Article Highlights

Capacitor life is exponentially related to temperature and linearly related to voltage.

Capacitor temperature is surprisingly high in industrial environments when we consider elevated enclosure temperatures as well as selfheating due to ripple current.

The rule of 10 is a simplistic model for determining the longevity of electronics. Each 10°C increase in temperature reduces the life by a factor of 2. More sophisticated models account for voltage, ripple current, and even airflow.
Introduction
The operational lifetime of an aluminum electrolytic capacitor is directly related to temperature. This brief presents a simplified method of calculating a capacitor’s operational life based on temperature and operating voltage. The capacitor’s actual life may vary significantly, as this model does not account for high ripple current, voltage surges, and care of the capacitor, such as proper reforming (or lack thereof) after an extended storage time. Figure 1 shows an image of a type 550C Cornell Dubilier Knowles aluminum electrolytic capacitor. We will estimate the operational life of this 5400 uF 500 VDC 550C542T500DN2B assuming the capacitor is installed in a motor drive in a hot industrial environment.
The equation presented in this brief is derived from the work of Sam G. Parler, Jr. and Laird L. Macomber in their Cornell Dubilier paper Predicting Operating Temperature and Expected Lifetime of AluminumElectrolytic Bus Capacitors. For brevity and clarity, we will simplify the equation. For an improved model please refer to Cornell Dubilier’s Thermal / Life Calculators.
Figure 1: Image of a Cornell Dubilier Knowles series 550C capacitor designed for long life in motor drive applications.
Tech Tip: Component failure rates are an application of statistics. They cannot be used to predict the date or time of failure for a specific electrical device. Refer to the U.S. DOD MILHDBK217 (Military Handbook) Reliability Prediction of Electronic Equipment for an introduction to Mean Time Between Failures (MTBF).
Lifetime estimate using the rule of 10
As a starting point we could simply say that the operational life of a capacitor is doubled for every 10°C reduction in temperature. For argument’s sake, let’s assume we carefully followed the VFD’s OEM recommendations and allow the equipment enclosure to reach the upper “acceptable” limit of 40°C. Furthermore, let’s assume the capacitor’s temperature is elevated an additional 35°C to account for the proximity to the IGBTs and heat generated by ripple currents. For those keeping track, the capacitor is not particularly happy living in a 75°C (167°F) sauna.
Tech Tip: The ripple current heating for the DC link capacitor is an estimate. Please see the Cornell Dubilier Knowles literature for an improved model that properly accounts for the heat generated by the ripple current and related harmonics. There is likely a superpositionlike element where the heat generated by each harmonic contributes to the overall temperature increase.
Our example capacitor as pictured in Figure 1 is rated for 10,000 hours at 105°C. Subtracting 75 from 105 we find three 10°C reductions. The capacitor should therefor live for three doublings multiplied by 10,000 hours. This equals 2 x 2 x 2 x 10,000, which equates to approximately 9 years.
Background for the rule of 10
The rule of 10 is related to the Arrhenius equation. Without getting into specifics, the equation implies that an exponential temperaturedependent chemical process is taking place inside the capacitor.
With increased mathematical rigor, our rule of 10 becomes:
Life \approx L_B 2^{\frac{T_B – T_A }{10}}
Where:

L_B is the base lifetime from the datasheet

T_B is the base temperature from the datasheet

T_A is the actual estimated internal temperature of the capacitor accounting for the can temperature and internal heating due to ripple current
The results are the same for our example capacitor:
Life \approx 10,000 * 2^{\frac{105 – 75 }{10}}
Life \approx 80,000 \ hours \approx 9 \ years
Refinement for applied voltage
The previous section implied that capacitor degradation is related to a chemical equation that takes place over a long period of time. It stands to reason that voltage will impact the speed at which this degradation takes place. This is another way of saying that things will last longer when operated well within the design limits. We can expect a cool capacitor with a low ripple current, and a low applied voltage to last longer than one operated at the design limits.
We can refine the previous equation with a multiplier that addresses the applied voltage as:
Life \approx M_V * L_B * 2^{\frac{T_B – T_A }{10}}
Where:

L_B is the base lifetime from the datasheet

T_B is the base temperature from the datasheet

T_A is the actual estimated internal temperature of the capacitor accounting for the can
*M_V is the voltage multiplier, calculated as 4.3 – 3.3(\frac{V_A}{V_B}), where V_A is the applied voltage and V_B is the base rated voltage from the datasheet.
Using our previous example, suppose the capacitor operates with a nominal 400 VDC. Since this is less than the rated 450 VDC we can expect the capacitor to have a slightly longer life. The equations suggests a lifetime of approximately 12 years.
M_V = 4.3 \  \ 3.3 (\frac{400}{450}) = 1.37
Life \approx 1.37 * 10,000 * 2^{\frac{105 – 75 }{10}}
Life \approx 12 \ years
Refinement for ripple current
Up to this point we have assumed that ripple current will result in capacitor selfheating. In the previous example, we assumed an “additional 35°C to account for the proximity to the IGBTs and heat generated by ripple currents.”
Ripple Current Multipliers
Ripple current can have a profound impact on capacitor longevity. We can use the datasheet’s rated ripple current to better understand the relationship by looking at the operation limits for a given design maximum ripple current.
A capacitor such as the featured 550C Cornell Dubilier Knowles is often used in a DC link capacitor in motor driver application. In a singlephase system, the capacitor will be subject to a 120 Hz current ripple. In a threephase system, the ripple current will be 360 Hz (full wave rectification assumed in both cases). We can refine the life expectancy using a threestep process:

