Electric Power Systems Research 172 (2019) 86–95
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Electric Power Systems Research
journal homepage: www.elsevier.com/locate/epsr
Sensitivity analysis of reignition overvoltage for vacuum circuit breaker in
offshore wind farm using experiment-based modeling
T
⁎
Y.L. Xin, W.H. Tang , J.J. Zhou, Y.H. Yang, G. Liu
School of Electric Power Engineering, South China University of Technology, Guangzhou 510640, China
A R T I C LE I N FO
A B S T R A C T
Keywords:
Offshore wind farms
Reignition overvoltages
Vacuum circuit breaker
Sensitivity analysis
This paper investigates the characteristics of reignition overvoltage of vacuum circuit breaker, and analyzes the
influences of reignition overvoltage on a power collection grid in offshore wind farms. An offshore wind farm
model, including an opening model of VCB, is developed based on a parameter fitting method in PSCAD/EMTDC,
which is experimentally validated covering main offshore wind farm components. The established laboratory
experiment setup comprises vacuum circuit breakers, cables, transformers and equivalent equipment of a wind
turbine. The experiment reignition overvoltages and currents are recorded to analyze its transient behavior,
contributing to understanding the occurrence mechanisms of reignition overvoltages in offshore wind farms.
Moreover, a sensitivity analysis is performed to identify factors affecting reignition overvoltages based on the
developed simulation model. The statistical result analysis indicates that four out of seven investigated factors
(including the capacitance (stray capacitance and cable length), the rate of rise of dielectric strength and the
opening phase angle of vacuum circuit breaker) have remarkable influences on reignition overvoltages of offshore wind farms.
1. Introduction
With the rapid development of wind turbine technology, offshore
wind farms (OWFs) offer many advantages compared to onshore ones,
such as impact on the landscape, noise reduction, generation capacity,
which lead to the significant growth of large OWFs in recent years
[1,2]. The power collection grid in an OWF is composed of long-length
cables, wind turbine transformers (WTTs), vacuum circuit breakers
(VCBs) and busbars [3]. The electrical configurations and conditions
are not like any other conventional industrial systems and onshore wind
farms. Wind energy is a random and intermittent source, which results
in the vast fluctuations in power generated by wind turbine (WTs). Thus
WTs may be switched on/off by VCBs several times a day [4], connecting/disconnecting WTTs to a wind park network. During the
switching operations of VCB, switching overvoltages (SOVs) are generated by chopping the current across the VCB before natural zero
crossing. Due to the unique configuration of the power collection
system and the lower surge impedance of cable than that of overhead
lines in OWFs, the current chopping in conjunction with capacitances of
cables and inductances of WTTs results in high-amplitude, high-frequency (HF) and high-steepness SOVs. Moreover, due to the dielectric
properties of VCB, multiple prestrikes/reignitions can occur. The above-
mentioned unfavorable combination increases the occurrence probability of HF SOVs.
Although the magnitude of these SOVs is less than the basic insulation level of a transformer, such a switching surge can prompt high
oscillation voltages inside transformer windings, which results in resonances and thus cause deterioration and failures of the equipment
insulation due to the aggregated effects [4–8]. Besides, due to the short
cable between the VCB and the WTT, when such a high-steepness
transient overvoltage propagates to the terminals of the WTT, the
steepness is still high, which causes the uneven distribution of interturn voltage of transformer windings and further causes the damage of
inter-turn insulation [7,9]. There is a significant number of transformer
failures reported at OWFs in the past years. Extensive researches have
revealed that such SOVs have become the prominent cause of insulation
failures of main components in OWFs, especially for transformers
[10–12], even though these transformers passed all standard tests and
complied to requirements. Furthermore, when an inductive load current is chopped during an opening process of VCB, generated reignition
overvoltages (ROVs) are more serious than that when other types of
currents are chopped [13]. Therefore, it is vital to investigate the
transient process and the characteristics of ROVs when switching off
WTs, and further ascertain main causes of ROVs in OWFs, providing
⁎
Corresponding author.
E-mail addresses: xin.yanli@mail.scut.edu.cn (Y.L. Xin), wenhutang@scut.edu.cn (W.H. Tang), epjiujiangzhou@mail.scut.edu.cn (J.J. Zhou),
epyhyang@mail.scut.edu.cn (Y.H. Yang), liugang@scut.edu.cn (G. Liu).
https://doi.org/10.1016/j.epsr.2019.02.008
Received 20 August 2018; Received in revised form 7 February 2019; Accepted 9 February 2019
0378-7796/ © 2019 Published by Elsevier B.V.
Electric Power Systems Research 172 (2019) 86–95
Y.L. Xin, et al.
quality. However, multiple reignition transients during an opening
process of VCB, the impact aspects of ROVs as well as the severity of
these effects are not fully studied yet, considering stray elements of
VCB, RRDS and initial opening phase angle.
In this paper, a 35 kV laboratory experiment platform, which is
consistent with the voltage level of the power collection grid of a real
OWF, is built to investigate reignition transient processes during the
switching-off procedure of VCB. Then the measurement results are
further obtained to accurately study the transient characteristics and
occurrence mechanism of ROVs in the power collection grid of OWF,
which are different from that during the switching-in operations in
[33]. Finally an OWF model is developed in PSCAD/EMTDC and validated experimentally, which is capable of simulating repeated strike
processes accurately. Based on the developed model, a SA is carried out
to investigate the main factors that influence ROVs.
