Varistor (VDR) Spice model

(SLO, ENG)

 Table of contents

Introduction
Goals
VDR Spice model
The test circuit

Analyses
1.Analysis of VDR voltage, current and energy caused by lightning strike
Results of the 1. analysis
2.Analysis of the test circuit during normal operation and lightning strike
Results of the 2. analysis
3.Analysis of the test circuit at variation of parameter Rd
Results of the 3. analysis
4.Analysis of the test circuit with added inductivity
Results of the 4. analysis

Summary

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1.INTRODUCTION:

   Varistors (VDR - Voltage Dependent Resistors)  are resistors with high non-linear dependence of their resistivity versus applied voltage.  When applied voltage is higher than rated voltage the resistivity of the varistor rapidly drops causing rapid increase of current. This phenomenon enables great applicability of VDRs as transient surge suppressors .
    Basic materials are ceramics, such as: ZnO and SiC. ZnO is more commonly used due to higher non-linearity.


    Non-linear U-I characteristic iof VDR can be expressed as:

                                        U(I)=C*Iß
                                    ali I(U)=K*Ua

    Where a is nonlinear exponent and is always and odd number.

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  2.GOALS:

The goal of this work is to build a spice model of the VDR, analyze the model in several conditions and draw some conclusion how to build effective circuits for surge protection.  Parameters of this model should be based on real measured characteristics. It should also include energy model to study the energy conditions of the element. This work will try to help to better understand factors that influence on reliability of various surge protection circuits. It will also show some general ways how to construct an effective surge protection circuit.

3.VDR SPICE MODEL:

    Basic data of VDRs provided by Slovenian manufacturer KEKO VARICON:

Vrms (Rated AC Voltage)......maximum continuous sinusoidal RMS voltage which may be applied to the component under continuous operating conditions at 25°C

Vdc (Rated DC Voltage)......maximum continuous DC voltage which may be applied to the component under continuous operating conditions

Vn (Varistor Voltage)......voltage across the varistor measured at a given reference current In, usually 1mA

Vc (Clamping Voltage Protection Level)......The peak voltage developed across the varistor under standard atmospheric conditions when  passing a standard 8/20 ms pulse

Ic (Class current)......A peak value of current which is 1/10 of the maximum peak current for 100 pulses at two per minute for the standard  8/20 ms pulse

Wmax (Rated Single Pulse Transient Energy)......Energy which may be dissipated for a single 10/1000 ms impulse of a maximum rated current , with rated RMS voltage or rated DC voltage also applied without causing device failure

Pmax (Rated Transient Average Power Dissipation)......Maximum average power which may be dissipated due to a group of pulses occurring within a specified isolated time period, without causing device failure at 25°C

Imax (Rated Peak Single pulse Transient Current)......Maximum peak current which may be applied for a single 8/20 ms impulse, with rated line voltage also applied, without causing device failure

C (Capacitance)......Capacitance between two terminal of the varistor measured at 1 kHz

In the table below data is presented for KEKO VARICON varistor, model CV230 K20.    

varistor model Vrms  Vdc  Vn  Vc  Ic  Wmax  P  Imax  C 
CV230K20  230V  300V  360V  595V  100A   168J  1W  6500A  1400pF 

 For model parameter extraction we use the following expression:  I(U)=(K×U)a

From the given table we extract two characteristic points (Vn, 1mA) in (Vc, Ic), and calculate both parameters K in a.

U1=360V, I1=1mA
U2=595V, I2=100A

a=ln(I2/I1)/ln(U2/U1)=ln(100/0.001)/ln(595/360)=22.91­=23

K=(aÖI)/U=(23Ö0.001)/360=0.002057

Parameter a has to be rounded to the first higher odd number.

    From graphically presented characteristic of varistor in log scale we can deduce, that characteristic starts to bend from the ideal linear dependence at high currents. We ascribe that to a parasitic resistance of varistor which is the sum of the resistance of both leads and ceramic body itself. 

We extract:
I=5000A   Uextr=840V

We calculate, what would be the voltage at I for ideal varistor:
Uideal=(aÖI)/K=(23Ö5000)/0.002057=740V

The difference between Uextr in Uideal can be interpreted as voltage drop on internal parasitic resistance:
DU=Uextr -Uideal=136V

Rvar=DU/I=136V/5000A=0.0272W








Rnv1.gif
 Basic VDR spice model is nonlinear voltage dependent
current source and parasitic resistance Rvar.
 
