# Effects of current limit for grid forming converters on transient stability:
analysis and solution

Kanakesh Vatta Kkuni, _Student Member_ , Guangya Yang, _Senior Member_ The
work is supported by Phoenix project, funded by Ofgem under Network Innovation
Competition programme, Project Direction ref: SPT / Phoenix / 16 December 2016
(https://www.spenergynetworks.co.uk/pages/phoenix.aspx). Kanakesh Vatta Kkuni
and Guangya Yang are with are with the Center for Electric Power and Energy,
Department of Electrical Engineering, Technical University of Denmark, 2800
Kgs. Lyngby, Denmark (e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Grid forming control applied to power converters which interface storage or
renewable generation to the power grid, has been identified as a potential
solution to facilitate a substantial share of converter-based renewable
generation in the power system. Analyzing the response of grid forming
converters (GFC) for large frequency, phase, and voltage events, particularly
when the GFC enters the current limit operation, is very important for system
stability, but studies on this have been limited. This paper presents a
quantitative and illustrative analysis of the impact of the current limit in
GFC on the transient stability of a system comprising of GFC. Furthermore, a
solution based on virtual active power is proposed to improve the transient
stability margin of the GFC when the GFC enters the current limit. Finally,
the analysis and the proposed method to enhance the transient stability are
verified by Power hardware in the loop (PHIL) experimental tests.

###### Index Terms:

Grid forming control, transient stability, synchronization stability,
converter control, current limit

##  I Introduction

The core of the bulk power system is evolving from conventional synchronous
machine-based generation (SG) to asynchronous power converter-based renewable
generation and energy storage. Ensuring continued reliability of the power
system when the fundamental nature of the power systems is altered with a
reducing share of synchronous generators is a challenge. The grid forming
control for converters (GFC) or virtual synchronous machine control is a
potential solution to mitigate the challenges caused due to reduction of SG
[1, 2]. GFC’s characteristics which are beneficial in ensuring system security
are: Higher stability margin, Instantaneous fault current contribution,
Inertial response, and instantaneous active power contribution to phase jumps
and system frequency changes. In recent years several variations of grid
forming control have been proposed. The difference between the GFC’s is mainly
attributed to how the synchronization loop or active power control and voltage
control is realized. The implementation has been ranging from simple active
power-frequency ($P-f$) and reactive power voltage ($Q-V$) droop control [3]
based electromechanical realization to a full realization of synchronous
machine dynamic equations [4, 5]. The studies about electromagnetic model
realization of GFC have been discussed in [6, 7, 8].

The SG has an overload capacity of several times its rated value during short-
term overload and grid faults. Such high overload capability is not typical
for a power electronic converter-based GFC, which emulates SG. Therefore, GFC
needs to have a robust overload and fault current limiter for protecting and
ensuring reliable GFC operation during significant transient events. Yet,
implementing the power or current limiters for GFC is challenging because an
instantaneous response is expected from GFC similar to a voltage source. In
addition, for GFC, the active power, which is influence by current limiting,
also acts feedback variable for synchronization. Consequently, there is a
possibility of wind up of power-based synchronization loop leading to
instability [3]. Thus the current limiter can negatively impact GFC responses,
particularly during transient events[9, 10, 3].

Switching to control that employs voltage-based phase-locked loop (PLL)
synchronization and controls the active and reactive current control during
overload and grid fault scenarios is an option for GFC [11]. However, the
solution is not robust as there is a need to preserve a complete additional
control set in the same digital control. Furthermore, the stability issues
caused due to PLL is also undesirable [9]. A backup PLL is not required in the
current limit methods employed in [12, 13] or with the virtual impedance-based
current limit method discussed in [3, 14]. However, it is important to
evaluate the transient stability of the GFC equipped with such current limit
methods for all possible transient events.

