The increase in percentage of inverter interfaced generation has resulted in engineering and mathematical insight being obtained into possible stability concerns that may arise due to the interaction of fast inverter controllers with a fast moving system. In such a scenario, it is always of interest to system planners to ascertain the exact percentage of inverter based generation beyond which, there is an absolute certain probability of stability issues. Recent results in literature have reported various such percentage values after which state-ofthe- art phase locked loop (PLL) based ‘grid following’ inverter controls would be unstable. In this paper, it will however be shown that generalization of these percentage values across every system and scenario may possibly be premature as with modifications to phase locked loop based controls, and with reasonable tuning of the controls, it can indeed be possible to operate an all inverter system with all inverters having phase locked loop based ‘grid following’ controls.

1. ฀ ฀ ฀ ฀ ฀ ฀ ฀
62
Abstract
The increase in percentage of inverter interfaced
generation has resulted in engineering and mathematical
insight being obtained into possible stability concerns
that may arise due to the interaction of fast inverter
controllers with a fast moving system. In such a scenario,
it is always of interest to system planners to ascertain
the exact percentage of inverter based generation
beyond which, there is an absolute certain probability of
stability issues. Recent results in literature have reported
various such percentage values after which state-of-
the-art phase locked loop (PLL) based ‘grid following’
inverter controls would be unstable. In this paper, it
will however be shown that generalization of these
percentage values across every system and scenario may
possibly be premature as with modifications to phase
locked loop based controls, and with reasonable tuning
of the controls, it can indeed be possible to operate an all
inverter system with all inverters having phase locked
loop based ‘grid following’ controls.
1. Introduction
With very few exceptions, almost all bulk power system
(BPS) connected large capacity inverter based resources
(IBR) have a control structure which is termed as ‘grid
following’ as it involves the use of a high bandwidth
synchronous reference frame PLL [1] controller which
is responsible for tracking the angle of the grid voltage
in order to allow the inverter to remain in synchronism
with the grid. PLL based inverter controls are largely
designed to control an inverter as a current source as the
objective of inverter based resources is predominantly
to provide a pre-defined value of active power (Pref
) and
reactive power (Qref
) while ensuring safe operation of the
inverter. To meet this objective the magnitude and angle
of the terminal voltage (|Vmag
|
by the inverter controls at every time step to generate
reference current commands as per (1).
(1)
Additionally, it must also be ensured that the actual
current drawn by the network from an inverter is the
same as the reference current, and thus, an additional
control loop exists to make changes to an inverter’s ac
output voltage |E| such that
(2)
where, Rf
+ jXf
represents the output filter impedance,
which can include both the impedance of the filter
inductance and inverter transformer. Since an inverter
is a current sensitive device, the control loop for the
evaluation of and ensurance of |I | Iref
| ref
must
be fast and achieve steady state within milli-seconds of
the occurrence of a change.
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Fig. 1. One line diagram of interface of each inverter
Increase in inverter based generation displaces
conventional synchronous machines which results in a
reduction in the available short circuit capacity in the
Operation of an ll nverter
ulk ower ystem with onventional
rid ollowing ontrols
D RAMASUBRAMANIAN*, W BAKER, and E FARANTATOS
Grid Operations & Planning Group, Electric Power Research Institute,
Knoxville, Tennessee, USA
KEYWORDS
All inverter power system, grid following, phase locked loop
*dramasubramanian@epri.com

2. ฀ ฀ ฀ ฀ ฀ ฀ ฀
63
Instead, controllers that would allow the grid to view an
inverter as a voltage source rather than a current source
would be required [4]–[6]. These controllers essentially
allow the magnitude and phase of the injected current to
be largely uncontrolled as long as it is within the current
limits of the inverter power electronic components. This
allows for fast injection of current into the network.
Although an inference may be made that such an
operation would not be possible if a PLL exists [7], in
this paper, the viability of operating a 100% inverter
based system with only PLL based ‘grid following’
control architectures will be presented. This operation is
made possible by,
es into the structure of the phase
locked loop,
tuning of the controller gains, and
an outer loop angle control.
