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

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.

### Step 1: 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?

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.

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.

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.

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.

The readings you got are shown in the attached image:

### Step 7: 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?

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

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.

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.