Calculate impedance manually - from data samples

[Prototyp_V1.0]

Hi.

Basic calculating of load impedance is fairly easy when familiar to complex numbers as same formulas is used as for a resistive load with no inductive or capacitive elements. But I want help regarding how to calculate momentary value of load impedance when there is a set of meassured samples of voltage and current.

In power grid there is line protection devices. Some of those calculates the impedance in forward direction of the power line, and based on a set of rules, it disconnects if low impedance.

I have seen some demonstration (years ago at school) of the data the devices is collecting, and the device is capable to sample the voltage/current much faster than the main frequency.

So let say - just for the cause of having an example - there is 10ms between each sample. Also I assume there exist avaiable a reference voltage that stay equal to the original voltage phase and amplitude (near perfect sine curve) - but doesn't know if this is neccesary to calculate impedance for each sample. By one sample, I mean all parameters (momentarly voltage and current per phase) that is possible to measure directly is avaiable.

My question goes: What does it takes for me to manually calculate the line load impedance when having, let say 100 samples is stored?

If anybody know this, an example with single phase line/load would be apprechiated.


Thanks in advance

 

[KlausST]

Hi,

You talk about "line protection devices".
They don't need to calculate impedance.
Calculating the current is enough.
Or - even better - the I x I x t integral.

If you really want to calculate impedance:
It is: I_RMS / I_RMS.

Often the mains voltage is very constant...then you don't have to measure/calculate it. Just replace V_RMS with a fixed value.

To measure the RMS value of a signal:
... either you use a dedicated RMS_to_DC IC
or you do it with software. Then you have to take care about nyquist.

Nyquist says your sampling frequency needs to be more than twice the highest input frequency of interest.
For a pure sine signal this means: sample frequency is more than twice of the sine signal frequency.
If your signal is distorted and you are interested in up to 31st overtone, then the sample frequency is more than 2 x 31 x fundamental frequency.
Additionally the samples (timing) need need to be equally distributed over a full wave (or multiple)

Example:
With a 50Hz mains frequency and pure sine wave...it is sufficient to take just three samples with a sample frequency of 150Hz.
Then you get three values: V1, V2, V3.
V_RMS = sqrt( (V1^2 + V2^2 + V3^2) /3)

RMS:
* Root = square root, (sqrt)
* Mean = average, (/3) = divide by sample count
* Square = each input value needs to be squared (^2)

Klaus

 

[CataM]

Klauss told you how to compute the magnitude of the impedance. If you also need the phase, you need to get the power factor out of your samples.

 

[Prototyp_V1.0]

Hi.

I know how to calculate impedance by RMS - but I need a method to calculate the phase angle. I assume it's not just by clocking between zeero crossing for voltage and current because under a fault scenario (short circuit), the curves may derivate quite a bit from a clean sin curve.

KlausST - I have to correct you for this statement: They don't need to calculate impedance. Calculating the current is enough.
Not true - the voltage in a power line may change depending of temperature and load, and therefore it's very important to ensure that the protection device is able to tell if the fault occurs on this line or the line that belongs to the neighbour company.

Therefore I tell the excact reason why I want to do this. It is because I do have access to samples from a less advanced protection device that does not operate with impedance.
The samples comes from this protection device logging function. It was recorded when a coincidence where another protection device in the grid failed.

Therefore this is a perfect work-case to study - and to the end I intend to get the impedance for a failing device so that the other protection unit (the one that fails) can be set up correctly according to expected impedance.

I'll probably import the data set into Excel and therefore I need to manually calculate the impedance.

When I think of this, I could set up Excel in a way that I count numbers of samples between zero cross for voltage and current and therefore being able to update phase angle ideally each 13.5ms pr phase.
But - the weakness is that during a period of failure - I assume that the complex number of impedance will fly all over the scale, snd there will be several false zeero crossing readings that will screw up the calculations.
Therefore I ask if there is a way to calculate impedance without concerning for false zero cross readings.

So having the samples data set - it is fairly easy to calculate the absolute value for impedance for each sample. The challenge is to calculate phase angle too.

 

[KlausST]

Hi,

Honestly...I can't think of what protection device you are talking about.
In our house there are only protection devices that don't measure the voltage.
Can you give a name or a link to a (similar) protection device.

It seems you don't want the impedance like Z = 50 Ohms...you want the complex representation of the impedance.
--> the real part and the imaginary part.

I want to recommend a DFT....but this can only be made with pure sinusoidal voltage waveform....but when I read your posts, then I assume your voltage isn't a pure sinewave.

Klaus

 

[CataM]

Therefore I ask if there is a way to calculate impedance without concerning for false zero cross readings.

Measure or compute the active power as accurate as you can. Then, it is easy to figure out the phase of your impedance.
Besides, I believe this is the most robust way to do it, if there is a fault, you will notice it into the active power and in the aparent power.

 

[Prototyp_V1.0]

Yes - well I can see what I got, once I got to download the data recording from the protection unit.
I may find a way to trick excel - like a bandpass filter for 50HZ to double check for zero crossing. I see I need to read up on digital filters now, that's not my strong side.

 

[FvM]

I feel that the intended characteristic of the impedance measurement and respective protective action should be specified before designing the device. We have heard nothing substantial yet. O.K., it's not our job to design it, but I suppose it would be helpful for you to know what you are actually doing.

Are we talking about 50 Hz impedance? Real component, complex or magnitude only? Response time of the impedance based overload decision? Immunity against rapid variation of reactive and harmonic currents, e.g. switching a compensator unit?

 

[tsan500]

Honestly...I can't think of what protection device you are talking about.

Impedance calculation is used on the distribution network protection and it is often called a distance protection. The relay itself is typically called a distance relay. First links I found on google:
https://electrical-engineering-portal.com/principles-characteristics-distance-protection
This tells the principle of distance protection. Examples of the protection relays,
https://w3.siemens.com/smartgrid/global/en/products-systems-solutions/protection/distance-protection/pages/overview.aspx

 

[FvM]

Impedance calculation is used on the distribution network protection and it is often called a distance protection.

Thanks for explaining the context. Transmission line property of distribution networks is the missing link to understand the operation principle. The math performed in working protection relays is much more complex than suggested in the initial post.