Modelling wind turbine generators in MATLAB/Simulink, determining

performance within a typical public utility electric power system.

Sourav Ranu

Department of electrical engineering.

Indian school of mines, Dhanbad.

Abstract: During the summer of 2012 from May 14th 2012 till July 13th a undergraduate from

Indian school of mines decided to work on modelling of wind turbine generators. The main objective

of the modelling was to design a robust and efficient models of different generators with Fast s

function so that they can be used in determining the performance within a typical public utility

electric power system.

Fast s Function: The fast s function code is the most comprehensive aero elastic simulator

capable of predicting both the extreme and fatigue loads of two and three bladed horizontal axis

wind turbines. Fast basically stands for Fatigue, Aerodynamic , Structures and Turbulence.

Fast code is basically combination of three different codes namely Fast 2 code for 2 axis horizontal

axis wind turbines, Fast 3 code for 3 axis horizontal axis wind turbines and AeroDyn subroutines for

horizontal axis wind turbines. Some changes were made in the computational loops and in the

kinematic calculations of fast code.

Simulink has the ability to incorporate Fortran routines in a block called S function. The FAST

subroutines were linked with a MATLAB standard gateway subroutine in order to use the FAST

equations of motion in an S-Function which can be incorporated in a Simulink model. This has led to

a great deal of flexibility in the wind turbine control implementation during simulation. Generator

torque control, nacelle yaw control, and pitch control modules now can be designed in the Simulink

environment and simulated while making use of the complete nonlinear aero elastic wind turbine

equations of motion available in FAST.

The wind turbine block shown below contains the S-Function block with the FAST equation of

motion. It also contains blocks that integrate the degrees of freedom accelerations to get velocities

and displacements.

Fig 1. FAST Wind Turbine Block

The FAST archive contains several files that are very much essential to FAST’s interface with Simulink

and the simulink model to run without any errors. Some of these files are FAST_SFunc.dll,

Simsetup.m, Read_FAST_Input.m.

Fig 2. Simulink Model OpenLoop.mdl

As we can see the wind turbine model has three inputs and one output. Electrical generated torque

and power must be supplied as the first input, Nacelle yaw position and rate demands must be

supplied as the second while the blade pitch demand angle for all the blades as the third. Data must

be provided in all the inputs for the simulink model to run.

Induction generator model: Basically there are two main types of induction generators used in the wind energy industries. These are doubly fed induction generator and squirrel cage induction generator. Both of them have the same stator structure only different rotor structure. In developing the induction generator space vector model following assumptions were made:

(i) The induction generator is symmetrical in structure and three phase balanced. (ii) The magnetic core of stator and rotor is linear with negligible core losses.

The space vector model of induction generator comprises mainly of three equations. These are voltage equations, flux linkage equations, and motion equation.

(i) The rotor and stator voltages are given as: Vs=Rs Is + p λs + jW λs Vr=Rr Ir + p λr + j(W-Wr)λr Where:

Vs , Vr - Stator and rotor voltage vectors(V).

Is , Ir- Stator and rotor current vectors(A).

λs, λr – Stator and rotor flux linkage vectors(Wb).

Rs, Rr- Stator and rotor winding resistance.(Ohm).

W- Rotating speed of the arbitrary reference frame (Rad/s)

Wr- Rotor electrical speed (Rad/s)

p- Derivative operator (p=d/dt)

(ii) The second set of equations are the stator and the rotor flux equations.These

are as follows:

λs = (Lls +Lm) Is + Lm Ir = Ls Is + Lm Ir

λr = (Llr +Lm) Is + Lm Is = Lr Ir + Lm Is

Where: Ls=Lls + Lm – Stator self-inductance (H).

Lr=Llr + Lm – Stator self-inductance (H).

Lls,Llr=Lls + Lm – Stator and Rotor leakage inductance (H).

Lm – Magnetizing inductance (H).

(iii) The third and final equation deals mainly with the dynamic behaviour of the rotor

mechanical speed in terms of the rotor mechanical and electrical torque.

