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Impact of Current Transients on the Synchronization Stability Assessment of Grid-Feeding Converters


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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.
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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 TermsSynchronization 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 [1]. However,
during a contingency, grid-feeding converters may lose
synchronization with the grid and lead to power oscillations
due to the PLL failure [2]. Different PLL implementations to
counteract voltage sags have been tested in [3]. However, the
full understanding of the synchronization stability of the grid-
feeding converter is still an open question. Reference [4]
provides an overview of the previous assessment of
synchronization stability. Reference [5] 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 [6] proposes a Quasi-Static
Large-Signal analysis, [7] proposes an Equal Area Criterion
and [8] proposes a phase portrait approach. According to the
comparison amongst these methods [4], 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:
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 [9]. 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
inductance parameters.
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
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
follows: 
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 [6] 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.,
in (4),
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: 
Where   .
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 [6]
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 
and substituting these into
(4) gives:
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:
 
where  
 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.
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
following cases:
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
all cases.
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.
[1] J. Rocabert, A. Luna, F. Blaabjerg and P. Rodríguez, "Control of Power
Converters in AC Microgrids," in IEEE Transactions on Power
Electronics, vol. 27, no. 11, pp. 4734-4749, Nov. 2012.
[2] O. Goksu, R. Teodorescu, C. L. Bak, F. Iov, and P. C. Kjær,“Instability
of wind turbine converters during current injection to low voltage grid
faults and PLL frequency based stability solution,” IEEE Trans. Power
Syst., vol. 29, no. 4, pp. 16831691, Jul. 2014
[3] A. Luna et al., “Grid voltage synchronization for distributed generation
systems under grid fault conditions,” IEEE Trans. Ind. Appl., vol. 51, no.
4, pp. 34143425, Jul. 2015.
[4] M. G. Taul, X. Wang, P. Davari and F. Blaabjerg, "An Overview of
Assessment Methods for Synchronization Stability of Grid-Connected
Converters Under Severe Symmetrical Grid Faults," in IEEE
Transactions on Power Electronics, vol. 34, no. 10, pp. 9655-9670, Oct.
[5] J. Chen, F. Milano and T. O'Donnell, "Assessment of Grid-Feeding
Converter Voltage Stability," in IEEE Transactions on Power Systems,
vol. 34, no. 5, pp. 3980-3982, Sept. 2019.
[6] D. Dong, B. Wen, D. Boroyevich, P. Mattavelli, and Y. Xue, “Analysis
of phase-locked loop low-frequency stability in three-phase grid-
connected power converters considering impedance interactions,” IEEE
Trans. Ind. Electron., vol. 62, no. 1, pp. 310321, Jan. 2015.
[7] H. Wu and X. Wang, "Transient Stability Impact of the Phase-Locked
Loop on Grid-Connected Voltage Source Converters," 2018
International Power Electronics Conference (IPEC-Niigata 2018 -ECCE
Asia), Niigata, 2018, pp. 2673-2680.
[8] H. Wu and X. Wang, "Design-Oriented Transient Stability Analysis of
PLL-Synchronized Voltage-Source Converters," in IEEE Transactions
on Power Electronics, vol. 35, no. 4, pp. 3573-3589, April 2020, doi:
[9] M. G. Taul, X. Wang, P. Davari and F. Blaabjerg, "An Efficient
Reduced-Order Model for Studying Synchronization Stability of Grid-
Following Converters during Grid Faults," 2019 20th Workshop on
Control and Modeling for Power Electronics (COMPEL), Toronto, ON,
Canada, 2019, pp. 1-7.
3 3.1 3.2 3.3 3.4 3.5
Time (s)
id (A)
Case 1
Case 2
Case 3
Case 4
3 3.1 3.2 3.3 3.4 3.5
Time (s)
Phase (rad)
3 3.1 3.2 3.3 3.4 3.5
Time (s)
Active power (pu)
Case 1
Case 2
3 3.1 3.2 3.3 3.4 3.5
Time (s)
Phase (rad)
(c) Case 2 phase angle
(b) Case 1 phase angle
(a) Active power comparison: case 1 vs. case 2
... Some other works on the current timescale dynamics are represented in Refs. 44,74,75 . The model can also be easily extended to include slower dynamical components. ...
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Differing from synchronous generators, there are lack of physical laws governing the synchronization dynamics of voltage-source converters (VSCs). The widely used phase-locked loop (PLL) plays a critical role in maintaining the synchronism of current-controlled VSCs, whose dynamics are highly affected by the power exchange between VSCs and the grid. This paper presents a design-oriented analysis on the transient stability of PLL-synchronized VSCs, i.e., the synchronization stability of VSCs under large disturbances, by employing the phase portrait approach. Insights into the stabilizing effects of the first- and second-order PLLs are provided with the quantitative analysis. It is revealed that simply increasing the damping ratio of the second-order PLL may fail to stabilize VSCs during severe grid faults, while the first-order PLL can always guarantee the transient stability of VSCs when equilibrium operation points exist. An adaptive PLL that switches between the second-order and the first-order PLL during the fault-occurring/-clearing transient is proposed for preserving both the transient stability and the phase tracking accuracy. Time-domain simulations and experimental tests, considering both the grid fault and the fault recovery, are performed, and the obtained results validate the theoretical findings.
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This letter applies voltage stability analysis to grid feeding converters in the presence of the converter stability versus the grid state and its operation. By applying this analysis, it is shown that the converter may become unstable if the converter reference power or current exceeds the line capacity. The letter proposes to use a conventional PV curve to determine the stability of the dynamic response of grid-feeding converters considering both power and current limits.
