Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength Characteristics Topics to be covered in the following: Insulators under polluted conditions Probability of flashover (Normal and Weibull distributions) Behavior of parallel insulation Coordination procedure: deterministic and statistical approach Correction with altitude of installation Clearances in air; "gap factors"

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Non-self-restoring insulation No method at present available for the determination of the probability of disruptive discharge Therefore, it is assumed that the withstand probability changes from 0% to 100% at the value defining the withstand voltage. Withstand voltage usually verified by application of a limited number of test voltages at standard withstand level with no disruptive breakdown allowed  "Procedure A" of IEC : [IEC ] The breakdown process is statistical in nature  to be taken into account, especially for impulse voltage stress!

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation The breakdown process is statistical in nature  to be taken into account, especially for impulse voltage stress! Self-restoring insulation Withstand capability can be evaluated by tests and be described in statistical terms. Therefore, self-restoring insulation is typically described by the statistical withstand voltage corresponding to a withstand probability of 90%. Withstand voltage verified by application of a limited number of test voltages at standard insulation level, allowing a certain number of discharges  "Procedure B" of IEC  "15/2-test"  usually applied procedure in the "IEC world"  "Procedure C" of IEC  "3+9-test" See next three slides ….

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation [IEC ] Comparison of Procedures B and C Only here both procedures are equivalent! Example: equipment at the borderline, rated and tested at its U 10, has a 82% probability of passing the test in Procedure B a better equipment, rated and tested at its U 5,5, has a 95% probability of passing the test in Procedure B a worse equipment, rated and tested at its U 36, has only a 5% probability of passing the test in Procedure B; with Procedure C, its probability of passing would be higher, the 5% probability of passing would be given for equipment rated and tested at its U 63 (see also next slide)

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Comparison of Procedures B and C Probability of breakdown P(U) Probability of passing the test "15/2" Probability of passing the test "3+9" Test voltage referred to conventional deviation Probability of passing the test: approx. 82 % at probability of breakdown of 10 % P(U)P(U) (U-U 50 )/Z

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation [IEC ] Comparison of Procedures B and C (IEC depiction) 50 Equipment that has a 5% probability of passing the 15/2-test, would have an approx. 40% probability of passing the 3+9-test

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Completely different approaches: Verification of withstand voltages (see slides before) Evaluation of withstand voltages Determination of the probability function P = P(U), defined by the three following parameters in case of a Normal or Gaussian distribution: U 50 … voltage under which the insulation has a 50% probability to flashover or to withstand Z … conventional deviation; Z = U 50 – U 16 U 0 … truncation voltage (cannot be directly determined) IEC : "For insulation co-ordination purposes, the up-and-down withstand method with seven impulses per group and at least eight groups is the preferred method of determining U 50 ". IEC : "For insulation co-ordination purposes, the up-and-down withstand method with seven impulses per group and at least eight groups is the preferred method of determining U 50 ".

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter û n breakdown no breakdown û1û1 û2û2 û3û3 û4û4 û5û5 ΔU  3% of û 1 Count starts here Probability of Disruptive Discharge of Insulation Up-and-down method (see HVT I, Ch. 5) Special case for determining U 50 General procedure see next slides…

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Examples see next slides…. See slide before! [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter û n group of 7 impulses with at least one disruptive discharge group of 7 impulses with no disruptive discharge û1û1 û2û2 û3û3 û4û4 û5û5 ΔU  3% of û 1 Count starts here Probability of Disruptive Discharge of Insulation Up-and-down method – Withstand procedure with m = 7 and n = 8

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter û n group of 7 impulses with no withstand group of 7 impulses with at least one withstand û1û1 û2û2 û3û3 û4û4 û5û5 ΔU  3% of û 1 Count starts here Probability of Disruptive Discharge of Insulation Up-and-down method – Discharge procedure with m = 7 and n = 8

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution Disruptive discharge probability described by a Gaussian cumulative frequency distribution: where U 50 … 50% discharge voltage (P(U 50 ) = 0.5) Z … conventional deviation In order to reflect the real physical behavior, this function has to be truncated at U 0 = U 50 – 3Z or U 0 = U 50 – 4Z (No discharge can occur at voltages below U 0 !)

