transient process in an induction motor

if anyone can show me how to use the numeric method runge-kutta to calculate the start of an induction motor in the transient period ,if you please with an example using parameters .
with regards

 

[electricpete]

Start with the rotational version of a=F/m
dw/dt = (Telec-Tmech)/J
where w = 2*pi*speed
Telec = motor torque as function of speed
Tmech = pump torque as function of speed
J = rotational inertia
Rearrange as dt = Jdw/(Telec-Tmech),
then integrate both sides to give:
t = J*Integral(1/[Telec-Tmech])dw from w=0 to w=2*Pi*F_operating.

If you know Telec and Tmech as a function of speed than the numerical integration is trivial and can be done on an excel spreadsheet.

You may wish to add a refinement which adjusts Telec based on V^2 if power system characteristics are known.

 

[jbartos]

Suggestion: The previous posting needs a little clarification, namely the w variable is the mechanical speed:
w=(2/p)x(ws-wr)=±(2/p)ws(1-s)in rad/s
ws=2xpixfs in rad/s
fs=frequency of supply voltage in Hz
s=slip in per unit
wr=2xpixfr in rad/s
fr is rotor current frequency in Hz
p is number of poles of the machine

 

[electricpete]

jbartos - Your clarification adds only confusion. If the motor torque-speed curve is given the quantities fs, s, wr, fr, p are irrelevant (they are inherent in the curve).

If any clarification is needed, it is that F_operating represents operating mechanical speed. (That should be obvious from the context).

 

all what you present both, for me is known ,but i know that after the park transformation that will be a system of equations that need to be resolved in a numerical method as the deff. equations are nonlinear,so if you show me the order that put the numeric method to work ,if it is available for you with numeric example ,the simple one .
regards

 

still wait for your detailed help .
thank you

 

[jbartos]

Suggestion: Reference:
1. Arthur R. Bergen "Power Systems Analysis" Prentice-Hall, Inc., 1986
Page 313 Equation 10.44 Mechanical equation
J(theta)"+D(theta)'+iq(lambdad)-Id(lambdaq)=Tm
in terms of Park Variables. Then, apply the Runge-Kutta Method.
2. Alternately, the engineering standard is over the motor acceleration time calculation, e.g.
Section 9.6.5 The Speed-Torque and Motor Accelerating Time Analysis on page 231 of IEEE Std 399-1990 (or newer issues) IEEE Recommended Practice for Industrial and Commercial Power System Analysis.

 

[jbartos]

Suggestion to electricpete (Electrical) May 17, 2002 marked ///\\Start with the rotational version of a=F/m
dw/dt = (Telec-Tmech)/J
where w = 2*pi*speed
///the "speed" instead of "frequency" is consider objectionable and confusing in this equation. Check any textbook on this subject. If you do not know which one, let me know, I will post some.\\