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1240
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010
STATCOM-Based Indirect Torque Control
of Induction Machines During Voltage
Recovery After Grid Faults
Jon Are Suul, Marta Molinas, Member, IEEE, and Tore Undeland, Fellow, IEEE
Abstract—This paper proposes a control method for limiting
the torque of grid-connected cage induction machines during the
recovery process after grid faults, by using a static synchronous
compensator (STATCOM) connected at the machine terminals.
When a STATCOM is used for transient stability improvement,
common practice is to design the control system to keep reactive
current at maximum level until the voltage has returned to its initial
value. This will result in high torques during the recovery process
after grid faults. The control method proposed in this paper is
intended to limit such torque transients by temporarily defining a
new voltage reference for the STATCOM control system. As torque
is controlled through the voltage reference of the STATCOM, the
method is labeled indirect torque control (ITC). The presented
concept is a model-based approach derived from a quasi-static
equivalent circuit of the induction machine, the STATCOM and
a Thévenin representation of the power system. For illustration
and verification, time-domain simulations of a wind power generation system with a STATCOM at the terminals of an induction
generator, are provided. As the objective of limiting the torque of
the induction machine is achieved, the derivation of the concept
proves to be reasonable. The approach is presented in its most
general form, oriented to torque limitation of induction machines
both in generating and motoring mode, and is not restricted to the
presented example.
Index Terms—Grid voltage recovery, induction machine stability, induction machine torque, low-voltage ride through (LVRT),
static synchronous compensator (STATCOM).
I. INTRODUCTION
PERATION of induction machines directly connected to
the power system has been an issue of investigations in
stability studies for a long time [1]–[6]. The characteristics of
induction motor loads and how their transient behavior influence the voltage stability of power systems is well known, and
the most relevant solution to improve system stability is often
reactive compensation close to the source of instability [7]–[10].
As wind turbines based on induction generators have been introduced into the power system to an extent where their influences
on the grid can not always be considered negligible, the issue
of voltage stability studies involving induction machines has
regained interest. This has attracted attention to investigations
O
Manuscript received February 28, 2009; revised July 18, 2009. Current
version published May 7, 2010. Recommended for publication by Associate
Editor J. Kokernak.
The authors are with the Department of Electric Power Engineering,
Norwegian University of Science and Technology, 7491 Trondheim,
Norway (e-mail: [email protected]; [email protected];
[email protected]).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2009.2036619
of static voltage stability limits of induction generators and the
need for reactive power compensation to allow for introduction of large-scale wind power production in the presence of
grid limitations [11]–[14]. Dynamic stability limits and transient stability of induction machines has also been investigated,
especially with respect to low-voltage ride through (LVRT) capability of wind turbines [15]–[22]. This has led to increased
focus on reactive power compensation for induction generators
based on power electronic solutions, for improvement of transient stability and LVRT capability [10], [23]–[33].
Solutions based in induction machines directly connected to
the grid still have a large share of the installed ratings in large
scale power systems, both as industrial motors and as generators for distributed generation systems like wind turbines and
small hydropower units [8], [34]–[36]. Therefore, shunt reactive
power compensation for stability improvement of induction machines will continue to be of significant importance with respect
to several aspects of power system operation. For improvement of transient stability, a static synchronous compensator
(STATCOM) will be the power electronic solution with the best
performance at low voltages, and will, therefore, contribute the
most to increase the capability of LVRT [9], [10], [28], [31],
[33], [37]. Increasing the LVRT capability by reactive power
compensation will, however, increase the torque capability of
the induction machine at speeds outside the normal operating
range, resulting in higher maximum torque, and correspondingly
higher stresses on the drive-train during the recovery process after the fault [24], [30], [31]. This will be the case since common
practice is to let the system operate with controllers running
into saturation, and thus controlling the STATCOM to provide
maximum reactive current through a grid fault and until the
voltage is recovered. Maximum reactive power compensation is
only needed to keep the system stable as long as the speed of
the machine is close to the stability limit, and therefore, it can
be possible to reduce the level of compensation after stability is
ensured to relieve the torque stresses on the drive train.
With the purpose of limiting the maximum torque of an induction machine during the recovery process after a grid fault, this
paper suggests a new way of setting the voltage reference during
the recovery process for the commonly used control structure of
a STATCOM originally designed to increase the LVRT capability of a grid connected induction machine. The proposed method
is a model-based approach implemented by temporarily redefining the voltage reference for the STATCOM as a function of the
speed of the induction machine. The method is labeled indirect
torque control (ITC) since the torque is indirectly controlled by
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SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS
Fig. 1. System under study with an induction machine connected to the grid
through a transformer and with a STATCOM connected at the terminals.
influencing the terminal voltage of the induction machine. An
application of torque control by a STATCOM to a realistic wind
turbine system has been briefly presented in [38], while this
paper is providing the theoretical basis and the derivation of the
ITC concept in the most general way.
