1. Introduction

2. An example of the leakage current measurement for HV surge arrester

3. Errors and their correction in determining the active component of the leakage current

3.3. Correction factors in leakage current measurements

Leakage current measurements, seemingly simple to carry out, require taking into account a number of correction factors - the influence of temperature - k_T, voltage - k_U and harmonic content (frequency) in order to convert the leakage current to a reference level determined, for example, by the temperature of 293 K, voltage amplitude U_c only with harmonic frequency primary. In principle, the measurement of leakage current should be abandoned in difficult weather conditions, when in the presence of dew, soot, atmospheric precipitation, the level of leakage current due to significant surface leakage may lead to incorrect conclusions (Figure 7).

3.3.1. Voltage and temperature correction factors in leakage current analysis

In order to obtain correct diagnostic conclusions from the measurements of the leakage current of the ZnO arresters, a number of analyzes were performed to determine the impact of the above factors by defining the correction factors - temperature k_T and voltage k_U. These coefficients are necessary to calculate the leakage current of the arrester measured in any voltage and temperature conditions determined by temperature and effective voltage, taking into account the content of higher harmonics. The leakage current is recalculated to the reference level set by the measurer in order to unambiguously compare the results of measurements carried out over a longer time horizon, when changes in both analyzed quantities clearly occur in operating conditions. The k_T and k_U coefficients should be determined for a given type of arrester after leakage current measurements carried out in various temperature and voltage conditions [2, 38]. Figure 17 shows examples of k_U coefficients for LV arresters with operating voltage U_c=275 V and rated discharge current 20 kA with time parameters 8/20 μs/μs. In addition, the data of the manufacturer of the LCM500 device used in the diagnostics of medium and high voltage limiters, tabulated in [38], has been added. Reference levels U/U_r=0.7 and T_w=293 K are proposed here.

The correction factors for LV arresters obtained in own measurements are similar to those for medium voltage surge arresters [38] only for the condition U/U_r>0.7. At the supply voltages, much greater discrepancies were obtained, which may be related to the very small values of leakage currents and additional errors in their measurement.

An increase in temperature causes a decrease in the permanent operating voltage in a manner dependent on the chemical composition of the varistor ceramics [39, 41]. With a significant content of iron and aluminum oxides, these changes can be even several times for the selected temperature [42]. Common temperature coefficients K defined by the formula (7) in [43] are given at the level of (0.5 ÷ 1)∙10^-3/K:

$$K=\frac{\Delta U}{U·\Delta T}=\frac{U_{Tw}\left(1mA\right)-U_{T0}\left(1mA\right)}{U_{T0}\left(1mA\right)·(T_W-T_0}$$

(7)

where:

• U_Tw(1 mA) – voltage at T_w and current 1 mA;
• U_T0(1 mA) - voltage at T₀ and current 1 mA;
• T_w – temperature of surge arrester;
• T₀ – temperature at reference level equal 293 K.

For most surge arresters in proper technical condition, the voltage at the forced leakage current with a temperature increase of 20 K decreases by about 1% [43]. Increased heat release in the varistor structure affects the voltage at its terminals and reduces the permissible levels of current and energy surges as a function of temperature.

Changes in the conductivity of the varistor structure γ measured at the reference voltage U_{1 mA}, i.e. also its temperature coefficients, occur according to different band characteristics [40, 41]. It turns out that the influence of the chemical composition on the γ(1/T_w) characteristic is a complex model containing several partial conductivities in a series-parallel system. However, regardless of the chemical composition of the varistor, the function describing the conductivity of the varistor from its leakage current is correctly approximated by the power function γ = aI^b with constants a and b [41]

Another method, more often used in practice, is to determine the value of the leakage current I(U_c) at the voltage of continuous operation of the arrester U_c, and then to calculate the temperature coefficients k_T, which are directly converted to the reference temperature, e.g. 293 K according to the equation (8):

$$I_{T0}\left(U_c\right)=k_T·I_T\left(U_c\right)$$

(8)

In order to determine the correction factors, ZnO varistors from two manufacturers, A and B, were used. In one case, the tests concerned 8 surge arresters with a continuous operating voltage of 275 V from manufacturer A. In the second case, varistors (10 pieces of each type) from manufacturer B were tested with a voltage of 0.28 kV, 0.5 kV, 1 kV and 3 kV. The surge arresters were stored in the thermal chamber for 5 hours until the temperature distribution in the varistor structure was normalized, and then the current-voltage characteristics were measured in the system with the correctly measured current, forcing a direct or alternating voltage coming in the second case from a sinusoidal voltage generator with a low content of higher harmonics.

