High-Voltage DC Fuse Ageing & Short-Circuit Failure in Resonant Converters

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Electrical Power and Energy Systems
journal homepage: www.elsevier.com/locate/ijepes
Analysis of high-voltage DC fuse’s ageing characteristics under the overload
pulse current carrying mode and the caused short-circuit failure in series-
resonant converter power source
Yu Zhang
⁎
, Jiancang Su, Lei Zheng, Rui Li, Binxiong Yu, Wei Shang
Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, P. O. Box 69 Branch 13, Xi’an 710024, China
ARTICLE INFO
Keywords:
High-voltage fast DC fuse
Short-circuit protection
Full-bridge series-resonant converter
Overload high-frequency pulse current carrying
Linear ageing
Fusing by overload pulse current
Short-circuit failure
ABSTRACT
As a key component in short-circuit protection, high-voltage fast DC fuse is broadly employed in high-power
charge sources. In this paper, the overload pulse current carrying and ageing effect of high-voltage fast DC fuse
which is used in series-resonant converter power source for short-circuit protection, is studied and analyzed.
Main focus is on the mechanism of the DC1600V/32A fuse ageing and the following cut-out effect under the
condition of high-frequency overload pulse current carrying. The effects on the full-bridge series-resonant
converter charge source after the fuse ageing and breaking are also analyzed. The ageing under pulse currents is
mainly caused by the repeated attacks of the heating-up and cooling on the fuse conductor. Four encountered
stages of the fuse conductor under the high-frequency overload pulse current carrying are put forward in order,
such as the linear ageing stage, the non-linear ageing stage, the fusing and arcing stage, and the arc extinguishing
stage. In the linear ageing stage which plays as the available fuse life time, the fuse conductor carries the pulse
currents normally and the temperature rise and fuse resistance R
f
both increase linearly. When the increment
ratio of R
f
reaches 10%, the fuse starts to work in the non-linear ageing stage in which R
f
increases nonlinearly
and the series-resonant period of the charge circuit is prolonged. As the alternately opening switches in the H-
bridge of the series-resonant converter are mismatched, the H-bridge is in short-circuit error, or the phenomena
of the ‘hard switching’and the failure for series-resonance occur. The circuit simulation and experimental results
both demonstrate the H-bridge short-circuit error in series-resonant converter charge source is induced by the
ageing of the fuse conductor under the overload pulse current carrying condition. In view of that, several ways
for improving the fuse conductor ageing are put forward.
1. Introduction
High-voltage DC fuse is broadly employed for short-circuit protec-
tion of important electronic devices in the fields of electrical electro-
nics, high-voltage equipment, converter charge source and battery
[1–4], and distribution systems [5,6]. The two main functions of the DC
fuse are current carrying and circuit cut-out. The cut-out time is the
crucial index to evaluate the fast protection ability of a fuse in a short-
circuit failure. In recent years, research on fast cut-out fuse at μs scale
was also carried out [7].In[7], a fast cut-out fuse “Sielins”filled with
solidified sand and single fuse body showed fast cut-out advantages in
comparison with “Ferraz”fuse under the similar fuse parameters.
The fuse current carrying modes include the DC current carrying
[1–4], AC current carrying [8], and pulse current carrying [9–12].At
present, however the fuse which is specially designed and employed for
high-frequency pulse current carrying is rare. Traditionally, when a DC
fuse is used for AC current carrying, the AC current amplitude can be 3
times of the maximum DC current carrying level. In series-resonant
converter power charge sources, the DC fuse need to be series con-
nected in the mother line of the converter to endure high-frequency
series-resonant current pulse with period of several dozens to hundred
μs, in order to obtain ultra-fast cut-out ability [7]. The DC fuse for high-
frequency pulse current carrying usually works in the overload mode
for the fast cut-out ability, which is to say the carrying pulse current
amplitude is much larger than the rated DC current amplitude. As a
result, the selection of the rated DC current is important to the high-
frequency pulse current carrying mode. Our studies showed that, if the
carrying pulse current amplitude was no more than 8 times of the rated
DC current amplitude, the DC fuse can be reliably used to carry the
overload high-frequency sinusoidal current pulses with the half period
https://doi.org/10.1016/j.ijepes.2019.105604
Received 27 May 2019; Received in revised form 5 September 2019; Accepted 7 October 2019
⁎
Corresponding author.
