This contribution will present thermal current interruption measurements performed in pure CO2 with a puffer circuit-breaker test device and establish a statistical method to assess the reignition probability as a function of the prospective current slope. Its efficacy will be demonstrated with measurements of the interruption limit scaling with respect to the pressure buildup inside the test device. A separate contribution will apply these methods to evaluate the influence of fluorinated additives on the switching performance

Christen, Dennis

Engelbrecht, Joseph

Franck, Christian

Pietrzak, Pawel

Simka, Philipp

English

CTU Open Journal Systems (Czech Technical University, Prague / České vysoké učení technické v Praze)

doi:10.14311/ppt.2023.1.36Plasma Physics and Technology 10(1):36–39, 2023 © Department of Physics, FEE CTU in Prague, 2023STATISTICAL METHODS FOR IDENTIFYING SMALL DIFFERENCES INTHE THERMAL INTERRUPTION PERFORMANCE OF SF6 ALTERNATIVESJ. Engelbrecht∗, P. Pietrzak, D. Christen, P. Simka, C. FranckHigh Voltage Laboratory, Swiss Federal Institute of Technology Zurich (ETHZ), 8092 Zurich, Switzerland∗ jengelbre@ethz.chAbstract.This contribution will present thermal current interruption measurements performed in pure CO2with a puffer circuit-breaker test device and establish a statistical method to assess the reignitionprobability as a function of the prospective current slope. Its efficacy will be demonstrated withmeasurements of the interruption limit scaling with respect to the pressure buildup inside the testdevice. A separate contribution will apply these methods to evaluate the influence of fluorinatedadditives on the switching performance [1].Keywords: switching arcs, gas circuit breakers, thermal interruption, CO2, SF6 alternatives.1. IntroductionA paradigm shift is underway in high-voltage powertransmission, with long-standing SF6-insulated de-signs being phased out in favor of alternatives withlower global warming potential. A number of pro-posed solutions for SF6-free gas circuit-breakers useCO2-based mixtures. In such mixtures the thermalswitching behavior is mainly set by the CO2 base gas,making the influence of additives challenging to detectexperimentally. To investigate the switching processesin these mixtures, a test device based on the puffercircuit-breaker principle has been developed, enablingthe study of pure gas properties under highly con-trolled conditions [2]. This contribution will presentthermal interruption limit measurements performedwith this device, and establish a statistical methodto assess the reignition probability as a function ofthe prospective current slope. The method will beused to show that the interruption limit in CO2 fol-lows a blow pressure scaling of 3.1 Aµs√bar . Using thisapproach, the interruption limit may be determinedwith an uncertainty much smaller than the scatter ofindividual test results, thereby allowing small changesin interrupting performance to be detected.2. MethodsExperiments were performed using the setup shownin Fig. 1, introduced in [2]. A hydraulic drive acts toseparate arcing contacts and compress a puffer volume.This generates a pressure difference ∆p that blows coldgas through the arcing region inside a PMMA nozzle,cooling and extinguishing the arc at a current-zero(CZ) crossing. Measurements were performed in CO2at a fill pressure of 5 bar for four blow pressure (i.e.∆p) settings. ∆p was varied by changing the openingspeed of the drive via its throttle setting, while thetiming of the drive trigger was adjusted such thatthe arc length measured by a linear potentiometerFigure 1. Interrupter region of puffer CB test device.was always 43 ± 1 mm at the first CZ crossing. Usingthis method the pressure buildup may be controlledto within ±100 mbar, as measured by two transientpressure sensors located inside the puffer cylinder.A synthetic test circuit was used to generate the testconditions: a high-current circuit (HCC) sustainedthe arc through the contact opening, and a current-injection circuit (CIC) controlled the dI/dt at CZ andthe transient recovery voltage (TRV) rise, at a fixed450 Ω surge impedance. This setup allows conditionsat CZ to be controlled with high reproducibility, in-dependently of the peak HCC current, as the CICsettings determine the prospective dI/dt, while thepuffer-breaker controls the pressure buildup with min-imal influence from backheating. It should be notedthat this setup produces a sustained TRV rise forat least 10 µs, a more prolonged voltage stress thanwould be applied in L90-like short-line fault (SLF)tests at the same dI/dt and du/dt, where the firstline peak would occur within the first several µs [3].To determine the thermal interruption limit, theapplied dI/dt and TRV must be varied while otherconditions at the interruption instant are held con-stant. In practice, this was done according to theprocedure introduced in [4]: the charging voltage ofthe CIC was varied in 1 kV increments between 15 kVto 30 kV, corresponding to changes in the prospectivedI/dt at CZ of