# Extracting the Resistive Current Component from a Surge Arrester’s Leakage Current without Voltage Reference

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- atmospheric discharges, and
- consequences of switch devices’ manipulations.

_{r}, which is the main indicator of the state of the surge arrester. With the help of finite element analysis [8], leakage currents can be determined under different conditions. A current decomposition-based method [17] can also be used. Here, the total leakage current is decomposed to study the impact of different parameters on the decomposition accuracy. Additionally, many methods have been introduced for measuring the resistive component of the total leakage current [18,19]. However, researchers in the area have also paid significant attention to evaluating the surge arrester’s condition to reduce network losses. An arrester is considered to be faulty when the resistive current value exceeds 0.6 mA, according to the IEC 60099-5:2013, 2013 [20]. If the arrester’s current exceeds this value and is not replaced, this produces additional power losses, financial losses, and a greater carbon footprint [21], as shown in Table 1.

## 2. Physical Background of the Arrester Monitoring Principle

_{t}), it is necessary to extract the resistive component (I

_{r}). During long-time operation, the arresters encounter thermal stresses, due to the power losses that are caused by the leakage current. The power dissipation can be calculated, as follows:

_{d}represents the average power-dissipation, W represents the energy, T is the period of voltage U(ωt) that causes the current I

_{t}(ωt), and ω represents the angular frequency. The current through a brand-new arrester is relatively small (the order of a few 10 µA), but, due to the high voltage, the dissipation becomes significant as the arrester deteriorates. It is also known that the voltage is contaminated by high order harmonics (the voltage in the observed power system is contaminated with a third harmonic U

_{3}= 0.1% of U

_{1}, fifth harmonic U

_{5}= 0.3% of U

_{1}and e.c.t.), mainly with the third and fifth harmonic components, so, the voltage and current in (1) can be described as the sum of higher harmonic components, as follows:

_{r,rms}exceeds the value that is defined by the Standard [29] $\left({I}_{r,rms}>600/\sqrt{2}\mathsf{\mu}\mathrm{A}\right)$, the arrester is in bad condition, and it should be replaced by a new one. A few different MOSA (ten samples) with a nominal voltage of 36 [kV]

_{rms}were randomly chosen for measurements, in order to design, in advance, so-called “static characteristics”. By presuming that the arresters are made from the same materials under the same production conditions and connected to the same supply voltage U, it is expected that they have statistically similar static characteristics as:

_{t}, and its resistive and capacitive components I

_{r}and I

_{c}, respectively. The harmonic distortion that was obtained as a projection of the phasor I

_{t}to the real (Re) axis causes that distortion of the resistive current is acceptable, and the magnitude ${\widehat{I}}_{r}$ is accurate enough for further analyses. However, at the same time when ${\widehat{I}}_{r}$ is extracted from the diagram, the grey shaded areas that are indicated in Figure 1a,c as I

_{t_avg}are also extracted, and it depends on φ and ${\widehat{I}}_{r}$, as follows:

_{t}, in the chosen interval (for example $\mathsf{\pi}/3\le \mathsf{\omega}t\le \mathsf{\pi}$), as follows:

_{t}) the measurement is performed at a few different operating points (different supply voltages U). The measurement set-up (the following equipment was used in the set-up: A Tr1-autotransformer up to 0.4 kV, a Tr2-transformer for galvanic isolation 1/N1 = 0.4/7 kV, a high voltage transformer, 1/N2 = 0.1/110 [kV], an oscilloscope RIGOL DS4034, multimeter Fluke 189. Arrester type SNO_U = 36 kV class DH producer IZOELEKTRO) is organised, as presented in Figure 2. Figure 3a–f show the measurement results obtained from CSV data (from an oscilloscope), of a randomly chosen arrester (Arrester type SNO_U = 36 kV class DH producer IZOELEKTRO, 2341 Limbuš, Slovenia). The magnitude of the resistive current component (${\widehat{I}}_{r}$) is extracted from the oscillograms at the instant when the voltage is at its peak (dU/dt = 0) at six operating points. Further, the measurements were performed on 10 arresters, in order to have a representative result. Table 2 shows the obtained measurement results. For every sample, the exact value of the phase angles (φ) and the magnitudes of ${\widehat{I}}_{r}$, are indicated for every operating point.

