The kvar is the easy part: sizing a capacitor bank in calculator #005

Power factor correction looks like the easiest calculation in the building: one formula, one number, order the bank. The formula really is easy — and it is not where capacitor banks get into trouble. They get into trouble at minimum load, during a large load rejection, and on a network with harmonics, all of which happen after the kvar figure has been signed off. This guide runs a real plant through calculator #005 and shows what the tool checks after the sizing is done.

What the tool does

Five things, in this order:

1. Sizing — required kvar from your load list, per load or combined, with simultaneity;
2. Step selection — a step sequence that reaches the target without overshooting, with the current per step and the control resolution;
3. Screening for the three failure modes — harmonic and resonance risk, overcompensation at minimum load, and overcompensation after a load rejection;
4. Equipment consequences — capacitor unit rating, design current, incoming device and cable, heat losses and enclosure duty;
5. Deliverables — a manufacturer-neutral specification, a step schedule, an engineering-review text and a Word report.

The standards it works to are the ones a purchaser actually cites: IEC 60831-1/-2 for the capacitor units, IEC 61921 for the low-voltage power factor correction bank, IEC 61439 for the assembly and IEC 61000 / IEEE 519 as the harmonic context.

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FREE and PRO: where the line runs

The calculator opens on two tabs, and the split is worth understanding before you start, because it follows the structure of the work rather than a page count.

FREE — open access, no account:

• project settings and basic network data;
• the load list, per load or combined, with simultaneity;
• the required kvar and the equipment options — the sizing itself;
• the calculation summary and the engineering visuals;
• the input-completeness matrix, which tells you what data is still missing before the result can be trusted.

In other words, the whole of Step 1 above is free: enter the loads, get 363,6 kvar, see what cos φ becomes, and read which inputs are still assumptions.

PRO — the checks that turn a number into a design:

• step bank optimisation — the step sequence, control resolution, cumulative current per step;
• minimum-load overcompensation check (Trap 2 below);
• large load rejection and controller-state simulation (Trap 3);
• voltage-rise risk and harmonic / resonance screening (Trap 1);
• compensation technology selection — standard bank against detuned, thyristor-switched or SVG/STATCOM, ranked;
• multi-option engineering comparison with scoring across kvar accuracy, control, low-load behaviour, rejection behaviour and harmonics;
• load profile and step response simulation across the load range;
• automatic protection and cable preselection, plus the heat-loss and enclosure inputs;
• manufacturer-neutral specification and issue lists;
• economic assessment against the tariff model;
• equipment database and model suggestions;
• the Word report and the equipment/step schedule export.

The PRO controls are visible but inert without a licence — deliberately, so you can see exactly what the tab does before paying for it, instead of guessing from a feature list. Everything in the worked example below that is marked (PRO) comes from that tab; the sizing itself does not.

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Worked example: a bottling plant on a 1 600 kVA transformer

400 V, 50 Hz, fed from a 1 600 kVA transformer at u_k = 6 %. Three load groups, all running together:

Measured distortion at the incomer: THD_i = 18 %, THD_v = 5 %, dominant orders 5, 7, 11. Minimum plant load 120 kW at 0,82. Target power factor 0,95 lagging.

Step 1 — the kvar, and the hand check

Q1 = 450 x tan(acos 0,78) = 450 x 0,8025 = 361,1 kvar
Q2 = 300 x tan(acos 0,82) = 300 x 0,6982 = 209,5 kvar
Q3 = 150 x tan(acos 0,86) = 150 x 0,5934 =  89,0 kvar

P  = 900,0 kW ;  Q = 659,4 kvar ;  S = 1 115,7 kVA
cos phi_1 = 900 / 1 115,7 = 0,807

Q_target = P tan(acos 0,95) = 900 x 0,3287 = 295,8 kvar
Q_c      = 659,4 - 295,8   = 363,6 kvar

The calculator returns 363,6 kvar required on the free tab, and — on PRO — proposes 400 kvar in 8 × 50 kvar steps — 72,2 A per step, 577,4 A at full bank. Both agree with the hand calculation to the last digit, because it is the same arithmetic:

I_step = 50 000 / (sqrt(3) x 400) = 72,2 A
I_bank = 400 000 / (sqrt(3) x 400) = 577,4 A

Step 2 — the nameplate is not the bank rating

This is where the first real mistake is usually made. The capacitor units are specified at 525 V on a 400 V system — standard practice, because it protects the dielectric against overvoltage and harmonic stress. A capacitor delivers reactive power proportional to the square of the applied voltage, so a unit that is rated 525 V delivers far less on a 400 V bus:

Q_delivered = Q_nameplate x (U_system / U_rated)^2
689 kvar nameplate x (400 / 525)^2 = 400 kvar delivered

The tool states it explicitly on the PRO step-bank panel: 400 kvar delivered at 400 V corresponds to about 689 kvar of capacitor-unit nameplate duty. The physics applies on any tier — the difference is whether the number is printed for you or you convert it yourself. Order "400 kvar of 525 V capacitors" and you get roughly 232 kvar of correction — a 42 % shortfall that will be blamed on the calculation.

Step 3 — the current the switchgear must carry (PRO)

IEC 60831-1:2014, Clause 21 is unambiguous:

Capacitor units shall be suitable for continuous operation at an r.m.s. line current of 1,3 times the current that occurs at rated sinusoidal voltage and rated frequency, excluding transients. Taking into account the capacitance tolerances of 1,1 C_N, the maximum current can reach 1,43 I_N.

