Power Factor verses Efficiency

[Besoeker]

OK. Then somewhere we went down the path of instantaneous power, average power, and time integrals. I guess I lost track of what point you were driving at.

I think it went pear shaped when the Maharaja posted this:

It is not correct to say there is no time element in KW

Power is an instantaneous value which means that his statement is incorrect.
Certainly we use average power in calculations and I take your point about better PF making more effective use of supply current carrying capacity.

As it happens, a discussion on power factor and cost savings is how I joined this forum about five years ago:

If you are not penalised for operating at low power factor, I'm not sure that installing PFC wil get you much benefit.
Sure, if installed at local MCCs, it would reduce losses in your distribution system. Correct to 0.95 and you could cut distribution loses by nearly 40%.
But 40% of what? Probably not a lot given that the distribution system (presumably) already exists and is rated for existing currents.
Transformer losses will also be reduced but again, this is not likely to a very great saving. In my experience, copper losses for the size of transformers you mention, is in the region of 1% of rating.

Bob makes a good point. Savings would be for I?R losses. System impedance is usually mostly reactive, so basing calculations on that would be a bit misleading. In the absence of any better information I usually take resistance to be 0.24 times the impedance.

In summary, I think for your particular application, it might be difficult to justify the capital cost of PFC based on energy savings alone.

Just my thoughts.

On a recent project, I included PFC on a fixed speed drive. It was a refurb and the motor type was changed. The new motor had a much worse power factor and the unit transformer supplying it would have been inadequately rated with the new motor. There was no option. But I probably would have included it anyway. The reduction in current meant smaller cables. At 600A and, given the length of run, the reduction in conductor costs far outweighed the additional cost of the PFC, capacitor, contactor, fuses, internal panel cables and associated hardware.

 

[jumper]

Apparent Power

:slaphead::slaphead::slaphead:

 

[mivey]

Power is an instantaneous value which means that his statement is incorrect.

Talking about instantaneous power in an AC system without the details just muddies the water and leaves a door open for more debate. Why not just shut all the doors?

Sahib did incorrectly talk about demand consumption. As was pointed out to him, the bill had consumption charges for energy but compensation charges for power. Demand on a utility bill is a consumption rate, not a consumption quantity.

Sahib did try to bring in time by talking about average power. It is correct that the kW on utility bills is dependent on time because not only is the active power a time integral, we bill for the average power over a demand period. Instantaneous power is simply not what we are talking about with power that oscillates in an AC system. Even for faults and things approaching instantaneous values, we usually associate it with a time interval because we ultimately are concerned about damage due to energy loss.

As far as I'm concerned, vaguely talking about instantaneous power is not clarifying the point that demand is a measure of the rate of energy flow, not a measure of energy consumption. But it is true our interest in demand is energy driven. Our interest in apparent power is that there are losses due to both electric fields and magnetic fields (think of iron and copper losses). As I stated, supply losses are a function of S².

Active power kW = 1/T * Integral{[0,T] v(t)i(t)dt}. For kW, the utility uses the average of the active power over a demand interval.

With steady DC, instantaneous power is not a time dependent function. Any real instantaneous value of power in an AC system is the power evaluated at a specific point in time because instantaneous power is a time varying function given by P(t) = P - Pcos(2ωt).

Even if we have steady-state conditions, we must correctly say that any value of "instantaneous active power" is for a time interval that is an integer value of a power cycle. With AC systems, there is simply a time dependency that can't be minimized. Speaking of instantaneous power but overlooking the underlying constraints only aggravates the discussion about the time dependency.

Directly addressing and clarifying the time-dependent nature of AC power helps nullify any argument about any so-called "demand consumption". Pulling the time rug out from under their feet, so to speak.

 

[mivey]

:slaphead::slaphead::slaphead:

Yeah, that one.

 

[mivey]

Even if we have steady-state conditions, we must correctly say that any value of "instantaneous active power" is for a time interval that is an integer value of a power cycle.

