curent course windturbines

CURENT Course

Wind Turbines

September 24, 2014

Joe H. Chow

Professor, Electrical, Computer, and Systems Engineering DepartmentCampus Director, NSF/DOE CURENT ERC

Rensselaer Polytechnic Institute

September 22, 2014

OutlineWind turbine types

Horizontal wind turbine energy conversion

Wind turbine blade pitch angle

Wind turbine active and reactive power control

References1 K. Clark, N. M. Miller, and J. J. Sanchez-Gasca, Modeling of GE

Wind Turbine-Generators for Grid Studies, version 4.4, September9, 2009.

2 M. Shao, N. M. Miller, J. J. Sanchez-Gasca, and J. MacDowell,Modeling of GE Wind Turbine-Generators for Grid Studies, version4.6, March 8, 2013.

3 S. Heier, Grid Integration of Wind Energy Conversion Systems, 2ndedition, Wiley, 2006.

4 Z. Lubosny, Wind Turbine Operation in Electric Power Systems,Springer, 2003.

5 P. Jain, Wind Energy Engineering, McGraw-Hill, 2011.

c©J. H. Chow (RPI-ECSE) Wind Turbines September 22, 2014 2 / 35

Wind Turbine Types

Horizonal wind turbines

use liftefficient and higher powercommercial power grid applications

Vertical wind turbines (Darrieus WT)

use dragless efficient and lower power

Horizontal Vertical


A wind farm off the shore of Danmark


Extracting Energy from Wind

1v

Wake decay

Wind flow direction

21 1

1KE

2aV v

2v 3v

RA

aV

aV

Wind turbine plane of rotation

23 3

1KE

2aV v

= density of air

Energy extracted

Ww =1

2Vaρ(v

21 − v23) (1)


Wind turbine power

Pw =dWw

dt=

d

dt(1

2Vaρ(v

21 − v23)) (2)

In quasi-steady state, v1 and v3 are constant, v2 = (v1 + v3)/2, ρ isfixed, and

dVa

dt= ARv2 (3)

Albert Betz (1919) – the maximum wind power output that can beextracted is

Pwmax =16

27AR

ρ

2v31 =

16

27KE1 =

16

27Po (4)

when v2 = (2/3)v1 and v3 = v1/3 (Betz Law).Note: you can readily derive this result if you know calculus.Power coefficient:

cp = Pw/Po (5)


Aerodynamics of Wind Turbine Blades

An airfoil

velocity

1v

leading edge trailing edgelower surface

upper surface

chord line

Chord line: a straight line connecting the leading edge to the trailingedge.Camber line: a line connecting the leading edge to the trailing edgebisecting the area of an airfoilAirfoils normally have a larger upper part (away from hub) than thelower part.


Lift and Drag on an Airfoil

wind velocityv

increased , decreased v p

symmetrical airfoil, balanced flow

wind velocityv

center of gravity

, u uv p

, v p

lift

drag

> , < lift >0 and upu uv v p p

angle of attack !

lift is perpendicular to wind velocity

drag is parallel to wind velocity


Pitch angle of a wind turbine blade

Constant wind speed across the turbine blade

1v

lift

!

tv

rv

1v

lift

!

tv

rv

1v

lift

!

tv

rv

close to hub middle tip

1 wind velocityv

blade velocitytv

relative velocityrv

blade pitch angle!

Note that the blade speed vt varies with the radius r; as a result, thepitch angle θ has to vary with the radius r, to keep the angle of attackα at optimal (about 6◦). (Same principle as propeller blades)


Wind Turbine Efficiency

Tip speed to wind velocity ratio λ = ωR/v1c©J. H. Chow (RPI-ECSE) Wind Turbines September 22, 2014 10 / 35

WT Control Systems

Yaw control - ring gears are used to steer the hub so that therotation of the WT blades are perpendicular to the wind direction(in power system analysis, assume WT is optimally pointed)

Pitch angle control - motors are used to turn the blades to changethe pitch angle so as to control the mechanical power capturedfrom the wind (pitch angle = 0 means maximum wind energycapture)

Power electronics control of electrical power generation

WT Operation

Cut-in speed - about 3-5 m/s wind velocity

Rated speed - is when rated power is produced, about 11.5 to 15m/s

Cut-out speed - stop (feather) for safety, about 25 m/s


Nacelle of a Wind Turbine

GE/Tacke 1.5 MW turbine


Wind Turbine Operationconstant rotor speed vs variable rotor speed


Types of Wind Turbine Generators

Four basic topologies based on grid interface:

Type 1 - conventional induction generator

Type 2 - wound-rotor induction generator with variable rotorresistance

Type 3 - doubly-fed induction generator (DFIG) or doubly-fedasynchronous generator (DFAG)

Type 4 - full converter interface

This lecture will be on the modeling and control of Type-3 WTG.