E-mail address: [email protected] (Y. Zhang).
Electrical Power and Energy Systems 117 (2020) 105604
0142-0615/ © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/BY-NC-ND/4.0/).
T

less than 50 μs. However, when the work mode of the overload pulse
current carrying lasts a long time, the narrow necks or the notches of
the fuse conductor are heated and cooled repeatedly [10–12], and the
ageing problem occurs. The continuously increased resistance of the
ageing narrow neck show important influence on the protected con-
verter charge source, including the short-circuit failure or circuit de-
stroy. However, the DC fuse ageing mechanism and effects on the
protected converter charge source under the overload high-frequency
μs-pulse current carrying are not in the focus of the present studies.
In this paper, the overload high-frequency μs-pulse current carrying
and ageing effect of high-voltage fast DC fuse is focused and analyzed.
Four encountered stages of the fuse conductor are put forward in order,
such as the linear ageing stage, the non-linear ageing stage, the fusing
and arcing stage, and the arc extinguishing stage. The linear ageing
mechanism of fuse and the non-linear ageing effects on the series-re-
sonant converter power charge source are analyzed and demonstrated.
At last, several practical ways for improving the fuse conductor ageing
are put forward.
2. Fuse conductor ageing and fusing problem in the series-
resonant converter charge source under high-frequency overload
pulse carrying
2.1. Full-bridge series-resonant converter circuit and its short-circuit
protection
The typical full-bridge series-resonant DC-DC converter circuit is
shown in Fig. 1(a). U
0
is the output voltage of the battery or DC power
source, while the current-restrict inductor L
0
and the rectifier diode D
0
are connected in series in the circuit bus after U
0
. Usually, the high-
voltage DC fuse R
f
is also connected in series in the circuit bus after D0,
in order to protect the converter system when short-circuit error occurs.
The series-resonant H bridge, the rectifier bridge, C
0
and a load capa-
citor C
L
are the main part of the converter. In practice, the short-circuit
error of the converter system is always caused by the short circuit of the
series-resonant H bridge or the rectifier bridge, and the rise time of the
short-circuit current lasts as long as ms scale. As a result, the arc ex-
tinguishing and cut-out time of the DC fuse ranges from ms to s, which
causes a problem that the fuse are not able to protect the battery or DC
power source under the large short-circuit current. In view of that,
reference [7] proposed a way for fast cut-out of DC fuse connected
between C
0
and the H bridge, as shown in Fig. 1(b). Based on the in-
stantaneous high pulse current attack from C
0
after the series-resonant
H bridge or the rectifier bridge has a short-circuit error, the DC fuse
obtain a fast cut-out ability with the cut-out time ranges from 30 to
50 μs.
As shown in Fig. 1(b), the DC fuse (Sielins DC1600V/32A) is con-
nected in the series-resonant circuit bus instead of in the DC circuit bus.
While the DC fuse obtains the fast cut-out ability, the DC fuse carries a
sinusoidal current pulse with frequency of 10 kHz and amplitude of
240 A under the normal state. Define the over-current coefficient as I
P
/
I
D
,ifI
P
and I
D
are the carried pulse current amplitude and the rated DC
current amplitude respectively. The over-current coefficient of the
DC32A fuse reaches 7.5 under the 10 kHz series-resonant pulse current
carrying mode.
2.2. Fuse conductor ageing and fusing problem under high-frequency
overload pulse current carrying
The fuse conductor has temperature rise and ageing problem under
the condition of current carrying in a long time [11,12]. This problem
will cause abnormal fuse cut-out and other following circuit failures.
However, the causal relationship between the fuse ageing and the cir-
cuit failures are not easy to discriminate, as it is difficult to observe the
fuse ageing directly. The fuse conductor is made of silver foil (purity
99.99%), and its ageing mechanisms contain two main types. One,
ageing caused by stress fatigue under the attacks of repeated heating
and cooling [13–16]. The other, ageing caused by physical-chemical
changes such as metal electromigration, welding spot fusing, metal
evaporation, flux metallurgical effect, chemical erosion, and silver ions
migration under humid environment [17,18].
