An Experimental Methodology for Modeling Surge Protective Devices: An Application to DC SPDs for Electric Vehicle Charging Stations

This work introduces an experimental methodology for time-domain modeling of low-voltage surge protective devices (SPDs), accounting for their sparkover performance as well as their resistive, inductive, and capacitive behavior. The modeling procedure is demonstrated through an application to a combination type SPD connected to the DC side of electric vehicle charging stations. An equivalent circuit model is developed based on experimental records acquired from applied voltages and currents of a wide frequency range and energy content. The developed lumped-circuit model yields results in very good agreement with experimental data regarding sparkover voltage, residual voltage, and energy absorption of SPDs, as illustrated through ATP-EMTP simulations. The proposed methodology can be an effective tool for surge protection and insulation coordination studies.

is necessary to properly assess the mitigation of overvoltages, evaluate the stress of equipment under protection, and carry out a reasonable risk assessment study against direct and indirect lightning-related surges [9], [10], [11], [12].
Although extensive work has been done for modeling and characterization of surge protective components [13], [14], it is a formidable task to integrate physical models into electromagnetic transients simulation programs.For practical engineering applications, low-voltage surge protective devices are commonly modeled following i) a purely resistive approach based on the voltage-current curves [15], [16], [17] or ii) frequency-dependent models developed for gapless highvoltage surge arresters [18], [19], [20].The accuracy of these modeling approaches in reproducing the transient performance of low-voltage SPDs for the entire surge current flow duration is questionable [21], [22].Thus, time-domain modeling of the complex behavior of SPDs in the case of electromagnetic pulses of variable frequencies and energy content is still an open topic.
This work introduces an experimental methodology for modeling low-voltage surge protective devices.The modeling procedure is demonstrated through an application to a commercially available combination type SPD, commonly integrated into converters used in electric vehicle fast chargers operating at 1 kV DC; a preliminary account of this has been provided in [23].A lumped-circuit model is developed based on standard and non-standard experiments involving i) lightning and switching impulse voltages up to 18 kV, ii) impulse current tests up to 30 kA, and iii) sinusoidal voltages.
The efficiency of the developed model, accounting for the sparkover performance as well as the resistive, inductive and capacitive behavior of the SPD, is validated through a comparison with experimental data regarding sparkover voltage, residual voltage, and energy absorption.The proposed model reproduces the recorded surge performance of the DC SPD under study very accurately, as illustrated through ATP-EMTP simulations; it is found to be more accurate than Pinceti and Giannettoni model [18], which is commonly used in the surge protection industry.The proposed modeling approach can be an effective tool for surge protection and insulation coordination studies [24], [25], [26], especially for emerging DC systems such as battery energy storage systems and electric vehicle charging stations [27], [28], [29], [30].

II. SURGE PROTECTIVE DEVICE UNDER STUDY
The device under test was a combination type DIN rail surge protective device (SPD) shown in Fig. 1 employing metal-oxide varistors (MOVs) between DC power lines and a gas discharge tube (GDT) connected between a common bar (CM) and ground (GND) that practically eliminates the leakage current to earth.The SPD under study is designed to be connected to charging stations operating at voltages up to 1 kV DC (U C ) and the protection mode under experimental investigation is the power line to ground (DC-GND), designated by the red dashed line in Fig. 1; the basic electrical characteristics of the DC SPD are given in Table I.

