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To: My Elek-Trak co-conspirators,
and Dan in particular because of his desire to use AC motors. (Dan, your
specific questions should be answered near the bottom.)
From: Steve
Naugler
Subject: An unsolicited lecture on
AC induction motor theory, dynamic braking, and regeneration. This does
not cover synchronous motors and universal AC/DC series wound motors. (Now
that I think of it, the DC theory e mail only covered permag and shunt wound
motors, not series wound motors.)
Again for any electrical engineers out there,
this will be somewhat shallow, but it may help others on understanding AC
induction motors motors. I am going to sidestep effects of
impedance.
First lets define some
variables:
N = shaft rpm
Nsync = motor synchronous rpm
Nslip = slip rpm
T = motor torque (we'll use in-lb)
HP = HP
k = constant
T = 63000 x HP/N or HP = T
x N / 63000
Have you ever noticed
that most AC induction motors have speed ratings like 1750 rpm? At first
glance you'd think an AC motor would run at its synchronous speed. Four a
4 pole motor (1750 rpm rated) that is:
Nsync = (60 cycles/sec) x (60 sec/min) x (4 poles/2 pole in a
NorthSouth pair) = 1800 rpm
Well, as it works out an induction motor is
called an induction motor because currents are induced in the rotor. But
you only create electrical current when you pass a conductor through magnetic
field lines of force. As the stator has its magnetic field rotating within
the motor housing at 1800 rpm, if the rotor were also rotating at 1800 rpm, the
rotor conductors would not be passing through any magnetic field lines but
rather moving with them. So, in order to generate a magnetic field in the
rotor, the rotor must be moving slower than the stator magnetic field for the
motor to produce mechanical power. (You can also move the rotor faster
than the stator magnetic field rotation and turn the thing into a generator of
AC power.) The faster the speed difference, the higher the induced rotor
current, the higher it's magnetic field, and the higher the torque the motor
produces. In truth, an induction's motor torque is proportional to slip
rpm, Nslip, or the speed difference between synchronous and actual
speeds.
Nslip = Nsync - N
T = k x Nslip = k x (Nsync - N)
An
example: You have an induction motor rated at 2 hp at 1750 rpm (Nslip = 50
rpm).
T = 63000 x 2 / 1750 = 72 in-lb.
Now we find that the motor is actually running
at 1775 rpm (Nslip = 25 rpm). With Nslip cut in half, torque is cut in
half to 36 in-lb. HP = 36 x 1775 / 63000 = 1.01 HP
What this means is that an AC
induction motor's torque and horsepower are both vary nearly linearly with the
slip rpm for speed both below (acts like a motor) and above (acts like a
generator) the motors synchronous rpm. An AC induction motor only runs at
nameplate speed for exactly nameplate conditions.
Regeneration: In
industry commercial inverters are used to vary AC motor speeds by intentionally
changing the frequency supplied to the motor. Now you can soft start the
motors vs. generating 3-5 times normal running torques at starting when started
at 60 Hz. Here you would start the frequency at 0 Hz and slowly ramp it to
60 Hz. (When you start a 1750 rated AC motor at 60 Hz, the slip rpm Nslip
= 1800 rpm. The impedance of the motor and resistance of the wires feeding
the motor are all that prevent starting torques more like 36 times normal
running torque.)
You can also select any other
frequency that doesn't overload the motor; AC motors are now variable speed
motors.
Back to regeneration.
If you overspeed the motor, the motor is returning the power back to its power
supply. When you use an inverter that has a variable frequency capability,
you turn the frequency down and your motor is a generator, returning its power
to the controller, until your new reduced speed is reached. Or you can
have a over running load, like when you drive your AC motor powered tractor down
a hill, and your motor is a generator.
Here is the problem in
industry: Most AC inverters cannot return the excess power to the power
line. There is a diode bridge that takes AC power and charges a capacitor
bank. (There are a very few specialized AC inverters that use a
bi-directional bridge of transistors to charge the capacitors or return power to
the AC line.) With diodes that is strictly a one way trip. The
capacitor bank is connected to the motor via a bridge of transistors or gate
turn off SCRs. This bridge is bi-directional. So whenever the motor
is a generator, the capacitor bank is charged up and potentially
overcharged. Some drives turn off to protect the controller. Some
drives switch on a resistor to dump the excess energy. Here we are not
really regenerative, although the motor does not know any better.
If you were to replace the
capacitor bank with batteries, like some electric cars, you now have the ability
to absorb a lot of energy from the motor, and you can easily be regenerative
over the entire speed range of the motor, whereas to regenerate with a DC motor
you need to do tricks with field windings and still may not be regenerative over
the entire speed range.
Dan, in your e mail to me you
said that your inverter was rated for 1500 W 120 VAC output with a 24 VDC input
and that you can use your inverter backwards as a 24 VDC charger. I
suspect that it is not truly bi-directional. Perhaps you could switch from
inverter to charger quickly, but once the speed of the motor fell off, you'd
probably loose all braking effect. I don't think with that inverter you
will regenerate. But Dynamic braking is still possible.
Dynamic braking:
Dynamic braking in an AC induction motor is also sometimes called DC injection
braking. You can even get such brakes to put on table saws and the
like. What you are doing is feeding the AC motor with DC current, which is
at 0 Hz. Think of the 0 Hz DC current as your new input which gives you a
synchronous speed of 0 RPM. Remember the equation from above, use 0 rpm
for Nsync, and use 1750 for N:
T = k x Nslip = k x (Nsync - N) = k x (0 - 1750) = - k x
1750.
Notice the - sign in front of the k.
That means that all that torque is negative so you are braking the load.
Actually, to keep torque manageable, you must limit current as to not break
shafts and the like.
Dan, there are two options you have for
braking your AC drive.
1. Buy the device sold to stop AC motors like table saws
and power it from the AC inverter output.
2. Disconnect your motor from the inverter and connect
it to the battery for 24 volts worth of DC injection braking. You may need
a resistor in series. And you must remove the DC as soon as the motor
stops or you will overheat it badly.
Lastly, can you use your 1500 watt
inverter? I don't think that its big enough. If it is, I believe
your best bet is an induction motor with a poly V belt (98% efficient) or a VX
series V belt (92-95% efficient) arrangement to get a good speed. Any
series wound universal motor I've seen is not good for continuous duty, and
you'll have all the same issues you'd have with a DC motor (brushes,
commutators).
Here is why I don't think that it is big
enough. 1.5 kW x 0.85 % efficiency x 1.341 hp/kW = 1.71 hp. Multiply
by 3 to get gasoline horsepower and you get 5.13 hp. When 22 inch push
mowers have 3.5 hp, you'd at best get enough power for a 32 inch deck. And
that's assuming a 100% duty cycle at 100% power for that inverter. Also,
5-7.5 hp 120 VAC single phase AC motors are somewhat hard to find.
The GE mower deck motors look small because
they get their power at high rpm. Consider that if a 22 in deck with a gas
engine turns 3600 rpm to get proper blade tip speed, a GE deck motor with the 14
inch blades would have to turn 5660 rpm to get the same tip speed. I
really ought to measure the blade speed with a strobe some time.
Dan, I too think that your best bet
is either a 24 VDC motor or a bigger inverter. If there were such things,
a 24 VDC to 240 VAC 3 phase would give you the best chance of finding a properly
sized motor.
Hope this all helps someone. Dan, I'm
not sure it helps you a lot.
Steve
Naugler |