 
 

Bvar 7 0 I=(0.002057*v(7))^23
Rvar 6 7 0.0272
 
 
 
 
 
 
 


We are also interested in energy that VDR absorbs:

Rnv3.gif
Voltage on capacitor can be expressed as:

Energy equation can be applied in a spice model as:

Ben 0 100 I=v(6)*i(Vvar)
Cen 100 0 1
Ren 100 0 100Meg
 
 Current of the dependent source is equivalent to the power on VDR, and voltage on the capacitance is the integral of this current (Power on VDR) which is the energy that VDR absorbs. We have to add Ren=100MW that we prevent a singularity in spice matrix.


The following program calculates  static I(U) characteristic of VDR by means of DC analysis with varying the DC source Vin.

Test.gif
karakteristika varistorja
Bvar 7 0 I=(0.002057*V(7))^23
Rvar 6 7 0.0272

*Tok skozi varistor
vvar    5 6 dc 0

*vzbujanje
vin 5 0 dc 1000V

.control
dc vin -1000 1000 5
plot i(vvar)
.endc

.end
 
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4.THE TEST CIRCUIT:

Rnv2.gif
Test circuit consists of :

We have two models of lightning source. First is for bare wire of the power distribution network and second is for isolated wire. Those two models are the results of real measurements on power distribution network. 

VDR Model has additional voltage source in series Vvar = 0V, which enables us to measure VDR current.




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5.ANALYSES:
 
Based on results of analyses we will build a surge protection circuit step by step and try to draw some conclusionsm which are those parameters that influence on the quality of protection circuits. All following analyses consider test lightnig impulse for bare wire (2100V). Anybody can reapply any other test impulse he wishes. VDR manufacturers test their products with standard 8/20 ms and 10/1000 ms test impulses and determine maximum ratings of current, voltage, energy and power of their elements. Our analyses base on measured lightning impulse and from that point of view it is adequate because energy is calculated directly, not on the presumption of standard impulse applied. 

     1. analysis comprises VDR model we just introduced with added resistivity representing concentrating resistivity of current paths between lightning source and VDR. Output and input voltages are V(5) and V(3), respectively. we will calculate voltage, current and absorbed energy of varistor at the moment of lightning strike.

    In 2. analysis a power source sinusoidal voltage 230V/50Hz is added, lightning impulse is delayed for 5ms.
    In 3. analysis the dependence of output voltage vs. Rd will be presented. We will find out the limits of protection circuit.
    In 4. analysis an inductivity Ld is added in series to Rd, that represents total inductivity of current paths between lightning source or just added inductivity as protection element, that limits high transient voltages.

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1.Analysis of VDR voltage, current and energy caused by lightning strike

Rnv5.gif
Analiza1
Bvar    7  0 I=(0.002057*v(7))^23
Rvar    6  7 0.0272
Vvar    5  6 dc 0
VSTRELA 2  0 EXP 0V 2100V 0m 1.5US 4US 70US
*VSTRELA 2  0 EXP 0V 1050V 0m 2.2US 10US 350US
RSTRELA 3  2 0.13
Rd      3  5 1
*energijski model
Ben    0 100 i=v(6)*i(Vvar)
Cen    100 0 1
Ren    100 0 100Meg
.control
tran 0.2u 250u 0 0.2u
plot v(3) v(5) i(Vvar)
plot v(100)
.endc
.end
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Results of the 1. analysis:

Analiza1.gif
Input voltage v(3) is lightning pulse with amplitude 1850V, while only 690V is maximum voltage on VDR v(5). Maximum current through VDR i(Vvar) is 1160A. We have to take into consideration that time scale is very short. Total energy that is consumed by varistor is only 30.5J (final voltage v(100)), therefore VDR does not degrades. Remaining energy is consumed by resistance Rd. If that resistance represents electrical fuse (230V/ 500mA), than this fuse would certainly blow. 