2.2.1. The temperature rise characteristics of the fuse under the condition of
overload pulse current carrying
In Fig. 2(a), the employed Sielins DC1600V/32A fuse consists of
fuse conductor (silver foil), quartz sand, ceramic tube, and the red-
copper end caps. The fuse conductor is in the middle along the ceramic
tube. The fuse conductor is surrounded by the filling quartz sand which
is solidified by the adhesive. The fuse conductor shown in Fig. 2(b) is
welded on the red-copper end caps at the two sides of fuse. The specific
heat capacities of the Al
2
O
3
ceramic tube and the quartz sand are de-
fined as C
1
= 750–840 J/ (kg·°C) and C
2
= 1100 J/(kg·°C), respectively.
In view of that C
1
and C
2
are close to each other, the ceramic tube and
the quartz sand can be viewed as an entire solid with the average
specific heat capacity as C
12
= 970 J/(kg·°C), approximately. The fuse
conductor has a specific heat capacity as C
Ag
= 232 J/(kg·°C). The mass
of the total fuse is as M= 0.118 kg, in which the main part is the mass
of the ceramic tube and the quartz sand. Under the heat insulation
approximation, if the fuse conductor works in the series-resonant con-
verter circuit shown in Fig. 1(b) for continuous 120 s, the generated
total heat energy Ecompletely conducts from the fuse conductor to the
quartz sand and the ceramic tube. As a result, the temperature rise on
the outside surface of the ceramic tube is as ΔT
V
:
≤
Δ
TE/(CM).
V12
(1)
In practice, the fuse conductor carries a 10 kHz sinusoidal pulse
current as shown in Fig. 2(c). However, when the current carrying lasts
every 10 ms, a 10 ms pause is between every two adjacent current
Fig. 1. The schematics of the short-circuit protection in full-bridge series-resonant converter charge source (a) fuse protection in the DC circuit bus at the output port
of U
0
; (b) fuse fast protection in the resonant circuit based on the burst high pulse current from the filter capacitor (C
0
) discharge when the converter has a short-
circuit failure.
Y. Zhang, et al. Electrical Power and Energy Systems 117 (2020) 105604
2

carrying stages. That’s to say, the duty ratio is 1:2 when the fuse carries
current repetitively. During the pulse current carrying course, the fuse
timely resistance R
f
increases as the fuse conductor gets a temperature
rise. In every 10 ms for current carrying, the total Joule heat can be
calculated as E
0
= 1.4 J under the heat insulation approximation. If E
0
completely conducts from the fuse conductor to the ceramic tube, the
received energy of the quartz sand and the ceramic tube is as
E=50E
0
t
D
when t
D
is defined as the total work time. Define the total
effective current carrying time as t
eff
,t
eff
=t
D
/2 under the duty ratio of
1:2. According to (1), the maximum temperature rise ΔT
V
on the out-
side surface of the ceramic tube is calculated under different t
D
s and
t
eff
s, as shown in Table 1.ΔT
V
increases linearly with t
D
, and the cor-
responding slope ΔT
V0
≈12 °C/20 s.
As to the 10 kHz/240 A series-resonant sinusoidal pulse current
shown in Fig. 2(c), its root-mean-square (RMS) value is about 100 A. So,
its heating effect of 10 ms is equivalent to the heating effect of DC100A.
As a result, constant DC current source can be used to substitute the
10 kHz/240 A series-resonant current source to test the heat effect of
the Sielins DC1600V/32A fuse. The equivalent test DC current flowing
through the fuse still had a duty ratio of 1:2 and amplitude of DC100A.
Thermistor (accurancy:0.3%@100 °C) was put on the middle outside
surface of the ceramic tube to test the tube temperature rise. The total
ceramic tube and the Thermistor were enveloped by a layer of thermal
insulation material to simulate the thermal insulation in vacuum. The
maximum temperature rise ΔT of the ceramic tube was tested under
different current carrying mode shown in Table 2. The tested results of
ΔT shown in Table 2 basically corresponded to the calculation results
shown in Table 1. The tested temperature slope was ΔT
0
= 12.6 °C/20 s,
which was also corresponds to the theoretical calculation value of ΔT
V0
.
