Lifetime calculation of Electrolytic Capacitors

On the process of making new inverter/converter products, we are talking about what type of topology will be used, power losses and cost estimation. It is easy to forgot about the Lifetime of capacitors. This article is quick note how to estimate lifetime of electrolytic capacitor (elcap) provided by JIANGHAI ¹. Other manufactures may have different ways to estimate lifetime of these capacitors. Please look up manufacturer application note for more detail.

Lifetime model

The lifetime $L$ of the electrolytic capacitor can be estimated by using numerical lifetime model:

$$ L = L_0 \cdot K_T \cdot K_R \cdot K_V $$

where

• $L_0$ is specified lifetime from the datasheet of given capacitor at norminal ripple.
• $K_T$ temperature factor (ambient temperature)
• $K_R$ ripple current factor (self-heating)
• $K_V$ voltage factor (operating voltage)

Temperature factor

Temperature factor $K_T$ can be calculated based on "10-Kelvin-rule" that is: a drop of the ambient temperature by $10K$ double the lifetime of capacitor.

$$ K_T = 2^{\cfrac {T_O - T_A}{10K}} $$

Where

• $T_0$ rated temperature
• $T_A$ ambient temperature

Ripple current factor

Ripple current factor $K_R$ is calculated as following.

$$ K_R = K_i^{A \cdot \cfrac{\Delta T_0}{10K}} $$

where

• $A = 1 - (\frac{I_A}{I_R})^2$
• $I_A$ ripple current in the application
• $I_R$ rated ripple current
• $\Delta T_0$ core temperature increase of the elcap
  • $T_0=105 ^{\circ}C$ typ. 3.5~5K
  • $T_0 = 85 ^\circ C$ typ. 3.5~10K
• $K_i$ empirical safety factor
  • $T_0=105 ^{\circ}C$ if ($I>I_R$) then $K_i = 4$ else $K_i = 2$
  • $T_0 = 85 ^\circ C \rightarrow K_i = 2$

Voltage factor

There are two cases need to take into account when calculate voltage factor $K_V$.

If $0.6 \le \cfrac{U_A}{U_R} \le 1$ then $$ K_V = \left( \cfrac{U_A}{U_R} \right) ^{-2.5} $$ else $$ K_V = 3.59 $$

where

• $U_R$ rated voltage
• $U_A$ actual operating voltage

References