Since the proposed control approach will only be active during
the recovery process after a grid fault, the normal operation of
the STATCOM and the induction machine will not be influenced.
Therefore, the presented concept can be considered to provide
transient torque control as an add-on feature of a STATCOM
initially designed for reactive power support and improvement
of transient stability. The main disadvantage of this additional
control feature will be that the recovery process after a fault
is made longer due to the limitation imposed on the machine
torque by the controller.
II. SYSTEM MODEL
The system under consideration is sketched in Fig. 1 and
consists of an induction generator directly connected to the
grid through a transformer, and a STATCOM connected at the
terminals of the induction machine. It should, however, be noted
that a system with an induction motor can be considered in the
same way. The derivation of the suggested control method is
based on a quasi-static approach, neglecting the flux transients
of the induction machine and the transient response of the grid.
This leads to the use of the well known per phase equivalent
circuit of the induction machine [11], [17], [18], [24], [30],
[31], [33], [39]. Although this approach is well established both
for steady-state calculations and for evaluation of static and
dynamic stability limits, it has not been previously used together
with a STATCOM for designing a dynamic control method.
The validity of this approach will be discussed later, but can
basically be justified because the objective of the presented
control method is to limit the torque and by that the acceleration
of the machine. It should also be noted that accuracy of control
is not of critical importance, as long as the objective of limiting
the maximum torque is achieved.
The quasi-static equivalent circuit representation of the system under study is shown in Fig. 2. In addition to the induction
machine equivalent, the circuit consists of a simplified representation of the grid by a Thevenin equivalent, and the STATCOM
represented as a controllable source of reactive current. In the
figure, v g , v 1 , and v m are phasors for grid voltage, induction
machine terminal voltage, and internal voltage at the magnetizing reactance, while ig , iSTATCOM , i1 , im , and i2 are line,
STATCOM, stator, magnetizing, and rotor current phasors. The
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Fig. 2. Quasi-static equivalent circuit for derivation of the control method
suggested during the recovery process after a grid fault. The model consists of
the traditional induction machine equivalent circuit, the STATCOM modeled as
a controllable reactive current source, and a Thevenin-equivalent of the grid.
grid impedance is given by rg + jxg while r1 , r2 are stator and
rotor resistance and x1 , xm , x2 are stator, magnetizing, and rotor
reactance. The model is expressed in per unit (pu) quantities,
with all parameter values referred to the stator of the induction
machine.
As long as quasi-static considerations are reasonable, the
model in Fig. 2 can represent the system both before and after
a grid fault. During a fault, the voltage at the generator terminals is assumed to be very low, such that the influence from the
STATCOM current on the response of the induction machine
can be considered negligible. The location of the fault is not of
specific importance, since the focus of the suggested approach
is the recovery process after a short circuit fault in the grid is
cleared. For simplicity, the fault is assumed to be at the terminals
of the machine when simulating the system for investigating the
validity of the presented control method.
The STATCOM is assumed to be current controlled with high
bandwidth current control loops, and to have a fast voltagecontrol loop acting on the reactive current reference [31], [32],
[40], [41]. However, the type of control system, the modulation
technique and the practical implementation of the inner control
loops have no significant influence on the proposed concept,
as long as the control structure can be tuned to obtain a fast
dynamic response.
The torque of the induction machine in per unit can be found
from simple calculations to be given by (1) [7]. With the reference directions indicated in Fig. 2, positive values for torque
τ em , slip s, and rotor current i2 correspond to motor operation
of the induction machine, while negative values of the same
variables correspond to generator operation
r2
(1)
τem = |i2 |2 .
s
III. INDIRECT TORQUE CONTROL CONCEPT
By phasor calculations on the equivalent circuit from Fig. 2
and application of (1), it is possible to calculate the quasi-static
conditions needed to obtain a specified torque at a specified
speed. In [31] and [33], it has been shown how this can be
used to estimate the rating of a compensation device needed to
maintain stability of the system as a function of the speed of
the machine when a fault is cleared. In the following sections,
it will be shown how the same approach can be used dynamically during the recovery process after a grid fault, to indirectly
control the torque of the induction machine by controlling the
terminal voltage with the STATCOM. The focus will be on
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1242
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010
derivation, explanation, and proof of concept, with verification
and illustration provided by detailed time-domain simulations.
A. Derivation of Voltage Reference Signal for the ITC
The starting point of the suggested control approach will be
to specify a torque reference that can be input to (1). This torque
reference should be selected with respect to known characteristics, measurements or estimations of the mechanical torque as
a compromise between limiting the torque and length of the recovery process. Solving for the rotor current i2 as a function of
the slip of the machine will result in (2), where the solution with
the positive sign should be chosen for motor operation while the
negative solution will be valid for generator operation
τem ,ref s
.