III. EXPERIMENTAL ARRANGEMENTS
For the determination of the transient response of the surge protective device under study (Fig. 1), standard lightning LI (1.2/50 µs) and switching SI (250/2500 µs) impulse voltages and standard impulse currents of 8/20 µs and 10/350 µs waveforms were used (Fig. 2(a) and (b)).Taking advantage of the available interchangeable components (Table II) of the High Voltage Laboratory of the Aristotle University of Thessaloniki, the line to ground (DC-GND) protection mode of the SPD was also stressed with non-standard (very fast-front) lightning impulse voltages (0.3/44 µs) and impulse currents (1/130 µs); details on impulse voltage and current waveforms are given in Table III.The impulse currents were recorded by using current transformers (Pearson: 301X, 110), and the residual voltage at SPD terminals was monitored by LeCroy HVP 120 probe (400 MHz) via twisted cables to minimize mutual inductance effects (Fig. 3).
For the determination of the capacitance and the leakage current of the DC SPD, sinusoidal (AC) and DC voltages were applied (Fig. 2(c)) with the aid of a 4.8 kVA AC power supply  (Agilent 6843A), and a DC power supply, respectively.The current was measured through the voltage drop, V RCur , across low inductance high-power resistors, R Cur , and a Keithley 196 System DMM current monitor; voltages were monitored by LeCroy HVP120 probe.For all configurations (Fig. 2) a Tektronix TDS 3064B digital oscilloscope (600 MHz) was employed to record the voltage/current measurements following the UL 1449 [32] and forthcoming IEC 61643-01 [33] standard procedures.) with an added component of the current-dependent arc resistance of the voltage-switching components; R(i) also incorporates the intrinsic resistance of the SPD conductive paths.c) an inductance, L, that is associated with the intrinsic inductance of SPD conductive paths [34] and the inductive-like behavior of the protective components, especially the effect of holes in surge current conduction via varistors [14], [35].II and III), respectively.Fig. 5(c) shows typical voltage records at the surge protective device terminals (DC-GND) for applied open-circuit voltages of ∼3 kV and ∼16 kV, 1.2/50 µs.The voltage at the SPD terminals, V SPD , increases up to the sparkover of the integrated gas discharge tube, GDT (sparkover voltage, V s ).Due to the sudden drop of the SPD impedance, V SPD decreases at the time instant of breakdown (time to breakdown, t b ); the higher the applied voltage, the shorter the time to breakdown and the higher the sparkover voltage (Fig. 5(c)) attaining values always lower than the declared protection level, U p , of 3.2 kV (Table I).After the breakdown of the GDT, a discharge current flows through the series-connected GDT and MOV components (Fig. 1); the residual voltage (∼1 kV) is the sum of the residual voltage of the MOV and the arc voltage of the GDT at the relatively low discharge current of the impulse voltage generator (<60 A).

A. Sparkover Performance
Fig. 6 depicts the voltage-time data points, V s -t b , of the sparkover performance of the SPD under study obtained from lightning and switching impulse voltage tests.As it can be deduced from the slope of the voltage-time curve for time to breakdown lower than 100 ns, there is a significant increase of the SPD sparkover voltage for transients with high voltage derivative (dV/dt).This observation stresses the need for an accurate representation of the response time of SPDs integrating voltage-switching components (spark gaps, gas tubes, etc.) as well as the investigation of the protection level of SPDs beyond the standard impulse voltage and current waveforms [36], [22].The sparkover performance of the SPD under non-standard impulse voltages is modeled by employing the integration method [37], [38] which can be mathematically described as follows: where t (µs) is the elapsed time after the impulse voltage application, t 0 (µs) is the instant when the applied voltage exceeds a threshold voltage, V 0 (kV), k is a factor accounting for the effects of the applied voltage amplitude and waveform [37], [39], and DE (kV k •µs) is the disruptive effect of the voltage at the SPD terminals, V SPD (kV); breakdown occurs at the time instant, t b , when DE becomes equal to or higher than the critical disruptive effect The appropriate values for integration method parameters shown in Fig. 6 are selected to minimize the deviation of simulation results with the experimental data points derived from impulse voltage tests representing fast-front [11] and slow-front  It is important to note that the sparkover voltage and time to breakdown of the SPD exhibit a statistical behavior since the breakdown of the voltage switching-components is stochastic in nature; an alternative statistical modeling approach treating DE * employed in (1) as a statistical quantity is presented in Appendix B. For the SPD under study, the stochastic sparkover performance of the integrated GDT depends on several parameters such as electrode morphology, material, and erosion as well as gas mixture composition and pressure [41], [42].I).It is noteworthy that the voltage spike of ∼2.7 kV, which is the sparkover voltage of the GDT, precedes the maximum residual voltage of the SPD (V M ∼ 1.8 kV), and it is associated with the declared protection level of the SPD (U p = 3.2 kV, Table I).

