# VOLTMETER - Line to Line Voltage calculation in 3Phase-4Wire system

#### rdd

Joined Nov 6, 2017
8
VOLTMETER - Line to Line Voltage calculation in 3Phase-4Wire system
Hello Dear Members,
I am developing software code for simple VOLTMETER for 3Phase-4Wire system.
Existing Hardware is as per attachment. I am stepping down the Analog AC voltage through 1MOhms resistor. Then as microcontroller ADC can't read -ve voltage so I am shifting the AC voltage on positive side by Potential Divider circuit. As VCC = 5V DC and I am using equal value resistors of 6.81KOhms for Potential Divider, then AC voltage will be shifted by 5/2 = 2.5V DC. Now DC shifted voltage is given to 10-Bit ADC as Analog Input. ADC reads this Input by taking few samples and calculates Line to Neutral voltage by Root-Mean-Square formula accurately.
Another formula is used to calculate Line to Line voltage as,
VRY(L-L) = Square root of ( (VR(L-N))2 + (VY(L-N))2 + ( (VR(L-N)) * (VY(L-N)) ) )

Till here everything is working perfectly. It's displaying R-Y-B (Line to Neutral) and R-Y-B (Line to Line) voltages accurately. Even if different voltages are present in R-Y-B lines also it is calculating both Line to Neutral and Line to Line voltages perfectly.
If only one phase voltage (say R-Ph) is connected between R-terminal & Neutral-terminal then also it is calculating both Line to Neutral and Line to Line voltages perfectly.
The issue is, in Single phase as only one phase voltage (say VRN = 240V) is available and if it is connected to all three Terminals (R-terminal, Y-terminal & B-terminal) [actual Y-Phase & B-Phase voltages are absent in single phase, so it is as good as Y & B terminals are shorted to R-terminal ] then as single phase voltage is given to all three Terminals, Line to Neutral voltages are perfectly calculated (R-N, Y-N & B-N voltages are equal since they are shorted together)
Now in above condition as single phase voltage (L-N = 240V) is given to all three Terminals, Line to Line voltages are Zero as there is no 1200 seperation between the phases so the phase difference is 00. But as per above formula for Line to Line voltage, there is no technique to identify Phase Angle so VOLTMETER is calculating the Line to Line voltages as 415V only. So all three Line to Line voltages (VRY, VYB & VBR ) are calculated as 415V instead of ZERO volt.
I agree that above situation is not a Standard Recommended one as per connection, since for 3-PH 4W System all three phases shall be 1200 apart in Balanced Load. For Single Phase, only R-terminal & Neutral-terminal shall be connected. But in case if we give single phase voltage to all three Terminals then showing 415V is also not correct.
Kindly suggest a technique in software to detect in case of Single phase connected to all three Terminals (R-terminal, Y-terminal & B-terminal), How to calculate & show Line to Line voltages as ZERO.

#### trebla

Joined Jun 29, 2019
489
It is difficult suggest anything without knowning full measuring scematics and software listing (how are MCU-s synchronized).

#### rdd

Joined Nov 6, 2017
8
It is difficult suggest anything without knowning full measuring scematics and software listing (how are MCU-s synchronized).
Thanks trebla for showing interest!
Schematic is very basic & simple as shown in attachment, 240V AC is being step downed to 1.5V AC(approx.) and DC Shifted by 2.5V DC by Potential Divider circuit so AC Peak to Peak voltage(2.5V +/- 1.5V = 1VDC to 4VDC) falls within DC Input range of 10-Bit ADC.
ADC's are perfectly synchronized to take samples from R-PH I/P, Y-PH I/P, & B-PH I/P as all R-Y-B (Line to Neutral) and R-Y-B (Line to Line) voltages are calculated accurately.
Issue is to detect if Single Phase voltage is connected to all three Terminals then R-Y-B (Line to Line) voltages shall be ZERO.

Regards,
RDD

#### trebla

Joined Jun 29, 2019
489
If all line terminals are shorted together, ADC readings are acquired at same time and no differences between ADC input capacitances aren't there then the problem is in your software. How are you calculating voltage results between different lines to get exactly $\sqrt{3}\times (R-N)$ even the lines are shorted together? Without looking at your code i have no glue.

#### MatthiasU

Joined Nov 25, 2020
2
If they're shorted together then obviously they're in phase, i.e. when one is at positive peak the other two will also be positive (same value except for tolerances and timing). If they're connected correctly then whenever one is at positive peak the other two will be negative at ~ 1/2 the voltage, and vice versa.

#### MatthiasU

Joined Nov 25, 2020
2
In other words, you can't determine line-to-line voltage by just measuring single voltages. You also need the phase angles, preferably by timing - to + zero crossings. Then the angle between A and B is (Tab-Taa)/360 and the resulting voltage is (Van-Vbn) * sin(2*angle).

However if I were you I'd not bother with all that, esp as it's just a guesstimate. Instead, just as you calculate the RMS of Vr, Vy and Vb by sampling them multiple times each cycle, you subtract these samples to obtain Vry=Vr-Vy, then calculate the RMS over these samples. If R-Y-B are connected, that calculation obviously yields (almost) zero.