#### 2.1. Extraction of the Resistive Current Magnitudes from the Arrester’s Leakage Current

_{φ}) and of current magnitudes (${\mathsf{\sigma}}_{{\widehat{I}}_{r}}$)

#### 2.2. Description of the Measurement Principle for the Average Value of Leakage Current at Certain Intervals

_{t}evaluated in the interval $\mathsf{\pi}/3\le \mathsf{\omega}t\le \mathsf{\pi}$. This interval can be chosen arbitrarily; in this case, it was chosen that the third harmonic component has no influence on average value, so the average value I

_{t_avg}, for the real-time measurement, can be evaluated, as follows:

_{t_avg}) were calculated for different arresters at different operating points, and they are collected in Table 3. The statistical parameters, the average phase delay φ, are calculated by (8), and the mean value I

_{t,mn}, which corresponds with the phase delay, is calculated, as follows:

_{t,mn}at certain interval (σ

_{It,mn}), are calculated at the same operation points as:

_{i}= 164.2°, I

_{t,mn,i}= 363 μA). Hence, the trend lines, represented by the linear function, are:

- when ${60}^{\xb0}<\mathsf{\phi}\le {\mathsf{\phi}}_{i}$;$${\widehat{I}}_{r}\left(\mathsf{\phi}\right)=-95.7\mathsf{\phi}+\mathrm{15,793}$$$${I}_{t,mn}\left(\mathsf{\phi}\right)=-38.1\mathsf{\phi}+6615.6$$
- when ${\mathsf{\phi}}_{i}<\mathsf{\phi}\le {180}^{\xb0}$;$${\widehat{I}}_{r}\left(\mathsf{\phi}\right)=-9.03\mathsf{\phi}+1593.7$$$${I}_{t,mn}\left(\mathsf{\phi}\right)=-7.56\mathsf{\phi}+1603.9$$

#### 2.3. Verification of the Proposed Algorithm

_{t_avg}was obtained. Figure 6 shows the proposed algorithm as a Unified Modeling Language (UML) diagram.

_{r_cal.}, was obtained by using the formulas according to the block diagrams that are shown in Figure 6.

_{t,mn}= 570 μA with the phase delay of φ = 159°. Accordingly, every measured I

_{t,mn}above this number indicates that the arrester should be replaced with a new one.

## 3. Surge Arrester Monitoring Device (SAMD)

_{t}) into digital representations for further analyses in the microcontroller or a Personal Computer (PC). The proposed circuit architecture deals with the smart sensor structures that are described in more details in [30,31,32,33].

_{t}) values (samples). As a part of the conversion, the signal acquisition circuit is designed as an instrumentation amplifier. The key characteristics are high input impedance, high common-mode rejection, low output offset, and low output impedance. After digitalisation of the leakage current (I

_{t}), it is necessary to extract the resistive current component ${\widehat{I}}_{r}$ using the algorithm that is based on the UML diagram shown in Figure 6. The resistive component can be calculated in the micro-controller, or digitalised leakage current can be sent through communication channels to the server, where the ${\widehat{I}}_{r}$ can be calculated offline, but in “soft” real time.

- galvanic isolation of the measured signal (safety reasons);
- acquire and prepare the analogue signal for digital conversion;
- collection of current samples in the range $\mathsf{\phi}\in ({\mathsf{\phi}}_{\mathrm{min}},{\mathsf{\phi}}_{\mathrm{max}})$; and,
- prepare information for wireless transfer to an off-line server.

#### 3.1. Electronic Circuits

_{t}was captured by using a current transformer with the appropriate ratio (1:300). Such a ratio was chosen as a compromise between the sensitivity to measurement of leakage current and the rejection of the currents’ strokes of a few hundreds of an Ampere (${I}_{t}:{I}_{t,stroke}=1:{10}^{7}$). This was solved by using an appropriate protection of the op-amp inputs. The battery voltage measurement and temperature measurement circuits were also integrated into the device.

#### 3.1.1. Protection Circuit

_{2}− V

_{1}< U

_{p}) (${U}_{p}=3\mathrm{V}$).

_{cm}), two line-bypass capacitors (C

_{cm}) for suppressing the CM noise signals and an across-the-line capacitor (C

_{dm}) for suppressing the Differential Mode (DM) noise signals.