Recently many studies have analyzed the transient stability of GFC [15, 9, 16,
13]. Some of these studies were conducted on GFC with no current limit
implemented [15, 9]. A current limit is likely to be triggered in a practical
transient event scenario. Therefore studying the GFC for transient events
requires the inclusion of the current limit for a practical understanding. The
transient stability of a droop-based grid forming converter with the current
limit is studied in [16, 13] and methods are discussed for improving the
transient stability, however, discussed approaches are not intuitive and
requires tuning of parameters. In addition, all the transients studies have
been restricted only to a voltage dip event when connected to an infinite
voltage source. A GFC, when operated in a microgrid in parallel with an SG and
virtual impedance current limit, can avoid the wind-up effect of the outer
loop for load change events [3]. However, only a limited evaluation of droop
control-based GFC only for load change events has been shown. The frequency
and phase jump events are significant in the present context for the power
system with a significant renewable share and low inertia. Therefore transient
events such as a change of frequency and phase jump can cause current limit
triggering for GFC. A detailed study on GFC under such transient events or in
the presence of an SG is missing in the literature. Furthermore, a
quantitative analysis of the transient stability of GFC for all the possible
events is also missing literature.

This paper first demonstrates the scenarios in which the current limit could
be triggered in a GFC working in a low inertia power system and outlines the
challenges in maintaining the GFC synchronism with the rest of the grid when
the current limit is triggered for each scenario. Then, to clarify the
stability phenomena when the current limiter is activated, a quantitative
analysis of transient stability for events such as phase jump and frequency
change events and voltage dip events when the current limiting algorithm is
employed in a GFC is presented in this paper. The transient stability margins
such as maximum phase jump, maximum rate of change of frequency, critical
fault clearing time, and methods to improve the synchronization stability for
all the three events described in this paper are detailed from the conducted
analysis. Finally, a coordinated overload and current limit for grid forming
converter employing virtual power, extending the transient stability margin
for all the grid events, are proposed in this paper. Conducted analysis and
the proposed solution to improve the transient stability of the GFC is
validated using power hardware in the loop (PHIL) experimental tests are
presented. The PHIL evaluation is conducted in a simplified equivalent circuit
and a modified lower inertia IEEE 9 bus system.

##  II Grid Forming Converter Configuration

Figure 1: The configuration of 3 phase grid connected GFC system Figure 2:
General Control System of GFC with current control inner loop and virtual
admittance

The single line diagram of the GFC considered in the paper is shown in Fig. 1.
The filter circuit comprises reactor $X_{f}$, capacitor of reactance $X_{Cf}$,
and damping resistor $R_{f}$. The point of common coupling (PCC) is at the
terminal of the filter capacitor, where measurements $v_{pcc}$, $i_{pcc}$, and
$i_{g}$ are taken. The reactance $X_{tf},X_{g}$ represents the reactance of
transformer and grid impedance, respectively. The grid forming control with an
inner current control loop with current references derived from virtual
admittance is used in this paper is as shown in Fig. 2 [5, 17, 8, 12]. The
power control system consists of inertia, frequency droop, and damping
emulation through active power control ($APC(s)$) with active power setpoint
($P_{o}^{*}$). The power output from the GFC measured at the PCC ($P_{pcc}$)
is typically chosen as the feedback power ($P_{fb}$) to the active power
control loop. A lead-lag (LL) compensator-based power controller ($PC(s)$) is
employed to emulate electromechanical behaviour of the synchronous machine
[17]. The compensator is given as

$\Delta\omega_{vsc}=\underbrace{\frac{K_{pp}s+K_{ip}}{s+K_{gp}}}_{\text{PC(s)}}*(P_{o}^{*}-P_{fb})$
(1)

The compensator $PC(s)$, similar to the swing equation-based electromechanical
model can realize virtual inertia constant, H, and frequency droop $R_{d}$. In
addition, LL-based electromechanical model has an additional degree of freedom
to increase the power control’s damping coefficient ($\zeta$). The parameters
($K_{pp},K_{ip},K_{gp}$) can be calculated from a given virtual inertia
constant H in seconds, power-frequency droop gains $R_{d}$ in pu and damping
coefficient ($\zeta$).

