Relaciones entre el sistema de control de gestión institucional

The closed-loop control of the IM with the reference determined by the static and dynamic characteristics of a PWT, drives the WTS as a close resemblance of a real PWT. Therefore, the characteristics of the PWT are captured through the modeling in the LabVIEW software. In addition, the modeling of IM and motor controller are also performed to determine the motor torque.

3.1.3.1

Physical Wind Turbine (PWT)

The static characteristics of a PWT are described in [138], and depend on the blade design coefficients, size, and environmental conditions. The power coefficient represents the efficiency of the wind turbine under different wind conditions. Therefore, the wind

0 5 10 0 10 20 0 0.2 0.4 0.6

Tip Speed Ratio Pitch Angle P o w er C o ef fi ci en t

speed and the turbine rotor characteristics are the key parameters to be considered in the design of a wind turbine simulator.

Dynamic Characteristics

The dynamic characteristic of any rotational machine can be represented by the dynamic equation of motion. The equation is the relationships between the turbine torque () and the generator torque (). Generator torque is the electrical torque which depends on the electrical load connected to the generator output.

A pictorial representation of turbine dynamics with a motor-generator (M-G) set is shown in Figure 3.4, where , , , and represent the torque, moment of inertia of the reference wind turbine, moment of inertia of the generator, moment of inertia of the motor, and the angular speed, respectively. With negligible friction losses and under the unity gear ratio assumption, the torque equation of a PWT can be expressed as follows [31]: 1:n Motor controller Generator (GEN) Torque Command Gear Box Generator (GEN) Induction Motor (IM)

Figure 3.4: Representation of turbine dynamics using (a) PWT and (b) M-G set

8 XG Y„ *3.1-

Similarly, the dynamic equation of the motor-generator (M-G) set can be represented as follows: 8 X G Y_{> *3.2-} (a) (b)

Substituting (3.1) in (3.2),

8 * -_{> *3.3-}

The term * -„

is the compensated torque and represented by ( . Hence, (3.3)

becomes

( 8 *3.4- Equation (3.4) can be implemented in the model of a PWT to match the dynamics of the

WTS with a PWT as shown in Figure 3.5.

Figure 3.5: Block diagram of WTS with the compensated torque

The wind turbine model block in Figure 3.5 consists of both static and dynamic characteristics of PWT, which determines the turbine torque based on the input wind speed () and feedback angular speed (). The turbine torque is then compensated to match the dynamics with a physical motor. The compensated torque is the command signal to the controller. The controller consists of the motor controller and the PI compensator, which is tuned using the refined Ziegler-Nichols rule [139]. The controller drives the IM with the same static and dynamic features as the PWT.

3.1.3.2

Induction Motor

The dynamic properties of the induction motor can be described by a set of nonlinear differential equations linking the stator and the rotor currents and voltages with the torque, speed, and angular position. The model is established under the following assumptions:

• The air gap is uniform

* - ( 1 G

• The flux density is radial in the air gap • The stator windings are identical, and • The magnetic saturation is not considered.

The modeling process is performed in the stator flux coordinate frame. The flux linkage in the stator and the rotor windings can be represented as

………†4

> 8 …†4 Q4‡……† *3.5-4 ………†4

> 8 …†ˆ Qˆ‡……† *3.6-ˆ where †, …†, Q and are the flux linkage, voltage, resistance and current with subscripts " and D representing stator and rotor, respectively. The fundamental fluxes in an AC induction machine can be expressed as a function of the stator and rotor currents [140]. 4 ………† 8 R‰*1 G Š4-‡……† G K4 ‹Œ‡……†Ž *3.7-ˆ ˆ …………† 8 R‰*1 G Šˆ-‡……† G Kˆ $‹Œ‡……†Ž *3.8-4 where, Š₄ 8  ‘ 1 and Šˆ 8  ‘ 1

L and θ_ˆ represent inductance and rotor angle respectively. The subscript and “ stand for magnetizing and imaginary. The developed torque of the motor can be expressed by

8 3_{2 R} “”‡……†X‡4 ……†Kˆ ‹•Y.– *3.9-

where is an electromechanical torque. A detailed description of (3.6), (3.9) and (3.11) is given in [141],[142]. The term within the square brackets in (3.7) represents a fictitious magnetizing current in the stator flux coordinates, that is

‡4

………………† 8 *1 G Š4-‡……† G K4 ‹Œ……† ‡ˆ and ‡………………† 8 4 — K4 ‹˜ *3.10-

where /, ‡………………†₄ and —₄ represent flux rotating angle, fictitious magnetizing current, and its magnitude in vector form, respectively. All other variables are represented in phasor form. From (3.10), one can obtain

K‹Œ‡……† 8 _ˆ — K₄ ‹˜ *1 G Š₄-‡……† *3.11-₄ Substituting (3.11) into (3.9), the torque produced can be expressed by

8 3_{2 R} “™‡……† g 4 — K4 ‹˜ *1 G Š4-‡……†h4 .

