Abstract— The synchronization instability in the presence of a
fault is a main issue for the dynamic behavior and control of
grid-feeding converters. In the literature, the synchronization
stability assessment is carried out considering the dynamics of
Phase-Locked Loops (PLL) but the transients of converter
currents are neglected. The letter shows that such a simplification
leads to inaccuracies and, thus, the current transients cannot be
neglected. The letter proposes a model that captures the effect of
such current transients on the converter synchronization. This
model allows assessing the transient behavior and, hence, the
stability, of power electronics converters with high accuracy,
comparable, in fact, to EMT models. The fidelity of the proposed
model is duly discussed in the case study.
Index Terms—Synchronization Stability, Grid-feeding
Converter, Phase-Locked Loop, Current Transients.
HE majority of renewable sources are interfaced through
‘grid-feeding/following’ converters, which use a Phase-
Locked Loop (PLL) for the synchronization and aims to inject
the assigned power or current into the grid . However,
during a contingency, grid-feeding converters may lose
synchronization with the grid and lead to power oscillations
due to the PLL failure . Different PLL implementations to
counteract voltage sags have been tested in . However, the
full understanding of the synchronization stability of the grid-
feeding converter is still an open question. Reference 
provides an overview of the previous assessment of
synchronization stability. Reference  proposes a steady-
state analysis, which studies whether there is a stable
operating point after the fault. Even though a stable operating
point exists, the converter may still not approach this point
during the fault and may lose synchronization. Taking into
account PLL dynamics, reference  proposes a Quasi-Static
Large-Signal analysis,  proposes an Equal Area Criterion
and  proposes a phase portrait approach. According to the
comparison amongst these methods , the Quasi-Static
Large-Signal is more precise than other methods. The purpose
of these models is to provide a mathematically model which is
computationally light compared to EMT analysis and which
provides insight into the mechanism giving rise to instability.
Since the dynamics of the current controller of the grid-
This work funded by the European Commission, under the project
EdgreFLEx, grant no. 883710 and by the Science Foundation Ireland (SFI)
under Grant Number SFI/15/SPP/E3125 and SFI/15/IA/3074.
Junru Chen is with the Electrical Engineering Department, Xinjiang
University, Urumqi, China (email: firstname.lastname@example.org)
feeding converter is much faster than the PLL mechanism, all
methods outlined above neglect the current controller
transients and make an assumption that the converter works on
the constant current mode. Consequently, the model of the
grid-feeding converter synchronization mechanism can be
simplified to 2nd-order . It is certainly true that, in some
cases, the inductance of the filter is large and the time constant
of the current controller is small. However, if these conditions
are not satisfied, the transients of the current controller are
significant and cannot be neglected. The grid-feeding
converter although using current control, is still based on the
voltage source converter, for which at the instant of the fault,
its terminal voltage cannot step change but remains fixed until
the next modulation of the PWM. In this circumstance,
existing synchronization stability assessment methods are not
accurate. Based on the Quasi-Static Large-Signal method, this
letter at first proposes a model to accurately reflect the
converter synchronization transients and then using this
model, can assess the converter synchronization stability. In
particular, it highlights the fact that the current transients can
give rise to instability depending on current controller and
II. GRID-FEEDING CONVERTER
The grid-feeding converter aims to control the output
current to track its reference
by actually varying
the terminal voltage . In order to track the reference
current, the converter applies the current controller as follows:
where are the PI controller parameters, is the
converter frequency, and is the filter inductance.
Figure 1 shows the control structure of the grid-feeding
converter, where a synchronous reference frame PLL (SRF-
PLL), which is detailed in Fig. 2, is used to detect the phase at
the point of the common coupling (PCC) for grid
synchronization, where is the transmission line impedance
of the converter connecting to the grid. When the phase is
locked (), the converter active and reactive current is
Junru Chen, IEEE Member, Muyang Liu, IEEE Member, Terence O’Donnell, IEEE Senior Member,
Federico Milano, IEEE Fellow
Impact of Current Transients on the Synchronization
Stability Assessment of Grid-Feeding Converters
Fig. 1. Grid-Feeding Converter system structure
Fig. 2. SRF-PLL structure
III. CONVERTER SYNCHRONIZATION STABILITY ASSESSMENT
A stable synchronization of the grid-feeding converter
( ) relies on the convergence of the PLL. Typically,
the assessment of the PLL stability only needs to consider the
PCC fault voltage. However, the assessment of
synchronization stability is different, in that it needs also to
consider the state of the grid and the transmission line
impedance. The line impedance has a negative effect on the
synchronization stability, which will be discussed later.
