Is there an objective standard for power measurement?
I've been confused. My background is not in EE, but I've been interested in the ways to measure power. I've learned that there are many different designs.
But then I wondered, does some power measurement implement an objective standard? Possibly at a similar level as the speed of electricity itself or something.
Since both DC voltage and DC current are primary quantum standards, they are as "objective" as it gets for DC power measurement, if the speed of light in vacuum is another standard to go by. DC voltage standard is a Josephson junction, and DC current standard is given by a fixed number of elementary charges per second per Ampere. Second is also a primary standard derived from counting hyperfine transitions in Cesium.
If you want higher frequency AC or RF power measurement, then there must be an apparatus that allows to compare the RMS power to DC power. Typically that's a microcalorimeter. For low frequency AC, it's possible to use DC voltage and DC current standards as a reference, since the rest of the measurement circuit can introduce very little error. This becomes unfeasible as the frequencies go up.
Power is usually calculated by multiplying current and voltage, but I think your question is about calibration. How do we know that when we measure 1.0mA on the ammeter it is really 1.0mA and not 1.1mA? Well, we know it produces 1.0V across a 1000Ω resistor. But how do we know the resistor is really 1000Ω? Well, our multimeter says so. But how do we know our when our multimeter says 1000Ω it's really 1000Ω and not 1100Ω? Well, we could use two multimeters. How do we know which one is right? Where does it end?
Scientists and engineers realized this was a problem all the way back in the year 1875, so they established the International Bureau of Weights and Measures. Originally they just made a metal rod and said "this is a meter" and they made a metal weight and said "this is a kilogram". You want to know whether your scale weighs kilograms accurately? Put the kilogram on it and see if it says 1.0 kilograms. Of course, that rod and that weight were very special and you couldn't use them to test just any old scale, so they made copies of the rod and the weight, and copies of the copies, and copies of the copies of the copies, and you'd test your scale on one of the copies.
Through over a century refinement it led to the SI (International System) of units we use today, where everything is defined based on fundamental units, no more "this rod is a meter long because I said so". (It took them until 2019 to get rid of the kilogram weight, though!)
So now, instead of having a very special rod under lock and key, there are labs where the world's best metrologists (people who study measurements) very carefully measure the distance light travels in a certain number of vibrations of a caesium atom, or whatever, and they can make metal rods that are very precisely one meter. Those rods aren't so special because you can make more of them, but they're still very expensive to make because they have to do these extremely accurate experiments, so most people still measure meters by using copies of copies of ... copies of rods made by measuring the speed of light and the vibration of caesium atoms.
You ever seen a 1-meter ruler? It's not 1 meter long. It's a bit longer, but the label that says 100cm is a meter apart from the label that says 0cm. So they actually start with these (plastic) rods that are not so accurate, then they paint accurate labels.
The same idea is used for electricity. It's very sensible to make a really precise ammeter without bothering to make it know exactly what an ampere is, then just see how it measures when you pass 1A through it, and then label that as 1A.
Someone makes a really good, super-high precision-ammeter, maybe 12 digits, but they aren't sure whether when it says 1.00000000000 that's actually 1.00000000000A, or a bit over, or a bit under. So they find the lab with the special equipment that counts exactly 6,241,509,100,000,000,000 electrons per second (not sure how they do that), they run that current through the ammeter and they note the ammeter says precisely 1.00062193145. Then, they adjust the software so it divides its reading by precisely 1.00062193145, and now it measures super-duper-accurate amperes. This is called calibration.
That ammeter's going to be really expensive (but cheaper than whatever measures the exact number of electrons per second) so its job is to sit in the calibration lab all day and be compared against things that are less expensive. A company that makes multimeters (actually, just about any electronics company) should have at least one ammeter that goes up to about 7 or 8 digits. Every few months, they take it to the calibration company with the super expensive one, and pay them to check it. The calibration company adjusts the software to divide the reading by whatever it says when their expensive one says 1.00000000000.
Then every multimeter the multimeter company makes gets checked and adjusted based on what their 7-digit ammeter says. And if asked how your multimeter was calibrated, they should be able to tell you: "we calibrated it against our equipment, which was calibrated against XXX calibration company, which was calibrated against NIST" or something like that. Probably with several more steps. What I just said isn't meant to be precise, just give a general idea.
They don't have to lose digits in each calibration, by the way. They do, because ammeters with less digits are cheaper, not to mention easier to use, but you could calibrate a 12-digit ammeter against another 12-digit ammeter, and only lose maybe half the last digit of accuracy.
Power is calculated as the product of current \$I\$ through a thing, and voltage \$V\$ across that thing:
$$ P = I \times V $$
Both can be measured easily enough. Measuring those parameters, and performing that calculation, tells you the number of Joules of energy being delivered each second, to the "thing", otherwise known as "power".
Power can vary over time, as voltage varies and/or current varies, and in such cases, you may be more interested in the average power delivered to the thing. Then you'll have to take frequent measurements of \$V\$ and \$I\$, and perform the calculation many times, and then take the average.
For certain systems, electric current and voltage vary "sinusoidally". One example is the electrical outlets in your home, which have a sinusoidal voltage, oscillating between +170V and −170V (in the US and Canada) or +340V and -340V (in Europe). Mathematically, these can be shown to be equivalent, in terms of power delivery, to a steady voltage of \$\frac{V_{PEAK}}{\sqrt{2}}\$, which would be 120V (US), and about 240V (Europe).
If the "load" is purely resistive, like a kettle, then current through the kettle will be proportional to voltage across it, and you can either calculate current as \$I = \frac{V}{R}\$, or measure the current, and calculate power as above.
Many appliances, though, are not purely resistive, and current is not proportional to voltage. In those cases, and if you don't have a explicit algebraic formula you can apply to calculate current, you again have to take frequent measurements, and take an average over time.
Those are the most common "standard" techniques for quantifying power, all of which are objective, since there is nothing subjective about the mathematics of it.
