Series Capacitor Application 1

[kartracer087]

Hi,

Say that my system voltage is 13,800Y/7,970V.

If one was to connect a capacitor that is nameplate rated 100kVAR 7,970V in series with a 50kVAR unit with nameplate rating of 7,970V, would these two series capacitors be able to provide me with roughly 33.3kVAR per the series capacitor rule? Will the actual kVAR of the series assembly be reduced from the calculated series rating of 33.33kVAR because the voltage across each individual unit is less than nameplate of 7,970V? Not sure how that works.

In this case would it be required to spec one unit at roughly 5,340V and the second unit at roughly 2,630V (this would be the approximate voltage split across each capacitor)? Or can the capacitors both be specified as 7,970V rated and you'll still get roughly the nameplate kVAR out of the series combined units?

Thanks,

 

[kartracer087]

I think this is correct, that specifying the 7,970V units is proper.

So basically the equivalent capacitance of 33kVAR at 7,970V is 1.392uF.

If I take my base voltage of 7,970V and 50 kVAR I get 2.09uF, and similarly if I use a 100kVAR I get 4.18uF.

Series capacitor ratings are like two parallel resistors, so the formula is the same except (C1*C2)/(C1+C2) instead of R1 and R2, thus

(2.09*4.18)/(2.09+4.18) = 1.392uF.

So this is exactly 33kVAR. The total voltage drop across both capacitances amounts to the total kVAR. To maintain the same relationship, this means the voltage across each capacitor is less than rated, hence the reason why the series connection is less. The actual capactance "seen" across each would be:

5,312V across the 50kVAR/7,970V rated capacitor = 22.22kVAR
2,656V across the 100kVAR/7,970V rated capacitor = 11.11kVAR

33.33kVAR total (reactive power across each capacitor sums in series capacitors).

Obviously this entire discussion is considering only one phase connected in wye. The other two phases could be identical for a combined bank rating of 100kVAR in this configuration.

 

[waross]

KVAR
Kilo (1000)
Volt
Amps
Reactive

Without some idea about the load, the Amps drawn by the load and how the load current is affected by the insertion of the series capacitors, your calculations are mostly meaningless.
In your case, KVAR = 1/1000 x ?Volts x ?Amps, as
it is affected by ?X/R ratio of the circuit.
Try using
Resistance of the load in Ohms
Capacitance of the capacitors in Farads
Inductance of the load in Henries

 

[kartracer087]

KVAR
Kilo (1000)
Volt
Amps
Reactive

Without some idea about the load, the Amps drawn by the load and how the load current is affected by the insertion of the series capacitors, your calculations are mostly meaningless.
In your case, KVAR = 1/1000 x ?Volts x ?Amps, as
it is affected by ?X/R ratio of the circuit.
Try using
Resistance of the load in Ohms
Capacitance of the capacitors in Farads
Inductance of the load in Henries

I'm not following?

If a load has say 1000kVAR of inductive load and 1000kW of resistive load and I provide hypothetically say a 500kVAR capacitor, then I'm improving the power factor either way. The original power factor before correction in that case would have been:

cos(atan(1000kVAr/1000kW) = 0.707.

Providing the 500kVAR nominal capacitor and keeping the kW the same in the circuit then my power factor is now:

cos(atan((1000kVAr-500kVAR)/(1000kW) = 0.894.

The capacitor doesn't really care its going to supply the kVAR of load that is needed based on the nominal design voltage. In this case all capacitors are in parallel with the load. Its just some "legs" of the paralleled bank have capacitors which are in series with each other.

Now granted if the system has some voltage drop then yes it won't be able to provide the same amount of kVAR for power factor correction, but in simplistic nominal rating terms, it is as basic as capacitive load is negative inductive load. Which improves the power factor. You also need to consider the type of load if the load is impacted by the supply voltage changes, if it is for example, a constant current load like an EV charger, then the maximum load supplied would vary with voltage since the charger will hold at a maximum the rated current.