Additionally, some insight of the reasons behind the
viability of such an operation of the system will be
discussed along with guidelines provided to transmission
planners. It must however be noted that the intention of
this paper is not to conclude that PLL based conventional
inverter controls would always work in every all inverter
system. Rather, it is to bring to light that like any other
control system, the base structure of the controller
can be made more robust with modifications. Further,
the stability of the bulk power system hinges upon its
many devices operating in a cooperative manner with
each other and as a result, even with individual ‘grid
following’ controls, a set of inverter devices could
potentially follow each other to bring about stability.
The following section describes the structure of the
inverter controls used in this study while a mathematical
system. Additionally, newer inverter based power plants
tend to be located geographically far away from load
centers and also from the nearest transmission bus. Thus,
they are connected to the bulk power system through long
transmission lines. While such an interconnection may
not be unique to IBRs and can equally occur with new
synchronous machine plants, longer transmission lines
have a larger impact on stability of IBRs than rotating
machines. In a system with long lines, small changes in
injectedcurrent|I| cancauselargechangesinterminal
voltage |Vmag
| . Upon occurrence of a system event
that causes a change in terminal voltage, the controls of
an inverter would try to change the value of their injected
current to satisfy their primary objective of injection of
a fixed magnitude of power. The control exerted to bring
about this change in injected current however cannot
occur instantaneously and as the PLL and the current
control loops are minimizing the input error, there would
be changes in the injected current which would result in
large changes in voltage and thus further increase the
required effort from the control loops thereby potentially
leading to an unstable scenario. Therefore, the root
cause of the instability is fast controllers trying to lock
onto a fast moving system in order to maintain rigid
current control. From basic control theory, we know
that use of high bandwidth fast controllers to control a
process in a fast moving system drastically reduces the
stability margin of the controller. Thus, it follows that
conventional ‘grid following’ inverter based generation
may be unable to operate in a 100% inverter system. It
has been independently shown in both [2] and [3] that
to achieve inverter based generation levels greater than
65% of the load served, the presence of ‘grid following’
controls would be detrimental to system stability.
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Fig. 2. Control architecture of each inverter
Fig. 3. PLL structure of each inverter

3. ฀ ฀ ฀ ฀ ฀ ฀ ฀
64
bandwidth control structures, have precedence for use
[16]. In implementing the outer loop angle droop control,
the angle reference ( ref
in Fig. 2), is the angle of the
terminal bus voltage of the inverter itself at a previous
point in time, when the system was in steady state [17].
The inclusion of the rate limit in the PLL control path
serves to slow down the controller without loss of
accuracy. Due to this, upon the occurrence of a fast
system event such as a fault in a low short circuit
area, due to the rate limit, the PLL changes its output
angle slowly. By changing slowly, it is ensured that the
injected current is not at a large erroneous angle with
respect to the terminal voltage. Further, by changing
slowly, the angle is perceived to be constant or frozen in
the immediate aftermath of a grid disturbance. In certain
PLL architectures, when the voltage magnitude goes
below a pre-defined threshold, the value of the angle
output is actually frozen at the last known value. While
this does provide a sense of robustness to the control,
it is more likely to be stable only as long as the system
angle during the event does not change by a large value.
In addition to the ramp rate limit on the PLL input, the
active power - frequency droop control loop and active
power - angle droop control loop play a vital role in
stabilizing the output of the converter. Here, it is assumed
that all frequency measurements used in the controller
come from the PLL. Further, vabc
and iabc
are filtered to
remove any high frequency components. As with shown
in the next section, these power control loops introduce
a measure of positive damping that is important for the
inverter system to ride through a disturbance.
3. Mathematical basis for viable
operation
In order to provide a mathematical basis for the viability
of this control system, consider an equivalent network
shown in Fig. 4. Here, first, all loads are represented by
a representative impedance for both active and reactive
power. As the IBR control architecture contains a fast
phase locked loop and inner current control loop, it
is represented as a controlled current source whose
current output i is a function of its terminal voltage.
Upon disconnection of the equivalent voltage source,
the equivalent circuit can be reduced as shown in Fig. 5.
Here, the disconnection of the equivalent source is
basis is provided in Section III. Sensitivity analysis and
comparative studies are discussed in Section IV.
