Power Electronic Conditioner

30.1.1.4 Power Electronic Conditioner

The power electronic conditioner is a converter that is mainly

6 ° 5 ° 4 ° used in variable speed applications. This converter is connected between the generator machine and the utility grid by an iso- FIGURE 30.3 Analytical approximation of C p (λ, β) characteristic lating transformer and permits different frequency and voltage (blade pitch angle β as parameter). levels in its input and output. The power converter is con- nected to the stator voltage or to the rotor of a wound rotor the turbine radius, and v w the wind speed). In Fig. 30.3 an machine. This system includes large power switches that can analytical approximation of the power coefficient C p (λ, β) is

be GTOs, Thyristors, IGCTs, or IGBTs arranged in different shown. topologies.

In Fig. 30.4 the power characteristic of a wind turbine P m is shown.

30.1.2 Simplified Model of a Wind Turbine

The power of the wind can be expressed by the following equations [1, 2]:

The mechanical power P m in the low speed shaft can be expressed as a function of the available power in the wind P v

P w = ρπ R 2 v 3 w (30.4) by the Eq. (30.3):

where ρ is the air density.

P m =C p (λ , β) ·P w

Substitution of Eq. (30.4) in Eq. (30.3) and including λ in such expression, the following can be obtained:

where C p (λ, β) is the power coefficient, which is a function of the blade angle β and the dimensionless variable λ =ω L R/v w

(where ω L is the angular speed on the low speed shaft, R is 2λ 3 ω L

V start

V rat

V Pmax

V stop

30 Wind Turbine Applications 795 β

C p ( λ,β)

C .ρ.π.R 5 .w p 2 L

2. λ 3 G

w L .R v w

FIGURE 30.5 Torque calculation block diagram.

where Q L is the torque in the low speed shaft that the wind of the wind turbines built so far have practically constant turbine draws from the wind.

speed, since they use an AC generator, directly connected to This Eq. (30.5) is represented in Fig. 30.5.

the distribution grid, which determines its speed of rotation. Neglecting mechanical losses, the total torque on the high

In the last few years, variable speed control has been added speed shaft, Q t is equal to the torque in the low speed shaft, to pitch-angle control design in order to improve the per- Q L , divided by the gearbox ratio, G.

formance of the system [11]. Variable speed operation of a wind turbine has important advantages vs the constant speed

(30.6) ones. The main advantages of variable speed wind tunnel are

G the reduction of electric power fluctuations by changes in Equation (30.7) shows the differential equation for the kinetic energy of the rotor, the potential reduction of stress

dynamics of the rotational speed that depends on the differ- loads on the blades and the mechanical transmissions, and ence of load and generator torque.

the possibility to tune the turbine to local conditions by adjusting the control parameters. On the other hand, vari-

dω r

Q t −Q e =J

(30.7) able speed control is normally used with fixed pitch angle

and very few applications using both controls have been In Eq. (30.7) J is the total inertia of the system referred to reported [12, 13]. the high speed shaft.

dt

In short, four different wind turbine types are provided Figure 30.6 shows the block diagram of the simplified depending on the controller [14]: mechanical model of a wind turbine. Also, it has been

• No control. The generator is directly connected to a con- the electrical torque Q e by the rotor speed ω r and the electrical

represented by the electrical power P e , obtained by multiplying

stant frequency grid, and the aerodynamics of the blade performance η.

is used to regulate power in high winds. • Fixed speed pitch regulated. In this case, the generator is

30.1.3 Control of Wind Turbines

also directly connected to a constant frequency grid, and pitch control is used to regulate power in high winds.

Many horizontal axes, grid-connected, and medium- to large- • Variable speed stall regulated. A frequency converter scale wind turbines are regulated by pitch control, and most

decouples the generator from the grid, allowing the rotor

STATIC

TORQUE

MODEL

J·s

796 J. M. Carrasco et al. speed to be varied by controlling the generator reaction the operation pitch angle, allowing an easier starting and opti-

torque. In high winds, this speed control capability is used mum running. Moreover, the power and speed can be limited to slow the rotor down until aerodynamic stall limits the through rotor pitch regulation. power to a desired level [15].

The control diagram is shown schematically in Fig. 30.7. • Variable speed pitch regulated. A frequency converter The generator torque Q e and the pitch angle β control the decouples the generator from the grid, allowing the rotor wind turbine. The control system acquires the actual generated speed to be varied by controlling the generator reaction electric power P e and the generator speed, ω r , and calculates torque. In high winds, the torque is held at a rated level,

e and the reference pitch and pitch control is used to regulate the rotor speed, and angle β ref , using two control loops [14].

the reference generator torque Q ref

hence, also the power [13]. In low winds it is possible to maximize the energy captured

A power converter will be mainly used in variable speed by following a constant tip speed ratio λ load line which cor- applications. In fixed speed control, a power converter could responds to operating at the maximum power coefficient. This

be used for a better system performance, for example, smooth load line is a quadratic curve in the torque-speed plane as it is transition during turn on, harmonics, and flicker reduction, shown in Fig. 30.8. During that time, the pitch angle is adjusted etc. Next, the operation of the most general controller, namely, to a constant value, the maximum power pitch angle. the variable speed pitch regulator controller is explained.

If there is a minimum allowed operating speed, then it is not Another controller can be obtained from this control scheme, possible to follow this curve in very low winds, and the turbine but will not be presented here.

is then operated at a constant speed N min shown in Fig. 30.8. On the other hand, in high wind speed, it is necessary to limit the torque Q rate or power P rate of the generator to a constant value.

The control parameters are: the minimum speed ω min r , the maximum speed in constant tip speed ratio mode ω max r , the