Maximum Radial MVA 5

[Mbrooke]

For all practical purposes, what is the maximum MVA you would design/load anyone line serving radial load? Say you had a radial load pocket of 600MVA-800MVA. Would you use two circuits? Four? Six? Right-of-Way width not an issue.

 

[7anoter4]

I am not sure I understood well the question.
In my opinion it depends on rated voltage and rated circuit breaker current.
If the limit is 4 kA circuit breaker then from 123 kV and up a single line is ok
One OHL of 4 cables of ACSR conductor type RAIL 954,000 kmils 45/7stranded 1005 A each [for instance] [Based on conductor temperature of 75°C; ambient temperature of 25°C; wind velocity of 2 ft/sec; in sun].
If you need a redundant supply line -it depends on circumstances-a 75% of total load each line can withstand the total load for a while.
A one and a half circuit breaker connection are usual.

 

[Mbrooke]

138kv. I can have any breaker up to 4,000 amps.

 

[cuky2000]

Transmission line loadbility is determined by multiple factors. One of the dominant factors is Surge Impedance Loading (SIL). For 138 kV transmission line the SIL_138kV≅ 50MVA. At best, the 138 kV operating in the thermal region can delivery for a short line 150 MW. So for 800 MVA at least 6 parallel overhead circuits and associated ROW and permitting.

For longer distances, a higher number of circuits are needed since the reduction in T. Line transmission capacity will be expected to operate the line in the voltage drop region or more severe in the stability limits zone. An economical analysis is recommended since appears a higher transmission voltage could be more cost-effective. A double circuit line is an option to reduce tower cost and ROW.

For illustration purposes, see the normalized T. Line Loadability curve below.

Hope this helps.

>>>

 

[bacon4life]

Only two circuits seems very unreliable for this much load. In my region, having a 115 kV line use bundled conductor is rare, so it having a 3 or 4 bundle conductor to hit 4000A seems pretty strange. Using 4000A rated equipment will limit your potential number of equipment suppliers, and will require to more complex construction.

Another consideration is the shape of the load profile. If you can perform all planned maintenance during low load seasons, you would not need as many lines as you will if you are likely to have circuits out of service for maintenance during heavy load seasons.

 

[cuky2000]

Another consideration that impacts the number of lines is the redundancy to address contingency events such as the N-1 or N-1-1 reliability criteria. Systems well designed should be able to withstand a sudden trip of one or more lines and allow redistribution of the power flow without creating unacceptable reliability conditions.

Besides using a good engineering practice considering redundancy, agencies may enforce increasing the number of lines. In the US, line reliability should comply with the regional system operator, ISO's, and NERC regarding contingency requirements.

 

[Mbrooke]

Whoa! I've got a lot to learn.

What are the physics behind the steady state stability limitation? Is this due to transformer tap changers boosting to compensate for voltage drop, causing more current draw on the transmission line, leading to more voltage drop, causing more tapping (boosting) and thus more voltage drop in a downward spiral? Or is this the result of a fault causing customer motors to stall leading to voltage depression that the radial load pocket can not recover from?

What do you mean by T in this statement?

For longer distances, a higher number of circuits are needed since the reduction in T.

Surge impedance loading... what are the disadvantages of running a line overs its SIL? 90-95% load power factor? Unity or otherwise obviously I will be drawing extra current to support the lines reactive needs limiting MW transfer.

What if a 138kv line was run at 200-300MW per circuit provided thermal was taken into account? Such as single ACSS conductor (with high temp hardware) or twinned ACSR? Twinned ACSR (like two 1590) would in theory reduce voltage drop?

627 amps seems kind of low, where as 1000-2000 amps just seems "normal" However, of course, physics will have the last say.

4000 amps I agree is impractical now that I think about it.

Line lengths I have in mind are 100 miles and under. However, just for my understanding- what if in the same example above twin conductor is used to limit voltage drop for longer lines?

Thanks for the graph! Do you have a bigger size I can download just for personal education purposes?

 

[Mbrooke]

Also, can you go into more detail about why SIL is one of the dominate factors? Is this because more reactive current is needed from the source to keep the lines magnetic field thus higher loading makes for impractical design ie wasted aluminum?

Also I see you saying 150MVA at 138kv... that would put me at 627 amps of active power... what conductor size are you using? Normally 954, 1272 and 1590 ACSR would be rated above 627 amps sag not factored in.

FWIW, I know of 69kv sub-transmission circuits carrying 1,200 amps.

