Title of Invention	METHOD FOR DESIGNING THE CAPACITOR BANK OF A WIND POWER GENERATOR
Abstract	A method for calculating capacitance value and magnetizing inductance value for an induction generator comprising the steps of representing the induction generator as a dynamic state equivalent circuit; obtaining an equation for terminal voltage from the above equivalent circuit for a stationary reference frame by setting co = 0; obtaining a 6th order polynomial from the above terminal voltage Equation in complex variable form V; generating the real part and imaginary part tif the 6th order polynomial by replacing the complex variable "s" in the 6th order polynomial as jco and substituting the value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - oo]; setting the real and imaginary parts of the above equation to zero and obtaining equations for C and Lm; solving the equations Obtained in the above step simultaneously and obtaining all the solutions for C and Lm; and extracting the capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for smooth sustained voltage build up in an induction generator.

Title of Invention

METHOD FOR DESIGNING THE CAPACITOR BANK OF A WIND POWER GENERATOR

Abstract

A method for calculating capacitance value and magnetizing inductance value for an induction generator comprising the steps of representing the induction generator as a dynamic state equivalent circuit; obtaining an equation for terminal voltage from the above equivalent circuit for a stationary reference frame by setting co = 0; obtaining a 6th order polynomial from the above terminal voltage Equation in complex variable form V; generating the real part and imaginary part tif the 6th order polynomial by replacing the complex variable "s" in the 6th order polynomial as jco and substituting the value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - oo]; setting the real and imaginary parts of the above equation to zero and obtaining equations for C and Lm; solving the equations Obtained in the above step simultaneously and obtaining all the solutions for C and Lm; and extracting the capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for smooth sustained voltage build up in an induction generator.