Actually equals the active power at 1/2 cycles as well.

 

[GoldDigger]

:slaphead::slaphead::slaphead:

+1
When dealing with distortion power factor, the angle theta can still be defined in exactly the same way and the definition of overall power factor is still the same, but the angle theta no longer has a physical relationship to a phase angle between two sinusoidal waveforms (i.e. voltage and current.)

And a thumbs up to mivey as well!

 

[Besoeker]

Talking about instantaneous power in an AC system without the details just muddies the water

Simply, power IS an instantaneous value. See post #99.

 

[GoldDigger]

Simply, power IS an instantaneous value. See post #99.

And like any instantaneous value, there is a well defined average value derived from it. But when you talk about the average, you have to specify the time period involved. There is a big difference between the average power for a time interval shorter than 1/2 cycle and a time interval more than hundreds of cycles long.

Conventional usage in this case considers "power" with no qualifiers to mean average power over a small integral number of cycles, less than the time period over which the load is usually cycled on or off. Average power is often used to refer to a 24 hour period during which the power varies from time to time between zero and full load.

Since common English usage is so inconsistent, it helps to add the words "instantaneous", "nominal", "average" or "daily average" if the reader is likely to be confused.
Code can rely strictly and consistently on definitions. Discussing with a customer or even another person in the trade is murkier. (As this thread clearly demonstrates.)
Since this is a code forum, I suppose we have a responsibility to be clear.

 

[mivey]

Actually equals the active power at 1/2 cycles as well.

I take that back. It will depend on the start point. Still true for integer values of the power cycle.

 

[mivey]

Simply, power IS an instantaneous value. See post #99.

For that example, yes. But that was not the power he was talking about.

 

[mivey]

When dealing with distortion power factor, the angle theta can still be defined in exactly the same way and the definition of overall power factor is still the same, but the angle theta no longer has a physical relationship to a phase angle between two sinusoidal waveforms (i.e. voltage and current.)

We've then moved from 2D polar coordinates to 3D spherical coordinates so we now have two angles.

θ=arccos(P/sqrt(P²+Q²))
and
φ=90? - arccos(sqrt(P²+Q²)/S)

 

[iceworm]

Active power kW = 1/T * Integral{[0,T] v(t)i(t)dt}. ...

Isn't " 1/T * Integral{[0,T] v(t)i(t)dt} " also the definition of "average power"?

ice

 

[Besoeker]

For that example, yes. But that was not the power he was talking about.

The unit of power is the Watt. One amp times one volt occurring at the same instant. Look at post #99.

 

[mivey]

Isn't " 1/T * Integral{[0,T] v(t)i(t)dt} " also the definition of "average power"?

ice

Yes, the average power over a complete period. Also known as: true power, active power, real power, wattage, rate of consumed energy, P, pf * S, etc.

 

[mivey]

The unit of power is the Watt.

That is indeed the unit. That does not mean all power measured is one amp times one volt. Units do not a measurement make. Power is energy per unit time.

One amp times one volt occurring at the same instant. Look at post #99.

Instantaneous power is not the power we are talking about with utility bills.

 

[Besoeker]

That is indeed the unit. That does not mean all power measured is one amp times one volt. Units do not a measurement make. Power is energy per unit time.

That's putting the cart before the horse.
Energy is power integrated over time.

Instantaneous power is not the power we are talking about with utility bills.

Utility bills are usually for energy, not power.
You pay for 1kWH if you use 1kWh. Regardless of how you use it. It could be a steady 1kW for one hour. Or 60kW for one minute of that hour. It would still be 1kWh. But you can't tell from the 1kWh how it was used.. Which brings me back to the point about putting the cart before the horse.

 

[mivey]

That's putting the cart before the horse.
Energy is power integrated over time.

Better go check the barn there farmer Brown, you've left the horse behind. Power is not "stuff" that you apply. Power is a rate: the rate of energy flow.