The rest of this paper is organized as follows: Section 2 presents the
research framework and methodology. Section 3 shows the laboratory
experiment setup and result analysis. Section 4 analyzes simulation
results. Section 5 evaluates the factors that affect ROVs by means of SA.
Finally, conclusions are drawn in Section 6.
valuable references for overvoltage protection design and equipment
insulation coordination procedures.
In past years, a number of researchers investigated the switching
transient phenomena in power collector grids of large OWFs and revealed the importance of the assessment of these transient phenomena
by means of simulations and field tests. These literatures mainly dealt
with the following issues: the importance of overvoltage studies in
OWFs [14,15], the accurate modeling of the pretrike/reignition phenomena of VCB [16–20], and the effects of prestrikes on transformers
[5–7]. In [9], a more refined VCB prestrike model was developed to
further improve the agreement between simulation results and measurements during the switching-in operations of VCB in the Burbo Bank
OWF. This work also investigated the switching transient phenomena
and the factors that affected transformer terminal voltages [21]. Due to
the limitation of commercial and safety aspects, only few types of field
tests were conducted. Thus in order to conduct more types of experiment and obtain a further understanding about SOVs in wind farms, a
laboratory experiment platform was built by ABB Corporate Research,
which had a similar layout with the power collector system of a wind
farm. Transient simulations based on this platform in PSCAD/EMTDC
were compared with measurements in [22–24]. Furthermore, several
traditional and novel protection methods were studied for the mitigation of HF SOVs [22,25–27]. Research results of these references provided valuable information for understanding HF switching transients
in wind farms.
However, the voltage level of the medium voltage (MV) cable
system in the laboratory experiment platform built by ABB was set up to
be a scaled representation (phase-to-ground voltage 10 kV), and the
rated voltage of the used VCB was 12 kV. Whereas, in real OWFs the
voltage level of the MV cable system is 33/35 kV [17], and the rated
voltage of VCB is 40.5 kV. Transient characteristics of reignitions (including the amplitude, frequency, steepness, the number of reignitions,
the occurrence probability of ROVs) are relevant with the structure and
parameters of a system, such as the nominal voltage and the opening
velocity of VCB. During the switching-off operation, reignitions occur if
the transient recovery voltage (TRV) is greater than the dielectric
strength between the two contacts of a VCB. The TRV increases proportionally with the rated voltage of a VCB. The rate of rise of TRV
(RRTRV) depends on the structure and parameters of the circuit. The
dielectric strength rises along with the increase of the distance between
the two contacts of VCB. Meanwhile, the rate of rise of dielectric
strength (RRDS) of the vacuum gap of VCB lies on the opening velocity
of the VCB. For a 40.5 kV VCB, compared with the 12 kV one, the
voltage level increases by 3.5 times. Hence, if the parameters of the load
side of VCB are kept as constant, the amplitude of TRV and the RRTRV
increase with the same multiples for a 35 kV linear system. Nevertheless, according to the opening velocity of VCBs with respect to different rated voltages reported in [28] and the technical parameters
provided by a VCB manufacturer [29], the opening velocity increases
less than 1 times, as does the RRDS. For the same opening time, the TRV
is more likely greater than the dielectric strength between the two
contacts of VCB. Consequently, the occurrence probability of multiple
reignitions of a 40.5 kV VCB is higher than that of 12 kV or lower. With
the configuration and parameters of the system unchanged, the values
of the above mentioned transient characteristics of reignitions in a
35 kV system are larger than that in 10 kV and lower systems. Thus,
according to the above analysis, the difference of these parameters
between 40.5 kV and 12 kV or lower VCBs leads to the difference in
reignition phenomena. Therefore, it is necessary to built a 33/35 kV
voltage level experiment platform to conduct more accurate research
for analyzing SOVs in OWFs.
A sensitivity analysis (SA) of OWF was conducted in [30,31], which
mainly focused on operation and maintenance cost and availability.
[32] provided a SA method for capacitor placement in radial distribution networks considering transient overvoltages due to capacitor
switching, which aimed to reduce power losses and ensure the power
2. Research framework and methodology
The method of SA measures model output variance against the
change in model inputs, resulting in identification of inputs that have
the largest influence on outputs. It can be used to reveal the uncertainty
associated with each input factor, as well as to identify variables to
create a meta-model [30]. In this research, in order to obtain a deep
understanding of the phenomena and occurrence mechanism of ROVs
in OWFs, a SA of ROV is performed to identify factors that affect ROVs.
The research methodology is implemented by three stages.
(1) Laboratory experiment platform
Measurements from a real OWF with various operation conditions
are certainly the best source of information for studying complex phenomena in OWFs. However some limitations exist, such as commercial
aspects, safety aspects as well as risks of damaging equipment.
Moreover, the voltage level of reported laboratory experiment platforms for SOV studies in OWFs is only 10 kV [22–24], and as analyzed
in Section 1 the overvoltage phenomena and characteristics of reignitions in a 35 kV system are not the same as that in the 10 kV level.
Therefore, it is necessary to investigate the transient characteristics and
occurrence mechanisms of ROVs for a 40.5 kV VCB system. To address
this issue, a laboratory experiment setup (i.e. a section of OWF), where
its voltage level of collector power system is consistent with that in a
real OWF, is constructed similar to the test setup built by ABB as reported in [22–24]. Then the characteristics of ROVs, reignition processes and its influences on the insulation of main components are
analyzed based on laboratory measurements. The characteristics are
evaluated by five main indictors of ROVs, including the peak (Vmax), the
maximum steepness (du/dt), the damped oscillation frequency (fn), the
number of reignitions and the arcing time.
