IX International Symposium on Lightning Protection th th 26 -30 November 2007 – Foz do Iguaçu, Brazil SURGE PROTECTIVE DEVICE RESPONSE TO STEEP FRONT TRANSIENT IN LOW VOLTAGE CIRCUIT. J.Marcuz S.Binczak J.M.Bilbault F.Girard LE2I UMR CNRS 5158 université de Bourgogne [email protected] laposte.net [email protected] [email protected] ADEE electronic avenue Alain Savary 21048 Dijon, France PONT DE PANY France Abstract - Surge propagation on cables of electrical or data lines leads to a major protection problem as the number of equipments based on solid-state circuits or microprocessors increases. Sub-microsecond components of real surge waveform has to be taken into account for a proper protection even in the case of surges caused by indirect lightning effects. The response of a model of transient voltage suppressor diode (TVS) based surge protection device (SPD) to fast front transient is analytically studied, then compared to simulations, including the lines connected to the SPD and to the protected equipment. Keywords: SPD, Surge Propagation, Fast transient, low Voltage Circuit, protection distance. 1.INTRODUCTION The lightning surges are highly destructive, especially for the last generation of electronic systems based on solid-state circuits and microprocessors. These systems work at very low voltage and are often ground insulated. These advanced electronic devices have a weak electrical surge withstand capability, therefore surge protection devices are widely used to protect electronic systems. It has been shown that sub-microsecond rise time is possible in subsequent return strokes , whereas building wiring does not always have sufficient damping effects for steep fronts  induced by close subsequent strokes, and can even imply overvoltages due to inductances. Therefore, for proper protection against steep front transients, surge protection devices (SPD) with extremely short timeresponse are needed nowadays. In low voltage power distribution systems, setting up SPD on the distribution board prevents side effects in the installation, avoiding the flow of surge currents in the branch circuits. But the way of setting up the SPD and especially the inductance of long connections to the protected line or to the grounding system, degrades SPD performances. Moreover, the length of connecting cables between the SPD and the load can produce reflection and resonance. These phenomena can increase the voltage at the load up to twice the protection level at SPD connection point notably for fast front transient. In this paper, an analytical study has been carried out in order to define the behavior of SPD under fast front transients. The analytical expressions have been compared with an electromagnetic transient simulation program (EMTP) for validation. In section II, we will consider the SPD between two infinite or matched lines. In section III, the influence of the load and line length is investigated. In section IV, a parametric study is conducted focusing on two parameters. 2.ANALYTICAL APPROACH 2.1 Modelling Figure 1 describes the electrical system under investigation, where the load is the electronic system to be protected and where the generator models an incoming surge by releasing fast front transients. In between, the SPD is connected to the lines and to the earth via cables. Earth is modeled by its inductance and its resistance , in the case of grounding by rods. Figure 1: electrical configuration under study. About the generator, bi-exponential waves will be considered. Bi-exponential waves are indeed usually introduced as the normalized waves induced by a stroke. In the case of infinite or matched lines, there is no need to define the load precisely, while section IV will deal with capacitive ones. The dynamical characteristics of the SPD are so that : - C is the stray capacity of SPD, ranging from few hundred pico-Farads to nano-Farads for TVS diodes. - RV is the nonlinear resistance, allowing deviating unwanted power. - L is the inductance of the earthing, which is estimated to be about 1µH. - RE is the earth resistance with the standard value of 10 ohms. The TVS diode based SPD could be seen as derivating from the IEEE recommended model for varistors  also known as the Durbak’s model, which is presented in Figure 2. Note that the second nonlinear resistance A1 is decoupled for the fast front transients (Figure 2) due to the inductive effect of L1. Thus, this part of the model is ignored. The resistance R0 has been inserted to avoid numerical instability during simulations  and has therefore no physical meaning. So, these parameters (grayed on Figure 2) are not taken into account in the following. The value of RON is the dynamic resistance of the TVS diode; it has been chosen from the parameter