An on-line capacitor state identification method based on improved RLS
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
Transportation Safety and Environment, 2021, Vol. 0, No. 0 1–13
https://doi.org/10.1093/tse/tdab007
Research Article
RESEARCH ARTICLE
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
An on-line capacitor state identification method
based on improved RLS
Shu Cheng1 , Chang Liu1 , Shengxian Xue2 , Maoyu Wang3 , Xun Wu1, *
and Yu Luo1
1
School of Traffic and Transportation Engineering, Central South University, Changsha 410075, China, 2 CRRC
Changchun Rail Car Co., Ltd, Changchun 130062, China and 3 Shenyang Bullet Train Section of China Railway
Shenyang Bureau Group Co. Ltd, Shenyang 110021, China
∗
Corresponding author. E-mail: xun.wu@csu.edu.cn
Chang Liu, http://orcid.org/0000-0002-8264-5261
Abstract
As an essential part of DC-Link in the power converter, capacitor plays a crucial role in absorbing
ripple current and suppressing ripple voltage. The health and residual service life of the DC-Link
capacitor is one of the decisive factors for the safety, stability, and efficiency of the system in
which it is located. Aiming at the shortcomings of existing methods, such as low dynamic
sensitivity of data update and fluctuation of identification results, a capacitor state identification
method based on improved RLS is proposed in this paper. The proposed method is optimized by
introducing the forgetting factor algorithm and root means square algorithm to modify the
iterative formula and final identification results. Compared with existing methods, this method
can identify the capacitor’s current state in real time and accurately. Finally, we successfully
verified the accuracy, robustness, and adaptability of the proposed method by a series of
experimental tests on a dSPACE platform.
Keywords: DC-Link capacitor; state identification; recursive least square algorithm
1. Introduction
on the DC bus to avoid generating high ampli-
Capacitors play an essential role in power convert- tude pulsating voltage at the DC side’s impedance
ers, such as high-power metal thin-film capacitors end. It can also effectively control the fluctuation
are widely used in traction drive system of elec- range of ripple voltage and reduce the influence
tric locomotives. In DC-AC conversion, capacitors of DC-side instantaneous overvoltage on switch-
absorb the pulsating current by being paralleled ing devices.
Received: 8 December 2020; Revised: 10 March 2021; Accepted: 10 May 2021
C The Author(s) 2021. Published by Oxford University Press on behalf of Central South University Press. This is an Open Access article distributed under
the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution,
and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com2 S. Cheng et al.
Although the capacitors’ performance has been the variable electronic network, but this method
improved gradually in recent years, the capaci- needs to make significant changes to the system.
tor is still one of the weakest parts of the sys- For the thin-film capacitors state identification,
tem [1, 2]. It can be attributed to the following Makdessi et al. [14, 15] proposed an aging model of
two reasons: on the one hand, the aging rate of the thin-film capacitor based on capacitance loss
capacitor usually increases exponentially in prac- and proposed the corresponding life estimation
tical application due to the influence of work- algorithm. Wang et al. [16] studied the aging and
ing voltage, charging and discharging frequency, failure of thin-film capacitors in a high humidity
temperature, and other factors, which will seri- environment and obtained the aging curve. Plaček
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
ously affect its performance and bring substan- et al. [17] studied the aging of thin-film capaci-
tial potential risks to the safe and stable opera- tors by impedance nonlinear measurement. Buat-
tion of the system. On the other hand, the capaci- tati et al. [18] used LMS to estimate the state of
tor must be replaced to ensure the system’s per- thin-film capacitors, but the estimation curve fluc-
formance and safety when its main parameters tuated. Based on the thin-film capacitor’s perfor-
decline to a specific state before the end of its life, mance advantages and its extensive applications,
which will cause a substantial increase in oper- this paper focuses on the research object of the
ating costs [3]. Therefore, the capacitor’s service thin-film capacitor, analyzes and studies its fail-
life can be extended by monitoring the parameters ure mechanisms and state identification methods,
and ensuring safe operation, reducing the opera- and finally extends them to other capacitors.
tion costs, and achieving a balance between safety At present, the DC-Link capacitor is mainly
and economy. repaired or replaced according to the mileage
Capacitor state identification mainly achieves of the train. Although the off-line maintenance
life prediction or maintenance guidance based has a high accuracy of parameters identifica-
on the tracking of capacitor life characterization tion, its maintenance frequency and occasions are
parameters. The electrolytic capacitor is one of the restricted by the specified driving mileage and
critical research objects of capacitor state identifi- maintenance point of the train, so it is not easy
cation technology. Pu and Nguyen, and others [4, to monitor the capacitors’ state in real-time. How-
5] proposed various calculation methods of capac- ever, the existing on-line state identification tech-
itor equivalent series resistance based on injec- nologies still need to be improved in parameter
tion current. These methods need to modify the tracking accuracy. Therefore, a new on-line capac-
original system, and the identification accuracy is itor state identification method is proposed in
not high. At the same time, it may cause poten- this paper. Compared with existing methods, this
tial control problems. Givi and Farjah [6, 7] identi- method can identify the current state of capaci-
fied the equivalent series resistance of capacitors tors accurately and maintain great identification
by designing integrated and split-core Rogowski accuracy at different carrier frequencies. Also, this
coils. Although it has certain identification accu- method has good adaptability and can be applied
racy, it is not practical. Kai Yao et al. [8] sam- to the state identification of the thin-film capac-
pled PWM signals and output voltage to estimate itors and aluminum electrolytic capacitors at the
the equivalent series resistance and capacitance same time.
