A Simpliﬁed Model of a Surge Arrester and Its Application in Residual Voltage Tests

: A simpliﬁed and accurate model of a surge arrester used in the residual voltage test is proposed in this paper. With the help of a genetic algorithm, the measured impulse current and residual voltage waveforms are utilized to determine circuit parameters of the proposed model and the generation circuit precisely. The technique starts from the circuit parameter determination using the preliminary experimental data with a lower current peak than that speciﬁed by the standard. From the determined model and with the help of the genetic algorithm, the circuit parameters and the charging voltage to obtain the speciﬁed current peak and the residual voltage can be estimated accurately. The validity of the proposed technique has been veriﬁed by experiments for the estimation of the appropriate current circuit parameters, the charging voltage, and the residual voltage. In addition, the application of the proposed model in the residual voltage tests is presented. From comparison of simulated and experimental results with the determined parameters, the impulse current and residual voltage waveforms are determined precisely. It is conﬁrmed that the proposed model and technique are attractive in the appropriate circuit parameter determination and the residual voltage estimation in the residual voltage tests of surge arresters. The proposed method also provides a good advantage for reduction of the number of trial and error experiments for obtaining the current waveform according to the standard requirement. Moreover, the unintentional damages of the arrester during the process of the waveform adjustment will be reduced signiﬁcantly. agreed well with the experimental result. The calculated peak voltage deviated from the experimental one by only 2%. However, the calculated residual voltage deviated from the experimental one. It was found that the calculated time to the peak of the residual was longer that the experimental one, and the spurious oscillation of the calculated residual voltage occurred in the late time or in the non-conductive state of the arrester.


Introduction
A surge arrester is a device widely used to protect electrical equipment from overvoltages due to lightning and switching operation in electrical power and telecommunication systems [1]. The arrester exhibiting dynamic and nonlinear characteristics diverts current to the ground to clamp the over-voltage to be lower than the insulation level of the protected high voltage equipment. To confirm the performance in over-voltage mitigation, the international standards [2-5] advise performing residual voltage tests on the arrester.
According to the standard [3] and in the residual voltage tests, four kinds of impulse current waveforms, i.e., steep impulse current (1/20 µs), high impulse current (4/10 µs), lightning impulse current (8/20 µs), and switching impulse current (30/80 µs), in different current peaks are injected to the arrester during tests. The residual voltages across the arrester associated with the different impulse current waveforms and peaks are examined. The impulse currents can be generated by a simple resistance, inductance, and capacitance circuit as illustrated in Figure 1. The current generation circuit is composed of the DC voltage source (V s ), the charging current limiting resistor (R L ), the charging capacitor (C), the spark gap (G), the series inductor (L e ), the series resistor (R e ), the shunt current measuring resistor (R SH ), and the surge arrester (SA). The most essential problem in residual voltage tests is that it is quite laborious fo test engineers to generate an accurate waveform and a current peak according to the standard requirement, because the uncontrolled parasitic impedance in the current gen eration circuit and the nonlinear characteristic of the arrester affect the current waveform significantly. Therefore, an accurate arrester model is necessary to use in controlling the current waveform. There are a lot of researchers developing the accurate model used fo designing insulation coordination and for obtaining successful high-voltage testing [6][7][8][9][10][11][12][13][14]. Furthermore, the effect of thermal stress under the arrester operation and experimental tests can be included in the model successfully [15]. However, the generation circuit and parasitic impedance are neglected in the process of mode construction. It leads to the models not being appropriate in the residual voltage test in real practice. Therefore, trial and error approaches for selecting the circuit parameters and the charging voltage are still necessary to employ in the real experiment. Severa experiments for waveform adjustment are carried out to obtain the required waveform and it sometimes unintentionally causes damage on the arrester during the test. It will be advantageous for test engineers if an effective technique for selecting the circui parameters and the charging voltage is developed.
This paper aims to propose a simplified and accurate model of a surge arrester and an effective technique for selecting the circuit parameters and the charging voltage to obtain the specified impulse current waveform in residual voltage tests. Moreover, the residual voltage associated the impulse current waveform is estimated precisely. With the help of a genetic algorithm, the unknown parasitic impedance was determined, and the other appropriate circuit parameters and the charging voltage can be selected. The validity of the proposed technique was verified by the experiments for determination of the appropriate current circuit parameters, the charging voltage, and the residual voltage associated with the specified current waveform. From comparison of the experimenta and simulated results, it was confirmed that the method is fairly highly accurate and very effective in the residual voltage tests of surge arresters. From this achievement, the proposed method is also very useful for the significant reduction of unintentiona damages to the arrester during the process of waveform adjustment.