VBR and clamping voltage VCL at peak pulse current IPP for a given surge duration. The dynamic resistance is calculated with the following formula  for pulse with 20µs duration. RON = VCL − VBR . I PP20µs (1) This value lies around few Ω for TVS diodes with VBR higher than 100 volts, so RON is fixed to 1 Ω. These values are estimated roughly and correspond to a wide range of magnitude values, whereas it depends notably on stand-off voltages and peak pulse power of the considered TVS diode. At the SPD location, the lines are considered long enough to be viewed as infinite or matched ones for the time duration of the front. Therefore the SPD can be regarded as being connected to two lossless lines of equal characteristic impedance RC. For usual installation cables, the characteristic impedance lies between 50 Ω and 200 Ω. So in figure 4.a, by a Thevenin and Norton equivalence, the value of Req (in Figure 4.b) is taken to be equal to half the characteristic impedance of lines: Req = RC 2 and VE1 = VE . 2 (2) Figure 2 : IEEE recommended model (from ) L0 is the inductance of the SPD including its connection to the line. The value of L0 could be included in L. TVS diodes present strong nonlinearity so V(I) is approximated to fit a piecewise linear function : RV(V) is a piecewise constant function. Therefore, it can only take two different values : ROFF before spark over and RON after, as illustrated in Figure 3. The transition between these two values corresponds to the transition voltage VBR of TVS diode. ROFF and RON are calculated according to  from the TVS diode parameters given on technical datasheets: leakage current at the stand-off voltage (IR @ VRM) breakdown voltage at test current (VBR @ IT) clamping voltage at maximum peak pulse current for given waveform (VCL @ IPP for 20µs pulse). The value of ROFF is assumed to be about 1 MΩ, IR at VRM and VBR at IT give the values of the static resistance under nominal voltage and breakdown voltage which lies between a few tens of kΩ and a few tens of MΩ. Figure 3 : approximated V(I) function of the RV model. In the following expressions, the subscript ON denotes that RV takes the value RON, idem for the subscript OFF. These subscript are also used to differentiate the voltages and variables before and after sparkover. a) Electrical circuit b) Equivalent electrical circuit Figure 4 : local modeling of SPD setup. From the electrical circuit of Figure 4.b, voltages VC and VP before spark over can be written in the Laplace domain: V 1 ( s).( s -Z1 )( s -Z 2 ) , VP OFF ( s) = E ( s -P1 )( s -P2 ) VC OFF ( s ) = VE1 ( s ) . LC ( s -P1 )( s -P2 ) (3) (4) VEn 1 (t ) = A(e − a (t + tb ) -e − b (t + tb ) )-VBR . n ( 1 V 1(s).(s-Z1)(s-Z2) +VPON (0)(s-Z3) n (s-P1)(s-P2) En 1 whereas P1,P2 are the roots of 2.2 Analytical expressions The usual waveform for lightning surge is the biexponential. If we consider for instance a 0,1/50 µs voltage wave, it is expressed by the following formula: VE1 (t ) = A(e-at - e-bt ) , 4 -1 7 (7) -1 where a=1,4.10 s and b=2,3.10 s . The bi-exponential surge is given in Laplace domain by VE1 ( s ) = A( 1 1 − ), s+a s+b (8) so the voltage at the nonlinear part of the SPD before spark over can be written after inverse Laplace transform as: e-a t e-b t − ( a + P )( a + P ) ( b + P )( b + P ) A 1 2 1 2 , (9) VCOFF (t) = P1 t P2 t LC b − a e e + P1 − P2 (a + P1)(b + P1) (a + P2)(b + P2) and the terminal voltage of the SPD is given introducing (8) in (3) expressed in time domain: e-at (a+Z1)(a+Z2) e-bt (b+Z1)(b+Z2) (b+P1)(b+P2) (a+P1)(a+P2) .(10) VPOFF (t) = A P1 t P2 t + b-a e (P1 -Z1)(P1-Z2) - e (P2 -Z1)(P2 -Z2) P1 - P2 (a+P1)(b+P1) (a+P2)(b+P2) The nonlinear resistance changes from ROFF to RON at tb, when the voltage at the nonlinear part of SPD (VC in Figure 4) reaches the reference voltage VBR. The point (tb,VBR) is taken as the new origin for VPON , so the surge is now expressed in this way with the additional (12) dVP dVEn1 ONn . -VEn (0)(s-Z4) + dt d t 0 0 (5) RV LCs ² + ( L + ( Req + RE ) RV C ) s + RV + Req + RE = 0 . (6) (11) Additional terms should be inserted here for right inverse Laplace transform. The values of VEn and VPn and those of their derivative at the new origin of the new coordinates are taken into account. VPON (s) = In equations (3) and (4), Z1, Z2 are the roots of RV LCs ² + s( L + RV RE C ) + RV + RE = 0 , subscript n used for terms expressed in the new coordinates. The diagram on the Figure 4.b implies the continuity of VC and IP. The expression of surge VE and its derivative are taken as continuous, so the derivative of IP and VP are also continuous. The continuity of VC implies those of the current through the nonlinear resistance and then through the capacity, thus the time derivative of VC is also continuous. These continuities lead to: VPON (0) = VPOFF (tb )-VBR , VEn1(0) = VE1(tb )-VBR , (13) n dVPON dt n = 0 dVPOFF dt and dVEn 1 tb = dt 0 dVE1 .