(2) Experiment-based modeling
Due to the difficulty in carrying out a large number of laboratory
tests, in this research a comprehensive OWF simulation model is built in
PSCAD/EMTDC according to the configuration and parameters of the
laboratory experiment platform. Based on laboratory measurements,
parameter fitting is implemented through two iterations. The first
iteration is to adjust the parameters of cables and transformer as well as
the opening time instant of VCBs, which ensures the peak values of
ROVs in simulations are consistent with actual measurements. The
second one is to adjust the RRDS of VCBs, which aims that the steepness
of ROVs in simulations agrees with measurements of experiments.
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Fig. 1. Research framework of the proposed method.
Fig. 2. Layout of laboratory experiment platform. (a) Simplified schematic. (b)
The experiment platform.
Consequently, an accurate simulation model is obtained, which can be
used for further analysis.
was carried out on the same experiment platform as reported in
[20,23,34,35], and according to the analysis results, the 1 km length of
Cable 1 in this research is sufficient for conducting HF transient analysis
in OWFs.
The references [13,23] stated that prestrike/reignition conditions in
circuit breakers with cables on both sides had shown resistive, inductive
and capacitive load currents, especially the former two which played a
dominant role in the studied system, gave rise transients. However the
inductive load current gave the worst case. In this research, the WT is
replaced by an inductive load. It is selected to produce an inductive
current larger than the typical chopping current of the VCB and a
magnitude that is equivalent to the rated current of transformer T2,
generating 100% of the rated power of a WT at the 0.69 kV voltage
level.
The electrical parameters of components utilized in the laboratory
platform are listed in Table 1. Thereinto, as the cost of 35 kV XLPE
cable is much high compared with that of 12 kV, the insulation of a 12/
20 kV cable was thickened to withstand short-time surge voltages occurred in a 35 kV system, which is used in the experiment.
(3) Sensitivity analysis
ROVs may reach values that are higher than the basic insulation
level, thereby applying a high electrical stress to OWF components, and
further damage the insulation of main components with cumulative
effects. Therefore, in order to reinforce the understanding on the occurrence mechanism of ROVs, find ROV causes and recognize factors
that have strong effects on ROV occurrence, in this stage a SA is performed based on the outputs produced by the develped simulation
model. The main distributions of ROV indicators are evaluated based on
simulation results when various factors change, leading to the identification of important factors resulting ROV occurrence.
The SA results not only illustrate a qualitative way to screen out
important factors in a computationally efficient manner, but also provide references for the insulation deign of main components, overvoltage protection and insulation coordination during the project development of OWFs. Fig. 1 shows the research framework of the
proposed method.
Table 1
Main parameters of the laboratory setup.
3. Laboratory setup and measurement analysis
3.1. Laboratory experiment setup
Due to the limitation of the laboratory space, a small section of an
OWF is built, which is based on the actual layout and the voltage level
in the collector grid of a real OWF [33]. The simplified schematic and
the laboratory experiment platform are shown in Fig. 2(a) and (b),
respectively.
In Fig. 2(a), Cable 1 and Cable 2 are the same type of submarine
cable, and the only difference between them is the length. Cable 2 is the
cable of 0.08 km length between a WTT located at the windmill nacelle
and a VCB. Based on the length of two similar configurations in [27,34],
the 0.08 km length of Cable 2 is used in this research for HF transient
analysis. Cable 1 represents the one between the transformer T1 located
at the substation platform and the first WTT on a feeder in the collection grid of OWF. The length of Cable 1 is a bit short compared with
that in a real OWF, but a similar study with only 294 m cable length
Main components
Parameters
Value
T1
Rated voltage
Apparent power
No-load current, I0
Short-circuit voltage, Uk
Rated voltage
Cross-section
Length of Cable1/Cable2
Rated voltage
Rated current
Chopping current
Rated voltage
Apparent power
No-load current, I0
Short-circuit voltage, Uk
Load losses, PCu
No-load losses, PFe
Inductive load
10/35 kV
2000 kVA
0.7%
7.78%
12/20 kV
3×35 mm2
1 km/0.08 km
40.5 kV
630 A
5A
35/0.69 kV
1600 kVA
0.8%
4.5%
14.5 kW
2.4 kW
1.0 mH
MV XLPE cable
VCB
T2
Load
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damped oscillation stage.
The TRV between the two contacts of VCB is determined by the
voltage difference between VMP1 and VMP2 in Fig. 2(a), which is the
best data source for the breaker dielectric withstand voltage (BDWV)
and reignition analysis. In this research, due to the limited experiment
resources, for simplification, the waveforms in Fig. 4 are used to analyze reignition processes similar to that discussed in [35].
During the second stage, high-magnitude and HF ROVs are observed
in Fig. 4. From the enlargement of Fig. 4(b), the TRV of phase C first
appears, and it indicates the current of this phase is first chopped at the
zero current of power frequency. At the beginning, the RRDS is lower
than the RRTRV, thus breakdowns occur between the two contacts of
VCB, which lead to HF transient surges. Such surges propagate to the
other two phases, and if the coupled currents meet the current chopping
conditions, the other two phases are forced to chop, which is named as
the virtual current chopping (VCC) as discussed in [28].