2. Structure of the controller
For the case studies conducted in this paper, the inverter
control model used is a generic representation of standard
controls. The one line diagram of the inverter interfaced
to the network is shown in Fig. 1 while a generic control
architecture is shown in Fig. 2 [8]–[12]. In this cascade
control architecture, the outer control loop generates
the current references for the inner current control loop
based on the control objective of the IBR. Although
there are various control methods utilized in the plant-
level and outer loop controllers for BPS connected IBR
as described in [13], one common control objective of
the outer loop controller is to regulate the ac terminal
voltage to develop iqcmd
and to regulate the dc voltage to
develop idcmd
. However, under an assumption of a stiff
dc bus (or fast dc bus voltage controller), an alternative
way of generating the value of idcmd
is directly from the
active power reference Pref
as shown in the figure. A stiff
dc bus could be unrealistic in an IBR resource without
availability of an energy storage buffer. However, as
the power system moves towards increased percentage
of IBRs, presence of energy storage devices (either as
standalone IBR systems or as part of a hybrid power
plant) is expected to increase. A current-controlled
inverter includes a PLL to track the angle of the grid
voltage t
. The specific implementation of a commercial
PLL is usually proprietary as it is critical to the
performance of the IBR. However, the synchronous
reference frame PLL (SRF-PLL) as shown in Fig. 3 is
the basic building block for three-phase applications
of a commercial PLL [14]. Given the primary focus of
this paper is not related to the PLL’s performance under
unbalanced and distorted grid conditions, the SRF-PLL
is determined to be adequate to represent the dynamics
of the PLL for the purpose of this paper. As the scope of
the paper is to primarily investigate fault ride through
behavior and response to load-generation imbalance, an
average model of the inverter is sufficient [9], [15].
This paper investigates the impact of additions to the
typical control structures as shown in red in Fig. 2 and
Fig. 3 to allow the use of the grid-following control
structure to operate in a 100% IBR grid. Additions
of this type, while being different from generic high

4. ฀ ฀ ฀ ฀ ฀ ฀ ฀
65
has a voltage control loop, the reactive power command
(and correspondingly iqcmd
) is itself a function of terminal
voltage. Hence, the current output from the IBR can be
written as,
(5)
The voltage control loop is represented as a single
proportional controller with a gain of Ka
.Applying Ohm’s
Law and Kirchhoff ’s Current Law at the IBR terminal,
(6)
(7)
where and
.
From this equation, it can be seen that if active power is
held rigid at the reference value, then mathematically,
the value of voltage angle 7
cannot be directly evaluated
and can instead take any value. If this value of angle can
attain any value in steady state, then during a transient,
a controller which relies on knowing the value of this
angle for operation may not be able to work satisfactorily.
Further algebraic manipulation of the equation results in
(8)
With a known value of Pref0
and Qref0
, then value of
voltage magnitude v7
can be evaluated. The expression
can be written as
assumed to occur after initialization of the system. In
this paper, blackstart of an inverter based system is out of
scope and will considered in the future. However, robust
and stable fault ride through behavior will be shown in
later sections of the paper.
In the first step of the reduction, the impedances Z34
, Z42
,
and ZL6
are converted from
resulting in,
(3)
Here, in addition to the load impedance, ZL5
and ZL6
also include the respective line charging admittances
es and impedance of the load
transformer. Z10
and Z40
are the impedances related to the
line charging admittances at buses 1 and 4 respectively.
In the second step, once again the
applied to obtain,
(4)
The current output from the IBR is a function of the
voltage at its terminals and also a function of the active
power and the reactive power command. Since the IBR
Fig. 4. Equivalent network of a small system
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Fig. 5. Reduction of equivalent network of small system
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5. ฀ ฀ ฀ ฀ ฀ ฀ ฀
66
all inverter system, the above analysis shows that when
controlled as a current source, an increase in active power
load can be discerned by the inverter using the resultant
voltage angle. Assuming that a decrease (or increase) in
voltage angle is to be related to a required increase (or
decrease) in electrical power output, then this natural
change in voltage angle as a disturbance occurs could be
used to serve as an indicator of the status of the system,
and as an input to an active power controller.