B. Resistive Behavior
The voltage-current characteristic of the SPD can be obtained by using the residual voltage, V R , at the peak of the current, I R , in order to avoid inductive effects on voltage measurement [34] since the current derivative, dI/dt, is practically zero at t R Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.( It must be noted that the V-I curve depicted in Fig. 8, fits the experimentally derived points (V R , I R ) at t R (dI/dt = 0, Fig. 7(b)) and differs from the V-I curve that is commonly provided by the SPD manufacturers that employ pairs of the maximum residual voltage, V M , and current, I R , that correspond to different time instants (t M , t R in Fig. 7(b)).It is important to note that the resistive behavior of the SPD can be described by a single voltage-current (V R -I R ) curve, that is found to be practically independent of current waveform (Fig. 8); V R -I R curve and the associated non-linear resistance, formulated by (2), can be used as a reference for estimating the inductive behavior of the SPD presented in what follows.

C. Inductive Behavior
The fact that the residual voltage of the SPD attains a maximum value, V M , at t M before the peak of the current at t R (Fig. 7(b)) signifies the inductive-like behavior of the SPD, which can be modeled by an equivalent inductance, L (AC' in Fig. 4).
The maximum residual voltage of the SPD, V M , can be well approximated as follows: where R(I) is given by ( 2), I M is the current at the time instant t M that the maximum residual voltage occurs, dI/dt is the current derivative at t M and L is the equivalent inductance.L can be evaluated based on (3) since all the other parameters  are known through experimental records.Equivalent inductance is associated with the intrinsic inductance of the conductive paths within the structure of the SPD [34], the inductive-like behavior of protective components, and it is contaminated by the mutual inductance of the measuring circuit [31]; the latter can be practically eliminated by employing a voltage measurement setup as shown in Fig. 3.An alternative procedure for a simplified estimation of L is the replacement of the non-linear protective components of the SPD by copper blocks [34].Such dummy SPD inductance can be measured through high precision impedance analyzers or via the residual voltage, V D (t), of the SPD during surge current flow, I(t) (Fig. 9); the latter can be formulated as: where R D is the intrinsic resistance of the dummy SPD.Fig. 10 shows the inductance, L, of the SPD under study (Fig. 1) determined by ( 3) and (4) for different impulse current experiments.It is obvious that the equivalent inductance depends on i) impulse current waveform and ii) current derivative; it is important to note that the dummy SPD analysis underestimates the equivalent inductance of the SPD since it ignores the inductive-like behavior of the surge protective components, especially the transient behavior of MOV for very fast-front surges [35].A constant L approach, determined at standard impulse currents based on (3), will be shown that provides a satisfactory agreement with experimental results; however, as it can be deduced from Fig. 10 and it is implied in literature [22], [43], [44], the inductive behavior of the SPD is dynamic in nature and L may vary during surge current flow.

D. Capacitive Behavior
The experimental setup of Fig. 2(c) is used to employ sinusoidal voltages to SPD components in order to determine the capacitances at the SPD equivalent circuit model (C R and C S in Fig. 4).For the SPD under study an AC voltage of 300V/ 1kHz was applied to the MOV (DC to CM in Fig. 1) and to the GDT (GND to CM in Fig. 1).The current flowing through the MOV or GDT (Fig. 11) at this voltage level (pre-breakdown region) can be described as follows [45]: where I C (t) is the capacitive component and I R (t) is the resistive component of the current.Considering that the current at the time instant of zero voltage, t 0 , is purely capacitive, the capacitance of the MOV, C R , or GDT, C S shown in Fig. 4 can be defined as: A constant C approach is followed, although it is discussed in literature that varistor capacitance C R may vary with voltage   [45], [46] since the capacitive behavior of the SPD does not significantly affect its surge performance.
The maximum continuous operating voltage of the SPD is applied and the leakage current to the ground is measured (Fig. 2(c)); thus R S shown in Fig. 4 is estimated (>10 GΩ).