(2)
i2 = ±
r2
By using the current i2 as the reference for phasor calculations, the stator current i1 corresponding to the calculated rotor
current will be given by (3). The full expression for the stator
voltage that corresponds to a specified torque reference will then
be given as a function of the slip by (4)
x2
r2
i1 = i2 + im =
+1−j
(3)
i2
xm
sxm
x2
r2
r2 x1
+
+ 1 r1 +
v 1 (s) =
s
xm
sxm
x2
τem ,ref s
r2 r1
+ j x2 +
+ 1 x1 −
±
xm
sxm
r2
(4)
v ref ,STATCOM (s) = |v 1 (s)|.
(5)
Defining the absolute value of the voltage from (4) as a speed
dependent reference voltage for the STATCOM control system
as given by (5), it is possible to indirectly control the torque of
the machine in the high-speed region towards a specified value.
This is only relevant after a grid fault, when the speed of the
machine is outside the normal operating range and the machine
will have to pass through the speed range around the pullout
torque during the recovery process.
B. Verification of ITC Concept by Time-Domain Simulation
To verify and illustrate the functionality of the suggested ITC
concept, a system with an induction machine directly connected
to the grid and a STATCOM connected at the machine terminals
R
/EMTDCTM software [42]. The
is simulated with the PSCAD
simulation model can be considered to represent a wind turbine
generator with rating in the range of 2 MW, and the main parameters of the simulated system are given in the Appendix [33]. The
R
/EMTDCTM model includes a full fifth-order dynamic
PSCAD
model of the induction generator, the simple grid equivalent and
a STATCOM with a control system based on voltage oriented
vector current control [31], [41], [43]. The main control loops
of the STATCOM are included in the simulation model, but
for simplicity and speed of simulation, an average model of
the voltage source converter is used instead of simulating the
Fig. 3. Structural block diagram of control system for STATCOM with ITC
modifying the voltage reference when the induction generator is operating in
the high-speed region during the recovery process after a grid fault.
pulsewidth modulation (PWM) switching pattern [44]. The proposed control concept is included in the simulation model by
implementing the ITC equations and using the voltage reference calculated from (5) as the reference value for the voltage
control loop of the normal STATCOM control structure when
the induction generator is operating in the high speed region.
This is shown in Fig. 3, where the block to the left of the figure
indicates how the ITC functionality is allowed to define a temporary, speed-dependent, value for the grid voltage reference.
Under normal STATCOM operation, the voltage reference will
be close to 1.0 pu as indicated in the figure. The ITC concept is
only overriding this reference value during the recovery process
after a fault, when the induction generator is operating in the
high-speed region.
Three cases have been simulated; one reference case with only
constant capacitor compensation to keep nominal voltage under
normal operating conditions, a second case with a STATCOM
for voltage control and LVRT capability, and the third case to
show how the STATCOM based ITC can be achieved as an
additional functionality. In all the simulations, the mechanical
input torque is considered to be constant during the simulation
time. In the case with ITC, the system is set to limit the torque
of the induction machine below 1.1 pu Simulation results are
shown for 10 s when the system is starting from stationary
conditions and is exposed to a 350 ms three-phase fault at the
terminals of the generator after 1 s of simulation time.
The main results from the simulations of the three cases are
collected in Fig. 4. The curves in Fig. 4(a) show the torque–
speed trajectory of the system for the different cases as starting
from steady state, through the fault and during the recovery
process. This figure clearly shows that the case with capacitor compensation is unstable, while the results with normal
STATCOM control and with ITC are identical up to the point
when the ITC comes into operation during the recovery process.
Fig. 4(b) is included, to illustrate the influence of the ITC more
clearly by focusing on the recovery process without showing the
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SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS
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Fig. 4. Obtained results from the three selected cases of simulation. Parts (a)–(c) show how the torque during the recovery process can be limited by the ITC, and
part (d) shows how this results in an almost linear reduction of speed during parts of the recovery process. Parts (e) and (f) show the resulting voltages in the three
different cases. (a) Simulated Torque–speed trajectories for the three selected cases. (b) Zoom of simulated torque–speed trajectories together with the calculated
torque–speed curve for 1.5 pu STATCOM current. (c) Electrical torque before, during, and after the fault for the three selected cases. (d) Speed of the machine
before, during, and after the fault for the three selected cases. (e) Voltage at the machine terminals before, during, and after the fault for the three selected cases.
(f) Simulated voltage-speed trajectories for the three selected cases.
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1244
influence from the torque transients when the fault occurs. This
figure also includes the torque–speed curve calculated from the
quasi-static equations of the system, to show the influence of the
flux dynamics on the system with normal STATCOM control.
An arrow indicates how the ITC comes into operation when the
torque of the machine reaches the set-point value.
Fig. 4(c) shows the torque as a function of time for the
three different cases and further illustrates how the ITC effectively limits the peak torque during the recovery process, while
Fig. 4(d) is showing the resulting speed as function of time.