Full Text	FORM 2 THE PATENTS ACT, 1970 (39 Of 1970) As amended by the Patents (Amendment) Act, 2005 & The Patents Rules, 2003 As amended by the Patents (Amendment) Rules, 2006 COMPLETE SPECIFICATION (See section 10 and rule 13) TITLE OF THE INVENTION Method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator APPLICANTS Indian Institute of Technology, Bombay, Powai, Mumbai 400076, Maharashtra, India, an autonomous research and educational institution established in India by a special Act of the Parliament of the Republic of India under the Institutes of Technology Act 1961 INVENTORS Agarwal Vivek of Electrical Engineering and Paluri Satya Vydeeswara Nataraj and Rajesh Kumar Thakur both of System & Control Engineering, IDP; all of IIT Bombay, Powai, Mumbai 400 076, Maharashtra, India and all Indian nationals PREAMBLE TO THE DESCRIPTION the following specifications particularly describe the nature of this invention and the method in which it is to be performed: FIELD OF THE INVENTION This invention relates to a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator. This invention particularly relates to a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator of a wind power generation system. The magnetizing inductance value calculated according to the invention is that for the saturated region of the induction generator. BACKGROUND OF THE INVENTION A wind power generation system generates electricity from wind energy and comprises an induction generator coupled to a wind turbine or windmill through a gear box and a control system. In a wind power generation system, the mechanical energy of the wind turbine is converted into electrical energy by the induction generator. In order to convert the wind energy into electrical energy efficiently, it is important that the induction generator operates smoothly. For smooth operation of the induction generator it is essential that the voltage generated in the stator windings is sustained and is without transients. If the voltage generated in the stator windings of the generator is not sustained and smooth, there will be vibrations in the wind turbine leading to wear and tear of the wind turbine thereby reducing its life. In order to initiate voltage generation by the induction generator (self excitation), a leading reactive power is provided to the stator windings of the generator by connecting a capacitor bank to the stator windings. It is essential that the capacitance value of the capacitor bank is such that at a given rotor speed, voltage generated in the stator windings is without large transients. Therefore, calculation of the capacitance value of the capacitor bank is very critical for the desired operation of the induction generator. It is known that the induction generator operates in the saturated region during the self-excitation [D. Seyoum, C. Grantham and F. Rahman, "The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine" IEEE Trans. Industry Applications, vol. 39, no. 4, Jul/Aug 2003, pp. 936-944]. It is also known that the maximum value of magnetizing inductance (Lmax) in the saturated region leads to sustained voltage generation in the stator windings [D. Seyoum, C. Grantham, and F. Rahman, "The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine" IEEE Trans. Industry Applications, vol. 39, no. 4, Jul/Aug 2003, pp. 936-944, and Thakur RK and Agarwal V, " Effect of excitation capacitance value on the transient behaviour of induction generator in wind energy conversion system", National Power Electronics Conference, Bangalore, Dec 2007]. Therefore, in order to accurately calculate the capacitance value it is essential to know the maximum value of the magnetizing inductance in the saturated region. But this value is not known and available. However, it is known that the magnetizing inductance value in the saturated region lies between zero and Lmax value in the unsaturated region [C. Grantham, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc, B, 136, (2) pp. 61-68, 1989]. It is possible to obtain the Lmax value in the unsaturated region experimentally [C. Grantham, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68, 1989]. For accurate calculation of the capacitance value it is necessary to take into consideration the magnetizing inductance value for the saturated region both in the steady state and dynamic state operating conditions of the induction generator. Per phase equivalent impedance method is used for the calculation of the capacitance value of the capacitor bank of an induction generator [T. Ahmed, 0. Noro, K. Matsuo, Y. Shindo and M. Nakaoka, "Minimum excitation capacitance requirements for wind turbine coupled stand-alone self-excited induction generator with voltage regulation based on SVC", IEICE/IEEE INTELEC03, Oct. 19-23, 2003 and A.M. Eltamaly, "New formula to determine the minimum capacitance required for self-excited induction generator", Power Electronics Specialists Conference, vol. 1, pp. 106 - 110, 23-27 June, 2002] . In this method the induction generator is represented as a steady state equivalent circuit as illustrated below: Vg = Air gap Voltage (Volt) Xir,Xls.X = Per phase terminal excitation capacitive impedance (H) Xs, Xr, X = Per phase stator, rotor (referred to stator) and load inductive impedance (H) Rs, Rr, R = Per phase stator, rotor (referred to stator) and load resistance (Q) F = Frequency (Hz) v = Speed The loop equation for the current (I) in the above circuit is as follows: where Z is the net loop impedance. The steady state equivalent circuit is obtained from the steady state operating condition of the induction generator. The capacitance value (Xc) in equation 1 is calculated by substituting Lm in equation 1 with the Lmax value for the unsaurated region and using iterative