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The mexican... Watt ? ? Calculate Watts on motors with Amp and Volt readings.

Picture of The mexican... Watt ? ? Calculate Watts on motors with Amp and Volt readings.
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Nowadays, it’s easy to measure watts to home appliances with Kill-A-Watt meters. However, living in Mexico, ordering one across the border would be cost prohibitive as shipping charges would be higher than the cost of the meter itself, and that's without taking into account import taxes!

Knowing that inexpensive Kill-A-Watt meters measure power on 120V circuits, a way will be shown to calculate power on any single phase motor load at any voltage. This same technique can be used on three phase motors as well except that you’ll have to adapt the formulas for three phase power calculation. For sake of simplicity, we’ll measure power on a 120V, 5000 BTU/h, thru-the-wall air conditioner.

 
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Step 1: Alternating Current Motors

Picture of Alternating Current Motors

Power on Alternating Current motors

Most people versed in alternating current electricity know that in order to measure power on electric motors, Amps and Volts readings would not be enough. There is another parameter – known as power factor- which affects the calculation of power in Alternating Current loads.

                       Power = (Volts)(Amps)(Power Factor)         [Watts]                                        (1)

 

Power Factor is the ratio of real power (measured in Watts) to apparent power (measured in Volts-Amperes or VA). Power Factor is a quantity that cannot be higher than unity.

                                                                 Power

                                 Power Factor = -----------------                                                            (2)

                                                              (Volts)(Amps)

In motors, real power is the one that does the actual work, the apparent power (VA) is made up of real power and reactive power. Reactive power produces the magnetic field that makes the shaft rotate. Unfortunately, an Amp meter measures total current in Amps which –in case of alternating current motors- is comprised of real current and reactive current, therefore, they are not easy to separate in order to calculate running Watts.

Step 2: If it is not easy, how is it done?

Picture of If it is not easy, how is it done?

 

You would need the following list of materials:

1 – Scrapped 16 AWG extension cord with plug.

1 – Scrapped Wall outlet box with two outlets.

1 – 35uF motor run capacitor I had kicking around in my junk box.

1 – Inexpensive plug.

2 – Quick connect terminals for the capacitor.

1 – Amp meter that also measures volts.

Warning: The following procedure is dangerous as it involves working with line voltage which can lead to potential injury or death.  Any attempt on the reader’s part to do what is shown on this instructable is under his/her own responsibility. This procedure is shown for educational purposes, only.

You would have to cut about a foot off the extension cord then crimp the quick connect terminals on one end of this cut off portion of the extension cord. Put the inexpensive plug on the other end of this same segment so you get what is shown between the Amp meter and the wall outlet on the picture. Note that the extension cord on the far right has no outlet with it.

 

Step 3: Putting the parts together.

Picture of Putting the parts together.
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Now, take the stripped ends of the extension cords and wire them to the scrapped wall outlet as shown on first picture of this step:

The hoops shown are important so you can clamp the Amp meter as will be shown.

Here are both, the capacitor and extension cords sets shown on third picture.

 

 

Step 4: Hooking up the whole thing.

Picture of hooking up the whole thing.
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Pull the Air Conditioner’s plug from the wall outlet and plug in the extension cord into the Air Conditioner’s wall outlet. Now plug in the Air Conditioner’s plug into the extension cord’s outlet as shown in the picture. Note that one of the outlets on the extension cord was shifted upwards to accommodate the Air Conditioner’s plug ground prong.

Step 5: Turn on the A/C and take readings.

Picture of Turn on the A/C and take readings.
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Plug in the capacitor into the other outlet, turn on the air conditioner and let it run for a few minutes until it stabilizes. Measure amperage on the extension cord

 

This is the amperage (2.81A) the air conditioner and the capacitor together are drawing from the line.

 

Measure the Amps drawn by the capacitor alone as shown (1.61A), now measure the amps the air conditioner is drawing alone (3.34A):

 

Now, measure the voltage (123.1V)and write down all the readings.

 

 

Step 6: Readings Summary

Picture of Readings Summary

The readings you got are shown in the attached image:

 

Step 7: Calculations

Picture of Calculations

Now, let’s calculate running power, let’s call I1 = 3.34A, I2 = 2.81A and Icap = 1.61A and plug these values in the following formula:

 

                                                 I1² - I2² - Icap²

Watts = (V) SQRT( I2²  + (----------------------------)² )

                                                           2Icap

 

                                                          3.24² - 2.81² - 1.61²

Watts = (123.1) SQRT( 2.81²  + (----------------------------)² )

                                                                 (2)(1.61)

 

Power = 344.9687  [ Watts]

                                               

To calculate power factor just use equation 2 with I1 as Amps:


Power Factor =   344.9687 /( (123.1)(3.34)) = 0.839

                                                                 

That would be it if you just want to calculate real power with the Mexican Watt meter, using Amp and Volt readings. If you are interested in knowing where this formula came from, continue with next step.

Step 8: Where did the formula come from?

Picture of Where did the formula come from?

Do you remember we talked earlier about real, apparent and reactive powers? Well, electrical engineers use the following right triangle to explain how these powers interact with each other. It happens that this triangle is formed by vectors which represent these powers, as a matter of fact, this triangle is known among electrical engineers as “the power triangle”. By multiplying Volts times Amps we get Apparent power vector whose angle is determined by the magnitudes of both, real and reactive power vectors.
 