Fig. 4(e) is showing the voltage at the generator terminals as a
function of time, and here it can be clearly seen that the system
is not able to recover the voltage in the case with only capacitor
compensation. It can also be seen that the voltage is actively reduced by the ITC during the recovery process to limit the torque,
but only after stability is ensured and the machine has started
to decelerate. This operation of the ITC as a secondary control
objective after stability is ensured is what makes the approach
reasonable, and is, therefore, a central point of the proposed concept. The trajectory of the voltage at the generator terminals with
respect to the generator speed is shown in Fig. 4(f), and in the
case of ITC this trajectory corresponds to the voltage reference
calculated from (4) and (5) during the recovery process.
The results plotted in Fig. 4 illustrate both the general behavior of a system with an induction machine and a STATCOM and
the specific influence of the presented ITC method, as can be
explained stepwise in the following points.
1) Before the fault, the system is in normal operation, and
the voltage at the terminals of the induction machine is
close to the nominal value as seen in Fig. 4(e). For the
cases with STATCOM, the voltage control structure of
the STATCOM is operating in the normal way and the
STATCOM is operating in the capacitive region to provide
reactive power to the induction generator.
2) When a fault occurs, there will be short circuit torque
transients in the induction machine as seen clearly from
Fig. 4(a) and 4(c). The STATCOM is not able to influence these torque transients, and they are not the focus
of this paper. Because of the serious fault with a low remaining voltage, the reactive current of the STATCOM
will have limited influence on the system voltage and on
the operation of the generator during the fault. Because of
the large voltage drop, the maximum current limit of the
STATCOM will be reached, and the STATCOM running
into saturation will operate as a constant source of reactive
current.
3) During the fault, the short circuit transients of the induction generator are damped, and afterwards the electrical
torque is almost negligible because of the low remaining
voltage, as seen in Fig. 4(a)–(c). Since the average electrical torque during the fault is close to zero, the applied
mechanical torque is causing an almost linear increase in
generator speed as can be seen in Fig. 4(d).
4) When the fault is cleared, the STATCOM will keep maximum current since the system is not capable of recovering
the voltage immediately due to the increased speed of the
generator shaft. The simulation with only reactive com-
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010
5)
6)
7)
8)
9)
pensation by constant capacitors results in the lowest voltage after the fault is cleared, leading to voltage collapse as
can be seen from Fig. 4(e). In this case, the system is seen
to be clearly unstable since it is not possible to recover
the voltage and return to the initial conditions. In the two
cases with STATCOM, the voltage after the fault is cleared
can be kept high enough for the system to be stable.
The two cases with the STATCOM give identical results
during and immediately after the fault is cleared. Since the
system is stable in these cases, the generator starts to decelerate after the fault is cleared as can be seen in Fig. 4(a),
(b), and (d), but as the speed of the generator is decreasing,
the torque capability of the machine is increasing.
With normal STATCOM control, the system will recover under maximum reactive compensation from the
STATCOM as shown by the blue dashed lines in Fig. 4,
and this result in a high transient torque during the recovery process. As can be seen in Fig. 4(b), and as discussed in [33], the dynamic recovery of the generator is
resulting in a torque capability that is slightly reduced
compared to the torque–speed curves that can be obtained
from quasi-static calculations, but still the torque is significantly higher than the rated torque.
In the case of recovery with ITC, the prioritized control objective of the STATCOM will change when the
torque of the machine reaches the set point of the indirect
torque control algorithm. The point when this condition is
reached and the ITC comes into operation is marked with
an arrow in the torque–speed trajectory of Fig. 4(b). Then
the voltage reference for the STATCOM control system
will be adjusted as a function of the speed of the generator
according to (5). The influence on the torque is clearly
seen by the red lines in Fig. 4(a)–(c), where the torque is
kept almost constant, and as a result the speed in Fig. 4(d)
is decreasing almost linearly.
As long as the indirect torque control is active, the torque
will be limited below the set-point value that has to be kept
larger than the applied mechanical torque. The influence
of the dynamic response of the machine and the grid, that
are not accounted for in the ITC equations, is resulting
in a torque that is slightly below the set point during the
recovery. This slight reduction in torque can be noticed
in Fig. 4(a), but can be better identified in the zoom of
Fig. 4(b). Although much smaller, the influence of the flux
transients of the machine in the case of ITC is similar to
the difference between the calculated quasi-static torque–
speed curve in Fig 4(b) and the simulated torque trajectory
of the system during recovery with normal STATCOM
control. The ITC is, however, intended to limit the torque
and this result in a slower deceleration of the rotor and by
that reduced influence of the transients in the machine and
in the grid. The assumptions made to derive the equations
of the ITC, therefore, prove to be valid, because the torque
of the machine is limited by applying the proposed control
concept.
As soon as the speed of the machine is recovered close to
its initial value before the fault and the voltage reaches the
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SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS
reference value of 1.0 pu, the main control objective of
the STATCOM with ITC will be shifted back the normal
voltage control.
10) The resulting influence on the voltage when limiting the
torque during the recovery process is shown in Fig. 4(e)
and (f). Although this reduced voltage at the machine
terminals will be the main drawback of the presented approach, the influence on the grid voltage will be less than
what can be seen in Fig. 4(e) because of the transformer inductance between the generator and the point of common
coupling (PCC). Since the control is limiting the torque
of the machine to a value that must be higher than the
applied mechanical torque, the reduced voltage will not
represent any risk of instability originated by the induction
generator.