Hence, with an electrical frequency - active power droop
controller and an angle droop controller enabled, the
input to the controller would be the electrical frequency
and angle evaluated by the phase locked loop from an
input sinusoidal voltage wave. The active power output
of the IBR now becomes,
(12)
Now, equation 8 can be written as,
(13)
Here, if Kferr
0, then = 1 in steady state. The equations
can be solved for both 7
and |v7
|. While the steady state
solution does not include the frequency droop portion,
the presence of frequency droop (i.e. Drp 0) is crucial
in the transient time frame as it results in reducing the
spread of the angle.Thus, with an active power controller,
the measured PLL angle is used to generate a frequency
signal which is subsequently used to guide the active
power command and thus active current command in a
favorable direction.
The performance validation of this control scheme will
be shown in the next section.
4. Simulation results
The ability of a single phase locked loop based inverter
to serve load in an isolated system is on the surface
thought to be not possible as it can be argued that a
phase locked loop by default requires an external grid/
voltage source to track in order to ascertain a value of
angle to be followed. While this is certainly true if such
an inverter is to blackstart a network, it need not be
true if an all inverter microgrid islands from the rest of
the network. The presence of outer loop controls now
becomes crucial and important. This hypothesis is tested
(9)
Thus, if then In other
words,ifthevoltagecontrollercanensurethatthereactive
power output command is proportional to the active
power command with the proportionality constant being
tan of the Thévenin equivalent admittance angle, then
the voltage magnitude would meet the required voltage
reference. However, knowledge of the admittance angle
during a transient is not straightforward as accurate
measurement of the admittance requires a known value
of voltage angle to serve as the reference for the angle of
current. Further, even if the value of voltage magnitude
is evaluated, the value of current cannot be uniquely
evaluated as a unique value of does not exist.
When controlled as a current source, the current injected
by the inverter can only change after v7 7
has been
measured.
Thus, for a brief instant of time after the occurrence
of a disturbance, the structure and/or characteristics of
the network (viewed by the inverter only as Geq
+ jBeq
)
would have changed but the current injected would be
the same as before the occurrence of the disturbance. Let
the injected current before the disturbance be defined as
it
, the terminal voltage defined as (v7 )t
, and the
equivalent admittance defined as (Geq
+ jBeq
)t
. Upon the
occurrence of a disturbance, the equivalent admittance
would change to (Geq
+ jBeq
)t+
while the injected current
would remain at it
. The change in terminal voltage due
to this can be evaluated as
(10)
For an increase in active power load, (Geq
)t+
(Geq
)t
.
Additionally, this will also result in (|Beq
|)t+
(|Beq
|) .
Thus, with no initial change in current injection, due to
the change in the equivalent admittance,
(11)
This reduction in the voltage angle can be likened to
‘slowing down’of the electrical voltage phasor.Although
the relationship between electrical power output and
measured frequency is still not definitely defined for an

6. ฀ ฀ ฀ ฀ ฀ ฀ ฀
67
around 38 MW and the surplus 4 MW being delivered to
the external grid.The IBR controls the voltage magnitude
at bus 7, however it initially does not have an active
power frequency controller. At t = 7s, the equivalent
source at bus 2 is disconnected without the occurrence
of any fault. Now, the entire active portion of the system
consists of a single inverter resource connected through
to static and dynamic loads. Since the
external grid has been disconnected, it can be expected
that the entire system would now become unstable as the
PLL has no grid to follow.