When you drive do you apply a speed over time to travel the distance? Of course not. We can measure your rate of travel at a given instant but that is based on you traveling in the first place.

Apply a force over a distance and we calculate the work done as force times distance. Do that work in a certain amount of time and we can calculate the average power as the amount of work done per unit time. Instantaneous power is the force times the velocity at a given instant. None of that is physically applying the speed of work times time. Power is a measure of energy flow.

Utility bills are usually for energy, not power. You pay for 1kWH if you use 1kWh. Regardless of how you use it. It could be a steady 1kW for one hour. Or 60kW for one minute of that hour. It would still be 1kWh. But you can't tell from the 1kWh how it was used.. Which brings me back to the point about putting the cart before the horse.

Utility bills include three basic costs: customer costs (costs regardless of usage, and influenced by customer size), demand costs (costs based on the peak rate of energy consumption), and energy costs (based on the quantity of energy used).

All three are included in the bill but demand costs may be hidden in the energy charges (more noticeable with tiered rates). In the past, it was not cost effective to meter the demand for low usage customers because of the meter costs vs. the size of the monthly bill. That will change in the age of smart meters and the residential and small commercial will eventually have rate structures similar to the larger customers (time of use rates do that to some extent).

Load profiles are used to find an equivalent energy charge that covers the demand and energy costs for customers with similar usage characteristics (rate classes). All covered in texts by authors such as Bonbright, Goodman, and many others.

 

[Besoeker]

Power is a rate

My point exactly.

 

[mivey]

My point exactly.

Well, we agree on that point anyway.

 

[mivey]

That is indeed the unit. That does not mean all power measured is one amp times one volt. Units do not a measurement make. Power is energy per unit time.

That's putting the cart before the horse.
Energy is power integrated over time.

See if this might help refresh your memory:

Power is the time rate of doing work...Electric power is the rate of doing electrical work...Work is being done at the rate of 1 W when a constant current of 1 A is maintained through a resistance by an emf of 1 V.

Power is the time rate of transferring or transforming energy. Electrical power is the time rate of flow of electrical energy. The instantaneous electrical power at a single terminal pair is equal to the product of the instantaneous voltage multiplied by the instantaneous current. If both voltage and current are periodic in time, the time average of the instantaneous power, taken over an integral number of periods, is the active power, usually simply called the power when there is no danger of confusion.

In technical usage, the word "power" is defined to mean "energy per unit time."

Power is the measure of the rate at which work is being done. In the case of a motor the average power P_avg being developed over a period of time is defined as the quantity of work delta_W done by the motor divided by the time interval delta_t required to do that work, and, in general, average power P_ave is defined to be P = delta_W / delta_t. {mivey: symbols modified to fit font}

If work is expressed as a function of time, the instantaneous power P being developed at any instant is defined to be P_inst = dW/dt.
It is sometimes convenient to express power in terms of a constant force F acting on an object moving at a constant velocity v
...
{mivey: text contains example of outboard motor causing water to exert force F on the propeller/boat when the boat is moving at constant velocity v}. The power delivered by the motor at any instant is F*dr/dt where r is the position of the boat. Because the time rate of change of position is the velocity of the boat, F*dr/dt = F*v.

The work to move a unit charge between two points in a field is simply the voltage V. When many units of charge are involved, the total charge is simply Q. When a charge Q moves through a potential difference, the total work involved is the product of charge x voltage, QV. Assume this work is stored as energy. This energy is the product of QV and has units of joules (J). The rate at which work is done is a measure of power. This is simply charge x voltage / time.

The current that flows in the load also flows in the coils of the generator. The magnetic field from this current pushes against the magnetic field that threads flux through the rotating coil. In order to rotate the shaft, a torque must be supplied that matches the repelling force between the two magnetic fields. This torque, acting through an angle of rotation, is force times distance or work. The rate at which this work is provided is power.