JdW/dt=Te-Tm

Simulation model for Induction Generator: The dq axis model of the induction

generator can be obtained by splitting the space vectors into their corresponding d and q axis

components and rearranging them

Fig 3.D axis equivalent circuit in arbitrary reference frame.

Fig 4.Q axis equivalent circuit in arbitrary reference frame.

The equations are rearranged to get the fluxes as:

λds = (Vds-RsIds+W λqs)/S

λqs = (Vqs-RsIqs+W λds)/S

λdr = (Vdr-RrIdr+(W-Wr)λqr)/S

λqr = (Vqr-RrIqr-(W-Wr)λdr)/S

We also know that [λ]=[L][I]

This leads to [I]=[L]^(-1)[λ]

The motion and the torque equation were given as:

Wr=(P/(J*S))(Te-Tm)

Te=3P/2(Iqs λds-Ids λqs)

The simulink block diagram of induction generator with FAST s function:

Fig5.Simulink block diagram of induction generator with FAST s function

wr

wr

iqs

ids

iqr

idr

Lqs

Lds

Lqr

Ldr

Power

Select LSS speed at entrance to gearbox (rpm)

1

Te,P

wm

OutData

Xa

Xb

Xc

Vds

Vqs

abc/dq

Out1

Yaw Controller

Xc

Xb

Xa

0

Vqr

0

Vdr

Time

To Workspace

0

Tm

Te

Subtract9

Subtract8

Subtract7

Subtract12

Subtract11

Subtract10

Subtract

-K-

Rs1

-K-

Rs

-K-

Rr1

-K-

Rr

Product6

Product5

Product4

Product3

Product2

Product1

Product

Out1

Pitch Controller

2

P

-K-

Ls2

-K-

Ls

-K-

Lr1

-K-

Lr

-K-

Lm3

-K-

Lm2

-K-

Lm1

-K-

Lm

1

s

Integrator4

1

s

Integrator3

1

s

Integrator2

1

s

Integrator1

1

s

Integrator

f(u)

Fcn

Gen. Torque (Nm) and Power (W)

Yaw Position (rad) and Rate (rad/s)

Blade Pitch Angles (rad)

OutData

FAST Nonlinear Wind Turbine

Clock

3

3P/2

-K-

1/J

-K-

1/D4

-K-

1/D3

-K-

1/D2

-K-

1/D1

Simulation Results: We know that during the system transients a very high inrush current

flows and a dc offset appears in all the stator currents Ias , Ibs, Ics. As there is three phase balanced

load so all the dc offset currents sum up to zero. As the magnetic field builds up generator core gets

magnetized by the stator currents and an electromagnetic torque is produced. As the generator is

operating below the synchronous speed it produces the positive torque which accelerates the

turbine and the generator finally reaches synchronous speed at which Te=Tm=o and it is in steady

state mode.

Synchronous generator model: There are mainly two categories of synchronous

generators namely wound rotor synchronous generators and permanent magnet synchronous

generators. The basic difference between the wound rotor synchronous generator and the

permanent magnet synchronous generator is the way in which rotor flux is produced. In wound

rotor synchronous generator field windings produce the rotor flux whereas in the permanent

magnet synchronous generator rotor flux is produced by the permanent magnets.

Our work bas basically on the type (iv) model that is permanent magnet synchronous generator

model. In these generators as the flux is produced by the permanent magnets so these generators

are basically brushless. Due to absence of field windings these generators are lighter in weight and

smaller in size.

Abc to dq transformation: We perform the park transformation from abc reference frame to

dq reference frame. The dq reference frame has two axis the direct axis and the quadrature axis .The

following transformation is used:

Vd=2/3(Va Sin(Wt)+Vb Sin(Wt-2*pi/3)+Vc Sin(Wt+2*pi/3))

Vq=2/3(Va Sin(Wt)+Vb Sin(Wt-2*pi/3)+Vc Sin(Wt+2*pi/3))

Where Wt=theta.