The calculator's design-current factor is an input, and it defaults to 1,30:

400 kvar bank:  I_N = 577,4 A
                x 1,30 = 750,6 A     (harmonics + overvoltage)
                x 1,43 = 825,6 A     (+ capacitance tolerance 1,1 C_N)

That is the difference between an 800 A device and a 1 000 A one, and between one 400 mm² cable and something larger. Set the factor to 1,43 if your specification follows the standard's worst case — the field is there precisely so the assumption is visible rather than buried.

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The three traps the sizing formula cannot see

Trap 1 — harmonics and resonance (PRO)

The bank and the supply transformer form a parallel resonant circuit. The screening order is:

h_res = sqrt(S_cc / Q_c)

S_cc = 1 600 kVA / 0,06 = 26,67 MVA
h_res = sqrt(26 667 / 400) = 8,17     (selected bank)
h_res = sqrt(26 667 / 363,6) = 8,56   (required bank)

The screening says no dominant harmonic sits near order 8, and the tool still refuses to call the design safe: with THD_i = 18 % it returns "high harmonic review priority" for a plain bank. That combination is the honest answer — resonance is not the only harmonic problem. A capacitor is a low impedance at high frequency, so it will attract harmonic current from the plant's drives whether or not it resonates, and the units carry that current on top of their fundamental duty.

The usual answer is a detuned reactor. Switch to 7 %, and the tuning frequency appears:

f_r = f / sqrt(p) = 50 / sqrt(0,07) = 189 Hz  ->  order 3,78
U_cap = U / (1 - p) = 400 / 0,93 = 430 V at the capacitor terminals

Tuned to 3,78 — below the lowest dominant harmonic (the 5th) — so the circuit can no longer resonate at 5, 7 or 11; it presents an inductive impedance there instead. Two consequences the calculator makes visible:

• the capacitors now sit at 430 V instead of 400 V, which is exactly why 525 V units were specified in the first place;
• the reactor dissipates. Heat in the enclosure goes from 200 W to about 3 400 W for this bank — an air-conditioning and IP-rating problem that the kvar formula never mentions.

Trap 2 — minimum load (PRO)

At night the plant drops to 120 kW at 0,82:

Q_min = 120 x tan(acos 0,82) = 83,8 kvar
first step = 50 kvar  ->  net Q = 33,8 kvar
cos phi = 120 / sqrt(120^2 + 33,8^2) = 0,963 lagging

It passes, and it passes because the step is 50 kvar. Had the design used 100 kvar steps, the first step alone would have pushed the plant into leading power factor at minimum load — the classic cause of nuisance tripping, controller hunting and utility penalties for leading kvar. The smallest step, not the total kvar, is what protects the plant at night.

Trap 3 — load rejection (PRO)

The one that damages equipment. The plant is running at 810 kW when 650 kW of process load trips off in one event. What remains is 160 kW at 0,82 — and up to 400 kvar of capacitors that the controller has not yet dropped:

Q_remaining = 160 x tan(acos 0,82) = 111,7 kvar
net Q = 111,7 - 400 = -288,3 kvar (capacitive)
cos phi = 160 / sqrt(160^2 + 288,3^2) = 0,485 leading

0,485 leading. For the seconds until the controller sheds steps — the OFF delay in this design is 10 s — the busbar sits with a large capacitive surplus, the voltage rises, and every motor and electronic supply on that board rides it out. The calculator runs the scenario for several credible pre-event states (one step, two steps, three steps, the controller's own target, the full bank) rather than one optimistic case, because the question is not "what was connected" but "what could plausibly have been connected".

The fixes are design decisions, not settings: smaller steps, a faster OFF delay, an interlock that dumps the bank on the trip signal, or dynamic compensation (thyristor-switched or an SVG) where the load profile is genuinely violent.

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What comes out at the end

A manufacturer-neutral specification you can put into an enquiry — rating, step arrangement, capacitor rated voltage, controller behaviour, CT ratio and location, discharge and reconnection timing, and the harmonic requirement — plus a step schedule, an engineering-review text and a Word report.

Check it against what IEC 61921 requires on the rating plate: rating of steps in kvar, the value of the series reactor (reactance ratio in % or tuning frequency), minimum and maximum ambient temperature, degree of protection, rated short-time withstand current I_cw, rated conditional short-circuit current I_cc where applicable, and the maximum permissible current. If your enquiry does not ask for those, the offers you receive will not be comparable.

Where this sits next to the other tools

• #002 Short-Circuit gives the short-circuit power at the connection point — the S_cc that sets the resonance order and the withstand rating of the panel.
• #004 Cable Ampacity sizes the feeder for the design current, which for a capacitor circuit is 1,3 to 1,43 times rated, not the rated current.
• Grid Tools runs the same power-factor correction study over a whole network when the compensation is distributed across several boards rather than sitting at one incomer.

The short version

The kvar figure is the part of this calculation that cannot go wrong: it is one line of trigonometry, and you can check it in your head. Everything that actually destroys capacitor banks — resonance with the supply transformer, leading power factor at minimum load, a capacitive surplus after a large trip, a nameplate confused with a delivered rating, a switchgear frame chosen for I_N instead of 1,43 I_N — sits in the checks that come after it.

Open calculator #005 →