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TEMPUS ENERGY: VOLTAGE DIPS
1: Introduction
When considering an electrical grid, a voltage dip occurs when a short circuit occurs as visualized in
Figure 1. The grid impedances 𝑍1 , 𝑍2 and 𝑍3 are smaller than 𝑍𝑙𝑜𝑎𝑑 . This implies that, in normal
conditions, 𝑢𝑔𝑟𝑖𝑑 (𝑡) is more or less the same as 𝑢𝑓 (𝑡). In case of a short circuit which shorts 𝑍3 and
𝑍𝑙𝑜𝑎𝑑 , only 𝑍1 and 𝑍2 limit the current. Due to this large short circuit current, a large voltage drop
appears across impedance 𝑍1 which implies 𝑢𝑔𝑟𝑖𝑑 (𝑡) will be much smaller than 𝑢𝑓 (𝑡). This is the
situation from the moment the short circuit occurs and this situation remains as long as the
protective devices have not eliminated the short circuit (e.g. during 1 second).
Figure 1: Voltage dip due to a short circuit
Figure 2: Evolution of the grid voltage during a voltage dip
A voltage dip can be noticed when the light goes out for a very short moment of time. In industrial
processes, a voltage dip can disturb the functioning of equipment implying a fully automated
production process can come to a standstill. This gives production losses since it can ask a lot of time
and effort to start up the production process again. The depth and the duration of the dip are very
important. The larger the depth and the larger the duration of the voltage dip, the more severe the
dip. This implies it is useful to eliminate the short circuit as fast as possible.
Figure 3: Voltage dips
Variations of the voltage level between 90% and 110% of the nominal voltage level are normal. One
speaks about a voltage dip when the remaining voltage level is between 90% and 10% of the
nominal voltage level and the duration of the dip can vary between 10 𝑚𝑠 and several seconds as
visualized in Figure 3. When the remaining voltage is lower than 10% of the nominal voltage level,
one speaks about a ‘voltage interruption’. A distinction is made between short interruptions and long
interruptions. A ‘voltage swell’ occurs when the voltage level is higher than 110% of the nominal
voltage.
Due to a short circuit, generally a voltage dip with a low voltage level is obtained during a relatively
short time (as long as the short circuit is not eliminated). In literature, also ‘sags’ are mentioned.
Sometimes, a sag and a dip are interchangeable terms. Sometimes, the word sag is used for a voltage
dip which has a limited depth but lasts for a longer time. For instance, this occurs due to a large load
consuming a large current causing a voltage drop across the grid impedance. A similar situation can
occur due to a high inrush current of e.g. an induction motor (which lasts longer than a short circuit
current). Indeed, an inrush current lasts longer than a short circuit current but an inrush current has
a smaller amplitude.
As the grid impedance decreases and as the current is consumed closer to the Point of Common
Coupling (PCC), i.e. the secondary of the feeding distribution transformer, the voltage dips are
smaller.
1.2: Wind turbines and wind farms
In case of a voltage dip, the speed of a wind turbine and the magnetization of the generator can
change implying the wind turbine must be disconnected from the grid. Especially when the power
production of the wind turbines is important, disconnecting these wind turbines from the grid is not
acceptable. By disconnecting the wind turbines from the grid, insufficient power is produced to
supply the loads (a power unbalance is created). Therefore, it is important to increase the “ridethrough” capacity of the wind turbines in case of a voltage dip. This means it is important to cope
with voltage dips (and grid disturbances in general) without disconnection and the wind turbines
should supply active and reactive power after the fault has been cleared.
2: Voltage dips due to short circuits
Figure 4: Impact of a short circuit on the grid
The grid visualized in Figure 4 contains two generators, grid impedances, circuit breakers and
electrical loads. The grid contains three voltage levels:
-
level 1 = the high voltage level,
level 2 = the medium voltage level,
level 3 = the low voltage level.
Two short circuits are considered: error F1 (in the high voltage grid) and error F3 (in the low voltage
grid). Only one single short circuit is considered at a time. In case short circuit F1 occurs, the voltage
dips which occur have remaining magnitudes of:
-
0% at load 1,
50% at load 2,
50% at load 3.
The depths of the voltage dips can be calculated by the equivalent circuit of Figure 5. Figure 5
visualizes the grid of Figure 4 and contains the grid impedances, the load impedances and the
voltage(s) applied by the generators (expressed in p.u.). The location of the short circuit F1 is also
indicated.
