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# Instability Mode Recognition of Grid-Tied Voltage Source Converters with Nonstationary Signal Analysis

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## Abstract

With the increasing penetration of voltage-source-converter (VSC) -interfaced distributed generations(DGs) in power systems, oscillation issues have been widelyconcerned whereas the root cause and nature of the oscilla-tion is sometimes not clear in real cases. This paper focuseson the instability mode recognition (IMR) based on a com-plete data-driven approach applied to the oscillation waveswhich can be obtained from the on-site recordings. To thisend, we explore the Hilbert-Huang Transform (HHT) fordiagnosing the root cause of instability, using only raw datasuch as the current and voltage waveforms which are acces-sible by operators. Special attention is paid to distinguishbetween the sub-synchronous oscillation (SSO) and the lossof synchronization (LOS) as they are two primary instabil-ity forms of grid-tied VSC which manifest with very similarwaveforms. The pros and cons of the considered signalanalysis tools in SSO and LOS recognition are discussed andnew lines of investigations are proposed. The analysis andresults presented in this paper could shed light on futuredata-driven analysis, e.g., serving as model-free or hybridmodel database for artificial intelligence-based stabilitydiagnosis and recognition. (PDF) Instability Mode Recognition of Grid-Tied Voltage Source Converters with Nonstationary Signal Analysis. Available from: https://www.researchgate.net/publication/360005412_Instability_Mode_Recognition_of_Grid-Tied_Voltage_Source_Converters_with_Nonstationary_Signal_Analysis [accessed Apr 18 2022].
1
Instability Mode Recognition of Grid-Tied
Voltage Source Converters with
Nonstationary Signal Analysis
Yu Zhang1, Sjur Føyen2, Chen Zhang1, Marta Molinas3, Olav Bjarte Fosso2, Xu Cai1*
1 Key Laboratory of Control of Power Transmission and Conversion, SJTU, Shanghai, China
2 Department of Electric Power Engineering, NTNU, Trondheim, Norway
3 Department of Engineering Cybernetics, NTNU, Trondheim, Norway
E-mail: xucai@sjtu.edu.cn
Abstract- With the increasing penetration of voltage-
source-converter (VSC) -interfaced distributed generations
(DGs) in power systems, oscillation issues have been widely
concerned whereas the root cause and nature of the oscilla-
tion is sometimes not clear in real cases. This paper focuses
on the instability mode recognition (IMR) based on a com-
plete data-driven approach applied to the oscillation waves
which can be obtained from the on-site recordings. To this
end, we explore the Hilbert-Huang Transform (HHT) for
diagnosing the root cause of instability, using only raw data
such as the current and voltage waveforms which are acces-
sible by operators. Special attention is paid to distinguish
between the sub-synchronous oscillation (SSO) and the loss
of synchronization (LOS) as they are two primary instabil-
ity forms of grid-tied VSC which manifest with very similar
waveforms. The pros and cons of the considered signal
analysis tools in SSO and LOS recognition are discussed and
new lines of investigations are proposed. The analysis and
results presented in this paper could shed light on future
data-driven analysis, e.g., serving as model-free or hybrid
model database for artificial intelligence-based stability
diagnosis and recognition.
Index terms: signal analysis, converter, oscillation, stability,
mode recognition, synchronization, HHT, EMD.
I. INTRODUCTION
Nowadays, while the power grid is taking the benefit
of voltage source converters (VSCs) to enable the
integration of various distributed generations (DGs), it
also suffers from harmonic oscillation issues caused by
power electronic devices, most of which are due to the
control interaction against the grid. In this context, two
kinds of instability issues of grid-tied VSCs have been
frequently reported in practical systems, i.e., the sub-
synchronous oscillation (SSO) and the loss of
synchronization (LOS) [1]. Both the SSO and LOS are
common oscillations in the 0~100Hz frequency range and
their oscillation waveforms appear very similar at visual
inspection and FFT spectral analysis.