Both theoretical calculation results and test results demonstrate the
temperature rise ΔT linear increases with the fuse work time T
D
in a
linear slope of ΔT
0.
When the fuse carries the pulse current, the fuse conductor and the
ceramic tube both conduct heat to the red copper caps of the fuse. In
practice, the temperature rise ΔT is smaller than the tested values in
Table 2. According to the Fourier’s law of heat conduction,
=
P
kS T LΔ/
.
c(2)
In (2),P
c
is the conducted heat with unit of W. kis the thermal
conductivity with the unit of W/(m·°C). Sis defined as the perpendi-
cular thermal conduction area, with the unit of m
2
.Lis defined as the
thermal conduction distance, with the unit of m. The thermal con-
ductivity of the fuse conductor is defined as k
1
= 429 W/(m·°C), while
the thermal conductivity of the quartz sand is defined as k
2
=10W/
(m·°C). As the total length of the fuse conductor is l
0
= 120 mm, the
heat conduction length from the middle point to the two sides of the
fuse conductor is about 60 mm. In Fig. 2(b), the current carrying and
the fuse resistance R
f
are mainly districted by the narrow necks of the
fuse conductor. As to the Sielins DC1600V/32A fuse, the effective
current flowing width is about 1/10 of the 6 mm fuse conductor width,
considering the 12 rows of narrow necks. The width of the fuse con-
ductor is 0.1 mm, as shown in Fig. 2(b). The heat conduction area S
1
along the fuse conductor can be calculated as
Fig. 2. The photo and basic structure of the fuse and the carrying pulse waveform (a) the photo of the Sielins DC1600V/32A fuse; (b) the basic structure of the fuse
conductor; (c) the waveform of the 10 kHz sinusoidal pulse current train for carrying.
Table 1
The theoretical calculation results of E and ΔT
V
when t
D
and t
eff
change, under
the heat insulation approximation.
Total work time t
D
(s) Total effective current carrying time
t
eff
(s)
E(J) ΔT
V
(°C)
20 10 1400 12.2
40 20 2800 24.4
60 30 4200 36.6
120 60 8400 73.2
Table 2
The tested maximum temperature rise ΔT of the ceramic tube and the linear
slope ΔT
0
under the modes of different t
D
s.
Total work time
t
D
(s)
Total effective current carrying
time t
eff
(s)
ΔT(°C) ΔT
0
(°C)/20 s
20 10 10.6 10.6
40 20 22 11.4
60 30 37.5 15.5
80 40 50.1 12.6
100 50 63.5 13.4
120 60 75.5 12
Average:12.6
Y. Zhang, et al. Electrical Power and Energy Systems 117 (2020) 105604
3

S
1
= 0.0006 × 0.0001 × 3 = 1.8 × 10
−7
m
2
. In view of that the heat
conduction is much faster along the normal parts of fuse conductor than
the 12 rows of narrow necks, the equivalent heat conduction length L
1
from the middle to the two sides of fuse conductor is about the length of
6 rows of narrow necks. Because the length of each row of narrow necks
is about 2 mm, L
1
= 0.002 × 6 = 0.012 m. In approximation, the heat
energy Eproduced by the fuse conductor is completely conducted to the
surrounding quartz sand and ceramic tube. The outside radius of the
ceramic tube is L
2
= 0.01 m, and the perpendicular thermal conduction
area S
2
from the fuse conductor to the quartz sand is about
S
2
≈0.006 × 0.12 × 2×(1–0.012/0.12) = 1.3 × 10
−3
m
2
. It can cal-
culate that k
1
S
1
/L
1
= 6.4 × 10
−3
and k
2
S
2
/L
2
= 1.3. That to say, the
heat conduction from the fuse conductor to the quartz sand is abso-
lutely the main part contrast to the heat to the copper caps, as k
2
S
2
/
L
2
≫k
1
S
1
/L
1
. Or in other words, the heat insulation approximation
model which neglects the heat conduction from the fuse conductor to
the two side copper caps, is correct.