$K_{ip}=\frac{\omega_{B}}{2*H},K_{gp}=\frac{K_{droop}}{2*H}\text{ where
}K_{droop}=\frac{1}{R_{d}}$ (2)

$K_{pp}=\zeta\sqrt{\frac{2\omega_{B}}{P_{max}H}}-\frac{K_{droop}}{2*H*P_{max}}$
(3)

Where $\omega_{B}$ is the base frequency of the system, $P_{max}$ is the
maximum static power transfer possible between the GFC and an infinite voltage
source. If the power-frequency droop is not required, the parameter
$K_{droop}$ is to be set to zero in (2)-(3). For the GFC electromagnetic
model, a quasi-stationary model has been shown superior to a dynamic
electromagnetic model model for GFC [8]. Variable superscripted with d-q are
variable vectors of the direct and quadrature frame original parameters
represented in the synchronously rotating reference frame defined by the
virtual rotor of the GFC ($\theta_{vsc}$). The electromagnetic model consists
of the internal voltage source ($E$) in series with an algebraic
representation of an impedance. It is realized by multiplying the difference
between the internal voltage source ($E^{*}$) of the GFC and PCC voltage
($v_{pcc}^{dq}$) with virtual phasor admittance resulting in reference
unsaturated stator current ($I^{dq*}_{pcc}$)

$I^{dq*}_{pcc}=\frac{E-v_{pcc}^{dq}}{R_{v}+jX_{v}}$ (4)

where $R_{v},X_{v}$ are the virtual internal virtual resistance and reactance
of the GFC. The virtual impedance is chosen such that the output impedance is
predominantly inductive with an X/R ratio of 10. The electromagnetic model of
the GFC also includes the current limiting algorithm. Fast acting current
limiters for GFC is critical as the GFC response to grid events is nearly
instantaneous. A circular current limit on $I^{dq*}_{pcc}$, as shown in (5) is
an ideal choice as it precisely limits current and preserves the angle of the
injected current and thus limiting the interaction with the active power-based
synchronization [18, 12].

The limited current vector $i_{pcc}^{dqLi{m^{*}}}$ is given by

$i_{pcc}^{dqLi{m^{*}}}=\frac{1}{KC_{lim}}*I^{dq*}_{pcc},\text{ where
}KC_{lim}=\frac{\left|I^{dq*}_{pcc}\right|}{I^{Lim}}$ (5)

$\left|I^{dq*}_{pcc}\right|$ is the magnitude of the unsaturated reference
current vector and is equal to $\sqrt{(I^{d*}_{pcc})^{2}+(I^{d*}_{pcc})^{2}}$
and $I^{Lim}$ is the nominal maximum peak current, and thus the vector
$i^{dqLim^{*}}_{pcc}$ is of the magnitude $I^{Lim}$ during current limited
operation.

The paper’s focus is on the interaction between the current limit and active
power control and its consequences on the transient stability of GFC.
Therefore, to preserve the paper’s brevity, the outer reactive power control
or voltage control is assumed to be slow. Thus, the voltage control and
reactive power control dynamics are not accounted for in this work. Also, the
DC link dynamics and other supervisory controls are not considered in this
paper for the sake of easier understanding.

##  III GFC analysis under current limit

The analysis assumes that the dynamics of the employed current limit are
faster than other control and thus time scale separated from the stability
study considered in the paper. Additionally, the paper’s focus is applying the
GFC on large power systems with a low R/X ratio; therefore, only the
reactances of the virtual impedances and grid impedances are considered in the
quasistatic analysis.

The active power ($P_{GFC}$) and the reactive power ($Q_{GFC}$) at the
internal voltage source ($E$) is given by

$P_{GFC}=\frac{E*Vg*\sin{\delta}}{X_{T}},Q_{GFC}=\frac{E^{2}-E*Vg*\cos{\delta}}{X_{T}}$
(6)

Where $X_{T}$ is the total reactance of the system from between the internal
voltage ($E$) and is equal to sum of $X_{tf}$, $X_{g}$ and $X_{v}$, and the
infinite voltage source and $\delta$ is the angle difference between the
internal voltage source and infinite voltage source and is equal to difference
between $\theta_{vsc}$ and $\theta_{g}$. The active and reactive power at the
internal virtual voltage source $E$ in the rotating dq frame defined by GFC
virtual angle ($\theta_{vsc}$) can also be written as