A. Motivation
In the past years, extensive works have been conduct-
ed to resolve the oscillation issues of the grid-tied VSCs,
especially those relating to stability. Although analytical
This work was supported by the National Natural Science Foundation of
China, under Grant 5183700.
approaches provide the necessary understanding and
insight into these new forms of stability issues, they are
merely applicable to simple systems. For practical and
complex power systems, modeling the entire system in
detail is often restricted by intellectual property issues
when different vendors are involved. Besides, prevailing
methods based on linear analysis are not sufficient and
often fail to reveal the real essence of harmonics observed
in Fourier spectra, because in such models, no physical
source is represented to which harmonics like those com-
ing from PWM, can be attributed. Therefore, the current
model-based methods have limited abilities to distinguish
among different modes of instability with similar mani-
festations. For example, if we want to know the reason
for the emergence of oscillation near the DG plants, one
usual way is to model the whole system and try to repro-
duce the phenomenon. However, this approach not only
implies a huge modelling effort but may also fail to evoke
the same instability scenario.
To complement the modelling approach and provide
insight from the real system, data-driven approaches can
be opted in such cases, and the main advantage is the
straightforward use of the on-site signals which carry
detail information of the oscillation. To this end, a pre-
liminary step is to identify the instability kind, referred to
as instability mode recognition (IMR). The restriction of
IMR analysis for power system operators is that, in most
cases, only the interfacing electrical data (e.g., voltage,
current and power) is available for analysis. The lack of
internal data of VSC control poses a great challenge to
the IMR, which means the IMR should be based on lim-
ited accessible signals, such as voltage and currents.
B. Nonstationary Signal Analysis
Frequency is an elemental descriptor of an oscillation,
and one might expect different instability modes to show
distinct frequency characteristics, yet the ordinary Fourier
spectra may be not enough in this context. To be specific,
frequency modulation (FM) effect has been reported in
both control-involved waveform distortion [2, 3] and
harmonic oscillation [4], indicating that the instantaneous
frequency (IF) [5, 6] of VSC is constantly varying, rather
than discrete frequency components, as is commonly
recognized. Besides, the site signals can be rather com-
plex that both the amplitude and the frequency are vary-
2
ing with time. However, the FFT lacks the ability to ana-
lyze such nonstationary signals, and therefore might not
be suitable for IMR.
In this regard, nonstationary signal processing meth-
ods such as time-frequency analysis (TFA) emerge as
promising candidates to explore. There are basically two
mainstreams of TFA, according to the definitions of IF.
The first is based on the orthogonality of the signal with
certain set of bases, e.g., short-time Fourier transform
(STFT), Gabor transform, wavelet transforms, which also
have the same and intrinsic problem of the uncertainty
principle as the FT, so that the frequency resolution will
lessen if a higher time resolution is obtained by a thinner
time window [7]. The second frequency definition is
based on the phase time derivative of the complex signal
(Section III.A) which is inherently capable to indicate the
varying frequency and amplitude of nonstationary signals.
However, the definition itself is derived from mono-
component signals, and is not suitable for signal contain-
ing more than one component.
One prominent solution is the Hilbert-Huang trans-
form (HHT) [8]. The key point is to use the empirical
mode decomposition (EMD) technique to sift intrinsic
mode functions (IMFs) from the signal, which generally
represent components with distinct physical meanings.
After the decomposition process, Hilbert transform (HT)
is applied on each IMF to process the complex signal,
from which the IF and instantaneous amplitude can be
calculated. Nevertheless, the strength of EMD is restrict-
ed when two signals of close frequency and amplitude are
mixed together, resulting in the well-known mode mixing
issue [9], which has been thoroughly addressed but was
not yet solved. Further effort including the ensemble
EMD (EEMD) [10], masking signal [11, 12] and hetero-
dyning [13] were reported to mitigate the mode mixing
issue, yet there are still some restrictions when using
these extended techniques. Moreover, a new method
called Fourier decomposition method (FDM) is proposed
in [7], which is a promising way to decompose the nar-
row-band signals and can be a good alternative to EMD.
In addition, to improve the computing stability and per-
formance of HT, direct quadrature (DQ) and normalized
Hilbert transform (NHT) are proposed in [14] to give a
better estimation of the instantaneous frequency.