The validity and accuracy of calculations on such a system based on quasi-static phasor analysis is briefly investigated
in [31] and [33], respectively, for the assessment of stability limits and requirements for reactive compensation in wind turbine
applications. As shown by the curves in Fig. 4, the influence
from the flux transients of the induction machine is similar in
this case as in the case described in [33], both for the conditions
around the stability limit and during the recovery process when
the speed returns to the initial conditions. Since the objective of
the ITC concept is to limit the torque of the induction machine
during the recovery process, the deceleration will be slowed
down compared to the case of recovery with maximum reactive
compensation. This will result in reduced influence from the
flux dynamics of the machine and the transient response of the
grid. Slower deceleration will also reduce the influence of the response time of the STATCOM control system. When the torque
reference is set close to the mechanical torque, the recovery process will be slow and the machine will operate close to stationary
conditions, so that only a small influence of the flux dynamics
and the controller response can be expected. This set of arguments support the validity of using a quasi-static model as the
basis for deriving the ITC concept, and shows how it is the implementation of the control method itself that makes the assumptions to be valid. The simulation results shown in Fig. 4 also verify this by illustrating the functionality of the proposed concept.
IV. ANALYSIS OF STATCOM CURRENT INJECTION WITH ITC
As observed in Fig. 4(e) and (f), the suggested control approach will reduce the voltage reference for the STATCOM
during the recovery process after a fault, to limit the torque of
the induction machine. This will result in a longer recovery process, and more reactive power drawn from the grid. Depending
on the parameters of the system and the torque reference used
to calculate the voltage reference for control of the STATCOM,
the STATCOM can even be controlled into inductive operation. This corresponds to actively controlling the STATCOM to
Aeq,ST + jBeq,ST = j
1245
consume reactive power for reducing the voltage at the machine
terminals, to slow down the recovery process.
Although the proposed ITC concept is introducing a new
control objective to the operation of a STATCOM, investing in
a STATCOM only for this purpose will not be a relevant option. As presented in the premises for the investigation, the ITC
should, therefore, mainly be considered as an add-on feature of
an already existing STATCOM intended for reactive power support and improvement of transient stability or LVRT capability.
Still, it will be important to know the current range needed for
the indirect torque control or to investigate what torque limitation can be achieved with a certain rating and a specified set of
system parameters. The required current as a function of speed
and the torque reference should, therefore, be derived from the
system model to verify the operational range of the STATCOM
when applying ITC during the recovery process.
Since losses of the STATCOM are neglected, the phasor of the
SATCOM current can be expressed by (6), where the constants
Aeq,ST and Beq,ST originates from (4) as given by (7), at the
bottom of this page.
v1
iSTATCOM = j
|iSTATCOM |
|v 1 |
= (Aeq,ST + jBeq,ST )|iSTATCOM |.
(6)
With the current directions indicated in Fig. 2, the grid current
will be the sum of the stator current of the machine and the
STATCOM current. The simple expression relating the currents
and the terminal voltage of the machine to the grid voltage is
given in (8)
v g = v 1 + (rg + jxg )(i1 + iSTATCOM ).
(8)
The power system is represented by a Thevenin equivalent,
where the voltage source is assumed to have a known, fixed
magnitude, and by substituting from (3), (4), and (6) into (8), the
only unknown variable for a specific speed will be the magnitude
of the STATCOM current. By defining equivalent resistances
and reactances as given in (9), (8) can be brought into the form of
(10), and by solving for |iSTATCOM |, the result is a second-order
equation as given by (11). The minimum solution to (11) will
result in the required STATCOM current to obtain the specified
torque as a function of the slip or the speed of the machine
x2
r2
r2
+
+ 1 (r1 + rg ) +
(x1 + xg )
req,i 2 =
s
xm
sxm
x2
r2
xeq,i 2 = x2 +
+ 1 (x1 + xg ) −
(r1 + rg )
xm
sxm
req,STATCOM = rg Aeq,ST − xg Beq,ST
xeq,STATCOM = xg Aeq,ST + rg Beq,ST
(9)
v g = (req,i 2 + jxeq,i 2 )i2 + (req,STATCOM
+ jxeq,STATCOM )|iSTATCOM |
(10)
−(x2 + ((x2 /xm ) + 1)x1 − (r2 r1 /sxm )) + j((r2 /s) + ((x2 /xm ) + 1)r1 + (r2 r1 /sxm ))
v1
=
.
|v 1 |
((r2 /s) + ((x2 /xm ) + 1)r1 + (r2 r1 /sxm ))2 + (x2 + ((x2 /xm ) + 1)x1 − (r2 r1 /sxm ))2
(7)
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IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010
Fig. 5. Simulation results showing the reactive current from the STATCOM and illustrating the difference between operation with normal voltage control
and operation with ITC during the recovery process. (a) STATCOM current–speed trajectories from simulation together with calculated characteristics of ITC.