From the results as shown in Fig. 4(c), the three-phase currents
interact with each other, thus multiple VCCs take place. Furthermore,
because of the current chopping in all the three phases, multiple
breakdowns appear between the two contacts of VCB until the withstand voltage of dielectric strength of VCB is larger than the TRV of
VCB, which bring more serious overvoltage. Due to the interaction of
the three-phase currents, it is derived that reignitions in one phase induce voltage strikes in the other phases. It should be noticed that,
among the 25 tests, reignition and multiple reignition phenomena occur
every time, while this reignition is rare in the 12 kV and lower systems
[28].
In addition, it is also seen that the contacts start to open in phase C,
which is approximately 0.3 ms earlier than that in the other two phases.
This time delay is stochastic. From Table 2, the overvoltage magnitudes
of the other two clearing phases (i.e. A, B) are much higher than that for
the first clearing phase (i.e. C). The numbers of multiple reignitions of
the three phases are not the same.
The arcs in the three phases do not extinguish strictly at the same
time in Fig. 4(b), but the oscillation frequency after the extinguishing of
arcs is same, which is about several hundred Hz. The damped oscillation frequency of measurement results (fnmeas) is equal to the inverse of
the average period of oscillation (i.e. 1.29 ms determined from Fig. 4),
that is 1/1.29 ms = 775.2 Hz. According to the nameplate data of T2
and the equivalent wind turbine load, the equivalent inductance of load
side (LE) is determined, i.e. 2.683 H. The total capacitance of load side
(CL) is equal to the sum of the equivalent single-phase to ground capacitance of Cable 2 (0.15 × 80 = 12 nF), the terminal stray capacitance of T2 (assuming 2 nF) and the capacitance of voltage divider
(assuming 1 nF), that is 15 nF. Therefore, the theoretical damped os1
cillation frequency (fntheor) is equal to 793.35 Hz ( fntheor = 2π L C ).
3.2. Data sampling configuration
The layout of voltage measurement points (VMPs, i.e. VMP1, …,
VMP4) and current measurement points (CMPs, i.e. CMP1) in the laboratory platform are depicted in Fig. 2(a).
Phase-to-ground voltages are measured by high-bandwidth resistance-capacitor voltage dividers, and the standard ratio and frequency bandwidth of voltage dividers are 10000:1 and 10 Hz–20 MHz,
respectively. Phase currents are measured using Pearson 101 current
transformers (CTs) with 50 kA peak current and 3 dB bandwidth from
0.25 Hz to 4 MHz. The standard ratio of CT is 0.01. In this study, only
one CT is installed at the load side of the VCB to measure the current of
phase B.
Signals from voltage dividers and CTs are recorded by a digital oscilloscope through coaxial cables. The voltage and current signals are
recorded using a sampling frequency of 50 Msa/s (i.e. mega samples per
second).
3.3. Measurement analysis
In this research, only the experiment data with the following two
configurations are analyzed, when transformer T2 is switched off by the
VCB:
• case 1: with no load
• case 2: with 1 mH inductive load connected
“No load” means that WTT (T2) is switched off with the low-voltage
side as an open-circuit, namely with WT not connected to the feeder.
Case 2 refers to the condition that WT is running at the rated power and
connected with WTT.
3.3.1. VCB switching-off with no load
Overvoltage measurements of the three phases at the 35 kV side of
WTT for case 1 are presented as the bold lines shown in Fig. 3, where
the curves marked as ‘UAm’, ‘UBm’ and ‘UCm’ represent the measurement results at VMP1. The curves marked as ‘UAs’, ‘UBs’ and ‘UCs’
represent the simulation results, which are discussed in Section 4.
It is expected to record some repetitive strikes during this opening
transient process. However, in Fig. 3, there is no reignition, and the
reason for this is related with the no-load current value. RRTRV
changes slowly compared with the RRDS of the VCB very soon after the
contact separation.
3.3.2. VCB switching-off with inductive load
Totally, 25 times of switching-off tests are carried out on the experiment platform for case 2. Due to the stochastic feature of VCB
switching operations, the results are different in each test. In this research, the waveforms on the 35 kV side of WTT, including the threephase voltages and the phase B current of one test, are depicted in
Fig. 4. The main indicators of the results are summarized in the row of
“Measurement” in Table 2.
From Fig. 4, the entire process for case 2 is divided into three stages.
The first one is the steady stage at the power frequency, and the second
is the reignition stage, which lasts about several milliseconds (around
3 ms for all 25 sets of tests). After the second one, it is turned into a
E L
The relative error between fntheor and fnmeas is only 2.3%, which verifies
that the obtained experiment results are correct.
According to the statistical analysis of all the 25 tests, the RRDS is
not exactly linear with respect to the separation distance of contacts,
furthermore the BDWV of each test result is not same. The dispersion
and nonlinearity of BDWV, reported in [23,34–36], make it difficult in
simulating the insulation strength against the operating time.
4. Simulation results using the experiment-based OWF model
This section introduces the derivation of an experiment-based OWF
model using PSCAD/EMTDC, based on both the nominal parameters of
main components as listed in Table 1 and experiment measurements.
4.1. Modeling of main components
The equivalent supply source is represented by an ideal voltage
source in Fig. 2. Cables are described by a frequency-dependent phase
model based on the geometry and electrical parameters of actual cables.
Fig. 3. Experiment and simulation results for case 1.