My post was mainly to confirm the impact of series capacitors and how their overall ratings will change based on the connection type. So that is to say you can obtain any 'nominal' total kVAR of capacitive power supply by changing the sizes and connection type (series or parallel) of the capacitors. Utilities very often call out banks as kVAR ratings, it is understood that is based on a specific supply voltage.

 

[waross]

I'm not following?

Review the difference between series and parallel.

 

[crshears]

I think I see what's going on . . .

I perceive OP wants to use shunt capacitors to supply local reactive power, but wants to stack the shunt caps in each phase in series pairs in order to divide the phase to ground voltage by two.

And in utility practice this is just how it's done; depending on the voltage ratings of the individual cans, there could be as few as two or as many as five [or more!] tiers of cap cans stacked up in series with each other per phase, which enabled building up caps for nominal phase-to-phase voltage ratings of 14, 28, 46, 115 and 230 kV.

It was quite common on 28 kV cap banks, starting from the neutral point, to see 24 cans in parallel, connected between the neutral point and intermediate red phase bus one, with a second tier of 24 cans stacked in parallel above that, meaning between intermediate red phase busses one and two, with a third tier of 24 cans in parallel placed in series between intermediate red phase bus two and the actual red phase. The design total reactive power output ratings for these cap banks typically ran from 19 to 33 MX; feel free to do the math.

CTs were placed in each of the three phase legs at the neutral point in order that if a cap fuse blew or a can failed internally, a neutral imbalance alarm would be initiated and field crews dispatched to inspect.

Actual series capacitors as used in 345 kV, 500 kV and 765 kV lines will, oddly enough, use a tier of caps in parallel so as to divide up the heavy current flows to more manageable values.

 

[kartracer087]

well this is more for getting specific MVAR ratings out of the bank, basically fine tuning the bank. Standard capacitor sizes limit the bank combinations. Like if you were going to install a 10MVAR bank it could have 17-200kVAR capacitors per phase but that amounts to 10.2MVAR at nominal voltage. Of course with some change in voltage you would see 10MVAR with a very slight reduction.

One utility uses 10MVAR and 20MVAR banks at 13.8kV and I wasn't sure how they develop those ratings using standard rated caps...

Thanks.

 

[crshears]

kartracer087: Of course with some change in voltage you would see 10MVAR with a very slight reduction.

Could be more than slight, since the lagging reactive output of a capacitor or cap bank varies as the square of the applied voltage; we noticed this especially when high voltages occurred, since the in service caps would only serve to aggravate the condition.

So your end goal is to tune a shunt cap to a fairly close tolerance? I certainly didn't get that right out of the gate . . . then again, maybe that's just me . . .

 

[kartracer087]

It might just come down to what they state as an operating voltage. Using identically sized and connected capacitors is preferred in station banks just for simplicity.

 

[crshears]

So why the precise sizing? is the reactive supply you get by using matching caps throughout too granular?

In way of understanding what you might be trying to accomplish, I re-read the relevant portion of the 1940s vintage books I have on electrical engineering, and the general rule of thumb seems at that time to have been to size synchronous condensers so as to obtain approximately 0.9 lagging power factor, since sizing at larger capacity didn't provide sufficient bang for the buck.

Obviously capacitors don't have the same level of capital intensity, but will your site geometry remain so fixed that you are planning to have zero reactive flow at your POCC for quite some time?

More information yields better answers.

 

[kartracer087]

Well more of a question I guess.

The utility they call them 10MVAR and 20MVAR capacitor banks but I think in reality if you were building them in racks since 10 and 20 are not easily divisible numbers considering you have three phases. Something like 10.2MVAR and 20.4MVAR (at nominal voltage of course) would be more easily obtainable given standard capacitor sizes 100, 200, 300, 400, and 500kVAR. When it gets into 3-phase you get into multiples of (1/3) in order to get even numbered banks in groupings of 10's. Its like how single phase transformers are rated 333kVA because a 3-phase bank is 1000kVA.

