Capacitors and phase converters

Delgado's first electric bill after the expansion carried a line Hector had never noticed before: a power factor penalty. The utility's meter showed the shop's demand at 0.75 power factor, and the tariff charged extra below 0.90. Ray proposed a capacitor bank. In the same meeting Hector mentioned a used lathe he had bought from a farm auction that needed three-phase power at his small satellite shop out on Route 9, where only single-phase service was available. That meant a phase converter. Both pieces of equipment have their own short articles in Chapter 4, Article 460 for capacitors and Article 455 for phase converters, and both produce a few reliable exam questions.

This lesson explains power factor and how capacitors correct it, the sizing of capacitor banks in kilovolt-amperes reactive, Article 460 rules for capacitor conductors, protection, disconnecting and discharge, the special case of capacitors connected at a motor, and Article 455 rules for rotary and static phase converters.

Power factor in brief

Induction motors draw two kinds of current: the in-phase current that does useful work, measured in kilowatts, and the magnetizing current that sets up the motor's magnetic field, measured in kilovolt-amperes reactive (kvar). The total current, measured in kilovolt-amperes, is the vector sum of the two. Power factor is the ratio of kilowatts to kilovolt-amperes. A shop full of lightly loaded motors can run at a power factor of 0.70 to 0.80, which means the wiring and the utility's transformers carry more current than the work requires.

A capacitor draws leading reactive current, opposite to the lagging reactive current of a motor. Installed near the motors, it supplies their magnetizing current locally so the utility does not have to. The kilowatts stay the same; the kilovolt-amperes and the current from the utility go down.

Sizing a capacitor bank

The kvar needed to improve the power factor from one value to another comes from the tangents of the two power factor angles. This is a standard exam calculation, and it does not depend on the code; it is basic electrical theory that master exams include.

Capacitor conductors: 460.8

Section 460.8(A) sets the ampacity of capacitor circuit conductors at not less than 135% of the capacitor's rated current. Capacitors carry more current than their rating would suggest because harmonic currents and voltages above nominal increase their current, and capacitors are manufactured with a tolerance that allows somewhat more kvar than marked. For a capacitor connected to a motor circuit, the conductors must also be at least one-third of the ampacity of the motor circuit conductors and not less than 135% of the capacitor current.

Protection, disconnecting and discharge

Section 460.8(B) requires an overcurrent device in each ungrounded conductor of a capacitor bank, with an exception for a capacitor connected on the load side of a motor overload device. The rating or setting is to be as low as practicable. Section 460.8(C) requires a disconnecting means in each ungrounded conductor for each capacitor bank, also with the motor-connected exception, and it must be rated at not less than 135% of the capacitor's rated current. The disconnect must open all ungrounded conductors at once.

Section 460.6 requires capacitors to have a means of discharging stored energy. In general terms, for capacitors of 1,000 volts or less, the residual voltage must be reduced to 50 volts or less within one minute after the capacitor is disconnected. Most capacitors have internal discharge resistors for this purpose. A motor winding connected directly across the capacitor, with no switch between them, also provides a discharge path. This rule is a favorite exam question because the numbers, 50 volts and one minute, are easy to state and easy to confuse with the five-minute value for higher voltages.

Capacitors at the motor

An alternative to a central bank is to connect a small capacitor directly at each motor, on the load side of the motor controller, so the capacitor switches on and off with the motor. This avoids overcorrection when motors are off. Section 460.9 then requires an adjustment to the overload setting, because the capacitor supplies part of the motor's magnetizing current, so the current through the overload relay drops. The overload must be selected based on the improved power factor of the motor circuit, not on the full nameplate current; otherwise the relay would allow the motor to overheat. The capacitor's kvar is also limited so that it does not exceed the value needed to raise the motor's no-load power factor to unity, which prevents self-excitation when the motor coasts down.

Phase converters: Article 455

A phase converter produces three-phase power from a single-phase supply, which lets three-phase motors run where the utility offers only single-phase service. There are two common kinds. A rotary phase converter uses an idler motor to generate the third phase and can run several motors and start them under load. A static phase converter uses capacitors to start a motor and then drops out, leaving the motor running on single phase with reduced capacity; it suits a single motor that starts lightly loaded.

Article 455 covers both. In general terms, 455.6 sets the ampacity of the single-phase supply conductors at not less than 125% of the phase converter's nameplate single-phase input full-load current. Where the converter's nameplate does not list the input current, the section bases the conductors on the three-phase loads served, using a multiplier to convert three-phase current to single-phase input. Section 455.7 requires overcurrent protection for the single-phase supply, 455.8 requires a disconnecting means, and 455.9 requires that single-phase loads connected on the load side of a converter not be connected to the manufactured phase, the phase the converter generates, because its voltage is not stable.

Section 455.9 matters on the Route 9 job because Hector wanted to plug a small 240-volt single-phase grinder into the same three-phase panel. Dana pointed out that it must be connected between the two utility conductors, not to the manufactured phase, and that the manufactured phase must be identified so no one makes that mistake later.

import math

def kvar_needed(kw, pf1, pf2):
    return kw * (math.tan(math.acos(pf1)) - math.tan(math.acos(pf2)))

def amps_3ph(kva, volts=480):
    return kva * 1000 / (math.sqrt(3) * volts)

print("kvar to go from 0.75 to 0.95 at 50 kW:", round(kvar_needed(50, 0.75, 0.95), 1))
print("Current before:", round(amps_3ph(50 / 0.75), 1), "A; after:", round(amps_3ph(50 / 0.95), 1), "A")
cap = amps_3ph(30)
print("30 kvar bank current:", round(cap, 1), "A; conductors and disconnect at 135%:", round(1.35 * cap, 1), "A")
print("Converter supply conductors:", 1.25 * 42, "A")

kvar to go from 0.75 to 0.95 at 50 kW: 27.7
Current before: 80.2 A; after: 63.3 A
30 kvar bank current: 36.1 A; conductors and disconnect at 135%: 48.7 A
Converter supply conductors: 52.5 A

Overcorrection, harmonics and placement

More capacitance is not always better. If a capacitor bank supplies more reactive power than the motors need, the power factor becomes leading, the voltage can rise, and at light load the bank can overcorrect badly. That is one reason central banks are often switched in steps by a controller that watches the power factor, adding or removing stages as motors start and stop. Fixed banks are sized for the base load that is always present.

Capacitors also interact with harmonic currents from drives, electronic ballasts and computers. A capacitor bank and the system's inductance form a resonant circuit, and if the resonance falls near a harmonic produced by the loads, the harmonic currents can be amplified, overheating the capacitors and blowing their fuses. In shops with many drives, engineers use detuned banks with series reactors. Exams rarely test the engineering, but they do test the reason capacitor conductors are sized at 135%: harmonics and overvoltage increase capacitor current.

Where to place the capacitors is a design choice. At the motor, each capacitor switches with its motor and relieves the feeder and branch circuit as well as the utility, but every motor needs its own unit and the overloads must be adjusted. At the panel or service, one bank serves many motors and is easier to maintain, but it does nothing for the branch circuits. Delgado's 30 kvar bank went at the shop's main distribution panel, on its own breaker, because the penalty was a utility charge and the branch circuits were already adequate.