$P_{GFC}=E*I^{d*}_{pcc},Q_{GFC}=-E*I^{q*}_{pcc}$ (7)

The magnitude of the current vector $I^{dq*}_{pcc}$ can then also be written
as

$\left|I^{dq*}_{pcc}\right|=\frac{\sqrt{P_{GFC}^{2}+Q_{GFC}^{2}}}{E}=\frac{M_{v}}{X_{T}}$
(8)

where $M_{v}$ is equal to $\sqrt{Vg^{2}+E^{2}-2*Vg*E*\cos(\delta)}$ The
generalized power transfer equation for the GFC can then be calculated from
(5),(6),(8)

$P_{GFC}=\left\\{{\begin{array}[]{*{20}{c}}{\frac{{E*Vg*\sin\delta}}{{{X_{T}}}},\hskip
56.9055pt\left|{{i_{pcc}}}\right|\leq{I^{Lim}}}\\\
{\frac{{E*Vg*\sin\delta}}{{\sqrt{V{g^{2}}+E{{}^{2}}-2E*Vg*\cos(\delta)}}}*{I^{Lim}},{\rm{}}\left|{{i_{pcc}}}\right|>{I^{Lim}}}\end{array}}\right.$
(9)

It can be observed that the power transfer under current limited case is
independent of the network reactance. When the drop across the virtual
resistance ($R_{v}$) is neglected the active power at the internal voltage
terminal is same as $P_{pcc}$. The power angle curves for the GFC with and
without limiter activation at different grid voltage conditions are shown in
Fig. 3. It could be seen that the unstable operating points occurs at much
lower phase angle ($\delta$) and maximum power transfer possible is greatly
reduced when under current limit.

Figure 3: Power angle curves for GFC with and without limiter activation at
different grid voltage conditions

###  III-A Internal impedance of GFC during current limit

Recalling from (4) and (5) under current limit case is equivalent to the
internal impedance $Z_{in}^{cc}$ as shown below

$Z_{in}^{cc}=KC_{lim}*(R_{v}+jX_{v})$ (10)

The value for $KC_{lim}$ is automatically set due to control objective in (5)
to ensure the value of peak value of the GFC current is equal to $I^{Lim}$.
Therefore for a given sustained disturbance at the PCC the, the input
reactance ($X_{in}^{{}^{cc}}$) for the current controlled GFC in current
limited case can be written as

$X_{in}^{cc}=K_{lim}*X_{v}$ (11)

A virtual impedance based current limiting increases the internal impedance of
the GFC for limiting the current [3]. For a given sustained disturbance, the
internal impedance of GFC with voltage control equipped with virtual impedance
based current limiting should be the same as in the case of GFC structure
considered in this paper with current control and circular current limiting.
This is because both the current limiting methodologies have similar objective
of keeping the output current below nominal value without directly changing
the phase of injected current. Hence, the analysis and conclusions derived
from this paper based on GFC structure with current control and circular
current also holds true for GFC employed with virtual impedance current limit.

##  IV Transient stability Evaluation of GFC

The synchronous generator (SG) transient stability focusing on rotor dynamics
is evaluated typically for fault cases. If the rotor angle of the SG is not
diverging with the rest of the system after the fault event, the SG is stable
against transient events. The transient stability of GFC with no current limit
during under-voltage dip events has been extensively studied [9, 15]. However,
GFC’s synchronization ability has not been evaluated for other large system
transients such as phase jumps. Furthermore, few studies have investigated the
response of GFC with the current limit during large disturbances.

