Arduino UNO project, Power Quality Meter, someone would call it’s PQ Monitor or PQ Analyzer.
I had already published a blog devoted RMS measurements on full band 20 – 20 000 Hz audio signals. ( Following my own style, I’d refer to already published materials whenever it’s possible, to save my time ). This time measurements performed on single AC Power Grid frequency. ( 60 Hz in Canada. Algorithm would works with 50 Hz as well).
Features:
- Graphic LCD display 128×64;
- First 5 harmonics presentation;
- RMS Voltage Indicator;
- Frequency Monitoring;
- THD calculation;
- Internal data up to 63-d !!! harmonics components in Real-Time;
The Holy Grail of this project, is a method of sampling input waveform. As there is only one main frequency (fundamental) at the input, I came up with idea to do a sampling period VARIABLE. There are at least 2 great advantages in this brilliant ( may I ? ) invention:
- It’s completely eliminate necessity of the windowing.
- Only ONE period of input waveform is enough for precise calculation.
First of all, windowing is really BAD on metrological side (for accuracy of results), smashing one single frequency bin to over 3 – 5 of it’s neighbors, significantly deteriorating input sensitivity, and plus it’s not able to eliminate limits discontinuity effects well – only attenuate them. Secondly, from software timing performance point of view, introducing windowing in the Real-Time application would automatically require to DOUBLE data throughput, as Overlap – Add procedure would be mandatory.
In it’s essence, I created a software PLL (Phase Lock Loop). Compare to a project with hardware based PLL (IC 74HC4046), no need for external chip this time. Engine is running on Timer1 features – CTC mode and capability to drive ADC Auto trigger. I will go into details in software section.
Hardware.
As you can see on the drawings, circuitry is quite simple, one LCD ( I used SparkFun LCD-00710, could be different ) and one IC, LM311 – comparator. Pay attention, that GEDA doesn’t have a library for such display, all details on LCD configuration, pin numbering etc you can find here. I haven’t experienced any difficulties with assembling LCD, except soldering bunch of wires and installing control brightness level pot. Thanks author of the GLCD library (great work!), there was no any troubles with software also.
Transformer is doing galvanic isolation, as they say – safety first! There is no part number ( requirements ), anything with primary windings for your local AC main ( 110V, 220V ) and about 10 V on secondary will be o’k. Values of the resistive voltage divider ( 22k and 2 x 4.7k ) may be adjusted proportionally for transformer with different secondary voltage output. Trick is to keep voltage level close to ~2V AC peak value at the arduino analog input # 5. There are two caps 2200 pF to filter out RF interference, and one trim pot to adjust comparators threshold ( not strictly necessary, you can replace with constant two resistors voltage divider ). Good decoupling of the +5V power lines should be done if LCD installed on the same board (as I did), otherwise, arduino goes crazy when it’s received a basket of interrupts on pin 2 (INT0).
SOFTWARE.
I’ve read an article in December’s issue of the Elektor magazine, that actually inspired me on this project. Even I had such idea in my mind for quite awhile, nevertheless Elektor’s publication accelerate this process. Do you still remember I called my method “brilliant”? And this is why: compare to project published in well known and respectful electronics magazine, my code is running 140 !!! TIMES faster ( compare 5 milliseconds to 700 milliseconds competitors ). I didn’t tweak any optimization. My software is running REAL-TIME in each AC period, keeping load of the microprocessor below 30 %. It’s capable to do a Real-Time monitoring of three phase power line. The only things which is slow down process, is LCD display refreshment. In current version, algorithm averages data over 32 cycles before outputs summary data report on the display, around 0.53 seconds period ( 1 / 60 / 32). During update display procedure (23 milliseconds or so) which is longer than 16.66 milliseconds period of the AC 60 Hz, one cycle is skipped. Depends on application, the task of updating screen could be split over many sub-frames, so instead of one big chunk of code, 32 smaller size chunks will go unnoticeable in background, fixing an issue of 33-rd lost frame. But I don’t think it’s necessary for monitoring purposes, may be only in Power Energy Meter project? I just can’t imagine, Elektor’s 2100 milliseconds overall time per cycle, when everything could be done in less than 7 milliseconds ( using split display subroutine ). It’s 300 times difference!.
THE MAGIC.
Software PLL / FLL – Frequency Lock Loop is build on TIMER1 VCO. Well, it’s not quite correct to call it VCO, probably FCO – Frequency Controlled Oscillator. Software adjusts oscillator in such a way, that number of captured samples per one AC waveform has to be exactly 128 . Look here:
if ( smpl_Nmbr > FFT_SIZE ) smpl_Time++;
if ( smpl_Nmbr < FFT_SIZE ) smpl_Time–;
OCR1A = smpl_Time;
OCR1B = smpl_Time;
If during one AC period ( 1 / 60 Hz = 16.66 milliseconds ) timer restarts more often than necessary (FFT_SIZE = 128), smpl_Time variable increasing, so TIMER1 FCO slow down. In opposite case, smpl_Time is decreasing, forcing clock to run faster. Track on quantity of captured samples goes as usual, via indexing input array variable – smpl_Nmbr, which increments every ADC “start conversion” event, triggered via channel B:
ISR(TIMER1_COMPB_vect)
{
if ( smpl_Nmbr < FFT_SIZE )
{
x_r[smpl_Nmbr] = ADC – adc_Offst; //
}
smpl_Nmbr++;
}
( Paralleling Timers two channel A and B was invented here.) The comparators main duty is to trigger digital pin 2 (INT0) exactly in the same point in time, relatively to input signal periodicity. Not necessary at zero. Synchronization point could be at any voltage level on the input waveform, it’s has nothing to do with zero-crossing. As software calculates complete FFT subroutine, for both REAL and IMAGINARY part (btw, referring link) , adjusting point (via pot) to exactly zero-cross simply push all energy in imaginary part (sine). Bringing this point to 45 degree would splits energy equally between real and imaginary parts. Later on, extracting square root from sum of two squares ( magnitude calculation ) simply annihilate any difference, magnitude is not changing with moving synchronization point up and down at all.
DC offset is adjusted in every cycle based on REAL (cosine) bin-0 magnitude:
temp = f_r[0];
if ( temp > 0 )
adc_Offst++;
if ( temp < 0 )
adc_Offst–;
Rolling Filter, the easiest one to implement and understand, and very efficient against spikes.
Arduino UNO sketch: download.
To be continue….
6 January, 2013.
I did some “resource management” in software, because data calculation in each cycle of AC waveform is not really necessary. Let me explain. There are 3 major hardware limits :
- ADC resolution
- Memory size / CPU performance
- Update Rate
In first version, calculation of harmonics magnitude content goes up to 63-rd. But as resolution of the Arduino ADC limited by 10-bits ( 9 plus sign ) it doesn’t make much sense for real world electrical grid, simply because magnitude starting from 5-th harmonics drops below noise floor – 6.02 x 9 + 1.76 = 55.94 dB (0.16%) There are two way to solved this issue: increase the FFT size, or use oversampling technics. First method is not possible due memory limits. Second one makes update rate too low for practical use.
In this software release, I limit calculation to first 7 harmonics, and show all of them on display (see photo). FFT size is the same, 128. But sampling clock running 8 times lower, so 8 AC cycles necessary to fill up input array with new data. Method – oversampling in time domain. It gives 3-bit gain in resolution, same as have 12-bit ADC, overall dynamic range 6.02 x 12 + 1.76 = 74 dB. (0.02%)
Version 2: download.