Figure 5: Equivalent circuit in case of short circuit F1
The impedances of load 1, load 2 and load 3 are very large in comparison with the grid impedances.
This implies (almost) no current is flowing in the impedances having a magnitude 0.5 and 1 (load
currents are much smaller than short circuit currents).
Figure 6: Equivalent circuit in case of short circuit F3
In case short circuit F3 occurs, the equivalent circuit visualized in Figure 6 is obtained. Notice the
presence of short circuit F3 instead of short circuit F1. The impedances of load 1, load 2 and load 3
are large in comparison with the grid impedances. Due to the short circuit, the voltage dips which
occur have remaining magnitudes of:
-
98% at load 1,
64% at load 2,
0% at load 3.
This example allows to conclude that a short circuit close to the power sources (level 1, high voltage
level, e.g. F1) have a larger impact on a larger number of loads. A short circuit farther removed from
the power sources (level 3, low voltage level, e.g. F3) has an impact on a smaller number of loads and
the impact is also smaller.
Loads fed by the low voltage grid (level 3) face a larger number of voltage dips and these dips have a
larger depth. Loads fed by the high voltage grid (level 1) face a smaller number of dips and these dips
generally have a smaller depth.
3: Immunity with respect to voltage dips
There exist curves which describe the required immunity with respect to voltage dips and swells.
Figure 7 visualizes the ITIC curve and Figure 8 visualizes the ANSI curve.
Figure 7: ITIC curve
When considering swells, the upper curve is relevant. When considering voltage dips, the lower curve
is relevant. During a limited time, the device must withstand large voltage deviations. The smaller the
deviation of the voltage level in comparison with the nominal voltage level, the longer the device
must be able to withstand this voltage deviation.
In order to avoid or reduce problems related with voltage dips, there are mainly two approaches.
First of all, it is important the reduce the emission of voltage dips (reducing the depth and the
duration of the voltage dips). By reducing the grid impedance, by reducing inrush currents, … a lot of
problems are reduced. Alternatively, using an automatic voltage regulator (suitable when considering
dips with a limited depth having a larger duration) or a dynamic voltage regulator (suitable when
considering dips with a large depth having a short duration) the voltage dip can be reduced.
Instead of reducing the emission, it is also possible to increase the immunity. For instance, a PC or a
PLC contains a power supply containing a capacitor. When a larger capacitor value is used, more local
energy storage is available implying a larger immunity with respect to voltage dips.
The immunity with respect to voltage dips strongly depends on the device. For instance contactors
and relays can be quite sensitive with respect to voltage dips and voltage interruptions. Rotating
induction motors store kinetic energy implying they keep rotating during the voltage dip or the
voltage interruption. Notice however, when the supply voltage is restored a new ‘inrush current’ is
consumed. This is especially important when a large number of motors are fed by the grid and they
all consume this “inrush current” at the same time.
Figure 8: ANSI curve
4: Voltage swells
Figure 9: Occurrence of a voltage swell
Consider Figure 9 where the original grid voltage 𝑢𝑓 (𝑡) is a sine having a constant amplitude.
Suppose the grid impedances 𝑍1 , 𝑍2 and 𝑍3 are inductive (or ohmic-inductive). In case 𝑍𝑙𝑜𝑎𝑑 is also
inductive or ohmic-inductive, the grid voltage 𝑢𝑔𝑟𝑖𝑑 (𝑡) is smaller than 𝑢𝑓 (𝑡). In case 𝑍𝑙𝑜𝑎𝑑 is
capacitive, the grid voltage 𝑢𝑔𝑟𝑖𝑑 (𝑡) is larger than 𝑢𝑓 (𝑡) giving a voltage swell.
5: Mitigation of voltage dips
In order to reduce the depth of a voltage dip in an existing grid, a number of approaches are possible.
A distinction will be made between an electromechanical voltage stabilizer, an electronic step
regulator, an electronic voltage stabilizer and a dynamic voltage restorer.
5.1: Electromechanical voltage stabilizer
Suppose there is a voltage dip but the depth of this voltage dip is limited implying the grid voltage is
still sufficiently high in order to be able to supply the required power. Since the grid is still able to
supply the power, the voltage stabilizer (the electromechanical voltage stabilizer) does not need
energy storage. Figure 10 visualizes an electromechanical voltage stabilizer.
