Wind Turbine Doubly-Fed Induction Generator (Phasor Type)

Implement phasor model of variable speed doubly-fed induction generator driven by wind turbine

Library

Simscape / Electrical / Specialized Power Systems / Electrical Machines

Description

The wind turbine and the doubly-fed induction generator (WTDFIG) are shown in the figure.

The Wind Turbine and the Doubly-Fed Induction Generator System

The AC/DC/AC converter is divided into two components: the rotor-side converter (C_rotor) and the grid-side converter (C_grid). C_rotor and C_grid are Voltage-Sourced Converters that use forced-commutated power electronic devices (IGBTs) to synthesize an AC voltage from a DC voltage source. A capacitor connected on the DC side acts as the DC voltage source. A coupling inductor L is used to connect C_gridto the grid. The three-phase rotor winding is connected to C_rotor by slip rings and brushes and the three-phase stator winding is directly connected to the grid. The power captured by the wind turbine is converted into electrical power by the induction generator and it is transmitted to the grid by the stator and the rotor windings. The control system generates the pitch angle command and the voltage command signals V_r and V_gc for C_rotor and C_grid respectively in order to control the power of the wind turbine, the DC bus voltage, and the reactive power or the voltage at the grid terminals.

Operating Principle

Power flow, as illustrated in the figure, describes the operating principle of the Wind Turbine Doubly-Fed Induction Generator.

The Power Flow

The parameters for the power flow figure are:

P_m	Mechanical power captured by the wind turbine and transmitted to the rotor
P_s	Stator electrical power output
P_r	Rotor electrical power output
P_gc	C_grid electrical power output
Q_s	Stator reactive power output
Q_r	Rotor reactive power output
Q_gc	C_grid reactive power output
T_m	Mechanical torque applied to rotor
T_em	Electromagnetic torque applied to the rotor by the generator
ω_r	Rotational speed of rotor
ω_s	Rotational speed of the magnetic flux in the air-gap of the generator, this speed is named synchronous speed. It is proportional to the frequency of the grid voltage and to the number of generator poles.
J	Combined rotor and wind turbine inertia coefficient

The mechanical power and the stator electric power output are computed as follows:

P_m = T_mω_rP_s = T_emω_s.

For a lossless generator the mechanical equation is:

$J \frac{d ω_{r}}{d t} = T_{m} - T_{e m} .$

In steady-state at fixed speed for a lossless generator T_m= T_em and P_m= P_s+ P_r.

It follows that:

$P_{r} = P_{m} - P_{s} = T_{m} ω_{r} - T_{e m} ω_{s} = - T_{m} \frac{ω_{s} - ω_{r}}{ω_{s}} ω_{s} = - s T_{m} ω_{s} = - s P_{s},$

where s is defined as the slip of the generator: s= (ω_s–ω_r)/ω_s.

Generally the absolute value of slip is much lower than 1 and, consequently, P_ris only a fraction of P_s. Since T_m is positive for power generation and since ω_s is positive and constant for a constant frequency grid voltage, the sign of P_r is a function of the slip sign. P_r is positive for negative slip (speed greater than synchronous speed) and it is negative for positive slip (speed lower than synchronous speed). For super-synchronous speed operation, P_ris transmitted to DC bus capacitor and tends to rise the DC voltage. For subsynchronous speed operation, P_r is taken out of DC bus capacitor and tends to decrease the DC voltage. C_grid is used to generate or absorb the power P_gc in order to keep the DC voltage constant. In steady-state for a lossless AC/DC/AC converter P_gc is equal to P_r and the speed of the wind turbine is determined by the power P_r absorbed or generated by C_rotor. The power control is explained below.

The phase-sequence of the AC voltage generated by C_rotor is positive for subsynchronous speed and negative for super-synchronous speed. The frequency of this voltage is equal to the product of the grid frequency and the absolute value of the slip.

