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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 Terms—Synchronization Stability, Grid-feeding

Converter, Phase-Locked Loop, Current Transients.

I. INTRODUCTION

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: junru.chen.1@ucdconnect.ie)

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.

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

decoupled.

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

T

2

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

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,

i.e.

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

3

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.

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

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.

TABLE I

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

SYNCHRONIZATION STABILITY

Case

1

2

3

4

QSLS

0.341

0.341

0.341

0.341

Proposed

0.362

0.439

0.382

0.543

EMT

0.363

0.449

0.386

0.569

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

method.

4

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

stability.

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.

V. CONCLUSIONS

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.

REFERENCES

[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. 1683–1691, 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. 3414–3425, 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.

2019.

[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. 310–321, 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:

10.1109/TPEL.2019.2937942.

[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

50

100

150

Time (s)

id (A)

Case 1

Case 2

Case 3

Case 4

3 3.1 3.2 3.3 3.4 3.5

0

0.5

1

1.5

2

Time (s)

Phase (rad)

QSLS

Proposed

EMT

3 3.1 3.2 3.3 3.4 3.5

-1

0

1

Time (s)

Active power (pu)

Case 1

Case 2

3 3.1 3.2 3.3 3.4 3.5

0

0.5

1

1.5

Time (s)

Phase (rad)

QSLS

Proposed

EMT

(c) Case 2 phase angle

(b) Case 1 phase angle

(a) Active power comparison: case 1 vs. case 2