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
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.
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.
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
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:
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.
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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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.
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.
1.Analysis of VDR voltage, current and energy caused by lightning strike
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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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.
Back to the TOC
2. Analysis
of the test circuit during normal operation and lightning strike
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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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.
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.
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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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.
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.
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
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.
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,.
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
Avtor: Marko Jankovec