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution Arguments for replacing the Gaussian by the Weibull distribution: the truncation value U 0 is mathematically included in the Weibull expression; the function is easily evaluated by pocket calculators; the inverse function U = U(P) can be expressed mathematically and is easily evaluated by pocket calculators; the modified Weibull expression is defined by the same parameters characterizing the truncated Gaussian expression: U 50, Z and U 0 ; the disruptive discharge probability function of several identical insulations in parallel has the same expression as that of one insulation and its characteristics can be easily determined from those of the single insulation.

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution General expression for Weibull distribution: where  … truncation value  … scale parameter  … shape parameter Modification for description of discharge probability of an insulation with a truncated discharge probability: (N may be 3 or 4)

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution Condition: Solving the equation to  :

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution Assuming that U 0 = U 50 – 4Z  N = 4 (reasonably accurate)

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution With x = (U – U 50 )/Z: Modified Weibull flashover probability Typical values for Z (if more accurate data are missing): For lightning impulses:Z = 0.03 U 50 [Z] = kV For switching impulses:Z = 0.06 U 50 For lightning impulses:Z = 0.03 U 50 [Z] = kV For switching impulses:Z = 0.06 U 50 And for U 10, resulting from the distribution function: U 10 = U 50 – 1.3 Z see also chapter 3

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Replacing the Normal (Gaussian) by a Weibull distribution [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel P(U)P(U)P1(U)P1(U)P2(U)P2(U)P3(U)P3(U)P4(U)P4(U)P5(U)P5(U)PM(U)PM(U) P‘(U) = ? Question: if the probability of flashover of one insulator at U is P(U), what is the probability P'(U) of M of these insulators connected in parallel to flashover?

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel Applying the rules of statistics: Probability of flashover of one single insulator: P(U) If many insulators of the same individual flashover probability are connected in parallel and one is looking for the probability of a flashover of one of them, this cannot be calculated by an addition of the individual probabilities. (Note: if this was the case, 100 parallel insulators of 10% flashover probability (P(U) = 0.1) would have a probability of P'(U) = 10 to flashover, which is mathematical nonsense.) Solution: consider the probability of withstand: W(U) = 1 – P(U) The probability that a number of M insulators withstands at the same time can be calculated by multiplication according to the rules of statistics: W total (U) = W 1 (U) · W 2 (U) · W 3 (U) · ….. · W M (U) = W(U) M = [1-P(U)] M The probability P'(U) that one out of M insulators flashes over is equal to the probability that not all insulators withstand at the same time, thus:

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel Flashover probability of M parallel insulations Introducing the normalized variable x M = (U – U 50M )/Z M : Comparison of both equations yields:

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel Replacing x and x M by their extended definitions: x = (U – U 50 )/Z x M = (U – U 50M )/Z M and because: U 50 – 4Z = U 50M – 4Z M = U 0  U 50M = U 50 – 4Z + 4Z M with

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel Example 1: For M = 200: U 50(200) = U 50 – 2.6 Z U 10(200) = U 50(200) – 1.3 Z 200 = U 50 – 3.1 Z M = 100, U 50 = 1600 kV, Z = 100 kV  Z M = 39.8 kV, U 50M = kV Example 2:

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel Example 2, continued: [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel [IEC ] Note: These values can directly be obtained from this equation: see Example 1: U 50(200) = U 50 – 2.6 Z

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Probability of Disruptive Discharge of Insulation Many insulations in parallel … also relevant for apparatus design three parallel external insulations one external insulation

