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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
1
Impact of Grid-Forming Inverters on
Protective Relays: A Perspective for Current
Limiting Control Design
Yifei Li , Student Member, IEEE, Heng Wu , Senior Member, IEEE,
and Xiongfei Wang , Fellow, IEEE
Abstract—Grid-forming (GFM) inverters can significantly
alter the fault characteristics of power systems, posing challenges to the proper function of protective relays for transmission lines. This article gives a holistic analysis of the
interaction between GFM inverter-based resources (IBRs)
and the supervising elements in protective relays, including
directional and phase selection elements. It is revealed that
the current limiting control (CLC) that is based on the current
reference saturation method adversely affects the performance of supervising elements that rely on the negativesequence quantities. In contrast, adopting highly inductive
virtual impedance in the CLC enables a reliable operation of
such elements. This finding provides insights into the design
of CLC for GFM IBRs from a protection perspective. It is further found that even with a highly inductive virtual impedance, the altered virtual impedance dynamics introduced by
the CLC can still lead to malfunctions of the incremental
quantity-based supervising elements. These theoretical findings are corroborated by simulations and controller hardwarein-the-loop (CHIL) tests.
Index Terms—Directional elements, grid forming, phase
selection elements, protective relay.
T
I. INTRODUCTION
HE supervising elements, including directional and phase
selection elements, are typically implemented in protective
relays for transmission lines in synchronous generator (SG)based power systems to determine fault direction and faulted
phases [1], [2], [3]. However, the massive integration of inverterbased resources (IBRs) is considerably changing fault characteristics of power systems, posing challenges to the reliability of
supervising elements [4].
The negative- and zero-sequence quantities are commonly used
by supervising elements for protection, which, however, cannot
distinguish the fault direction during a symmetrical fault, as well as
Received 10 February 2025; revised 6 June 2025; accepted 16 July
2025. (Corresponding authors: Heng Wu; Xiongfei Wang)
Yifei Li is with the Department of Energy (AAU Energy), Aalborg
University, 9220 Aalborg, Denmark (e-mail: yili@energy.aau.dk).
Heng Wu is with the School of Electrical Engineering, Southeast
University, Nanjing 210096, China (e-mail: hengwu@seu.edu.cn).
Xiongfei Wang is with the Department of Electrical Engineering, Tsinghua
University, Beijing 100084, China (e-mail: xiongfei@tsinghua.edu.cn).
Digital Object Identifier 10.1109/TIE.2025.3594454
differentiate the single-phase-to-ground fault from the double-phaseto-ground fault [3], [5]. To tackle this challenge, the positivesequence quantities are often used [6], yet they are affected by the
load conditions [7], [8]. To mitigate the adverse effects of load conditions, the incremental quantities are further implemented [9].
The impact of grid-following (GFL) IBRs on the reliability of
supervising elements that are based on sequence and incremental quantities has been extensively studied in [3] and [5]. Unlike
GFL IBRs, grid-forming (GFM) IBRs operate as slowly changing voltage sources behind impedances [10], with fault characteristics highly dependent on the current limiting control (CLC)
[11], which has fundamentally different impacts on the reliability of supervising elements.
There are generally two types of CLC methods, which are the
current reference saturation method and the virtual impedance
method [12], [13]. The current reference saturation method can
be realized through the instantaneous limiter, the priority-based
limiter, or the circular limiter [11]. The instantaneous limiter
cannot fully utilize the overcurrent capability of IBRs, while the
priority-based limiter may keep GFM IBRs within the currentlimiting mode even after the fault is cleared [14]. The circular
limiter overcomes the two drawbacks, making it the most practical current reference saturation method [12].
The virtual impedance with different X/R ratios can also be
directly implemented for the CLC. It is found in [15] and [16] that
increasing the X/R ratio brings inherent conflicts among the smallsignal stability, the transient stability, and the current limiting
dynamics of GFM IBRs. In [17], it is pointed out that the GFM
capability can be improved when the X/R ratio of the virtual impedance matches that of the passive impedance formed by the passive
filter, the transformer, and the grid impedance, which are highly
inductive in transmission grids. Therefore, using a highly inductive
virtual impedance for current limitation is recommended in [18].
Extensive research works on the design of CLC for GFM
IBRs are reported, but they are mostly from the perspective of
stability, transient performance, and GFM capability [12], [15],
[19]. Yet, the impact of CLC on the reliability of protective
relays, especially supervising elements, remains an open issue.
In [20] and [21], it is found that the CLC does not introduce significant impacts on distance elements. However, the findings in
[20] and [21] are mainly derived from numerical simulations,
which offer limited analytical insights. Moreover, the impact of
CLC on the supervising elements that are based on sequence
and incremental quantities has not been considered yet [22].
© 2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License.
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2
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
This article, thus, attempts to bridge the gap by providing a
systematic analysis on the impacts of different CLCs of GFM
IBRs on the supervising elements employing the sequence and
incremental quantities. First, based on symmetrical component
theory and Kirchhoff’s laws, the preconditions for the reliable
operation of supervising elements are derived. The impact of
GFM IBRs on these preconditions is then examined. Consequently, analytical insights into the design of CLC for GFM
IBRs from a protection perspective are provided. The main findings are summarized as follows.
1) By comparing the fault characteristics of SGs and GFM
IBRs, the control dynamics of GFM IBRs that affect the
reliability of supervising elements are identified. It is
found that, under the typically slow outer-loop control
[10], the internal voltage source of the IBR exhibits a
negligible difference from that of the SG with respect to
the impact on supervising elements. However, the CLC
has a substantial impact and is significantly different
from that of SG-based systems.