Its likely they are just referring their 10MVAR and 20MVAR banks as actually 10.2MVAR and 20.4MVAR banks at the nominal voltage. At 99% Voltage 10.2MVAR and 20.4MVAR ends up being 10MVAR and 20MVAR. So they could be considering the bank rating operating at 99% of the nominal capacitor nameplate voltage.

 

[waross]

the general rule of thumb seems at that time to have been to size synchronous condensers so as to obtain approximately 0.9 lagging power factor,

My understanding was that historically, PF penalties kicked in at 90% lagging PF.
Correcting the PF to 90% gave the economic benefit of avoiding the PF penalties.
There was no economic benefit to correcting to above 90%.
Historically, VAR consumption was reported as KVARHrs per month and PF penalties were based on KVARHrs per month.
PF correction was based on calculating additional KVARHrs per month.
eg: One large motor ran 23 Hrs per day, every day.
5 KVAR would correct the PF to 90%.
10 KVAR would be connected and switched with the motor for 10 x 23 x 30 = 6900 KVARHrs per month.
A second larger motor ran two shifts, 5 days per week.
10 KVAR would correct the PF to 90%.
20 KVAR would be corrected and switched with the motor for 20 x 16 x 20 = 6400 KVARHrs per month.
Caps may be added to large customer owned transformers to offset the magnetizing current.
The simple way would be to divide KVARHrs per month by hours per month and use "Bulk Correction".
That could lead to excessively high voltage on the graveyard shift when all that was connected was the capacitor bank and the lighting.
That in turn would lead to frequent lamp burnout.
And, the more lamps that burned out, the higher the voltage may go, leading to.....
Back when PF correction was as much art as science.

 

[waross]

Caps in series:
Example;
Two 10 KVAR caps in series.
Each cap gets 50% voltage.
At 50% voltage, each 10 KVAR cap develops 2.5 KVAR.
So, 20 KVAR connected yields 5 KVAR effective.
Dissimilar caps in series will divide the voltage in the inverse ratio of their KVAR ratings.
KVAR production at reduced voltage will be the square of the ratio of applied voltage over rated voltage.
You do the math.
I worked on a capacitor station inserting capacitors in series with a 500,000 Volt transmission line.
The individual capacitors were rated at 17,000 Volts.
There were banks and banks of series/parallel connected capacitors to get the required Voltage and Current ratings.

 

[kartracer087]

Caps in series:
Example;
Two 10 KVAR caps in series.
Each cap gets 50% voltage.
At 50% voltage, each 10 KVAR cap develops 2.5 KVAR.
So, 20 KVAR connected yields 5 KVAR effective.
Dissimilar caps in series will divide the voltage in the inverse ratio of their KVAR ratings.
KVAR production at reduced voltage will be the square of the ratio of applied voltage over rated voltage.
You do the math.
I worked on a capacitor station inserting capacitors in series with a 500,000 Volt transmission line.
The individual capacitors were rated at 17,000 Volts.
There were banks and banks of series/parallel connected capacitors to get the required Voltage and Current ratings.

Edit - whoops was trying to respond to your first comment

Depends on the utility. The issue becomes loading on the substation at lower power factors. Correcting to close to unity is generally preferred particularly when the transformer will be fully loaded in contingency conditions. The load power factors are more easily obtained because of AMI metering and all feeders are metered fully these days with digital power meters. Estimated power factors for an unknown site can be estimated based on similar customers. Utilities typically use 0.85 to 0.90 range for considering uncorrected load power factor. Depends heavily on the site. Some facilities that have newer equipment (such as chillers) on VFD will have higher displacement power factors due to the drive capacitors. True power factors in those loads are harder to correct for because you need harmonic filtering to do that.

 

[bacon4life]

Keep in mind that IEEE Std 18 call for a tolerance of -0% to +15%. This is a much wider range than most other equipment. Trying to select precise values may lead to problems if future replacements have different actual capacitance. Also, the capacitance of a specific can can change over time.