#### 3.1.2. Signal Acquisition Circuit

_{ts}) was converted to voltage difference on the resistances R

_{0}. Because of the properties of the almost infinite open loop gain of the op-amp A

_{1}and the used feed-back by R

_{f}, it follows that:

_{0}indicates the resistances in the input loop of the operational amplifier A

_{1}and I

_{ts}= I

_{t}/300 (${V}_{2}-{V}_{1}=2{R}_{0}{I}_{ts}\Rightarrow {V}_{2}-{V}_{1}=0.47\mathrm{mV}$). Additionally, the alternative input signal must be transformed into a unipolar signal appropriate for A–D conversion of voltage at the output of the measurement system (U

_{oA}

_{3}). Figure 9 shows the scheme of the chosen electronic circuit. The frequency analyses of the electronic circuit were considered in order to design a suitable gain and band-pass. Assuming that the operational amplifiers were the same type, and after analyses of the scheme in Figure 9, it follows:

_{β}= R

_{f}/R

_{0}represents closed-loop gain, β

_{1}= 1/ω

_{t}, α

_{2}= 1/(Bω

_{t}

^{2}), α

_{1}= 1/(Bω

_{t}), $B={R}_{0}/({R}_{F}+{R}_{0})$ (${R}_{0}=47\mathsf{\Omega},{R}_{F}=100\mathrm{k}\mathsf{\Omega}$), ω

_{t}is unity-gain bandwidth (${\mathsf{\omega}}_{t}=2\mathsf{\pi}f\Rightarrow $ ${\mathsf{\omega}}_{t}=2\mathsf{\pi}4\times {10}^{5}rad/s$ (from the data sheet)) (usually specified on the data sheets of op. amps.), and U

_{p}denotes the power supply voltage. Using (20) and considering that $s\to 0$, the output voltages can now be calculated as:

_{p}/2 = 0) was excluded, as follows:

_{b}represents the small-signal bandwidth frequency (f

_{b}= 188 Hz), which can be obtained after the short calculation:

_{β}, a frequency ω

_{b}, and y denote the circuit parameters, as is the absolute form of the function $H(j\mathsf{\omega})$, as follows:

_{β}depends on the resistances R

_{f}and R

_{0}; if these change by $\pm 1$%, the A

_{β}changes by ±2, so it follows

_{β}and, consequently, on the resistances R

_{f}and R

_{0}.

#### 3.1.3. Microcontroller and Communication Unit

- 12-bit analogue-digital converter (ADC),
- operational amplifier,
- two ultra-low-power comparators with reach communication interfaces, and
- development supports, etc.

#### 3.1.4. Battery

## 4. Experimental Results

#### 4.1. Experimental Test-Bench

#### 4.2. Calibration of the Measurement Devices

_{p}/2 was added to the analogue signal, which represents the leakage current (I

_{t}) information. After the ADC conversion, the obtained measurement results were sent using the communication unit to the “distribution centre” (computer or server). The information that was sent to the server was coded as a series of numbers representing the leakage current I

_{t,}but in the unit of quants not in the μA. Definitely, this information must be calibrated in the proper unit μA [34]. For calibration purposes, the measurement constants were calculated from the properties of the entire measurement chain that are described in Section 3.1.

#### 4.2.1. Measurement Constant

_{0,min}(0.5 V) was applied on the ADC, the input was obtained for:

_{0,max}(2.5 V) was applied on the ADC, input was obtained for:

_{t}reaches a magnitude over 1500 μA, so this range guarantees the appropriate consideration of the surge arresters’ “health” while measuring the resistive component of the leakage current.

#### 4.2.2. Verification of the Calibration Process

_{t_avg}corresponds with the resistive component of ${\widehat{I}}_{r}$ = 783 μA.

#### 4.3. Measurement Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) Current and voltage wave shape when U = 27 [kV]

_{rms}; (

**b**) Phasor diagram, when Φ = 72°; (

**c**) Current and voltage wave shape when U = 37 [kV]

_{rms}; and, (

**d**) Phasor diagram, when Φ = 64°.

**Figure 3.**Measured current (I

_{t}) and voltage (U) with oscilloscope (CSV files) I

_{t}:

**i**arrester leakage current;

**ii**measured arrester voltage (U): (

**a**) at U = 25 kV

_{rms}, φ = 173.0°, ${\widehat{I}}_{r}$ = 61 μA; (

**b**) at U = 27 V

_{rms}, φ = 172.0°, ${\widehat{I}}_{r}$ = 61 μA; (

**c**) at U = 31 kV

_{rms}, φ = 166.8°, ${\widehat{I}}_{r}$ = 107 μA; (

**d**) at U = 36 kV

_{rms}, φ = 164.2°, ${\widehat{I}}_{r}$ = 199 μA; (

**e**) at U = 37 kV

_{rms}, φ = 160.7°, ${\widehat{I}}_{r}$ = 545 μA; (

**f**) at U = 39 kV

_{rms}, φ = 158.2°, ${\widehat{I}}_{r}$ = 847 μA.