of the capacitors by model derivation. Abdenad-
her et al. [9] used different forms of Kalman fil-
2. Failure mechanism and the equivalent
ters to identify the equivalent series resistance
and capacitance of aluminum electrolytic capac- model of the thin-film capacitor
itors. Lee et al. [10] proposed a capacitor state Although thin-film capacitors have higher reli-
identification method based on model calcula- ability and longer service life than aluminum
tion. This method has sure identification accuracy electrolytic capacitors, they will inevitably appear
but can only be used for off-line detection. Lee aging, failure and, other problems. The main
et al. [11] proposed a capacitor state identification reasons are dielectric breakdown due to poor self-
method based on RLS (Recursive least squares), healing, separation of jet end from capacitor wind-
but the calculated value of capacitance fluctuated ing, and excessive capacitance loss.
wildly. Gasperi [12] proposed a state identifica-
tion method based on the capacitor impedance a) If the thin-film capacitor breaks down, the
multi-component model. Wu et al. [13] achieved capacitor will not reach the open-circuit state
the capacitor state identification by designing in hundreds of milliseconds and become theTransportation Safety and Environment, 2021, Vol. 0, No. 0 3
of the capacitor, and its decay rate will increase
exponentially after a certain degree of aging; ESR
will gradually increase with the aging of the capac-
Fig. 1. The equivalent circuit of a film capacitor itor.
impedance state (usually dozens of Ohm). At 3. State identification method based on the
this time, the dielectric melting phenomenon
improved RLS method
caused by heating in the capacitor will lead to
severe damage and even explosion of capaci- In the DC-Link capacitor state identification pro-
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
tors; cess, if C and ESR are calculated directly by the
b) The contact surface gradually degenerates capacitor terminal voltage and the current flow-
under the joint action of electrical stress, ther- ing through the capacitor, it will lead to signifi-
mal stress and mechanical stress, and finally cant errors in the identification results. The rea-
causes the jet end to fall off. In pulse power sons include but are not limited to: a) Differential
applications, the separation of the jet ends will enlarge the error; b) Integral will accumulate
from the capacitors winding results in open- error; c) If the capacitor current is over zero, the
circuit faults [19]; calculation results will be overflow.
c) If the contact surface degenerates, the equiv- Therefore, an improved RLS capacitor state
alent series resistance ESR and loss factor identification method based on the relationship
tanδ of the capacitor will increase significantly between the voltage and current is proposed in
according to the number of pulses applied to this paper.
the capacitor, which causes the increase of
heat loss. 3.1 Principle analysis
Generally, the equivalent structural circuit of The core idea of the least-square method is when
a thin-film capacitor is shown in Fig. 1. C is the the unknown parameters are calculated according
capacitance, ESR is the equivalent series resis- to the known data, the unknown parameters’ opti-
tance, and ESL is the equivalent series inductance. mal solution should make the sum of the square
The main parameters of the equivalent circuit of the difference between the observed value and
model are introduced as follows: the calculated value multiplied by its correspond-
ing weight. The least-square method can be used
a) C is the most important and intuitive electri-
in both static and dynamic systems and used in
cal parameter of the capacitor. The quality of
both linear and nonlinear systems. Besides, it is
the thin-film capacitor is directly affected by
widely used in system identification based on its
its size, tolerance, and variation;
excellent adaptability and simplicity.
b) ESR is an essential factor for the heating and
Suppose that the time series y(t) is an n-order
loss of capacitors. ESR will cause power loss autoregressive model AR(n):
when current flows through the electrode of
the film capacitor, which will lead to the heat- y (t) = a1 y (t − 1) + a2 y (t − 2) + . . . + an y (t − n) + ε (t)
ing of the electrode and the capacitor. There-
(1)
fore, ESR is also one of the main factors limit-
ing the rated current of thin-film capacitors;
where y(t), y(t-1), . . . , y(0), . . . , y(1-n) are the known
c) ESL is the capacitor’s parasitic inductance due
observation data; ai (i = 1, 2, . . . , n) are the
to the current passing through the electrode
unknown parameters; ε(t) is the white noise with
and skin effect at high frequency. In general,
zero mean, and its variance is σ 2 . The parameters
ESL can be ignored. Therefore, the RLC series
ai , σ 2 , and their corresponding estimations can be
structure of the thin-film capacitor can be sim-
calculated from the observed data.
plified as an RC series circuit.