(b) Simulated reactive current from the STATCOM with normal operation and with ITC.
seen in the current trajectory since the current is kept at the same
value during both the acceleration and the deceleration of the
machine. In the case with ITC, the modification of the voltage
(req,i 2 i2 )2 + (xeq,i 2 i2 )2 − |v g |2
× |iSTATCOM | + 2
= 0. reference for the STATCOM is starting to act on the system
req,STATCOM + x2eq,STATCOM
as soon as the torque capability of the induction machine is
reaching the specified set-point value and the STATCOM cur(11)
rent is a result of this modified voltage reference. Therefore, the
STATCOM current follows the trajectory of the red curve in
The same approach has been used to estimate the required
Fig. 5(a) until the system has returned to the initial state before
rating of compensation devices in [31] and [33] for obtaining
the fault. Comparing this current trajectory resulting from the
LVRT. The main contribution of the presented concept is that the
simulation of the ITC and the result obtained by plotting the
calculations are used dynamically for implementing the indirect
solution of (11) as a function of speed, only a small difference
torque control as a model-based control concept that is shown to
is observed and this difference is mainly caused by the flux dybe reasonable through the recovery process of the system after a
namics of the machine and the delay in response caused by the
fault. Therefore, the characteristics obtained from (11) must be
PI-controllers of the STATCOM control structure.
considered for the whole speed range of the induction machine,
From the presented results, it is seen that the ITC is coneven if the result is corresponding to inductive operation of the
trolling the STATCOM into inductive operation for limiting the
STATCOM.
torque when the machine is passing through the speed region
Fig. 5 shows the STATCOM current resulting from the simwith the highest torque capability. Assuming that the current
ulation of the two cases with STATCOM that were presented
rating of the STATCOM has been determined by LVRT requirein Fig. 4. The trajectories of the STATCOM current with rements and that the current limit for operation in the inductive
spect to the generator speed in the cases with and without ITC
region is equal to the capacitive current limit, it is seen that
are shown in Fig. 5(a), while Fig. 5(b) shows the simulated
the ITC is operating well within these limits. Since the ITC is
STATCOM currents as function of time. Fig. 5(a) also shows
proposed as an additional feature that has relevance only during
the calculated STATCOM current as a function of speed, resultthe recovery after a fault, the most realistic approach will be to
ing from solving (11) with the same torque reference as used
implement the ITC to operate within the current limits set by the
for the simulations.
main design criteria. The implementation of the ITC as an addInspecting the results in Fig 5(a) and (b), it can be seen how
on functionality of a STATCOM can then provide additional
the STATCOM current both with and without ITC is immevalue to an investment made for other purposes, as one among
diately controlled to the maximum available rating when the
other incremental software features giving advantages to supplifault occurs. When the grid fault is cleared, there is a transient
ers intending to further exploit the potential of the STATCOM
response in the STATCOM due to the grid transients, but the
technology.
current is quickly settled at the maximum value and the current
is still identical for both cases since the torque of the machine
V. IMPACT OF GRID PARAMETERS ON ITC
is lower than the reference value specified for the ITC. For the
The reactive current from the STATCOM needed to achieve
case with the normal STATCOM control, maximum reactive
current is kept until the system is recovered, and this is barely ITC during the recovery process depends on the system
|iSTATCOM|2 +
2i2 (req,i 2 req,STATCOM + xeq,i 2 xeq,STATCOM)
2
req,STATCOM
+ x2eq,STATCOM
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SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS
1247
Fig. 6. STATCOM current as function of generator speed for different grid inductance values. (a) Required STATCOM current at stability limit as function of
speed. (b) Required STATCOM current as function of speed with ITC and torque reference of 1.1 pu.
parameters, and the widest relevant parameter range can be
expected for the grid impedance. Since the grid impedance is
determined by the strength and the R/X-ratio of the grid at the
point of connection for the induction machine, it is of importance to estimate how different grids will influence the operation
of the suggested control method. The largest variation can be
expected in the grid inductance, and the influence on the current required for ITC is, therefore, investigated for a range of
different values of the grid reactance xg , while all other parameters of the systems are kept constant at the values given in the
Appendix.
As a starting point, Fig. 6(a) is showing the STATCOM current as a function of speed when (11) is solved with a torque
reference equal to the mechanical torque of 1.0 pu for different
values of the grid reactance. This corresponds to operation at
the stability limit of the system, in a similar way as the current profiles calculated in [31]. Fig. 6(b) shows the results when
(11) is solved for a torque reference value of 1.1 pu, and gives
the STATCOM current needed for the ITC for 5 different per
unit values of the grid reactance. By comparing the results in
Fig. 6(a) and (b) it can be seen that the current needed to obtain
the specified torque is always more capacitive than the current
calculated at the stability limit. This indicates how the ITC only
can have priority as a control objective after stability of the
system is ensured.