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Fig. 4. TRV at the 35 kV side of WTT for Case 2: (a) 0–0.1 s transient voltages; (b) 30–33 ms HF transient voltages; (c) Voltage and current during HF arcing.
contact gap, arc reignitions occur. Consequently, the envelope line of
the TRV curve is the BDWV. In most of the published literatures
[41–43], the RRDS is set as a constant and then the BDWV is represented as a linear curve. However, according to the measured voltages in Fig. 4(b) and in [35], it is seen that during the switching-off
operations of VCB, the opening speed of the VCB contacts is varied and
the dielectric withstand of the contacts gap increases nonlinearly with
respect to time. If the BDWV is modeled by using a straight line with a
constant slope (e.g. RRDS) [35], it is not accurate. Thus, in this research, in order to improve the accuracy of the proposed VCB opening
model, considering the overall RRDS variation trend of the three-phase
BDWV in different periods, the BDWV of VCB model is grouped into
several pieces. Each piece is fitted by utilizing the first-order linear
polynomial of BDWV, which represents the BDWV as a function with
respect to time [42,43]. As for the HFQC, it is represented as a linear
function as discussed in [41–43].
Table 2
Overvoltage indicator comparison between measurements and simulation results with the inductive load.
Configuration
Vmax
kV
du/dt
kV/μs
fn
kHz
No. of reignitions
–
Arcing time
ms
Measurement
A
B
C
123.01
156.45
89.98
148.31
148.30
100.49
0.78
43
22
34
2.7
Simulation
A
B
C
132.58
141.85
106.29
202.75
181.42
93.78
0.67
40
32
39
2.8
WTT is modeled by adding stray capacitances between the terminals of
the unified magnetic equivalent circuit embedded in PSCAD/EMTDC
[37]. Since this research specifically studies the transient characteristics
for a short-time switching-off process of VCB, the WT equivalent model
is represented as an inductive load [14,38,39].
As reported in [15,18,19,40], an accurate representation of circuit
breaker in a simulation tool is an important guarantee of consistence
between measurements and simulation results. In this research, based
on the proposed methods in [9,41–43], an accurate opening model of
VCB is developed. The proposed VCB opening model consists of an
electrical model and a time logic controlling algorithm modular. The
controller, which is programmed by FORTRAN, controls the state of
VCB by continuously monitoring the current (Ibr) and the terminal
voltage (Vbr) across the two contacts of an ideal switch while the simulation is running. According to the research results [9,41–43], the
most important three parameters are involved for accurately simulating
physical phenomena of VCB during the switching-off operations accurately, including chopping current, BDWV (also regarded as RRDS) and
HF quenching capability (HFQC). Generally, the chopping current is
strongly dependent on the choice of contact material [22], thus for the
same VCB, the chopping current is the same, which is verified by many
researches [9,41]. In this research the mean value provided by the VCB
manufacture is 5 A, hence it is set to the power frequency chopping
current in the following analysis.
When the TRV between the two contacts exceeds the BDWV of the
di
= C × (t − to) + D
dt
(1)
where t is the instant time, to is the moment of contact separation, C and
D control the HF quenching capability. Eq. (1) gives the critical value of
di/dt, and if this derivative at the zero crossing is lower than the limit,
an arc is extinguished.
The completeness of the time logic controlling algorithm is also
important for improving the accuracy of the proposed VCB model,
which includes the varied duration time of each reignition, the arc
voltage and especially the refined criteria for switching between different states. In this research, based on the relevant statistical data in
[9,44], the single-phase reignition algorithm flowchart of the VCB
opening model is obtained as depicted in Fig. 5. In Fig. 5, t is the simulation time, △t is the time step, topen is the contact separation time,
treopen is the single ignition time, t1 is the specified time for determining
the fully opening state. Ich1 and Ich2 are the power frequency chopping
current and the HF chopping current, respectively. Pre _ Ibr is the previous time current across the VCB, Vdw is the BDWV. |dIbr/dt| is the
absolute value of the derivative of Ibr, and the critical dIbr/dt is the HF
current quenching capability of the VCB, which is calculated by (1).
Firstly, a general test circuit in [41] is built to verify the
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Fig. 5. The flow chart of reignition algorithm.
Fig. 7. Parameter verification of simulation model for VCB opening operations
based on measurement records.
effectiveness and accuracy of the developed VCB model in this research,
where the BDWV is represented as a linear function like most preliminary verification methods in the published literatures [9,16]. Fig. 6
shows the TRV and the current waveforms of VCB and the corresponding magnified views. From Fig. 6, it is seen that the developed
VCB model in this research is capable of emulating the power frequency/HF current chopping, varied arcing time, interruption debacles
for lower arcing times and arc voltage, etc. Compared with the simulation results of the built model in [45], the developed VCB model in
this research is capable of simulating the real physical phenomena and
HF transient characteristics comprehensively and accurately.