Rewrite equation (1) into the following form:
The scientific and simplified equivalent circuit
model will help the research and design of the on- y (t) = ϕ T (t) θ + ε (t) (2)
line capacitor state identification method.
At present, it is generally considered that C and where
ESR are the main characteristic parameters of the
capacitor state [20–22]. C will decay with the aging ϕ T (t) = [y (t − 1) , . . . , y (t − n)]4 S. Cheng et al.
θ = [a1 , a2 , . . . , an ]T P(t) is defined as a matrix of n × n order
then, writing the residual error ε(t) as −1
P (t) = T (t) (t) θ (9)
T
ε (t) = y (t) − ϕ (t) θ (3)
the sum of squares of the residuals is therefore, equation (8) can be written as
2
J = it = 1ε 2 (i) = 1 y (t) − ϕ T (t) θ (4)
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
θ (t) = P (t) T (t) Y (t) (10)
when the sum of squares of residuals J is the mini-
mum, we can obtain the estimation θ (t) of param-
at the next moment, there are
eters. Besides, the matrix-vector form of the obser-
vation sequences can be obtained by y(1), y(2), . . . ,
y(t) is shown as follow: θ (t + 1) = P (t + 1) T (t + 1) Y (t + 1) (11)
Y (t) = (t) θ + (t) (5)
according to the matrix inversion formula, we can
where obtain the recurrence form of P(t+1) as follow:
T
Y (t) = [y (1) , y (2) , . . . , y (t)]
T P (t + 1) = P (t) − P (t) ϕ (t + 1) ·
(t) = ϕ T (1) , ϕ T (2) , . . . , ϕ T (t)
−1
1 + ϕ T (t + 1) P (t) ϕ (t + 1) ×
T
(t) = [ε (1) , ε (2) , . . . , ε (t)]
ϕ T (t + 1) P (t) (12)
thus, equation (4) can be written as
T
J = [Y (t) − (t) θ ] [Y (t) − (t) θ ] (6) the recurrence formula of parameter estimation θ
(t +1) is
to minimize J and make the partial derivative of
the function concerning θ equal to zero, then
θ (t + 1) = θ (t) + P (t) ϕ (t + 1) ·
T (t) (t) θ = T (t) Y (t) (7) −1
1 + ϕ T (t + 1) P (t) ϕ (t + 1) ·
thus, we can obtain the estimated value θ (t) of
y (t + 1) − ϕ T (t + 1) θ (t) (13)
parameter θ at time t as
−1
θ (t) = T (t) (t) θ T (t) Y (t) (8) where
where T (t)(t) is a nonsingular matrix.
When the order of the model AR(n) is large, the θ (0) = θ 0 , y (i) = 0 (i ≤ 0)
inverse matrix of T (t)(t) θ is calculated at each
time t, which will greatly increase the amount
of calculation and occupy much running mem- combining with the estimation of ε (t) in equation
ory, and it is not suitable for on-line parameter (2), we can obtain the estimated value σ ε 2 (t) of σ 2 ε
identification. Therefore, using the recursive cal- is
culation method to obtain new estimation results
by modifying the previous estimation results with
new observation data. It can update the existing σ ε 2 (t) = it = 1ε 2 (i) /t (14)
parameter estimation values until their accuracy
is satisfactory. Its core idea can be expressed as:
θ (t) = θ (t -1) + correction term. the recurrence formula is as follow:Transportation Safety and Environment, 2021, Vol. 0, No. 0 5
dynamic changes. However, if the forgetting fac-
tor is small, the error of the optimal approximate
solution will increase. The state parameters of
the DC-link capacitor studied in this paper have
apparent time dynamic characteristics, which are
Fig. 2. Flow chart for recursive least square method suitable for applying the time attenuation algo-
rithm. Therefore, it is necessary to select an opti-
σ ε 2 (t) = σ ε 2 (t − 1) + it mal parameter value between improving the sys-
tem dynamic response speed and reducing the
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
= 1 ε (t) − ε (t − 1) /t
2 2 approximate solution error. In this paper, we use
(15)
the most direct and straightforward method to
summarize the experimental rules. Based on the
The calculation flow chart of the RLS method is
above principles analysis, we determine the opti-
shown in Fig. 2. So far, the estimation θ (t) of θ can
mal value of the forgetting factor as 0.92 through
be recursively calculated.
the method of taking values one by one.