Conventional Surge Arrester Model
There are many proposed models of surge arresters but most of them are no applicable in residual voltage tests since the parasitic impedance and generation circui are not taken into account in the process of model construction. For the sake of clarity, an experiment of the residual voltage test on a surge arrester with the rated voltage of 9 kV and the nominal discharge current of 10 kA was considered as a test case. As shown in Figure 1, the setting circuit parameters in the experiment were composed of the charging capacitance of 2 µF, the series resistance (Re) of 0.1 Ω, the series inductance (Le) of 25 µH and the charging voltage (Vch) of 69 kV. The IEEE model [6] as illustrated in Figure 2 wa utilized in a circuit simulator to calculate the impulse current and residual voltage The most essential problem in residual voltage tests is that it is quite laborious for test engineers to generate an accurate waveform and a current peak according to the standard requirement, because the uncontrolled parasitic impedance in the current generation circuit and the nonlinear characteristic of the arrester affect the current waveform significantly. Therefore, an accurate arrester model is necessary to use in controlling the current waveform. There are a lot of researchers developing the accurate model used for designing insulation coordination and for obtaining successful high-voltage testing [6][7][8][9][10][11][12][13][14]. Furthermore, the effect of thermal stress under the arrester operation and experimental tests can be included in the model successfully [15]. However, the generation circuit and parasitic impedance are neglected in the process of model construction. It leads to the models not being appropriate in the residual voltage test in real practice. Therefore, trial and error approaches for selecting the circuit parameters and the charging voltage are still necessary to employ in the real experiment. Several experiments for waveform adjustment are carried out to obtain the required waveform and it sometimes unintentionally causes damage on the arrester during the test. It will be advantageous for test engineers if an effective technique for selecting the circuit parameters and the charging voltage is developed.
This paper aims to propose a simplified and accurate model of a surge arrester and an effective technique for selecting the circuit parameters and the charging voltage to obtain the specified impulse current waveform in residual voltage tests. Moreover, the residual voltage associated the impulse current waveform is estimated precisely. With the help of a genetic algorithm, the unknown parasitic impedance was determined, and the other appropriate circuit parameters and the charging voltage can be selected. The validity of the proposed technique was verified by the experiments for determination of the appropriate current circuit parameters, the charging voltage, and the residual voltage associated with the specified current waveform. From comparison of the experimental and simulated results, it was confirmed that the method is fairly highly accurate and very effective in the residual voltage tests of surge arresters. From this achievement, the proposed method is also very useful for the significant reduction of unintentional damages to the arrester during the process of waveform adjustment.

Conventional Surge Arrester Model
There are many proposed models of surge arresters but most of them are not applicable in residual voltage tests since the parasitic impedance and generation circuit are not taken into account in the process of model construction. For the sake of clarity, an experiment of the residual voltage test on a surge arrester with the rated voltage of 9 kV and the nominal discharge current of 10 kA was considered as a test case. As shown in Figure 1, the setting circuit parameters in the experiment were composed of the charging capacitance of 2 µF, the series resistance (R e ) of 0.1 Ω, the series inductance (L e ) of 25 µH, and the charging voltage (V ch ) of 69 kV. The IEEE model [6] as illustrated in Figure 2 was utilized in a circuit simulator to calculate the impulse current and residual voltage waveforms. The circuit parameters of the model were composed of two series resistors (R 0 and R 1 ), two series inductors (L 0 and L 1 ), two nonlinear resistors (A 0 and A 1 ), and a parallel capacitor (C 0 ). With the help of a genetic algorithm as described in Section 4, those circuit parameters of the model were determined by matching the residual voltage from simulation with that from the experiment. As shown in Figures 3 and 4, the calculated current waveform agreed well with the experimental result. The calculated peak voltage deviated from the experimental one by only 2%. However, the calculated residual voltage deviated from the experimental one. It was found that the calculated time to the peak of the residual was longer that the experimental one, and the spurious oscillation of the calculated residual voltage occurred in the late time or in the non-conductive state of the arrester. capacitor (C0). With the help of a genetic algorithm as described in Section parameters of the model were determined by matching the residua simulation with that from the experiment. As shown in Figures 3 and 4 current waveform agreed well with the experimental result. The calculate deviated from the experimental one by only 2%. However, the calculated r deviated from the experimental one. It was found that the calculated tim the residual was longer that the experimental one, and the spurious os calculated residual voltage occurred in the late time or in the non-conduc arrester.