C_rotor and C_grid have the capability of generating or absorbing reactive power and could be used to control the reactive power or the voltage at the grid terminals.

C_rotor Control System

The rotor-side converter is used to control the wind turbine output power and the voltage (or reactive power) measured at the grid terminals.

Power Control

The power is controlled in order to follow a pre-defined power-speed characteristic, named tracking characteristic. An example of such a characteristic is illustrated by the ABCD curve superimposed to the mechanical power characteristics of the turbine obtained at different wind speeds.

Turbine Characteristics and Tracking Characteristic

The actual speed of the turbine ω_r is measured and the corresponding mechanical power of the tracking characteristic is used as the reference power for the power control loop. The tracking characteristic is defined by four points: A, B, C, and D. From zero speed to speed of point A, the reference power is zero. Between point A and point B the tracking characteristic is a straight line, the speed of point B must be greater than the speed of point A. Between point B and point C the tracking characteristic is the locus of the maximum power of the turbine (maxima of the turbine power versus turbine speed curves). The tracking characteristic is a straight line from point C and point D. The power at point D is one per unit (1 pu) and the speed of the point D must be greater than the speed of point C. Beyond point D the reference power is a constant equal to one per unit (1 pu).

The generic power control loop is illustrated in the figure.

Rotor-Side Converter Control System

The actual electrical output power, measured at the grid terminals of the wind turbine, is added to the total power losses (mechanical and electrical) and is compared with the reference power obtained from the tracking characteristic. A Proportional-Integral (PI) regulator is used to reduce the power error to zero. The output of this regulator is the reference rotor current Iqr_ref that must be injected in the rotor by converter C_rotor. This is the current component that produces the electromagnetic torque T_em. The actual Iqr component of positive-sequence current is compared to Iqr_ref and the error is reduced to zero by a current regulator (PI). The output of this current controller is the voltage Vqr generated by C_rotor. The current regulator is assisted by feed forward terms which predict Vqr.

Voltage Control and Reactive Power Control

The voltage or the reactive power at grid terminals is controlled by the reactive current flowing in the converter C_rotor. The generic control loop is illustrated in the figure.

Wind Turbine V-I Characteristic

When the wind turbine is operated in voltage regulation mode, it implements the following V-I characteristic.

As long as the reactive current stays within the maximum current values (-Imax, Imax) imposed by the converter rating, the voltage is regulated at the reference voltage Vref. However, a voltage droop is normally used (usually between 1% and 4% at maximum reactive power output), and the V-I characteristic has the indicated slope. In the voltage regulation mode, the V-I characteristic is described by the following equation:

V = V_ref + X_sI,

where:

V	Positive sequence voltage (pu)
I	Reactive current (pu/Pnom) (I > 0 indicates an inductive current)
X_s	Slope or droop reactance (pu/Pnom)
Pnom	Three-phase nominal power of the converter specified in the block dialog box

When the wind turbine is operated in var regulation mode, the reactive power at grid terminals is kept constant by a var regulator.

The output of the voltage regulator or the var regulator is the reference d-axis current Idr_ref that must be injected in the rotor by converter C_rotor. The same current regulator as for the power control is used to regulate the actual Idr component of positive-sequence current to its reference value. The output of this regulator is the d-axis voltage Vdr generated by C_rotor. The current regulator is assisted by feed forward terms which predict Vdr.

Vdr and Vqr are respectively the d-axis and q-axis of the voltage Vr.

Note:

for C_rotorcontrol system and measurements the d-axis of the d-q rotating reference frame is locked on the generator mutual flux by a PLL which is assumed to be ideal in this phasor model.
the magnitude of the reference rotor current Ir_ref is equal to $\sqrt{I_{d r_ref}^{2} + I_{q r_ref}^{2}}$ . The maximum value of this current is limited to 1 pu. When Idr_ref and Iqr_ref are such that the magnitude is higher than 1 pu, the Iqr_ref component is reduced in order to bring back the magnitude to 1 pu.