A. ATP-EMTP Simulation Model of the SPD
The surge protective device under study (Fig. 1) can be modeled by using the equivalent lumped-element circuit (Fig. 4) that is integrated into ATP-EMTP [47] as shown in Fig. 12; this ATPDraw model reproduces the non-linear performance of the integrated gas discharge tube (GDT) and metal-oxide varistors (MOVs).Modeling details are given in Table IV.

B. Comparison With Experimental Data
The efficiency of the developed ATP-EMTP simulation model (Fig. 12 and Table IV) has been validated through comparison Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.with experimental data.A comparison against the experimentally derived sparkover voltage of the surge protective device (SPD) under study is considered for a wide range of lightning (1.2/50 µs, 0.3/44 µs) and switching impulse voltages (250/2500 µs) up to 18 kV.From Fig. 13 it is evident that there is a good agreement between the simulated and measured sparkover voltages of the SPD.The simulation error was generally less than 10% (max 14.8%) as detailed in Table V for 3 impulses per voltage level; the simulation accuracy is satisfactory when considering the expected spread of the sparkover voltage of the integrated GDT [41], which is typically declared within 20% by GDT manufacturers [48].Nevertheless, to further improve the accuracy of the predictions of the proposed deterministic modeling approach on the sparkover performance of SPDs, an alternative statistical method is proposed in Appendix B; this method yields a range of sparkover voltage instead of a fixed value (Fig. 18).Fig. 14 shows simulation results together with voltage and current records from impulse current tests.The computed residual voltage of the SPD (V M , V R as defined in Fig. 7(b)) with the proposed model is in very good agreement with the experimental data (simulation error < 6%) derived from impulse current tests up to 30 kA, 8/20 µs, 2.5 kA, 10/350 µs and 6.2 kA, 1/130 µs (Table VI); these upper limits were about 50% of the surges producing irreversible degradation to SPD components.On the contrary, the agreement of the Pinceti and Giannettoni (P&G) model [18] (details in Appendix A), commonly used in surge protection industry, is not always adequate, besides the use of 2 non-linear resistive elements, especially for non-standard current waveforms and peak values afar the reference level of 10 kA; the latter is understandable since the P&G model has been developed for high voltage surge arrester and a lot of technical data required as inputs are not provided by manufacturers of low-voltage SPDs.A necessary modification of the original  P&G model is introduced by the authors to yield simulation results with acceptable errors (<15%) as shown in Fig. 14(a).Model has been adapted as follows: i) non-linear resistances A0, A1 were calculated based on the residual voltage V R , instead of V M , at 10 kA, 8/20 µs ii) L0, L1 were computed based on resistive residual voltage V R at 10 kA 8/20 µs and V M at 10 kA 1/T2 µs instead of using V M values at 10 kA, 8/20 µs and 1/T2 µs; an application is shown in Appendix A.
It is noteworthy that the proposed model predicts the development of a maximum residual voltage beyond the protection level of the SPD for ∼6 kA, 1/130 µs, whereas the adapted P&G model underestimates (6%) the overshoot of the residual voltage (inset graph Fig. 14(c), measured V M = 3.22 kV); this overshoot is important when considering the very fast-front transient performance of SPDs in cases such as subsequent lightning strokes [41] and nuclear electromagnetic pulses [49].
In order to evaluate the efficiency of the developed model to reproduce the SPD transient behavior for the complete surge current duration an additional comparison is made for the energy absorption, E, of the SPD defined as: where V SPD (t) is the voltage across the SPD during surge current flow, I(t).The proposed model yields results in excellent agreement with the recorded energy absorption, that is one of the main parameters determining the SPD failure probability, with simulation errors generally lower than 3% (max 4.8%) whereas the adapted P&G model computations are associated with errors up to 15% (original model yields errors up to 25%).These results are very encouraging when considering that the measurement error of voltage and current records is within 3% and that voltage-current characteristics of metal-oxide varistors of the same type may vary up to 10% [50].