Afterwards, the fitting process for parameter verification is performed for case 1 and case 2 (the BDWV is represented by the above
described piecewise linear method). Although the most important
parameters (i.e. no-load losses and no-load current of T2) for the steady
state before de-energization are on the nameplate, in order to ensure
the accuracy of simulation results, the waveforms of the three-phase
voltage for case 1 are firstly checked. Since it is relatively simple, thus
the flow chart of the fitting process for case 1 is not shown. The entire
fitting process for parameter verification for case 2 is demonstrated in
Fig. 7 [46].
developed component models. The results for case 1 show a good
agreement with the measurements. For case 2, although the difference
in the repetitiveness of strikes exists when the simulation is compared
with the measurements, the other indicators and HF waveforms obtained in the simulations are close to the measurements. Especially the
HF transient voltage of phase C at the terminals of the WTT is simulated
with a good accuracy, as shown in Fig. 8(b). The difference of the other
two phases may be caused by setting the same RRDS for all the three
phases in this simplified simulation. Thus the convergence can be recognized as satisfactory between laboratory measurements and simulation results for the two cases, which further verifies the effectiveness
and accuracy of the proposed component models (especially the VCB
opening model). Compared with the proposed VCB opening model in
[41], the accuracy of the developed VCB model is more accurate. Then
the fitted parameters of the simulation model can be utilized to carry
out further analysis on ROVs caused by switching VCBs in OWFs.
5. Overvoltage causes and sensitivity analysis
4.2. Simulation results and feature analysis
This section investigates the influence factors of ROVs using SA. The
main aspects that affect ROVs during the operation of OWFs are stray
components and electrical parameters (i.e. RRDS of BDWV and HFQC)
of VCBs, different cable length between VCB and WTT and opening
phase angles of VCB.
The simulation waveforms are presented as the thin lines shown in
Fig. 3 and Fig. 8 for the two studied cases, respectively. Moreover, the
main indicators of ROVs for case 2 are listed in the “Simulation” row of
Table 2.
There are similar transient behaviors under the two cases using the
Fig. 6. TRV and current across the VCB on the test circuit. (a) TRV and current across the VCB. (b) The magnified views of TRV and current.
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Y.L. Xin, et al.
Fig. 8. Simulation verification results for case 2. (a) HF transients in simulation in three phases. (b) Comparison of HF transients between simulation and measurement in phase C.
research a switching impulse ratio (assumed as SIR) between SIL and
line terminal AC as 1.8 is used to determine the rated SIL approximately, which is consistent with the statistical range (1.8–2.0) in IEC
standard 60076-3 [50]. Thus the rated single-phase to ground peak
voltage
for
switching
impulse
conditions
is
103 kV
2
(70 × 1.8 × 3 = 103 kV). As for the rated withstand voltage steepness,
there is no recommendation in current insulation coordination standards. Moreover, when calculating the rated withstand voltage steepness, the value of front time is not arbitrarily set, therefore in order to
satisfy the parameter setting of the rated SIL for the duration of
switching impulses, in this research the rated front time of switching
impulses is still set as 10 μs to 100 μs. Then the rated withstand voltage
for switching impulses divided by the rated front time of switching
impulses is assumed to be the rated withstand steepness of transformers
for switching impulses, which is 10.3 kV/μs (i.e. 103 kV/
10 μs = 10.3 kV/μs).
As listed in Table 3, Vmax and du/dt for the three phases are above
103 kV, 85 kV/μs (marked in bold italics), respectively, which are
larger than the rated SIL 103 kV and the rated steepness 10.3 kV/μs,
and particularly in some cases the values are greater than the rated
2
basic insulation level (170 × 3 = 138 kV), resulting in serious damage
to the insulation of transformers and even to other main equipment.
From the above observations, the typical capacitance of the applied
VCB model is about 20–70 pF, and its stray inductance and resistance
are dependent on the environmental situation and cleanness of VCB
electrodes, which are within 10 to 120 nH, and from 10 to 1500 Ω,
respectively. It is worth mentioning such results can provide guidance
for improving a VCB design process.
5.1. Influences of stray elements of VCB
The stray elements in a VCB can lead to series resonances, the values
of which cannot be directly calculated from the design parameters of
VCB [41]. In this research, the range in a similar study [9] is adopted
and further expanded to analyze their effects on ROVs caused by VCB
opening operations. The stray resistance and inductance are changed
from 10 to 1500 Ω and from 10 to 120 nH, respectively. Twelve different values of stray capacitances from 10 to 120 pF (the interval is
10 pF) are studied. According to the statistical analysis results conducted in this study, when the stray resistance and inductance vary,
they have no significant effects on ROVs, as a result the statistical
distribution is not shown here. When the stray capacitance varies, three
indicators of three-phase ROVs are statistically analyzed, including
Vmax, du/dt and reignition number (ReigNo.). The simulation results are
listed in Table 3.
As shown in Table 3, when the stray capacitance varies, it has different impacts on the three phases, and the relationship between the
value of the stray capacitance and the overvoltage indicators is not
linear. From the results in Table 3, Vmax, ReigNo . and du/dt of phase A
show no noticeable changes with the variation of the stray capacitance,
which are within 10% for most cases. Whereas, du/dt of the other two
phases (phases B and C) varies remarkably, the relative difference of
which is high. For example, du/dt of phase B remains at about 150 kV/
μs and du/dt of phase C is around 90 kV/μs for most cases. In comparison, the values of du/dt (phase B) are about 180 kV/μs for 6 cases
(marked in bold in Table 3), the relative difference of which is 20%
compared with 150 kV/μs. Moreover, for 10 pF, 80 pF and 100 pF
(marked in bold in Table 3), the values of du/dt (phase C) are very high,
the maximum of which is about 151 kV/μs, and the relative difference
is above 40% than 90 kV/μs for most cases. Above all, it is derived,
when the capacitance is about 20–70 pF, du/dt of ROVs is relatively
small, leading to less insulation stress.
