**Introduction**

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

where J is the polar moment of inertia of the rotor, w is the angular 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,

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.

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.

The modified circuit model satisfying the rotor resistance is shown in Fig. 1. Since E1=ImwLm 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 power associated with the rotational emf is Pe=3Re[E1(1-s)I’*2]=3 which is 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.

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 b with respect to sE2 and acting in the opposite sense to it.

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(f2+b)]. 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.

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.

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=kIsIrsinq=kIsImsinds=kIrImsindr. Im, the magnetizing current space-vector, represents the resultant air-gap flux vector and Issinds (Irsindr) 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 Issinds (Irsindr).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 Issinds (Irsindr) 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 air-gap flux vector (i.e., the magnetizing current vector Im), it is said to be the air-gap flux oriented.

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 Ö3/2 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:

With reference to Fig. 6, replacing qe by (qe-qr) 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:

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 and

(veds )2 + (veqs)2 + (ve0s) = v2as + v2bs + v2cs

**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.

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.

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.

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