Capacitor Bank Protection: A Breakthrough In Temperature Compensation

October 19th 2020

In a previous post, we demonstrated how impedance-based protection (21C) is a perfect complement to the more traditional voltage-differential protection (87V). Impedance-based protection is providing a more natural feedback to its users and can be easily used in a condition-based monitoring program for maintenance.

However, one of the drawbacks sometimes raised about this protection scheme is that bank capacitance varies throughout the day as temperature changes. Moreover, this variation is not even across the bank because of variations in sun and shade. Ultimately, this could lead to a false alarm or to nuisance tripping.

In this post, we will highlight the effects of temperature on capacitor bank impedance and demonstrate a new breakthrough approach one can use to address this issue.

Effect of temperature on capacitor bank impedance

As stated in existing literature, the capacitance variation of a bank due to temperature can easily reach ± 2% for a temperature range of ‑30oC to 60oC. Temperatures within this range are to be expected when factoring in the sun exposure. Also, sun exposure will result in uneven variation across the bank.

When the number of capacitors elements per string is high, for example more than 30, an impedance variation of ± 2% is in the same order as a single capacitor element failure. If the protection element is configured to raise an alarm for single capacitor elements losses, a false alarm could result from the temperature variation.

Note that this effect can also be observed with a voltage differential protection scheme. Like demonstrated in our previous post, the 87V element can be translated to a ratio of impedances. It can be assumed that ambient temperature has little effect on this element, but uneven sun exposure will result in a change of ratio.

From that perspective, compensation of temperature-induced impedance variation becomes a desirable feature for any protection scheme.

Attempts at temperature compensation

Temperature compensation of impedance consists in dynamically adjusting the expected impedance of the protection element, like shown in the following illustration.


Different methods were proposed in the past to compensate impedance for temperature variations. The most obvious method consists in using a sensor to measure temperature in the surroundings of the capacitor bank. While this method is straightforward, requiring an external sensor puts an additional burden on commissioning. It is also an extra piece of hardware that could be subject to failure. Since only one input is used, the method cannot factor in for uneven sun exposure.

Another proposed method performs temperature compensation on the impedance of a string based on the average impedance of the neighboring strings. This method assumes that temperature variation will mostly affect the impedances of the strings equally. While this method eliminates the need for a probe, it does not account for uneven sun exposure neither.

Time-based temperature compensation

The drawbacks of these temperature compensation methods led us to propose a new way to perform compensation we call “Time-Based Temperature Compensation”.

Instead of comparing the measured impedance value to a fixed expected impedance, the 21C element compares it to a temperature-compensated expected impedance value. This value is generated by an algorithm that behaves according to the following guidelines:

  • Any slow variation in the impedance is related to temperature. If a slow increase or decrease is measured, the expected impedance will be moved accordingly
  • If the impedance varies quickly, either a grid disturbance is under way, or we are in the presence of a capacitor element failure. The following rules apply:
    • If the measured impedance stabilizes near the same point it was prior to the event, the event is ignored
    • Else, a capacitor element has failed. Thus, the difference between impedance prior and after the event will be calculated and summed up into a cumulative error register. Temperature-compensated expected impedance will be adjusted in a way that capacitor element failures will never be considered as a normal operating value.

As a failsafe measure, the temperature-compensated expected impedance is constrained to ±3% of the commissioned impedance. This is enough to cover typical variations associated with temperature.

This proposed mechanism is patent pending.

Examples of operation

The following presents the results obtained when applying the proposed temperature compensation algorithm to an impedance-based protection element in a few operating conditions.

The first case presented here shows the behavior with a temperature variation over a day, from -30oC to 25oC. The first figure displays the measured impedance and the temperature-compensated expected impedance calculated by the relay. It shows the impedance varies in magnitude more than the configured threshold for alarm, which is set to 1% of the commissioned impedance of 3900 Ω. However, thanks to temperature compensation, the second figure also shows that no alarm signal is raised.


The second case highlights an actual capacitor failure in the bank. The following figure shows the event relative to the impedance thresholds.


The next figures compare the magnitude of the measured impedance and the actual temperature-compensated expected impedance.


After the measured impedance exits the alarm impedance circle for the configured operating time (200 ms), the alarm signal raises. This is not a typical operating time for the first alarm level, but this delay was chosen to simplify the view of the behavior.

The first figure also showed that even if a capacitor fails and the measured impedance falls, the temperature-compensated expected impedance that is output from the algorithm still stays the same.

Conclusion: temperature compensation without a probe is possible

The temperature compensation algorithm presented above ensures safe and reliable use of 21C protection elements under varying temperature conditions. Moreover, the usage of this mechanism gives an advantage over the use of traditional voltage differential elements (87V) that are not compensated for temperature variations. Further, the method does not require any additional equipment to be installed.

To learn more on how to improve bank health monitoring and reduce maintenance costs with an impedance-based protection, simply send us an email at and request a copy of our white paper.


Stay Informed


Subscribe to our newsletter to receive the latest articles.

Subscribe to our newsletter