approximately 0.33 A/µs over a rangefrom 5 A/µs to 10 A/µs. Sets of 3–7 measurements36vol. 10 no. 1/2023 Statistical Methods for Evaluating Interruption PerformanceFigure 2. a) Scatter plot of 44 test outcomes in CO2as a function of blow pressure and prospective dI/dt(data points may overlap) b) Box-plot representationof measurement results.were performed at each setting, covering a range from100% success rate to 100% failure rate, providing agood measure of the scatter of interruption outcomes.3. Results & Discussion3.1. Interruption Limit DeterminationA scatter plot showing the outcome of each test per-formed for one pressure setting in CO2 as a functionof the prospective dI/dt is presented in Fig. 2a, withinterruption successes and failures indicated by colorand plotted as a function of the measured blow pres-sure at CZ. Substantial scatter is evident, with bothsuccesses and failures occurring over a 2 A/µs range.In order to determine a limit value from this data, wedefine the limit as the dI/dt at which there is an equallikelihood of a reignition or a successful interruption.The rate of change of the interruption probability withrespect to dI/dt should be maximized near this value,minimizing the uncertainty.One method for determining the limit is with quan-tiles chosen to span the overlap of the two distributions.This can be visualized with the box-plot shown in Fig.2b. Here the data from the scatter plot is groupedinto two separate distributions for the interruptionsuccesses and failures. To examine only the influ-ence of the prospective dI/dt, all tests are treated ashaving the same blow pressure of 5.8 ± 0.1 bar. Thebox-plot denotes the quartiles of both distributions:the colored regions represent the central 50%, boundedat the upper and lower quartiles, while the whiskersextend to the extrema of measured values that liewithin 1.5 interquartile range of the central distribu-tion, with outliers plotted individually. Taking thedifference between the upper quartile of successes andthe lower quartile of failures provides an estimatedlimit of 7.6 A/µs that can be perceived visually as themidpoint between the blue and orange boxes.This approach provides a reliable measure of the in-terruption limit and a good representation of the scat-Figure 3. a) Histogram of thermal interruption testoutcomes as a function of prospective dI/dt. b) Plotof estimated probability distribution and interruptionlimit determined from measurement results.ter of test results, however it has several drawbacks.The method is somewhat sensitive to the samplingapproach; e.g. if more measurements are performedunder low dI/dt conditions with a high likelihoodof success than are performed at high dI/dt wheremore failures are expected, the limit may be skewedto a lower dI/dt value. This issue can be somewhatmitigated by a careful sampling approach centered onthe interruption limit, but this requires foreknowledgeof the expected limit and reduces flexibility duringtesting. The uncertainty of the limit is also difficultto quantify with this method, despite box-plots pro-viding a good indication of the range in which theoutcome of an individual test is uncertain.To establish the uncertainty, it is useful to considerthe data using statistical methods aimed at estimat-ing the underlying probability distribution. Fig. 3acontains a histogram with the measurements from Fig.2. Each bin contains one dI/dt setting, and representsthe outcome of n independent trials, each of whichhad nominally the same probability p of a successfulinterruption, resulting in nS successes and nF fail-ures. The results in each bin are therefore describedby the binomial distribution B(n, nS, p), where p is afunction of the prospective dI/dt.With this description, an estimate for p and itsuncertainty at each dI/dt setting can be obtainedusing the so-called Wilson score interval [5],p ≈nS + 12 z2n + z2 ±zn + z2√nSnFn+ z24 , (1)where z is set based on the target confidence level, tak-ing a value of 1 for an interval spanning 1σ uncertainty.Several methods have been proposed for estimating37J. Engelbrecht, P. Pietrzak, D. Christen et al. Plasma Physics and Technologyp, however the Wilson interval has ideal propertiesfor describing the present experiment, namely thatit may be reasonably applied to datasets with a lownumber of trials and/or values of p near 0 or 1 [6].In Fig. 3b, estimated confidence intervals and valuesof p are plotted beneath the corresponding bins fromthe histogram, demonstrating lower uncertainty forsettings with a higher number of trials. These pointsindicate the probability of interruption p(dI/dt) withmeaningful uncertainty, and form a distribution withempirically known properties. p should decrease mono-tonically with dI/dt, approaching 1 at low dI/dt and0 at high dI/dt. These properties describe an inversecumulative distribution function (ICDF). To evaluatethe interruption limit based on our estimated proba-bilities, we make the assumption that the underlyingdata is normally distributed and therefore can be fitwith a Gaussian ICDF, with the points individuallyweighted by their uncertainties. This fit is shown inFig. 