VI. CONCLUSION
A novel experimental methodology has been introduced for modeling low-voltage surge protective devices (SPDs).An application has been made to a combination type SPD connected to the DC side of electric vehicle charging stations and an equivalent lumped-element circuit model has been developed.The experimental investigation of the transient performance of the DC SPD for a wide range of impulse voltage (2.5 kV-18 kV) and impulse current (0.5 kA -30 kA) tests has shown that: r The sparkover performance of the SPDs can be evaluated through voltage-time (V s -t b ) curves derived from impulse voltage tests.The integration method proved an efficient tool for modeling the sparkover performance the SPD against overvoltages with time to front in the range of ∼0.3-250 µs and time to half of ∼40-2000 µs.
r The resistive behavior of the SPDs can be described by a single voltage-current (V R -I R ) characteristic curve, derived from residual voltage measurements at the time instant of the peak of the impulse current (zero current derivative).The voltage-current curve is found to be practically independent of the surge current waveform unlike the V-I curves provided by SPD manufacturers that employ pairs of the maximum residual voltage and peak current that correspond to different time instants.
r The maximum residual voltage of SPDs during surge cur- rents is associated with the intrinsic inductance of SPD conductive paths and the inductive-like behavior of the integrated protective components.The inductive behavior of the SPD can be modeled through a lumped inductance that is found to be dynamic in nature.A constant inductance estimated at nominal discharge current can be adopted as a simplified approach for modeling the overshoot of the residual voltage at the wavefront without compromising Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.
the accuracy at the wave-tail for a wide range of surge currents with time to front between ∼1-30 µs and time to half between ∼20-400 µs.
r The capacitive behavior of the SPD, that does not signifi- cantly affect its transient behavior, can be evaluated at the time instant of zero voltage under low frequency tests.The developed model has been in ATP-EMTP; a comparison of simulation results with experimental data has shown that: r The proposed model yields satisfactory results for standard and non-standard (very fast-front) impulse voltages with simulation errors less than 15% in the SPDs sparkover voltage.The integration method-based approach predicts satisfactorily the SPD performance for fast-front and slow-front overvoltages; a statistical modeling approach is needed for further improvement in the prediction of the sparkover performance of SPDs.
r The proposed model yields excellent results for standard and non-standard (very fast-front) impulse currents with simulation errors generally less than 5% in the SPDs residual voltage and the associated energy absorption.The inclusion of a series inductance in series with a single current-dependent resistance, masking the capacitive behavior of the SPD, yields very good results in modeling the transient behavior of the SPD for a wide range of surge currents.The Pinceti & Giannettoni model, besides its frequency-dependent behavior, is less accurate on modeling low-voltage SPDs, especially under non-standard impulse currents; a necessary modification is proposed for model implementation to low-voltage SPDs so as to yield simulation results with acceptable errors.

APPENDIX A EQUIVALENT CIRCUIT MODELS
Equivalent circuit models of voltage-limiting and voltageswitching SPDs are shown in Fig. 15.
Pinceti and Giannettoni model [18] employed at AC branch of Fig. 4 (DC to CM in 1).Original model details, and values as adapted by the authors for low-voltage SPDs are given in Fig. 16.

