Steady State Analysis of Autonomous WindEnergy Conversion System Employing

Induction Machines for Irrigation Purpose

Kanoj B, Arjun MA B Raju and Satish Annigeri

Department of Electrical and Electronics Engineering,B. V. B. College of Engineering and Technology,

HUBLI-580 031, KARNATAKAabraju@bvb.edu

December 29, 2012

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 1/18

Overview

1 Objective of the Presentation2 Block Diagram and Flowchart3 Wind turbine and Induction Machine Specifications4 Equivalent Circuit5 Building Mathematical Model6 Why Python and SciPy?7 SciPy Code for solving nonlinear algebraic equations8 Results9 Conclusion

10 References

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 2/18

Objective of the presentation

To use Scientific Python as a computational toolfor steady state analysis of wind energy

conversion system

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 3/18

Block diagram and flow chart

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 4/18

Wind Turbine and Induction Machine Specifications

Wind turbine specifications:Swept area radius r = 1.27 mcut-in wind speed vc = 3 m/srated wind speed vr = 15 m/sfurl-on wind speed vf = 25 m/sInduction Machine specifications3 Phase, 50 Hz, 4 pole, 5 HP, 1450 rpm, 415 VStator resistance rs = 5.2 ΩRotor Resistance rr = 4.66 ΩStator and rotor reactances xs and xr = 2.46 ΩCore resistance rc = 746.40 Ω

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 5/18

Equivalent Circuit

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 6/18

Building Mathematical Model

Applying Kirchhoff’s voltage law to the loop current Ig theresulting equation is

IgZg = 0Zg = Z1 + Z2 + Z3

Z1 =Zr Zm

Zr + Zm

Zm =F jXmRm

Rm + F jXm

Z2 = Rs + F jXs

Z3 =(Rl + F jXl)jXc

Rl + F jXl + jXc

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 7/18

Substituting Z1, Z2 and Z3, we get

−XlXc + jXlRlF

−FRl + j(Xc − F 2Xl)+

Rs

F+ jXs +

−Xr Xm + jXmRr

F−vRr

F−v + j(Xr + Xm)= 0

Its a complex non-linear algebraic equation and is solvedfor F and Xm by separating real and imaginary parts andequating them to zero separately.

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 8/18

Solving Non Linear Equations

Non linear equations can be solved numerically eitherwriting our own code in compiled languages like:

1 C or C++2 Fortran

or using the readily available routines in interpreterlanguages like:

1 MATLAB2 Scilab and3 Octave4 Python

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 9/18

Why Python and Scipy?

Free and open-source software, widely used, with a vibrantcommunity.It has rich modules/libraries.Well thought out language, allowing to write very readableand well structured code.Capability of handling complex numbers and equations.Possibility of improving performance comparable tocompiled languagesPossibility of developing GUI application.

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 10/18

Why Python and Scipy?

1 SciPy is an Open Source library of scientific tools forPython.

2 It gathers a variety of high level science and engineeringmodules together as a single package.

3 Using numpy, scipy and matplotlib modules, one can thinkof replacing a well known proprietary software.

In this presented work, we have used the followingroutines from scipy.optimize

fsolve()newton krylov() andmatplotlib.pyplot

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 11/18

SciPy Code For Solving Non-Linear Equations

def funct(x):

Xmg = x[1]

F = x[0]

Zl = (Rl/F) + (1j*Xl)

Zc = (-1j*Xc)/(F**2)

Zcc = (Zl * Zc ) /(Zl + Zc)

Zsg = (Rs/F) + (1j*Xs)

Zrg = (Rr/(F-v)) + (1j*Xr)

Zmg = ((F/Rc) + (1/(1j* Xmg)))**(-1)

Zaa = (Zmg * Zrg)/(Zmg + Zrg)

g = Zaa + Zsg + Zcc

out = [real(g)]

out.append(imag(g))

return array(out)

D = fsolve(funct,array([1.0, 1.0]))

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 12/18

Results

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 13/18

Results

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 14/18

Results of Python against Matlab

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 15/18

Conclusion

Python code executes faster than the correspondingMatlab code by a factor of about 7.197474264.Ten iterations of Matlab code using fsolve() took 1.8346 s,whereas Python fsolve() took 0.254894971848 s, andnewton krylov() took 1.17562890053 s.newton krylov() function of python executes faster thanfsolve() by a factor of 4.612209068

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 16/18

L. Shridhar, Bhim Singh, C. S . Jha and B.P. Singh,“Analysis of Self Excited Induction Generator feedingInduction Motor”, Analysis of Self Excited InductionGenerator feeding Induction Motor,pp. p. 390 - 396, June,1994.

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 17/18

THANK YOU

Kanoj B, Arjun M A B Raju and Satish Annigeri SciPy 2012 18/18