Figure 10: Electromechanical voltage stabilizer
The control algorithm will not be studied here, only the basic approach will be discussed. The output
voltage between N and OUTPUT will be measured and fed back in order to control a motor M. The
motor moves the contact 3 of the autotransformer T2. This autotransformer has the output grid
voltage as an input (nodes 1 and 4).
The output voltage of autotransformer T2 is available nodes 3 and 6. It is possible to make this
voltage smaller or larger and also the polarity can be chosen. The voltage coming from the nodes 3
and 6 is applied to the isolation transformer T1 having a fixed winding ratio. The output voltage of
transformer T1 is mounted in series with the input grid voltage. This allows to mitigate voltage dips
and voltage swells i.e. to obtain an output voltage which is closer to the nominal voltage level.
Figure 11 visualizes the input-output-characteristic of the electromechanical voltage stabilizer. In
case of input voltage variations between −15% and +15%, the output voltage is varying between
– 𝑂. 5% and +0.5%. This means a large accuracy of the voltage level is obtained. Even when
considering input voltage variations of more than 15%, the output voltage variation is relatively
limited (e.g. 5%). A continuous, and not a stepwise, voltage regulation is obtained. The load (power
factor, amplitude of the current, …) has only a very limited effect on the output voltage.
Figure 11: Input and output voltage of an electromechanical voltage stabilizer
Figure 12: Transient behavior of an electromechanical voltage stabilizer
Notice however such an electromechanical voltage stabilizer has a number of drawbacks and
limitations. The electromechanical voltage stabilizer contains moving parts. This implies the response
time is quite large; 300 ms (15 periods of the grid voltage) is a typical value as visualized in Figure 12.
In case of a sudden change of the input grid voltage (increase or decrease), it takes approximately
300 ms before the original nominal voltage level is restored.
5.2: Electronic step regulator
Figure 13 visualizes an electronic step regulator. Notice the autotransformer which provides the total
required voltage. An electronic circuit measures the input voltage. This measurement result
determines how a number of relays must be switched in order to determine the number of primary
windings, the winding ratio and finally the output voltage.
Figure 13: Electronic step regulator
The approach using the electronic step regulator provides a number of advantages. An electronic
step regulator is less expensive than an electromagnetic voltage stabilizer. Moreover, the weight and
the dimensions are smaller.
In case the relays are replaced by semiconductor devices, there are no moving parts (although also
the realizations based on relays are reliable). The electronic step regulator has a smaller response
time i.e. there is a typical response time of 1 to 1.5 periods of the grid voltage (20 – 30 ms).
Figure 14 visualizes the input-output-characteristic of the electronic step regulator. Notice the
adjustments of the output voltage occur stepwise which is a disadvantage. The variations in the
output voltage are larger compared to the electromechanical voltage stabilizer (±6% in the present
example even when there are only limited variations in the input voltage level).
Figure 14: Input and output voltage of an electronic step regulator
5.3: Electronic voltage stabilizer
Figure 15 visualizes an electronic voltage stabilizer. Using a controllable H bridge, the grid voltage will
be converted to the required voltage level (with an appropriate phase) using PWM (e.g. with a
switching frequency of 20 kHz). The output voltage over the load is measured and compared with
the desired reference voltage allowing to control the H bridge. Using a transformer, the output
voltage of the H bridge will be transformed to an appropriate voltage level which is placed in series
with the available grid voltage.
Figure 15: Electronic voltage stabilizer
The approach of Figure 15 provides a number of advantages. The stabilizer is very fast having a
response time of for instance 0.5 periods of the grid voltage (10 ms). This implies it is also possible to
deal with fast voltage dips (although the depth must be limited).
An electronic voltage stabilizer has a low weight and its dimensions are small. The output voltage can
be adjusted very accurately.
5.4: Dynamic voltage restorer
Electromechanical voltage stabilizers, electronic step regulators and electronic voltage stabilizers do
not need energy storage. This implies they can only be used in case the grid is still able to supply the
required power (which is not possible when the voltage dips have a large depth). At the other hand
side, since no energy storage is needed, there is no limit on the duration of the voltage dip since the
grid still supplies the required power.
