Wind Electric Generators and Control
Isha T.B.
Of the various renewable energy sources, wind energy has emerged as the most viable
source of electric power, and is economically viable with the conventional sources. The
wind energy conversion systems or wind turbines require certain control systems. It is
desirable to reduce the drive train loads and protect the generator and the associated
equipment from overloading, by limiting the turbine power to the rated value up to the
furling speed. At gust speeds, the machine has to be stalled. At low and moderate wind
speeds, the aim should be to capture power as efficiently as possible. Wind turbines can
have four different types of control mechanisms, viz., Pitch angle control, Stall control,
Yaw control and Power Electronic control. This pare discusses only the power electronic
control of wind turbines.
Power Electronic Control
In a system incorporating a power electronic interface between the generator and the load
(or the grid), the electrical power delivered by the generator to the load can be
dynamically controlled. The instantaneous difference between the mechanical power and
the electrical power changes the rotor speed following the equation
d Pm  Pe

where J is the polar moment of inertia of the rotor,  is the angular
dt

speed of the rotor, Pm is the mechanical power produced by the turbine and Pe is the
electrical power delivered to the load. Up on integration, this equation yields,
t2
1
J  22   21   Pm  Pe dt
t1
2
The advantage of this method of speed control is that it does not involve any mechanical
action and is smooth in operation. A disadvantage is that fast variation of speed requires a
large distance between the input power and output power. This results in a large torque
and hence increased stress on the blades. Moreover, continuous control of the rotor speed
By this method implies continuous fluctuation of the power output to the grid, which is
usually undesirable for the power system.
J


For every wind turbine, there can be five different ranges of wind speed, which require
different speed control strategies.
1 Below a cu-in speed, the machine does not extract power. If the rotor has a sufficient
starting torque, it may start rotating below this wind speed. No power is extracted and
the rotor rotates freely.
2. At normal wind speeds, maximum power is extracted from wind. Therefore, to track
the maximum power point, the rotational speed has to be changed continuously in
proportion to the wind speed.
3. At high winds, the rotor speed is limited to a maximum value depending on the design
limit of the mechanical components. In this region, the power output is not proportional
to the cube of the wind speed.
4. At even higher wind speeds, the power output is kept constant at the maximum value
allowed by the electrical components.
5. At a certain cutout or furling wind speed, the power generation is shut down and the
rotation stopped in order to protect the system components. The last three regimes can be
realized with yaw control, pitch angle control and eddy-current or mechanical brakes. In
the intermediated speed range, the control strategy depends on the type of electrical
power generating system used and can be divided into two basic categories.i.e., the
constant speed generation scheme and variable speed generation scheme.
The generation schemes for wind electrical conversion systems depend primarily on the
type of output required as well as the mode of operation of the turbine. Two types of
generators generally find application in wind power conversion, synchronous and
induction machines. Besides being commonly used as drives in the industry, three phase
induction machines have earned much favor as wind generators because of qualities such
as ruggedness, reliability and manufacturing simplicity. They constitute the largest
segment in the wind power industry today. Two types of induction machines have been
used: squirrel cage type and the wound-rotor type. In the kilowatt range, former is used
and in megawatt range, the latter is used. Their principles of operation is basically the
same, they differ only with respect to the application.
In the general circuit model of induction motor, the stator referred voltage drop across the
I 2' R' r
(1  s)
slip-dependant resistor in a more complex form is V 
(1)
s
I 2' Rr'
Re-writing
in terms of E1, we get V2=E1(1-s)+j(s-1)Xlr’I’2.
(2)
s
But, from Fig.1, E1=I’2 (R’r+jX’lr)+V2
(3)
The combination of equations (2) and (3) yields
E1=I’2(R’r+jsX’lr )+E1(1-s)
(4)
Fig. 1: Modified equivalent circuit model of induction motor
The modified circuit model satisfying the rotor resistance is shown in Fig. 1. Since
E1=ImLm where Lm is the magnetizing inductance, the emf E1(1-s) is proportional to the
rotor speed and the magnetizing current. This is therefore, a rotational emf. The total
E12 s(1  s) Rr'
power associated with the rotational emf is
which is
Rr'2  s 2 X lr'2
the mechanical power output, Pm of the machine (Re denotes the real part of). The new
circuit model emphasizes the the concept of rotational emf and highlights the similarities
between the induction motor, synchronous motor and the dc motor.
Pe=3Re[E1(1-s)I’*2]=3
The stator draws a compensating load current I’2 to counteract the rotor mmf inorder to
sustain the air-gap flux set up by the magnetizing component of the exciting current Im.
