The current in amperes of an oscillatory discharge can be obtained using Equation 3, where V is the peak DC charge level in volts, L is the total inductance of the discharge circuit in henries, C is the capacitance value in farads, R is the total equivalent series resistance of the discharge circuit in ohms, t is time to peak current in seconds, , and m= R/2L.

Equation 3

The magnitude of the first current peak in amperes is given by Equation 4, and the time in seconds to the first current peak can be obtained using Equation 5.

Equation 4

Equation 5

The first current peak will not occur precisely at the first quarter period of the discharge cycle but at a time slightly before. This is the phase angle at which the peak current occurs and is described by the term tan 1 (N/M) in Equation 5. As the ratio of R/L increases the time to the first current peak decreases.

The current frequency in cycles per second at discharge can be obtained by using Equation 6

Equation 6

When R is very significantly smaller than L, the R2/4L2 term may be disregarded.

Voltage reversal (V) during discharge, which is the ratio between the magnitude of the initial voltage peak and the succeeding voltage peak, can be expressed as a percentage using Equation 7.

% V_t - 100exp(-R/4LF)

The application conditions of charge voltage, discharge frequency, voltage reversal and duty cycle, all directly impact energy storage capacitor life.

The life of an energy discharge capacitor is expressed in the number of charge/discharge cycles which can e performed before failure. A failure is generally considered as a drop below the required energy transferred ( usually loss of capacitance), the inability to store energy until required (usually a severe decrease insulation resistance or a short), or an open circuit (usually end connection failure).

Discharge life may be increased by reducing the changing voltage, or by increasing dielectric thickness appropriately. The cost per joule is increased by voltage derating, and energy density is sacrificed by increasing dielectric thickness. By overrating the capacitor dielectric, the cost per joule is decreased but life is decreased.

Alternate means of increasing the ofe of an energy discharge capacitor are: 1) to minimize voltage reversal, 2) decrease the discharge frequency, and 3) reduce the charge time prior to discharge.

The energy discharge capacitor’s life is reduced if the peak discharge current is excessive for the type of end connection and if the duty cycle is increased. Increasing the duty cycle, or repetition rate, reduces life when the temperature rise, due to the resistance of the end connection, and/or the resulting loss inherent to the dielectric system, exceeds the thermal capability of the dielectric.

Graph 3 represents the estimated life as a function of operating temperature and charge voltage of a wax impregnated energy storage capacitor constructed with 9µ Metallized paper and 6µ Plain polyester.

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