C. Aim of This Paper
The IMR is urgently called for monitoring and fault
analysis of the high-penetrated DG integration, and HHT
has shown its great potential to extract the IF from the
field signals. To the best of authors’ knowledge, IMR has
been rarely reported in power system utilities, yet there
has not been any attempt on utilizing data-driven-based
approaches for this purpose. This paper aims to make an
initial exploration that can further indicate its potential
usefulness. To motivate a measurement-based analysis of
the instability phenomena, we firstly derive the expres-
sion of the oscillation signals for SSO and LOS, and
present a simple FFT-based spectra. Then, HHT-based
method is applied to the same signals, and naturally pro-
vides an entirely different inherently nonlinear and non-
stationary perspective. We follow up with discussion on
the obstacles which must be overcome to pave way for
real time IMR.
U
g
Z
g
L
f
U
s
I
s
VSC
P,Q
POC
g
1
~g
6
PWM
Modulation
U
cdq
Current
Control I
sdq, ref
abc
dq
abc
dq
abc
dq
θθ
I
s
U
s
U
sdq
I
sdq
U
sdq
I
sdq
PLL
U
sq
θθω
pll
Fig. 1 Schematic diagram of a grid-tied VSC.
(a) Voltage and frequency waveform profiles for the SSO case
(b) Voltage and frequency waveform profiles for the LOS case
Fig. 2 POC Voltage and PLL frequency profiles of the SSO and LOS.
Beat wave effect can be clearly seen for both cases. is three-phase
POC voltage,  is PLL frequency,  and  are  axis voltage
and current. Each of the signals are scaled to per unit values.
II. MODELLING OF OSCILLATION WAVEFORMS
Although the mechanism of the SSO and LOS has
been well understood, currently the analytical expressions
of the instability signals are not yet derived. Therefore,
we try to recreate the instability signals first, according to
the mechanisms described below.
A. Mechanism of The SSO and LOS
The schematic diagram of the grid-tied VSC is shown
in Fig. 1. SSO is basically caused by insufficient damping
due to strong control interaction against the grid, espe-
cially for low SCR systems, which, therefore, can be
triggered by both loss of transmission line or mild change
of system condition. It is a small-signal instability issue
0.8 11 .2 1.4 1.6 1 .8
-2
0
2
Us
0.8 11 .2 1.4 1.6 1 .8
40
50
60
pll
0.8 11 .2 1.4 1.6 1 .8
-1
0
1
2
Usdq
0.8 11 .2 1.4 1 .6 1.8 t ( s)
-1
0
1
2
Isdq
Ch ange of S CR
t (s)
t (s)
t (s)
0.8 11 .2 1.4 1 .6 1.8
-2
0
2
U
s
0.8 11 .2 1.4 1 .6 1.8
50
60
pll
0.8 11 .2 1.4 1 .6 1.8
-1
0
1
2
U
sdq
0.8 11 .2 1.4 1 .6 1.8
-1
0
1
2
I
sdq
Volt age di p
Frequency saturation
t (s)
t (s)
t (s)
t (s)
3
that occurs in a slowly varying steady-state operating
point. When SSO happens, any involving states would
oscillate around their equilibrium point, including  axis
voltage , current  and the frequency of PLL ,
as is shown in Fig. 2(a). Therefore, the output voltage is
both frequency and amplitude modulated (AM-FM) due
to the varying PLL frequency, which agrees with the
findings in [4]. Beat wave effect can be observed in the
voltage signal at point of connection (POC).
On the other hand, LOS is definitely one kind of
large-signal instability caused by severe voltage dip, e.g.,
short circuit. The basic reason for the LOS is that the PLL
frequency diverges upwards during the transient and fail
to get back even after the restoring of grid voltage [15],
as is shown in Fig. 2(b). Once the LOS occurs, the refer-
ence frame of VSC control will never be aligned with the
voltage vector at POC, instead, it rotates with a frequency
slip and begins to swing. However, the current control
still keeps stable and track its reference well, because the
instability only involves the PLL. If the converter does
not suffer overmodulation, the current could be near
perfectly controlled on the  axis, which is well illus-
trated in Fig. 2(b). Although there is no AM-FM modula-
tion with LOS signal, the voltage at POC contains at least
two components at different frequencies, and the beat
waves effect is also observed in the POC voltage signals.
Beat waves are also evident in the  currents.