In the controller, Drp was set to 0.0, while Kferr
and K
were set to 2.0 and 0.55 respectively. The PLL controller
gains were set to Kp,pll
= 60.0 and Ki,pll
= 700.0 while the
inner current control loop was tuned to have a damping
coefficient of 0.7 and time constant of 0.01s resulting in
Kip
= 0.24 and Kii
= 73.0 for a filter reactance of 0.15pu
on the MVAbase of the converter. The outer loop voltage
controller had values of Kvp
= 0.1 and Kvi
= 10.0. The
inverter was set to reactive current priority mode with
a maximum current limit of Imax
= 1.1pu and maximum
reactive current limit of Iqmax
= 1.0pu. Fig. 7 shows the
active power output of the IBR and electrical frequency
measured at the terminals of the IBR at bus 7, while the
voltage magnitudes at the IBR bus, equivalent source
bus, and feeder substation is as shown in Fig. 8. As
expected, when the equivalent source is disconnected,
the IBR control loop is unable to lock onto any grid signal
resulting in an unstable scenario. Upon disconnection of
the equivalent source, the active portion of the system
has a surplus generation of about 15MW and since the
PLL does not have a stiff voltage that it can follow, the
controllers of the IBR do not have the controllability to
take action based on this change in load angle on the grid.
Note that although the controllers have observability of
the change, they do not have controllability to react to
the change and so they continue to try and maintain the
pre-disturbance level of active power resulting in an
unstable system.
With a value of Drp = 20, the active power and electrical
on two systems, one small and one large. All simulations
were carried out in electromagnetic transient simulation
software PSCAD® .
A. Small Test System
A seven bus system as shown in Fig. 6 was used for
analysis. The source at bus 2 is representative of the
external system to which the rest of these six buses are
connected. The source impedance of the source at bus
2 was set to 13.0pu on its self MVA base of 1000 MVA
while an inverter based resource was connected to bus 7.
The static loads on bus 5 and bus 6 were represented by
constant current active power and constant impedance
reactive power. Additionally, on bus 6, a small
distribution feeder with a few three phase induction
motor loads and unbalanced phases was also connected.
The total load drawn by the feeder was around 1.0 MW.
The IBR has a standard control structure as shown in
Fig. 2 with a fast inner phase locked loop to determine the
grid angle, an inner current control loop to ensure rigid
current control, and an outer voltage magnitude-reactive
power controller and frequency-active power controller.
The inner control loops (i.e. phase locked loop and
current control loop) are present in some form in every
inverter based resource connected to the grid today. The
outer frequency control loops are however not present
in most inverters connected to today’s power network.
Federal Energy Regulatory Commission (FERC) Orders
842 however mandate future IBRs connected to the
bulk power system to have a functional active power-
frequency governor droop like control. Additionally, the
NERC IRPTF has also specified performance guidelines
[11], [18] that could be beneficial for the bulk power
system, and they include performance specifications
for frequency-active power control and voltage-reactive
power control. Thus, the control architecture used for the
IBRs in this study can be the expected control for near
term future IBRs that connect to the system.
Initially, the equivalent source is connected and the flow
of power is as shown in Fig. 6 with the IBR generating
Fig. 6. Single line diagram of small seven bus system under study

7. ฀ ฀ ฀ ฀ ฀ ฀ ฀
68
interfaced) devices. An optimal controller gain tuning
exercise would have to be carried out while keeping
these risks in mind.
A comparison of the change in magnitude and phase
angle of the inverter terminal voltage and injected
current is shown in Fig. 11. Upon the occurrence of the
disturbance (i.e. disconnection of the equivalent source),
due to the loss of load (as the equivalent source was
sinking active power), the terminal voltage magnitude
and angle increase with a large rate of change. On the
other hand, the magnitude and angle of the injected
current are comparitively slower to change as their
change is governed by the control loops of the inverter.
However, due to the presence of the frequency droop
controller which transiently guides the active power
command, the system is able to arrive at a stable operating
point. The traces in these figures also validate the
analytical reasoning that has been previously described.
frequency is as shown in Fig. 9 while the voltage
magnitude is shown in Fig. 10. It can be seen that inspite
of not having a grid to ‘follow’, the system is stable
upon disconnection of the equivalent source and the sole
inverter in the system is able to serve load. It is possible
that the transient values of voltage and frequency may be
unacceptable with today’s protection setting thresholds
however it must be kept in mind that as the objective of
this analysis to investigate the conceptual operation of
an all IBR system, the control system architecture used
for this analysis is neither an optimal control system,
nor is it designed from the perspective of being a robust
control system. Further, a high frequency harmonic
filter would have to be used. Additionally, as with any
control scheme, the presented control scheme does not
necessarily mitigate the risk of sub-synchronous or
super-synchronous control interactions in the presence
of series compensated transmission lines, other network
resonances, or local dynamic (or power electronic
Fig. 8. Voltage magnitude of IBR for disconnection of equivalent source
Fig. 7. Active power of IBR and electrical frequency for disconnection of equivalent source

8. ฀ ฀ ฀ ฀ ฀ ฀ ฀
69
following’. Before the disconnection of the external
grid, the inverter controller follows the angle of the
external voltage source in order to set its own angular
position to deliver the required active and required
power. However, when the external voltage source is
disconnected, what is the grid for the inverter to follow?
