How Can Electrolytic Capacitors work for AC Motor Starting?
Electrolytic capacitors are essentially polar components, and are rated for DV voltages. They cannot sustain reversal of polarity, and a voltage of reverse polarity can damage the capacitor (they are practically a short-circuit in reverse direction), though a very low voltage of say, below 1 V AC for short time may not affect it significantly. Electrolytic capacitors used for rectifier / filter applications do carry an AC component superimposed over DC voltage.
Electrolytic capacitors, as used in rectifier / filter circuits, do appear to carry AC current, like some ripples bypassed through them. However, actual mechanism of current carrying is merely charging and discharging of capacitor electrodes on continuous basis, following the terminal voltage variations. This is seen, by an external observer, as current carried by capacitor.
In case of AC superimposed over DC, overall voltage across capacitor remains essentially DC, and the polarity across capacitor never gets reversed. The AC voltage component could be a sine wave supply frequency voltage, or a ripple voltage consisting of several harmonics. Capacitor value in such cases is kept sufficiently high so as to offer low impedance path to undesired high frequencies. Low frequencies or DC components get passed on to output side of rectifier.

These AC components do have an effect on capacitor by way of dielectric losses (tan delta), which must be kept under permissible limits. It must be kept in mind that losses in electrolytic capacitors are much higher than those in electrostatic capacitors. Manufacturers of electrolytic capacitors often mention permissible ripple content in data sheets. Electrolytic capacitors used for motor start applications for single phase motors are rated with AC voltages. Capacitor start motors have a capacitor connected in series with their auxiliary winding to give a high starting torque to the motor, and the capacitor is not needed once the motor starts. Large value of capacitor is desired for getting a substantial torque, and this could only be effectively achieved by electrolytic capacitors.
Motor start capacitor is effectively a combination of two DC electrolytic capacitors connected back-to-back. They use two anodes (which make one capacitor each with electrolyte), and sometime a separate common cathode. The electrodes coming out of the casing are both de facto anodes, and common cathode is internal to the capacitor. When an external voltage is applied, one capacitor of this series combination is effective and the other (being reverse in polarity) acts as a short-circuit. On reversal of external voltage polarity during the other half cycle, the other capacitor comes into play, while the first one gets reverse polarity and is short-circuited. This process enables the capacitor to effectively carry the AC current. This is how the capacitor carries AC current of motor winding.
Loss factor of this capacitor is very high compared to an electrostatic capacitor – below 3% for a well-designed capacitor. For 230 V Ac motor, 100 μF capacitor at rated voltage gives a current of 7.25 A, and about 1670 VA. At 2% power factor, the watt loss in capacitor can be calculated as 33 Watts, which is very high, and will heat the capacitor extremely fast. Hence it is mandatory to remove the capacitor from service in time once its purpose is served. A centrifugal switch is provided on motor shaft, which disconnects the capacitor once a speed of 70% of nominal speed is achieved. The capacitor thus remains in circuit for about two seconds. It then needs enough cooling time to ensure safe temperature before it can be used in circuit again.
All standards for motor start electrolytic capacitor stipulate a cooling period by specifying the duty of capacitor as 3 seconds ON, followed by 177 seconds OFF period. They sometimes mention this duty cycle as 1.7% duty (1.7% of on/off cycle). The centrifugal switch is a critical component, which must operate reliably to ensure satisfactory and safe operation of motor start capacitor.
In recent years, there has been a development of metallized capacitor made from very thin MPP film in place of electrolytic capacitor. The size is comparable to electrolytic capacitor, and it does away with stringent requirements of electrolytic capacitor, though it is costlier.

Sometimes designers create a non-polarized electrolytic capacitor by physically connecting two DC capacitors back-to-back in a circuit, with diodes in parallel, as shown in figure. The diodes bypass the capacitor in reverse polarity, and one diode is in circuit at a time. This way full value of one capacitor is available all the time. However, this means two separate capacitors, and diodes, requiring large physical size. Specially made non-polarized electrolytic capacitors are available in market for such applications (similar to motor start capacitor construction described above). However, these capacitors, used either say, must remain in circuit for short durations only.