Energy storage capacitor banks supply pulsed power in all manner of high-current applications, including shockless compression and fusion. As the technology behind capacitor banks advances with more precise switching and higher energy density, fast discharge capacitors can reliably support more advanced applications.
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The energy storage capacitors selected for large banks must feature low inductance, high peak current, strong fault tolerance and excellent reliability over their lifespan. When working to specify high energy capacitors, consider the following charge, hold and discharge profile for a capacitor in an RLC circuit (Figure 1).
Figure 1: Hold and discharge profile for a capacitor in an RLC circuit
The following questions address crucial factors that influence capacitor performance, reliability and longevity in high-energy pulse applications. Answering them will help us ensure that you have the right capacitors for your design.
What capacitance and voltage conditions will your high energy capacitors be subjected to?
By definition, the energy stored in a charged capacitor is:
where C is capacitance (F) and V is the charging voltage (V).
There are a few real-world factors that influence the mathematical relationship here. Depending on the charging method, achievable voltage varies. Further, capacitor discharge is never 100 percent efficient. Knowles Precision Devices is prepared to discuss your energy storage goals and help you establish capacitance and charging voltage targets.
What’s your strategy for capacitor charging?
Considering the amount of energy at play, power supply choice is an important design parameter. Regardless of the charging mode (e.g., constant voltage, constant current, constant power or resonant charging), shorter charge time is favorable to avoid prefiring. Figure 1 shows constant current charging time as the first stage in the hold and discharge profile.
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How long do you need the capacitor to hold its charge?
The second stage in the hold and discharge profile, shown in Figure 1, is the hold time. Account for this period in your design process as excessive hold times impact overall safety and reliability.
How quickly must the capacitor bank discharge its energy into the circuit?
Discharge time is determined by RLC circuit parameters, so share as much as you can about the circuit the capacitor bank will discharge into.
What is the expected ringing period, if any?
The damping of the RLC circuit your capacitor bank is discharging into may cause voltage ringing. Share if you have specific design criteria around the ringing period.
What is the expected voltage reversal?
The expected voltage reversal is the reverse peak voltage that occurs during the pulse discharge process of the capacitor. Reversal happens due to the parasitic inductance in the circuit, which causes energy to oscillate between the capacitance and inductance. The oscillation causes a reverse voltage and current to briefly appear across the capacitor, such that it’s measurable at each pulse. Capacitors have different rated tolerances for reverse voltage.
What is the desired shot life?
Shot life, expressed as a percentage of survival probability, indicates the number of charge/discharge cycles that a capacitor can endure before failure. Capacitor lifespan depends on factors like the percentage voltage reversal, ringing frequency, temperature and operating voltage. Knowles Precision Devices offers statistical analyses to understand capacitor survival rates in context.
What is the target pulse repetition rate?
The target pulse repetition rate should be set to achieve a reasonable shot life for the capacitor. In addition to selecting materials with high dielectric strength and low loss, depending on the target rate, specialized cooling methods might be needed for heat dissipation and mechanical reinforcement.
In addition to a thorough understanding of the specs detailed here, it's important to consider your form factor, as it imposes additional size constraints on capacitor selection. We’ll also want to understand your energy density targets and expected operating temperature to contextualize the details above.
Contact us to discuss or read more on pulse discharge.
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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,
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.
KVAR
Kilo ()
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/ 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 kVAR of inductive load and kW 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(kVAr/kW) = 0.707.
Providing the 500kVAR nominal capacitor and keeping the kW the same in the circuit then my power factor is now:
cos(atan((kVAr-500kVAR)/(kW) = 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.
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.
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 s 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.
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 kVA.
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.
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 = 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 = 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.
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.
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:
- 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.
- 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.
- If the the capacitor bank has inrush reactors, include the inductance of the reactor when calculating the overall kvar for the cap bank installation.
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:
- 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.
- 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.
- 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.