C_grid Control System

The converter C_gridis used to regulate the voltage of the DC bus capacitor. In addition, this model allows using C_gridconverter to generate or absorb reactive power.

The control system is illustrated in the figure.

Grid-Side Converter Control System

The control system consists of:

Measurement systems measuring the d and q components of AC positive-sequence currents to be controlled as well as the DC voltage Vdc.
An outer regulation loop consisting of a DC voltage regulator. The output of the DC voltage regulator is the reference current Idgc_ref for the current regulator (Idgc = current in phase with grid voltage which controls active power flow).
An inner current regulation loop consisting of a current regulator. The current regulator controls the magnitude and phase of the voltage generated by converter C_grid(Vgc) from the Idgc_ref produced by the DC voltage regulator and specified Iq_ref reference. The current regulator is assisted by feed forward terms which predict the C_gridoutput voltage.

The magnitude of the reference grid converter current Igc_ref is equal to

$\sqrt{I_{d g c_ref}^{2} + I_{q r_ref}^{2}}$

. The maximum value of this current is limited to a value defined by the converter maximum power at nominal voltage. When Idgc_ref and Iq_ref are such that the magnitude is higher than this maximum value, the Iq_ref component is reduced in order to bring back the magnitude to its maximum value.

Pitch Angle Control System

The pitch angle is kept constant at zero degrees until the speed reaches point D speed of the tracking characteristic. Beyond point D the pitch angle is proportional to the speed deviation from point D speed. The control system is illustrated in the following figure.

Pitch Control System

Turbine Model

The turbine model uses the Wind Turbine bloc of the Renewables/Wind Generation library. See documentation of this model for more details.

Induction Generator

The doubly-fed induction generator phasor model is the same as the wound rotor asynchronous machine (see the Machines library) with the following two points of difference:

Only the positive-sequence is taken into account, the negative-sequence has been eliminated.
A trip input has been added. When this input is high, the induction generator is disconnected from the grid and from C_rotor.

Parameters

The WTDFIG parameters are grouped in four categories: Generator data, Converters data, Turbine data, and Control parameters. Use the Display listbox to select which group of parameters you want to visualize.

Generator Tab

External turbine (Tm mechanical torque input)

When you select this parameter, the Turbine tab is not visible, and a Simulink^® input named Tm appears on the block, allowing to use an external signal for the generator input mechanical torque. This external torque must be in pu based on the nominal electric power and synchronous speed. For example, the external torque may come from a user defined turbine model. Following the convention used in the induction machine, the torque must be negative for power generation. Default is cleared.

Nominal power, line-to-line voltage and frequency

The nominal power in VA, the nominal line-to-line voltage in Vrms and the nominal system frequency in hertz. Default is [1.5e6/0.9 575 60].

Stator

The stator resistance Rs and leakage inductance Lls in pu based on the generator rating. Default is [ 0.00706 0.171].

Rotor

The rotor resistance Rr' and leakage inductance Llr', both referred to the stator, in pu based on the generator rating. Default is [ 0.005 0.156].

Magnetizing inductance

The magnetizing inductance Lm in pu based on the generator rating. Default is 2.90.

Inertia constant, friction factor and pairs of poles

Combined generator and turbine inertia constant H in seconds, combined viscous friction factor F in pu based on the generator rating and number of pole pairs p. Default is [5.04 0.01 3].

You may need to use your own turbine model, in order for example, to implement different power characteristics or to implement the shaft stiffness. Your model must then output the mechanical torque applied to the generator shaft. If the inertia and the friction factor of the turbine are implemented inside the turbine model you specify only the generator inertia constant H and the generator friction factor F.

Initial conditions

The initial slip s, electrical angle Θ in degrees, stator phasor current magnitude in pu, stator phasor current phase angle in degrees, rotor phasor current magnitude in pu and rotor phasor current phase angle in degrees. Default is [0.2 0 0 0 0 0].