Consequently, if the rotor changes its current as a result of any other source of emf in its
circuit, the stator would be unable to detect the inclusion of this additional emf in the
rotor circuit, as the same change in the rotor circuit and power factor can be effected by
the inclusion of appropriate values of resistance and inductance (capacitance) in the rotor
circuit. Fig. 2 shows the rotor equivalent circuit with an additional emf Ej injected at an
angle  with respect to sE2 and acting in the opposite sense to it.
Fig. 2: Rotor circuit model with rotor injected emf
The electrical power crossing the air-gap can be expressed as Pag=Pcu+P2+Pm where
Pm=(1-s)Pag, Pcu is the copper loss and P2 is the power fed into the auxiliary source
(injected emf). After substitution of each of the components and re-arranging, we can
write Pm=3((1-s)/s)[I’2R’r+E’jI’2cos(2+)]. These equations suggest Fig. 3 as the modified
version of the per-phase stator-referred conventional equivalent circuit of the induction
motor with injected emf in the rotor. Such an induction machine is also known as a
doubly-fed induction machine (DFIM), because of the two power sources employed.
Fig. 3: Stator-referred equivalent circuit with injected emf in the rotor
Since motoring convention has been followed, Pag and Pm will be negative in the
generating mode. P2 has been considered positive for the power absorbed by the auxiliary
source, that is the power flowing out of the slip-ring terminals. The electrical power
associated with the slip-dependant secondary resistance and the auxiliary emf shown in
Fig. 3 represents the mechanical power. With respect to the flow of power between the
motor shaft and the stator, the behavior of the induction machine, as a result of auxiliary
power control, can be divided in to four operating modes:
Mode I: s<1, Pm>0 -- Subsynchronous motoring operation
Mode II: s<0, Pm>0 – Supersynchronous motoring operation
Mode III: s<1, Pm<0 – Subsynchronous generating operation
Mode IV: s<0, Pm<0 – Supersynchronous generating operation
In the normal mode of operation of induction motor, rated speed will be obtained when
the stator carries rated current. For this configuration, the operating speed range of the
generator is small if the stator current is not to exceed its rated value. This is the
conventional use of the induction machine. Any attempt to extract power from the rotor
by inserting an external resistance in the rotor circuit will shift the torque-speed curve,
and the net output power at a given speed will drop with respect to the conventional use
of the same machine. However, if an electrical source in proper phase is connected to the
rotor circuit, the induction machine will be able to feed more power to the supply than
with conventional use. This is because the rotor current will be able to go above the value
corresponding to the conventional use of the same machine without exceeding the rated
rotor current.
Control of machines in the dynamic state
Various modulation techniques are used to study the transient performance of the
machine under dynamic conditions. A generally used one is a dynamic d-q model, space
vector modulation and spiral vector modulation. Out of these, the dynamic d-q model is
discussed here in detail.
Dynamic d-q model
Fig. 4: Spatial mmf phasor diagram
Vector control techniques for ac motor drive systems have gained wide acceptance in
high-performance, variable speed applications by creating independent channels for
torque and flux controls. In a similar manner, vector control strategies have been
proposed for active and reactive power control of the induction generator. Stator and
rotor currents flowing through balanced sinusoidally distributed windings setup
respective resultant space mmf vectors which may be defined in terms of the current
space vectors Is and Ir as shown in Fig. 4. The developed electromagnetic torque is
proportional to the product of the magnitudes of the two current vectors and the sine of
their space phase difference, i.e., Te=kIsIrsin=kIsImsins=kIrImsinr. Im, the magnetizing
current space-vector, represents the resultant air-gap flux vector and Issins (Irsinr)
represents the torque producing current vector. These two rotating space vectors are
always in quadrature. The essence of vector control is to force the moving stator and rotor
current vectors Is and Ir to take these magnitudes and positions that enable independent
control of Im and Issins (Irsinr).This is achieved by the appropriate control of the
magnitude and phase of the actual stator (rotor) currents. Vector control makes an
induction machine behave like a dc machine with Issins (Irsinr) analogous to the
armature current and Im analogous to the field excitation. Assuming currents flowing
through a pair of two orthogonally spaced fictitious identical windings, replacing the
original balanced three-phase stator and rotor windings can also produce the same current
vectors. Such a transformation is known as a reference frame transformation. However,
for this, a mere replacement by a two-phase winding is not sufficient. A further insight is
necessary to develop the complete mathematical model. Owing to the smooth air gap, the
self inductances of the stator and rotor windings are constant, but the mutual inductance
between them vary with the rotor displacement relative to the stator. This variation of the
stator-to-rotor mutual inductances makes the induction motor analysis complicated in
terms of real variables, as the voltage equations become non-linear. In order to eliminate
the effect of variation of mutual inductances, and thus, facilitate analysis, a change of
variables can be devised for stator and rotor variables. This gives a fictitious magnetically
coupled two-phase machine, in which the rotor circuits are not only made stationary, but
also aligned with the respective stator windings. In this way, all the inductances become
constant. These orthogonally placed balanced windings, known as the d-q windings may
be considered stationary or moving with respect to the stator. Fig. 5 shows two such sets,
one stationary and one rotating. In the stationary reference frame, the ds and qs axes are
fixed on the stator with either the ds or qs axis coinciding with the stator a-phase axis. The
rotor de-qe axis may be either fixed on the rotor or made to move at the synchronous
speed. If one of axes of the synchronously rotating reference frame coincides with the airgap flux vector (i.e., the magnetizing current vector Im), it is said to be the air-gap flux
oriented.