Real Power [Watts] is represented by a horizontal vector, reactive power [VAR] is represented by a vertical vector and apparent power [VA] is represented by the vector addition of both, real power and reactive power vectors. Using right triangle relationships, we have:

                                           

VA² =  Watts² + VAR²


 

In order to calculate Real Power [Watts] we need both, apparent power and reactive power, however,  reactive power is also an unknown.

 

 

Step 9: Enter the capacitor

Picture of Enter the capacitor

Here is where the capacitor comes in. It happens that capacitors draw also reactive power whose vector direction is opposite to the reactive power drawn by inductive loads such as motors. The effect of the capacitor in this power triangle can be seen in the picture.

The introduction of the capacitor into the circuit reduced total current drawn by both, the motor and the capacitor, it can be seen that VA2 vector is smaller than VA1. The difference between VAR1 and VAR2 is due to the capacitor’s power which is 180 degrees opposite to VAR1, here that is shown as Cap = VAR1 – VAR2.

 

Step 10: The equations.

Picture of The equations.

The introduction of the capacitor into the circuit reduced total current drawn by both, the motor and the capacitor, it can be seen that VA2 vector is smaller than VA1. The difference between VAR1 and VAR2 is due to the capacitor’s power which is 180 degrees opposite to VAR1, here that is shown as Cap = VAR1 – VAR2.

From here we can derive the following equations:

VA1² = Watts² + VAR1²                                                                                                      (3)

VA2² = Watts² + VAR2²                                                                                                       (4)

Cap = VAR1 – VAR2                                                                                                             (5)

From (5), we determine VAR1

VAR1 = Cap + VAR2

Substituting VAR1 in (3) we get:

VA1² = Watts² + (Cap + VAR2)²

Watts² = VA1² - (Cap + VAR2)²                                                                                            (6)

From (4) we have:

Watts² = VA2² - VAR2²

Equating with (6)

VA2² - VAR2² = VA1² - (Cap + VAR2)²                                                                                 (7)

VA2² - VAR2² = VA1² - Cap² - 2CapVAR2 – VAR2²

As VA1 = (V)(A1), VA2=(V)(A2), VAR2 = (V)(AR2) and Cap = (V)(Acap), then we have:

(V²)(A2²) – (V²)(AR2²) = (V²)(A1²) – (V²)(Acap²) – 2(V²)(Acap)(AR2) – (V²)(AR2²)

Which would be reduced to:

A2² = A1² - Acap² - 2(Acap)(AR2)

2(Acap)(AR2) = A1² - A2² - Acap²

              A1² - A2² - Acap²

AR2 = ----------------------------                                                                                                  (8)

                         2(Acap)

               

 Substituting in (4)

                                                A1² - A2² - Acap²

(V²)(A2²) = Watts² + (V²)(----------------------------)²

                                                          2Acap

 

 

                                                A1² - A2² - Acap²

Watts² = (V²)(A2²)  + (V²)(----------------------------)²

                                                          2Acap

 

               

                                                            A1² - A2² - Acap²

Watts = SQRT( (V²)(A2²)  + (V²)(----------------------------)² )

                                                                     2Acap

 

               

Substituting I1 = A1, I2 = A2 and Icap = Acap, we get the formula:

                                                 I1² - I2² - Icap²

Watts = (V) SQRT( I2²  + (----------------------------)² )

                                                           2Icap

 

Which turns out to be the formula we used earlier to calculate power.

This method is useful whenever you need to take power readings on electric motors and no power meter is available, which is the reason it was called the Mexican Wattmeter. As it is said up north, "Its accuracy is close enough for government work" provided no significant harmonics are present.

Note: This method to measure power works only with linear loads such as motors, it cannot be used with electronic loads such as computers. To measure power on electronic loads you have no choice but to use a real power meter.
 

 

I don't get the joke, just doesn't make any sense, but at least your procedure is good
rlarios (author)  kukulcangod1 year ago
If you refer to the name of the instructable as the joke, it's a play on words which obviously backfired.

Speaking of names, is there any reference between yours and the mayan feathered serpent deity?

Have a great day!
I just realize myself how rough I must've sound in my comment I apologize for that was having a bad moment at work...Very smart ! Yes , kukulcangod is the god of knowledge , I was born during the equinox same time the pyramyd of kukulcan produces the shadow of the feathered deepens descending again from the skies
My friend, wireless electricity was their specialty as well , in fact a form of it now called bio energy, or zero point energy, or gone etc. Modestly but like them I have been able to extract energy from the ground, orienting my electrodes north south and with a special circuit...Great instruct able continue on Thanks.
rlarios (author)  kukulcangod1 year ago

Happy birthday kukulcangod !

I thought of you today, I just saw a video on youtube about the feathered serpent going down the pyramid.

rlarios (author)  kukulcangod1 year ago
Hey Kukulcangod, no problem, that's OK, we're only human.

What kind of loads have you been able to feed with the energy you extract from the ground?
Hisart3 years ago
Very detailed! Nicely done!
I see you have a meter, how accurate is this procedure?
rlarios (author)  Hisart3 years ago
Capacitors tend to draw harmonic currents which should affect the power triangle relationship. As to how accurate this is, well, I would say that +/- 10% accuracy compared to a power meter.

In spite of this wide difference, this method beats having to guess power when there is no power meter available.
bearstuff3 years ago
I don't get the Mexican reference. What does this have to do with Mexico or Mexicans?
Looks like Mr. Rafael is from Mexico. (see second to last paragraph of ible)
rlarios (author)  Hisart3 years ago
You got that right, sir ! I am from Mexico.