Referring to Fig. 1, the relationship between the PCC
voltage and grid voltage is as follows:
Assuming that the phase angle of the PCC bus voltage is
the reference angle, the phase of the grid voltage is .
Then, using a dq-axis reference frame, (3) can be rewritten as
A successful synchronization ensures after a
contingency in the loop of Fig. 2. Note that due to the
harmonics, cannot be exactly zero in practice. However,
this letter focuses on the fundamental frequency
synchronization, and we thus assume that, thanks to the action
of the PLL, is null in steady state. The synchronization
transients (3) can be divided into a grid-synchronization loop
and a self-synchronization loop, where the grid-
synchronization loop is the negative-feedback used to cancel
positive-feedback effects from the self-synchronization loop
so that overall is regulated to zero. During a transient of the
grid state change, e.g. a voltage sag, changes resulting in a
transient . Thus for example, if is positive,
will continuously increase. In a “healthy” PLL, the increase in
can cancel the effect from the positive . However,
if the phase is over 90 ºwhile has not been
canceled, then a further increase in leads to a
reduction, which can never cancel the effect
from thus resulting in the synchronization instability.
In the remainder of this section, we first outline the Quasi-
Static Large-Signal analysis discussed in  as it serves as
starting point for the proposed converter stability assessment,
which is given in Section II.B.
A. Quasi-Static Large-Signal analysis
The assessment of the synchronization stability is to
determine whether the phase converges during the fault.
The present assessment methods, Quasi-Static Large-Signal
(QSLS) analysis, Equal Area Criterion and phase portrait
assume that the current remains fixed, i.e.,
during the transient of the synchronization. This is because the
time constant of the current controller is much faster than that
of the PLL. Therefore, only and are variables in (4),
which leads to:
According to (5), the large-signal model of the PLL,
considering converter connection to the grid through a
transmission line, is given in Fig. 3, where the grid-
synchronization is indicated by , and the self-
synchronization is indicated by
. Since the
converter output angle is defined to be zero, then the phase
error is .
Fig. 3. Quasi-static large-signal model of the PLL 
In Fig. 3, the self-synchronization loop only contains the
transient movement. However, the grid-feeding
converter is based on the voltage source converter (VSC), for
which the terminal voltage is changed only by the
current controller (1,2). At the instant of the fault, the PWM
of the converter does not change and the converter terminal
voltage remains fixed. As a consequence, the current at this
instant step increases.
Compared with the assumption of a fixed current in the
previous methods, this transient current leads to a larger
positive feedback introduced by the self-synchronization loop
, which results in a larger during the transient. In
other words, the transient current has the potential to lead to
synchronization instability, and this aspect cannot be assessed
by previous analysis methods, e.g. Fig. 3.
B. Proposed synchronization stability assessment
In this section, we take in account the current transients and
propose an improved method for synchronization stability
assessment. Defining as the transient current change,
and substituting these into
The self-synchronization loop (6) now has two parts: one is
the transient converter frequency effect, and the other is the
transient current effect. At the instant of the fault, the
converter terminal voltage has not been changed, and its value
can be computed as:
is the pre-fault phase.
Defining as the converter terminal voltage
change, then the relationship of the current to the converter
terminal voltage is:
where the transient current change can be computed.
Note, the current references
may be changed after the
fault occurrence for the purpose of the fault ride through or
reactive power compensation. Thus, the initial converter
terminal voltage is computed in (7,8) via the
current reference at pre-fault, while the transient converter
terminal voltage in (9,10)
should use the current reference during the fault.
Note, at the instant of the fault , i.e., changes to
, but the converter cannot instantly respond so that it
has an unchanged terminal voltage, phase and frequency, i.e.,
. However, as the
current is the consequence of the voltage difference between
the converter and grid, its value at the transient is significantly
changed and this change can be computed as follows:
Equations (11) indicates that the transient current depends
on 1) the voltage change due to the fault, ; 2) the initial
converter operating point, ; 3) the transmission line, ; 4)
the filter inductance, .
The changed current feeds back into the current controller
(1)-(2), thus resulting in the change of the converter terminal
voltage, as follows:
Fig. 4. Advanced synchronization stability assessment
From (12) and (13), the decay of the current transient
depends on the PI parameters of the current controller.
Equations (7)-(13) represent the effects of the current
dynamics on synchronization stability. Substituting these into
(6) gives the proposed model of the PLL, whose scheme is
shown in Fig. 4.
IV. VALIDATION EXAMPLE
A real-time Electromagnetic Transients (EMT) simulation
solved in Matlab/Simulink is used to validate the proposed
synchronization stability assessment in comparison with the
conventional QSLS methods. A 10 kV, 1 MW grid-feeding
converter connected to a 50 Hz grid through an
transmission line is discussed. The current limit in amplitude
is 81.65 A. We consider maximizing the active power during
the voltage sag, i.e.