Studying the curves in Fig. 6, it can also be seen that the curves
for the different grid inductances are crossing each other at high
speeds. The point of intersection indicates the speed where the
terminal voltage needed to obtain the required torque will be
higher than the grid voltage, and to obtain this condition reactive
power has to be delivered to the grid from the point where the
STATCOM is connected. In that case, the required capacitive
current will be highest for strong grids, where the influence
from reactive current on the voltage is low. For speeds below
this point of intersection, the STATCOM current needed to keep
the specified torque is less capacitive when the grid reactance
is reduced. This corresponds to the stability consideration from
[31], where less reactive compensation is needed to keep the
system stable when the grid reactance is low because a stronger
grid is capable of delivering more reactive power to the induction
machine. With respect to torque control, this shows that more
inductive current is needed to limit the peak torque during the
recovery process in a strong grid, while little current is needed
in a weak grid that is less stable without reactive compensation.
The influence of the grid reactance on the most inductive
current needed to limit the torque below the set-point value
during the recovery process is illustrated clearly by the plot
in Fig. 7(a) that shows the maximum inductive current needed
to limit the torque to 1.1 pu, plotted as a function of the grid
inductance. As seen, the required inductive current goes towards
infinity when the grid inductance goes towards zero, while the
current at the peak torque becomes capacitive for large grid
inductances. The situation with a capacitive current in Fig. 7(a)
corresponds to a situation where the peak torque of the machine
is lower than the specified torque reference, and in this case the
system would be close to the stability limit or even unstable
without reactive compensation from the STATCOM in normal
operation. Another result illustrating the same tendency is seen
in Fig. 7(b), that shows the speed at the peak torque as a function
of grid inductance. The influence from the grid inductance on
the peak torque is also indirectly indicated by the curves in
Fig. 6, where it can be seen how the current required to limit the
torque will be reduced, and also that the speed at the pull-out
torque of an induction generator will be reduced, when the grid
inductance is increased.
In case of an induction generator in a wind turbine, or a
large induction motor for an industrial load, the connection to
the grid will usually be through a dedicated transformer. If this
transformer is directly connected to a typical voltage level for
distribution systems like 11 or 22 kV, the transformer inductance
is usually in the range of 5–6% referred to the transformer
rating. For the system configuration in Fig. 1, the transformer
impedance will be the minimum grid impedance if the system is
connected directly to a strong grid. A grid reactance of 0.06 pu
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1248
IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 5, MAY 2010
Fig. 7. Peak inductive STATCOM current for ITC as function of grid reactance and corresponding speed where peak inductive current occurs. (a) Minimum
(most inductive) STATCOM current needed to obtain ITC with 1.1 pu torque, as a function of grid reactance. (b) Speed at the point of maximum torque, where the
most inductive STATCOM current is needed to obtain ITC during the recovery process.
is, therefore, considered as a realistic minimum value, and used
as the minimum value for the plots in Fig. 6. Still, such a low grid
inductance would require a very large reactive current to limit
the torque, and this will also have as a consequence that large
reactive power will flow from the grid. On the other side, it can
be seen from Fig. 7(a), that when the grid reactance is increasing
towards 0.20 pu, the induction machine will require support of
reactive current from the STATCOM even around the peak of
the torque–speed curve. For higher reactances, reactive power
compensation will be needed to keep the system stable even
in normal operation, and it will be difficult to ensure transient
stability of the system with respect to grid faults. At the same
time, the grid inductance and the flux transients of the induction
machine might dominate the response of the system after a
fault is cleared and the control of the STATCOM itself can be
challenging.
According to the presented results, the most relevant range of
grid reactance for implementation of the presented ITC concept
can be considered to be between 0.10 and 0.20 pu. However,
the parameters of the induction machine might influence this
range, since a machine with lower inductances or higher losses,
and correspondingly higher peak torque, will be more stable.
Also, the resistance of the grid will influence the stability of
the system, although the expected range of variation for grid
resistance will be lower than for the grid inductance.
VI. CONCLUSION
A control concept for limiting the torque of a grid-connected
induction machine during the recovery process after a grid fault
by use of a STATCOM has been suggested. The proposed concept is a model-based approach derived from a quasi-static
model of the induction machine, the STATCOM and the grid,
and was presented as a secondary control objective of a STATCOM intended to improve the stability of an induction machine
directly connected to the grid. The suggested method for indirect
torque control was tested by detailed timed-domain simulations
when applied to a model of a wind generation system consisting of an induction generator with a STATCOM connected at
the terminals. In case of grid faults, it was shown how the full
current capacity of the STATCOM can be first utilized to extend
the stability limit of the induction generator, before the indirect
torque control comes into operation. It was further demonstrated
how the proposed method controls the STATCOM to limit the
maximum torque of the generator during the recovery process
after the fault. The initial control objectives of the STATCOM
operation for voltage regulation in normal operation and improved LVRT capability in case of grid faults are not influenced
and the simulation results show how the system returns to normal operation when the speed of the induction machine is back
to the initial value before the fault.