A dynamic voltage restorer contains energy storage which allows to restore voltage dips with a large
depth (and even voltage interruptions). The dynamic voltage restorer is only able to function
properly as long as there is still energy stored in the storage device (e. g. a capacitor or a flywheel)
which implies only (relatively) short time voltage dips and short time voltage interruptions can be
restored. Figure 16 visualizes a dynamic voltage restorer (DVR) which contains such a storage device
providing a DC voltage. This DC voltage is converted into an AC voltage which is placed in series with
the available grid voltage.
Figure 16: Dynamic Voltage Restorer
6: Voltage dip mitigation at wind farms
6.1: Importance
The number of wind turbines and wind farms has increased significantly the last few years. Since the
nominal powers of these wind turbines are also increasing, the amount of installed wind power
increases very fast and is important to maintain the power balance in the grid.
Nowadays, variable-speed wind turbines containing Doubly-Fed Induction Generators are quite
common. In case of a voltage dip (e.g. also due to a short circuit which is not related with the
operation of the wind farm), traditionally the wind turbine is automatically disconnected from the
grid in order to protect the entire installation including the power electronic converter. The wind
turbine is reconnected with the grid when the fault is cleared (after the voltage dip) and the voltage
is returned to its normal value.
When an entire wind farm is disconnected from the grid due to e.g. a voltage dip, it is very hard for
the grid operators to maintain the power balance. Therefore, wind turbines must be able to cope
with voltage dips (and grid disturbances in general) without being disconnected from the grid
(during the voltage dip, the wind turbine is not allowed to consume active or reactive power). This
so-called ride-through capability must ensure the wind generator injects the normal active and
reactive power once the fault has been cleared. This ride-through capability is not only important
when considering wind turbines equipped with a doubly-fed induction generator i.e. it is important
for wind turbines with all types of asynchronous and synchronous generators.
6.2: Mitigation of voltage dips
In order to obtain the ride-through capability of a wind farm with respect to a voltage dip, there are
mainly two approaches:
-
Using devices like a DVR or a D-STATCOM, the voltage dip can be eliminated (or its depth and
duration can be limited) implying the wind turbines will not be disconnected from the grid.
Improving the behavior of the wind turbine technology in order to withstand the voltage
dips.
First, the use of a DVR and a D-STATCOM will be discussed. As already visualized in Figure 16, a DVR
(Dynamic Voltage Restorer) can be used to compensate the voltage dips at the coupling transformer
between the wind farm and the public electricity grid. Figure 17 visualizes this situation.
Figure 17: Series compensation using a Dynamic Voltage Restorer (Alvarez et al.)
Notice in Figure 17 the Thévenin equivalent circuit (𝐸𝑆 and 𝑍𝑆 ) of the public electricity grid with the
Point of Common Coupling (PCC) between this public grid and the wind farm. Using a Voltage Source
Inverter (VSI), energy stored in a capacitor can be injected into the grid giving a voltage which is
placed in series with the available grid voltage. The voltage obtained by the VSI is filtered by a low
pass filter (components 𝐿𝑓 and 𝐶𝑓 ) giving a sine voltage.
Figure 18 visualizes the use of a D-STATCOM shunt compensation approach. Notice the Thévenin
equivalent circuit (𝐸𝑆 and 𝑍𝑆 ) of the public electricity grid with the Point of Common Coupling (PCC)
between this public grid and the wind farm. Using a coupling transformer, the D-STATCOM injects
current to the system in order to mitigate dips in the grid voltage.
Figure 18: Shunt compensation using a D-STATCOM (Alvarez et al.)
A D-STATCOM contains a DC energy storage device, a voltage source inverter (VSI) and a coupling
transformer (due to the reactance of the coupling transformer, a suitable adjustment of the
amplitude and the phase of the VSI voltage allows to control the active and reactive power
exchanges).
6.3 The ride-through capability of the wind turbines
When studying the capabilities of wind turbines to remain grid connected during and after a voltage
dip, a distinction is needed between the used generator technologies. More precisely, a distinction is
made between wind turbines
-
-
containing a squirrel cage induction generator which is connected with the grid without the
use of a power electronic convertor,
containing a doubly-fed induction generator (the rotor is connected with the grid using a
back to back frequency converter, the stator is connected with the grid without the use of a
power electronic convertor),
containing a synchronous generator where the stator is connected with the grid using a back
to back frequency convertor.