 

[7anoter4]

It seems to me that the voltage drop of about 800 MVA on a single line of 2.5
miles [138kV] will be 5%, indeed and for 50 MVA 5% voltage drop will be for 45
miles.
A usual OVL of 110-400 kV R1=0.03; X1=0.41-0.25 ohm/km; cap.=10-14 nF/km
If g=length*sqrt[(R1+jX1)*(G+jωC)] Z=sqrt[(R1+jX1)/(G+ jωC)]
X1=0.25 cap=10/10^9 F; G=0
U1=U2*ch(g)+I2*Z*sh(g) U2=138/sqrt(3) and I2=S2/sqrt(3)/138[kA] P.F.0.85

 

[Mbrooke]

What conductor size did you use 7anoter? I don't think 800MVA on a single circuit is wise- but I will sure be thinking about voltage drop regardless.

 

[7anoter4]

I didn't calculate. I took the data from the next table.
In fact 138 is closer to 110 so actually in the calculation
I took R = 0.07 and X = 0.41. I made a mistake when copying here.

 

[Mbrooke]

Thats alright- rough figures are fine. Any idea what conductors those are based off of? I can guess based off an ACSR catalog but don't have one in front of me atm.

Personally, what option would you choose? Right of way is unlimited, double circuit towers in use.

I'm debating either 1,200 amps per circuit or 2,000 amps per circuit. 4000 is officially off the book. Possibly 3,000.

 

[cuky2000]

Mbrook,

Here are some responses to your inquires:

a) Do you have a bigger size: Yes, I will post it later after solving some difficulties downloading a pdf. If there is another way to send you the file, please let me know.

b) What do you mean by T in this statement? T= Transmission

c) Why SIL is one of the dominate factors?  To evaluate transmission line performance, conductor rating ampacity is not enough. For example, a better indicator of a real power transferred in a radial line is P=E_s.E_r/X.Sin(δ). The max. power is achieved if sin(δ)=1 (δ=90o) and also if the receiving end and sending end voltages E_s=E_r. In this case P_SIL = V²/Z_c.
_{An example of the SIL as a useful indicator of the line performance is as follows: 1)Line loaded @ the surge impedance the voltage profile is constant along the line. 2) For load > SIL voltage is reduced at the receiving end and the opposite happens that may require shunt capacitor or reactor compensation for heavy and light load respectively.}

d)What are the physics behind the steady-state stability limitation? A typical T. Line operate in the real world approx.: 35⁰ <δ< 45⁰ limiting the power transfer to approximate to 70% to allow enough margin to withstand any sudden transient distrurbance
_{NOTE: • < 90o stable region. • > 90o & < 135o transient region. • > 135o unstable region.}

e) Twinned ACSR (like two 1590) would in theory reduce voltage drop? what if in the same example above twin conductor is used to limiting voltage drop for longer lines? The economics also should be considered. In many cases is hard to justify the investment of large conductors for a particular load. See also the response below.

f) What conductor size are you using? Normally 954, 1272 and 1590 ACSR would be rated above 627 amps sag not factored in. Considering The function Z_c=k.Ln(D_m/R_b) varies somehow slow in the following range around 360Ω < Zc< 400Ω and 48MW < SIL <54 MW (Ballpark Average ≅50 MW for 138 kV). See the sheet below indicating a rough calc for the three cable scenarios suggested in your post with a couple of tower dimensions that we hope helps with determining the number of lines.

 

[Mbrooke]

You can Email me if you need to- I'll post a link if you ask for it without hesitation.

With that said I am blown away by your response being so detailed and in depth. I would give you another Gold star, but, I am limited to one start per member per thread.

c) Why SIL is one of the dominate factors? To evaluate transmission line performance, conductor rating ampacity is not enough. For example, a better indicator of a real power transferred in a radial line is P=Es.Er/X.Sin(δ). The max. power is achieved if sin(δ)=1 (δ=90o) and also if the receiving end and sending end voltages Es=Er. In this case PSIL = V2/Zc.
An example of the SIL as a useful indicator of the line performance is as follows: 1)Line loaded @ the surge impedance the voltage profile is constant along the line. 2) For load > SIL voltage is reduced at the receiving end and the opposite happens that may require shunt capacitor or reactor compensation for heavy and light load respectively.

As I understand this voltage drop will be worse when loaded above the line's SIL and/or with lagging load power factor. So basic voltage drop equations will not cover this.

Can you give a description of how to calculate voltage drop for lines loaded over SIL at 0.85PF?

Question- why delta (δ) and not phi in these equations? The equations I'm used to revolve around arcoss and phi ie cosine phi for power factor as part of voltage drop:

Ze = R × PF + X L sin[arccos(PF)]

https://www.electronics-tutorials.ws/accircuits/power-triangle.html

also if the receiving end and sending end voltages Es=Er

Are you saying that at SIL loading at unity Power factor, a receiving voltage of say 140,000 volts will result in a load end voltage of 140,000 volts?

And, at loading below SIL, 140,000 volts may rise to 141,000 volts?

d)What are the physics behind the steady-state stability limitation? A typical T. Line operate in the real world approx.: 350 <δ< 450 limiting the power transfer to approximate to 70% to allow enough margin to withstand any sudden transient distrurbance
NOTE: • < 90o stable region. • > 90o & < 135o transient region. • > 135o unstable region.