2) The theoretical analysis reveals that only the highly
inductive virtual impedance-based CLC can guarantee
the reliable operation of negative-sequence quantity-based
supervising elements, while the current reference saturation
methods, including the circular limiter, the instantaneous
limiter, and the priority-based limiter, compromise the reliability of supervising elements and are thus unsuitable for
practical applications. Moreover, it is found that with the
typically slow outer-loop control [10], the rapidly changing
dynamics of IBR output impedance induced by the CLC,
including both the current reference saturation and virtual
impedance methods, can lead to malfunctions of supervising elements that rely on incremental quantities.
Based on these findings, the key contributions of this article
are listed as follows.
1) The finding that current reference saturation methods are
inadequate from a protection perspective has not been recognized in prior art. This is evidenced by recent studies
[11], [13], and [23], which continue to work on these methods without addressing their protection-related limitations.
2) Leveraging control theory and Kirchhoff’s laws, this article
provides analytical insights into the impact of GFM IBRs on
supervising elements. In contrast, [20] and [21] focus primarily on the impact of GFM IBRs on distance elements,
rather than supervising elements, and rely predominantly on
numerical simulations conducted under limited scenarios.
3) The analytical findings presented herein can enhance industry confidence in employing negative-sequence quantitybased supervising elements in systems using the highly
inductive virtual impedance method. The findings also caution against the direct use of incremental quantity-based
supervising elements.
II. PRECONDITIONS OF SUPERVISING ELEMENTS
This section presents the fault characteristics in single
SG-based power systems, which serve as the basis for
Fig. 1.
Single SG-based power system.
Fig. 2. Sequence networks of the single SG-based power system during
a bcg fault. (a) Sequence network. (b) Pure-fault sequence network.
deriving the preconditions for the reliable operation of supervising elements.
A. System Description
Fig. 1 depicts the single SG-based power system, where i
and v represent the current and voltage at bus 1, ig and ve
denote the current and voltage at bus 2, respectively. vg represents the voltage of the grid. Zg denotes the impedance of the
grid. Zs and Zl correspond to the impedances of the collection
transmission line and the transmission line between bus 1 and
bus 2. Fx and Fy represent the fault points for reverse and forward faults, respectively. Distance relays R1 and R2 are assembled at bus 1 and bus 2. The distance relays incorporate
distance elements and supervising elements, including directional and phase selection elements [1]. This work focuses on
supervising elements. The bcg (phase b to phase c to ground)
bolted fault is taken as an example here to illustrate the preconditions for supervising elements.
B. Fault Characteristics Employed by Directional
Elements
Fig. 2(a) presents the sequence network when a bcg fault
occurs at Fy. vSG, and XSG are the internal voltage and output
impedance of the SG, respectively. The subscripts 1, 2, and 0
represent positive-, negative-, and zero-sequence quantities,
respectively. The variable m denotes the fault location. Applying
Kirchhoff’s law for Fig. 2(a), the angle differences between voltages and currents of negative-sequence quantities (u2) and
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LI et al.: IMPACT OF GRID-FORMING INVERTERS ON PROTECTIVE RELAYS
3
zero-sequence quantities (u0) are expressed as
8
v2
>
u2 ¼ / ¼ / − ðZs2 þ jXSG2 Þ
>
>
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
i2
>
<
Ze2
v0
>
>
u0 ¼ / ¼ / − ðZs0 þ jXSG0 Þ
>
>
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
i0
:
(1)
Ze0
where Ze2 and Ze0 represent the effective impedances for negativeand zero-sequence quantities, respectively. Following (1), the u2
and u0 are determined by the X/R ratios of the effective impedances, which are formed by the transmission line and SG output impedances. Since the transmission line and SG output impedances are
highly inductive, both u2 and u0 approach −90 under a forward
fault. In the case of a reverse fault, e.g., the fault occurs at Fx, i2 and
i0 hold opposite angles to those for a forward fault. Consequently,
u2 and u0 for a reverse fault are opposite in phase to those presented in (1), which approach 90 . For further details, refer to [24].
For symmetrical faults that do not involve negative- and zerosequence quantities, the positive-sequence quantities are employed
to determine the fault direction. To mitigate the influence of load
conditions, the incremental, rather than total positive-sequence
quantities, are employed to identify the fault direction.
Fig. 2(b) illustrates the pure-fault sequence network for incremental quantities, where Di1 ¼ i1−ipre1, and Dv1 ¼ v1–vpre1. The
subscript “pre” stands for the pre-fault quantities. efy denotes the
pre-fault voltage at the fault location Fy. For analysis of protective relays, the dynamics of vSG1 and XSG1 of the SG in the fault
sequence network are generally assumed to be similar to those
in the pre-fault circuit [4], [25]. Therefore, the vSG1 is canceled
out in Fig. 2(b) based on superposition theory. From the
positive-sequence circuit in Fig. 2(b), the angle difference
between Dv1 and Di1 (Du1) is given by
Du1 ¼ /
Dv1
¼ / − ðjXSG1 þ Zs1 Þ
|fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl}
Di1
(2)
Ze1
where Ze1 is the effective impedance for positive-sequence
quantities. Du1 is also determined by the X/R ratio of the effective impedance.
Fig. 3(a)–(c) illustrate the operation principle of directional
elements that are based on incremental, negative-sequence, and
zero-sequence quantities, respectively. The fault direction can
be identified based on Du1, u2, and u0. Due to the inducive
nature of the SG output impedance and the transmission line
impedance, the forward fault is identified when Du1, u2, and u0
fall within the forward zone where the angle is around −90 ,
while the reverse fault is identified when Du1, u2, and u0 fall
within the reverse zone where the angle is around 90 . The corresponding nonoperating angle is denoted as unon, which is typically set between 30 and 60 [24], and designed to improve the
reliable operation of directional elements.