(14) dt tb For equation (12), the roots Z3 and Z4 can be expressed such as Req 1 1 . (15) Z3 = − + and Z 4 = − L R C R ON ON C Then the expression of VPON in time domain in the new n coordinates is : e- a (t + tb ) (a + Z1 )( a + Z 2 ) e-b (t + tb ) (b + Z1 )(b + Z 2 ) (a + P1 )(a + P2 ) (b + P1 )(b + P2 ) P1 t -b tb - a tb ( )( )( ) e P Z P Z be ae 1 1 1 2 VP ON (t ) = A + n ( P1 - P2 )(a + P1 )(b + P1 ) P t -b tb - a tb 2 - ae ) - e ( P2 - Z1 )( P2 - Z 2 )(be ( P1 - P2 )(a + P2 )(b + P2 ) e P1 t ( P1 - Z1 )( P1 - Z 2 ) e P2 t ( P2 - Z1 )( P2 - Z 2 ) Z1Z 2 (16) - VBR + P1 ( P1 - P2 ) P2 ( P1 - P2 ) P1P2 e P1 t ( P1 - Z 3 ) - e P2 t ( P2 - Z3 ) +VP ON (0) n ( P1 - P2 ) e P1 t ( P1 - Z 4 ) - e P2 t ( P2 - Z 4 ) -VE n 1 (0) ( P1 - P2 ) dVP dVEn 1 e P1 t - e P2 t ON n + . dt d t P1 - P2 0 0 The expression of VCONn is obtained in the same way. To connect the two curves correctly, VP corresponds in old ON n coordinates to VPON (t ) = VPON (t − tb ) + VBR . (17) n 2.3 Comparison with EMTP The diagram of the Figure 4 is simulated with EMTP, using a piecewise linear resistance with the values given in Figure 3 and no flashover. Expressions of VC and VP are plotted (Figure 5) and show a very good match with EMTP simulations. circuit in parallel with the SPD; in the second case, a wave will travel forward and backward on the line between SPD and load. Considering global damping effects for the wave front by capacitive elements of the circuit and transmission lines frequency dependent losses, first reflections are expected to give the highest level for VL(t). The impedance of protected equipment is considered here to be capacitive according to . It corresponds indeed to the case of ground insulated electronic devices viewed in lineto-ground mode. The value of this capacitive load suggested in  is considered to be in the top of the range of values for CL. The generator being still considered to be matched, the influence of the left line can be considered only as delayed constant time before the surge reaches the SPD, that is, without incidence on voltage evolution at the right part of Figure 6.a. Therefore, we could consider the left part of Figure 6.a as a Thevenin generator with Vth (s) expressed as in equation (4), but with Req=RC and VE instead of VE1. Zth is expressed such as: Zth = Figure 5 : comparison between theoretical curves and EMTP simulation curves for a 5kV - 0.1/50µs wave with L=1µH, C=1nF and Req =50Ω: plain line VE , dashed line : VC (squares : EMTP), dash-dotted line : VP (circles : EMTP), dashed line : IP (triangle : EMTP) This method could be used with more precisely piecewise linear V(I) function for the approximation of the nonlinear resistance RV, if we use more values for the dynamical resistance of TVS diode. Using a continuous nonlinear V(I) function to model RV leads to an analysis approach of dynamical systems. 3 TAKING LINES REFLECTION IN ACCOUNT For usual insulated cables in the low voltage system, the speed c of the waves in the cables is approximately a third of the speed of the light (usually more for power cables, less for data cables). For fast transient, the lines connecting protected equipment whose length exceeds 10 meters could be seen as infinite for the first hundred nanoseconds of the surge. When the line between SPD and protected equipment is short (less than 10 meters long) or after the first hundred nanoseconds, the influence of the line and its load has to be taken into account. In the first case, the parameters of the line can be considered as localized ones, so the line behaves like a LC resonant RC (RV LCs² + s(L + RV REC) + RV + RE ) .(18) RV LCs² + s(L + RV (RE + RC )C) + RV + RE + RC a)system with line b)system after Thevenin tranform Figure 6 : Thevenin transform of complete system In Laplace domain, the reflection ratios at the source and the load ending the line are respectively: Γ0 = Zth − RC , Zth + RC Γl = 1 − RC CL s , 1 + RC CL s (19) which gives in Laplace domain the voltage at a distance x from the entrance of the right line whose length is d: - x - 2(d- x) c ) k R (e c +Γle V(x, s) = VTH (s) C RC + ZTH ∑e-2nτ ( ΓoΓl ) n , (20) n=0 k is the number of reflexions in the plotted duration. VP(s) is the voltage at the point x=0. The expression of the forward traveling wave VP1 before any reflection is given by: VP1 ( s) = VTH ( s) RC . RC + ZTH (21) Note that introducing (18) in (21) leads to VP (s) then VP (s), which corresponds to simplification of Figure 4.b. OFF ON 4 PARAMETRIC STUDY Considering a suitable earth electrode, parameters L and RE are respectively fixed to 1µH and 10Ω. Breakdown voltage of TVS diode is