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air Factors influencing the dielectric strength of the insulation: magnitude, shape, duration and polarity of the applied voltage electric field distribution in the insulation homogeneous or non-homogeneous electric field electrodes adjacent to the considered gap and their potential type of insulation gaseous liquid solid combination of two or all of them impurity content and the presence of local inhomogeneities physical state of the insulation temperature pressure other ambient conditions mechanical stress history of the insulation (aging, damage) chemical effects conductor surface effects Covered by equations U 50RP = f(d) where U 50RP … 50% probability breakdown voltage of a rod-plane-configuration d … gap spacing Covered by equations U 50 = f(U 50RP, K) where K … gap factor K is a factor indicating how much higher the electrical strength of a particular electrode configuration is in comparison with the rod-plane- configuration (which gives least dielectric strength); factors K were experimentally found for standard switching impulse voltage stress

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Gap factors (Table G.1 of IEC ) Insulation Strength in Air

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Gap factors (Table G.1 of IEC ) Insulation Strength in Air

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Gap factors (Table G.1 of IEC ) Insulation Strength in Air

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Gap factors (Table G.1 of IEC ) Insulation Strength in Air

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Gap factors [Electra No. 29 (1973), pp )] Electrode configuration K Rod-plane Rod-structure (under) Conductor-plane Conductor-window Conductor-structure (under) Rod-rod (h = 6 m, under) Conductor-structure (over and laterally) Conductor-rope (under and laterally) Conductor-crossarm (end) Conductor-rod (h = 6 m, under) Conductor-rod (h = 3 m, under) Increasing dielectric strength Insulation Strength in Air

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to power-frequency voltages (IEC , Annex G) with U 50RP … crest value in kV d in m; d ≤ 3 m for d > 2 m exact for d < 1 m; conservative for 1 m ≤ d ≤ 2 m Insulation Strength in Air influence of rain in an air gap negligible; but for insulators to be considered! pollution for insulators to be considered! altitude correction required! ≈ 300 kV/m (r.m.s. value) (assuming U 0 = U Z and Z = 0.03 U 50 )

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to slow-front overvoltages (IEC , Annex G) with U 50RP … in kV; for positive polarity at most critical front-time (see Ch. 3) d in m; d ≤ 25 m Insulation Strength in Air with U 50RP … in kV; for positive polarity standard switching impulse voltage (see Ch. 3) d in m; d ≤ 25 m Note: for K ≥ 1.45 U 50neg. may become lower than U 50pos.

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to slow-front overvoltages (IEC , Annex G) Insulation Strength in Air (assuming U 0 = U Z and Z = 0.06 U 50 ) influence of rain in an air gap negligible; but for insulators to be considered! altitude correction required!

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to slow-front overvoltages (IEC , Annex G) Insulation Strength in Air For phase-to-phase insulation similar gap factors as for phase-to-earth insulation can be applied. But: the influence of negative and positive components has to be taken into account by a factor α: [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to fast-front overvoltages (IEC , Annex G) with U 50RP … in kV; for positive polarity d in m; d ≤ 10 m Insulation Strength in Air Note: for negative LI voltages, dielectric strength is higher and increases non- linearly with gap spacing! i.e. linear increase with gap spacing The gap factors K (found for SI voltages!) cannot be directly applied. From experimental investigations: with K + ff … fast-front overvoltage gap factor for positive polarity K …... gap factor for SI voltage according to tables

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation response to fast-front overvoltages (IEC , Annex G) Insulation Strength in Air influence of insulators to be considered particularly for range II! less influence from long insulators without metallic parts (long rod, composite, station post) than for cap-and-pin insulators altitude correction required! virtually no influence of rain neither for air gaps nor for insulators Estimation of negative line insulator flashover voltage (in order to determine lightning overvoltages impinging on a substation: Conventional deviation: Z ≈ 0.03·U 50 for air gaps and positive polarity Z ≈ 0.05·U 50 for air gaps and negative polarity Z ≈ (0.05 … 0.09)·U 50 across insulators Conventional deviation: Z ≈ 0.03·U 50 for air gaps and positive polarity Z ≈ 0.05·U 50 for air gaps and negative polarity Z ≈ (0.05 … 0.09)·U 50 across insulators

