MainsFrequency2.0

Project MainsFrequency2.0
A simple mains frequency counter
Status	In progress
Contact	bertrik
Last Update	2023-05-30

Introduction

This project is a reboot of this earlier main frequency counter, aiming for more accuracy and lower latency.

It's based on the Arduino platform, using an ESP8266 to do the wifi/network/MQTT stuff. The frequency measurement principle is to measure the time between zero crossings (in a statistically robust way).

Concept

Instead of just counting pulses from zero-crossings, we sample the actual 50 Hz waveform and try to estimate the zero-crossing as accurately as possible.

Desired end result:

• get more accurate frequency measurement, aiming for 1 milli-Hertz accuracy
• get more responsive frequency measurement, i.e. instantaneous value (1 second), not a running average over 50 seconds.

A suitable module for relatively safely sampling the mains voltage is this ZMPT101B module. It contains a transformer and an op-amp circuit.

More information about this module:

• https://www.electroschematics.com/voltage-sensor/

Algorithm for getting accurate instantaneous frequency out of it:

• Sample the mains frequency waveform during approximately one second (say 5 - 10 kHz)
• Determine the median, lower and upper quartiles of the waveform, and shift data so its values are symmetrically around zero
• Calculate zero crossings by doing linear regression to find the zero-crossing of the wave in the region around the zero crossing (in between the quartile values), this gives sub-sample time resolution
• The linear regression runs a kind of state machine, just keeping track of sum(x), sum(y), sum(x*x), sum(x*y) is enough to perform a linear regression at any time
• Do this over the approximately 50 cycles contained in the one second data and determine average frequency

-> this should give about 1 millihertz frequency resolution in one second

Ideas:

• While playing around with an STM32 blue pill, it turned out you might not need a mains power interface at all. A piece of wire picks up ambient 50 Hz already. Typical accuracy of the STM32 clock crystal appears a bit lower than that of the ESP8266, but for visualisation this might not be so important. We don't need the WiFi-functionality of the ESP8266 if just visualizing. This simplifies things: required hardware is just bluepill + piece-of-wire + RGB LED ring.
• A raspberry pi pico appears to be able to satisfy many requirements:
  • Able to sample mains frequency directly from ambient signals on its sensitive A/D input, without the need for a transformer circuit
  • Able to sample a signal with good timing accuracy, it has a crystal better than 30 ppm (0.0015 Hz at 50 Hz)
  • Allows control of a LED ring using FastLED for visualisation (not possible with STM32)
  • Has WiFi support, although a bit iffy on the Arduino platform, for publishing directly to mqtt
  • Relatively inexpensive

Visualisation

There are (at least) the following two ways we can output the data:

• publish frequency as a number over WiFi / MQTT for visualization as a graph-over-time on our grafana server
• idea: directly on a LED ring. The ring shows an integer number (e.g.) of 50 Hz cycles, with the color of the pixel indicating the analog value

Mains waveform ring

Concepts:

• The LED ring shows the raw waveform over time. Position along the ring is time, intensity/color is based on the instantaneous value of the mains voltage. So (for example) three 50 Hz cycles show up as 3 dark spots and 3 light spots around the ring, approximately 120 degrees apart. Basically it shows the phase compared to a reference 50 Hz frequency.
• The LED ring is drawn based on a reference time (derived from the crystal oscillator), assumed to be exactly 50 Hz. A slightly fast mains waveform results in a clockwise rotation of the waveform pattern, a slightly slow mains waveform results in a counter-clockwise rotation of the waveform pattern.
• Use a colourful gradient, not just intensity. Example: https://github.com/FastLED/FastLED/wiki/Gradient-color-palettes

Calculation:

• Mains frequency is nominally 50 Hz, so period is 20 ms (0.02 sec)
• With three waveforms around the ring, the ring represents 60 ms of mains signal
• Intended LED ring has 24 RGB LEDs, so 60ms / 24 LEDs = 2.5 ms per LED. So we could sample the waveform at 400 Hz, and put 1 sample on each LED.
• Example: 16 LED ring -> sample frequency 266.66.. Hz, or sample at 800 Hz and average 3 samples/LED
• Example: 40 LED ring -> sample frequency 666.66.. Hz, or sample at 2000 Hz and average 3 samples/LED
• Example: 45 LED ring -> sample frequency 750 Hz
• Example: 60 LED ring -> sample frequency 1000 Hz

Hardware

For measurement with an ESP8266, like a Wemos D1 mini or nodemcu, you need to put a 180k ohm resistor in line with the output from the ZMPT101B to the A0 input. The A0 input already has a 220k/100k resistive divider, effectively becoming a 400k/100k resistive divider with the series resistor, scaling down the 0-5V range to the 0-1V range required for the ADC on the ESP8266.

The "blue pill" seems to have too low accuracy of the built-in crystal, about 100 ppm, while we need about 20 ppm to get 1 mHz resolution. Notes about blue pill crystal accuracy: https://sparklogic.ru/arduino-for-stm32/accurate-blue-pill-clock-frequency-adjustment.html

Connections

ZMPT101B	Wemos D1 mini	Remark
GND	GND	Ground
VCC	5V	Powers the ZMPT101B from the wemos D1 mini
OUT	A0	Analog mains waveform, 0..5V, 180 kohm resistor in series

Software

Github project: https://github.com/bertrik/MainsFrequency

To flash the esp8266:

• install platformio
• enter the esp8266sampler directory

 cd esp8266sampler

• compile and upload

 pio run -t upload