Predicting DC generator response

[DH2]

I am creating a scale model wind turbine using a DC motor as a generator and would like to predict the motor response analytically. Generally speaking, the flow will spin the rotor (as in the turbine's), which will spin the motor, and then there will be what I'm calling the motor response, and then an output voltage and current from the motor. What I gather from various sources, though, is that there's a dynamic interaction between the shaft input and the motor response such that the original rpm and torque input at the shaft will be affected by the motor response which will create an adjusted rpm and torque input at the shaft which will be affected by the motor response and so on until it equilibrates. Is this about right? If so, how can I mathematically describe this iterative process using the original shaft inputs and the motor specifications? Furthermore, now what happens when a load is applied in series such that the generator is actually powering something?

 

[Hesch]

how can I mathematically describe this iterative process using the original shaft inputs and the motor specifications? Furthermore, now what happens when a load is applied in series such that the generator is actually powering something?

You must make a model as for the wind turbine, the generator and its load.
I suggest that you do this by means of Laplace transform.
Having closed/reduced some loops in the model you can calculate a steady state balance.
Just set the wind speed to something and add/subtract power to the output.

To make a model for the generator is easy, but I'm not familiar with the wind turbine ( think it's hard ).

 

[anorlunda]

Creating a dynamic model based on first principles is a beloved passion of many regulars on this forum. I encourage you to take the effort to do it.

However, your question is very broad. The correct answer is a differential equations course, where the last chapter is Laplace Transforms as Hesch said. You can't get that from an online forum.

Alternatively, you could use one of the many modern simulation software packages which allow you to simulate everything while understanding nothing about what you are doing. Excuse my personal bias for showing through.

Good luck.

 

[jim hardy]

Is this about right? If so, how can I mathematically describe this iterative process using the original shaft inputs and the motor specifications? Furthermore, now what happens when a load is applied in series such that the generator is actually powering something?

hmmm

Mother Nature loves a balance.
She will establish one between power absorbed by your turbine blades and power converted to electricity by your generator.
The difference (hopefully small) divides, part is lost to friction and part goes into accelerating the machine.

So i'd set it up as an energy balance
friction loss proportional to shaft speed
power absorbed by turbine ƒ(windspeed^3 - blade speed^2)
assume some moment of inertia I for machine, its kinetic energy is ½Iω²

these two equations describe the electrical behavior of a DC machine
open circuit voltage = KΦ X RPM, where K is a constant and Φ is flux,
(hint: permanent magnet generators have constant Φ so start with one of those)
torque in ft-lbs= (same KΦ) X Armature Amps X 7.04
so a load on generator causes it to convert mechanical energy (torque X ω) into electrical energy(volts X amps) which flows to loadI think you could iterate with a finite difference loop , step = Δtime
start with assumed windspeed and shaft speed
do
calculate energy absorbed by blades from wind
calculate generator voltage
calculate generator current
calculate energy output from generator
calculate energy loss to friction
calculate net energy acceleration or deceleration of shaft in current time step
calculate new shaft speed
increment time
loop

That's a place to start.