Figure 4: Simplified quasi-static GFC connected to infinite bus

In this section, the transient performance of GFC with adn without the current
limit implemented is analyzed during system events such as voltage dips, phase
shift, and a RoCof event, and conditions for GFC to maintain synchronism for
each event is qualitatively described. All events typically co-occur but are
studied separately here for an intuitive understanding. The quasi-static model
shown in Fig. 4 is solved numerically. The total reactance ($X_{T}$),
including the internal reactance of 0.3 pu, is chosen at 0.5 pu, both the
internal GFC voltage and infinite bus voltage are assumed to be 1 pu for the
analysis, and the current limit is set to be 1.1 pu. The damping coefficient
($\zeta$) has been set to 0.4 to study underdamped control.

###  IV-A GFC response against RoCoF

The infinite voltage source frequency $\omega_{g}$ is varied from 50 Hz to 48
Hz at a rate of change of frequency (RoCoF)-1 Hz/s. The response of the GFC
against the specified RoCof with inertia constant H of 10 s is shown in Fig.
5.

Figure 5: GFC response for a 1 Hz/s ROCOF

When the infinite voltage source is decelerating, a similar deceleration is
required from the virtual rotor of the GFC to stay in synchronism. The
necessary deceleration power in pu ($P_{dec}$) for the virtual GFC rotor is
given by

$P_{dec}=-1*\frac{2*H}{f_{vsc}^{n}}*RoCof=0.4pu$ (12)

Where the $f_{vsc}^{n}$ is the nominal frequency of the GFC. When the GFC with
no current limits and operating at a power setpoint of 0.8 pu with an
operating point at point 1 (Fig. (5)) is presented with a RocoF event, the
rotor angle moves in the trajectory 1-2-3 and settles at point 3 such that a
deceleration power of 0.4 pu is impressed on the virtual rotor according to
(12). However, point 3 is not reachable for the current limited case as shown
in Fig. 5. Therefore the trajectory on the power angle curve with current
limit follows 1-4-5, and beyond point 5, an unstable operating point is
reached, and synchronism is lost, which is reflected in all the curves in Fig.
5. When the GFC is also programmed to provide frequency droop ($Rd$) the
condition in (12) is modified to

$P_{dec}=-1*\frac{2*H}{f_{vsc}^{n}}*RoCof+\frac{\Delta\omega_{vsc}}{Rd*\omega_{vsc}^{n}}$
(13)

From (13) one can also conclude that dynamically reducing $P_{set},H,Rd$ are
some of the options to ensure $P_{dec}$ on the virtual rotor and maintain
synchronism.

###  IV-B GFC response against phase jump

Figure 6: GFC response for a phase jump of 40 deg

The GFC is expected to respond instantly to phase jumps in line with a voltage
source behavior expected of GFC. The GFC response to simulated infinite
voltage phase jump of $40^{\circ}$ is shown in Fig. 6 with power set point at
0.9 pu $P_{set}$. The grid phase jump is simulated by changing $\theta_{d}$ in
Fig. 4. From the power angle curve ($P-\delta$) of current limited and no
limit cases, it is seen that the maximum phase shift between the infinite
voltage source and GFC internal voltage is significantly reduced from
$\delta_{max}$ to $\delta_{max}^{lim}$. For the simulated phase shift, the
trajectory without limiter shifts from point 3 to 1 instantly and then falls
back to 3. Whereas for GFC with the current limit, the trajectory instantly
moves from 3-4 and thus marginally beyond the stable operating point 4 and
loses synchronism. For a given $P_{set}$ the maximum phase shift margin
possible ($\delta_{mar}$) can be solved from (9).

The inertia and damping parameters do not impact the stability margin as the
instability expected is the instantaneous response.

###  IV-C GFC response voltage dip

The event simulates a power system fault case. The infinite bus voltage is
reduced to 0.5 pu for 0.3 s with a $P_{set}$ at 0.8 pu. The power angle curve
reduces in magnitude with the reduction in infinite bus voltage, causing the
virtual rotor to accelerate. For the unlimited case, the power angle
trajectory is 1-2-5-7 and back to 1. The conventional equal area criterion for
transient stability is applicable in this case, and the acceleration area
1-2-5-7 is well less than the decelerating area 5-7-9. However, the
accelerating area 1-2-3-5 is higher for the current limited case than the
available decelerating area 5-6-8 and the momentum gained during acceleration
results in rotor angle crossing the unstable equilibrium point 8 and
instability.