Determine the multiplier: The datasheet for the type 550C Cornell Dubilier presents a ripple current multiplier of 1.0 for a 120 Hz system and 1.31 for a 360 Hz system as highlighted in Figure 2.

Retrieve the maximum ripple current from the datasheet. The 550C542T500DN2B is rated for 20.9 A at 120 Hz at 85°C.

Interpret the chart: Figure 3 shows the expected operating life for a capacitor as a function of temperature and rated ripple using the multipliers we located in step 1.
If we continue with our 75°C scenario, we see that the capacitor will not last long if subjected to the 20.9 A ripple current. As indicated by the green dots on Figure 3, we can expect 3.4 years in a 120 Hz system, or just over a year on a 360 Hz system. Obviously, we do not want to run the capacitor with elevated temperatures with high ripple currents.
Figure 2: Ripple Current Multiplier for the type 550C Cornell Dubilier.
Figure 3: Capacitor life expectance as a function of temperature and the rated ripplecurrent multiple. The green dots are associate with 120 Hz and 360 Hz operation at 75°C for the featured capacitor.
Tech Tip: The data from Figures 2 and 3 converge to the rated specifications for the capacitor when we consider temperature, ripple current, physical orientation, balanced current between any capacitor pairs, and airflow. According to the datasheet, “Type 550C is rated for 20,000 h life with full ripple current, rated voltage, 85°C and 100 lfm airflow while mounted horizontally. Horizontal mounting is more severe than vertical mounting.”
Refinement for ripple current
Recall that we used a voltage multiplier to refine the capacitor’s life expectancy when operating at reduced voltage. We can perform a similar operation by incorporating a ripple current multiplier.
At this point we need to stop and acknowledge that we have entered the realm of the professional power engineer. Enhanced models are outside the scope of this introductory article.

Our previous models can provide a ballpark life estimation for a capacitor.

Advanced models must account for the fundamental frequency as well as harmonics. This should extend to worst case application in an unbalanced threephase system.

The airflow will depend on the enclosure. For example, a VFD is a compact device with challenging and perhaps conflicting requirements for cooling the capacitor as well as the power semiconductors.

It may be prudent to contact the OEM to construct “test” capacitors that feature internal temperature sensing probes. This will provide the best life estimate and identify any problem areas in your finished product.

There are a host of other considerations that we have not explored, including voltage transients, thermal cycling, and loadside impacts such high start current, overloads, and short circuit.
Please refer to the link in the related information section at the end of this article. There you will find detailed guidelines from Cornell Dubilier Knowles. Several of the documents will bring you to online calculator that can account for the selfheating due to ripple current.
Parting thoughts
This article presents a several models that may be used to calculate the operational life of a capacitor. It begins with the broad rule of 10 which indicates that the life of electronics is reduced by a factor of two for each 10°C increase in temperature. The model was refined to include a voltage multiplier which suggests that the capacitor longevity increases with lower voltages. The final model includes a ripple current multiplier that suggests longer life at reduced ripple current. Unfortunately, we stop before arriving at an equation as a meaningful answer requires us to consider the fundamental ripple current and harmonics. However, Figure 3 strongly suggests a longer life with reduced ripple current.
Taken together, we see that life is increased for a capacitor when operated well with its design maximums. We prefer a cool environment with relatively low voltage and low ripple current. Before we accept that simple assumption, remember that capacitors are a relatively expensive component. Over specification can result in a significant cost increase.
As we conclude, consider the legend of Henry Ford. To cut costs, his engineers conducted a failure mode analysis of the Model T. They singled out the kingpin as a mechanism that never failed. Ford’s response was to reduce the kingpin’s quality to match the quality of the other components thereby reducing the total cost of the car.
The lesson is simple: select all system components to match the desired system longevity to reduce the total cost.
There is little point in overspecifying the capacitor(s) to outlive the semiconductors.
Best wishes,
APDahlen
Related information
Please follow these links to related and useful information:

Cornell Dubilier’s Aluminum Electrolytic Capacitor Application Guide

SelectingandapplyingDCLinkbuscapacitorsforinverterapplications093020a1.pdf (cde.com)
About this author
Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique electronics and automation foundation built over a 27year military career as a technician and engineer which was further enhanced by 12 years of teaching (interwoven). With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABETaccredited EE program, served as the program coordinator for an EET program, and taught componentlevel repair to military electronics technicians. Dahlen has returned to his Northern Minnesota home and thoroughly enjoys researching and writing articles such as this.