Moreover, according to the commonly used calculation method and
statistical results of the switching impulse level (SIL) in [47–49], in this
5.2. Influences of VCB electrical parameters
During operations of VCB, it is very important to properly model the
BDWV curve and HFQC when analyzing ROV characteristics. Therefore
it is necessary to study the impact of their variations on ROVs. The
BDWV during the opening of VCB increases upward as a whole (as
marked by the dotted arrow in Fig. 4(b)). The legend depicted in
Fig. 9(b) is also applied to Fig. 10(a).
In Section 4, the RRDS of BDWV is modeled by piecewise linear
fitting with the unit of kV/ms, which is defined as the changed BDWV
(kV) per unit of time (s or ms). Since the BDWV rises as the contact
distance (mm) increases, the contact distance and the opening speed
(m/s) of all the three phases are approximately equal, which result in an
approximate opening time and RRDS of BDWV. Hence in this subsection the RRDS is simplified and roughly assumed to have the same value
(kV/ms) as a constant for the convenience of comparison. The BDWV is
expressed as a linear function between RRDS and the opening time,
which is also adopted in published literatures [13].
The RRDS of VCB changes from 10 to 60 kV/ms (the interval is
10 kV/ms) for each phase. From the curves and the statistical results
shown in Fig. 9, it is noticed that Vmax is above 85 kV in most cases and
the highest when the RRDS is 40 kV/ms (i.e. the 4th simulation), which
is larger than the rated SIL 103 kV. In addition, when it is below 40 kV/
Table 3
Variations of main indicators when the VCB stray capacitance changes.
SimNo.
1
2
3
4
5
6
7
8
9
10
11
12
Vmax (kV)
du/dt (kV/μs)
ReigNo.
A
B
C
A
B
C
A
B
C
147
127
125
136
122
125
121
141
134
133
125
147
123
140
141
142
144
140
138
136
123
142
138
140
113
111
108
104
114
113
112
103
112
106
110
109
215
190
190
207
193
193
194
203
185
203
190
218
154
150
186
182
151
150
192
137
151
181
177
187
137
92
91
94
88
88
88
151
92
134
93
92
43
43
41
45
46
40
45
44
42
42
39
42
33
34
33
34
35
32
32
36
32
33
33
35
35
35
32
34
37
34
36
34
34
35
34
35
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Y.L. Xin, et al.
Fig. 9. The influences of RRDS on ROVs from 10 kV/ms to 60 kV/ms. (a) The HF transient voltage curves. (b) Distribution of three ROVs indicators.
ms, a slower switching speed leads to a lower Vmax and du/dt, which
relieves ROV stresses on the insulation of transformer windings. However, it is also noted that if this parameter is too small, more reignitions
occur. Therefore it is necessary to take into account comprehensively
the influences of these aspects to select an appropriate value of RRDS.
In this study, the HFQC varies from 1e4 to 1e6 kA/μs, and according
to the simulation results and statistical analysis of ROVs, when it is
below 40 kA/μs, it has an impact on producing multiple ROVs. In
comparison, when above 40 kA/μs, it reveals no obvious changes on
ROVs, thus such results are not depicted.
Table 4
The relation between the opening phase angle and ROV amplitude.
Brk . angle (°)
Amplitude (kV)
Brk . angle (°)
Amplitude (kV)
25
45
80
125
132
171
167
111
79
−106
−128
−168
229
239
261
290
330
358
−125
−95
−63
127
139
167
5.4. Influences of cable length between VCB and WTT
5.3. Influences of phase angle when switching off WTT
The cable length between VCB and WTT is changed from 20 to
200 m in simulations to study its effects on ROVs. The results are shown
in Fig. 10.
Fig. 10(b) depicts the first reignition of phase C, which is chosen for
comparison since in this phase, the current chopping is observed, and
when the cable length is less than 80 m, the overall effect of the three
indicators is relatively good in terms of reduced value of du/dt and
ReigNo..
The variation of the cable length has no evident influence on Vmax of
ROVs as shown in Fig. 10(a). du/dt almost remains for up to 40 m, but
for 80 m, it is the lowest, and for 100 m it reaches the highest. Then as
the cable length further increases, it almost remains unchanged. As for
ReigNo., with the increase of cable length ranging from 20 m to 80 m, it
decreases, and it is the lowest for 80 m, which is similar to du/dt.
However, when the cable length is 100 m, it reaches the highest value,
which is much larger than the other cases. After that, it is nearly invariable with the increase of the cable length.
When the cable length is below 80 m, Vmax for phases A and B is
above 110 kV, which is greater than the rated SIL. du/dt is still large,
thus an overvoltage protective device should be installed to protect the
insulation damage for main components.
From Fig. 10(b), it is obvious that longer cables lead to a slower
slope of ROV, due to their larger shunt capacitance and recovery period
of the transient voltage. The rise time of TRV depends on the cable
In order to study the effects of opening phase angle on ROVs, it
varies from 0° to 360° in simulations. The peak voltage of phase C is
depicted in Table 4.
Table 4 reveals that when the VCB breaks the voltage close at the
maximum value of voltage, i.e. 90° and 270°, the amplitude of ROV is
low, which is less than the rated SIL 103 kV. When the VCB breaks the
voltage close to a zero crossing point, i.e. 0° and 180°, the amplitude is
high and almost 1.7 times of the rated SIL, which results in serious
insulation failure of main components, even causes the power system
instability if without protective devices.