C. Fault Characteristics Employed by Phase
Selection Elements
The fault phases can be identified based on the one-to-one
mapping between fault types and the angle differences between
Fig. 3. Phase angle characteristics of directional elements. (a) Incremental quantity-based element. (b) Negative-sequence quantity-based
element. (c) Zero-sequence quantity-based element.
sequence quantities at the fault location, e.g., between if2 and if1
(df21), as well as if2 and if0 (df20) [25]. However, the relay cannot
directly measure the fault-location quantities. Thanks to the
highly inductive nature of the impedance in SG-based power
systems, the angles of the negative- and zero-sequence quantities at the relay-assembled measurement point roughly correspond to those at the fault location and can be expressed as
8
i2
ð1 − mÞZl2 þ Zg2
>
>
(
>
</ if 2 ¼ / Ze2 þ Zl2 þ Zg2
/i2 /if 2
(3)
)
>
ð1 − mÞZl0 þ Zg0
i0
/i0 /if 0 :
>
>
:/ ¼ /
if 0
Ze0 þ Zl0 þ Zg0
In contrast, the phase angles of i1 and if1, are not necessarily
equal due to the load conditions in the positive-sequence circuit.
Thus, incremental quantities are used to address this mismatch
issue. By applying Kirchhoff’s law to the sequence network
shown in Fig. 2(b), it is derived that
/
Di1
ð1 − mÞZl1 þ Zg1
¼/
) /Di1 /if 1 :
if 1
Ze1 þ Zl1 þ Zg1
(4)
Fig. 4 elaborates the principle of phase selection elements,
where the angle difference between i2 and Di1 (Dd21), and the
angle difference between i2 and i0 (d20) are used simultaneously
to identify fault types. When Dd21 and d20 fall within the fault
bands, the corresponding fault types are identified. To enhance
the robustness of the phase selection element, the angle bands
(615 for Dd21, and 630 for d20), instead of fixed values, are
applied to identify fault types [26].
D. Preconditions
A quantitative analysis of the X/R ratio of the effective
impedance is further conducted to explicitly identify the preconditions for the reliable operation of both directional and phase
selection elements. According to (1) and (2), under a forward
fault, the X/R ratio of the effective impedance should be approximately greater than 0.58 (corresponding to 30 ) to ensure u2,
u0, and Du1 fall within the forward fault band, as illustrated in
Fig. 3.
Based on (3) and (4), the effective impedance should exhibit
an X/R ratio similar to that of Zl þ Zg, to ensure that the phase
angles of the relay-measured and fault-location currents are
approximately equal, i.e., /i2 /if2, /i0 /if0, and /Di1 /Dif1. Given that the X/R ratios of Zl and Zg are typically
greater than 3 [17], the X/R ratio of the effective impedance Ze
should likewise exceed 3. Moreover, the assumption of the
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Fig. 4.
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Principle for phase selection elements. (a) Dd21. (b) d20.
superposition theory should remain valid when employing incremental quantities.
Therefore, the supervising elements operate reliably with the
following preconditions:
1) The effective impedance is highly inductive, i.e., the
X/R ratio of the effective impedance is greater than 3.
2) The difference in source dynamics, including internal
voltage source and output impedance dynamics, between
the fault sequence network and the pre-fault circuit is
negligible.
It is worth noting that the preconditions discussed in this
study are derived based on transmission-level power systems,
which are typically characterized by highly inductive impedance.
Moreover, distance relays incorporating supervising elements are
not generally used in distribution-level power systems, where a
combination of circuit breakers, reclosers, and fuses is commonly
employed [8].
III. IMPACTS OF GFM CONTROL ON
SUPERVISING ELEMENTS
This section first presents the sequence network model of
GFM IBR-based power systems, based on which the control
loop that affects the reliable operations of supervising elements
is identified.
A. System Description
Fig. 5(a) depicts the main circuit of a GFM IBR-based power
system, which is used to illustrate the impacts of GFM control
on supervising elements. Here, a constant dc-link voltage (vdc)
is assumed, as the dc voltage is usually taken over by a frontend converter [16]. The symbols it and vt are the current and
voltage at the point of common coupling (PCC), respectively. Xf
denotes the filter inductance. A short-circuit fault is assumed to
occur at the transmission line between the bus 1 and the bus 2.
Fig. 5(b) shows the control loops of the GFM IBR. To eliminate the second-order harmonics during asymmetrical faults, the
sequence control is used, and the all-pass filter (APF) is used to
decompose the positive- and negative-sequence quantities [27].
The GFM control comprises two control layers, i.e., outerloop control and CLC. The outer-loop control is responsible for
generating the voltage magnitude and phase angle references for
the internal voltage source [11]. Here, power control is used as
an example to illustrate the function of outer-loop control. Specifically, the power control employs an active power controller
(APC) to generate the angle reference href1 for the dq transformation. Further, the reactive power controller (RPC) is used to
Fig. 5. Main circuit and control schemes of the GFM IBR-based power
system under study. (a) Main circuit. (b) Control loops.
generate the voltage magnitude reference (Eref1) for the internal
voltage source. To maintain a balanced internal voltage, the reference for negative-sequence voltage magnitude (Eref2) is set to
0 [28]. Besides the power control, the CLC methods, including
current reference saturation and virtual impedance methods, are
essential for IBRs to prevent overcurrent. For simplicity, the
same CLC strategy is adopted for the positive- and negativesequence quantities.
B. Sequence Network Model
Fig. 6 shows the sequence network of the GFM IBR-based
power system when a bcg fault occurs, where the connecting
manner at the fault point is determined by fault types and is not
affected by the GFM control. Moreover, the D-Y0 transformer
bypasses the direct GFM control of the IBR for zero-sequence
quantities. Consequently, the zero-sequence effective impedance (Ze0) observed from the relay-assemble point at the bus 1
only consists of the leakage impedance of the transformer,
which is highly inductive. Thus, according to (1), the supervising element relying solely on the zero-sequence quantities can
operate reliably. However, such a directional element is susceptible to the mutual coupling from adjacent circuits [29]. Moreover, zero-sequence quantities are absent during phase-to-phase
faults.