If the fuse conductor conducts heat to the quartz sand and the
ceramic tube under the maximum heat generation power P
0
of the fuse
conductor (P
0
=50E
0
= 70 W), P
0
=50E
0
=k
2
S
2
ΔT
x
/L
2
according to
(2). The maximum temperature difference ΔT
x
between the fuse con-
ductor and the outside surface of ceramic tube is theoretically calcu-
lated as ΔT
x
= 53.8 °C. From the tested data when t
D
= 120 s shown in
Table 2, the temperature of the outside surface of ceramic tube is about
20 + 75.5 = 95.5 °C (room temperature: 20 °C). The maximum tem-
perature of the narrow necks at the middle of the fuse conductor can
reach 95.5 + ΔT
x
= 149.3 °C. However, if the heated fuse conductor
gets an insufficient cooling, the maximum temperature of the narrow
necks becomes much larger than 149.3 °C which is calculated based on
the room temperature.
2.2.2. The inside structural characteristics of the fuse under the condition of
overload pulse current carrying
As to the Sielins DC1600V/32A fuse, the typical inside structures of
the short-circuit cut-out fuse conductor and the overload ageing fuse
conductor are shown in Fig. 3 (a) and (b), respectively. When the fuse
conductor cuts out due to a real short-circuit failure, the essential cut-
out I
2
t is fast set on the fuse conductor in the time scale of 30 μsbyan
instantaneous short-circuit current pulse [7]. Because the energy de-
position time for fuse arcing forming and arc distinguishing is as short
as μs scale, the heat cannot conduct from the fuse conductor to the
quartz sand in time. As a result, it can be viewed as a heat insulation
course, and the quartz sand around the narrow necks of fuse conductor
cannot be heat to the glassy state. However, during an overload pulse
current carrying course, heat conducts from the ageing necks to the
surrounding sand, and the sand around the high-temperature ageing
neck is heated to the glassy state in a long continuous time. As a result,
concrete sand is adhesive with the ageing neck in the anatomy photo
shown in Fig. 3(b). As the overload pulse current is much smaller than
the instantaneous short-circuit current, the overload pulse current can
only provide the I
2
t for the cut-out of the ageing neck while the other
narrow necks of the fuse conductor remain unchanged, as shown in
Fig. 3(b). This point is the most important difference between the short-
circuit cut-out mode and the overload ageing cut-out mode.
2.2.3. Four dividing stages of the fuse ageing and fusing under the overload
high-frequency pulse current carrying
In the full bridge series-resonant converter charge source shown in
Fig. 1(b), the fuse in the protected circuit bus carries the sinusoidal
pulse current of 10 kHz/240 A, and the fuse conductor is always at-
tacked repeatedly by the circulation of heating and cooling. The linear
expansion coefficients of the fuse conductor and the surrounding quartz
sand are 19.5 μm/°C and 0.55 μm/°C respectively, with the ratio of
35.5:1. When the temperature of the fuse conductor rises from 20 °C to
150 °C according to (2), the expanded length of the total fuse conductor
along the length direction is (150–20) × 19.5 = 2.54 mm, which is
mainly contributed by the narrow neck expansion. As to each row of
narrow necks, the expanded length is about 0.25 mm, which is about 1/
10 of the total length of each narrow neck. After the repeated expansion
stress attacks caused by the heating and cooling, some of the narrow
necks become longer and thinner which corresponds to the ageing
tendency. As a result, the resistance and the flowing current density of
the ageing neck becomes larger and larger [15,16]. When the ageing
neck is expanded to a critical point without recovery, the temperature
of the ageing neck fast rises to the melting point and the ageing neck is
fusing with generated electrical arcs. At last, the fuse conductor cuts out
only from the ageing neck.
In view of that the entire course aforementioned lasts a long time, it
can be divided into four stages as follows. Define the static resistance of
the fuse conductor under the room temperature as R
f0
. Firstly, the linear
ageing stage: in this long stage, the fuse carries the overload resonant
pulse current without failure, and the R
f0
increment ratio ≤10%. In
other words, the effective pulse current carrying lifetime of fuse is just
the linear ageing stage time. Secondly, the nonlinear ageing stage: in
Fig. 3. The typical structures of the Sielins
DC1600V/32A fuse conductor under the
“short-circuit cut-out mode”and the
“overload ageing cut-out mode”(a) the X-
ray photo of the fuse conductor with all
necks cutting out under the “short-circuit
cut-out mode”; (b) the anatomy photos of
the fuse conductor with only the ageing
neck (surrounded by concrete sand) cut-
ting out under the “overload ageing cut-
out mode”.