Therefore, the capacitor parameter estimation
3.2 On-line state identification based on formula that considers weight improvement is
improved RLS method modified as follow:
Although the RLS method can be used to estimate
θ (i) = θ (i − 1) + P (i − 1) ϕ (i) ·
the parameters, there are some problems, such as
the decrease of dynamic sensitivity of data updat- −1
λ + ϕ T (i) P (i − 1) ϕ (i) ×
ing, the fluctuation, and divergence of the iden-
tification results of micro parameters, which will
y (i) − ϕ T (i) θ (i − 1) (17)
seriously affect and limit the performance and
practical application of this kind of identification P (i − 1) − P (i − 1) ϕ (i) ·
P (i) = −1 /λ
methods. Therefore, it is necessary to improve and λ + ϕ T (i) P (i − 1) ϕ (i) ϕ T (i) P (i − 1)
optimize the identification algorithm to improve
its convergence and accuracy. (18)
where θ (0) and P(0) can be calculated by a small
3.2.1 Dynamic weight improvement based on for- amount of measured data and a non-recursive
getting factor. The parameter estimation error of method.
the RLS method may increase with the increase
of observation data. The reason is that the previ- 3.2.2 Error elimination based on root mean square
ous data occupy a significant weight in the whole algorithm. In general, the parameters calculated
recursive process, which makes the algorithm less by the above formulae have good tracking ability,
sensitive to new data. Considering that both C and such as the parameter identification of the alu-
ESR change with time, this paper reduces this phe- minum electrolytic capacitor. However, the thin-
nomenon’s influence on identification results by film capacitor identification algorithm is prone to
using the forgetting factor to weaken the impact have large fluctuations and low convergence due
of previous data, which makes parameter identifi- to the minimum ESR (milliohm level) in the cal-
cation have better tracking ability. culation process. The estimated value of the algo-
Therefore, equation (4) is modified to obtain the rithm will have a significant deviation from the
improved performance index: actual value. The RLS online identification results
of a thin-film capacitor are shown in Fig. 3. It can
2 be seen that the estimated value of the ESR fluctu-
J = it = 1λt−i y (t) − ϕ T (t) θ (16)
ates between 0.0012 and 0.0016 .
Aiming at the result divergence problem,
where λ is the forgetting factor, and its value improving the recursive algorithm to obtain sta-
is between 0 and 1. When λ is equal to 1, it is ble estimation results by the following root mean
a standard RLS method. Generally, the smaller square calculation formula.
the forgetting factor λ is, the greater the weight
of the latest measurement data is, the smaller
the influence of historical data is, and the more t
1 2
sensitive the system is to the current external f (t) R MS = f (t) (19)
Ts
t−Ts6 S. Cheng et al.
from equation (22), the transfer function of the
(a)
DC-Link equivalent circuit can be obtained as fol-
low
UC (s) 1 + s · E SR · C
H(s) = = (23)
IC (s) sC
using bilinear transformation, get
(b) 2 1 − z−1
s= (24)
T 1 + z−1
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
where T is the sampling period. Transforming
equation (23) into the following discrete form
T
−1 T
2C
+ E SR + 2C − E SR z−1
H z = (25)
Fig. 3. The thin-film capacitor identification results: (a) C; 1 − z−1
(b) ESR. order
T
b0 = 2C + E SR
(26)
T
b1 = 2C − E SR
then equation (25) can be expressed as
b0 + b1 z−1
H(z−1 ) = (27)
1 − z−1
Fig. 4. Equivalent circuit of DC support link when the T is small enough, the amplitude-
frequency characteristics and phase-frequency
where t is the time, f(t) is the input signal, and Ts characteristics of discrete-time are consistent
is the fundamental period. The discrete form is as with those of continuous-time. Transforming
follow: equation (27) into the following form
UC (i) = UC (i − 1) + b0 I (i) + b1 I (i − 1) + ε (i)
N
i=1 fi2
f R MS = (20)
N = ϕ T (i) θ + ε (i) (28)
where N is the number of observations in a period. where
Compared with the existing methods, the pro- T
ϕ T (i) = [UC (i − 1) , I (i) , I (i − 1)]
posed method ensures fast identification and
improves the convergence and accuracy of iden- θ = [1, b0 , b1 ] (29)
tification results, and its structure is more super-
Therefore, combining with improved recursive
ficial.
formulae based on the proposed method, the
parameters of b0 and b1 can estimate by uC and iC ,
3.2.3 On-line state identification method based on
to obtain the estimated values of C and ESR pro-
improved RLS method. The equivalent circuit of
cessed by the root mean square algorithm.
the DC support link is shown in Fig. 4. Without
considering the influence of parasitic inductance, (b0 + b1 )
the DC-Link capacitor can be equivalent to an RC E SR = (30)
2
series circuit. The uC is the DC-side voltage, and T
the iC is the capacitor current. C= (31)
(b0 + b1 )
In the time domain, the following differential
equations can describe the relationship among uC , So far, the proposed method can achieve on-line
iC , C, and ESR. DC-Link capacitor state identification.