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air Independent from the theoretical and empirical background given so far, IEC offers tables on minimum clearances in air (Annex A). Not all values of these tables can be derived from above equations, as they additionally take into account withstand values instead of U 50 -values feasibility economy experience average influence of environmental conditions (pollution, rain, insects, …)

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air [IEC ]

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter [IEC ] Procedure for Insulation Coordination in Four Steps Flow chart of IEC (Figure 1) we are here! Next slide Sorry, no time this year

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air Performance criterion  IEC , Cl. 3.2 According to definition 3.22 of IEC 71-1, the performance criterion to be required from the insulation in service is the acceptable failure rate (R a ). The performance of the insulation in a system is judged on the basis of the number of insulation failures during service. Faults in different parts of the network can have different consequences. For example, in a meshed system a permanent line fault or an unsuccessful reclosure due to slow-front surges is not as severe as a busbar fault or corresponding faults in a radial network. Therefore, acceptable failure rates in a network can vary from point to point depending on the consequences of a failure at each of these points. Examples for acceptable failure rates can be drawn from fault statistics covering the existing systems and from design projects where statistics have been taken into account. For apparatus, acceptable failure rates R a due to overvoltages are in the range of 0.001/year up to 0.004/year depending on the repair times. For overhead lines acceptable failure rates due to lightning vary in the range of 0.1/100 km/year up to 20/100 km/year (the greatest number being for distribution lines). Corresponding figures for acceptable failure rates due to switching overvoltages lie in the range 0.01 to per operation. Values for acceptable failure rates should be in these orders of magnitude.

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air Altitude correction In general, withstand or breakdown voltages must be corrected for air density (pressure, temperature) and absolute humidity. Temperature and absolute humidity tend to cancel out each other. Thus correction is mainly required for pressure, which has its strongest influence in the altitude of installation. Therefore, in the procedure of insulation coordination, an altitude correction must be performed in the step from the coordination withstand voltage U cw to the required withstand voltage U rw. Air density vs. altitude: (regression of experimental data) where H … altitude above sea level in m Voltage correction depends on voltage shape (the kind of pre-discharges), thus a voltage- dependant factor m is introduced:

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Strength in Air Altitude correction [IEC ] m = 1 for LI voltage m = acc. to Figure 9 for SI voltage m = 1 for short-time alternating voltage m = 0.5 for long-time alternating voltage and tests under pollution Final altitude correction factor:  approx. 1.3% per 100 m (for m = 1) Note: this has been proven only up to 2000 m! For higher altitudes investigations still to be done!  EPRI China, Tibet test station in 4300 m altitude Note: this has been proven only up to 2000 m! For higher altitudes investigations still to be done!  EPRI China, Tibet test station in 4300 m altitude

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter [IEC ] Procedure for Insulation Coordination in Four Steps Flow chart of IEC (Figure 1) we are here!

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Procedure for Insulation Coordination in Four Steps From U cw  U rw whereK a … altitude correction factor K s … safety factor, taking into account: differences in equipment assembly dispersion in product quality quality of installation aging effects other unknown influences Internal insulation: no altitude correction (K a = 1) K s = 1.15 *) Internal insulation: no altitude correction (K a = 1) K s = 1.15 *) External insulation: K a = f(m,H) = exp(m·H/8150) K s = 1.05 External insulation: K a = f(m,H) = exp(m·H/8150) K s = 1.05 *) for on site tests on complete GIS, a factor K s = 1.25 is sometimes recommended in order to take volume effects into account

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Procedure for Insulation Coordination in Four Steps From U cw  U rw H/m U/kV Assumption: U cw = 1000 kV Internal insulation: U rw = 1.15·1000 kV = 1150 kV External insulation: U rw = 1.05·exp(H/8150)·1000 kV Example (for m = 1) ≈

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter [IEC ] Procedure for Insulation Coordination in Four Steps Flow chart of IEC (Figure 1) we arrived here!

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Coordination For calculation examples, see IEC , Annex H!

Fachgebiet Hochspannungstechnik Overvoltage Protection and Insulation Coordination / Chapter Insulation Coordination