3b, and corresponds to a normal distribution witha mean value µ = 7.6 A/µs and width σ = 0.7 A/µs.For comparison with this fit, an empirical ICDF thatdoes not rely on assumptions about the distribution isalso useful. Binary datasets do not translate directlyto such an empirical representation, however one maybe estimated using the method proposed by Turnbull,also plotted in Fig. 3b [7].By definition, µ occurs at the p = 0.5 crossing ofthe ICDF and so corresponds to the thermal inter-ruption limit. The uncertainty of the limit is thenequivalent to σµ = σn , the uncertainty in the mean ofthe distribution, and σ provides an indication of thescatter around this value, i.e. the region in which theoutcome of an individual trial cannot be predictedto within 1σ confidence. Hence the method yields aninterruption limit of 7.6 ± 0.1 A/µs for CO2 at a blowpressure of 5.8 bar, but indicates that for at least 84%certainty of a successful interruption, dI/dt shouldnot exceed 6.9 A/µs.3.2. Pressure Scaling in CO2To confirm the efficacy of this method, it was used tostudy the scaling of the thermal interruption limit inCO2 with respect to the blow pressure at CZ. Pres-sure dependence has been studied thoroughly in SF6and shown to scale approximately with √p [8], whiletheoretical models predict the same √p scaling inde-pendent of blow gas [9]. Fig. 4 shows the results:the interruption limit determined using the binomialprobability estimation method is plotted with errorbars indicating the limit uncertainty σµ. Good agree-ment is observed between this method and the afore-mentioned box-plot quantile method, with all datapoints lying within the indicated uncertainty. Simi-lar agreement is observed for the plotted fits to thefunction a√∆p, with both methods yielding values ofa = 3.1 Aµs√bar . The expected scatter is indicated bythe shaded blue region in this figure, determined byfitting the same a√∆p function to µ + σ and µ − σ,providing an uncertainty band that agrees with theexperimentally observed scatter, as evidenced by theextrema indicated with orange error bars.An interruption limit of 7.7 A/µs was determined forthe highest investigated blow pressure of ∆p = 6.2 bar.This finding is comparable to other values reported inliterature: Uchii et al. showed a thermal interruptionlimit for CO2 near 7.5 A/µs in the absence of signifi-cant nozzle ablation, however the blow pressure wasnot reported [10]. Stoller et al. determined a limitof approximately 11.2 A/µs at a higher blow pressureof ∆p = 11 bar [11]; extrapolation of our fit predictsa slightly lower limit of 10.4 A/µs at this pressure.It should also be noted that this study assumed aninterruption performance scaling with the square-rootof the absolute stagnation pressure p0, contrary to ourfindings, which suggest that the performance scaleswith√∆p. Fitting our data instead to √p0 producesa noticeable mismatch, with the fit suggesting thatthe interruption performance should increase moreslowly with blow pressure than is observed in our mea-surements. This disagreement lies well outside of ourestimated uncertainty interval, however we note thatseveral factors influencing the uncertainty have notbeen fully accounted for with the present approach,and will be discussed in the following section.3.3. DiscussionWithout further knowledge of the interruption prob-ability distribution, the use of a normal distributionmay be questioned. This assumption cannot be con-clusively tested based on the limited number of ex-periments performed, however all results show goodsymmetry about p = 0.5, and the fits agree well withthe estimated empirical ICDF. If the assumed distribu-tion is incorrect, the calculated interruption limit maybe affected, depending on the asymmetry of the realdistribution about µ. Any influence resulting fromsuch deviation should manifest as a systematic shiftthat similarly influences all results, such that relativecomparisons between gases and other experimentalparameters may still be made. Upcoming work willtest this assumption by performing a large numberof trials with the same experimental configuration,thereby allowing for both the long-term consistency ofthe results and the underlying probability distributionto be better characterized, affording higher confidenceto the stated uncertainties.Another influence which could not be completelycontrolled for throughout the pressure scaling com-parison is the erosion of the PMMA nozzle. Testswere performed at reduced peak current, limiting ero-sion such that the pressure buildup at one experimentsetting of ∼40 shots remained within the reported±100 mbar uncertainty interval. It was thus inferredthat erosion in the throat region of the nozzle wasminimal, as previous measurements showed a decayin blow pressure at higher currents with more sig-nificant erosion. The same nozzle was then used to38vol. 10 no. 1/2023 Statistical Methods for Evaluating Interruption PerformanceFigure 4. Pressure scaling of thermal