Simplified and Accurate Model of a Surge Arrester
In the results presented in Section 2, the conventional arrester m inaccurate results when they were compared to the experimental ones. I simplified and accurate model of a surge arrester as shown in Figure 5 overcome the problems of the conventional model. The circuit paramete waveforms. The circuit parameters of the model were composed of two series resistors (R0 and R1), two series inductors (L0 and L1), two nonlinear resistors (A0 and A1), and a parallel capacitor (C0). With the help of a genetic algorithm as described in Section 4, those circuit parameters of the model were determined by matching the residual voltage from simulation with that from the experiment. As shown in Figures 3 and 4, the calculated current waveform agreed well with the experimental result. The calculated peak voltage deviated from the experimental one by only 2%. However, the calculated residual voltage deviated from the experimental one. It was found that the calculated time to the peak of the residual was longer that the experimental one, and the spurious oscillation of the calculated residual voltage occurred in the late time or in the non-conductive state of the arrester.

Simplified and Accurate Model of a Surge Arrester
In the results presented in Section 2, the conventional arrester model provided inaccurate results when they were compared to the experimental ones. In this section, a simplified and accurate model of a surge arrester as shown in Figure   waveforms. The circuit parameters of the model were composed of two series resistors (R0 and R1), two series inductors (L0 and L1), two nonlinear resistors (A0 and A1), and a parallel capacitor (C0). With the help of a genetic algorithm as described in Section 4, those circuit parameters of the model were determined by matching the residual voltage from simulation with that from the experiment. As shown in Figures 3 and 4, the calculated current waveform agreed well with the experimental result. The calculated peak voltage deviated from the experimental one by only 2%. However, the calculated residual voltage deviated from the experimental one. It was found that the calculated time to the peak of the residual was longer that the experimental one, and the spurious oscillation of the calculated residual voltage occurred in the late time or in the non-conductive state of the arrester.

Simplified and Accurate Model of a Surge Arrester
In the results presented in Section 2, the conventional arrester model provided inaccurate results when they were compared to the experimental ones. In this section, a simplified and accurate model of a surge arrester as shown in Figure

Simplified and Accurate Model of a Surge Arrester
In the results presented in Section 2, the conventional arrester model provided inaccurate results when they were compared to the experimental ones. In this section, a simplified and accurate model of a surge arrester as shown in Figure 5 is proposed to overcome the problems of the conventional model. The circuit parameters of the model were composed of the internal resistor (R 0 ) in parallel with the internal inductor (L 0 ), the nonlinear resistor (A 0 ), and the damping resistor (R 2 ) in series with the internal capacitor (C 2 ). As mentioned above, the generation circuit, the parasitic impedance, i.e ductance (Lp) and series resistance (Rp), and the nonlinear characteristic of a sur must be taken into account in the real impulse current generation. The simplif lent circuit including the parasitic impedance and the proposed arrester mod trated in Figure 6. In real practice, it is possible to measure the charging capac charging voltage (Vch), and the arrester capacitance precisely, but it is quite ha ure other circuit parameters. However, the characteristic of the nonlinear resist be approximated from the experimental results of voltage and current across t As shown in Figure 7, in this paper, a piecewise linear curve drawn through th the data of voltage and current of the arrester was employed to represent the ch of the nonlinear resistor. A genetic algorithm was employed to search the unkn parameters of the generation circuit and of the arrester model to match resid (vr) waveforms from the experiment. As mentioned above, the generation circuit, the parasitic impedance, i.e., series inductance (L p ) and series resistance (R p ), and the nonlinear characteristic of a surge arrester must be taken into account in the real impulse current generation. The simplified equivalent circuit including the parasitic impedance and the proposed arrester model is illustrated in Figure 6. In real practice, it is possible to measure the charging capacitance, the charging voltage (V ch ), and the arrester capacitance precisely, but it is quite hard to measure other circuit parameters. However, the characteristic of the nonlinear resistor (A 0 ) can be approximated from the experimental results of voltage and current across the arrester. As shown in Figure 7, in this paper, a piecewise linear curve drawn through the center of the data of voltage and current of the arrester was employed to represent the characteristic of the nonlinear resistor. A genetic algorithm was employed to search the unknown circuit parameters of the generation circuit and of the arrester model to match residual voltage (v r ) waveforms from the experiment.  As mentioned above, the generation circuit, the parasitic impedance, i.e., series inductance (Lp) and series resistance (Rp), and the nonlinear characteristic of a surge arrester must be taken into account in the real impulse current generation. The simplified equivalent circuit including the parasitic impedance and the proposed arrester model is illustrated in Figure 6. In real practice, it is possible to measure the charging capacitance, the charging voltage (Vch), and the arrester capacitance precisely, but it is quite hard to measure other circuit parameters. However, the characteristic of the nonlinear resistor (A0) can be approximated from the experimental results of voltage and current across the arrester. As shown in Figure 7, in this paper, a piecewise linear curve drawn through the center of the data of voltage and current of the arrester was employed to represent the characteristic of the nonlinear resistor. A genetic algorithm was employed to search the unknown circuit parameters of the generation circuit and of the arrester model to match residual voltage (vr) waveforms from the experiment.