In contrast, the positive- and negative-sequence output impedances, i.e., Zv1 and Zv2, are characterized by the GFM control.
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LI et al.: IMPACT OF GRID-FORMING INVERTERS ON PROTECTIVE RELAYS
5
dynamics of the internal voltage source are anticipated for the
GFM IBRs [10]. Moreover, Eref2 is set to zero. Consequently,
internal voltages for positive- and negative-sequence quantities
are given by
eref1 epre1
Eref2 ¼ 0:
Fig. 6. Sequence network of the GFM IBR-based power system under a
bcg fault.
Following (6), the internal voltage sources of the GFM IBRs
are like those of the SG, as shown in Fig. 2. Therefore, these
two preconditions remain not significantly affected by the
power control.
Notably, the power control is only one form of outer-loop
control [11]. To preserve GFM capability, as required by grid
codes, other types of outer-loop controls, e.g., matching control,
droop control, and virtual oscillator control, should likewise be
designed to operate on slow timescales to provide the corresponding voltage references [30]. Therefore, the validity of (6)
holds, and the analytical approach presented in this work for
power control is also applicable to these alternative outer-loop
control methods.
In contrast, the effective impedances observed from the relayassemble point at bus 1, as defined in [18], are expressed as
8
2
2
>
<Ze1 ¼ n Zv1 þ jn Xf 1 þ jXT1
Ze2 ¼ n2 Zv2 þ jn2 Xf 2 þ jXT2
>
:
Ze0 ¼ jXT0
Fig. 7.
Illustration of the detailed power control diagrams.
The exact characteristics will be detailed in Section IV. Notably,
when the virtual impedance method is used and the virtual impedances are added directly to the voltage modulation reference,
the filters (Xf1, Xf2) are part of the sequence network. Otherwise,
they are excluded [11].
C. Impacts of Control Loops of GFM IBRs
Fig. 7 illustrates the control schemes for APC and RPC,
which determine the internal voltage source eref1. KpR and KiV
are the proportional and integral gains for RPC, respectively.VN1
is the nominal voltage magnitude. D is the P-x droop coefficient. KpP and H represent the virtual damping and inertia constants, respectively. By employing the power control in Fig. 7,
the magnitude and phase angle of the internal voltage for the
positive-sequence quantities are expressed as
ð
8
>
>
¼
½ðQref − Q1 ÞKpR þ VN1 KiV þ V1
E
< ref1
ð
ð
(5)
1
>
>
:/eref1 ¼ ðPref − P1 Þ
þ KpP :
2H
The power control adjusts eref1 to fulfill its function, thereby
influencing the internal voltage source dynamics of the IBR.
However, the output of the RPC is constrained around 1 p.u.
[10], and the bandwidth of APC is typically limited below 5 Hz
through adjusting KpP and H shown in (5) [30]. Therefore, slow
(6)
(7)
where n is the turns ratio of the transformer. When the virtual
impedances are not added directly to the voltage modulation reference or the current reference saturation method is employed,
the filters (Xf1, Xf2) are excluded from the effective impedances
(Ze1 and Ze2) [11]. Based on (5), the power control primarily
affects the internal voltages. With the internal voltage dynamics
altered slowly, the CLC swiftly adjusts the output impedance
(Zv1 and Zv2) to limit the fault current [12]. In this case, the
effective impedance dynamics are affected based on (7). Consequently, the two preconditions are potentially influenced by
the CLC.
Therefore, depending on whether the control loops affect the
preconditions, the challenges for supervising elements in GFM
IBR-based systems are formulated as follows.
1) The typically used slow power control does not cause
significant differences in the performance of supervising
elements compared with those in SG-based power systems.
2) The impact of CLC on the performance of both negativesequence quantity-based and incremental quantity-based
supervising elements requires further investigation.
IV. IMPACTS OF CLC METHODS ON NEGATIVE-SEQUENCE
QUANTITY-BASED SUPERVISING ELEMENTS
This section examines the impacts of CLC methods on the
negative-sequence quantity-based supervising elements and
identifies the protection-interoperable CLC method.
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Fig. 8.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Control scheme of the current reference saturation method.
Fig. 9. Current reference saturation method. (a) Circular limiter.
(b) Priority-based limiter. (c) Instantaneous limiter.
A. Current-Limiting Operation
Due to the limited current, the output impedance (Zv1 and Zv2)
is much greater than the impedance of the power filter and the
transformer, causing the X/R ratio of the output impedance to
dominate that of the corresponding effective impedance. Thus,
based on (1), (3), and (7), the reliability of negative-sequence
quantity-based elements is ensured when the output impedance
Zv2 is highly inductive. The X/R ratio of the output impedance
of GFM IBR is thus analyzed, considering the current reference
saturation and virtual impedance methods.
1) Current Reference Saturation Method: Fig. 8 shows the
control scheme of the current reference saturation method [11],
whose impact on the output impedance is investigated. r
denotes the relationship between i tdqref2 and itdqref2. When the
current limit is reached, the voltage integral controller is set to
zero to prevent windup. Therefore, the effect of the voltage integral controller can be discarded. Moreover, the closed-loop current control is approximated as a unity gain in the analysis,
considering that its bandwidth is much higher than the voltage
loop, i.e.,i tdqref2 itdq2 .
Based on Fig. 8, the relationship between internal voltage and
PCC voltage is given by [12]
edqref2 − vtdq2 ¼
1−r
itdq2
Kpv r
|ffl{zffl}
Fig. 10. Virtual impedance method. (a) Virtual admittance approach.
(b) Virtual impedance approach.
mainly resistive, while /r cannot be predefined for the prioritybased and instantaneous limiters. Moreover, the magnitude of r
is affected by fault conditions and cannot be predefined either.
