The statistical method of IEC 60071-2 first sets an acceptable failure rate and then calculates the failure risk by combining the overvoltage distribution with the insulation's probability of disruptive discharge. For slow-front overvoltages there is a simplified version that compares two points: the overvoltage exceeded 2 % of the time and the voltage the insulation withstands with 90 % probability. For lightning, the failure rate is the risk multiplied by the total number of overvoltages.
Short answer
The statistical method of IEC 60071-2 calculates the probability that the insulation fails, instead of setting a fixed margin. An acceptable failure rate is defined first. Then the overvoltage distribution is combined with the insulation’s probability of disruptive discharge to obtain the failure risk, which is compared with that criterion. Each design alternative is evaluated by its risk. This guide summarizes clauses 3.1.4, 3.2, 3.3.2.2 and 3.3.3.2 of the 1996 edition.
What it calculates and what it is for
The method is based on the frequency of each overvoltage source, the probability distribution of the overvoltages from that source and the insulation’s probability of discharge. Repeated for different insulations and different network states, it gives the total rate of outages due to insulation failure in the system. This estimates the failure frequency as a function of design decisions.
The standard acknowledges a practical limit: in theory the insulation could be optimized if the cost of each failure were known, but that cost is hard to evaluate. For that reason it is usually better to oversize the insulation slightly than to optimize it, and the design relies on comparing risks between alternatives. When there is no test data on equipment failures, the deterministic method is used, which does not calculate risk and has its own guide.
The criterion: the acceptable failure rate
Insulation performance is judged by the number of failures in service. The consequences depend on location. A permanent line fault, or a failed reclosing due to a slow-front overvoltage, weighs less in a meshed network than a busbar fault or an equivalent one in a radial network. That is why the acceptable failure rate (Ra) changes from one point of the network to another.
The standard gives orders of magnitude, not mandatory values:
| Case | Acceptable failure rate |
|---|---|
| Equipment, due to overvoltages | 0.001 to 0.004 per year, depending on repair time |
| Overhead lines, due to lightning | 0.1 to 20 per 100 km per year (the high value applies to distribution lines) |
| Switching overvoltages | 0.01 to 0.001 per operation |
For non-self-restoring internal insulation there is no method to calculate the discharge probability. It is assumed to go from 0 % to 100 % exactly at the value that defines the withstand voltage.
How the discharge probability is described
In self-restoring insulation, the discharge probability P(U) grows with the peak value U of the impulse. The curve is described with three parameters:
- U50: voltage with 50 % probability of discharge.
- Z: conventional deviation, the difference between U50 and the voltage with 16 % probability of discharge (Z = U50 − U16).
- U0: truncation voltage, the maximum value below which a discharge is no longer possible. It cannot be determined by practical tests and is often omitted for simplicity.
For the slow front, the standard recommends a modified Weibull distribution instead of the Gaussian. It coincides with the Gaussian at the 50 % and 16 % points, and is truncated at U50 minus four deviations. If there are no field or laboratory data, the standard suggests Z = 0.03 U50 for lightning impulses and Z = 0.06 U50 for switching impulses. The voltage with 90 % probability of withstand is U10 = U50 − 1.3 Z, which is how IEC 60071-1 describes withstand capability.
How the failure risk is calculated
The phase-to-earth failure risk is the integral, over all voltages, of the product of the overvoltage probability density and the insulation’s discharge probability. Graphically, it is the area where the upper tail of the overvoltage distribution overlaps the discharge zone of the insulation.
- Overvoltage distribution. Determined for each event that causes them
- Discharge probability. Described with U50, Z and truncation
- Failure risk. Calculated by combining both curves
- Failure rate. Risk times the number of events per year
- Criterion. Compared with the acceptable failure rate
The calculation rests on three assumptions about each overvoltage: peaks other than the highest are ignored, the highest peak has the shape of the standard switching impulse, and all have the polarity most severe for the insulation. If several independent peaks appear in one switching operation, the total risk for the phase is 1 minus the product of (1 minus the risk of each peak).