1
uC (t) = E SR · i C (t) + idt (21)
C 4. Experimental verification
in the complex frequency domain, equation (21) C and ESR are identified in this section by
can be written as observing the uC and iC to verify the proposed
1 method’s accuracy and effectiveness. The exper-
UC (s) = E SR · IC (s) + · IC (s) (22) iment divides into three parts:
sCTransportation Safety and Environment, 2021, Vol. 0, No. 0 7
Table 1. Measurement parameters sent to dSPACE for calculation. After RLS esti-
Name Parameter
mates the C2 and ESR with forgetting factor λ,
the root means square calculation is carried out
HIOKI IM3536 measuring Measurement accuracy = 0.05% to obtain the final identification results. Simulta-
instrument
Thin-film capacitor (500 Hz) C = 6 568 μF
neously, the identification results are compared
ESR = 0.00 141 with the measurements to observe the proposed
Thin-film capacitor (1 kHz) C = 6 625 μF method’s accuracy under the same conditions,
ESR = 0.00 142 and the error percentage of each parameter is
Thin-film capacitor (3 kHz) C = 7 216 μF
ESR = 0.00 151
calculated.
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
Aluminum electrolytic C = 6 623 μF As shown in Fig. 5, generally, the DC-Link capac-
capacitor (500 Hz) ESR = 0.0266 itor comprises two capacitors in series, which are
Aluminum electrolytic C = 6 669 μF the same type and the same or similar specifi-
capacitor (1 kHz) ESR = 0.0251
cations. Therefore, the parameter identification
Aluminum electrolytic C = 7 660 μF
capacitor (3 kHz) ESR = 0.0240 principle of capacitor C1 is the same as that of C2 ,
Experimental parameters λ = 0.92 which will not be repeated here.
N = 100
Carrier frequency = 1 kHz
4.1 Accuracy verification
The C and ESR decrease or increase slowly with
time, and they also change obviously under the
influence of various external factors. Whether
these parameters can be tracked accurately within
the given error range is essential for measuring
the proposed method.
The input monitoring results of the Improved
RLS algorithm are shown in Fig. 6(a). The ampli-
tude of the AC flowing through the measured
capacitor is stable at about 40 A. The DC termi-
nal voltage of the capacitor is maintained at about
299 V, which can realize the stable input of the
identification system and ensure the stable output
Fig. 5. Schematic diagram of the capacitor state on-line of the identification results. The on-line identifica-
identification tion results of C are shown in Fig. 6(b), where the
horizontal axis shows the relative time (unit: sec-
onds). It can be seen that the C maintains at about
a) The accuracy verification;
6 539 μF, which is almost the same as the off-line
b) The robustness verification;
measurements in Table 1. The error shows that the
c) The adaptability verification.
estimated values are smaller than the actual mea-
To test two samples of capacitors at room surements in this period, and the error percent-
temperature and different frequencies before the age is stable at 0.9%∼1.8%. The on-line identifica-
experiment. The experimental instruments and tion results of ESR are shown in Fig. 6(c), and the
parameters are shown in Table 1. It should be estimated values distribute between 1.418 m and
noted that each measurement value is obtained 1.478 m, which is close to the off-line measure-
from the average value of 10 measurement data ment of 1.42 m. The estimated ESR values are
to minimize the error. more significant than the actual measurements in
The schematic diagram of capacitor state on- most cases, and the absolute values of error per-
line identification is shown in Fig. 5. The DC- centage are stable within 4%. Therefore, the pro-
Link consists of two capacitors that C1 and C2 , posed method has good accuracy.
with the exact specifications in series in prac-
tice. The experiments carried out in this sec-
4.2 Robustness verification
tion only identify the state of C2 . In the experi-
ment, firstly, we load the state identification algo- The frequency of ripple current and voltage will
rithm into dSPACE. The voltage and current cor- change with the converter’s carrier frequency fluc-
responding to C2 are collected by the sensor and tuation, which will change the C and ESR.8 S. Cheng et al.
Considering the influence of carrier frequency
on identification parameters, the on-line state
identification of thin-film capacitor with the car-
rier frequency of 500 Hz and 3 kHz is verified in
the experiment. As shown in Fig. 7(a), the current
flowing through the capacitor and the capacitor’s
terminal voltage can be kept at a stable level. Com-
pared with the case of 1 kHz carrier frequency,
their fluctuation frequency is reduced, but their
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
amplitude remains unchanged. The state identi-
fication results of C are shown in Fig. 7(b) when
the carrier frequency is 500 Hz. The C is constant
at 6 500 μF. Compared with the off-line measured
values, the error percentage distributes between
0∼2%. The state identification results of ESR are
shown in Fig. 7(c) when the carrier frequency is
500 Hz. The estimated values are between 1.45 m
and 1.48 m, and they are more significant than
the actual measured values during this period,
and the absolute values of the error percentage are
between 2%∼6%. Compared with the case of car-
rier frequency equals to 1 kHz, the error of estima-
tion increases slightly.