Dynamic model of synchronous generator: In order to simplify the analysis this model

was modelled in synchronous rotor frame. In the rotor circuit the field current is represented by

constant current source If.

Ld,Lq=q and d axis inductances

R=Resistance of the stator windings

Iq Id=q and d axis currents

Vd , Vq=q and d axis voltages

We=Angular velocity of the rotor

λ =Amplitude of the flux induced by the permanent magnets of the rotor in the stator phases

P=Number of pole pairs

Te=Electromagnetic torque

Fig 6. Simplified DQ axis equivalent circuit in arbitrary reference frame.

Id and Iq can also be written as:

Id=1/S(Vd-Rid+LqPWrIq)/Ld

Iq=1/S(Vq-Riq-LqPWrId-λPWr)/Lq

Here s represents the laplace parameter and 1/s is the integrator.

Now,

Wr= (P/J)*(1/S)*(Te-Tm)

Where Wr is the rotor speed.

The simulink block diagram of permanent magnet synchronous generator

with FAST s function:

Fig7. Simulink block diagram of Synchronous generator with FAST s

function.

theta

Vds

Vqs

Wr

Theta

Ids

Te

Iqs

simpowermodel

Wr

Vcs

Vbs

Vas

Te

Iqs

Ids

2/3

Gain1

2/3

Gain

cos

2*pi/3

cos

2*pi/3

2*pi/3

sin

cos

2*pi/3

sin

sin

Simpowermodel subsystem:

Ids

Iqs

P Wr Iq Lq

P Wr

Ld Id

P Wr

L r P Wr

Lq Iq

Select LSS speed at entrance to gearbox (rpm)

5

Iqs

4

Te

3

Ids

2

Theta

1

Wr

OutData

Yf Iq

Out1

Yaw Controller

-C-

Y r

Time

To Workspace

Scope

-K-

Rs1

-K-

Rs

-K-Rpm to radian/s

Power

Out1

Pitch Controller

4

P

Lq Iq Id

Ld Id Iq

f(u)

Fcn

Gen. Torque (Nm) and Power (W)

Yaw Position (rad) and Rate (rad/s)

Blade Pitch Angles (rad)

OutData

FAST Nonlinear Wind Turbine

Clock

6

3P/2

-K-

1/Lq

-K-

1/Ld

Yr P Wr

Lq P Wr Iq

Ld Id P Wr

1

s

1

s

1

s

2

Vqs

1

Vds

Simulation result for synchronous generator: The speed waveform justifies the fact that the wind turbine used has got two blades. We know that

the synchronous generators are highly under damped, hence the torque waveform oscillates with a

frequency much less than the input frequency .Same goes with the quadrature axis current because

the reference frame used is synchronous reference frame.

Future work: (i) Testing the model with faults (both one phase and three phase).

(ii) Building a model of converter and to control the speed of the generators.

(iii) Running an actual setup on the basis of the simulation parameters.

(iv) Modelling s function based on our own parameters so that it will be easy to use it in

future.

References: (i) Power Conversion and Control of Wind Energy Systems, Wiley publications, IEEE Press,

By (Bin Wu, Yongqiang Lang, Navid Zargari, Samir Kouro)

(ii) FAST User`s Guide by Jason M. Jonkman and Marshall L.Buhl.Jr, Technical Report

NREL/EL-500-38230, August 2005.

(iii) Matlab/Simulink Help section.

(iv) Modelling and Control of direct driven PMSG for ultra large wind turbines by Ahmed

M.Hemeida, Wael A.Farag, Osama A.Mahgoub, World Academy of Science Engineering

and Technology.

Modelling wind turbine generators in

MATLAB/Simulink , determining

performance within a typical public

utility electric power system

By: Sourav Ranu

Dept. of Electrical Engineering, Indian School Of Mines, Dhanbad.

Project Sponsor: Dr. Herbert Hess.

Dr. Herbert Hess

(Professor and project mentor)