The correction factors were determined in two operating states - at direct voltage (manufacturer A and B) on the basis of standard current-voltage characteristics and at alternating voltage (only manufacturer A) by determining the resistive component of the leakage current according to the methodology described in [44].

Figure 18 shows exemplary current-voltage characteristics of the tested surge arresters at the continuous operating voltage U_c = 275 V and the rated discharge current 20 kA, 8/20 μs. Above the DC voltage corresponding to the amplitude of the continuous operating voltage, a slight effect of temperature on the leakage current level is observed.

On the basis of the measured I(U) characteristics, the k_T coefficients for direct voltage, shown in Figure 19, were calculated. These coefficients for varistors from manufacturers A and B, marked for similar continuous operating voltage, are significantly different. The determined correction factors, especially at low ambient temperatures, are characterized by a significant dispersion of the current value results.

For surge arresters from manufacturer A, the course of the k_T(T_w) coefficient was additionally determined from the measurements of the active component of the leakage current at alternating voltage, which is similar to the data given in [38] for the temperature range (263 ÷ 303) K. For higher temperatures, slightly higher values of the coefficient were observed k_T, which may result from the properties of the tested ZnO ceramics (Figure 20).

The data from the publication [45] show that with the identical chemical composition of materials, a change in the temperature profile of the sintering process leads to visible differences in the pre-breakdown characteristics only in the field of tests performed at direct voltage. It follows that the determination of temperature and voltage coefficients should be performed with alternating voltages.

Figure 21 compares the impact of the arrester dimensions related to the continuous operating voltage U_c on the course of the temperature coefficient k_T. The increase in the voltage U_c and thus the volume of the varistor significantly reduces the influence of temperature on the leakage current, which is indicated by the flatter k_T(T_w) characteristic.

3.3.2. Correction due to higher voltage harmonics

Figure 22 shows the shape of the voltage and current of the arrester, respectively, at the mains voltage lower than the continuous operating voltage U<U_c, when there is a small level of the resistive component, but with a significant distortion of the current waveform due to higher harmonics of the supply voltage.

In order to determine the influence of the harmonic frequency of the voltage on the value of the leakage current for the tested arresters, the results of the I(f) characteristics tests were used, on the basis of which the characteristics of the module z(f) and the displacement angle ф(f) of the arrester impedance for voltages in the range from 150 to 340 V were calculated.

The impedance characteristic of the limiter enables the introduction of a correction for the content of higher harmonics by implementing the following algorithm:

• calculation of the content of higher harmonics u_k and i_k in the supply voltage and leakage current;
• calculation of the theoretical, higher harmonics of the leakage current i_tk, based on the characteristics obtained in impedance measurements and the FFT fast Fourier transform algorithm for the supply voltage;
• correction of the content of higher harmonics in the measured leakage current according to the i_k-i_tk action.

The correction of higher harmonics, which allows to obtain the waveform of the corrected leakage current i_cor(t), can occur for all lines of higher harmonics, even up to the order of 100, or only for those that cause a significant change in the current of a given harmonic. In practice, due to the dominance of the odd harmonics 3rd, 5th, 7th, 9th, 11th, 13th, 15th in the supply voltage, it is sufficient to consider only the listed frequencies (Figure 23 and Figure 24).

Correction of the current waveform occurs up to the frequency of 50 Hz (non-distorted voltage) and allows to compare the leakage current results for the measured surge arresters, even with a strongly distorted voltage. The obtained waveform of i_cor(t) allows for the correct calculation of parameters important for the assessment of the technical condition of the arrester: leakage current, resistive component on the basis of active power according to [44]. The relative error related to the measurement results at undistorted voltage, in the case of calculating the active component for the corrected leakage current i_cor(t), does not exceed 5%. The proposed concept of correcting the measurements of surge arresters obtained at distorted voltages, provided that the frequency characteristics obtained from the manufacturer for a given type of arrester are available, makes it possible to compare test results and track changes in the leakage current and its active component. This is important for predicting the aging rate of the arrester during operation.

