Power Factor Measurement with PICs

Hi, egyr. What's a PIC? I'm not familiar with the acronym.

Hello, PIC is a trade mark for the Microchip microcontroller family. Here is the Link http://www.microchip.com/stellent/idcplg?IdcService=SS_GET_PAGE&nodeId=74 Such microcontroller are quite reliable and low cost. You can also findd a lot of support from various software/hardware developpers, such as complilers, programmers etc. Best Regards.. Enrique...

A cheat that I used on a different processor was to create a lookup table on the angles. Imagine an array that contains 3600 entries - this will give you an accuracy to .1 of a degree angle. Assign the respective cosine value (from a file) to each index into the array. The advantage of this technique is that it's FAST but not super accurate.

Thankyou jmoliere, Yes the lookup table can do the job, one interrogation I have is that I dont know yet is the accuracy I'll need, this is first time to me to build a power factor meter for industrial purposes, it must only logg (not to control anything) 3 Phase Voltage, Current and Power Factor & time for energy quality supervision. I got another tip from Kjennejohn in a PIC discussion group is to add a low cost PIC math cooprocessor here is the link: http://awce. com/pak1. htm, I didnt knew math coprocessors where avalible, for this kind of instument I'm building may be the cost aprox $30.00usd is not a problem but for some other low cost projects cost will be important. I'm gonig to implement both solutions the lookup table and the math cooprocessor to get knowledge and experience on this matter. Once again thankyou....

You might look at some of Microchip's DSP libraries for their DSPic controllers. Also the lookup table can work very well if you have enough space for it. Also you may want to take a look at the TI MSP430 parts. They have a version that has three A-D converters that can sample simultaneously which could be useful.

Thanks rcapper, I w'll give a good look at the DSP libraries and to the TI MSP430 and I'll come back to give comment about it. Best Regards and thanks for your help.... enrique.

Hello,
as jmoliere says you can build a lookup-table. Your memory may be small, if so, try to reduce the number of items:

For a resolution of 0.1 deg you dont need 3600 values but only 900 as the triangular functions are symmetric and can be completely described with a data set for 0-90 deg.

There are two ways to make a basic calculation as the largest gradient around zero determines the voltage or current resolution:

1. Your phase resolution is a must. Then take the 1/asin(alpha) and get the amplitude resolution of one half wave. In this example you get

sin(0.1)=1.745E-3 1/sin(0.1)=572

Full scale resolution is 572*2=1144, thats a little bit better than 10 bits.

2. Your ADC-resolution is given (mostly, because of hardware specs). Example: 12 bit

The least significant bit makes 0.488E-3 (resolution of amplitude, 1/2048)
asin(LSB)=2.79E-2 deg (worst resolution of period, determines the minimum
lookup table content.

Regards Uwe

Right uweka, the jmoliere is a good choice, 0.1 degree I think is perfect, memory may not be a problem because this instrument as you may notice will logg all aquired data into a big I2C memory array. Please see the reply I did to jmoliere to findout my next steps. --- o --- Thankyou jmoliere, Yes the lookup table can do the job, one interrogation I have is that I dont know yet is the accuracy I'll need, this is first time to me to build a power factor meter for industrial purposes, it must only logg (not to control anything) 3 Phase Voltage, Current and Power Factor & time for energy quality supervision. I got another tip from Kjennejohn in a PIC discussion group is to add a low cost PIC math cooprocessor here is the link: http://awce. com/pak1. htm, I didnt knew math coprocessors where avalible, for this kind of instument I'm building may be the cost aprox $30.00usd is not a problem but for some other low cost projects cost will be important. I'm going to implement both solutions the lookup table and the math-coprocessor to get knowledge and experience on this matter. Once again thankyou.... --- o --- Best Regards..

Forgot to tell you, "Excelent and well documented comments" Regards..

I am impressed with your thoughts for determining the optimum number of lookup points, although much of it is "over my head". What about approximating the Cosine curve as a number of straight line segments, and do the lookup with straight line interpolation between points. Would this reduce the number of lookup points while leaving the magnitude of error sufficiently small? Or would this make the programming and related portions of the application too cumbersome for the processor being used?

-JMM

Hello JMM,

I hope I understand you right. The lookup table consists of numbers xn, xn+1 ---- xn+m which already describe the end points of the single line segments.

xn ; xn+1 ---> segm 1
xn+1 ; xn+1 ---> segm 2
.....

Of course then you can reduce your number of pairs and afterwords divide these segments in a linear way. In the 0 ... 90 deg and 180 ... 270 deg range you get a small positive angle error and in the range of 90 ... 180 and 270 ... 360 deg a negative phi error. But I didn`t evaluate wether its more effective to implement an interpolation routine or to put in some more lookup points. I think it depends totally on the hardware you use.

In other applications par example you can simply produce a rather good sine wave with harmonic distortion of less than 1% using 16 points per quarter wave.


Tnx for your additional hint.
Regards Uwe

Uwe--

Yes, you understood my thought. One can even reduce the error further (or make the points further apart while staying within the same maximum error) by placing the points slightly beyond the actual value of the sine wave's curve, instead of at the actual value of the curve for that point. Thus the straight line segment starts above the curve at its first point, but then the curve crosses above the line segment and back below it before reaching the next point. The process would continue for each succeeding point. A least-squares type of formula could determine the value of each point for a given spacing of points along the curve.

--JMM

This may be a bit off the wall, but Bhaskara developed a formula for approximating the sin of angles. I just used to to calculate the sin of 1pi radians, and the value produced was .840 (vs .841 for my Windows' calculator). Here is an article that includes the formula. At some angles, this approximation can be off by 1.9%, but maybe it could work for your purposes, particularly if you put in some conditionals to correct the calculation for angle ranges where the deviation is greatest.

Hi Blink, Definitively this is another aproach, I'm already tryng the formula with excel, it could be useful to reduce cost and execution time, besides it is easy to implement with regular compilers. Thank you Blink....!