B. Modelling of The Oscillation Signals
According to the waveforms in Fig. 2(a), assume all
signals in  frame comprise a DC component and a
sinusoidal component for the SSO case. Then, the refer-
ence voltage is represented by:
() = +cos(+)
() = +sin(+) (1
)
and the PLL frequency is modelled by:
() =[1+cos(+)] (2
)
where ,, denote the oscillation amplitude, the
harmonic frequency on the  axis, , the phase
angle,  and  the DC component of the voltage, and
the synchronous frequency. The phasor form of (8) is:
()()=+(+)+−(+)
3
where =+
and =−
. Next, the PLL angle is
added to (3) to get the voltage phasor on  axis:
()()=
()()()
=()++()++
+(()−−)
4
where:
=
+
, =arctan( 
⁄ )
() =()d =+
sin(+)
Equation (4) indicates that the PCC voltage consists of
three frequency-modulated signals, as is shown in Table I.
The center frequencies of these FM signals are ,(+
),(), that is one center fundamental frequency
00.05 0 .1 0.15 0.2 0 .25 0.3 0. 35 0.4 0.45
-2
0
2
(b) Plot of PCC Voltage Us for LOS
00.05 0 .1 0.15 0.2 0 .25 0.3 0. 35 0.4 0.45 t ( s)
-2
0
2
(a) Plot of PCC Voltage Us for SSO
t (s)
Fig. 3 Recreated artificial signals of instability of the PCC voltage
based on assumed modelling in equations (4) and(5).
TABLE I
COMPONENTS IN POC VOLTAGE WHEN SSO OCCURS
Amplitude
Instantaneous Frequency
(1+cos(+))
+
(1+cos(+))+
−
(1+cos(
+))
and two harmonic frequencies in each side. Besides, the
mirror frequency effect, firstly reported in [16], is also
reflected in this modelling while the amplitude of mirror
frequency component vanishes when  axes are sym-
metric, i.e.,
= 
or
= −
, which also agrees with
the findings in [16]. Besides, it should be noted that the
frequency of each component of the VSC is oscillating,
which is beyond the describing capability of the ordinary
linear modelling, for it is only applicable when the fre-
quency oscillation is minor, i.e., 0. In short, the
waveform of PCC voltage during the SSO includes three
AM-FM components of which the IFs are varying around
different center frequencies.
For the LOS, assume that the current could always be
controlled and is equal to its reference. Then, the PCC
voltage is formulated by:
()()=+(()+)
5
where
()()= denotes the grid voltage vec-
tor, () =()d is the PLL frequency, and is
the summation of current phase and impedance angle.
This indicates, theoretically, that the LOS waveform only
contains the background grid voltage and one single FM
signal with IF of ().
According to the voltage expression in (4) and (5), the
PCC voltage could reflect the frequency information of
the oscillation in VSC, which is crucial to determine
which kind of instability is dominant To verify the signal
modeling, we use the following values to recreate the
signals, and the transient period is temporarily ignored for
the sake of simplicity:
 =0.5, =0.0,=1.0,= 0.5,
=1.2,=0.8,=0.15,,= 0,=
for LOS: () =2×60Hz
4
Fig. 4 FFT spectrum of PCC voltage with different time windows. Top
and bottom subplots are FFT spectra with time windows of 2s and 0.5s.
The recreated signals are plotted in Fig. 3. These arti-
ficial signals resemble the voltage signals in Fig. 2, and
the beat wave effect is observed for both SSO and LOS.
We remark that (4)~(5) is only one possible modelling.
C. Fourier Analysis on Steady Oscillations
The frequency-domain spectrum with the steady state
is investigated via Fast Fourier Transformation (FFT).
The FFT spectra are plotted in Fig. 4.
Firstly, we applied FFT on both SSO and LOS at time
period of two seconds, and plot the result on the top fig-
ures, where the frequency resolution is good. Two main
sidebands can be observed in SSO, mostly due to the AM
effect (beat wave effect) of the signal, and even more tiny
sidebands at ± are distinguishable, which is actu-
ally the spectra of FM effect. While for the LOS, there
are only two main components in the signal, which is the
50Hz background grid voltage and VSC output voltage at
the saturated PLL frequency of 60Hz.