The proposed method can be used provided that the arrester is supplied with voltage U<U_c and there is no strong distortion of the leakage current associated with the presence of a resistive component greater or comparable to the capacitive current. In the case of U>U_c, the correction is also possible, provided that the impedance characteristic for the arrester with a high value of the active component of the leakage current is available.

3.3.3. Failure to determine the leakage current under non-reference conditions

In order to determine the conversion factor of the measured leakage current value into the actual value, the appropriate correction factors given in point 3.3 should be taken into account. For this purpose, assuming the correct calibration of the current clamps, the following formula should be used:

I_T0(U_c) = k_T ∙ I_T(U_c)

(9)

where coefficients k_U, k_T, k_THD result from dependencies (10 - 12) determined empirically for a selected type of surge arresters.

$$k_U=\frac{I_{U_c}}{I_{U_x}}$$

(10)

$$k_T=\frac{I_{293K}}{I_{xK}}$$

(11)

$$k_{THD}=\frac{I_{50Hz}}{I_{def}}$$

(12)

The k_T and k_U coefficients can be read directly from the appropriate k_T(T) and k_U(U) graphs. This type of data is sometimes provided by manufacturers in data sheets. The results of tests contained in publications on the influence of ambient temperature on the level of leakage current indicate different waveforms of the value of leakage current measured at different test voltages for a specific type of arrester. For example, for surge arresters with a rated voltage of 120 kV, a 20% increase in the leakage current was found in relation to the reference temperature of 303 K [46]. The k_THD factor, on the other hand, depends on the content of individual harmonics during the measurement. In order to calculate it, the algorithm given in point 3.3.2 should be used. This coefficient can be estimated approximately by giving the ratio of the RMS values of the 50 Hz fundamental harmonic band to the leakage current of the varistor.

A cursory analysis of the dependencies listed in Figure 25, Figure 27 and Figure 28 allows to directly determine the maximum additional measurement error introduced during, for example, a temperature of 323 K.

During the error analysis, the leakage current of 6 low-voltage surge arresters was first measured for different voltages and temperatures. The obtained results made it possible to determine the correction factors k_U and k_T for individual surge arresters and the averaged factor, which in the further part of the analysis was used to convert the measurement results obtained at voltage U and temperature T to reference values, in this case 275 V and 293 K. Due to the different the technical condition of the tested arresters and the dispersion of characteristics being a feature of varistor production, errors were calculated for conversion into reference values for individual arresters, which are shown in Figure 26.

Figure 25. Comparison of the corrected waveform of the leakage current i_cor(t) with the current of the fundamental harmonic.

Figure 25. Comparison of the corrected waveform of the leakage current i_cor(t) with the current of the fundamental harmonic.

Figure 26. Errors obtained when using temperature coefficients when converting measurement results to reference values U=275 V and T=293 K.

Figure 26. Errors obtained when using temperature coefficients when converting measurement results to reference values U=275 V and T=293 K.

Figure 27. Influence of the level of voltage harmonics on the leakage current of the arrester.

Figure 27. Influence of the level of voltage harmonics on the leakage current of the arrester.

Figure 28. Influence of voltage harmonics on the active component of the leakage current.

Figure 28. Influence of voltage harmonics on the active component of the leakage current.

In order to determine the influence of higher voltage harmonics on the value of the leakage current, simulations were performed in the Mathcad program using the averaged impedance characteristics of the surge arresters. On their basis, the values of the leakage currents and the active component were calculated during the operation of the arrester at 230 V, on which only one odd harmonic of the order of 3 to 49 with an amplitude of 10 V (4.3%), 20 V (8.7%) was imposed. and 50V (21.7%). The influence of the phase angle of the superimposed voltage harmonic on the value of the leakage current was also checked.

The results of the numerical analyzes obtained indicate that the leakage current of the arrester strongly depends on the frequency of the higher voltage harmonic. The change of the current for a higher harmonic with an amplitude of 20 V imposed on the base waveform with a frequency of 50 Hz increases by as much as 411% from the 3rd to the 49th component. For higher frequencies of the higher harmonic, a significant capacitive component is introduced, visible in the leakage current of the arrester (Figure 27).