**Figure 4.**Description of average value I

_{t_avg}and its relation with pair ($\mathsf{\phi}$, ${\widehat{I}}_{r}$).

**Figure 5.**Static characteristics of ${\widehat{I}}_{r}={\widehat{I}}_{r}\left(\mathsf{\phi}\right)$ and ${I}_{t,mn}={I}_{t,mn}\left(\mathsf{\phi}\right)$.

**Figure 6.**UML diagram for the functional mapping algorithm, ${I}_{t\_avg}\to \mathsf{\phi}\to {\widehat{I}}_{r\_cal.}$.

**Figure 9.**(

**a**) Analogue signal acquisition circuit; (

**b**) PCB (printed circuit board) with components of the measurement device.

**Figure 12.**Calibration procedure; the roman letters i, ii and iii indicate measurements at 0.80U, 1.00U, and 1.20U, respectively.

**Figure 13.**Verification of the calibration process when the supply voltages to the surge arrester were: (

**a**) 0.9 U; (

**b**) 1.1 U; and, (

**c**) 1.275 U.

Annual for 1 MOSA | Annual for 12,090 pcs of MOSA | |
---|---|---|

Power losses [MWh] | 0.486 | 5.872 |

Financial losses [€] | 35.4 | 428.312 |

Carbon footprint [t] | 0.133 | 16.4416 |

**Table 2.**Resume of measured phase delay φ and resistive component ${\widehat{I}}_{r}$ extracted from the oscilloscope.

Sample 1 | Sample 2 | Sample 3 | Sample 4 | … | Sample N | Mean Val. | Relative σ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

φ_{1}[°] | ${\widehat{\mathit{I}}}_{\mathit{r},1}$ [μA] | φ_{2}[°] | ${\widehat{\mathit{I}}}_{\mathit{r},2}$ [μA] | φ_{3}[°] | ${\widehat{\mathit{I}}}_{\mathit{r},3}$ [μA] | φ_{4}[°] | ${\widehat{\mathit{I}}}_{\mathit{r},4}$ [μA] | .… | φ_{N}[°] | ${\widehat{\mathit{I}}}_{\mathit{r},\mathit{N}}$ [μA] | φ [°] | ${\widehat{\mathit{I}}}_{\mathit{r}}$ [μA] | U_{rms}[kV] | σ_{φ}[%] | $\mathsf{\sigma}{\widehat{\mathit{I}}}_{\mathit{r}}$ [%] |

157 | 812 | 158 | 847 | 158 | 847 | 155 | 755 | …. | 156 | 750 | 157 | 802 | 39 | 0.31 | 3.9 |

159 | 510 | 160 | 521 | 161 | 545 | 160 | 475 | …. | 159 | 480 | 160 | 500 | 37 | 0.36 | 4.3 |

162 | 220 | 163 | 214 | 165 | 199 | 162 | 195 | …. | 163 | 183 | 163 | 202 | 36 | 0.59 | 7.3 |

165 | 107 | 166 | 102 | 167 | 107 | 164 | 95 | …. | 166 | 102 | 166 | 103 | 33 | 0.67 | 4.8 |

168 | 66 | 169 | 56 | 169 | 61 | 171 | 56 | …. | 171 | 60 | 170 | 59 | 31 | 0.88 | 5.8 |

173 | 33 | 172 | 33 | 173 | 36 | 174 | 36 | …. | 173 | 37 | 173 | 35 | 25 | 0.39 | 5.5 |

**Table 3.**Resume of the calculated average values of leakage current I

_{t}, measured with an oscilloscope in the intervals ${60}^{\xb0}\le \mathsf{\phi}\le {180}^{\xb0}(\mathsf{\pi}/3\le \mathsf{\omega}t\le \mathsf{\pi})$, according to the relation ${I}_{t\_avg}={I}_{t\_avg}\left(\mathsf{\phi}\right)$.