Figure 7: GFC response for a voltage dip of 0.5 pu

Most of the existing studies have only evaluated the transient stability of
the GFC for fault cases. In practise, GFC is not a rotational rigid body as
SG, wherein it is difficult to achieve the mechanical power input reduction
during fault cases through fast valving or by dynamic braking resistors,
thereby limiting the acceleration torque. Both fast valving and dynamic
braking can be easily implemented in a GFC by dynamically changing the power
reference or simply freezing the power-based synchronization for a short
duration [19, 20], provided there are sufficient capacity for energy
dissipation. Another possibility is to increase P-F droop $Rd$, increase
programmed inertia H, the stability margin improves as the rotor acceleration
is reduced with higher inertia and damping, unlike the RoCof case.

##  V Proposed virtual power based GFC

The challenge with saturating current is that the active power output becomes
insensitive to change of phase, thereby rendering the synchronization control
ineffective. In addition methods such as dynamically changing $H$ and $R_{d}$
is complicated and contradictory for different transient events as explained
in the previous section. To counter such limitation, this paper proposes
utilizing the unsaturated current references ($I_{pcc}^{dq*}$) for power
measurements for the synchronization loop instead of active power measurements
at the PCC, i.e. the active power feedback to $APC(s)$ is chosen as

$P_{fb}=P_{virt}=\frac{3}{2}(V_{pcc}^{d}.I_{pcc}^{d*}+V_{pcc}^{q}.I_{pcc}^{q*})$
(14)

One could also measure the virtual unsaturated power at the GFC virtual
internal voltage terminals. Utilizing the virtual unsaturated power as the
feedback or controlled parameters for the power synchronization is analysed in
this section.

Figure 8: Electrical equivalent circuit of the GFC with unsaturated active
power feedback as synchronisation during current limit

###  V-A Analysis of virtual power based GFC

For calculation of the virtual power, the unsaturated current references are
used, whereas the GFC actual output current when GFC enters the current limit
is the saturated current defined by Eq. (5). When the GFC is not in the
current limit operation, there is no difference between the $P_{virt}$ and
$P_{pcc}$ as long as the current control dynamics are neglected. In practice,
the current controller is much faster than the power control loop, and thus
the impact of current control dynamics on the choice of power feedback is
minimal. Hence an equivalent electrical circuit as shown in Fig. 8 can be
drawn to represent the GFC employed with virtual power feedback. During the
current limit operation with virtual power feedback, dividing the current
reference by $KC_{lim}$ is equivalent to dividing the net grid side reactance
by $KC_{lim}$ as shown in Fig. 8.

Figure 9: Power angle curves for GFC with and without limiter activation with
virtual unsaturated power feedback for power synchronism loop Figure 10: GFC
response for a 1 Hz/s ROCOF with virtual power feedback Figure 11: GFC
response for a phase jump of 40 deg with virtual power feedback Figure 12: GFC
response for a voltage dip of 0.5 pu with virtual power feedback

From the equivalent circuit shown in Fig. 8 the unsaturated active and
reactive power when when $\left|{{i_{pcc}}}\right|>{I^{Lim}}$ can be
calculated

$P_{unsat}=\frac{E*Vg*\sin{\delta}}{Xv+X_{T}/KC_{lim}},Q_{unsat}=\frac{E^{2}-E*Vg*\cos{\delta}}{Xv+X_{T}/KC_{lim}}$
(15)

The $KC_{lim}$ can be calculated similar to (8)

$KC_{lim}=\frac{\sqrt{Vg^{2}+E^{2}-2*Vg*E*\cos(\delta)}}{Xv+X_{T}/KC_{lim}}*1/I^{lim}$
(16)

simplifying one can write

$KC_{lim}=(\frac{Mv}{I^{lim}}-X_{T})/Xv$ (17)

Thus virtual unsaturated power when $\left|{{i_{pcc}}}\right|>{I^{Lim}}$ for
can be simplified and written as independent of $KC_{lim}$ as

$P_{virt}=P_{unsat}=\frac{E*Vg*\sin{\delta}}{X_{v}+Xv.XT/(Mv/I^{lim}-XT)}$
(18)

From (15) and (18) one can easily observe that the current limit activation
inherently extend the peak of the power angle characteristics when virtual
power $P_{virt}$ is utilized as the feedback variable even beyond the power
transfer limit for unlimited case. This can be verified by plotting the power
angle curve for GFC with virtual power feedback as shown in Fig. 9. This
feature greatly increases the synchronization stability margin of all the
cases discussed in the previous section.