Next, if we reduce the time window to 0.5s, as is
shown in the bottom subfigures of Fig. 4., then the fre-
quency resolution is reduced so that the Fourier spectra is
blurred, due to the well-known uncertainty principle. For
FFT with sampling frequency and samples, the
frequency resolution and required time window are:
∆ =⁄ ⇒ = 
= 1 ∆
(6
)
It implies that if we want to get a better resolution of the
frequency, the time window should be extended to sever-
al seconds. Therefore, Fourier analysis is applicable at the
III. INSTABILITY MODE RECOGNITION ON TRANSIENT
In real systems, the signals can be nonstationary, espe-
cially for the LOS, which is beyond the capability of FFT
analysis. Any other Fourier or wavelet based short-time
transform also need enough steady periods for the good
performance of TFA. In the following sections, we begin
to explore the capabilities of HHT, which has the inherent
ability to process nonstationary signals, to give new indi-
cators and criterions for the IMR.
A. The Hilbert-Huang Transform
Suppose ()= ()cos() be a mono-component
signal with varying amplitude and frequency, where ()
is the instantaneous amplitude (IA) and () be the phase
angle. To obtain the phase angle, the quadrature signal is
required, i.e., ()= ()sin(), which can be obtained
from the Hilbert transform (HT):
() = 1
()
−  (7
)
Then, complex signal ()= ()+() =()() is
built from the signal () and its quadrature (), where
the phase angle can be calculated by:
()=arctan(() () ), (8
)
Then, the IF is defined by:
()=d()
d . (9
)
This definition is elegant and meaningful. However,
for the signals from the real world, it can be difficult to
directly apply due to the following two reasons. First,
most of the signals are multi-component and need separa-
tion before calculating the IF with (9). Second, HT has
many problems in finite signal processing that sometimes
yields a poor estimation of the quadrature, which would
cause the incorrect computation of the IF and IA.
To solve the first issue, Huang put forward the EMD
to sift IMFs from the signal [8]:
1. Let =1 and () be the initial residual ();
2. Find the extrema of ();
3. Interpolate the maxima (minima) to get the upper
(lower) envelope () and ();
4. Compute the mean of the envelop and assign it as
the new residual: +() =(()+())/2;
5. Subtract the -th IMF: ()=()+();
6. Check if the stop criterion is meet [8]. If not, then
let =+1 and loop back to procedure No.2.
Finally, the origin signal is decomposed to a series of
IMFs [(),,−()] and one last residual ():
()=() + ()
−
= (10
)
Each IMF is regarded as a mono-component signal,
which is intuitively true. However, mode mixing issue is
found in EMD when IFs of two components are close to
each other. It is theoretically proved in [9] that, for the
following signal:
()=cos(2)+cos(2+),
(
11
)
It is only possible to separate each component easily if
 <1 and  < 0.67, where =
and  = 
.
Otherwise, the mode mixing will occur and these two
components are unable to be separated by ordinary EMD.
For example, if we directly use EMD to decompose the
SSO signal, the first IMF will be almost the same as the
raw signal, as is shown in Fig. 5, because the IF of the
components in SSO (see Table I) are quite close with
each other so that to cause the mode mixing. This indi-
cates that the first IMF comprises of more than one com-
ponent and thus the IF shown as Hilbert spectra is mean-
ingless, as is plotted in Fig. 6, because the definition is
SSO (Twin = 2.0 sec)
020 40 60 80 100
0
0.5
1
SSO (Twin = 0.5 sec)
020 40 60 80 100
0
0.5
1
LOS (Twin = 2.0 sec)
020 40 60 80 100
0
0.5
1
LOS (Twin = 0.5 sec)
020 40 60 80 100
0
0.5
1
5
only applicable for mono-component signals. The same
thing will happen for the LOS signal as well because the
IF of PLL is close to that of the background grid voltage.
B. Signal Heterodyning for Decomposition
To solve the mode mixing issue, the frequency ratio
between each IMF should be relatively large. To this end,
frequency heterodyning is one possibility to alleviate the
mode mixing issue, because the spectra of a signal can be
shifted by multiplying a heterodyning signal [13]. Given
a two-component real signal:
()=()cos2+()cos2
(
12
)
Its spectra can be shifted by signal heterodyning:
() =()2cos2
=()cos2∆+()cos2∆
+()cos(2(+))
+()cos(2(+))
(
13
)
where ∆=  and ∆=. Let  be
slightly lower (or greater) than the smaller (larger) one of
{,}, then it will be possible to find such  to meet
the requirement of decomposition. Two components of
higher frequency are also produced, which is obviously
out of the octave of the first two. Therefore, the IMFs for
these high-frequency components can be filtered or de-
composed easily and should be discarded.