taken at 1kV. 4.1 Stray capacity of SPD Figure 8 shows that a high value of SPD stray capacity have benefic impact on protection distance in case of fast front transient. The time tb when the SPD sparks over depends on the steepness of the wave and the values of C, RC and L although the inductance has lesser influence. Figure 7 : Voltage at the load for a 5kV 0.1/50µs surge at the end of a 6 meters line loaded with CL=100 pF and 1µH, C=10nF, RC=100 Ω and VBR=1kV The expression of VP (s), then VP (s), could be obtained with the same method used in section II with rather more tedious calculus. Here VL(t) is obtained using the convolution product to perform inverse Laplace transform of (20). OFF ON For high values of C and steep front, the first reflection occurs before spark over (tb) while the stray capacity limit the voltage variation at the SPD (case of short lines as for Figure 7). The graph of maximum voltage at the load versus the distance presents local minima the time tb is a multiple of the back and forth travel time of the wave on the. 4.2 Load capacity A high capacity of the load implies resonance on the line and degrade protection level even with short distances and small values of C (Figure 9). For both high values of C and CL global damping effect of capacitive components make this degradation of protection less effective (Figure 10). A parametric study is now available. The maximum voltage at the load ending the line (Vmax on Figure 7) can be found according to each parameter of the circuit (C, L, CL, RE, d, b, VBR, ). Nevertheless, the study which is presented in the following section only take into account conducted lightning effects on the line upstream from the SPD. Figure 9 : Maximum voltage at the load vs. line length for a 5kV 0.1/50µs wave with load capacity CL as a variable parameter. C=100pF, CL=[100pF,10nF], L=1µH, RE=10Ω, Rc=100Ω and VBR=1kV. Figure 8 : Maximum voltage at the load vs. line length for a 5kV 0.1/50µs wave with stray capacity of SPD C as a variable parameter C=[100pF, 10nF], CL=100pF, L=1µH, RE=10Ω, Rc=100Ω and VBR=1kV. In the case of long protected line, analytical expression of maximum voltage at the load end can be obtained including the line length and load impedance. A very nice agreement between theoretical calculations and EMTP simulations validates our analytical approach. Moreover, it becomes possible to analyze the role of each component of the device separately. Namely, the influence of the load, line impedance and SPD characteristics versus line length on the surge propagation can be studied to evaluate distance of protection in different cases. 6 Figure 10 : Maximum voltage at the load vs. line length for a 5kV 0.1/50µs wave with load capacity CL as a variable parameter. C=10nF, CL=[100pF,10nF], L=1µH, RE=10Ω, Rc=100Ω and VBR=1kV. ACKNOWLEDGMENT We thank the Regional Council of Burgundy (France) for financial support. 7 4.3 Wave front steepness. Figure 11 shows that with a high value of SPD stray capacity C and a small value of load capacity CL, the maximum voltage at the end of a 9 meters length line will be 1.7kV for a 5kV 100 ns front duration surge although it is above 1.8kV for a 5 meter long line.        Figure 11 Maximum voltage at the capacitive load vs. line length for a 5kV wave with wave front duration as variable parameter. plain line : 100ns, dashed line : 300ns, dotted line 600ns. Other parameter : C=10nF, CL=100pF, L=1µH, RE=10Ω, Rc=100Ω and VBR=1kV. 5 CONCLUSION This work shows an analytical approach of the surge response of TVS based SPD to fast transient. It appears that for fast transient, a high value of the stray capacity of SPD can have a positive effect on protection level for fast transient. REFERENCES Leteinturier, Hamelin, Eybert-Berard, “Sub microsecond characteristics of lightning return stroke current”, IEEE trans. on EMC, 33(4), p. 351-357 (1991). F.Martzloff, ”The Propagation and Attenuation of Surge Voltages and Surge Currents in Low-Voltage AC Circuits”, IEEE Transactions on Power Apparatus and Systems, PAS-102, May 1983. S. Wotjas, A. Rousseau Impulse and High Frequency Tests of Lightning Earthing. Proceeding of ICLP 2004 Avignon. France. A.Bayadi, N.Harid, K.Zehar , S.Belkhiat “Simulation of metal oxide surge arrester dynamic behavior under fast transients”, Proc. IPST2003 in New Orleans, USA, (2003) IEEE Working Group 3.4.11, “Modeling of metal oxide surge arresters”, IEEE Transactions on Power Delivery, Vol. 7, N° 1, pp. 302-309, 1992 B.Rivet, “calculation of Transil apparent dynamic resistance”, SGS Thomson application note AN575/0393. 1995 Annex K.1.2 of IEC 61643-12 standard, “Surge protective devices connected to low-voltage power distribution systems - Part 12: Selection and application principles”, (2002).