The cases studies conducted in the previous section are repeated with virtual
power feedback and the results are as depicted Fig. 10-12. As shown in the
figures the GFC with virtual power feedback when in current limited operation
can sustain all the large transient events discussed in this paper.

TABLE I: PHIL Scaling for the VSC hardware

Symbol | Description | Physical Value | Scaled to Simulation
---|---|---|---
$V_{vsc}$ | Amplifier voltage | 123 V | 12.3kV
$P_{vsc}$ | VSC power | 1.5 kVA | 70 MVA

Figure 13: Power hardware in the loop configuration for GFC testing Figure 14:
PHIL GFC connected to infinite voltage source, response for a 1 Hz/s ROCOF
Figure 15: PHIL GFC connected to infinite voltage source, response for a phase
jump of 40 deg  Figure 16: PHIL GFC connected to infinite voltage source,
response for a voltage dip of 0.5 pu Figure 17: Power hardware in the loop
with RTDS simulated modified IEEE-9 bus system

##  VI Experimental results

The analysis presented in the previous section is validated through power
hardware in the loop (PHIL) simulation. The configuration of the power
hardware in the loop study is as shown in Fig. 13. Firstly, the PHIL study is
conducted for GFC connected to an infinite voltage source to validate the
analysis presented in section IV. The 230 kV infinite voltage source with
Thevenin grid impedance and 230/12.3 kV transformer is simulated in Realtime
Digital Simulator (RTDS). The per unit values of the grid impedances and
tranformer impedances remain the same as in section IV with a base power of
100 MVA. A SEMIKRON SkiiP Voltage Source Converter (VSC) stack with an
inductive filter and current and voltage sensors and a 2.5 kVA SPITZENBERGER
SPIES PAS 2500 linear amplifier are the hardware elements used in the
experimental study. An Ideal Transformer interface method is used to interface
the real-time simulation, and the hardware via the amplifier [21]. The RTDS
I/O cards are used to exchange the PCC voltage from RTDS to the amplifier and
the current coming into the amplifier to the RTDS. This exchange ensures that
the VSC is part of the power system network. The voltage and current signal
between the RTDS and the hardware is scaled, and the scaling ratio is shown in
Table. I. The current feedback signal is conditioned with a first-order low
pass filter with a time constant of 250 $\mu s$ to eliminate noise and ensure
the stability of the PHIL.

Figure 18: The response from GFC for the VSC1 disconnection event,H is 10 s,
$P_{set}$of 0.0 pu, and P-f frequency droop $R_{d}$ of 5$\%$ Figure 19: The
response from GFC for the VSC1 disconnection event,H is 10 s, $P_{set}$of 0.5
pu, and no P-f frequency droop

The VSC switching frequency is set to 10 kHz, and the inductive filter for the
VSC stack is 8 $mH$. The GFC control with a proportional inner current control
and the current limit discussed in the paper is implemented on an FPGA-based
digital controller from National Instruments (NI). The control is discretized
using a trapezoidal integration method with a sampling time of 40 $\mu s$. The
internal control variables such as $P_{virt},\omega_{vsc}$ are captured in the
NI controller and transferred to the real-time controller via direct memory
access (DMA) first-in-first-out (FIFO) buffers and then saved to a file upon a
configurable trigger event. The waveforms at the PCC are captured in the RTDS
run time interface. Both sets of data are exported to MATLAB and replotted for
enhanced clarity. The PHIL results for the infinite bus case are shown in Fig.
14-16. The PHIL results shown for RoCoF, phase jump, and fault events are in
good agreement with the analysis presented in Section IV. The reactive current
at the PCC ($Iq_{GFC}$) is also plotted for the voltage dip case.

