MainsFrequency2.0

Project MainsFrequency2.0
A simple mains frequency counter
Status	In progress
Contact	bertrik
Last Update	2023-03-16

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

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	Power
OUT	A0	Analog mains waveform, 0..5V

Software

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