As shown in Fig. 8(a), compared with the case
of 1 kHz carrier frequency, the current and voltage
can still maintain a stable amplitude level. The dif-
ference is that the fluctuation frequency increases
significantly, but it does not affect the stable out-
put of identification results. The state identifica-
tion results of C are shown in Fig. 8(b) when the
carrier frequency is 3 kHz. The estimated values of
C keep around 7 100 μF, and the error percentage
is less than 1.9% compared with the case of offline
measurement. The state identification results of
ESR are shown in Fig. 8(c) when the carrier fre-
quency is 3 kHz. The estimated values of ESR keep
around 1.53 m, and the error percentage relative
to the case of off-line measurement is less than
2%. Compared with the case of carrier frequency
equals to 1 kHz, the error of estimation decreases
slightly. Therefore, it can be considered that the
change of carrier frequency has no effect on the
state identification of C but has a slight impact
on the state identification of ESR. The ESR esti-
mations deviate slightly from the measured val-
ues when the carrier frequency decreases. How-
ever, the ESR estimations are slightly close to
Fig. 6. Identification results of C and ESR when the carrier
the measured values when the carrier frequency
frequency is 1 kHz: (a) The terminal voltage of the capacitor
and the current flowing through the capacitor when carrier
increases.
frequency is 1 kHz; (b) Identification result of capacitance Therefore, the proposed method can track the
C of thin film capacitor when carrier frequency is 1 kHz; (c) parameters accurately even under different car-
Identification results of ESR equivalent series resistance of rier frequencies.
thin film capacitor when carrier frequency is 1 kHz.Transportation Safety and Environment, 2021, Vol. 0, No. 0 9
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
Fig. 7. Identification results of C and ESR when the carrier Fig. 8. Identification results of C and ESR when the carrier
frequency is 500 Hz: (a) The terminal voltage of the capacitor frequency is 3 kHz: (a) The terminal voltage of the capacitor
and the current flowing through the capacitor when carrier and the current flowing through the capacitor when carrier
frequency is 500 Hz; (b) Identification result of capacitance frequency is 3 kHz; (b) Identification result of capacitance
C of thin film capacitor when carrier frequency is 500 Hz; (c) C of thin film capacitor when carrier frequency is 3 kHz; (c)
Identification results of ESR equivalent series resistance of Identification results of ESR equivalent series resistance of
thin film capacitor when carrier frequency is 500 Hz. thin film capacitor when carrier frequency is 3 kHz.10 S. Cheng et al.
4.3 Adaptability verification
In different applications, the models and types
of capacitors are different. Therefore, the pro-
posed method should still achieve a significant
parameter tracking effect after replacing different
capacitors.
The DC-Link capacitor is replaced by an alu-
minum electrolytic capacitor instead of a thin-film
capacitor to verify the proposed method’s appli-
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
cability. As shown in Fig. 9(a), the AC’s amplitude
flowing through the measured capacitor is stable
at about 10 A, and there is a small DC offset in the
current. The DC terminal voltage of the capacitor
is maintained at about 299 V, which can realize
the identification system’s stable input and ensure
the stable output of the identification results. The
state identification results of the C are shown in
Fig. 9(b) when the carrier frequency is 500 Hz.
The estimated values of C are constant around
6 645 μF. Compared with the off-line measured
values, the error percentage distributes between
0∼1%, which has better parameter tracking abil-
ity. The state identification results of the ESR are
shown in Fig. 9(c) when the carrier frequency is
500 Hz. The estimated values are relatively sta-
ble, which keep around 26.6 m. The absolute
value of the error percentage relative to the case
of off-line measurement is less than 0.6%, which
can also achieve a satisfactory parameter tracking
effect.
As shown in Fig. 10(a), both the current flow-
ing through the capacitor and the capacitor’s ter-
minal voltage can be kept at a stable level. Com-
pared with the 500 Hz carrier frequency, the fluc-
tuation frequency is increased, but the ampli-
tude remains unchanged. The state identification
results of C are shown in Fig. 10(b) when the car-
rier frequency is 1 kHz. The estimated values of
C are constant at 6 680 μF. Compared with the
case of off-line measurement, the error percent-
age distributes between 0∼1%. The state iden-
tification results of ESR are shown in Fig. 10(c)
when the carrier frequency is 1 kHz. The esti-
mated values keep around 25.09 m, and the
absolute value of the error percentage is within
1%. The proposed method under the current car- Fig. 9. Identification results of C and ESR of the aluminum
rier frequency has the same parameter track- electrolytic capacitor when the carrier frequency is 500 Hz:
ing ability as that at the carrier frequency of (a) The terminal voltage of the capacitor and the current
500 Hz. flowing through the capacitor when carrier frequency is 500
As shown in Fig. 11(a), compared with the Hz; (b) Identification result of capacitance C of aluminum
electrolytic capacitor when carrier frequency is 500 Hz; (c)
500 Hz carrier frequency, the current and volt-
Identification results of equivalent series resistance ESR of
age can still maintain a stable amplitude level.