Fig. 5: Angular relationships between reference axes
A vector-controlled scheme need not always be designed with respect to the air-gap flux.
It may also be designed with respect to the stator or rotor flux with corresponding
advantages or limitations. In field oriented control (FOC), the stator phase currents are
first estimated in a synchronously rotating reference frame and then transformed back to
the stationary stator frame to feed the machine. To carry out the transformation, with the
invariance of power as the necessary criterion, and assuming the equivalent two-phase
windings to have 3/2 times as many turns per phase as the three-phase winding, the
fictitious stator d, q, 0 variables are obtained from the state variables (a,b,c) through a
transform (similar to the park transform in synchronous machines) defined as:
where e is the angle of the moving de axis with respect to the stator a-phase winding as
shown in Fig. 5. In the equation above, f can represent voltage, current or flux-linkage.
This transformation is based on the assumption of a distributed sinusoidal winding. The
phase variables are obtained from the d, q, 0 variables through the inverse of the
transformation matrix in the above equation.
With reference to Fig. 6, replacing e by (e-r) in the above equations, defines the same
transformations for the rotor quantities. The stator d,q variables in the reference frame
fixed to the stator, with the d-axis aligned along the a-phase axis, are related to the phase
variables as follows:
In the synchronously rotating reference frame defined by the de-qe axes, the dynamic
voltage equations of a three phase symmetrical induction machine in terms of the
equivalent two phase system, defined by the previous equations are given by:
vdse  rsidse  peds   eeqs
vqse  rsiqse  peqs   e eds
vdre  rr ' idre  pedr  ( e   r )eqr
vqre  rr ' iqre  peqr  ( e   r )edr
The electromagnetic torque in terms of the rotor currents is: Te=M(p/2)(ieqsiedr-iedsieqr)
Where M is the mutual inductance and p is the number of poles.
Active power, P=(vedsieds+veqsieqs), Reactive power, Q=(veqsieds-vedsieqs) and
(veds )2+(veqs)2= 3V2
where V is the RMS input voltage. For balanced sets, v0 and i0 will be zero. Whether
balanced or not, the relations given below always hold good:
P=(vedsieds+veqsieqs+ve0sie0s) = vaia + vbib + vcic
(veds )2 + (veqs)2 + (ve0s) = v2as + v2bs + v2cs
and
The wound field synchronous machine
In wind electric power generation systems, two types of wind turbines are generally used.
These are variable speed and constant speed turbines. The high power variable speed
synchronous generator, with field windings on the rotor, is a serious competitor for the
wound rotor induction motor. In particular, direct drive variable speed systems use
synchronous machines. As the name indicates, unlike in a wound rotor induction
machine, the rotor of a synchronous machine runs in synchronization with the field
produced by the stator winding currents. The salient aspect of the machine windings is
considered for analysis purpose.
This vector control technique applied to a real time system is shown below.
Fig. 6 shows the schematic diagram and block diagram of a stand-alone power generation
scheme using two bi-directional converters and a dc link capacitor. The capacitor is
charged to a small value initially and the control is initiated by injecting a small value of
current in both the d and q-axes of the rotor current. While the d-axis current establishes
the stator flux, the q-axis current has a direct control of the dc link capacitor voltage.
When the capacitor voltage reaches a predetermined reference value, both converters are
controlled in such a way that the net power flowing to the capacitor is zero. At this point,
the load switch along with the filter is turned ON. At steady state, the system operates
exactly as a conventional slip power recovery drive except that the combined reactive
power demand of the machine and load is supplied by both the converters instead of the
grid.
Fig. 6: Schematic diagram of a Variable Speed Constant Frequency system
The complete control involved in the implementation of this generation system is shown
in Fig. 7. A simulation and practical validation of the system proved excellent voltage
regulation for a speed range of half to double the synchronous speed and various load
power factors.
Fig. 7: Control schemes for the Stand-alone Generation System