Y. Zhang, et al. Electrical Power and Energy Systems 117 (2020) 105604
4

this stage, R
f0
increases abruptly with the current carrying time tin a
nonlinear mode to a level which is comparable to the series-resonant
impedance Z
r
of the converter. The nonlinear ageing stage is an ac-
celerated ageing state which is much shorter than the linear ageing
stage. Thirdly, the fusing and arc forming stage: only one of the fuse
narrow necks (called as the ageing neck) is fusing with forming electric
arcs under the instantaneous large pulse current, and the fuse resistance
fast drops to a low level. Fourthly, the arc extinguishing and cut-out
stage: the electric arc is extinguished as the 100 μs scale resonant cur-
rent dies out, and the fuse resistance recovers to a high impedance level
which corresponds to the cut-out state of fuse.
3. Linear ageing characteristics of the fuse conductor under the
overload pulse current carrying mode
As the carried 10 kHz/240 A sinusoidal current pulse train shown in
Fig. 2(c), the pulse current heating effect in each 10 ms of the carried
pulse train is equivalent to the heating effect of its root-mean-square
(RMS) current DC100A. In practice, the DC100A current with the duty
ratio of 1:2 in each 20 ms is employed to equate and substitute the
10 kHz/240 A sinusoidal current pulse.
3.1. The maximum temperature rise characteristics of the ceramic tube of
the ageing fuse under the DC100A current carrying
Usually, the tested temperature rise in the middle of the fuse
ceramic tube is higher than other places. Under the room temperature,
when the fuse carried the equivalent DC100A current in different
constant time modes (after the current carrying, the fuse cooled down
to the room temperature), the tested maximum temperature rise ΔT
max
in the middle of the fuse ceramic tube had linear increment relations
with the current carrying batch number m,asFig. 4(a) shows. In
Fig. 4(a), the same fuse orderly experienced 5 current carrying modes in
experiment as “DC100A/63s”,“DC100A/60s”,“DC100A/56s”,
“DC100A/53s”, and “DC100A/30s”. Because the fuse conductor of the
same fuse was ageing continuously, the 5 fitted ΔT
max
~mlines had
different “ΔT
max
intercepts”but almost the same straight slope. The
general linear relation of the 5 fitted ΔT
max
~mlines based on the
tested results is as follows.
=+m
Δ
T0.3ΔT
.
max max0 (3)
In (3), m is the current carrying batch number, and ΔT
max0
is the
general ΔT
max
intercept. The straight slope which also reflects the fuse
ageing speed, is about 0.3 °C/batch. The linear relation of ΔT
max
~m
shown in (3) had good recurrence in experiment.
3.2. The linear ageing resistance characteristics of the fuse conductor under
the DC100A/60s current carrying mode
Under the room temperature, the fuse worked under the equivalent
DC100A/60s current carrying mode. After each continuous 60 s for
current carrying, the fuse cooled down to the room temperature. This
carrying mode is equivalent to the effect of T
D
= 120 s (shown in
Table 1) with duty ratio of 1:2. Define the static resistance of fuse under
room temperature before each batch of current carrying as R
f0
, and
define the dynamic resistance of fuse when the fuse ceramic tube
temperature reaches ΔT
max
as R
f.
The fitted linear lines of R
f0
~mand
R
f
~mbased on the tested datum are shown in Fig. 4(b) and (c). The
linear expressions of R
f0
~mand R
f
~mare as follows.
⎧
⎨
⎩=+ = =
=+ = =
RkmRk mbatchR
RkmRk mbatchR
, 0.01 Ω/ , 6.1~6.2 mΩ
, 0.1 Ω/ , 13~15 mΩ
f
f
01 011 01
2022 02 (4)
The experimental results reveal when R
f0
reached ~7 mΩor R
f
reached 20–22 mΩ, the linear ageing stage was over and the nonlinear
ageing stage started. The linear ageing slopes k
1
and k
2
shown in (4)
had good recurrence in experiment.