The reason is that an inductive current flows through the VCB,
causing the voltage to lead the current by 90°. This means that when the
VCB breaks the voltage at around its zero crossing, the current is interrupted around its maximum, which causes a TRV with a high amplitude, which leads to multiple reignitions.
Table 4 also reveals that for the opening phase angles from 90° to
270°, the TRV starts by rising, resulting in a positive first amplitude,
further bringing an opposite superposition with the power frequency
voltage (i.e. ROV). Similarly for the opening phase angles from 270° to
90°, the TRV starts by falling, which finally leads to a positive superposition with the power frequency voltage. The reason for this relation
is the directions of the current, which are opposite in the two intervals.
Fig. 10. The influences of cable length on ROV for cable length from 20 m to 200 m. (a) Distribution of three ROVs indicators. (b) The first reignition curves of phase
C for cable length from 20 m to 80 m.
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Y.L. Xin, et al.
Based on the verified OWF model, the sensitivity analysis is performed to analyze the effects of VCB stray resistance, inductance and
capacitance, BDWV and HFQC of VCB, cable length and opening phase
angle on ROVs. The results of sensitivity analysis show that at the WTT
terminals there are significantly harmful overvoltages due to reignitions, and identify the important factors affecting ROVs, which mainly
comprise capacitance, especially the RRDS of BDWV and the opening
phase angle of the VCB.
According to the above experiment/simulation results and analysis
in this research, the opening velocity of VCB should be optimized, when
the rated voltage changes from 12 kV to 40.5 kV in consideration of
reignitions and breakdown voltages. Moreover, effective overvoltage
mitigation measures should be taken for suppressing such fast-front
ROVs, such as synchronized switching controllers for controlling the
point-on-wave of energization/deenergization and resistor-capacitor
snubbers.
In the future research, the proposed sensitivity analysis framework
can be further expanded by considering different fault cases and
switching-on operations as well as protection measures of SOVs. In
addition, it is also necessary to study if reignition may cause internal
resonance in a transformer and investigate which switching condition
may cause severe SOVs by the evaluation of severity factors. Moreover,
based on the extensive measurements and the obtained simulation
model, the cumulative probability of the maximum overvoltages and
the rate of rise of the transient current should be statistically analyzed
by considering the stochastic opening phase angle and the different
operation configurations.
capacitance value and the cable length connected to the VCB, which can
provide references for ROVs mitigation of both the du/dt and the
ReigNo..
5.5. Technical discussions
To sum up, the characteristics of ROVs are mainly influenced by the
stray capacitance of the VCB, the cable length between WTT and VCB,
especially the RRDS of BDWV as well as the opening phase angle of the
VCB. The former two factors can be grouped into one class, namely
capacitance. ROVs are concerned with the relation between RRDS and
RRRV. The opening phase angle has effects on the value of chopping
current and the amount of energy stored in the inductive load, leading
to the influences on ROVs. Therefore, these issues verify the correctness
of the above results of SA. Moreover, it is also confirmed by the energy
balance analysis as illustrated below.
The transient voltage caused by current chopping is termed as
“Chopping Overvoltage”. The magnitude of the overvoltage is determined by Eq. (2) [28].
The energy at current interruption is equal to the energy at the
chopping peak voltage,
Umax =
L 2
Ich + Uo2
C
(2)
where Ich is the chopped current value in amps, Uo is the peak voltage
across the inductive load at the instant of chopping in volts, Umax is the
maximum chopping overvoltage in volts.
From (2), since the capacitance is located at the donominator, a
minor change produces relatively large influences on ROVs.
Acknowledgment
The authors acknowledge the support of Guangzhou Zhiguang
Electric Ltd., China for providing high voltage laboratory platform to
carry out this research and the National Natural Science Foundation of
China (No. 51477054).
6. Conclusion
This paper aims to develop a sensitivity analysis methodology to
identify important influence factors of ROVs generated during the
switching-off operations of VCB in OWFs. The results of the performed
study contribute a deep understanding of the transient phenomena and
occurrence mechanism of ROVs, which are also beneficial for component designers and operators of OWFs to improve component/OWF
design against HF ROVs or select the least vulnerable opening angle.
The implementation of the proposed sensitivity analysis method is
undertaken based on a 35 kV laboratory experiment platform and an
experiment-based OWF model.
The 35 kV laboratory experiment platform, which reflects the actual
layout and the voltage level in the collector grid of a real OWF, is established for the accurate analysis of ROVs. The transient voltages at
the 35 kV side of WTT and the currents across the VCB are measured.
The measurement results demonstrate that in most cases there are
multiple reignitions in all the three phases after the current chopping of
the first opening phase when VCBs switch off WTs. Due to the multiple
VCCs caused by the interaction of three-phase currents, high-magnitude, high-front and HF ROVs are initiated at the terminals of WTTs.
In order to predict the premature insulation problems and reduce
the risk of failure in the main components of the OWF collector system,
an experiment-based OWF model has been developed based on the
proposed VCB model and parameter fitting process. The verification of
the proposed experiment-based OWF model is carried out by comparing
the transient voltages in simulation with that in measurements for two
configurations (i.e. with no load and with an inductive load connected,
respectively). The main indicators of ROVs derived in simulations are
evaluated, which are close to those in experiments, including the peak,
the maximum steepness, the oscillation frequency, the number and the
duration time of reignitions. In summary, the developed experimentbased OWF model can accurately replicate multiple reignitions during
the switching-off manoeuvres of VCB in OWFs, which is suitable for
switching-off transient studies.
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