The inverter resource is the only remaining active energy
source in the system and should have to conceptually
be responsible for forming the grid in order for loads
to be served. However, apart from the outer loop active
power and voltage controls (which has been termed as
‘grid supporting’ controls in literature and have also
been listed to require the presence of an external grid),
the inner fast control loops of this inverter are similar to
conventionally accepted ‘grid following’ controls.
Thus, if the injection of current from a current source
is varied in a manner that will oppose the direction of
change in terminal voltage, it is potentially possible
A comparison of the voltage magnitude and phase angle
at bus 7 is shown in Fig. 12 for varying values of droop
gain of the controller. With very low frequency droop
control (Drp = 2), immediately after the disturbance (i.e.
disconnection of equivalent source) the angle increases
with a large rate of change as the change in injected
current is lower than the needs of the system. With an
adequate value of droop, the rate of change of angle is
slower and ultimately stable.
The analytical reasoning and the working of the controls
hold true even for a subsequent increase in load. At
t = 9.0s, the load at bus 5 is increased by 6 MW and
1.5 Mvar (a 20% load increase). The additional load also
has a characteristic of constant current for the active
power and constant impedance for the reactive power.
The electrical frequency and active power output of the
inverter is shown in Fig. 13.
This operation brings into question the notion of ‘grid
Fig. 9. Active power of IBR (with active power frequency droop) and electrical frequency for
disconnection of equivalent source
Fig. 10. Voltage magnitude of IBR (with active power frequency droop) for disconnection of
equivalent sourc

9. ฀ ฀ ฀ ฀ ฀ ฀ ฀
70
The rest of the system is equivalenced and represented by
two equivalent generators located within one bus away
of each other. The equivalent generators are represented
as ideal voltage sources. The total load in this portion of
the system is 450 MW/68 Mvar, represented as constant
power static load. Each inverter is set to operate on a local
voltage control mode wherein they aim to control the
for the closed loop control to be stable. It however
goes without saying that time delays in measurement,
communication channels (if any), and values of gains
will influence the stability profile of the closed loop
system.
B. Large Portion of Utility System
To observe the performance of this all PLLbased inverter
control on a larger system with more than one inverter
source, a portion of the grid of a large North American
electric utility has been used. The section of the system,
as shown in Fig. 14, consists of 9 inverter interfaced
power plants (labeled A to I), with a total capacity of
894.3 MVA and total dispatch level of 450 MW. The
MW size and short circuit rating at each inverter location
is tabulated in Table I.
Fig. 11. Change in IBR terminal voltage and injected current magnitude and phase angle for disconnection of
equivalent source
Fig. 12. Variation of voltage magnitude and phase angle at bus 7 for variation in droop gain
TABLE I. Short circuit strength at inverter locations
Inverter MVA Rating MW SCR at POI SCR at terminal
A
B
C
D
E
F
G
H
I
60
166
190
166
8
25
25
117
125
50
100
100
100
7
15
15
30
30
3.328
6.499
3.934
4.775
31.705
10.145
10.145
11.91
15.215
1.696
4.315
4.084
4.371
12.578
10.022
9.934
10.393
11.079

10. ฀ ฀ ฀ ฀ ฀ ฀ ฀
71
The short circuit strength at the terminals of each IBR
(not at the POI) after the trip of G1 and G2 are tabulated
in Table II. There is some uncertainty in the industry
regarding the representation of fault current contribution
from IBRs during evaluation of SCRs. In an all IBR
system (such is the scenario after trip of G1 and G2)
all IBRs can either be assumed to be constant current
sources which do not contribute fault current or IBRs
can be assumed to be controlled current sources whose
control algorithms could provide a maximum of 1pu fault
current. The SCRs under both scenarios are tabulated in
Table II.