83_{2 R} “ ›‡……† g 4 — K4 $‹˜ *1 G Š4-‡……†hœ4. 83_{2 R} — “X‡4 ……†K4 $‹˜Y

83_{2 R} — _{4 4,} *3.12- where, ‡……†K₄ $‹˜ 8 ₄ V_4,

The final torque equation as shown in (3.12) demonstrates that the mechanical torque of the motor can be controlled by the quadrature axis of the stator current (_4,), provided that the magnetizing current remains constant. Hence, the motor controller which operates in vector torque mode (VTM) provides the controlled stator current based on the reference torque signal.

3.1.3.3

Motor Controller in VTM

The dynamics of an electric machine are affected by two quantities: torque and speed, either of which can be used to control the machine. In the torque control mode, the torque is used as a controlled variable and the speed is determined by loads. Vector control decouples the flux from the torque, which can be controlled in two independent loops as expressed in (3.12), where the torque is controlled independently from the flux by controlling the quadrature axis of the current.

A motor controller in a VTM has the potential to produce superior dynamic performance, as it relies on independent torque control. Under VTM control, the motor controller tracks the reference torque signal with fast dynamics and accurate steady state operation [133]. The reference torque signal in the WTS can be subject to abrupt changes due to variations in the wind speed. In addition, it can also have a wide dynamic spectrum. Hence, a motor controller in the vector torque mode is adopted in the WTS. A block diagram of the vector control of an induction motor in the torque mode is shown in Figure 3.6.

Current regulator IM model Vector control calculation abc-dq dq-abc PID Gate signal generator IM Constant term -

Figure 3.6: Vector torque mode control of the induction motor

where U₄ and ₄ are the stator voltages and currents with subscripts , and DK representing axes frame, frame and reference, respectively. The diagram shows only one loop for torque control, as torque mode control is implemented in the WTS. The flux is assumed to be constant. The reference torque (Tref) is compared with

the motor torque (T), and the error is minimized by a PID controller. This current regulator monitors the current in axes as per the reference value, and the outputs are the axes voltages, which are the reference signals to the gate drive of the converter. The gate drive is used to trigger the converter on/off modes to supply the required power to the motor. The stator currents are fed back to the motor model to estimate the motor torque based on (3.12) and the flux.

The interesting aspect of Figure 3.6 is to identify the angle (/-, which is the prime parameter to transform between and frames. Usually, the motor speed is measured and fed back into the motor model to identify the angle, but in the stator field coordinates, the flux rotating angle is estimated by using a flux observer. This is achieved by using (3.5) and substituting………† 8 R₄ ‡………………† ₄, ‡……†K₄ $‹˜ 8 ₄ V_4, and U………†K₄ $‹˜ 8 U₄ VU4, respectively.

R‡_{> 8 U}………………†4 4,K‹˜ž Q44,K‹˜ *3.13-

Using (3.10) in (3.13), one obtains,

R* — K4 ‹˜_- > 8 U4,K‹˜ Q44,K‹˜ ˆS 4ˆS _{U4, U4!} 4! 4, / 4,ˆS U4!

R — _{> K}4 ‹˜G VR/_{> K}‹˜— 8 U4 4,K‹˜ Q44,K‹˜

Canceling K‹˜ from both sides and dividing the equation into real and imaginary part as shown below

R — _{> 8 U}4 4 Q44 *3.14- R/_> — 8 U4 4, Q44, *3.15-

where, ˜ 8 and — 8 _{4 4} (magnitude in vector form)

Equations (3.14) and (3.15) can be implemented in the IM model block shown in Figure 3.6 as a flux observer.

abc-dq

abc-dq

-

-

Figure 3.7: Configuration of the flux observer

The structure of the estimation algorithms for the rotating angle is shown in Figure 3.7. The estimated angle is utilized in an induction motor control. Hence, the inner loop of the WTS is closed to control the torque in the vector mode.