In such cases, Zv2 is not necessarily inductive based on (8). Consequently, the supervising elements that rely on negativesequence quantities may malfunction with the current reference
saturation method.
2) Virtual Impedance Method: Fig. 10 presents the block diagram of the virtual impedance method, where the virtual admittance scheme is shown in Fig. 10(a), and the virtual impedance
scheme is shown in Fig. 10(b), which can be implemented with
or without the voltage and current controls. The GLPFX represents the low-pass filter, which is used to eliminate the adverse
impact of virtual inductance on small-signal stability [19]. The
IBR output impedance under virtual admittance and virtual
impedance approaches for the negative-sequence quantities are,
respectively, given by [10]
x1 Lv2
Rv2 ¼ max RvN2 ,
,
nX=R2
0
1
B
Lv2 ¼ max@LvN2 ,
(8)
Zv2
where Kpv is the voltage control proportional gain. Following
(8), the output impedance is determined by Kpv and r. r is a
complex number, which is determined by the current reference
saturation method.
Fig. 9 illustrates the current reference saturation method with
the circular limiter shown in Fig. 9(a), the priority-based limiter
shown in Fig. 9(b), and the instantaneous limiter shown in
Fig. 9(c) [11]. For the circular limiter, /r is zero, and Zv2 is
Rv2 ¼
Vt2
C
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA
2
Ilim2 x1 1 þ 1=nX=R2
KX2 ðIt2 − Ith2 Þ
Xv2
, Xv2 ¼
nX=R2
0
It2 P Ith2
It2 < Ith2
(9)
(10)
where nX/R2 represents the X/R ratio. Ilim2 is the current limit.
RvN2 and LvN2 constitute the virtual admittance in normal
operation of GFM IBR. KX2 is the proportional gain of the
adaptive virtual impedance. Ith2 is the current threshold
beyond which the virtual impedance is activated. Once the
current limitation is triggered, the virtual impedance and the
virtual admittance are defined as Zv2 ¼ Rv2 þ jXv2 and Yv2 ¼
1/(Rv2þjx1Lv2), respectively.
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LI et al.: IMPACT OF GRID-FORMING INVERTERS ON PROTECTIVE RELAYS
7
TABLE I
SUMMARY OF SUPERVISING ELEMENTS PERFORMANCE UNDER VARIOUS
CLC METHODS
Directional
Element
CLC
Output
impedance
TABLE II
IMPACT OF X/R RATIO ON SYSTEM DYNAMICS
Phase Selection
Elements
Du1
u2
u0
Dd21
d20
Highly inductive
(X/R ratio 3)
?
?
Not highly inductive
(X/R ratio <3)
?
?
Based on (1), (3), (9), and (10), implementing a small nX/R2
adversely affects the performance of supervising elements that
rely on the negative-sequence quantities. In contrast, when a sufficiently large nX/R2 is implemented, the supervising elements
can continue to operate reliably.
A quantitative analysis of the required nX/R2 values is further
conducted. Based on the preconditions for the reliable operation
of the supervising elements established in Section II, the effective impedance (Ze2) should be highly inductive, i.e., the X/R
ratio of Ze2 should exceed 3. Both the filter impedance (Xf2) and
transformer impedance (XT2) are nearly purely inductive, as
noted in [17], [31]. Consequently, based on (7), to ensure the
X/R ratio of Ze2 exceeds 3, nX/R2 should not be less than 3.
B. Protection-Interoperable CLC Method
Table I summarizes the performance of supervising elements
with different CLC strategies. The supervising elements that rely
solely on zero-sequence quantities (u0) are not impacted by the
CLC. However, supervising elements that rely on u2 and d20 can
only operate effectively if the effective impedance remains highly
inductive. Hence, the CLC method based on the inductive virtual
impedance is identified as the protection-interoperable CLC
method. All the current reference saturation methods, which
introduce either an output resistor (the circular limiter), or an output impedance with an undefined impedance angle (the instantaneous limiter and the priority-based limiter), would jeopardize the
reliability of supervising elements that are based on the negativesequence quantities, and should not be employed in practice.
While this conclusion is evident from a protection perspective, it
remains underrecognized in literature, as evidenced by the ongoing focus on various current reference saturation methods in
recent studies [22].
C. Impact on System Dynamics
Table II summarizes the impact of the X/R ratio of virtual
impedance on the system dynamics, including GFM capability,
transient stability, small signal stability, and transient overcurrent limitation. In [17], it is noted that a highly inductive virtual
impedance, i.e., X/R ratio greater than 3, is beneficial for GFM
capability. Moreover, in [15], it is revealed that increasing the
X/R ratio enhances transient stability but compromises smallsignal stability. Further, it is found in [16] that transient current
cannot be effectively limited when the virtual impedance has a
high X/R ratio.
High X/R
ratio
GFM
Capability
Transient
Stability
SmallSignal
Stability
Transient
Overcurrent
Limitation
The adverse impact of highly inductive virtual impedance on
small-signal stability can be mitigated by applying a cascading
low-pass filter [GLPFX ¼ xX/(sþxX)] to the virtual inductance
in the dq reference frame, as proposed in [19] and illustrated in
Fig. 10(b). Here, xX ¼ 0.1 p.u. according to [19]. In the dq reference frame, the frequency of the fundamental quantities becomes
0 Hz. Consequently, for fundamental quantities, GLPFX ¼ 1, and
the low-pass filter does not affect the reliability of the supervising
elements that rely on fundamental quantities.
To address the adverse impact of highly inductive virtual
impedance on transient overcurrent limitation, an additional virtual resistor in series with a high-pass filter [GHPFR ¼ s/(s þ
xR)] is implemented in [15]. The cut-off frequency of the highpass filter in [15] is set as 159.2 Hz. Moreover, in the dq reference frame, GHPFR ¼ 0 for the fundamental quantities, indicating that the virtual resistor is not applied to the fundamental
quantities. Therefore, the supervising elements that are based on
fundamental quantities are not affected. Furthermore, considering that IBRs are typically capable of withstanding temporary
overcurrent [32], the virtual impedance can be designed to consistently maintain a high X/R ratio, prioritizing the requirements
of supervising elements.