Genetic Algorithm
A genetic algorithm (GA) is inspired by the process of natural selection. The genetic algorithm is a kind of stochastic optimization. In this paper, the genetic algorithm [16,17] was utilized to search the appropriate circuit parameters, i.e., the equivalent inductance

Genetic Algorithm
A genetic algorithm (GA) is inspired by the process of natural selection. The genetic algorithm is a kind of stochastic optimization. In this paper, the genetic algorithm [16,17] was utilized to search the appropriate circuit parameters, i.e., the equivalent inductance (L e ), the equivalent resistance (R e ), the internal arrester inductance (L 0 ), the internal arrester resistance (R 0 ), the damping resistance (R 2 ), and the charging voltage (V ch ). The genetic algorithm searches the input parameters (the circuit parameter in the vector form; X) to minimize objective function (Ob(X)), as given in Equation (1).
where v r(exp) and v r(sim) are the residual voltages from experiment and simulation using the arrester model. i is the ith residual voltage point and n is a number of points of the measured and simulated residual voltages.
The flow chart based on the genetic algorithm for searching the most proper circuit parameters is presented in Figure 8. Step 1: Import the recorded waveform data

Start
Step 2: Step 4: Calculate the residual voltage of the arrester model Step 5: Choose the initial population Step 3: Figure 8. Flowchart of the presented genetic algorithm.

Verification of the Proposed Model
To express the validity of the proposed model, two experiments were carried out on two arresters. The first and the second arresters had the nominal discharge currents of 10 kA and 2.5 kA, respectively. In the first experiment, the lightning impulse current of 10

Verification of the Proposed Model
To express the validity of the proposed model, two experiments were carried out on two arresters. The first and the second arresters had the nominal discharge currents of 10 kA and 2.5 kA, respectively. In the first experiment, the lightning impulse current of 10 kA was generated through the first arrester. The nonlinear characteristic of the arrester as shown in Figure 7 was used in the model construction. The genetic algorithm was utilized to search the appropriate unknown circuit parameters. As shown in Figures 9 and 10, the calculated current and residual voltage waveforms agreed well with the experimental results. The time to peak of the calculated residual voltage was almost the same time of the experimental one. The calculated peak current and voltage deviated from the experimental ones by only 0.25% and 0.2, respectively. agreements of the generated currents and the residual voltages were found in both cases As shown in Figures 3 and 4, the calculated current waveform agreed quite well with the experimental result. The time to peak of the calculated residual voltage was almost the same time of the experimental one. The calculated peak current deviated from the experimental one by 5%. The high oscillation of the residual voltage occurred around the peak time, which is quite different from the model one.
It was confirmed that the proposed model is fairly highly accurate for the residua voltage tests.   agreements of the generated currents and the residual voltages were found in both cases As shown in Figures 3 and 4, the calculated current waveform agreed quite well with the experimental result. The time to peak of the calculated residual voltage was almost the same time of the experimental one. The calculated peak current deviated from the experimental one by 5%. The high oscillation of the residual voltage occurred around the peak time, which is quite different from the model one.
It was confirmed that the proposed model is fairly highly accurate for the residual voltage tests.   In the second experiment, the steep impulse current of 2.5 kA was generated through the second one. The comparisons of the generated currents and the residual voltages from the experiment and from the proposed model are shown in Figures 11 and 12. Good agreements of the generated currents and the residual voltages were found in both cases. As shown in Figures 3 and 4, the calculated current waveform agreed quite well with the experimental result. The time to peak of the calculated residual voltage was almost the same time of the experimental one. The calculated peak current deviated from the experimental one by 5%. The high oscillation of the residual voltage occurred around the peak time, which is quite different from the model one.