APPENDIX B STATISTICAL APPROACH FOR MODELING THE SPARKOVER PERFORMANCE
The integration method, presented in Section IV-A, is inherently deterministic with simulation errors up to 15%; however, by treating the critical disruptive effect DE * as a statistical quantity rather than a fixed value, the stochastic sparkover performance of the SPDs can be modeled yielding a range of sparkover voltage under the same overvoltage conditions.As an illustrative example for the DC SPD under study, the following equation defines the criterion of breakdown at time instant (t = t b ) that DE becomes equal to or higher than the critical disruptive effect   where r takes random values between 0 and 1 for each simulation run, t (µs) is the elapsed time after the impulse voltage application, t 0 (µs) is the instant when the applied voltage exceeds a threshold voltage, V 0 (kV), t b is the time to breakdown, DE (kV•µs) is the disruptive effect of the voltage at the SPD terminals, V SPD (kV); DE * is uniformly distributed between 0.005 and 0.035 kV•µs based on (8).Such a statistical variation of DE * can be integrated into ATP-EMTP environment through MODELS language [51] as shown in Fig. 17.
Employing (8) in ATP-EMTP (Fig. 17) for multiple simulation runs, a range of sparkover voltage is obtained even under the same overvoltage conditions; this is shown in Fig. 18, which depicts the borders of the voltage-time variation corresponding to the range of DE * (0.005-0.035 kV•µs).As an illustrative example, Fig. 19 shows the SPD sparkover simulation results under 11.2 kV, 0.3/44 µs for the mean value of DE * (0.02 kV•µs) employed in the conventional integration method that yields error on sparkover voltage of ∼15% and the value of 0.011 kV•µs that lies within the statistical range of DE * that accurately predicts the sparkover voltage (error < 1%).

Fig. 1 .
Fig. 1.Schematic diagram of the DIN rail SPD under study.

Fig. 5 (
Fig. 5(a) and (b) depict the open circuit (per unit) lightning impulse (1.2/50 µs and 0.3/44 µs) and switching impulse (250/2500 µs) voltages produced by the impulse voltage generator (Fig. 2(a), TablesII and III), respectively.Fig.5(c) shows typical voltage records at the surge protective device terminals (DC-GND) for applied open-circuit voltages of ∼3 kV and ∼16 kV, 1.2/50 µs.The voltage at the SPD terminals, V SPD , increases up to the sparkover of the integrated gas discharge tube, GDT (sparkover voltage, V s ).Due to the sudden drop of the SPD impedance, V SPD decreases at the time instant of breakdown (time to breakdown, t b ); the higher the applied voltage, the shorter the time to breakdown and the higher the sparkover voltage (Fig.5(c)) attaining values always lower than the declared protection level, U p , of 3.2 kV (TableI).After

[ 40 ]
transients; V 0 is taken from the right side of the curve (t b →Ý) and then k, DE * are computed to fit the experimental data associated with the upturn region of the voltage-time curve.

Fig. 7 (
Fig. 7(a) depicts the impulse currents (per unit) of standard (8/20 µs and 10/350 µs) and non-standard (1/130 µs) waveform produced by the impulse current generator (Fig. 2(b), Tables II and III), respectively.Fig. 7(b) shows a typical record of the transient response of the SPD (DC-GND) under study when stressed with the nominal discharge current, I n , of 12.5 kA, 8/20 µs (TableI).It is noteworthy that the voltage spike of ∼2.7 kV, which is the sparkover voltage of the GDT, precedes the maximum residual voltage of the SPD (V M ∼ 1.8 kV), and it is associated with the declared protection level of the SPD (U p = 3.2 kV, TableI).The voltage-current characteristic of the SPD can be obtained by using the residual voltage, V R , at the peak of the current, I R , in order to avoid inductive effects on voltage measurement[34] since the current derivative, dI/dt, is practically zero at t R

Fig. 8 .
Fig. 8. Voltage-current (V R , I R ) characteristic curve of the SPD (DC-GND); data points derived from impulse current tests.

Fig. 18 .
Fig. 18.Sparkover voltage versus time to breakdown under fast-front transients based on the statistical modeling approach.

TABLE I ELECTRICAL
CHARACTERISTICS OF SURGE PROTECTIVE DEVICE

TABLE II COMPONENTS
OF GENERATORS EMPLOYED IN IMPULSE VOLTAGE AND IMPULSE CURRENT EXPERIMENTS Fig. 3. Residual voltage measurement; adapted from [31].

TABLE III APPLIED
IMPULSE VOLTAGES AND IMPULSE CURRENTS

TABLE IV ATP
-EMTP MODELING OF THE SPD and voltage derivative

TABLE V SIMULATION
ERRORS IN SPARKOVER VOLTAGE OF THE SURGE PROTECTIVE DEVICE Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.