For the three phases there are two ways of counting, depending on how the distribution was built:
- Phase-peak method, with equal insulation in the three phases: the total risk is 1 − (1 − R)³.
- Case-peak method: the total risk is equal to R.
If one polarity is clearly more severe for the insulation, the risk values can be divided by two. Phase-to-earth and phase-to-phase risk are calculated separately only if the two insulations do not share an electrode; if they do, the actual risk is usually lower than the one calculated separately.
Simplified version for slow front
The standard proposes simplifying with one point from each curve: the statistical overvoltage (the one exceeded 2 % of the time, Ue2) and the statistical withstand voltage (the one the insulation withstands with 90 % probability, Ucw). Their ratio is the statistical coordination factor (Kcs). Figure 8 of the standard gives the failure risk as a function of Kcs, for the two peak methods and for three Ue2 values that the figure labels.
Two facts from that figure help in judging the result. A change of one order of magnitude in risk corresponds to only about a 5 % change in dielectric strength. And extreme variations in the insulation deviation, an overvoltage distribution far from Gaussian or, above all, the shape of the overvoltage can shift the curve by up to an order of magnitude.
Lightning
For lightning overvoltages, the method uses the probability distribution of the representative lightning overvoltages. The relative frequency of each amplitude is obtained by dividing its return rate by the total number of overvoltages. The risk is calculated with the procedure above, and the insulation failure rate is the risk multiplied by the total number of lightning overvoltages. For internal insulation, a 100 % probability of withstand up to the assumed voltage and 0 % above it is assumed.
What not to do
- Do not compare the calculated risk with a value in the acceptable-rate table as if it were a requirement: they are orders of magnitude, and each network sets its own according to the consequences.
- Do not use the simplified Kcs version outside the range of figure 8 or with distributions very different from those assumed.
- Do not take the result as an exact value: the standard itself admits errors of one order of magnitude in the risk.
To go further, see Surge arrester protective level: Upl and Ups, Slow-front overvoltages: switching and fault, Overvoltage when energizing and reclosing a line and Insulation coordination in substations above 245 kV.
When to call us
A statistical study needs the overvoltage distributions of the network and the actual arrester and insulation data. At Tiza Group we do it within engineering design and studies for medium, high and extra-high voltage substations, remotely and worldwide. Write to us and we will quote the study.
Related guides
- Insulation coordination under IEC 60071: the steps
- Deterministic insulation coordination method
- Surge arrester protective level: Upl and Ups
- Slow-front overvoltages: switching and fault
- Insulation coordination in substations above 245 kV
References
- IEC 60071-2:1996, Insulation co-ordination, Part 2: Application guide, clauses 3.1.4, 3.2, 3.3, 3.3.2.2 and 3.3.3.2, figures 4 to 8 and annexes C and D.
- IEC 60071-1:2006, Insulation co-ordination, Part 1: Definitions, principles and rules.
Frequently asked questions
What is the acceptable failure rate in insulation coordination?
It is the performance criterion the standard asks of insulation in service: how many overvoltage failures are accepted. IEC 60071-2:1996 (clause 3.2) gives orders of magnitude: between 0.001 and 0.004 per year for equipment, and between 0.1 and 20 per 100 km per year for lines subject to lightning.
Which parameters describe the discharge probability of an insulation?
Three: U50 (voltage with 50 % probability of discharge), the conventional deviation Z (difference between U50 and the voltage with 16 % probability) and the truncation voltage U0, below which no discharge occurs. Without data of your own, the standard recommends Z equal to 0.03 U50 for lightning and 0.06 U50 for switching impulses.
What does the statistical coordination factor Kcs mean?
It is the ratio between the statistical withstand voltage of the insulation (with 90 % probability of withstand) and the statistical overvoltage (the one exceeded 2 % of the time). Figure 8 of the standard relates it to the failure risk. A change of one order of magnitude in risk corresponds to about a 5 % change in dielectric strength.