methodologies such as Newton- Raphson method. Since equation 1 is obtained from the steady state operating condition of the induction generator and since tne value of Lm used is the Lmax value for the unsaturated region the capacitance value obtained is not accurate. D-q model based eigenvalue sensitivity method is also used for the calculation of the capacitance value of the capacitor bank [Li Wang and Ching-Huei Lee, "A novel analysis on the performance of an isolated self-excited induction gnerator", IEEE Trans. Energy Conversion, 12, (2), pp. 109-117, June 1997, C. Grantam, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68, 1989, and D. Seyoum, C. Grantham, and F. Rahman, "The dynamics of an isolated self-excited induction generator driven by a wind turbine" The 27th Annual Conference of the IEEE Industrial Electronics Society, Vol. 2, pp. 1364-1369, Dec. 2001]. In this method the induction generator is represented as a dynamic state equivalent circuit as illustrated below: (b) Per phase stator and rotor (referred to stator) resistance (H) Per phase stator and rotor (referred to stator) inductance (H) Rotor quadrature and direct axis voltage (Volt) Stator quadrature and direct axis voltage (volt) Stator quadrature and direct axis currents (Amp) Rotor quadrature and direct axis currents (Amp) Per phase magnetizing inductance (referred to stator) (H) Per phase capacitance (F) The terminal voltage equation obtained from the above circuits is as follows: The capacitance value C is calculated from equation 2 by substituting Lm in equation 2 with the Lmax value for the unsaturated region and using iterative methodologies like Gauss-Siedel method. The equivalent circuit is obtained from the dynamic state of operation of the induction generator. This method is comparatively more accurate as it takes into account the dynamic state of operation of the induction generator. However, this method is also not very accurate and reliable as it makes use of the value of Lmax for the unsaturated region. The above methods do not give the Lmax value for the saturated region. This value would have been useful to calculate the electrical torque and power output of the induction generator theoretically. The Lmax value could have been used to design the induction generator for optimal performance. OBJECTS OF THE INVENTION An object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator, which method results in accurate calculation of capacitance value for generation of smooth sustained voltage in the stator windings of the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method results in the maximum value of magnetizing inductance for the saturated region of operation of the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method results in increased life of the components/systems connected to the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method is simple and easy to carry out. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in the induction generator of a wind power generation system, which method results in accurate calculation of capacitance value for generation of smooth sustained voltage in the stator windings of the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method results in the maximum value of magnetizing inductance for the saturated region of operation of the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method results in increased life of the wind turbine connected to the induction generator. Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method is simple and easy to carry out. DETAILED DESCRIPTION OF THE INVENTION The following is a detailed description of the invention with reference to the accompanying drawings, in which: Fig 1 is a computer simulated waveform of the voltage generated in the stator windings of an induction' generator when the rndcctroir generator was operated using the capacitance value calculated using the D-q method; and Fig 2 is a computer simulated waveform of the voltage generated in the stator windings of an induction generator when the induction generator was operated using the capacitance value calculated using the method of the invention. According to the method of the invention the induction generator is represented as a dynamic state equivalent circuit as illustrated below: Per phase stator and rotor (referred to stator) resistance (Q) Per phase stator and rotor (referred to stator) inductance (H) Rotor quadrature and direct axis voltage (Volt) Stator quadrature and direct axis voltage (volt) Stator quadrature and direct axis currents (Amp) Rotor quadrature and direct axis currents (Amp) Per phase magnetizing inductance (referred to stator) (H) Per phase capacitance (F) The terminal voltage equation is obtained from the above equivalent circuits for a stationary reference frame by setting ω=0. The terminal voltage equation obtained is as follows: (3) -th A 6 order polynomial is obtained from the terminal voltage equation at (3) in complex variable form 's 'by using Laplace transform and taking the determinant of the matrix. :th The 6 order polynomial is obtained as follows: Laplace transform of equation (3) in complex variable form "s" results in (4) (5) and (6) The characteristic polynomial of the terminal voltage equation (4) is obtained by taking the determinant of the matrix A in equation (6). rth The 6 order polynomial obtained is as follows: The real part and imaginary part of the 6th order polynomial is generated by replacing the complex variable 's' in the 6th order polynomial as jco and substituting the value of Lm as [0 -Lmax value in the unsaturated region] and value of C as [0 - ω]. The real part and imaginary part are generated as follows: (9) The real part on the RHS in equation (9) is as follows : (10) The