Therefore, a highly inductive virtual impedance can enhance
the GFM capability and transient stability of IBRs. Moreover,
its adverse effects on small-signal stability and transient overcurrent limitation can be effectively mitigated using established
methods that do not interfere with supervising elements based
on fundamental quantities.
Moreover, the CLC that is based on the inductive virtual
impedance only guarantees reliable operations of negativesequence quantity-based supervising elements. The impacts of
CLC methods on incremental quantity-based supervising elements will be further investigated in the next section.
V. IMPACTS OF CLC METHODS ON INCREMENTAL
QUANTITY-BASED SUPERVISING ELEMENTS
This section first develops the pure-fault sequence network
model for the GFM IBR-based power system. Based on this
pure-fault sequence network, the impacts of CLC methods on
incremental quantity-based supervising elements are analyzed.
A. Pure-Fault Sequence Network Model
Fig. 11 presents the sequence networks under a bcg fault for a
GFM IBR-based power system, where Zeg1 ¼ (1−m)Zl1 þ Zg1.
Zeq20 is the equivalent parallel impedance for negative- and
zero-sequence circuits. Since incremental quantity-based supervising elements rely on electrical quantities in the pure-fault
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TABLE III
MAIN CIRCUIT PARAMETERS
Fig. 11. Sequence networks during a bcg fault. (a) Fault sequence network. (b) Pre-fault sequence network. (c) Pure-fault sequence network.
sequence network for operation, deriving this sequence network
is essential to assess the impact of the CLC method on these elements. Using nodal analysis, the voltage at the fault location for
the fault sequence network, as shown in Fig. 11(a), and the voltage for the pre-fault sequence network, as shown in Fig. 11(b),
are derived by
vf 1 ¼
efy ¼
v1 mYl1 þ vg1 Yeg1
Yl1 þ Yeg1 þ Yeq20
(11)
vpre1 mYl1 þ vg1 Yeg1
mYl1 þ Yeg1
(12)
Dv1
(13)
Based on (13), the pure-fault sequence network for the GFM
IBR-based system is obtained, as shown in Fig. 11(c). The only
difference from the SG-based power system, illustrated in
Fig. 2(b), lies in the equivalent impedance seen from Bus 1, i.e.,
Dv1/Di1.
Applying Kirchhoff’s law for the fault and pre-fault sequence
networks, the relationship between Dv1 and Di1 in Fig. 11(c) is
expressed as
Dv1 neref1 − nepre1 − n2 i1 Zv1
¼
−ðn2 jXf 1 þ jXT1 Þ:
Di1
i1 − ipre1
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Meaning
Value
vg
Grid voltage (L-L, Peak)
220 kV (1.732 p.u.)
f1
Grid frequency
50 Hz
S
Rated power
100 MW (1 p.u.)
n
Turns ratio
33 kV/220 kV
vdc
DC-link voltage
40 kV
l
Length of transmission line
100 km
Zl1/l
Positive-sequence line impedance
0.03þj0.34 X/km
Zl0/l
Zero-sequence line impedance
0.18þj1.19 X/km
Zg
Grid impedance
0.01 H
to −90 is significantly affected by the term Zad. Therefore, the
characteristics of Zad must be thoroughly analyzed.
B. Current-Limiting Operation
With the typical slow power control shown in Fig. 7 adopted,
it is assumed that eref1epre1. Based on (14), Zad is expressed as
Zad ¼
where the symbol Y stands for admittance. Subtract (12)
from (11), we have the following equation:
zfflfflfflfflfflfflffl}|fflfflfflfflfflfflffl{
ðv1 − vpre1 Þ mYl1 − efy Yeq20
Dvf 1 ¼ vf 1 − efy ¼
:
mYl1 þ Yeg1 þ Yeq20
Symbol
(14)
Zad
In SG-based power systems, eref1 epre1, and the I1 is
much greater than Ipre1 [8]. From (14), it is derived /Zad −90 , causing /(Dv1/Di1) −90 . Consequently, the circuit
seen from the bus 1 can be characterized by a highly inductive
impedance, as shown in Fig. 2(b). In this case, the incremental
quantity-based supervising elements can operate reliably according to (2) and (4).
However, in the GFM IBR-based system, /(Dv1/Di1) requires
further investigation. Based on (14), the proximity of /(Dv1/Di1)
−n2 i1 Zv1
i1 − ipre1
(15)
where the angle of i1 does not necessarily align with that of
i1−ipre1. Moreover, unlike SG-based systems, I1 is close to Ipre1
in GFM IBR-based systems due to the current limit. Therefore,
when the current reference saturation method is employed,
/Zad cannot be predefined. Further, based on (15), even if a
highly inductive Zv1 is implemented, /Zad may still deviate
from −90 . Under these circumstances, based on (14), /(Dv1/
Di1) can significantly deviate from −90 . Consequently, the
incremental quantity-based supervising elements may malfunction due to the impact of CLC.
VI. VERIFICATION RESULTS
To verify the theoretical findings, electromagnetic transient
simulations and hardware-in-the-loop testing results are given in
this section. The main circuit shown in Fig. 5(a) is implemented,
and its main parameters are provided in Table III.
Notably, to improve the accuracy of phasor estimation in the
protective relay, digital filters are employed to suppress noise
and extract the fundamental components [1]. Moreover, the tolerance bands inherent in supervising elements further help compensate for the error caused by the inaccuracy of phasor
estimation [26]. Consequently, supervising elements effectively
mitigate these estimation inaccuracies.
