# Calculate the max current for a powerline

#### Raffallo

Hello All!
I'm new in this forum, so if I select wrong subject or something then sorry.
I'm very, very far from physic, so I need your help.
In work, I have to calculate max current for HV power line.
As input have conductor temperature [*C] and material parameters (the resistance in ohm of the conductor at 20 *C, the conductor diameter limited in c, factor of absorption for conductor's surface).
I totally don't know how to calculate it. I've found some mathematical formulas on the internet, but there I need much more parameters which I don't have.
As result, I want to have [W/cm2].

Can someone help me with mathematical formulas and give an example?
In my example I have R20C = 0,0583, temperature = 10 [*C], D = 3.1049999924 [cm], factor of absorption 2,30E-05

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#### PhanthomJay

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I can’t do the calculation without the aid of a computer, but the maximum current that a conductor can handle depends upon the maximum temperature it can support without damage. Current flow in the conductor causes heating. A 3cm diameter bare aluminum conductor for example in 10 degrees C air with a light wind can heat up to as much as 100 degrees C without annealing of if its strands for short term emergency loading with a current of well over 1000 Amps. The actual current in the wire depends upon the magnitude of the load (megawatts, or MVA) it is sourcing.

#### Raffallo

Thank you PhanthomJay!
So if I have the maximum temperature that a conductor can handle how can i calculate the macimum carrent for this parameters that shouldn't be dangerous?

EDIT: I think, that I need a max current in given temperature.
Can someone help me with mathematical formulas of this calculations?

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#### PhanthomJay

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What type of conductor is it? Aluminum, copper, aluminum outer strands with steel inner strands, special conductor? The safe conductor temperature for a continuous AC current using aluminum conductor is about 75 degrees C, higher for short term load. With special hi temperature conductor, you can go much higher, 200 degrees C or more, a lot of current. We need more data like it’s material and type and number of strands.

#### Raffallo

OK, probably I need to start again in other way.
I'm analysing HV power lines and theirs potentially collisions with vegetation.
To calculate these collisions I use temperature, wind, material, and other parameters that affects the line sag and the swing. It works good from years, so we can go to the next step.
Now I need to do simple tool that will calculate max current for the power line when there is no vegetation found. So I iterate through the temperature and drop it for example by 5 *C until the vegetation will be not found. In my example in 10 *C I don't have collisions with vegetation. And now i need to calculate max current in this temperature for this power line. It cannot be for only one material, but for all materials which I have in the data base.

There is any general mathematical formula that I can use for this?
What parameters should I have except those I gave in the first message?
If you would be so kind I will send tomorrow one example set of parameters and ask you to calculate the maximum current to future checking correctness of my calculations.

#### anorlunda

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Usually, only the power company knows or cares about those numbers. I'll assume that you don't work for the power company, because you have to ask how to do these calculations on the Internet. Correct?

Do you work for the vegetation trimming company, and your assignment is to market your services to the power company by calculating how much more power they can transmit if the vegetation is well trimmed. Correct?

Unfortunately, max current is only the tip of the iceberg. The limitations are partially because of temperature, but also stability, and reliability. In addition, most of the power lines never run at max or do so only a few hours out of the year. So the calculation for how much money they might save by trimming is much more complicated than what you are asking about.

However, the ampacity and max temperature, and ohms/km resistance, of a conductor are not numbers we calculate, but rather numbers provided by the manufacturer. The manufacturer might also provide a sample calculation for current-temperature relationship.

There may be formulas to calculate the temperature of a long, un-insulated cylinder in air when given the joules per meter heat generation and the ambient temperature. I don't know that formula, but someone else might.

#### PhanthomJay

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Gold Member
if You know what temp the conductor must be to safely clear the trees, you must know the sag and tension in the conductor. So to clear the ground, you need to be a safe distance above it based on voltage and Codes. It’s probably in the order of 6 to 10 meters depending on voltage. Determine that temperature at that sag and you need a
computer software to calc the current, or use tables, but this is not a one size fits all tabulation, it depends on copper or aluminum, span length, elasticity and thermal coefficients, air temp, sun intensity, wind, and more. And tension...if you can safely increase the wire tension, you decrease the sag. Or you can put in another taller pylon. You have to be clear about what you are trying to do. Your conductor might be able to handle 1000 amps or more if ground clearance is not an issue. And you shouldn’t have tall vegetation greater than a couple of meters anyway. More than once a tree has blacked out millions of customers.

#### Raffallo

@anorlunda Not exactly. I'm working in GIS company, that analyze power lines for clients, including potential collisions with dangerous objects and remarks like a damaged pole. One of the clients wants to know what the maximum current in "safe exercise" can have on each power line that they have. The safe exercise they define like the moment when the collisions to vegetation will not be found in given conditions. So we have a process to detect these collisions and I need to drop temperature until I don't find any vegetation in given conditions.
When I found this temperature I need to calculate the maximum current. I have materials (with parameters provided by the manufacturer) for these powerlines, sag, length, voltage and other geometry parameters which can be helpful.
I found somewhere article (in the attachment at page 3) with formulas to calculate something that I need, but there I need parameters that I don't have, like environment temperature, alpha, and epsilon. I tried to use default parameters for alpha and epsilon, but I still don't have the temperature for the environment, and for this formulas, environment temperature needs to be smaller than the conductor temperature (this is obviously of course).

So I've decided to write in this forum to get some ideas, formulas for these calculations, etc.
I don't know why the client wants this information, but unfortunately, I need to finish it this week.

What formulas can I use for this? Or maybe I need to use tables for it? I can implement tables in the soft if it will be necessary, but I need possible the most universal solution to calculate the maximum current for different materials, voltages, temperatures, etc.