imaginary part on the RHS in equation (9) is as follows : (11) The Lmax value in the unsaturated region is obtained experimentally for a particular rotor speed of the induction generator [C. Grantham, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68, 1989]. The real and imaginary parts are set to zero and a pair of equations is obtained for C and Lm. The equations for C and Lm are as follows: The above equations are solved simultaneously using interval analysis method to obtain all the solutions for C and Lm. The capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region is extracted from the solutions obtained for C and Lm for smooth sustained voltage build up in an induction generator . The following example is illustrative of the invention but not limitative of the scope thereof. Example 1 A. Using the d-q based eigenvalue sensitivity method, the capacitance value was calculated for a three phase induction generator of the following specification: V= 220V I=4.8A f=60Hz Rotor Speed= 377 rad/sec The Lmax value in the unsaturated region was obtained experimentally and was found to be 0.28H. Lm in the terminal voltage equation (2) was substituted by this value of Lmax. Eigenvalue sensitivity method was used to calculate the value of capacitance. The capacitance value obtained was 84.97 uF. When the above induction generator was operated using the calculated capacitance value, the voltage generated in the stator windings is as seen in Fig 1. The waveform portion comprising the transients is marked as A. B. The capacitance for the same induction generator for the same rotor speed was calculated using the method of the invention. The capacitance value obtained was 34 uF and the corresponding value of magnetizing inductance for the saturated region obtained was 0.23 H. When the above induction generator was operated using the calculated capacitance value, the voltage generated in the stator windings is as seen in Fig 2. The waveform portion comprising the transients is marked as B. It is very clear from the above comparative example that when the induction generator is operated using the capacitance value calculated using the method of the invention the transients generated in the stator windings are of reduced amplitude. This results in reduced vibrations of the systems/components such as a wind turbine connected to the induction generator thereby leading to increased life of such systems/components. It is very evident from the above example that the method of the invention is simple and easy to carry out. The method of the invention results in the value of Lmax for the saturated region which can be used to calculate the electrical torque and power output of the induction generator theoretically. The method of the invention can, therefore, be used to design the induction generator for optimal performance. We claim: 1. A method for calculating capacitance value and magnetizing inductance value for an induction generator comprising the steps of: a. representing the induction generator as a dynamic state equivalent circuit; b. obtaining an equation for terminal voltage from the above equivalent circuit for a stationary reference frame by setting ω = 0; c. obtaining a 6th order polynomial from the above terminal voltage equation in complex variable form 's'; d. generating the real part and imaginary part of the 6th order polynomial by replacing the complex variable 's' in the 6th order polynomial as joy and substituting the value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - 00]; e. setting the real and imaginary parts of the above equation to zero and obtaining equations for C and Lm; f. solving the equations obtained in the above step simultaneously and obtaining all the solutions for C and Lm; g. extracting the capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for smooth sustained voltage build up in an induction generator. 2. A method as claimed in claim 1, wherein the 6l order polynomial is obtained using laplace transform and taking the determinant of the matrix of terminal voltage equation. 3. A method as claimed in claim 1, wherein the Lmax value in the unsaturated region is calculated experimentally. 4. A method as claimed in claim 1, wherein the equations obtained for C and Lm are solved simultaneously using interval analysis method. 5. A method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system comprising the steps of: a. representing the induction generator as a dynamic mathematical model; b. obtaining an equation for terminal voltage from the above mathematical model at ω = 0; c. obtaining a 6th order polynomial from the above terminal voltage equation in complex variable form 's'; d. generating the real part and imaginary part of the 6th order polynomial by replacing the complex variable 's' in the 6th order polynomial as jco and substituting the value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - ω]; e. setting the real and imaginary parts of the above equation to zero and obtaining equations for C and Lm; f. solving the equations obtained in the above step simultaneously and obtaining all the solutions for C and Lm; g. extracting the capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for smooth sustained voltage build up in an induction generator. 6. A method as claimed in claim 5, wherein the 6th order polynomial is obtained using laplace transform and taking the determinant of the terminal voltage equation. 7. A method as claimed in claim 5, wherein the Lmax value in the unsaturated region is calculated experimentally. 8. A method as claimed in claim 5, wherein the equations obtained for C and Lm are solved simultaneously using interval analysis method. Dated this 23rd day of October 2008 (Prita Madan) Of Khaitan & Co Agent for the Applicants