For balanced three-phase systems, the space vector of
voltage and current can be obtained by Clarke transform
on three-phase signals. Therefore, complex demodulation
performance, since it can shift the frequency without
producing high frequency components. We give an ex-
ample on how the complex demodulation works. Given a
two-component complex signal:
() =()j2π+()j2π (14
)
Complex rotation j2π is adopted for heterodyning:
() =Re{()j2π}
=Re{()j2π+()j2π}
=()cos2+()cos2∆
(
15
)
The decomposition performance relates much with the
heterodyning frequency. For the SSO, because there are
three oscillating components at the center frequency of
,(+),(), and it can be hard to choose a
single heterodyning frequency to separate them all. One
possible solution is to set  =50Hz, so that the center
frequencies of each will be shifted to 0Hz and ±, re-
spectively. According to the expressions in Table I, the
last two components will mix with each other as one
single component with mean frequency of :
+
cos+̃()+−
cos−+̃()
=cos̃()cossiñ()sin
cos̃()sin
=
+
̃()cos+tan−̃() 
⁄ 
(
16
)
Fig. 5 EMD for the artificial SSO signal  where mode mixing occurs.
Fig. 6 Hilbert spectra for the first IMF (IMF1 in Fig. 5) of SSO through
the ordinary EMD. The colormap denotes the IA of the complex signal.
Fig. 7 Hilbert spectra for the IMF of instability mode of SSO (left) and
LOS (right) with different heterodyning frequencies.
where ̃() denotes the oscillating term in Table I. If <
, then the oscillation of the IF will be lessened, which
will be shown later that can pose a threat to the IMR if
the indicator becomes less distinct. Therefore, some other
frequencies should be tried so as to find the best one.
For illustration, we decomposed the artificial signals
by three heterodyning signals at 50Hz,45Hz and 42.5Hz.
The IFs representing the instability mode of the SSO are
plotted in Fig. 7(a)(c)(e). It can be seen that the mean of
IF is 65Hz, and the vibration frequency of the IF is 15Hz,
which coincides with the analysis above. For the SSO,
the IF variation of 65Hz-component with  =50Hz is
lower than that of the others, which verified the analysis
above. In comparison, the IFs of the instability mode for
LOS case are plotted in Fig. 7(b)(d)(f). A 60-Hz compo-
nent is observed in the spectra and there is no distinct
oscillation on the IF as is found in the SSO case. When
 =42.5Hz, the best decomposition performance for
-2
0
2
Signal
-2
0
2
IMF 1
-0.1
0
0.1
IMF 2
-0.02
0
0.02
IMF 3
500 1000 1500 2000 2500 3000 3500 4000
0
0.01
0.02
0.03
Residual
(sam pl es)
0
6
SSO is witnessed, as the (+) component is isolated
from the others; While for the LOS, this heterodyning
frequency gives the worst result for the frequency shift is
not enough for EMD to work well. It shows that the IF
can be a good indicator to distinguish the LOS from SSO.
C. The Proposed Method
1) Algorithm for extracting the instability signal
Now an overview of the whole procedure to separate
the instability oscillation signal from either SSO or LOS
is described below. Some additional measures are taken
to improve the decomposition of the results:
1. Apply Clarke Transform to the three-phase signal,
or skip this if a single-phase signal is used;
2. Take signal heterodyning or complex demodula-
tion to shift the spectra (try on different  for the
good of EMD performance);
3. Pass the signal through a lowpass filter;
4. Decompose with EMD to obtain IMFs;
5. Calculate the IF and IA for each IMF by HT, DQ,
NHT or other else methods;
6. Add the heterodyning frequency to each IF, and
plot the Hilbert spectrum.
The lowpass filter is used to smooth the transients and
remove high frequency dynamics and noises, which is
crucial to get good results. This step should be placed
after the frequency shifting, which could facilitate the use
of filter with lower cut-off frequency. Besides, this pro-
cess is regarded as one standard preprocess of EMD for
the purpose of anti-aliasing, and discrete events so that
we can process EMD with a lower sampling frequency.