Applications of the Proposed Method in the Residual Voltage Test
It is hard for a test engineer to control the current waveform and peak without a and error approach. Therefore, in this section, an effective technique is proposed to de mine the charging voltage for obtaining the current waveform according to the stand requirement. The technique starts from the determination of the unknown circuit par eters of the generation circuit and the proposed arrester model as shown in Figure 6. current and residual voltage waveforms from the preliminary test with the lower cur peak specified by the standard were utilized to determine the circuit parameters. Th the previous determined model and a genetic algorithm were employed to search charging voltage to obtain the specified current peak.
To confirm the validity of the proposed technique, some experiments on the resid voltage tests were carried out on two surge arresters with the rated voltage of 9 kV. first arrester had the nominal discharge current of 5 kA and the second one had the n inal discharge current of 2.5 kA.
According to the standard requirement [3] for the residual voltage test of the li ning impulse current, 0.5, 1.0, and 2.0 times the nominal discharge current are genera through the arrester and the residual voltages are examined. In the preliminary exp ment, the charging capacitance and voltage were set to be 2 µF and 30 kV, respectiv and the measured internal capacitance was 56 pF. From the known circuit parameters to obtain the lightning impulse current waveform [18,19], the total inductance of abou µH was required, so the series inductor (L) with inductance of 30 µH was connecte It was confirmed that the proposed model is fairly highly accurate for the residual voltage tests.