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2. Analysis of the test circuit during normal operation and lightning strike
Rnv4.gif
Analiza2
Bvar    7  0 I=(0.002057*v(7))^23
Rvar    6  7 0.0272
Vvar    5  6 dc 0
Vin     1  0 dc 0 sin 0 311V 50Hz
VSTRELA 2  1 EXP 0V 2100V 5m 1.5US 5004US 70US
*VSTRELA 2  1 EXP 0V 1050V 5m 2.2US 5010US 350US
RSTRELA 3  2 0.13
Rd      3  5 1
*energijski model
Ben    0 100 i=v(6)*i(Vvar)
Cen    100 0 1
Ren    100 0 100Meg
.control
tran 10u 20m 0 10u
plot v(3) v(5)
plot v(100)
.endc
.end
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Results of the 2. analysis:

Analiza21.gif
Figure present VDR current during applied sinusoidal power source voltage (230V/50Hz) without lightning impulse applied. Mean current value is negligible, because VDR is selected such that it meets the following values Vrms=230V in Vn=360V. Consequently VDR under continuously applied sinusoidal voltage 230Vrsm shouldn't conduct. That can be clearly seen from the figure since maximum current is 35mA.
 
 












Analiza2.gif
In this analysis we included a lightning impulse and set it on the top of the sinusoidal wave (delayed for 5ms), that represents the worst case. The peak of impulse at input is now 2150V, which is for 310V more than in previous analysis, where only lightning impulse was applied to the circuit. Results show that peak voltage on varistor (705V) is not significantly higher. But current spike 1420A and energy absorbed energy 51J is much higher.












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 3.Analysis of the test circuit at variation of parameter Rd

In this analysis we will vary the parameter Rd by means of voltage controlled current source Brd and DC analysis of varistor voltage at 311V and 2100+311V applied in input. Output load is Rb=500W.


Analiza3
Bvar    7  0 I=(0.002057*v(7))^23
Rvar    6  7 0.0272
Vvar    5  6 dc 0
Vin     2  0 dc 2100
RSTRELA 3  2 0.13
Rb      5  0 500
*napetostno krmiljeni upor Rd
Brd      3  5 I=(V(3)-V(5))/V(101)
Vr 101 0 1
Rr 101 0 1Meg
.control
*analiza izhodne napetosti v odvisnosti
*od Rd pri 311V in pri 2100V+311V
dc  vr 0.001 100  1 vin 311 2411 2100
.endc
.end
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Results of the 3 analysis:
Analiza3.gif

 

We vary Rd from 1W to 1kW. We can deduce that at low resistances Rd output voltage at 2411 V input voltage is highly dependent from Rd . At higher Rd this dependence greatly decreases (upper curve). We can conclude that very low resistances (a few W) for Rd can be used to achieve optimal results. We can quickly see that determination of this optimal resistance Rd is highly dependent of  expected load resistance. That is very important for normal conditions, when 230Vrms is applied and nominal load is applied. We tend to use small resistances for Rd in order to assure minimal power dissipation.

We can conclude that there is no sense to use larger resistances of Rd than a few ohms. Standard (200mA/230V) fuse has its resistivity about 1W.






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4.Analysis of the test circuit with added inductivity:
A questions arises, why don't we add a small inductivity in series that will reduce voltage spikes. To improve the model we add also a parasitic capacitance of VDR. 

Rnv2.gif
Analiza4
Bvar    7  0 I=(0.002057*v(7))^23
Rvar    6  7 0.0272
Vvar    5  6 dc 0
Cvar  6  0 1400p
Vin     1  0 dc 0 sin 0 311V 50Hz
VSTRELA 2  1 EXP 0V 2100V 5m 1.5US 5004US 70US
*VSTRELA 2  1 EXP 0V 1050V 5m 2.2US 5010US 350US
RSTRELA 3  2 0.13
Rd      3  4 1
Ld 4  5 200u
*energijski model
Ben    0 100 i=v(6)*i(Vvar)
Cen    100 0 1
Ren    100 0 100Meg
.control
tran 10u 20m 0 10u
plot v(3) v(5) i(Vvar)
plot v(100)
.endc
.end

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Results of the 4. analysis
Analiza4.gif

We can see that inductivity indeed reduces the voltage spike, for it is lower (631V, before it was 705V) but it also stretches. Current spike is significantly lower (only 301A, before it was 1420A!). But most important is energy consumption by VDR. In this case its a little lower (33J, before it was 51J), but this difference is not so big due to larger impulse duration.