Full Text

FORM 2
THE PATENTS ACT, 1970 (39 Of 1970)
As amended by the Patents (Amendment) Act, 2005
&
The Patents Rules, 2003
As amended by the Patents (Amendment) Rules, 2006
COMPLETE SPECIFICATION (See section 10 and rule 13)
TITLE OF THE INVENTION
Method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator
APPLICANTS
Indian Institute of Technology, Bombay, Powai, Mumbai 400076, Maharashtra, India, an autonomous research and educational institution established in India by a special Act of the Parliament of the Republic of India under the Institutes of Technology Act 1961
INVENTORS
Agarwal Vivek of Electrical Engineering and Paluri Satya Vydeeswara Nataraj and Rajesh
Kumar Thakur both of System & Control Engineering, IDP; all of IIT Bombay, Powai, Mumbai 400 076, Maharashtra, India and all Indian nationals
PREAMBLE TO THE DESCRIPTION
the following specifications particularly describe the nature of this invention and the method in which it is to be performed:

FIELD OF THE INVENTION
This invention relates to a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator.
This invention particularly relates to a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator of a wind power generation system.
The magnetizing inductance value calculated according to the invention is that for the saturated region of the induction generator.
BACKGROUND OF THE INVENTION
A wind power generation system generates electricity from wind energy and comprises an induction generator coupled to a wind turbine or windmill through a gear box and a control system. In a wind power generation system, the mechanical energy of the wind turbine is converted into electrical energy by the induction generator. In order to convert the wind energy into electrical energy efficiently, it is important that the induction generator operates smoothly. For smooth operation of the induction generator it is essential that the voltage generated in the stator windings is sustained and is without transients. If the voltage generated in the stator windings of the generator is not sustained and smooth, there will be vibrations in the wind turbine leading to wear and tear of the wind turbine thereby reducing its life. In order to initiate voltage generation by the induction generator (self excitation), a leading reactive power is provided to the stator windings of the generator by connecting a capacitor bank to the stator windings. It is essential that the capacitance value of the capacitor bank is such that at a given rotor speed, voltage generated in the stator windings is

without large transients. Therefore, calculation of the capacitance value of the capacitor bank is very critical for the desired operation of the induction generator. It is known that the induction generator operates in the saturated region during the self-excitation [D. Seyoum, C. Grantham and F. Rahman, "The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine" IEEE Trans. Industry Applications, vol. 39, no. 4, Jul/Aug 2003, pp. 936-944]. It is also known that the maximum value of magnetizing inductance (Lmax) in the saturated region leads to sustained voltage generation in the stator windings [D. Seyoum, C. Grantham, and F. Rahman, "The dynamic characteristics of an isolated self-excited induction generator driven by a wind turbine" IEEE Trans. Industry Applications, vol. 39, no. 4, Jul/Aug 2003, pp. 936-944, and Thakur RK and Agarwal V, " Effect of excitation capacitance value on the transient behaviour of induction generator in wind energy conversion system", National Power Electronics Conference, Bangalore, Dec 2007]. Therefore, in order to accurately calculate the capacitance value it is essential to know the maximum value of the magnetizing inductance in the saturated region. But this value is not known and available. However, it is known that the magnetizing inductance value in the saturated region lies between zero and Lmax value in the unsaturated region [C. Grantham, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc, B, 136, (2) pp. 61-68, 1989]. It is possible to obtain the Lmax value in the unsaturated region experimentally [C. Grantham, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68, 1989]. For accurate calculation of the capacitance value it is necessary to take into consideration the magnetizing inductance value for the saturated region both in the steady state and dynamic state operating conditions of the induction generator.