interruptionlimit, and accompanying√∆p fits.perform tests at the different pressure settings. Af-ter the measurement series of ∼120 shots concluded,minor erosion of the throat and converging regionof the nozzle was noted, suggesting that the averageflow conditions experienced by the arc may have var-ied slightly between experimental settings. Lookingahead to measurements in other SF6 alternative gasmixtures, comparisons will always be performed with anew, un-arced nozzle, and so should share comparableflow conditions over each measurement series.In addition to these factors, our results show un-characteristically late reignition times of up to 10 µsafter CZ [4]. Analysis of voltage collapse waveforms,presented in [1], suggests the possibility of a differentfailure mechanism for the later reignitions, perhapsresulting from "hot dielectric" processes, as opposed tothe classical understanding of thermal failures drivenby runaway post-arc current heating. This findingraises the possibility that the present results under-estimate the true thermal limit in CO2, particularlyfor SLF switching duties where the first line peakoccurs only a few µs after CZ. The alternative failuremechanism may also explain the observed differencesin pressure scaling behavior.4. ConclusionsA method has been demonstrated for determining thethermal interruption limit in a puffer circuit-breakerexperiment by estimating the underlying probabilitydistribution. The method was applied to interruptionmeasurements in CO2, and compared with a simplerapproach based on the overlapping quantiles of in-terruption successes and failures. The two methodswere shown to produce similar results, demonstrat-ing that the interruption limit scales according to3.1 Aµs√bar across the four blow pressures investigated.The probabilistic method allows for better estimationof the likelihood of a successful interruption at an ar-bitrary dI/dt setting, and of the certainty with whichthe interruption limit may be determined based onthe measurements. The suitability of this method islimited to experimental configurations where all testconditions are able to be reproduced to a high degreeof precision, however it has been shown that in suchconditions and with a sufficient number of trials, theinterruption limit may be determined with a degree ofcertainty much higher than suggested by the width ofthe scatter. Such precision may prove invaluable whenassessing the influence of minor changes to experimen-tal parameters including gas mixture composition, arclength, and nozzle design.AcknowledgementsThe authors would like to thank Enrico Graneris, FabianMächler, Mahir Muratovic, and Martin Seeger for theirvaluable contributions to this work, which was made possi-ble by financial support from Hitachi Energy Switzerland.References[1] P. Pietrzak et al. Thermal arc interruption performanceof CO2 and CO2/C4F7N mixture. To appear in 24thSymposium on Physics of Switching Arc, 2023.[2] C. Franck et al. Comparative Test ProgramFramework for Non-SF6 Switching Gases. B&HElectrical Engineering, 15:19–26, 2021.doi:10.3929/ethz-b-000508915.[3] D. Peelo. Current Interruption Transients Calculation,chapter 5, pages 111–123. John Wiley & Sons, Ltd,2020. ISBN 9781119547273.doi:10.1002/9781119547273.ch5.[4] J. Engelbrecht et al. Evaluating conductance decay andpost-arc current in axially blown CO2 arcs. To appear inProc. of the XXIII Int. Conf. on Gas Discharges, 2023.[5] E. Wilson. Probable inference, the law of succession,and statistical inference. Journal of the AmericanStatistical Association, 22(158):209–212, 1927.doi:10.1080/01621459.1927.10502953.[6] S. Wallis. Binomial confidence intervals andcontingency tests: Mathematical fundamentals and theevaluation of alternative methods. Journal ofQuantitative Linguistics, 20(3):178–208, 2013.doi:10.1080/09296174.2013.799918.[7] B. W. Turnbull. Nonparametric estimation of asurvivorship function with doubly censored data.Journal of the American Statistical Association,69(345):169–173, 1974.[8] A. Plessl. The Influence of Pressure Profiles on GasBlast Arc Interruption. Proc. of the VII Int. Conf. onGas Discharges, pages 32–35, 1982.[9] T. Christen and M. Seeger. Current interruption limitand resistance of the self-similar electric arc. Journal ofApplied Physics, 97(10):106108, 2005.doi:10.1063/1.1913802.[10] T. Uchii et al. Thermal interruption capability ofCO2 in a puffer-type circuit breaker utilizing polymerablation. IEEE/PES Transmission and DistributionConference and Exhibition, 3:1750–1754, 2002.doi:10.1109/TDC.2002.1177719.[11] P. Stoller et al. CO2 as an Arc Interruption Mediumin Gas Circuit Breakers. IEEE Transactions on PlasmaScience, 41(8):2359–2369, Aug 2013.doi:10.1109/TPS.2013.2259183.39

Statistical Methods for Identifying Small Differences in the Thermal Interruption Performance of SF6 Alternatives

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Statistical Methods for Identifying Small Differences in the Thermal Interruption Performance of SF6 Alternatives

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