Applications of the Proposed Method in the Residual Voltage Test
It is hard for a test engineer to control the current waveform and peak without a trial and error approach. Therefore, in this section, an effective technique is proposed to determine the charging voltage for obtaining the current waveform according to the standard requirement. The technique starts from the determination of the unknown circuit parameters of the generation circuit and the proposed arrester model as shown in Figure 6. The current and residual voltage waveforms from the preliminary test with the lower current peak specified by the standard were utilized to determine the circuit parameters. Then, the previous determined model and a genetic algorithm were employed to search the charging voltage to obtain the specified current peak.
To confirm the validity of the proposed technique, some experiments on the residual voltage tests were carried out on two surge arresters with the rated voltage of 9 kV. The first arrester had the nominal discharge current of 5 kA and the second one had the nominal discharge current of 2.5 kA.
According to the standard requirement [3] for the residual voltage test of the lightning impulse current, 0.5, 1.0, and 2.0 times the nominal discharge current are generated through the arrester and the residual voltages are examined. In the preliminary experiment, the charging capacitance and voltage were set to be 2 µF and 30 kV, respectively, and the measured internal capacitance was 56 pF. From the known circuit parameters and to obtain the lightning impulse current waveform [18,19], the total inductance of about 30 µH was required, so the series inductor (L) with inductance of 30 µH was connected to the generation circuit. As shown in Figure 13, the current waveform deviated from the standard requirement due to effects of the parasitic impedance and the arrester. From the experimental results of current and residual voltage waveforms as shown in Figures 13 and 14, the circuit parameters were determined by using the equivalent circuit in Figure 6. The equivalent inductance (L e ), the equivalent resistance (R e ), the internal arrester inductance (L 0 ), the internal arrester resistance (R 0 ), and the damping resistance (R 2 ) were 41.2 µH, 0.1 Ω, 4.1 µH, and 3.7 kΩ, respectively. From the determined circuit parameters, the total inductance in the circuit was 45.3 µH (L e + L 0 ). Therefore, the series additional inductance of 14.7 µH was required to obtain the lightning impulse current waveform specified by the standard. Another experiment with an additional inductance of 15 µH was carried out to confirm the validity of the proposed technique. Furthermore, using the proposed technique, the calculated charging voltage of 34 kV associating with the current peak of 2.5 kA was set in the experiment. It was found that as shown in Figure 13, the current waveform according to the standard specification was generated when the corrected circuit parameter was applied in the generation circuit. Moreover, the calculated residual voltage agreed well with that from the experiment as shown in Figure 14. The time to peak of the calculated residual voltage was almost the same as the experimental one. The calculated peak current and voltage deviated from the experimental ones by only 0.55% and 0.35%, respectively.
Energies 2021, 14, x FOR PEER REVIEW 9 residual voltage agreed well with that from the experiment as shown in Figure 14 time to peak of the calculated residual voltage was almost the same as the experim one. The calculated peak current and voltage deviated from the experimental ones by 0.55% and 0.35%, respectively.  In a similar manner, the proposed technique with the equivalent circuit assoc with the current peak of 2.5 kA was applied to search the appropriate charging vol associated with the current peaks of 5 kA and 10 kA. The piecewise linear curve us Energies 2021, 14, x FOR PEER REVIEW residual voltage agreed well with that from the experiment as shown in Figure 1 time to peak of the calculated residual voltage was almost the same as the experi one. The calculated peak current and voltage deviated from the experimental ones b 0.55% and 0.35%, respectively.  In a similar manner, the proposed technique with the equivalent circuit ass with the current peak of 2.5 kA was applied to search the appropriate charging v associated with the current peaks of 5 kA and 10 kA. The piecewise linear curve u  In a similar manner, the proposed technique with the equivalent circuit associated with the current peak of 2.5 kA was applied to search the appropriate charging voltages associated with the current peaks of 5 kA and 10 kA. The piecewise linear curve used to estimate the nonlinear characteristic of the nonlinear resistor (A 0 ) is illustrated in Figure 15. From the proposed technique, the equivalent inductance (L e ), the equivalent resistance (R e ), the internal arrester inductance (L 0 ), the internal arrester resistance (R 0 ), and the damping resistance (R 2 ) were 27.1 µH, 0.1 Ω, 4.0 µH, and 3.6 kΩ, respectively. The charging voltages to obtain the current peaks of 5 kA and 10 kA were 46 kV and 69 kV, respectively. Comparisons of the experiment and simulated waveforms by the proposed technique are shown in Figures 16 and 17. Good agreement was found in the case of 5 kA current peak but deviation occurred in the case of 10 kA current peak. In the case of 5 kA current application, the calculated peak current and voltage deviated from the experimental ones by only 0.73% and 0.88%, respectively. In the case of 10 kA current application, the calculated peak current and voltage deviated from the experimental ones by 4.1% and 8.1%, respectively. However, in terms of current generation in the case of 10 kA current peak, the deviation is acceptable because the current peak deviation of 4.1% was less than 10% according to the standard tolerance.     To obtain higher accuracy in the generation of the 10 kA current peak, technique was applied to model the equivalent circuit using the waveforms the 5 kA current peak and it was employed to determine the charging vol the current peak of 10 kA. From the experimental results of current and res waveforms as shown in Figures 15 and 16, the circuit parameters were d using the equivalent circuit in Figure 6. The equivalent inductance (Le), t resistance (Re), the internal arrester inductance (L0), the internal arrester re and the damping resistance (R2) were 26.9 µH, 0.1 Ω, 2.4 µH, and 3.1 kΩ Using the model of the 5 kA current peak, the calculated charging voltage Time (µs) To obtain higher accuracy in the generation of the 10 kA current peak, the proposed technique was applied to model the equivalent circuit using the waveforms in the case of the 5 kA current peak and it was employed to determine the charging voltage to obtain the current peak of 10 kA. From the experimental results of current and residual voltage waveforms as shown in Figures 15 and 16, the circuit parameters were determined by using the equivalent circuit in Figure 6. The equivalent inductance (L e ), the equivalent resistance (R e ), the internal arrester inductance (L 0 ), the internal arrester resistance (R 0 ), and the damping resistance (R 2 ) were 26.9 µH, 0.1 Ω, 2.4 µH, and 3.1 kΩ, respectively. Using the model of the 5 kA current peak, the calculated charging voltage to obtain the current peak of 10 kA was 67.3 kV and a charging voltage of 67.5 was set in the experiment. Comparison of the generated currents by simulation with the proposed model and that from the experiment is shown in Figure 18. In addition, the comparison of the experimental and simulated residual voltages is shown in Figure 19. A better agreement between the simulated and experimental was found. The calculated peak current and voltage deviated from the experimental ones by only 0.43% and 0.56%, respectively. nergies 2021, 14, x FOR PEER REVIEW current peak of 10 kA was 67.3 kV and a charging voltage of 67.5 was set ment. Comparison of the generated currents by simulation with the propos that from the experiment is shown in Figure 18. In addition, the comparison imental and simulated residual voltages is shown in Figure 19. A better a tween the simulated and experimental was found. The calculated peak cur age deviated from the experimental ones by only 0.43% and 0.56%, respecti   In a similar manner, the proposed technique was applied for the residu on the arrester with the nominal discharge current of 2.5 kA. The prelimina steep impulse current was carried out at the current peak of 1.25 kA. For the current generation, the charging capacitance, the charging voltage, and the sistance were set to 2 µF, 78 kV, and 38 Ω, respectively, and the measured i itance was 50 pF. From the calculation using the proposed technique, the ductance (Le), the equivalent resistance (Re), the internal arrester inductanc ternal arrester resistance (R0), and the damping resistance (R2) were 14 µH, and 198 Ω, respectively. Using the proposed technique to obtain the curre kA, the calculated charging voltages was 134.5 kV and the setting charging experiment to confirm the validity of the proposed technique was 135 kV. of the experiment and simulated waveforms by the proposed technique are ures 20-22, in which good agreement is found. It was confirmed that the p nique is very effective in the residual voltage tests. In the case of 2.5 kA cu tion, the calculated peak current deviated from the experimental one by 7 still in the standard tolerance. In a similar manner, the proposed technique was applied for the residual voltage test on the arrester with the nominal discharge current of 2.5 kA. The preliminary test with a steep impulse current was carried out at the current peak of 1.25 kA. For the steep impulse current generation, the charging capacitance, the charging voltage, and the additional resistance were set to 2 µF, 78 kV, and 38 Ω, respectively, and the measured internal capacitance was 50 pF. From the calculation using the proposed technique, the equivalent inductance (L e ), the equivalent resistance (R e ), the internal arrester inductance (L 0 ), the internal arrester resistance (R 0 ), and the damping resistance (R 2 ) were 14 µH, 0.1 Ω, 2.8 µH, and 198 Ω, respectively. Using the proposed technique to obtain the current peak of 2.5 kA, the calculated charging voltages was 134.5 kV and the setting charging voltage in the experiment to confirm the validity of the proposed technique was 135 kV. Comparisons of the experiment and simulated waveforms by the proposed technique are shown in Figures 20-22, in which good agreement is found. It was confirmed that the proposed technique is very effective in the residual voltage tests. In the case of 2.5 kA current application, the calculated peak current deviated from the experimental one by 7.8%, which is still in the standard tolerance.