Table III shows the initial values for K and Drp for
all 9 inverters. The values of Drp for the individual
inverters were arbitrarily chosen. However, as inverters
H and I had the maximum available headroom, their
droop gain was set to a high value. Firstly, it has been
checked if the system remains stable for faults at any
of the three locations with K = 0 at all the inverters.
The results suggest that the system does remain stable,
provided inverter A is tripped following the clearance of
fault at location 1. This trip would be allowed because
fault location 1 is the POI of inverter A. Therefore, for
the rest of the simulations it is assumed that inverter A
trips followed by the fault clearance at location 1.
voltage magnitude at their own terminals and not at the
point of interconnection. No secondary voltage control
devices such as STATCOMs or SVCs are in service
within each inverter plant. With this configuration, the
two equivalent generators, henceforth referred to as
G1 and G2, have a power flow solution of -20 MW/34
Mvar and 16 MW/-30 Mvar respectively. It can be seen
that with this dispatch level of the inverter plants, and
the loading level in this system, the flow to/from the
equivalent generators are initially minimal.
If the equivalent sources G1 and G2 are disconnected
from the network, then the entire system becomes an all
inverter system. In such an operation paradigm where the
system is 100% IBR, it is imperative that the IBRs have
some form of active power sharing enabled. In Fig. 2,
the gains K and Drp govern the proportion of active
power sharing burden taken upon by the inverter. After
becoming a 100% IBR system, subsequent faults were
applied at the 69kV POI of Inverter A (fault location 1),
138 kV POI of inverters C, E, F, and G (fault location 2),
and roughly at the middle of the system (fault location 3).
In all situations, the IBRs were controlled in a reactive
current priority mode which aims to inject reactive
current during fault until the current limit.
Fig. 13. Active power of IBR (with active power frequency droop) and electrical frequency for
disconnection of equivalent source and subsequent increase in load
TABLE II. Short circuit strength at inverter locations
Inverter MVA Rating MW SCR assuming IBR fault contribution is zero SCR assuming IBR fault contribution is 1pu
A
B
C
D
E
F
G
H
I
60
166
190
166
8
25
25
117
125
50
100
100
100
7
15
15
30
30
1.727
3.214
3.652
3.289
12.728
10.135
10.234
8.125
8.537
2.880
4.518
4.937
4.595
13.913
11.539
11.634
10.871
11.422

11. ฀ ฀ ฀ ฀ ฀ ฀ ฀
72
inverter I, H, or E had to have a nonzero value of Drp.
When only inverters A, B, C, and D had a nonzero value
of droop, Fig. 15 depicts the frequency of the system,
unstable for a fault at location 2. Even with nonzero K
at all inverters, the system gets unstable if all the other
inverters aside from A, B, C, and D have Drp = 0. But,
when inverter H is assigned a nonzero value of Drp in
addition to inverters A, B, C, and D Fig. 16 and Fig. 17
show the stable active power and frequency.
At first, this response may seem counter-intuitive as
traditionally, the frequency-active power droop control
loop is not associated with aiding fault ride through.
However, it can be seen from Fig. 18 that even with a
small value of Drp, the controller aids in the fault ride
through by immediately reducing the injected active
current which reduces the phase separation of the inverter
with respect to the rest of the system. By reducing the
phase separation, upon fault clearance, the inverter is
able to ride through the fault and stay synchronized.
For location 3, if inverter I has Drp = 0, none of the
other major inverters (B, D, H and I) can have Drp = 0.
Also, inverter B and H cannot have Drp = 0 at the same
time. Therefore, nonzero values of Drp for inverters
A, B, C, and I and inverter A, C, H, and I are the two
TABLE III. Initial Drp and K
Inverter A B C D E F G H I
Drp 20 2 20 2 2 2 2 50 50
K err .05 .05 .55 .05 .05 .05 .05 .05 .05
Next, the stability of the system has been checked for
Drp = 0. It was found that as Drp in converter control
has a stronger impact in terms of system stability,
it is critical to have Drp 0 for most of the inverters.