Noted. But what exactly makes it unstable though- tap changers or voltage that can not recover at the load? Or am I viewing this the wrong way?


Being honest half of this I'm starting to understand- a liken it to RL circuits with shunt capacitors and such. At least thats when I'm envisioning just evenly distributed across a 50-100 mile line.

Just have to get a better handle on the math.

 

[Mbrooke]

Alright- I have an example for practical discussion loosely based off of a real world system.


600MVA load pocket severed by a double circuit tower. 1,255 amps per phase 2156 bluebird, 70 miles from source to load.

Below the 1625 ampacity rating, yet above the SIL. How would you roughly compute voltage drop and in turn stability for this line?

 

[cuky2000]

Many of the questions above are focus on the voltage drop (VD) issue and how this is related to the traditional approach to calculate it.
First, we need to understand the model used for those calculations:
[ul]
[li]-The traditional voltage from the formula is derived from a simple series resistance and reactance circuit.[/li]
[li]-This provides a good approximation for a short line.[/li]
[li]-For medium line length, a Π circuit model provides more accurate results[/li]
[li]-A shunt admittance (Y/2) is introduced modifying the traditional equitation somehow more complex.[/li]
[/ul]
I hope this forum doesn't get tired of illustration. This indicates two circuits (A & B) to model a short line and medium-length lines using the Two-Port Method to determine the associate voltage drop.
An interesting observation to keep in mind is that during the light load scenario, rather than decrease, the receiving end voltage could increase (Ferranti effect) due to the distributed capacitance along the line.
_{It should be noted, that a proper design the line regulation should consider the effect at not load (voltage rise) or at full load (voltage reduction) and switch shunt reactors or capacitors to maintain the receiving end voltage within the ISO window usually ±5% of the nominal system voltage. In any circumstance, the rising voltage should exceed the maximum equipment rating.}

 

[cuky2000]

Let's focus now on the 600 MW transmission. If we could pretend for a minute be in a Utility Planning Department, the first option to suggest is a double circuit at 230 kV OH line to delivery P_total=600 MW considering the following:
[ul]
[li]SIL_pu≅2.4 for 70 miles line length............._{>>>Estimated from the curve above<<<} [/li]
[li]1 pu SIL_230kV=134MW; ............................._{>>>Assumed from table above<<<<}[/li]
[li]∴No Lines=P_total/ (SIL_pu≅2.4 xIL_230kV)=600MW/(2.4x134MW)=1.87≅1-Double circuit line.[/li]
[/ul]
The voltage drop will be within ±5% of the allowable voltage range 218kV< V_operation<242kV
To meet the N-1 reliability criteria, an additional line is required.
[ul]
[li]CONCLUSION: 3 lines are needed at 230 kV[/li]
[li]OPTION: Install a series cap bank capable to deliver 600 MW in the event that the second line became unavailable.[/li]
[/ul]

 

[Mbrooke]

Tired of illustration? Are you kidding me? The more the better. Your pictorials are the best and most professional I've seen to date. You could make macho $$$$$ if you were to make a book out of them.


Regarding all this, let me digest.

But I want to ask- what is wrong with using 138kv for 600MWs? Or does physics not allow it? I can cite some real world applications where this is normal.

 

[Mbrooke]

Can you define short line, medium line and long line in length?

 

[cuky2000]

I'm hoping someone else joining with the question. Here is some of the answer I can think of:

a) What is wrong with using 138kv for 600MWs? b) Does physics not allow it?. If economics and reliability is not an issue, this can be done. However, consider the following indicators:
[ul]
[li]Power Delivery Ratio: 2.6<P_230kV/P_138kV<2.8[/li]
[li]Cost Ratio: of 1.30<$C_230kV/$C_138kV<1.40[/li]
[li]Other Consideration: Substation cost, ROW, O&M cost,licensing & permitting, etc.[/li]
[/ul]

b)Can you define a short line, medium line, and long line in length:
_{This is an arbitrary classification that many years back was driven by simplification of the calculation and perhaps easy to explain in a Power System courses. Today With the availability of computers and software, this classification is less relevant. See the bottom note in the illustration above (highlighted in green) the ABCD parameter with hyperbolic functions is currently used in computer calculation without classifying T. Lines by length.}

Below is a general consensus on how to classify line:
[ul][li] Short: L< 50mi (80 km)................................_{Circuit Model: Resistance and reactance in series}[/li]
[li] Medium: 50mi(80km )<L< 150mi(240km)......_{Circuit Model: Added to (1)lumped shunt capacitance (Π or T configuration)}[/li]
[li]Long: L>150mi(250km).................................._{Circuit Model: Uniform distributive parameters}[/li]
[/ul]