Per phase equivalent impedance method is used for the calculation of the capacitance value of the capacitor bank of an induction generator [T. Ahmed, 0. Noro, K. Matsuo, Y. Shindo and M. Nakaoka, "Minimum excitation capacitance requirements for wind turbine coupled stand-alone self-excited induction generator with voltage regulation based on SVC", IEICE/IEEE INTELEC03, Oct. 19-23, 2003 and A.M. Eltamaly, "New formula to determine the minimum capacitance required for self-excited induction generator", Power Electronics Specialists Conference, vol. 1, pp. 106 - 110, 23-27 June, 2002] . In this method the induction generator is represented as a steady state equivalent circuit as illustrated below:

Vg = Air gap Voltage (Volt)
Xir,Xls.X = Per phase terminal excitation capacitive impedance (H)
Xs, Xr, X = Per phase stator, rotor (referred to stator) and load inductive impedance (H)
Rs, Rr, R = Per phase stator, rotor (referred to stator) and load resistance (Q)
F = Frequency (Hz)
v = Speed
The loop equation for the current (I) in the above circuit is as follows:

where Z is the net loop impedance.
The steady state equivalent circuit is obtained from the steady state operating condition of the induction generator. The capacitance value (Xc) in equation 1 is calculated by substituting Lm in equation 1 with the Lmax value for the unsaurated region and using iterative methodologies such as Newton- Raphson method. Since equation 1 is obtained from the steady state operating condition of the induction generator and since tne value of Lm used is the Lmax value for the unsaturated region the capacitance value obtained is not accurate.
D-q model based eigenvalue sensitivity method is also used for the calculation of the capacitance value of the capacitor bank [Li Wang and Ching-Huei Lee, "A novel analysis on the performance of an isolated self-excited induction gnerator", IEEE Trans. Energy Conversion, 12, (2), pp. 109-117, June 1997, C. Grantam, D. Sutanto and B Mismail, "Steady state and transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68, 1989, and D. Seyoum, C. Grantham, and F. Rahman, "The dynamics of an isolated self-excited induction generator driven by a wind turbine" The 27th Annual Conference of the IEEE Industrial Electronics Society, Vol. 2, pp. 1364-1369, Dec. 2001]. In this method the induction generator is represented as a dynamic state equivalent circuit as illustrated below:

(b)

Per phase stator and rotor (referred to stator) resistance (H)
Per phase stator and rotor (referred to stator) inductance (H)
Rotor quadrature and direct axis voltage (Volt)
Stator quadrature and direct axis voltage (volt)
Stator quadrature and direct axis currents (Amp)
Rotor quadrature and direct axis currents (Amp)
Per phase magnetizing inductance (referred to stator) (H)
Per phase capacitance (F)

The terminal voltage equation obtained from the above circuits is as follows:

The capacitance value C is calculated from equation 2 by substituting Lm in equation 2 with the Lmax value for the unsaturated region and using iterative methodologies like Gauss-Siedel method.
The equivalent circuit is obtained from the dynamic state of operation of the induction generator.
This method is comparatively more accurate as it takes into account the dynamic state of operation of the induction generator. However, this method is also not very accurate and reliable as it makes use of the value of Lmax for the unsaturated region.
The above methods do not give the Lmax value for the saturated region. This value would have been useful to calculate the electrical torque and power output of the induction generator theoretically. The Lmax value could have been used to design the induction generator for optimal performance.
OBJECTS OF THE INVENTION
An object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in an induction generator, which method results in accurate calculation of capacitance value for generation of smooth sustained voltage in the stator windings of the induction generator.
Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method results in the maximum value of magnetizing inductance for the saturated region of operation of the induction generator.

Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method results in increased life of the components/systems connected to the induction generator.
Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value, which method is simple and easy to carry out.
Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for smooth sustained voltage build up in the induction generator of a wind power generation system, which method results in accurate calculation of capacitance value for generation of smooth sustained voltage in the stator windings of the induction generator.
Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method results in the maximum value of magnetizing inductance for the saturated region of operation of the induction generator.
Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method results in increased life of the wind turbine connected to the induction generator.