. The PLL PI
parameters are 0.022/0.392. The test examples include the
● Case 1: , , ; for
which the current controller time constant is 0.1 ms.
● Case 2: , , ; for which
the current controller time constant is 0.5 ms.
● Case 3: , , ; for which
the current controller time constant is 0.1 ms.
● Case 4: , , ; for which
the current controller time constant is 0.5 ms.
The tests aim to assess the converter synchronization
stability in response to a voltage sag. Table I records the
minimum value of voltage sag for which the converter remains
stable as obtained from the QSLS analysis, the proposed
assessment method, and from EMT simulation.
From Table I, it appears that the QSLS method returns the
same result in all cases, and its estimated values are much
lower than the value obtained from EMT simulation. This is
because the QSLS method neglects the current transient, while
the other parameters remain identical as in Fig. 3 and in (5) for
MINIMUM FAULT VOLTAGE (PU) FOR WHICH THE CONVERTER REMAINS
STABLE AS COMPUTED BY THE DIFFERENT METHODS FOR THE DIFFERENT
CASES. *THE HIGHER THE VALUE OF VOLTAGE, THE LOWER THE
On the other hand, the proposed method considers current
transients and, thus, shows a much higher accuracy. The
values estimated with the proposed method approach those
obtained from EMT simulation but are consistently slightly
lower. This difference is due to the transients on the
inductance, which slows down the process of the current back
to the reference and resulting in a slightly larger phase.
Comparing case 1 to case 2, or case 3 to case 4, the increase of
the current controller time constant decreases the
synchronization stability. Moreover, comparing case 1 to case
3, or case 2 to case 4, the reduction in the filter inductance
worsens the synchronization stability. Note also that these
circumstances further decrease the accuracy of the QSLS
In order to further verify the accuracy of the proposed
model, we compared with QSLS and EMT in real-time
simulation as results shown in Fig. 5 and Fig. 6, where the
fault occurs at 3 s and is cleared at 3.1 s. When the grid
voltage sags to 0.363 pu, the converter with case 1 parameters
will be stable while that with case 2 parameters, which has a
longer time constant, will be unstable. This can be seen in Fig.
5 (a) which shows that the active power output of the case 2
oscillates after the voltage sag. The rest of the figures in Fig.
5 shows the phase transients obtained from the proposed
method and QSLS method in comparison with the EMT result,
where is computed by the phase detected from the PLL
minus the grid phase. It can be seen that in Fig. 5 (b) for case
1, both the proposed and QSLS methods effectively show a
stable synchronization in response to the fault. However, the
QSLS method gives a lower peak value compared to the EMT
result, whereas the peak value can be accurately obtained by
the proposed method. For case 2 as shown in Fig. 5 (c), only
the proposed method can accurately reflect the loss of
synchronization, which results in the continuous increase in
the phase, leading to the power oscillation as shown in Fig. 5
(a). Since the QSLS neglects the current transients, its
modelled phase transient for case 2, Fig. 5 (c) is identical to
that in case 1, Fig. 5 (b), which cannot reflect the real phase
transients and fails to precisely determine the synchronization
Fig. 5. Result when steps down to pu at 3 s and recovered at 3.1 s.
The current transients in the d-axis from the EMT
simulation are shown in Fig. 6. The grid voltage only sags to
0.569 pu, which is the highest value in Table I representing to
the minimum allowable voltage for all cases remaining stable.
Case 1 with the larger filter inductance and faster current
controller has the lowest current transients. This is the reason
that the accuracy of the QSLS method in this case is higher
than other cases as shown in Table I. The lower filter
inductance and the slower current controller as indicated in
(11) and (12,13) respectively lead to higher current transients,
for which the peak current boosts the phase as indicated in
(6) and sometimes results in the instability as shown in Fig. 5.
This letter proposes a novel synchronization stability
assessment method that considers converter current transients.
The case study shows that neglecting such transients leads to
inaccurate stability assessment as the computed stability range
is larger than the actual one, especially for low values of the
filter inductance and for relatively slow current transients. The
proposed method proves to be more accurate and comparable
to the results that can be obtained from a detailed EMT model.
Fig. 6. d-axis current transient result when steps down to pu and
recovered at 3.1 s.
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3 3.1 3.2 3.3 3.4 3.5
3 3.1 3.2 3.3 3.4 3.5
3 3.1 3.2 3.3 3.4 3.5
Active power (pu)
3 3.1 3.2 3.3 3.4 3.5
(c) Case 2 phase angle
(b) Case 1 phase angle
(a) Active power comparison: case 1 vs. case 2