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#### anorlunda

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OK, thank you for clarifying. Doing that on a GIS scale sounds like a challenge. I can't imagine how to model all those tree branches. Branch location? Growth per year? Motion in the wind?

But thanks to that paper you linked, the model is more clear.

Alpha is the change in resistivity as a function of temperature. If the conductors are aluminum, here are the numbers from https://www.engineeringtoolbox.com/resistivity-conductivity-d_418.html

The environment temperature refers to the weather. Use the all time record high temperature for the region. There is an exception. I recall one news report from California of additional sag in lines above a wild fire. Flames also carry ionized gases. I would put a note in my GIS study that fires are not explicitly modeled.

The article mentions the mechanical load due to icing. In some locations, worst case happens on the hottest day of summer. In other locations worst case happens during an ice storm in winter.

The article does not mention sway of the conductors. I find that surprising. Sway during high wind conditions can bring the conductors closer to tree branches.

I think you should clarify with the customers if icing and sway can be excluded from consideration.

But I do not know the numbers for $\epsilon$ and $\delta_B$ in the following. Perhaps other PF members can help with that.

#### Raffallo

This whole article isn't a very good example of my calculations or the whole process of detecting collisions. I just tried to use some similar formulas.
In our soft in the collisions detecting, we have included sway of power lines and icing.
But still, I think that this mathematical formula is bad in my case because I need to calculate the simulated maximum current. I have simulated temperature of the conductor and his material. Like can you read there, there is a requirement that environment temperature must be smallest than conductor temperature, but in my calculations, I don't even have this temperature. To calculate the conductor temperature I include to my detecting the weather parameters as icing, sway, etc. So now, I want to calculate the maximum current with only the material and temperature of the conductor. I'm very weak in physics and things around this subject. I'm just programmer with geodesy title.

I am wondering if there are other designs (and I think that somebody mentioned something in this article) and how to use them in my case.

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#### anorlunda

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Gold Member
have simulated temperature of the conductor and his material. Like can you read there, there is a requirement that environment temperature must be smallest than conductor temperature, but in my calculations, I don't even have this temperature. T
I would interpret that to mean the outdoor temperature. For example, the temperature in Warsaw right now is 24 C. Obviously, conductor temperature must be greater than that. So, worst case sag will happen at the highest outdoor temperature. It appears that the 29C was the highest temperature in Warsaw in the past year.

#### Raffallo

If you have right so then how to calculate conductor temperature from environment temperature?
I'm almost 100% sure that we use temperature of conductor to simulate sag etc.

#### PhanthomJay

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Gold Member

-What is the voltage of the line?

-What is the required clearance of the conductors to the ground for the worst loading case (This value is given by the Code...you don't want the conductors to sag so much that they get too close to a 4 m tall tractor trailer and kills someone).

-What type and material is the conductor? You cannot generalize..every conductor has different characteristics .

-ruling span. .

- conductor tension/sag at a known temperature

Once you have all the parameters, then similar to how you kept lowering the conductor temperature to see where there were ni vegetation contact issues, you now start increasing the temperature to see how hot the conductors can get to have no clearance issues above ground or road, and knowing the conductor temp you can let a computer calculate or at least estimate the current in the conductor (caution: computer analysis always needs a sanity check).

the max current in the line then depends not only on it being low enough to prevent conductor damage thermally (annealing), but it also depends on having proper clearance above ground ( and stability, reliability, acceptable line losses, as anorlunda noted).

#### Raffallo

I have a lot different power lines, sags, materials, and other parameters. That is the biggest problem, that I need to prepare tool to calculate maximum current for given parameters.

Now I have working tool that do what you posted. I change temperature until I don't find vegetation collisions, and now I need to calculate maximum current.
You write about computer calculations or estimations. Can you tell me more about it? Where I can find some formulas for it or something that can guide me?

#### anorlunda

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Gold Member
I change temperature until I don't find vegetation collisions, and now I need to calculate maximum current.
Can you clarify what you mean by collisions? As @PhanthomJay pointed out, there are codes for the minimum distance between conductors to the ground or other objects. The code distance will depend on voltage. When you say collision, that sounds like you are using zero distance.

#### Raffallo

No, no. As collision I mean that in the distance from conductor there is a part of an object. So for an example in distance 5,50m from conductor i have a tree.

#### JBA

While it does not solve your problem Section 2 and Figure 2-4 of the attached document related to your problem related to line current vs solar and air heating may be of interest to you.

#### anorlunda

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Gold Member
One of the clients wants to know what the maximum current in "safe exercise" can have on each power line that they have.
On second thought, I changed my mind. If the client is a power utility, they probably would not accept a calculation protocol from a GIS contractor

The request is backward. They should be telling you how to calculate max current given the clearances you measure by laser. They could ask you to do the detailed calculation for each span, but using calculation procedures they provide.

#### Raffallo

But the proplem is that I have not any formulas :) thats why I've asked here

#### anorlunda

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Gold Member
But the proplem is that I have not any formulas :) thats why I've asked here
Ask the client. The client is more likely to accept the answers if he know where the formulas came from.

The below IEEE Std is one reference standard that addresses your issue, it is available by download for US$129. #### anorlunda Mentor Gold Member The below IEEE Std is one reference standard that addresses your issue, it is available by download for US$129.

That's correct, but it is the customer who should say which standard to use. The GIS contractor should still ask the customer.

JBA

In my opinion,in the Annex B from IEEE 738 it is presented a calculation program in Basic.
https://www.justbasic.com/

"Calculate the max current for a powerline"

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