On the other hand, the active component of the leakage current with the same content of higher harmonics at the level of 8.7%, which is exceeding the permissible values in distribution and transmission networks, increases in relation to the 50 Hz component by only 6% (Figure 28).

A simplified correction of the leakage current value may consist in calculating the fast Fourier transform from the waveform of the measured current and calculating the current only from the first harmonic. In addition, having the phase of the electric field strength or directly the supply voltage, you can calculate the phase shift between the current and voltage waveforms for the first harmonic and, on this basis, calculate the active current component in a simplified way. In the case of LV arresters, this procedure gives correct results with an error not exceeding 10%, as shown in Figure 29.

On the basis of the obtained simulation results, in accordance with the guidelines [47], it is possible to abandon the introduction of correction factors for the value of the active component of the leakage current, especially that with the increase in the order of the harmonic in power networks, its amplitude strongly decreases. The permissible contents of voltage harmonics of higher orders from the 26th and above are not normalized. The guidelines of the standard [35] end on the 25th order, for which the content is required at the level of 1.5%, and for even harmonics of the 6th - 24th order it is 0.5%. The total content of higher harmonics in the supply voltage THD cannot be higher than 8%.

4. Conclusions

References

1. Goran Dobric, Zlatan Stojkovic,, Zoran Stojanovic, Experimental verification of monitoring techniques for metal-oxide surge arrester, IET Generation, Transmission & Distribution, 2019. [CrossRef]
2. EN IEC 60099-5:2018, Surge arresters - Part 5: Selection and application recommendations.
3. P. PAPLIŃSKI, J. WAŃKOWICZ, H. ŚMIETANKA, P. RANACHOWSKI, Z. RANACHOWSKI, S. KUDELA, M. ALEKSIEJUK, COMPARATIVE STUDIES ON DEGRADATION OF VARISTORS SUBJECTED TO OPERATION IN SURGE ARRESTERS AND SURGE ARRESTER COUNTERS, Arch. Metall. Mater. 65 (2020), 1, 367-374. [CrossRef]
4. Fernando S. N., Raghuveer M. R., Technique to examine the influence of voltage harmonics on Leakage Current Based MOSA Diagnostic Indicator, 2000 Annual Report Conference on Electrical Insulation and Dielectric Phenomena, 2000 Conference on Electrical Insulation and Dielectric Phenomena, 15-18 October 2000, vol. 2, s. 596 – 599, ISBN 0-7803-6413-9. [CrossRef]
5. PN-EN 60099-4:20015, Ograniczniki przepięć - Część 4: Beziskiernikowe ograniczniki przepięć z tlenków metali do sieci prądu przemiennego.
6. PN-EN 60099-5:2014-01, Ograniczniki przepięć -- Część 5: Zalecenia wyboru i stosowania.
7. Koseda H., Wrocławski M., Przepięcia w sieci 15 kV i 110 kV koncernu Energa, Materiały Międzynarodowej Konferencji Bezpieczeństwo i niezawodność nowoczesnych systemów rozliczeniowo – pomiarowych ze zdalnym odczytem i zdalnym monitoringiem parametrów sieci, Serock 2005.
8. Arup Kumar Das and Sovan Dalai, Recent Development in Condition Monitoring Methodologies of MOSA Employing Leakage Current Signal: A Review, IEEE SENSORS JOURNAL, vol. 21, no. 13, pp. 14559-14568, July 1, 2021. [CrossRef]
9. Abdullah Munir, Zulkurnain Abdul-Malek, Rai Naveed Arshad, Resistive Leakage Current Based Condition Assessment of Zinc Oxide Surge Arrester: A Review, 13th International Conference on the Properties and Applications of Dielectric Materials (ICPADM 2021.
10. Instrukcja Standardy eksploatacji urządzeń elektroenergetycznych w PGE Dystrybucja S.A. Oddział Łódź-Teren.