aluminum electrolytic capacitor when carrier frequency is
The difference is that the fluctuation frequency 500 Hz.Transportation Safety and Environment, 2021, Vol. 0, No. 0 11
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
Fig. 10. Identification results of C and ESR of the alu- Fig. 11. Identification results of the C and ESR of the alu-
minum electrolytic capacitor when the carrier frequency is minum electrolytic capacitor when the carrier frequency is
1 kHz: (a) The terminal voltage of the capacitor and the cur- 3 kHz: (a) The terminal voltage of the capacitor and the cur-
rent flowing through the capacitor when carrier frequency rent flowing through the capacitor when carrier frequency
is 1 kHz; (b) Identification result of capacitance C of alu- is 3 kHz; (b) Identification result of capacitance C of alu-
minum electrolytic capacitor when carrier frequency is 1 minum electrolytic capacitor when carrier frequency is 3
kHz; (c) Identification results of equivalent series resistance kHz; (c) Identification results of equivalent series resistance
ESR of aluminum electrolytic capacitor when carrier fre- ESR of aluminum electrolytic capacitor when carrier fre-
quency is 1 kHz. quency is 3 kHz.12 S. Cheng et al.
Table 2. Research results about capacitor state on-line iden- parameter estimation and improves the con-
tification in recent years vergence degree of the identification algorithm
Reference Application Identification accuracy while ensuring fast identification;
d) Combined with the actual measured values,
[4] PWM Inverter |ErrorESR | < 3.5%
the proposed method’s correctness and fea-
[23] Buck Converter |ErrorESR | < 4.2%/7.6%
[10] Motor speed control |ErrorESR | < 2.1%/5.1% sibility are comprehensively verified from the
system accuracy, robustness, and adaptability based
[24] Uninterruptible power |ErrorESR | < 5.0%/10% on the dSPACE platform. Finally, the perfor-
supply
mance of the proposed method is proved by
|ErrorESR | < 5.6%
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
[25] DC/DC Converter
comparing it with the existing methods.
increases significantly, but it does not affect the Supplementary data
stable output of identification results. The state Supplementary data is available at Transportation
identification results of C are shown in Fig. 11(b) Safety and Environment online.
when the carrier frequency rises to 3 kHz. The
estimated values of C are constant at 7 650 μF,
and the absolute value of the error percentage Acknowledgement
is within 1.7% compared with the case of off-
Project fund No: Natural Science Foundation of
line measurement. The state identification results
Hunan Province (2020JJ5757).
of ESR are shown in Fig. 11(c) when the carrier
frequency is 3 kHz. The estimated values keep
around 24 m, and the error percentage is almost
Conflict of interest statement
zero.
It can see that when the measured object is an None declared.
aluminum electrolytic capacitor, the state identi-
fication accuracy is better in most cases, and the
References
effect of state identification is improved compared
with the thin-film capacitor. Therefore, it can be 1. Lee KW, Kim M, Yoon J. Condition monitoring of DC-link
considered that the proposed method has specific electrolytic capacitors in adjustable-speed drives[J]. IEEE
Trans Ind Appl 2008; 44:606–1613.
applicability.
2. Song Y, Wang B. Survey on reliability of power electronic
Table 2 presents the research results about systems[J]. IEEE Trans Power Electron 2013; 28:591–604.
capacitor state identification in recent years. Com- 3. Buiatti GM, Martı́n-Ramos JA, Amaral AM et al. Condi-
pared with the above experimental results, the tion monitoring of metallized polypropylene film capaci-
proposed method’s calculation accuracy is better tors in railway power trains[J]. IEEE Trans Instrum Meas 2009;
58:3796–805.
than some current research results.
4. Pu XS, Nguyen TH, Lee DC. Fault diagnosis of DC-link capac-
itors in three-phase AC/DC PWM converters by online esti-
mation of equivalent series resistance[J]. IEEE Trans Indust
5. Conclusions Electron 2013; 60:4118–27.
In this paper, the state identification methods of 5. Nguyen TH, Lee DC. Deterioration monitoring of DC-link
capacitors in AC machine drives by current injection[J]. IEEE
DC-Link capacitors have been well studied. The
Trans Power Electron 2015; 30:1126–30.
main work is as follows: 6. Givi H, Farjah E, Ghanbari T. Switch fault diagnosis and
capacitor lifetime monitoring technique for DC–DC convert-
a) This paper makes a deep analysis of the failure ers using a single sensor[J]. IET Science, Measurement & Tech-
principle of the thin-film capacitors. It is con- nology 2016; 10:513–27.