The presented control method was shown to make the STATCOM capable of indirectly controlling and limiting the torque
of an induction machine during the recovery after a grid fault, by
modulating the terminal voltage and the flow of reactive power
in the investigated system. By comparing results from the detailed time-domain simulations with calculations based on the
model used to derive the proposed concept, it has been shown
that the influence of the neglected dynamics of the induction machine and the grid is a slight reduction of torque. The accuracy
of the torque limitation will, therefore, be increased by setting
the torque reference closer to the applied mechanical torque,
but this will also increase the length of the recovery process. It
should, therefore, be clear that it is the torque limitation introduced by the ITC method that gives validity to the quasi-static
model used for the derivation of the concept.
Analysis of the operating range of the STATCOM needed to
obtain the Indirect Torque Control is presented in the paper,
and the influence of the grid impedance is investigated. It is
shown that for most conditions, the STATCOM is required to
operate both in the capacitive and inductive region and that the
maximum inductive current will decrease by increasing grid
inductance. For very strong grids, the suggested method will,
therefore, require a high inductive current from the STATCOM
and result in a large flow of reactive power from the grid.
The main drawback of limiting the torque of the induction
machine in the suggested way is the lengthened recovery process, since the machine shaft will need longer time to return to
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SUUL et al.: STATCOM-BASED INDIRECT TORQUE CONTROL OF INDUCTION MACHINES DURING VOLTAGE RECOVERY AFTER GRID FAULTS
the initial speed when the torque is controlled to be closer to the
mechanical torque. It should, however, be noted that the ITC
concept mainly requires software modifications with respect to
a normal STATCOM control system, and it should, therefore,
be considered as a possible add-on feature that can increase the
functionality and value of a STATCOM installed with another
main purpose. Although this might currently be most relevant
for wind generation systems with induction generators, the concept presented in this paper is general and can be applied for
torque limitation of induction machines operated both as generators and as motors. For a possible practical implementation,
there should be a tradeoff between the maximum torque and the
length of the recovery process. In cases where the method can
be considered relevant, it should also be investigated together
with other practical aspects of the considered application.
APPENDIX
TABLE I
MAIN PARAMETERS OF INVESTIGATED SYSTEM
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Jon Are Suul received the M.Sc. degree from the
Norwegian University of Science and Technology,
Trondheim, Norway, in 2006. He is currently working toward the Ph.D. degree in the Department of
Electric Power Engineering, Norwegian University
of Science and Technology.
From 2006 to 2007, he was with SINTEF Energy Research, Trondheim, Norway, where he was
engaged in simulation of power electronic systems.
In 2008, he was a guest Ph.D.-student for 2 months
at the Energy Technology Research Institute of the
National Institute of Advanced Industrial Science and Technology (AIST),
Tsukuba, Japan. His current research interests include control of power electronics converters in power systems and for renewable energy applications.
Marta Molinas (M’94) received the Diploma degree
in electromechanical engineering from the National
University of Asuncion, Asuncion, Paraguay, in 1992,
the M.Sc. degree from Ryukyu University, Okinawa,
Japan, in 1997, and the Doctor of Engineering degree
from Tokyo Institute of Technology, Tokyo, Japan, in
2000.
She was a Guest Researcher with the University
of Padova, Padova, Italy during 1998. From 2004 to
2007, she was a Postdoctoral Researcher with the
Norwegian University of Science and Technology
(NTNU), Trondheim, Norway. She is currently with the Department of Electric
Power Engineering at NTNU as full Professor since 2008. From 2008 to 2009,
she was a JSPS Research Fellow for 10 months with the Energy Technology
Research Institute at the National Institute of Advanced Industrial Science and
Technology (AIST), Tsukuba, Japan. Her research interests include wind/wave
energy conversion systems, and power electronics and electrical machines in
distributed energy systems.
Dr. Molinas is actively engaged as a Reviewer for IEEE TRANSACTIONS ON
INDUSTRIAL ELECTRONICS and IEEE TRANSACTIONS ON POWER ELECTRONICS.
She is an AdCom member of IEEE Power Electronics Society.
Tore Undeland (M’86–SM’92–F’00) received the
M.Sc. degree and the Ph.D. degree in electrical engineering from the Norwegian University of Science
and Technology (NTNU), Trondheim, Norway, in
1970 and 1977, respectively.
He has been with the Department of Electric
Power Engineering at NTNU as full-time Professor since 1984. He has also been Adjunct Professor at Chalmers University of Technology, Göteborg,
Sweden, since 2000, and is a Scientific Advisor to
SINTEF Energy Research, Trondheim, Norway. His
research interests include power electronics and wind energy systems. He is the
coauthor of the well-known book Power Electronics, Converters, Applications
and Design.
Mr. Undeland has been the President of the European Power Electronics
Society and a Member of the Norwegian Academy of Technological Sciences,
Trondheim.
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