A. Simulation Results
The theatrical analysis is first validated through simulations
performed on the PSCAD/EMTDC platform. The sampling
time is 10 ls.
Fig. 12 illustrates the simulation results for the phase angle of
the output impedance under the current reference saturation
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LI et al.: IMPACT OF GRID-FORMING INVERTERS ON PROTECTIVE RELAYS
9
Fig. 12. Phase angles of the virtual impedance for negative-sequence
quantities under current reference saturation methods.
Fig. 14.
Fig. 13.
CHIL testing setup. (a) Hardware devices. (b) Topology.
Angles of (Dv1/Di1) and zad.
TABLE IV
TRIPPING ACCURACY UNDER VARIOUS CLC METHODS
CLC Methods
u2
d20
Du1
Dd21
Circular limiter
0.0%
27.8%
36.6%
16.7%
Priority-based limiter
30.6%
23.6%
34.6%
9.3%
Instantaneous limiter
8.3%
8.3%
57.8%
1.9%
Virtual impedance (0 )
0.0%
45.8%
17.8%
0.0%
Virtual impedance (90 )
100.0%
100.0%
50.4%
9.3%
method, where the fault type considered is an ag fault. The
phase angles of the negative-sequence output impedance
under the circular, the priority-based (only the active current is
injected), and the instantaneous limiters are −0.5 , −51.6 , and
36.2 , respectively. The results indicate that a highly inductive
output impedance is not always assured with the current reference saturation methods.
Fig. 13 illustrates the simulation results for the case of an ag
fault with m ¼ 0.01 and Rg ¼ 30 X, where a highly inductive virtual impedance is triggered. Here, Rg denotes the phase-toground fault resistance. Due to /Zad ¼ 8.1 , /(Dv1/Di1) deviates from −90 . Consequently, the incremental quantity-based
supervising elements may malfunction, as indicated by (2)
and (4).
Table IV summarizes the tripping accuracy of supervising
elements under various short-circuit fault conditions, including
phase-to-ground fault resistances (Rg ¼ 0, 10, 25, and 50 X),
phase-to-phase fault resistances (Ra ¼ 0, 10, 25, and 50 X), fault
locations (m ¼ 0.01, 0.5, and 0.9), fault inception angles (0 ,
45 , and 90 ), and fault types (ag, bg, cg, abg, acg, bcg, ab, ac,
and bc). Simulation results are recorded at 60 ms after fault
inception [33], [34].
Under circular limiter and resistive virtual impedance-based
CLC, the output impedance of the IBR is predominantly resistive, resulting in 0.0% tripping accuracy for u2 and low
Fig. 15. Experimental results of the negative-sequence quantity-based
supervising elements under various phase angles of Zv2. (a) u2. (b) d20.
accuracy for d20. Under priority-based limiter and instantaneous
limiter, the X/R ratio of IBR output impedance is not predefined
and is not necessarily inductive, leading to low tripping accuracy for both u2 and d20. In contrast, when a highly inductive
virtual impedance-based CLC is applied, the tripping accuracy
of both u2 and d20 reaches 100.0%. However, regardless of the
type of CLC employed, the tripping accuracy of Du1 and Dd21
is low. These tripping accuracy results are consistent with the
theoretical analysis.
B. Hardware-in-the-Loop Testing Results
Fig. 14(a) shows the controller hardware-in-the-loop (CHIL)
setup that is used in this work. Three RT BOX3 units, as shown
in Fig. 14(b), are implemented with the GFM control, the IBRbased system plant, and relay algorithms, respectively. The voltage and current at the PCC (vt and it) are transferred from the
plant unit to the controller unit to generate the PWM signal.
Similarly, the voltage and current signals at the bus 1 (v and i)
are sent to the relay unit to determine the fault direction and
identify the faulted phases. To ensure tight synchronization
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IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS
Fig. 16. Experimental results of supervising elements relying on negative- and zero-sequence quantities during a bcg fault. (a) Circular limiter is triggered. (b) Highly inductive virtual admittance is triggered. (c) Highly inductive virtual impedance is triggered.
Fig. 17. Experimental results of incremental quantity-based supervising elements during an ag fault. (a) Circular limiter is triggered. (b) Highly inductive
virtual admittance is triggered. (c) Highly inductive virtual impedance is triggered.
between the plant and controller units, an intentional delay of
50 ls is applied to vt and it during their transfer. Likewise, an
intentional delay of 50 ls is applied to v and i transmitted to the
relay unit. Moreover, the model computation in the plant unit is
completed within a time constraint of 10 ls, while the computations in the controller and relay units are completed within
50 ls. To enhance the accuracy of the CHIL results, a sub-cycle
average model of the IBR is employed in the plant unit, as
described in [35] and [36]. The workstation is used for programming RT BOX3 units, and the oscilloscope is used to record the
waveforms generated by the relay unit.
Fig. 15 presents the experimental results for u2 and d20 under
the virtual impedance method with varying phase angles of Zv2.
Here, an ag fault occurs in the transmission line between the bus
1 and the bus 2 with m ¼ 0.5 and Rg¼20 X. The data is recorded
at 60 ms after fault inception [33]. In Fig. 15(a), when the X/R
ratio of Zv2 is not smaller than 0.6, u2 falls within the forward
fault band. In Fig. 15(b), when the X/R ratio of Zv2 is not smaller
than 3, d20 falls within the ag fault band. Moreover, as the X/R
ratio increases, both u2 and d20 gradually approach their ideal
values of −90 and 0 , respectively.
