig. 14: Variation of rotor voltage THD with Cd at
1850 rpm
Applying curve fitting to the plotted rotor voltage
versus Cd shown in Figure 14, the following
polynomial is deduced:
(17)
where x stands for Cd and the calculated
coefficients are given by:
p1= 28.43 (- 51.4, 109.3)
p2= - 4.239(-12.9, 4.433)
p3=2.397(2.26, 2.535)
Goodness of fit:
SSE (sum squared error): 0.01517
The minimum value of the rotor voltage THD at
1850 rpm is 2.29%., occurred at Cd=0.065F, as
shown in Figure 15a. The minimum value of the
rotor voltage THD at 1900 rpm is 0.83%, occurred
at Cd=0.01F, as shown in Figure 15b. These results
help to choose a value for Cd according to the
operating speed range, since Cd for minimum THD
differs according to the speed.
(a) at 1850 rpm
(b) at 1900 rpm
Fig. 15: Minimum THD of rotor voltage
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3.3 Effect of DC Link Capacitor on DC
Voltage Ripple
Ripple is wasted power, and has many undesirable
effects on the DC circuit. It heats its components,
causes noise and distortion. The DC-link capacitor
is the most vulnerable component of a voltage
conversion system. It is responsible approximately
for 30% of failures in power converters, [11]. The
current flowing through the capacitor causes power
loss over the effective series resistance (ESR),
leading to temperature rise, which results in
shortening the life span of the capacitor, [12]. In
back to back converters system, the DC-link
capacitor is subjected to constant stress, since it
handles the current, flowing through it from the
rectifier and the inverter sides, [13]. To prolong the
lifespan of the Cd, connecting more capacitors in
parallel to share the ripple current was suggested.
This approach is effective in terms of failure
prevention. However, it increases the size and the
cost of the system, [14]. Hence studying the DC
current and DC voltage ripples as a function of the
DC link capacitor is essential for the safety of power
electronics components.
Also comparing the value of Cd giving
minimum DC ripples with the Cd value (given in
the last section) resulting in minimum THD, enables
the choice of the DC link capacitor for optimal
operation of the DFIG.
Figure 16, Figure 17, Figure18 and Figure 19
demonstrate the DC link voltage and current at 1850
rpm and Cd=0.025 F, 0.01F, 0.0075F, and 0.005
respectively. As expected, the ripples of voltage and
current increase as Cd decreases. To study the level
of DC ripples at higher speeds, Figure 20, Figure 21,
Figure 22 and Figure 23 demonstrate the DC link
voltage and current at 1900 rpm and Cd=0.025F,
0.01F, 0.0075F, and 0.005 respectively. Higher
ripples occurred at higher DFIG speed.
Fig. 16: DC link voltage and current at 1850 rpm &
Cd=0.025 F
Fig. 17: DC link voltage and current at 1850 rpm
& Cd=0.01 F
Fig. 18: DC link voltage and current at 1850 rpm &
Cd=0.0075 F
Fig. 19: DC link voltage and current at 1850 rpm &
Cd=0.005 F
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Fig. 20: DC link voltage and current at 1900 rpm &
Cd=0.025 F
Fig. 21: DC link voltage and current at 1850 rpm &
Cd=0.01 F
Fig. 22: DC link voltage and current at 1850 rpm &
Cd=0.0075 F
Fig. 23: DC link voltage and current at 1900 rpm &
Cd=0.005 F
The DC link voltage ripple is plotted versus Cd
in Figure 24 and Figure 25 at 1850 rpm and 1900
rpm respectively. These plots prove the increase in
voltage ripple as speed increases. It also shows an
exponential decrease in voltage ripple with an
increase in Cd.
Similarly, Figure 26 and Figure 27 prove the
increase in DC link current ripples as the speed
increases from 1850 rpm to 1900 rpm. These plots
demonstrate the fast decrease in current ripples as
Cd increases.
Fig. 24: DC link voltage ripples versus and current
Cd at 1850 rpm
Fig. 25: DC link voltage ripples versus and current
Cd at 1900 rpm
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Fig. 26: DC link current ripples versus and current
Cd at 1850 rpm
Fig. 27: DC link current ripples versus and current
Cd at 1900 rpm
4 Applications
The results obtained from the simulations can be
applied to design the AC/DC/AC converter
interfacing a generator or an electrical drive with the
grid to minimize the harmonics injected into the
grid. Also, the starting current and voltage transients
can be reduced by using a DC link capacitor at
starting different from the DC link capacitor during
steady state operation. Hence it is clear that Cd
affects the power quality of the DFIG, [15].
The DC link capacitor affects greatly the fault
ride-through and fault recovery for grid-connected
generators or motors, [16].
5 Conclusion
The starting voltage and current transients of a
double-fed induction generator (DFIG) operating at
super-synchronous speed are investigated when
varying the values of the DC link capacitor (Cd).
The stator current, rotor current, and rotor voltage
harmonics are also calculated as Cd is varied. These
variables are calculated at two super-synchronous
speeds.
The starting transients settling time and the
harmonics of the stator current, rotor current, and
rotor voltage are highly affected by the value of the
DC link capacitance. However, the magnitude of the
starting current and starting voltage transients are
not affected by Cd.
The value of the DC link capacitor (Cd) that
results in minimum stator current harmonics is
deduced. Also, the values of Cd that lead to
minimum rotor current harmonics and minimum
rotor voltage harmonics are deduced. Mathematical
equations relating the minimum THD of these
variables with Cd are deduced. These equations aid
in designing the DC link variables that minimize
THD. The results proved that the DC link capacitor
resulting in minimum stator current harmonics
differs from Cd which led to minimum rotor current
harmonics, and Cd which led to minimum rotor
voltage harmonics. Since the stator is directly
connected to the grid, it is recommended to employ
the DC link capacitance that results in minimum
stator current harmonics, to avoid grid voltage
distortion.
Also, the influence of Cd on the DC link
voltage and current ripples is investigated. Results
prove that the DC link voltage and current ripples
are smoothed as Cd increases.
Future work will focus on the role of Cd during
symmetrical and unsymmetrical grid faults and its
influence on the fault recovery time.
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Contribution of Individual Authors to the
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The authors equally contributed in the present
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problem to the final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
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