Sample 1 | Sample 2 | Sample 3 | Sample 4 | … | Sample N | Mean | Relative σ | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

φ [°] | I_{t_avg,1}[μA] | φ [°] | I_{t_avg,2}[A] | φ [°] | I_{t_avg,3}[μA] | φ [°] | I_{t_avg,4}[μA] | … | φ [°] | I_{t_avg,N}[μA] | φ [°] | I_{t,mn}[μA] | U_{rms}[kV] | σ_{φ}[%] | σ_{It,mn}[%] |

157 | 643 | 158 | 665 | 158 | 664 | 155 | 621 | … | 156 | 640 | 157 | 646 | 39 | 0.73 | 2.5 |

159 | 546 | 160 | 548 | 161 | 545 | 160 | 523 | … | 159 | 522 | 160 | 537 | 37 | 0.43 | 2.2 |

162 | 426 | 163 | 420 | 165 | 418 | 162 | 380 | … | 163 | 401 | 163 | 409 | 35 | 0.68 | 4.1 |

165 | 359 | 166 | 353 | 167 | 356 | 164 | 340 | … | 166 | 365 | 166 | 355 | 33 | 0.46 | 2.4 |

168 | 329 | 169 | 319 | 169 | 318 | 171 | 314 | … | 171 | 321 | 170 | 320 | 31 | 0.72 | 1.5 |

173 | 298 | 172 | 294 | 173 | 301 | 174 | 305 | … | 173 | 310 | 173 | 299 | 25 | 0.27 | 2.0 |

Measured Values | Phase | Calculated (15)–(18) | Scope Value | Relative Error |
---|---|---|---|---|

I_{t_avg} [μA] | φ [°] | ${\widehat{I}}_{r\_cal.}$ [μA] | ${\widehat{I}}_{r}$ [μA] | ε [%] |

665 | 156.25 | 839 | 847 | 0.9 |

643 | 156.86 | 783 | 812 | 3.6 |

522 | 160.01 | 480 | 480 | 0.0 |

418 | 162.74 | 218 | 199 | −9.8 |

356 | 165.06 | 103 | 107 | 3.5 |

319 | 169.95 | 59 | 56 | −5.4 |

298 | 172.72 | 34 | 33 | −3.0 |

570 | 158.75 | 600 |

SAMD Measured | Oscilloscope Measured | Relative Error |
---|---|---|

I_{t_avg} [μA] | I_{t_avg} [μA] | ε_{rel} [%] |

327.3 | 331.4 | −1.24 |

372.1 | 375.8 | −0.98 |

605.2 | 642.5 | −5.81 |

SAMD Measured | Calculated (15)–(18) | Reference Scope Value | Absolute $\mathbf{Error}\mathbf{of}{\widehat{\mathit{I}}}_{\mathit{r}}$ | Relative $\mathbf{Error}\mathbf{of}{\widehat{\mathit{I}}}_{\mathit{r}}$ |
---|---|---|---|---|

I_{t_avg} [μA] | ${\widehat{I}}_{r\_cal.}$ [μA] | ${\widehat{I}}_{r}$ [μA] | ε_{abs} [μA] | ε_{rel} [%] |

327.3 | 69.0 | 79.1 | 10.1 | −12.8 |

372.1 | 103.2 | 97.0 | 6.2 | 6.3 |

409.7 | 197.0 | 195.3 | 1.7 | 0.9 |

411.1 | 201.1 | 204.2 | −3.1 | −1.6 |

457.0 | 316.5 | 311.0 | 5.5 | 1.6 |

581.2 | 628.5 | 628.0 | 0.5 | 0.1 |

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**MDPI and ACS Style**

Vončina, V.; Pihler, J.; Milanovič, M. Extracting the Resistive Current Component from a Surge Arrester’s Leakage Current without Voltage Reference. *Sensors* **2021**, *21*, 1257.
https://doi.org/10.3390/s21041257

**AMA Style**

Vončina V, Pihler J, Milanovič M. Extracting the Resistive Current Component from a Surge Arrester’s Leakage Current without Voltage Reference. *Sensors*. 2021; 21(4):1257.
https://doi.org/10.3390/s21041257

**Chicago/Turabian Style**

Vončina, Vid, Jože Pihler, and Miro Milanovič. 2021. "Extracting the Resistive Current Component from a Surge Arrester’s Leakage Current without Voltage Reference" *Sensors* 21, no. 4: 1257.
https://doi.org/10.3390/s21041257