Analiza41.gif If we zoom into the previous figure, we notice that oscillations occur after the pulse expire. That it the consequence of stored energy in added inductivity Ld. This energy then alternate in oscillating circuit, which consits of Ld and Cvar and slowly dissipates in resistivities. That relatively large amplitude of oscillations at the beginning is because of rapid increase of varistor resistivity. Added inductivity causes interference disturbances, besides that it should be relatively large. If it is added it certainly should be air coil.











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6.SUMMARY:
 
Everything we did till now was just theory and a few simulations. But we can draw some conclusions out of the results. In first analysis we found out that fuse in circuit blows after lightning strike. But it can't blow immediately. It takes some time to heat the wire to the cutout temperature. No fuse can blow in a few ms. In reality fuse blows long after voltage spike has expired. But at lightning strike usually lots of secondary voltage spikes occur that reflect from discontinuities on the network. At this can fuse can be of assistance for VDR can absorb only certain energy at a time declared by manufacturer.

 In our analyses we didn't include any device that VDR will protect. It turns out that resistivity of load doesn't affect significantly if resistivity of Rd is small enough comparing to load resistivity Rb (third analysis).

 

A few guidelines how to pick the right VDR for our application: 

1.Normal conditions:
   Vn, varistor voltage (at current 1mA). That is where VDR starts to protect. All voltage in normal conditions should be lower. Parameters Vrms and Vdc of the chosen element should be higher or equal than actual voltages at normal conditions. 

2.Absorbed energy at transient voltages:

   absorbed energy can be calculated by means of approximation formula, that ascribes a  square impulse to a certain current impulse. 

                    E=K*Ip*Vc*T

K is shape constant and it is:: K=1 for square impulse, K=1.4 for 8/20 ms and 10/1000 ms standard test impulse. Ip is the amplitude of current spike, Vc is voltage on varistor and T is width of the impulse.  

 

 

Standard current impulse 8/20 ms

3.Maxumum transient voltage that  can be applied on protected circuit
    From I(U) curve we can read the clamping voltage at expected current spike.Chosen VDR should have Vc (clamping voltage) equal or lower.

4.Imax, maximum current spike of the VDR  should be higher from maximum current spike expected.

5. From diagram that represents spike current amplitude versus impulse timel
we can deduce suitable VDR. Energy that VDR can absorb without failure depends also from impulse length and number of impulses that repeat in one packet at period tr.

6.Power dissipation and heat transfer is important when continuous impulses are present which energy VDR absorbs. If VDR in pause time between adjacent impulses can't transfer enough heat it will eventually burn. VDRs have relatively low heat conductibility therefore are not suitable for such applications,.






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All analyses were made with Spice Opus. All text files *.cir can be used directly or you can copy  the code written in this html file and and paste it into  appropriate file *.cir.
 
All your comments and contributions will be appreciated

 Marko.Jankovec@fe.uni-lj.si

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Thanks goes to dr. Tadej Tuma for tutorship and help and MSc. Andrej Levstek for data and help.


Some VDR manufacturers and their addresses: 


 KEKO VARICON d.o.o.
Grajski trg 15
8360 ZUZEMBERK
SLOVENIA

TEL:                       +386 7 308 70 71
                              +386 7 308 76 71
   
                                  +386 7 302 26 33
FAX:                      +386 7 308 76 34


ISKRA VARISTOR, d.o.o
Stegne 35
1000 LJUBLJANA
SLOVENIA

Tel:    +386 1 551 15 98
          +386 1 559 11 41
          +386 1 559 92 78
Fax:    +386 1 507 65 67



C.CONRADTY NÜRNBERG GmbH & Co.KG
8500 Nürnberg 1
Postfach 17 52
DEUTCHLAND
Tel: (09 11) 54 88 1
Fax:(09 11) 54 88 211


SAS (SINO-AMERICAN SILICON PRODUCTS INC.)
8, Industrial East Road Sec. 2
Science Based Industrial Park
HSINCHU, TAIWAN, R.O.C.
Tel: 886-3-5772233

E-Mail : Saspi@shts.seed.net.tw

 


Avtor: Marko Jankovec

E-Mail:Marko.Jankovec@fe.uni-lj.si
email.gif (15902 bytes)

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