Power and energy measurement basic theory and key points

 1) Key point:

Voltage measurement is done in parallel

And Current measurement is done in series.

2) ADC is used for energy measurement:

> Sigma delta is preferred over SAR ADC as; sigma delta provides better accuracy.

> For low frequency high accuracy sigma delta ADC is best choice

> For higher sampling rates let say more than 16kHz, SAR ADC is better.

> Typical range for SAR is 10-12 bits, typical range for sigma delta is 20-24 bits.

> MSP430i2021 is chip with dual channel sigma delta ADC.

3) ADC output depends upon resolution and reference voltage:

https://learn.sparkfun.com/tutorials/analog-to-digital-conversion/all

4) Nyquist criteria:

As per Nyquist criteria your sampling frequency needs to be twice than original signal being sampled to recontract signal properly.

However practical sampling rates are always higher than Nyquist rate.

For example, to measure a 50Hz voltage signal, 4kHz sampling might be used.

5) Harmonics:

Power can be defined in terms of fundamental or total.

Fundamental power is power at 50hz or 60hz , total power consider harmonics as well.

Harmonics are multiple of fundamental waves like 150Hz , 250 Hz. These are odd harmonics.

Note that even harmonics do not have impact on shape of signal. Because impact of positive cycle is cancelled by negative cycle.

Harmonics are also a decisive factor while power calculations.

Odd harmonics change the shape of signal. But even harmonics will not.

Similar way 3^rd harmonics have most impact, then 5^th and further on , going ahead harmonics have lesser and lesser impacts in power calculations.

Presence of harmonics decides quality of power. More harmonics bad quality, less harmonics better quality.

Harmonics are introduced by capacitive and inductive loads.

6) Aliasing effect:

Aliasing is effect, where higher frequency signals overlaps on lower frequency signal. This can occurs in real life like 250Hz signal can appear on 50Hz, 450Hz signal can appear on 250Hz.

It is complecated to understand but you can consider a paper folding phenomenon to understand aliasing effects.

< https://www.youtube.com/watch?v=pAPz5ivJaWk >

7) Anti-aliasing filters:

As we discussed earlier , as we move to higher frequencies in terms harmonics , the effect of those harmonics becomes weaker , so even though there would be higher frequencies falling on fundamental 50Hz, their effect will be lower say 0.0001%.

So basically anit-aliasing filter is a low pass filter ( which blocks any higher frequency ) . Anti-aliasing filter is designed using capacitor and resistors.

A filter has cut-off frequency. Ideal filters have brick wall type response, but practical response have sloppy response.

Filter cut-off frequency is decided based on how many harmonics you want to measure.

8) Filter design basics:

Remember that a capacitor blocks DC signal / low frequency signal and allows high frequency to pass through.

That is why a capacitor is placed across a “full wave rectifier” which provides path to ground for sine waves and we get high quality DC signal.

On other hand, inductor allows to pass DC signal and blocks ac signal.

Here DC can be taken as low frequency and AC can be taken as high frequency.

Here is one popular picture to remember this :-)

At high frequency capacitor act as short and at lower frequency capacitor act as open.

9) Leading and lagging current:

In energy measurement energy is basically power integrated over time and power is basically voltage multiplied with current.

So, between voltage and current you need to select a reference.

Mostly voltage is taken as reference.

So only current leads or lags, not voltage as voltage is reference.

Remember the word CIVIL -> C IV means in capacitive load ( C ) I leads V

                                                    VI L means in inductive load ( L ) I lags V.

Pretty easy haan

 

10)  Doing some FFT :

There are 2 domains in signal processing time domain and frequency domain. The real world is time domain.

Imagine in live music performance, Tabla ( kind of Indian drum ) being low frequency and guitar being high frequency, can you tune your ear to listen them separately ?? not possible right ?

Human ears have a range a of frequency 20 Hz to 20 kHz and we hear that all.

So , time domain is very easy to understand just put time ( t ) on X axis and draw the signal. In time domain "shape" is most important.

Now , frequency domain , as this is frequency domain we are not interested in shape of a signal , but we are interested in which different frequency signals got mixed to generate this shape ???

So in frequency domain we are interested in different individual frequencies and their power values ( amplitude ).

To get these frequencies we do FFT.

There is something called Fourier transform , Discrete Fourier transform in signal processing.

But FFT which is fast Fourier transform that is something we can do in microcontroller, as it works on finite set of sample numbers and not on infinite samples.

FFT is basically multiplying a unit signal of certain frequency with a given signal to check if that signal is present in that signal or not.

If that signal in present we will get value otherwise zero.

11) Voltage , current sine wave formula :

V = Vmax sin ( 2*pi*f*t )

V = Imax sin ( 2*pi*f*t )

Basically “t” decides the shape of signal , everything else is fixed , f, Vmax and Pi.

12 ) Power factor :

As we discussed earlier current mostly leads or lags the voltage based on inductive or capacitive loads.

This difference of angle between voltage and current is phi. If you take cosine it is called power factor.

Power factor is Cos(phi).

13) Current and power factor :

As voltage is our reference, current is  I*cos(phi) .  as it is already shifted with certain factor.

Remember full wave is 2*pi ( 360 ).

Ideal power factor is “1” so phi need to be “0” degree , means voltage is in sync with current.

 

14) Voltage measurement circuitry:

To measure voltage, you need to decrease the voltage to bring in the range of ADC.

There are 2 method to do this: voltage transformer or resistor divider. Voltage transformer provides isolations between input and output. But resistor divider does not offer those isolation.

Most of the cheap multimeter uses register dividers. As voltage transformer is bulky and expensive.

14) Current measurement circuitry:

For current measurement you need to bring current down using a current transformer then use a shunt to convert this current into voltage ( V = IR ) as our ADC only read voltage.

15) Types of Isolations:

if you want to separate your grounds you need to use certain isolations.

Isolations can be either optical or Electromagnetic. Opto isolators are example of optical isolation, a transformer is electromagnetic isolation.

16) Voltage translators:

When one of your device understands one voltage levels and other device understand different voltage levels then you need voltage translators to both can talk.

This are RS232 levels:

Data circuits	Control circuits	Voltage
0 (space)	Asserted	+3 to +15 V
1 (mark)	Deasserted	−15 to −3 V

 

But for TTL levels +5V is logical 1 and 0V is logical 0. So, you need some voltage translator. Max232 is type of voltage translator.

17) Measuring DC voltage:

DC voltage measurement is very is easy you can take multiple samples and take average , the more samples you can better the accuracy.

18) Measuring frequency:

Frequency = 1 / time period. So in AC signal you know your sampling rate i,e time between two samples , then you know total samples between two zero crossing . So you count total number of samples between two zero crossing and calculate time period. Then do reciprocal of time-period this will give you frequency.

19) Calibrating your measurements:

Calibrations are done based on straight line formula, so you calculate 2 factors. offset factors and multiplier factor. Based on linearity of your measuring instruments you might need multiple multiplier factors.

Besides this you might need to calibrate your power factor calculations as well. (power factor calibration is little complex) , you need to read rotation matrix for this :

< https://en.wikipedia.org/wiki/Rotation_matrix >

20) Linearity of measurement:

Linearity depends upon many factors. But resistors are ideally considered linear and transformers have non-linearity in response. Besides this temperature also affects linearity.