2) Criteria on instability mode recognition
From the procedure above, the first criterion to judge
whether an oscillation within 0~100Hz is SSO or LOS is
by observing the IF oscillation:
Criterion I: In steady oscillating period, if regular os-
cillation is observed in the target IF, of which the oscil-
lating frequency is the same as the frequency difference
between the mean of the target IF and the fundamentals,
then the instability mode should be the SSO; otherwise, it
should be the LOS.
Naturally, real measurement devices contain transients
as well. The transient also conveys information of the
type of instability, due to the frequency evolution process
with different kind of instability. As is shown in Fig. 2,
the frequency of PLL is not constant during the voltage
dip, but keeps climbing until reaching the limitation.
Therefore, the transient period will help with the IMR of
the VSC, which gives rise to the second criterion:
Criterion II: If a recognizable rise is observed in the
target IF in the transient process, then the instability
mode should be the LOS; otherwise, it should be SSO.
As HHT is intended precisely for extraction of physi-
cally relevant information of multicomponent, nonlinear
and nonstationary waveforms, there is no need to restrict
analysis to the steady state, which means that the pro-
posed method to extract the target IF is also applicable to
the transients. We shall show in the following section
how the HHT-based IMR algorithm enables joint use of
IV. SIMULATION TESTS
A. Verification on Simulation Signals
The first case will demonstrate the procedure for both
the SSO and LOS. The circuit topology is shown in Fig. 1,
and the simulation settings are the same as well to trigger
the SSO and LOS, of which the waveforms are shown in
Fig. 2. Only the signals of POC can be used for IMR, e.g.,
voltage and current. A heterodyning frequency of 45Hz is
adopted for the LOS and 43Hz for the SSO. Three-phase
POC voltage signals are processed in this case, which is:
(1) passed through a 3rd-order Butterworth lowpass filter,
(2) rotated (heterodyned) with a 45Hz/43 Hz complex
exponential, (3) decomposed with EMD. Then, through
the direct quadrature [14], the instantaneous frequency is
yielded for each IMF. The heterodyning frequency is
added to the IF. Finally, the Hilbert spectrum is calculat-
ed from the IF and IA, then filtered with a gaussian filter
for a smooth appearance.
The resulting spectra are shown in Fig. 8, where the
analysis is based on windows from = 0.3s to =2.5s.
The long duration of the signal is needed to ensure that
the heterodyned signal has enough periods for EMD to
work well. But this is not an insurmountable restriction,
for example, joint use of masking signals and heterodyn-
ing has potential to reduce the required length of the time
window. As can be clearly seen from the first figure, the
VSC suffered a period of low voltage before the fault is
cleared, during which the IF of one IMF went through an
obvious rising, which indicates that the oscillation mode
is LOS. While for the other one, a distinct oscillating
frequency appears suddenly above the fundamental fre-
quency, hence the oscillation mode is SSO.
(a) (b)
Fig. 8 Hilbert spectra of the voltage measurements after heterodyning
and EMD. (a) LOS. Dashed black line is the PLL frequency. (b) SSO.
For comparison, the dashed black line is the PLL frequency for the LOS,
and the PLL frequency plus the oscillating frequency for the SSO.
B. Measurement quality
At first sight it might be unclear how to select meas-
urements for IMR. Which is the better choice of voltage
and current to be a good indicator? Where should the
measurements be located? To answer these questions, we
discuss a few challenges with the decomposition and
some traits of the signals. The current and voltage meas-
urements are decomposed by the aforementioned process
and the results are plotted in Fig. 9 and Fig. 10, we will
see that the current signal is more distinct as an instability
indicator for the LOS case, and decomposition of the
7
current is not strictly necessary. This is because the con-
verter regulates the current to follow the frequency of the
PLL, while it (almost) suppresses the fundamental. The
same argument does not hold true for the PCC voltage
measurements, as the current at the fundamental is sup-
pressed, the grid PCC voltage must equal the grid voltage.
In the SSO case for a single VSC, there is no such clear
distinction between the current and voltage measurements,
for they will both have a nonnegligible fundamental and
hence must be decomposed. The LOS presents the great-
est challenge for IMR, due to the short duration of the
fault. The amplitude of the LOS and fundamental should
be slowly varying or constant in the entire window, lest
the frequency information be obscured.
(a) (b) (c) (d)
Fig. 9 Hilbert spectra for current and voltage for the LOS case, with or
without decomposition. (a) current without EMD, (b) current with EMD,
(c) voltage without EMD, (d) voltage with EMD.