11. Zhongjun Fu, Student Member, IEEE, Jianyu Wang, Arturo Bretas, Senior Member, IEEE, Yun Ou, and Genyuan Zhou, Measurement Method for Resistive Current Components of Metal Oxide Surge Arrester in Service, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 33, NO. 5, OCTOBER 2018. [CrossRef]
12. S. Mohamed Arshad, Asanka.S. Rodrigo, Modified Phase Shifting of Leakage Current to Condition Monitoring of Metal Oxide Surge Arresters in Power System. [CrossRef]
13. A.K. Das et al.: Cross Spectrum Aided Surface Condition Assessment of Metal Oxide Surge Arrester Employing Convolutional Neural Network. [CrossRef]
14. Vandilson R. N. Barbosa , Student Member, IEEE, George R. S. Lira , Member, IEEE, Marianna B. B. Dias , Student Member and Edson G. Costa , Senior Member, IEEE, Estimation of Metal Oxide Surge Arresters’ Useful Life Based on Time Series Forecasts, IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 37, NO. 2, APRIL 2022, IEEE. [CrossRef]
15. J. Lundquist, L. Stenstrom, A. Schej, and B. Hansen, “New method for measurement of the resistive leakage currents of metal-oxide surge arresters in service,” IEEE Trans. Power Del., vol. 5, no. 4, pp. 1811–1822, Oct. 1990. [CrossRef]
16. B. Lee and S. Kang, “A new on-line leakage current monitoring system of ZnO surge arresters,” Mater. Sci. Eng., B, vol. 119, no. 1, pp. 13–18, 2005. [CrossRef]
17. G. R. S. Lira and E. G. Costa, “MOSA monitoring technique based on analysis of total leakage current,” IEEE Trans. Power Del., vol. 28, no. 2, pp. 1057–1062, Apr. 2013. [CrossRef]
18. M. Khodsuz and M. Mirzaie, “Evaluation of ultraviolet ageing, pollution and varistor degradation effects on harmonic contents of surge arrester leakage current,” IET Sci., Meas. Technol., vol. 9, no. 8, pp. 979–986, Nov. 2015. [CrossRef]
19. A. Metwally, M. Eladawy, and E. A. Feilat, “Online conditio monitoring of surge arresters based on third-harmonic analysis of leakage current,” IEEE Trans. Dielectr. Electr. Insul., vol. 24, no. 4, pp. 2274–2281, Sep. 2017.
20. W. Doorsamy and P. Bokoro, “Condition monitoring of metal-oxide surge arresters using leakage current signal analysis,” in Proc. IEEE Int. Conf. High Voltage Eng. Appl. (ICHVE), Athens, Greece, Sep. 2018, pp. 1–4. [CrossRef]
21. A.K. Das, B. Ghosh, S. Dalai, and B. Chatterjee, “Sensing Surface contamination of metal oxide surge arrester through resistive leakage current signal analysis by mathematical morphology,” IEEE Sensors J., vol. 20, no. 16, pp. 9460–9468, Aug. 2020. [CrossRef]
22. K. Das, S. Dalai, and B. Chatterjee, “Deep learning-based surface contamination severity prediction of metal oxide surge arrester in power system,” IET Sci., Meas. Technol., pp. 1–9, Feb. 2021. [CrossRef]
23. Schei, Diagnostics techniques for surge arresters with main reference to on-line measurement of resistive leakage current of metal-oxide arresters, in International Conference on Large High Voltage Electric Systems (CIGRÉ 2000), 2000, pp. 1-10.
24. S. Shirakawa, F. Endo, H. Kitajima, S. Kobayashi, K. Goto, and M. Sakai, "Maintenance of surge arrester by a portable arrester leakage current detector, IEEE Transactions on Power Delivery, vol. 3, no. 3, pp. 998-1003, 1988. [CrossRef]
25. A.H. Khavari, A. Munir, and Z. Abdul-Malek, Circuit-based Method for Extracting the Resistive Leakage Current of Metal Oxide Surge Arrester, Bulletin of Electrical Engineering and Informatics, vol. 9, no. 6, 2020. [CrossRef]
26. Lundquist, L. Stenstrom, A. Schei, and B. Hansen, New method for measurement of the resistive leakage currents of metal-oxide surge arresters in service, IEEE Transactions on Power Delivery, vol. 5, no. 4, pp. 1811-1822, 1990. [CrossRef]