The PHIL study is expanded to a modified IEEE-9 system representative of
future low inertia system with limited SG as shown in Fig. 17. Two of the
synchronous generators of the at bus IEEE-9 bus system (at bus 3 and bus 1)
are replaced with a commonly used 100 MVA grid following VSC’s with active and
reactive power control [22]. The hardware GFC is connected to the IEEE 9 bus
system at bus 9, the scaling and method of the PHIL interface remain the same
as discussed before. The transmission line parameters are the same as the
original IEEE 9 bus system [23]. The dispatch power of the SG in the system is
adjusted to set the system frequency to 50 Hz. Also, the P-f droop of the SG
governer is by default 5$\%$. A generation disconnection event of the grid
following VSC1 generating 100 MW is considered in this study. Two cases with
different droop parameters and dispatch power from grid forming converter are
considered in this study. The rotor of the synchronous generator has under
damped oscillatory behavior for a load or generation disconnection event. The
response from GFC for the VSC1 disconnection event when the programmed inertia
constant is 10 s and power setpoint of 0.5 pu is shown in Fig. The active
power response of GFC, as well as the rotor speed of the SG($\omega_{sg}$), is
shown in Fig. 18. And the response from GFC for the VSC1 disconnection event
when the programmed inertia constant is 10 s and power setpoint of 0.0 pu, and
P-f frequency droop $R_{d}$ of 5$\%$ is shown in Fig.19 In both cases, GFC,
when utilizing measured active power, loses synchronism. In contrast, a
seamless entry to the current limiting and a seamless exit from the current
limit is achieved when virtual active power is used for synchronization

##  VII Conclusion

The analysis presented in this paper has revealed the potential transient
stability problem for a GFC is greatly accentuated when the GFC enters a
current limited operation under differen system events. This paper presents
the necessity to evaluate the transient stability problem with transients such
as large frequency events, phase jumps, and voltage dips instead of limiting
the transient stability analysis just to a fault conditions. A quantitative
and illustrative study for the GFC with current control operating against
large transient is presented. The paper proposes utilizing the internal
virtual power derived from unsaturated current references for ensuring the
synchronization under large transients when output GFC current is limited. The
results from the Power hardware in the loop (PHIL) experimental tests both on
a single GFC connected to an infinite bus as well as on a modified IEEE-9 bus
system demonstrates the transient stability challenges for a GFC and the
validates of enhanced transient stability of using a virtual power for GFC
synchronization.

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|  Kanakesh Vatta KKuni (S’18) is a PhD student at the Technical University of
Denmark (DTU). He received his Master’s degree in Electrical Engineering from
the Indian Institute of Technology Bombay in the year 2014. From 2016 to 2018,
he was Research Engineer in Berkeley Education Alliance for Research in
Singapore, while from 2014 to 2016, he worked as a Research Engineer in Energy
Management and Microgrid Lab of the National University of Singapore (NUS).His
research interests include power system stability, power converter control and
microgrids.
---|---
|  Guangya Yang (M’09, SM,14), senior researcher at Technical University of
Denmark. He obtained PhD from the University of Queensland, Australia in 2008
afterwards joined Technical University of Denmark as postdoctoral fellow,
researcher, and later associate professor. From 2020 to 2021, he was full-time
working for Orsted as specialist on electrical design, control, and protection
of large offshore wind farms. His research field is security, stability and
protection of power systems, with focus on offshore wind applications. He is
member of IEC TC88 and TC8, and senior member of IEEE. He has received
numerous research grants as principal investigator with the recent H2020
Marie-Curie Innovative Training Networks project InnoCyPES (2021-2025) as
coordinator. He is currently leading the editorial board of the IEEE Access
Power and Energy Society Section, and is editorial board member of IEEE
Transactions on Sustainable Energy, IEEE Transactions on Power Delivery, and
Journal of Modern Power System and Clean Energy.
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