Fig. 16 shows the testing results of supervising elements that
are based on the negative- and zero-sequence quantities. It is
assumed that a bolted bcg fault with m ¼ 0.5 occurs between the
bus 1 and the bus 2, with its inception time indicated by the red
arrow. In Fig. 16, the forward fault band is highlighted in blue,
while the bcg fault band is highlighted in grey. In Fig. 16(a), the
circular limiter is triggered. Under this circumstance, Zv2 is
resistive. Consequently, u2 falls outside of the forward fault
TABLE V
PARAMETERS OF CHIL SETUP
Symbol
Meaning
Value
Tsp
Sampling time of the plant unit
10 ls
Tsc
Sampling time of the controller unit
50 ls
Tsr
Sampling time of the relay unit
50 ls
fsw
Switching frequency
10 kHz
band, and d20 falls outside of the bcg fault band. As a result, the
supervising elements do not issue a trip approval, and the distance relay fails to trip. In contrast, u2 falls within the forward
fault band, and d20 falls within the bcg fault band within 2 cycles
after fault inception when a highly inductive virtual admittance
or impedance is triggered, as shown in Fig. 16(b) and (c),
respectively.
Fig. 17 shows the testing results of the incremental quantitybased supervising elements during a forward ag fault, where
m ¼ 0.01 and Rg¼20 X. It is worth mentioning that the fault
resistance does not affect Dd21 during an ag fault [37]. Here, the
forward fault band for Du1 is highlighted in blue, while the ag
fault band for Dd21 is highlighted in grey. In Fig. 17(a), the circular limiter is triggered, making Du1 fall outside of the forward
band, and Dd21 fall outside of the ag band. Further, as shown in
Fig. 17(b), even with a highly inductive admittance triggered
and the slow power control employed, Du1 falls outside of the
forward fault band, and Dd21 falls outside of the ag fault band.
Fig. 17(c) presents the results with a highly inductive virtual
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LI et al.: IMPACT OF GRID-FORMING INVERTERS ON PROTECTIVE RELAYS
11
impedance triggered. In this case, Dd21 deviates from the ag
fault band, and Du1 approaches the boundary of the forward
fault band. Consequently, the supervising elements do not issue
the tripping of the distance relay. The results confirm the correctness of the theoretical analysis.
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VII. CONCLUSION
In this article, the impacts of GFM IBR on the supervising elements of protective relays, including directional and phase selection
elements, are analyzed. The findings are concluded as follows.
1) The supervising elements are adversely affected by the
current reference saturation method. In contrast, by using
the protection-interoperable CLC method, the supervising
elements that are based on the negative-sequence quantities
can operate reliably.
2) Even with the adoption of typical slow power control
and the protection-interoperable CLC method, the incremental quantity-based supervising elements may still malfunction. Thus, the incremental quantity-based supervising
elements should not be directly used.
Simulations and CHIL tests have confirmed the findings.
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Yifei Li (Student Member, IEEE) received the
B.S. degree from Hebei University of Technology, Tianjin, China, in 2018, and the M.S.
degree from Zhejiang University, Hangzhou,
China, in 2021, both in electrical engineering.
He is currently working toward the Ph.D. degree
in electronic engineering with the Department of
Energy, Aalborg University, Aalborg, Denmark.
His research focuses on the coordination
between converter control and grid protection.
Heng Wu (Senior Member IEEE) received B.S.
and M.S. degrees from Nanjing University of
Aeronautics and Astronautics (NUAA), Nanjing,
China, in 2012 and 2015, respectively, and the
Ph.D. degree from Aalborg University, Aalborg,
Denmark, in 2020, all in electrical engineering.
From 2015 to 2017, He was an Electrical
Engineer with NR Electric, Nanjing, China. He
was a Postdoctoral Researcher with Aalborg
University, from 2020 to 2021, an Assistant Professor and Leader of Electronic Power Grid
(eGRID) Research Group with Aalborg University, from 2022 to 2025.
He is currently a Professor with the Southeast University, Nanjing. His
research interests include the modelling and stability analysis of the
power electronic based power systems.
Dr. Wu serves as the Chairman of IEEE Task Force on Frequencydomain Modeling and Dynamic Analysis of HVDC and FACTS, the subgroup leader of Cigre WG B4/C4.93 and Cigre WG B4.101, and the
expert member of GB grid forming best practice expert group formed by
National Energy System Operator, U.K. He is identified as world’s top
2% scientist by Stanford University from 2019. He serves as an Associate Editor of IEEE TRANSACTIONS ON POWER ELECTRONICS. He was a
recipient of the 2023 IEEE Transactions on Power Electronics Prize
Paper AWARD.
Xiongfei Wang (Fellow, IEEE) received the B.S.
degree in electrical engineering from Yanshan
University, Hebei, China, in 2006, the M.S.
degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 2008, and
the Ph.D. degree in energy technology from Aalborg University, Aalborg, Denmark, in 2013.
From 2009 to 2022, he was with Aalborg University where he became an Assistant Professor
in 2014, an Associate Professor in 2016, a Professor and the Founding Leader of Electronic
Power Grid (eGRID) Research Group, in 2018. From 2022 to 2025, he
was a Professor with KTH Royal Institute of Technology, Stockholm,
Sweden, and a Part-time Professor with Aalborg University. He is currently the Xinghua Chair Professor with Tsinghua University, Beijing,
China. His research interests include modeling and control of power
electronic converters, stability and power quality of power-electronicdominated power systems, and high-power electronic systems.
Dr. Wang serves as the Editor-in-Chief of IEEE TRANSACTIONS ON
POWER ELECTRONICS, the Chair of IEEE International Roadmap on HighPower Electronics for Modern Energy Grids, and the Chair of IEEE
Power Electronics Society (PELS) Technical Committee (TC 8) on Electronic Power Grid Systems. He received 11 IEEE Prize Paper Awards,
the 2016 AAU Talent for Future Research Leaders, the 2018 IEEE Richard M. Bass Outstanding Young Power Electronics Engineer Award, the
2019 IEEE PELS Sustainable Energy Systems Technical Achievement
Award, and the 2022 Isao Takahashi Power Electronics Award.