Wind Turbine Types


GE DFAG WTG Schematics


WTG Dynamic Models


Rotor Model

One-mass model - The rotor and generator combined into a singlemass:

2(Hr +Hg)ω̇gen = −Dωgen + (Tmech − Telec) (6)

where Hr and Hg are the rotor and generator inertia constants,respectively, ωgen is the rotor velocity, Tmech is the mechanical torquederived from the wind, and Pelec = Telecω is the electrical powersupplied to the grid.

Two-mass model - The rotor and generator modeled as separatemasses: see the following pageThis model allows the study of the torsional forces on the shaft betweenthe rotor and the gear. The torsional mode is typically about 2 Hz.


Two-Mass Rotor Model


GE WTG Mechanical Model Parameters


Converter Control Block Diagram


Turbine Control Model Block Diagram: Active Power Control


Turbine Pitch Control

Purpose: control the pitch angle θ to generate the desired mechanicalpower and keep the rotor speed ω at a constant value with steady wind.

1 If the wind speed is less than the rated speed, then θ is set to 0deg (the minimum angle) to capture the maximum amount ofpower from the wind. Thus this control circuit is not active.

2 This control circuit is active when the wind speed is above ratedand/or when WT is operating at a de-rated (de-loaded) condition.

Notations:

Wind power model consists of the curves shown in Fig 5-5.

Rotor model is shown in Fig 4-10. ω is the wind turbine rotorspeed (different from the system nominal freq. at 60 Hz).

pinp is the (pre-delayed) Pelec.

pstl is the desired power output of the WTG (power setpoint(Pord))


Control Functions

There are 3 PI (proportional-integral) controllers with anti-winduplimits:

1 Pitch control - provides direct pitch angle adjustment to correctthe rotor speed error ωerr

2 Torque control - uses the rotor speed error ωerr to drive pinp to bepstl (Pord)) in steady state

3 Pitch compensation - moves the pitch angle so that in steadystate, Perr = pinp - pstl = 0

Steady-state analysis: The three integrators will force ωerr = 0 andPerr = 0. Thus the integrator in the torque control will be equal to pstl(desired power), and the integrators in the pitch control and pitchcompensator will sum to the pitch angle command θcmd.


WindINERTIA Model

The power electronics interface of Type-3 and Type-4 WTGisolates the inertias of the WTG from the power grid. As a result,the power output of the WTG is not impacted by freq. deviation.The wind inertia emulation control is to provide some frequencyresponsiveness of the WTG.The control is a “rate” control, i.e., it is a temporary action thatgoes away in steady state. As a result, it can be fed directly toPord without going through the pitch control or compensation.


WindINERTIA ModelTime response of wind inertia model

Note that in steady state, the output electrical power falls back to itsinitial value.J. Aho, A. Buckspan, J. Laks, P. Fleming, Y. Jeong, F. Dunne, M.Churchfield, L. Pao, and K. Johnson, “A tutorial of wind turbinecontrol for supporting grid frequency through active power control,” inAmerican Control Conference (ACC), 2012, pp. 3120-3131.c©J. H. Chow (RPI-ECSE) Wind Turbines September 22, 2014 26 / 35

Reactive Power Control Models

Two control modes:

1 Terminal bus voltage control2 Constant power factor control


Reactive Power Control Models

Hybrid control mode: perform terminal bus voltage control, untilreactive power generation constraints are encountered; if so, performconstant power factor control


Electrical Control Model

1 Use Pord and Qcmd to determine voltages and currents to interfacewith the AC grid

2 A DFAG is modeled as a constant current source (negative load) inparallel with a shunt reactance, implying that the network solutionin a simulation program will be iterative (nonconforming load)


Five-Bus Test System

1 An aggregate wind turbine model (to represent a wind farm)supplying power to an infinite bus

2 Steady state: wind at 14 m/s, pitch angle at about 10 deg togenerate 160 MW


Disturbance response

1 Active power control subject to wind gust: Sinusoidal windvariation for one cycle, going from 14 m/s down to 10 m/s andback up to 14 m/s

2 Reactive power control subject to short-circuit fault: Short circuitfault for 100 ms, no change in wind speed. What causes theoscillations?


Low-Voltage Ride Through and Zero-Voltage Ride

ThroughWTG should stay on line under low-voltage and zero-voltageconditions. The following sample specification says that the WTGshould stay online if the terminal bus voltage stays within atime-dependent envelop.


Low Voltage Power LogicUnder low-voltage conditions, the ability of the WTG to deliver activepower is limited. Thus a LVRT control block is designed to reduce theactive power during such circumstances.


curent course windturbines

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