The use of a squirrel cage induction generator implies a (practically) fixed speed whereas the use of a
doubly-fed induction generator or a synchronous generator allow the generator to operate at
variable speed.
6.3.1: A wind turbine with a squirrel cage induction generator
Consider a wind turbine with a squirrel cage induction generator connected with the grid without the
use of a power electronic convertor as visualized in Figure 19. The grid frequency is fixed and the
speed of rotation of the generator is somewhat higher than its synchronous speed. Due to the
gearbox, the speed of rotation of the generator is significantly higher than the speed of rotation of
the blades of the wind turbine.
Figure 19: Wind turbine with an asynchronous generator
Due to a voltage dip, the speed of the generator will increase when the wind speed remains the same
(the evolution of the generator speed is visualized in Figure 20). Due to the voltage dip, only a
smaller electrical power is injected into the grid but when the rotor blades provide the same torque
i.e. the same mechanical power, an excess of power occurs. This excess of power is stored as kinetic
energy in the rotating blades, gearbox and rotor. This implies the speed of the generator indeed
increases as visualized in Figure 20. For instance in Figure 20, the speed increases from 1506 rpm to
1542 rpm (the speed is not allowed to become larger than the breakdown speed in generating
mode).
If the over-speed protection threshold is reached, the wind turbine i.e. the generator is disconnected
from the grid and stopped which leads to an interruption of the power production. Therefore, it is
important to limit the generator speed during the voltage dip. Changing the over-speed protection
threshold of the generator is often quite difficult.
The squirrel cage induction generator is directly connected to the grid implying there is no possibility
to control the power flow to the grid. By changing the pitch angle of the rotor blades, the wind
turbine torque can be decreased which limits the increase of the speed of the generator. By
decreasing the mechanical power, less kinetic energy must be stored implying a smaller increase of
the speed of rotation (the increase of the speed can be limited but cannot be avoided).
When considering the same type of wind turbine having a squirrel cage induction generator, due to
the voltage dip the generator will be demagnetized. The demagnetization depends on the depth and
the duration of the voltage dip. Once the voltage dip is cleared, the squirrel cage induction machine
will absorb a reactive current to restore the magnetization. Due to this reactive current, the overcurrent protection threshold could be reached implying the generator is disconnected from the grid
and stopped which leads to an interruption of the power production. This leads to the second
objective i.e. reducing the demagnetization of the generator during the voltage dip in order to keep
the stator currents under the over-current threshold once the voltage dip has been cleared (or to
reduce the stator current once the voltage dip has been cleared in all demagnetization conditions).
Figure 20: Evolution of the generator speed is case of a voltage dip (source: Laverdure)
To conclude, the two main objectives during the voltage dip are:
-
limiting the generator speed,
reducing the effect of generator demagnetization.
6.3.2: A wind turbine with a doubly-fed induction generator
A wind turbine with a variable speed of rotation is visualized in Figure 21. The stator of the generator
is connected with the three phase grid without the use of a power electronic converter. Using a
frequency converter (back to back power electronics converter), power can be extracted from the
rotor windings or power can be injected into the rotor windings. In case power is extracted from the
rotor windings, the machine behaves as a generator when its speed is higher than the synchronous
speed. In case power is injected into the rotor windings, the machine behaves as a generator when
its speed is lower than the synchronous speed. Since the machine is able to function as a generator
with speeds higher and lower than synchronous speed, a large variable speed range can be obtained.
Figure 21: Wind turbine with a doubly-fed induction generator
Also when considering a wind turbine with a doubly fed induction generator, it is important to limit
the generator speed and to control the generator demagnetization and magnetization in order to
limit the magnetization current. Moreover, it is important to ensure a normal operation of the
frequency converter.
Figure 22: Doubly-fed induction generator in a wind turbine
Figure 22 visualizes the doubly-fed induction generator driven by the blades of the wind turbine. Due
to the gearbox, the speed of rotation of the generator is higher than the speed of rotation of these
blades. The stator of the generator is connected with the grid without using a power electronic
converter i.e. by the switch S. The back to back power electronic converter behaves as a frequency
converter having a DC bus and the DC voltage is constant (no voltage ripple) due to the capacitor C.
In case of a voltage dip, the right converter CONV 2 can only inject a limited power into the grid.