27. Z. Abdul-Malek, Novizon, and Aulia, A new method to extract the resistive component of the metal oxide surge arrester leakage current, in 2008 IEEE 2nd International Power and Energy Conference, 2008, pp. 399-402. [CrossRef]
28. M. Khodsuz and M. Mirzaie, An improved time-delay addition method for MOSA resistive leakage current extraction under applied harmonic voltage, Measurement, vol. 77, pp. 327-334, 2016. [CrossRef]
29. Y. Han, Z. Li, and H. Zheng, A new method to extract the resistive current of MOA based on least square, in Properties and Applications of Dielectric Materials (ICPADM), 2015 IEEE 11th International Conference on the, 2015, pp. 312-315: IEEE. [CrossRef]
30. Y. Han, Z. Li, H. Zheng, and W. Guo, A decomposition method for the total leakage current of MOA based on multiple linear regression, IEEE transactions on power delivery, vol. 31, no. 4, pp. 1422-1428, 2016. [CrossRef]
31. G. Dobrić, Z. Stojanović, and Z. Stojković, The application of genetic algorithm in diagnostics of metal-oxide surge arrester, Electric Power Systems Research, vol. 119, pp. 76-82, 2015. [CrossRef]
32. Patent PL 194370 B1, Urządzenie do diagnozowania stanu zużycia ograniczników przepięć, zwłaszcza ograniczników znajdujących się w eksploatacji.
33. Marek Olesz, Determining the leakage current resistive component by the orthogonal vector method, September 2018, Conference: 2018 34th International Conference on Lightning Protection (ICLP). [CrossRef]
34. Euler C. i inni, Inductive current sensor based on nanocrystalline alloys, XIX Imeko World Congress, Fundamental and Applied Metrology, 2009, Portugal, pp. 840 - 843.
35. PN – EN 50160: 2010, Parametry napięcia zasilającego w publicznych sieciach elektroenergetycznych. 2: – EN 50160.
36. PN-EN 61869-1:2009, Przekładniki – Część 1: Wymagania ogólne.
37. PN-EN 61869-3:2011, Przekładniki – Część 3: Wymagania szczegółowe dotyczące prze-kładników napięciowych indukcyjnych.
38. Hinrichsen V., Monitoring of High Voltage Metal Oxide Surge Arresters, VI Jornadas In-ternacionales de Aislamiento Eléctrico, Bilbao, 22./23.10.1997, Paper 6.4.
39. Larsen V., Lien K., In-Service Testing and Diagnosis of Gapless Metal Oxide Surge Ar-resters, Materiały IX International Symposium on Lightning Protection, 26th-30th No-vember 2007 – Foz do Iguaçu, Brazil.
40. Fernandez-Hevia D. i inni: Bulk-grain resistivity and positive temperature coefficient of ZnO-based varistors, Applied Physics Letters vol. 82, no. 2, 13 January 2003, pp. 221 – 214. [CrossRef]
41. Li S. i inni, The relation between residual voltage ratio and microstructural parametres of ZnO varistors, Materials Letters 59, 2005, pp. 302 - 307. [CrossRef]
42. Sawalha A. et al., Electrical conductivity study in pure and doped ZnO ceramic system. Physica B 2009, vol. 404, pp. 1316-1320. [CrossRef]
43. EPCOS, SIOV Metal Oxide Varistors, General technical information, Epcos AG, April 2011. 20 April.
44. Olesz M.: Algorytmy obliczania składowej czynnej prądu upływowego ograniczników przepięć, Przegląd Elektrotechniczny 11a, 2012.
45. Fujiwara Y., Shibuya Y, Imataki M, Nitta T.: Evaluation of surge degradation of metal oxide surge arrester, IEEE Trans. Power App. PAS 101, 1982, pp. 978-985. [CrossRef]
46. Woo C. L. i inni (Zulkurnain Abdul-Maleka, Saeed Vahabi Mashaka), Effect of Ambient Temperature on Leakage Current of Gapless Metal, Jurnal Teknologi, vol. 64, no. 4, 2013, pp. 157–161.
47. Xu Z. i inni, A current ortogonality metod to extract resistive leakage current of MOSA, IEEE trans. On Power Delivery, vol. 28, no. 1, January 2013. [CrossRef]