7. Farjah E, Givi H, Ghanbari T. Application of an efficient
cluded that the decrease of capacitance value
rogowski coil sensor for switch fault diagnosis and capacitor
is related to the increase of impedance; ESR monitoring in nonisolated single-switch DC–DC con-
b) Based on the equivalent model of capacitance, verters[J]. IEEE Trans Power Electron 2017; 32:1442–56.
the characteristics of the primary identifica- 8. Yao K, Cao C, Yang S. Noninvasive online condition monitor-
tion parameters are analyzed in detail; ing of output capacitor’s ESR and C for a flyback converter[J].
IEEE Trans Instrum Meas 2017; 66:3190–9.
c) An improved RLS method is proposed for on-
9. Abdennadher K, Venet P, Rojat G. A real-time predictive-
line state identification of capacitors. Com- maintenance system of aluminum electrolytic capacitors
pared with the existing methods, the proposed used in uninterrupted power supplies[J]. IEEE Trans Ind Appl
method significantly improves the accuracy of 2010; 46:1644–52.Transportation Safety and Environment, 2021, Vol. 0, No. 0 13
10. Lee KW, Kim M, Yoon J. Condition monitoring of DC-link 18. Buiatti GM, Martı́n-Ramos JA, Amaral AM et al. Condi-
electrolytic capacitors in adjustable-speed drives[J]. IEEE tion monitoring of metallized polypropylene film capaci-
Trans Ind Appl 2008; 44:1606–13. tors in railway power trains[J]. IEEE Trans Instrum Meas 2009;
11. Lee DC, Lee KJ, Lee KJ et al. Online capacitance estimation 58:3796–805.
of DC-link electrolytic capacitors for three-phase AC/DC/AC 19. Fuchang L, Xin D, Jin L et al. On the failure mechanism of
PWM converters using recursive least squares method[J]. metallized polypropylene pulse capacitors[C]. 2000 Annual
IEE Proceedings-Electric Power Applications 2005; 152: Report Conference on Electrical Insulation and Dielectric Phenom-
1503–8. ena, Victoria, BC, Canada, 2000: 592–5.
12. Gasperi ML. Life prediction modeling of bus capacitors in 20. Li Z, Li H, Lin F et al. Lifetime prediction of metallized film
AC variable-frequency drives[J]. IEEE Trans Ind Appl 2005; capacitors based on capacitance loss[J]. IEEE Trans Plasma Sci
41:1430–5. 2013; 41:1313–8.
Downloaded from https://academic.oup.com/tse/advance-article/doi/10.1093/tse/tdab007/6312790 by guest on 13 August 2021
13. Wu Y, Du X. A VEN condition monitoring method of DC-Link 21. Wang H, Blaabjerg F. Reliability of capacitors for DC-link
capacitors for power converters[J]. IEEE Trans Indust Electron applications in power electronic converters—an overview[J].
2019; 66:1296–306. IEEE Trans Ind Appl 2014; 50:3569–78.
14. Makdessi M, Sari A, Venet P. Metallized polymer film capac- 22. Makdessi M, Sari A, Venet P et al. Accelerated ageing of met-
itors ageing law based on capacitance degradation[J]. Micro- allized film capacitors under high ripple currents combined
electron Reliab 2014; 54:1823–7. with a DC voltage[J]. IEEE Trans Power Electron 2015; 30:2435–
15. Makdessi M, Sari A, Venet P. Lifetime estimation of 44.
high-temperature high-voltage polymer film capacitor 23. Yao K, Tang W, Hu W. A Current-sensorless online ESR and
based on capacitance loss[J]. Microelectron Reliab 2015; 55: C identification method for output capacitor of buck con-
2012–6. verter[J]. IEEE Trans Power Electron 2015; 30:6993–7005.
16. Wang H, Nielsen DA, Blaabjerg F. Degradation testing and 24. Abdennadher K. A Real-time predictive-maintenance sys-
failure analysis of DC film capacitors under high humidity tem of aluminum electrolytic capacitors used in uninter-
conditions[J]. Microelectron Reliab 2015; 55:2007–11. rupted power supplies[J]. IEEE Trans Ind Appl 2010; 46:1644–
17. Plaček M, Mach P. Monitoring of metalized film capacitors 52.
degradation with impedance nonlinearity measurement[C]. 25. Givi H. Switch fault diagnosis and capacitor lifetime mon-
IEEE 19th International Symposium for Design and Technology in itoring technique for DC–DC converters using a single sen-
Electronic Packaging, Galati, 2013: 263–6. sor[J]. IET Science, Measurement & Technology 2016; 10:513–27.You can also read