(a) (b) (c) (d)
Fig. 10 Hilbert spectra for current and voltage for the SSO case, with or
without decomposition. (a) current without EMD, (b) current with EMD,
(c) voltage without EMD, (d) voltage with EMD.
The PCC current meets this criterion (no need for de-
composition) for the single converter case, but we present
a multi-converter system to illustrate that it is not always
so. The performance of the proposed decomposition is
examined in multi-converter network, as is illustrated in
Fig. 11, where two converter stations are connected in
parallel to a bus with a local load. The SC fault is applied
on the common bus for 200ms to trigger the LOS.
The spectra for the LOS case are shown in Fig. 12. It
seems as if the target IMF of the PCC voltage is hardly
visible, as its amplitude is very low compared to the fun-
damental. More importantly, the LOS ramp is not visible.
However, if we decompose the PCC current, then we
could obtain the spectra in Fig. 13(a), which looks much
clearer than the voltage. It seems that the current is a
better indicator than the voltage, for it wouldn’t attenuate
as the distance increases, but the decomposition is needed
because the PCC current contains both the LOS signal
from the faulted VSC and the normal signal at 50Hz.
Moreover, the LOS IMF can be weakened by the load
current, as is shown in Fig. 13(b), which indicates that
measuring the current that goes to the grid is not very
robust. Therefore, the measurement position is also very
crucial to the IMR and need further exploration.
L
g1
= 0.3pu
L
g2
= 0.3pu
L
g3
= 0.1pu
I
d1
= 1pu
I
d1
= 0.5pu
U
poc1
U
poc2
U
pcc
SCF
Grid
current
PCC
current
current
U
g
PCC
Fig. 11 Test case for multi-converter network scenario.
Fig. 12 Hilbert spectrum of the PCC voltage for multi-converter system.
(a) (b)
Fig. 13 Hilbert spectrum of the current (a) PCC current which excludes
(a) (b)
Fig. 14 Hilbert spectra for the decomposed current when overmodula-
tion happens in (a) LOS and (b) SSO.
C. Overmodulation Effects
Both LOS and SSO are likely to inflict overmodulation
on the converter. Though normally interpreted in terms of
the harmonic spectrum, we apply the same procedure to
see the instantaneous properties of POC current during
overmodulation, the results are shown in Fig. 14.
The same analysis on the POC voltages is omitted,
though it yields similar spectra. The LOS ramp is still
captured very well, as overmodulation takes effect only
after the fault is cleared. However, the LOS IMF exhibits
larger frequency oscillations than the SSO in steady state,
8
which is caused by more severe overmodulation of LOS
than of SSO. Therefore, the performance of the proposed
method highlights the importance of criterion II. Further
investigations are needed to determine if the steady state
can be included in IMR, or if overmodulated SSO and
LOS IMFs are practically indistinguishable.
V. CONCLUSION
This paper focuses on the IMR issue of the VSCs via
interfacing measurement signals. We concluded that two
ordinary kinds of instability within 0~100Hz, namely the
SSO and LOS, can be identified and be distinguishable
from each other by complete data-driven approach. We
firstly recreate the PCC voltage signal for the SSO and
the LOS, in order to obtain the key features of the signals
from their mathematical expressions. FFT is firstly ap-
plied to get the frequency spectrum for the initial cogni-
tion of the instability signals. It is found that the frequen-
cy component of the converter output voltage and the
background grid voltage are so close that the EMD de-
pendent mode mixing issue can possibly happen, which is
then verified by applying EMD on the raw signal of PCC
voltage. Complex demodulation (signal heterodyning) is
adopted to shift the background 50Hz signal to a very low
frequency component, so that the instability IMF can be
isolated and analyzed. In this way, the residual signal
only contains the converter output that reflects the fre-
quency variation in the converter. Two criteria for IMR
of SSO and LOS are put forward, where we remark on
the importance of transient stage of the signals. Besides,
we also discuss on the need for decomposition for voltage
and current signals, improve the performance on multi
converter system, and make suggestion on the measure-
ment location. Finally, we observed the current signal
could be distorted due to overmodulation and thus the
corresponding IMF profile will be affected. However,
since the signal hasn’t been rebuilt to reflect the over-
modulation effect, this issue is not well resolved and
hence need further investigation.
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