Another object of the invention is to provide a method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system, which method is simple and easy to carry out.
DETAILED DESCRIPTION OF THE INVENTION
The following is a detailed description of the invention with reference to the accompanying drawings, in which:
Fig 1 is a computer simulated waveform of the voltage generated in the stator windings of an induction' generator when the rndcctroir generator was operated using the capacitance value calculated using the D-q method; and
Fig 2 is a computer simulated waveform of the voltage generated in the stator windings of an induction generator when the induction generator was operated using the capacitance value calculated using the method of the invention.
According to the method of the invention the induction generator is represented as a dynamic state equivalent circuit as illustrated below:

Per phase stator and rotor (referred to stator) resistance (Q)
Per phase stator and rotor (referred to stator) inductance (H)
Rotor quadrature and direct axis voltage (Volt)
Stator quadrature and direct axis voltage (volt)
Stator quadrature and direct axis currents (Amp)
Rotor quadrature and direct axis currents (Amp)
Per phase magnetizing inductance (referred to stator) (H)
Per phase capacitance (F)

The terminal voltage equation is obtained from the above equivalent circuits for a stationary reference frame by setting ω=0. The terminal voltage equation obtained is as follows:

(3)

-th
A 6 order polynomial is obtained from the terminal voltage equation at (3) in complex variable form 's 'by using Laplace transform and taking the determinant of the matrix.

:th
The 6 order polynomial is obtained as follows:

Laplace transform of equation (3) in complex variable form "s" results in

(4)

(5)

and

(6)
The characteristic polynomial of the terminal voltage equation (4) is obtained by taking the determinant of the matrix A in equation (6).

rth
The 6 order polynomial obtained is as follows:

The real part and imaginary part of the 6th order polynomial is generated by replacing the complex variable 's' in the 6th order polynomial as jco and substituting the value of Lm as [0 -Lmax value in the unsaturated region] and value of C as [0 - ω]. The real part and imaginary part are generated as follows:
(9) The real part on the RHS in equation (9) is as follows :

(10)

The imaginary part on the RHS in equation (9) is as follows :
(11)

The Lmax value in the unsaturated region is obtained experimentally for a particular rotor
speed of the induction generator [C. Grantham, D. Sutanto and B Mismail, "Steady state and
transient analysis of self-excited induction generators", IEE proc. B, 136, (2) pp. 61-68,
1989].
The real and imaginary parts are set to zero and a pair of equations is obtained for C and Lm.
The equations for C and Lm are as follows:

The above equations are solved simultaneously using interval analysis method to obtain all the solutions for C and Lm. The capacitance value and corresponding magnetizing inductance (Lmax) value for the saturated region is extracted from the solutions obtained for C and Lm for smooth sustained voltage build up in an induction generator .
The following example is illustrative of the invention but not limitative of the scope thereof.
Example 1
A. Using the d-q based eigenvalue sensitivity method, the capacitance value was calculated for a three phase induction generator of the following specification:
V= 220V
I=4.8A
f=60Hz
Rotor Speed= 377 rad/sec

The Lmax value in the unsaturated region was obtained experimentally and was found to be 0.28H. Lm in the terminal voltage equation (2) was substituted by this value of Lmax. Eigenvalue sensitivity method was used to calculate the value of capacitance. The capacitance value obtained was 84.97 uF.
When the above induction generator was operated using the calculated capacitance value, the voltage generated in the stator windings is as seen in Fig 1. The waveform portion comprising the transients is marked as A.
B. The capacitance for the same induction generator for the same rotor speed was calculated using the method of the invention.
The capacitance value obtained was 34 uF and the corresponding value of magnetizing inductance for the saturated region obtained was 0.23 H.
When the above induction generator was operated using the calculated capacitance value, the voltage generated in the stator windings is as seen in Fig 2. The waveform portion comprising the transients is marked as B.
It is very clear from the above comparative example that when the induction generator is operated using the capacitance value calculated using the method of the invention the transients generated in the stator windings are of reduced amplitude. This results in reduced vibrations of the systems/components such as a wind turbine connected to the induction generator thereby leading to increased life of such systems/components. It is very evident from the above example that the method of the invention is simple and easy to carry out. The

method of the invention results in the value of Lmax for the saturated region which can be used to calculate the electrical torque and power output of the induction generator theoretically. The method of the invention can, therefore, be used to design the induction generator for optimal performance.

