Piggott turbine modeling

Estimation of electricity production and blade/tower loads for Hugh Piggott designs, using BEM theory and simple PMG-battery charging model

Hanan Einav Levy

ScopeA BEM code with a battery charging generator model was written in matlab (also runs on the open source octave)This presentation shows the basics of the modelAnd comparison to measurementsThe code is open for any one to use!Also, a web page is being written, for allowing non octave savvy individuals to use this code, for designing and reviewing their Hugh Piggott turbinesThe model is made of two parts:

BEM - Blade Element MomentumBattery charging PMG model

Code algorithmGeometry

Chord twist profileat several point along the radius

Wind speed

RPM range

Blade power and thrust

coefficients

TSR = π60

RPM ·RVTSR = Tip Speed Ratio:

Part 1

Code algorithmBlade power and thrust

coefficients

Generator, Battery & system

parameters

+

Part 2

Test subject: WindAids’ 4 meter design

Are we using the best generator for these blades?How much will we gain by

modifying it?

BEM theoryPart 1

BEM theoryUsing conservation of momentum/energy/mass on annular rings of flow volume through the bladesUsing 2D blade section data - from measurements, or simulations (xfoil,JavaFoil )Results: prediction of Shaft power, and blade loads for every blade RPM and windspeed (usually - the combination of both through ,where R is the blade radius and V is the wind speed )

TSR = π60

RPM ·RV

BEM input 1: Blade geometry

BEM input 2: airfoil properties

NACA 4412

BEM input 2: airfoil properties

NACA4412 Re = 250K-750K

BEM output: force distribution at each TSR

BEM output: Power coefficients vs. TSR

Estimating the Power CurveBalance of power - Blade shaft power = generator shaft powerAll that’s missing is - a model for the generator shaft power vs. RPM, and generator electrical power vs. RPM

Part 2

Generator modelAxial flux Permanent Magnet Generator charging a battery

VPMG

RPMG

Rwire ΔVBR

VBatt

rBatt

I

Vd

KPMG - Voltage constantRPMG - stator resistance model parameters can be calculated based on Hugh Piggott’s model (from windpower workshop) Assuming 2 phases activeOr measured from the PMG

VPMG = KPMG ·RPM

KPMG = 12050

RPMvolt

⎡⎣⎢

⎤⎦⎥

VPMG

RPMG

Rwire ΔVBR

VBatt

rBatt

I

Vd

Generator modelAxial flux Permanent Magnet Generator charging a battery

Equations:

Where Vd was capped according to controller limitation (31V for a 24V machine)

I = KPMGRPM −Vbatt − ΔVBRRPMG + Rwire + rbatt

Vd = KPMGRPM − I(RPMG + Rwire )− ΔVBRPbatt =Vd ·IPShaft = KPMGRPM ·I

Sources:1 - Massachusetts Institute of TechnologyDepartment of Electrical Engineering and Computer Science 6.685 Electric MachinesClass Notes 6: DC (Commutator) and Permanent Magnet Machines2005 James L. Kirtley Jr.

2 - J. R. Bumby, N. Stannard and R. MartinA Permanent Magnet Generator for Small Scale Wind Turbines

VPMG

RPMG

Rwire ΔVBR

VBatt

rBatt

I

Vd

Generator modelAxial flux Permanent Magnet Generator charging a battery

PMGPermanent Magnet GeneratorVPMG

RPMG

Rwire ΔVBR

VBatt

rBatt

I

Vd

The generator model output Example of real PMG numbers

Missing: KPMG reduction and RPMG increase at high currents

Estimating the power curve - WA4Putting it together

Comparison to measurements is good (but not enough measurements)

Estimating the power curve - Piggott 3 mComparison to measurements is not very good - Section data from NACA 44XX

measurements , resulting in a wrong Cp vs TSR curve

Concluding remarksModel is sufficiently accurate

Can help decide if generator winding need changing

Quantify how to change best wind speed efficiency of turbine

Or to identify poor blade configuration

Concluding remarksNeeds improvement

Many possible measurement errors

Amp/volt measurement

wind measurement

Many possible modeling errors

Generator/Battery/wire resistance

Blade profile propertiesfor wooden blades

I’m working on a site for this program

At the moment at It’s at http://gs.playstix.net/piggott/

Will include an option to upload your blade geometry & generator parameters, and use the code to predict outputs, calibrate to measurements and see how changes in gen. parameters effect performance etc.

work is at an early stage… probably up and working by the middle of the year

Code is written in Octave, and is open-source - http://gitorious.org/piggott-turbine-design/piggott-turbine-design

That’s me. Wish I was here in Dakar!