The document describes a Blade Element Momentum (BEM) model and battery charging generator model developed in Matlab to estimate electricity production and blade/tower loads for Hugh Piggott wind turbine designs. The model consists of a BEM code that uses turbine geometry and airfoil data to predict shaft power and blade loads, and a generator model that balances blade power with generator output. Test results show the model accurately estimates performance for one turbine design but less accurately for another, identifying areas for improvement. The open-source code and a future web interface are intended to help turbine designers evaluate and optimize their designs.

1. 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

2. Scope
A 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 model
And comparison to measurements
The code is open for any one to use!
Also, a web page is being written, for allowing non octave
sav vy individuals to use this code, for designing and
reviewing their Hugh Piggott turbines
The model is made of t wo parts:
BEM - Blade Element Momentum
Battery charging PMG model

3. Part 1
Code algorithm
Blade power
Geometry and thrust
at several coefficients
point along Chord t wist profile
the radius
Wind speed
RPM range
π RPM ·R
TSR = Tip Speed Ratio: TSR =
60 V

4. Part 2
Code algorithm
Blade power
and thrust
coefficients
+
Generator,
Battery & system
parameters

5. Test subject:
WindAids’ 4
meter design
Are we using the best
generator for these blades?
How much will we gain by
modifying it?

6. Part 1
BEM theory

7. BEM theory
Using conser vation of momentum/energy/
mass on annular rings of flow volume through
the blades
Using 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
π RPM ·R
through TSR = 60 V ,where R is the blade
radius and V is the wind speed )

8. BEM input 1:
Blade geometry

9. NACA 4412
BEM input 2:
airfoil properties

10. NACA4412 Re = 250K-750K
BEM input 2:
airfoil properties

11. BEM output: force
distribution at each TSR

12. BEM output: Power
coefficients vs. TSR

13. Part 2
Estimating the Power Curve
Balance of power -
Blade shaft power =
generator shaft power
All that’s missing is -
a model for the generator
shaft power vs. RPM, and
generator electrical power
vs. RPM

14. Generator model
Axial flux Permanent Magnet Generator charging a battery
Rwire ΔVBR
I
RPMG
rBatt
Vd
VPMG VBatt

15. Generator model
Axial flux Permanent Magnet Generator charging a battery
Rwire ΔVBR I
KPMG - Voltage constant RPMG
rBatt
Vd
RPMG - stator resistance VPMG VBatt
model parameters can be VPMG = K PMG ·RPM
calculated based on Hugh 120 ⎡ RPM ⎤
K PMG =
Piggott’s model (from windpower workshop) 50 ⎢ volt ⎥
⎣ ⎦
Assuming 2 phases active
Or measured from the PMG

16. Generator model
Axial flux Permanent Magnet Generator charging a battery
Equations: Rwire ΔVBR I
K PMG RPM − Vbatt − ΔVBR RPMG
I= Vd
rBatt
RPMG + Rwire + rbatt VPMG VBatt
Vd = K PMG RPM − I(RPMG + Rwire ) − ΔVBR
Pbatt = Vd ·I
PShaft = K PMG RPM ·I
Where Vd was capped according
to controller limitation (31V Sources:
for a 24V machine)
1 - Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science 6.685 Electric Machines
Class Notes 6: DC (Commutator) and Permanent Magnet Machines
2005 James L. Kirtley Jr.
2 - J. R. Bumby, N. Stannard and R. Martin
A Permanent Magnet Generator for Small Scale Wind Turbines

17. ΔVBR
PMG
Rwire I
RPMG
rBatt
Vd
VPMG VBatt
Permanent Magnet Generator
The generator model output Example of real PMG numbers
Missing: KPMG reduction and RPMG increase at high currents

18. Estimating the power cur ve - WA4
Putting it together
Comparison to measurements is good (but not enough measurements)

19. Estimating the power curve - Piggott 3 m
Comparison to measurements is not very good - Section data from NACA 44XX
measurements , resulting in a wrong Cp vs TSR curve

20. Concluding remarks
Model 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

21. Concluding remarks
Needs improvement
Many possible measurement
errors
Amp/volt measurement
wind measurement
Many possible modeling errors
Generator/Battery/wire
resistance
Blade profile properties
for wooden blades

22. 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!