Conclusions
A simplified and accurate model of a surge arrester for the residual vol proposed in this paper. The validation of the proposed model was verified with some experiments. Furthermore, the technique for the estimation of parameters and the charging voltage to obtain the specified current wavef was proposed. In addition, the residual voltage associated with the specifie estimated precisely. The validity of the proposed technique was verified ments. It was confirmed that the proposed technique is very useful in the re

Conclusions
A simplified and accurate model of a surge arrester for the residual vo proposed in this paper. The validation of the proposed model was verified with some experiments. Furthermore, the technique for the estimation of parameters and the charging voltage to obtain the specified current wavef was proposed. In addition, the residual voltage associated with the specifie estimated precisely. The validity of the proposed technique was verified ments. It was confirmed that the proposed technique is very useful in the re

Conclusions
A simplified and accurate model of a surge arrester for the residual voltage tests was proposed in this paper. The validation of the proposed model was verified in comparison with some experiments. Furthermore, the technique for the estimation of setting circuit parameters and the charging voltage to obtain the specified current waveform and peak was proposed. In addition, the residual voltage associated with the specified current was estimated precisely. The validity of the proposed technique was verified by the experiments. It was confirmed that the proposed technique is very useful in the residual voltage tests of arresters and helps test engineers in the selection of appropriate circuit components without a trial and error approach.
Funding: This project is funded by National Research Council of Thailand.