There are many ways to get round numbers for capacitor banks including:

1. Round/truncate the precise nameplate to a nice number. We have one bank rated 119.25 kV 112.5 MVAR on the detailed schematic, but most documentation refers to it as 112 MVAR.
2. Purchase a capacitor rated a different nominal voltage. For example purchase a 14.4 kV capacitor for operation on a 13.8 kV system. When applied on the 13.8 KV system, a 14.4 kV 100 kvar capacitor it would operate as 13.8 kV 91.8 kvar capacitor. It is common to choose the cap bank voltage to be several percent higher than the system nominal voltage. For the above mentioned 112.5 MVAR cap bank, it is modeled as a 115 kV 104.2 MVAR in our power flow program. On a typical day, it operates more like 106 MVAR @ 116 kV.
3. If the the capacitor bank has inrush reactors, include the inductance of the reactor when calculating the overall kvar for the cap bank installation.

 

[kartracer087]

Keep in mind that IEEE Std 18 call for a tolerance of -0% to +15%. This is a much wider range than most other equipment. Trying to select precise values may lead to problems if future replacements have different actual capacitance. Also, the capacitance of a specific can can change over time.

There are many ways to get round numbers for capacitor banks including:

1. Round/truncate the precise nameplate to a nice number. We have one bank rated 119.25 kV 112.5 MVAR on the detailed schematic, but most documentation refers to it as 112 MVAR.
2. Purchase a capacitor rated a different nominal voltage. For example purchase a 14.4 kV capacitor for operation on a 13.8 kV system. When applied on the 13.8 KV system, a 14.4 kV 100 kvar capacitor it would operate as 13.8 kV 91.8 kvar capacitor. It is common to choose the cap bank voltage to be several percent higher than the system nominal voltage. For the above mentioned 112.5 MVAR cap bank, it is modeled as a 115 kV 104.2 MVAR in our power flow program. On a typical day, it operates more like 106 MVAR @ 116 kV.
3. If the the capacitor bank has inrush reactors, include the inductance of the reactor when calculating the overall kvar for the cap bank installation.

Yeah I agree and I can see how the MVAR ratings change with square of voltage based on the math. The actual supply MVAR really depends on what you define the operating voltage at for the exact kVAR you need out of the system. You are also right that people do like to round numbers a bit. 20.4MVAR ----> 20MVAR and so on. Realistically I think it is preferred to use standard individual capacitor ratings to build a bank like 50, 100, 200, 300, 400, 500, and 600kVAR. I know custom values are available but would likely be more costly and special order.

 

[crshears]

My emphasis was operations, not engineering, and us non-engineers preferred to just round the shunt cap rating to the nearest even whole number. This number was placed on the station operating display immediately next to the symbol for the cap in question so it was always readily known what effect the switching of any particular cap would have.

waross:
I worked on a capacitor station inserting capacitors in series with a 500,000 Volt transmission line.
The individual capacitors were rated at 17,000 Volts.
There were banks and banks of series/parallel connected capacitors to get the required Voltage and Current ratings..

Sounds much like the one I operated; series caps were always shunted with an appropriate breaker while the line was placed on potential, after which the shunting breaker was opened to place the series caps in service. Being series caps, when there was no load on the line and therefore next to zero current, switching the caps in service had no discernible effect.

Closing a shunt breaker while a line was on load, however, caused a pronounced increase in that circuit's impedance, and with both of the circuits in the corridor being paralleled in the switchyards at both ends, a noticeable load shift from the no-caps ckt to the caps i/s circuit could be and was observed.

 

[waross]

As I understand, series caps are used to compensate for line inductive reactance.
The KVARs of both the inductive reactance and the capacitive reactance are current dependant, when they are well balanced, they tend to stay balanced with changes in load current. They reduce the line impedance and thus reduce the line voltage drop.