Indeed, the maximum current must not be exceeded and due to the lower voltage level only a
smaller power is injected into the grid by the transformer. In case the power generated by the wind
turbine remains the same (which is normal when the wind speed and the wind power remains the
same), the left converter CONV 1 sends more power to the DC bus with capacitor C than consumed
by converter CONV 2. The excess of power can be stored into the capacitor implying an increase of
the capacitor voltage. In order to avoid an intolerable increase of the capacitor voltage, the excess of
power can be dissipated in the resistor Rd by closing switch Sd.
By changing the pitch angle of the blades, the mechanical power and also the generated power can
be reduced. This implies the excess of power which will be stored in the capacitor or dissipated in the
resistor Rd will be limited.
Alternatively, it is also possible to disconnect the generator from the grid during the voltage dip using
switch S. The rotor winding is short circuited through external resistances Rc which is called crow-bar
protection. Moreover, the converter CONV 1 is blocked. The grid side converter CONV 2 is able to
operate as a D-STATCOM.
Due to a voltage dip, a demagnetization of the doubly-fed induction generator occurs. After clearing
the voltage dip, there is a need for reactive power to obtain a re-magnetization of the generator. This
re-magnetization is partially fulfilled by the power electronic converter. This implies the generated
voltage recovers more quickly its initial value than when considering squirrel cage induction
generators (when considering a squirrel cage induction generator, the reactive power flow to obtain
re-magnetization must be supplied entirely by the grid which slows down the recovery of this
generated voltage).
6.3.3: A wind turbine with a synchronous generator
Figure 23 visualizes a wind turbine with a synchronous generator which also has a variable speed of
rotation. Contrary to the configurations of Figure 19 and Figure 21, the configuration of Figure 23 is a
direct drive system without a gearbox. The synchronous generator has a low speed of rotation
requiring a large number of pole pairs. As the speed of the rotor blades changes, also the speed of
rotation of the generator changes implying also the frequency of the generated voltage changes. A
frequency converter is needed to inject the full power into the electrical grid (when considering
Figure 21, only the smaller rotor power must be transferred by the frequency convertor). Notice also
a rectifier is needed to excite the synchronous generator.
Figure 23: Wind turbine with a synchronous generator
Also when considering a wind turbine with a synchronous generator and a frequency convertor, it is
important to limit/control the generator speed and to ensure a normal operation of the power
electronic converters.
Similar with the situation visualized in Figure 22, a dissipative resistor can be mounted in parallel with
the DC bus of the frequency converter. In case of a voltage dip, the power which can be injected by
the grid side converter is limited. This implies the power generated by generator is larger implying
there is an excess power which will be stored in the capacitor of the DC bus or it will be dissipated in
the dissipative resistor. By changing the pitch angle of the blades, the mechanical power and also the
generated power can be reduced. This implies the excess of power which will be stored in the
capacitor or dissipated in the dissipative resistor will be limited.
In case the mechanical power provided by the blades is higher than the mechanical power converted
into electrical power by the generator, the excess of mechanical power will be stored as kinetic
energy i.e. the speed of the blades and the generator will increase. Due to the large inertia of the
whole system (a direct driven generator has a large number of poles increasing the inertia), the
speed increase is limited and can be further reduced using pitch control.
Due to a voltage dip, there is no demagnetization of the synchronous generator due to the back to
back frequency converter. This allows to recover the voltage quickly (faster than it is the case when
considering a doubly-fed induction generator) to its initial value once the voltage dip has been
cleared.
References
Alvarez C., Amaris H. and Samuelsson O., Voltage dip mitigation at Wind Farms,
Bousseau P., Gautier E., Garzulino I., Juston P. and Belhomme R., Grid impact of different
technologies of wind turbine generator systems (WTGS), European Wind Energy Conference EWEC,
Madrid, June 16-19, 2003.
Lavendure N., Roye D., Bacha S. and Belhomme R., Mitigation of voltage dips effects on wind
turbines,
Mohammadi M. and Akbari Nasab M., Voltage Sag Mitigation with D-STATCOM in Distribution
Systems, Australian Journal of Basic and Applied Sciences, vol. 5 (5), pp. 201-207, 2011.
Nasiraghdam H. and Jalilian A., Balanced and Unbalanced Voltage Sag Mitigation Using DSTATCOM
with Linear and Nonlinear Loads, World Academy of Science, Engineering and Technology 4, 2007.