Generally speaking, the linear ageing stage of the Sielins DC1600V/
32A fuse exists a long time under the overload pulse current carrying
mode, which just corresponds to the total current carrying lifetime of
the fuse. Define the initial static fuse resistance under room tempera-
ture as R
f01
. In the linear ageing stage, R
f0
linearly increases from R
f01
and the stable recurrent variable scale of R
f0
is (R
f01
−R
f0
)/R
f0
≤10%.
As a result, the expended time for the increment of 10%R
f0
is the
normal prediction lifetime of the fuse under the overload pulse current
carrying mode.
=lifetime R t k10% /
.
fD01 (5)
4. Nonlinear ageing characteristics of the fuse conductor under
the overload pulse current carrying mode
4.1. Nonlinear ageing characteristics
At the last of the linear ageing stage of Sielins DC1600V/32A fuse,
once (R
f0
-R
f01
)/R
f01
≥10%, the fuse fast goes into the nonlinear ageing
stage. Firstly, R
f0
and R
f
respectively fast increase from 7 mΩand
20 mΩto hundreds of mΩor even Ωrange. After the fuse temperature
recovers to the room temperature, R
f0
and R
f
can not fall back.
Secondly, the transition between the linear and nonlinear stages is
usually completed through only one or a few current carrying batches.
Thirdly, though the fuse resistance is far away from its normal level, no
electric arcs are formed at the ageing narrow neck of the fuse con-
ductor. Pulse currents still flow through the series-resonant converter
circuit shown in Fig. 1(b), but the series-resonant characteristics of the
protected converter are changed due to the remarkable increment of R
f
.
The changes of the series-resonant characteristics can cause an un-
anticipated converter circuit failure.
4.2. The failure mechanism of the series-resonant converter caused by the
nonlinear ageing fuse resistance
As the typical series-resonant H bridge of converter shown in
Fig. 1(b), its soft-switching work mode is as follows. Firstly, the switch
pair S1-S3 is triggered simultaneously by the square voltage pulse
T_pulse1 with pulse width of T
r
/2, and the generated series-resonant
current I
r
(the positive half-period) in the converter circuit is as “a”
shown in Fig. 5. When t = T
r
/2, I
r
goes to 0, and S1-S3 turns offsi-
multaneously. During the stage T
r
/2 < t ≤T
r
, the negative half-period
of I
r
shown as “b”is generated by the freewheel diodes D1 and D3
which respectively have anti-parallel relations with S1 and S3. When
t=T
r
, the continuing I
r
goes to 0 and the first resonant period is over.
After that, S1–S4 and D1–D4 all turn off. During the stage
T
r
+ΔT
r
<t≤3T
r
/2 + ΔT
r
, the switch pair S2-S4 is triggered si-
multaneously by the square voltage pulse T_pulse2 with pulse width of
T
r
/2, and the generated series-resonant current I
r
(the negative half-
period) in the converter circuit is as “c”shown in Fig. 5. When t = 3T
r
/
2+ΔT
r
,I
r
goes to 0, and S2-S4 turns offsimultaneously. During the
stage 3T
r
/2 + ΔT
r
<t≤2T
r
+ΔT
r
, the positive half-period of I
r
shown as “d”is generated by the freewheel diodes D2 and D4 which
respectively have anti-parallel relations with S2 and S4. When
t=2T
r
+ΔT
r
, the continuing I
r
goes to 0 and the second resonant
period is over. After that, S1–S4 and D1–D4 all turn off. As aforemen-
tioned, the two triggering pulses T_pulse1 and T_pulse2 recur alter-
nately, with the interval of T
r
/2 + ΔT
r
.
In the series-resonant converter circuit shown in Fig. 1(b), the re-
sonant impedance Z
r
is as Z
r
=(L
r
/C
r
)
0.5
. As to the typical R-L-C circuit,
the resonant current I
r
contains some important characteristic para-
meters, such as the resonant frequency f
r
, resonant period T
r
, and time
constant τ. Under the underdamping state(R
f
<2Z
r
), critical damping
state (R
f
=2Z
r
) and the overdamping state (R
f
>2Z
r
), the theoretical
I
r
=I
r
(R
f
,t) is calculated as
Y. Zhang, et al. Electrical Power and Energy Systems 117 (2020) 105604
5