Generator efficiency at cut in speed.

[Markcw]

I have been playing around trying some experiments with a small turbine and was wondering what would the generator efficiency would when it starts to make ,let's say 5 watts, my little pmg is rated at 300 watts at 28v at 300rpm, they say it is about 87% efficient at full speed, , again I am aware this is dependant on a lot of things, I have been using a 12v lead acid battery as well as a 16v lithium battery , I wouldn't expect it to be that efficient at kick in , has anyone got any idea what it might be or how I can calculate it.
Many thanks

[SparWeb]

It takes a fair bit of scientific elbow grease to prove anything is "X efficient".

One thing you can say is that efficiency does go down as the load goes up in a PM generator.  That may be counter intuitive, so here's one thing to consider:  The loss of energy in waste heat is calculated with I^2*R, a formula you might have seen before.  The "I" is current and "R" is resistance.  For a coil that has a resistance of (for example) 20 ohms, putting 2 Amps through it you lose this much heat: 
(2A)^2 * (20Ohm) = 80 Watts  (Heat loss)

At the same time, it's making useful power with that 2 Amps into your 28V battery:
(2A) * (28V) = 56 Watts  (useful power)

My example (totally made up) makes this scenario:
Output power = 56 Watts
Input power = 56 Watts + 80 Watts = 136 Watts

Efficiency = 56 / 136 = 41%

Now that you have an example of the math, let's see what you can do with your starting point:

5 W / 28V = 0.18 A

(0.18A)^2 * (20Ohm) = 0.64 Watts  (Heat loss)
Output power = 5 Watts
Input power = 5 Watts + 0.64 Watts = 5.64 Watts

Efficiency = 5 / 5.64 = 88%

So even though I started with a lucky guess, I think I get the same result, and it works out OK.

At higher power the output goes up, and the efficiency goes down.  No free lunch, man.

[Markcw]

Thanks so much sparWeb for that, I hadn't thought of that one I have been trying to measure the rotary torque with not much luck . I can find out the coils resistance and will do the calculations and let you know how it works out .
Thanks for the kind help
Mark

[Markcw]

Ok have had some time to work it out
Phase resistance is 1.79ohms
Rpmv = 7.5
Into a 12.5 v lead acid battery
4.8w at .390 amps = 2.72w = 63%

Into a 16.5 lithium 4.8w = .300 a
= 1.61w =75%

25v lead acid 3.2w =.130a  =.302w
=90%.
Interesting to see into a 9v lithium it was only 50% efficient.

There are other losses I think starting torque is 0.1nm
And I am not sure what the losses on the bridge rectifier are I was reading that they are about 80% efficient .
Once again many thanks for the help
Mark

[Adriaan Kragten]

The efficiency at low power depends very much on the type of generator. If you have a PM-generator made from an asynchronous motor, there is an iron stator stamping within the coils. This stator stamping increases the generated voltage but it causes iron losses and therefore the generator needs a certain small unloaded torque at low rpm. Apart from this torque, there is also a torque for the bearings and the seal on the generator shaft. All torques together give a certain power loss at low rpm. If the generated power is low, this power loss has a large effect on the efficiency. If the genered power is used to charge a battery, charging starts at a rotational speed when the open generator voltage is larger than the battery voltage. The effciency curve starts at this rotational speed and it increases strongly until it has a maximum at a somewhat higher rotational speed. The efficiency decreases at higger rotational speeds, mainly because of copper losses. Examples of measured efficiency curves for such a generator are given in my public report KD 78.

An axial flux PM-generator with no iron in the coils has no iron losses and the torque at low rpm is only caused by the bearings and the seal on the generator axis. So this type of generator can have a high peak efficiency but the efficiency at high rotational speeds can be lower. As such generators have a large air gap, the magnetic flux through the coils is much smaller than for a generator with an iron stator stamping and therefore more turns per coil are needed to get a certain voltage. This results in more copper losses at high power.

[Markcw]

Many thanks for the information, I have an axial flux pmg so very low starting torque, it's interesting how the losses mount up, I see that the old American multi blade has an efficiency of 30% I wonder what it is after all the losses have been taken into account
Mark

[Adriaan Kragten]

For wind turbine rotors, one is not talking about the aerodynamic efficiency but about the Cp. The difference is explained at page 15 of my public report KD 35. The maximum Cp of a multi bladed slow running rotor is rather low. The main reason is the strong wake rotation because of the high torque level (see figure 4.2 KD 35). But the blades also have a lot of drag because of the supporting structure and the blade length is normally much shorter than R (see formula 6.3 KD 35). Traditional multi bladed rotors are designed to drive a single acting piston pump which has a large peak torque (see KD 294). A high starting torque coefficient is therefore more important than a high maximum Cp.