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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 =+

ℎsin(ℎ+)

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(ℎ+))

+

(1+cos(ℎ+))+

−

(1+cos(

ℎ

+))−

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,= −

forSSO: =2×50Hz,ℎ=2 ×15Hz

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 ±ℎ 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

steady stage of oscillation.

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

can be adopted instead of signal heterodyning for better

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()cos−siñ()sin

≈cos−̃()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

transient and steady-state stages.

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

Load

I

d1

= 1pu

I

d1

= 0.5pu

U

poc1

U

poc2

U

pcc

SCF

Grid

current

PCC

current

Load

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

the load current; (b) grid current which includes the load current.

(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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