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Grid-connected converters exposed to weak grid conditions and severe fault events are at risk of losing synchronism with the external grid and neighboring converters. This predicament has led to a growing interest in analyzing the synchronization mechanism and developing models and tools for predicting the transient stability of grid-connected converters. This paper presents a thorough review of the developed methods that describe the phenomena of synchronization instability of grid-connected converters under severe symmetrical grid faults. These methods are compared where the advantages and disadvantages of each method are carefully mapped. The analytical derivations and detailed simulation model are verified through experimental tests of three case studies. Steady-state and quasi-static analysis can determine whether a given fault condition results in a stable or unstable operating point. However, without considering the dynamics of the synchronization unit, transient stability cannot be guaranteed. By comparing the synchronization unit to a synchronous machine, the damping of the phase-locked loop is identified. For accurate stability assessment, either nonlinear phase portraits or time-domain simulations must be performed. Until this point, no direct stability assessment method is available which consider the damping effect of the synchronization unit. Therefore, additional work is needed on this field in future research.
Conference Paper
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The phase-locked loop (PLL) is widely used in the grid-connected voltage source converter (VSC) for the purpose of grid synchronization. The impact of the PLL on the small-signal stability of VSC has recently been revealed, yet its influence on the transient stability of the VSC has seldom been addressed. This paper thus presents a comprehensive analysis on the transient stability effect of the PLL. It points out that the conventional equal-area criterion (EAC), which is used to analyze the transient stability of the synchronous generator (SG), cannot be extended to analyze the PLL effect, even though a dynamic analogy between the PLL and the swing equation of the SG can be found. The phase portrait is thus used in this work, and it shows that the long settling time and a high damping ratio of the PLL can enhance the transient stability of the VSC. Finally, the experimental tests are performed to verify the effectiveness of the theoretical analysis.
Synchronous reference frame (SRF) phase-locked loop (PLL) is a critical component for the control and grid synchronization of three-phase grid-connected power converters. The PLL behaviors, especially its low-frequency dynamics, influenced by different grid and load impedances as well as operation mode have not been investigated yet, which may not be captured by conventional linear PLL models. In this paper, we propose a state-feedback quasi-static SRF-PLL model, which can identify and quantify the inherent frequency self-synchronization mechanism in the converter control system. This self-synchronization effect is essentially due to the converter interactions with grid impedance and power flow directions. The low-frequency nonlinear behaviors of the PLL under different grid impedance conditions are then analyzed, which forms the framework of evaluating the impacts of the large penetration level of distributed generation units, weak grid, microgrid, and large reactive power consumption in terms of the frequency stability of PLL. Specifically, the PLL behavior of the converter system under islanded condition is investigated to explain the PLL instability issues and the related islanding-detection methods in early publications and industry reports.
The actual grid code requirements for the grid connection of distributed generation systems, mainly wind and photovoltaic (PV) systems, are becoming very demanding. The transmission system operators (TSOs) are especially concerned about the low-voltage-ride-through requirements. Solutions based on the installation of STATCOMs and dynamic voltage regulators (DVRs), as well as on advanced control functionalities for the existing power converters of distributed generation plants, have contributed to enhance their response under faulty and distorted scenarios and, hence, to fulfill these requirements. In order to achieve satisfactory results with such systems, it is necessary to count on accurate and fast grid voltage synchronization algorithms, which are able to work under unbalanced and distorted conditions. This paper analyzes the synchronization capability of three advanced synchronization systems: the decoupled double synchronous reference frame phase-locked loop (PLL), the dual second order generalized integrator PLL, and the three-phase enhanced PLL, designed to work under such conditions. Although other systems based on frequency-locked loops have also been developed, PLLs have been chosen due to their link with dq0 controllers. In the following, the different algorithms will be presented and discretized, and their performance will be tested in an experimental setup controlled in order to evaluate their accuracy and implementation features.
In recent grid codes for wind power integration, wind turbines are required to stay connected during grid faults even when the grid voltage drops down to zero; and also to inject reactive current in proportion to the voltage drop. However, a physical fact, instability of grid-connected converters during current injection to very low (close to zero) voltage faults, has been omitted, i.e., failed to be noticed in the previous wind power studies and grid code revisions. In this paper, the instability of grid side converters of wind turbines defined as loss of synchronism (LOS), where the wind turbines lose synchronism with the grid fundamental frequency (e.g., 50 Hz) during very deep voltage sags, is explored with its theory, analyzed and a novel stability solution based on PLL frequency is proposed; and both are verified with power system simulations and by experiments on a grid-connected converter setup.
The enabling of ac microgrids in distribution networks allows delivering distributed power and providing grid support services during regular operation of the grid, as well as powering isolated islands in case of faults and contingencies, thus increasing the performance and reliability of the electrical system. The high penetration of distributed generators, linked to the grid through highly controllable power processors based on power electronics, together with the incorporation of electrical energy storage systems, communication technologies, and controllable loads, opens new horizons to the effective expansion of microgrid applications integrated into electrical power systems. This paper carries out an overview about microgrid structures and control techniques at different hierarchical levels. At the power converter level, a detailed analysis of the main operation modes and control structures for power converters belonging to microgrids is carried out, focusing mainly on grid-forming, grid-feeding, and grid-supporting configurations. This analysis is extended as well toward the hierarchical control scheme of microgrids, which, based on the primary, secondary, and tertiary control layer division, is devoted to minimize the operation cost, coordinating support services, meanwhile maximizing the reliability and the controllability of microgrids. Finally, the main grid services that microgrids can offer to the main network, as well as the future trends in the development of their operation and control for the next future, are presented and discussed.