We claim:
1. A method for calculating capacitance value and magnetizing inductance value for an induction generator comprising the steps of:
a. representing the induction generator as a dynamic state equivalent circuit;
b. obtaining an equation for terminal voltage from the above equivalent circuit for a
stationary reference frame by setting ω = 0;
c. obtaining a 6th order polynomial from the above terminal voltage equation in
complex variable form 's';
d. generating the real part and imaginary part of the 6th order polynomial by
replacing the complex variable 's' in the 6th order polynomial as joy and substituting the
value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - 00];
e. setting the real and imaginary parts of the above equation to zero and obtaining
equations for C and Lm;
f. solving the equations obtained in the above step simultaneously and obtaining all
the solutions for C and Lm;
g. extracting the capacitance value and corresponding magnetizing inductance (Lmax)
value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for
smooth sustained voltage build up in an induction generator.
2. A method as claimed in claim 1, wherein the 6l order polynomial is obtained using
laplace transform and taking the determinant of the matrix of terminal voltage equation.

3. A method as claimed in claim 1, wherein the Lmax value in the unsaturated region is calculated experimentally.
4. A method as claimed in claim 1, wherein the equations obtained for C and Lm are solved simultaneously using interval analysis method.
5. A method for calculating capacitance value and magnetizing inductance value for the induction generator of a wind power generation system comprising the steps of:
a. representing the induction generator as a dynamic mathematical model;
b. obtaining an equation for terminal voltage from the above mathematical model at
ω = 0;
c. obtaining a 6th order polynomial from the above terminal voltage equation in
complex variable form 's';
d. generating the real part and imaginary part of the 6th order polynomial by
replacing the complex variable 's' in the 6th order polynomial as jco and substituting the
value of Lm as [0 - Lmax value in the unsaturated region] and value of C as [0 - ω];
e. setting the real and imaginary parts of the above equation to zero and obtaining
equations for C and Lm;
f. solving the equations obtained in the above step simultaneously and obtaining all
the solutions for C and Lm;
g. extracting the capacitance value and corresponding magnetizing inductance (Lmax)
value for the saturated region from the solutions obtained for C and Lm obtained in step (f) for
smooth sustained voltage build up in an induction generator.

6. A method as claimed in claim 5, wherein the 6th order polynomial is obtained using laplace transform and taking the determinant of the terminal voltage equation.
7. A method as claimed in claim 5, wherein the Lmax value in the unsaturated region is calculated experimentally.
8. A method as claimed in claim 5, wherein the equations obtained for C and Lm are solved simultaneously using interval analysis method.
Dated this 23rd day of October 2008
(Prita Madan)
Of Khaitan & Co Agent for the Applicants

Documents:

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Patent Number

272522

Indian Patent Application Number

2286/MUM/2008

PG Journal Number

15/2016

Publication Date

08-Apr-2016

Grant Date

05-Apr-2016

Date of Filing

23-Oct-2008

Name of Patentee

INDIAN INSTITUTE OF TECHNOLOGY, BOMBAY

Applicant Address

POWAI, MUMBAI

Inventors:

#	Inventor's Name	Inventor's Address
1	AGARWAL VIVEK	ELECTRICAL ENGINEERING IIT, BOMBAY, POWAI MUMBAI 400076
2	PALURI SATYA VYDEESWARA NATARAJ	SYSTEM & CONTROL ENGINEERING, IDP; IIT, BOMBAY, POWAI, MUMBAI 400076,
3	RAJESH KUMAR THAKUR	SYSTEM & CONTROL ENGINEERING, IDP; IIT, BOMBAY, POWAI, MUMBAI 400076,

PCT International Classification Number

F02D41/00

PCT International Application Number

N/A

PCT International Filing date

PCT Conventions:

#	PCT Application Number	Date of Convention	Priority Country
1			NA