Furthermore, it has been observed that it is essential for
inverter C to have a nonzero Drp gain as it is the largest
inverter in the system. The system could survive a fault
at location 1 with Drp = 0 at C, but every other inverter
had to have a nonzero Drp gain. Since location 1 is at
the point of interconnection of inverter A, which is the
weakest location, at least 7 out of 9 inverters needed
to have a nonzero droop gain for the system to remain
stable after a fault.
However, for faults at location 2 and 3, it was found that
inverter A cannot have a zero droop gain. Hence, with
the conclusion that both inverter A and C need to have a
nonzero droop, it has been checked if the system remains
stable with Drp = 0 at all other inverters for location 2 and
3. It was observed that for the system to survive a fault at
location 2, in addition to inverters A, B, C, and D, either
Fig. 14. Single line diagram of large system under study
'
,
/
ϯ
Ϯ ϭ
'ϭ
'Ϯ

12. ฀ ฀ ฀ ฀ ฀ ฀ ฀
73
These results show that even with conventional PLL
based controls, it could be possible to have a stable and
reliable operation of an all inverter system with PLL
based controls. However, it should be recognized that
the ability of such controls to operate in any system
configuration and operating point has to be further
studied. Additionally, in this paper, only three phase
faults have been considered. In future work, the impact
of unbalanced faults will be considered.
TABLE IV. Inverters requiring nonzero Drp and K
Fault Location Nonzero K err Nonzero Drp
1 - At least 7 from B,C,D,E,F,G,H,I
2 - A,B,C,D,I, A,B,C,D,H, A,B,C,D,E
3 C A,B,C,I
3 B A,C,H,I
combinations for the system to be stable after a fault
at location 3. However, with K = 0 at all inverters,
even these two combinations do not ensure stability.
Fig. 19 shows the system is unstable with K = 0 at all
inverters and Drp = 0 at all but inverters A, C, H, and
I. Fig. 21, showing the active power flows of all nine
inverters depicts that the system stability can be restored
by assigning a nonzero K at inverter B. Fig. 21 shows
that the system frequency is stable and very close to
60 Hz.
Hence, the summarized result is presented in Table IV. It
shows where K and Drp are required to be nonzero in
order for the system to be stable after a fault in a certain
location.
Fig. 15. Frequency for fault at location 2 with nonzero K at all, and nonzero Drp only at inverter A, B, C, D.
Fig. 16. Active Power for fault at location 2 with K = 0 for all, and nonzero Drp at A, B, C, D and H.

13. ฀ ฀ ฀ ฀ ฀ ฀ ฀
74
Fig. 17. Frequency for fault at location 2 with K = 0 for all, and nonzero Drp at A, B, C, D and H.
Fig. 18. Active current command response to frequency for variation in value of Drp at inverter H
Fig. 19. Frequency for fault at location 3 with K = 0 for all, and nonzero Drp at inverters A, C, H and I.

14. ฀ ฀ ฀ ฀ ฀ ฀ ฀
75
for a specific type of ‘grid forming’ inverter controls,
transmission system planners have to carefully evaluate
the performance of existing controls to ensure that these
would not be suitable for their needs. Alternatively,
the specifications of what is meant to a ‘grid forming’
converter have to be laid out strictly in terms of expected
performance requirements rather than specific control
architecture.
6. References
[1] S. Achilles and J. MacDowell, “Challenges of OEMs Developing
New Capabilities,” [Online]: https://www.esig.energy/resources/
2019-spring-working-group-meetings/, March 2019.
[2] M. Yu, “Framework for assessing stability challenges in future
converter-dominated power networks,” Ph.D. dissertation,
University of Strathclyde, 2018.
5. Conclusion
It has been shown in this paper that for certain loading
levels and controller gains, conventional grid following
based inverter controls are capable of serving load in an
all inverter grid. Additionally, even without a stiff grid
frequency that can be ‘followed’, upon the occurrence
of bolted three phase faults, the inverters are able to
successfully ride through the event. Contrary to popular
belief wherein satisfactory riding through a fault is
attributed to the voltage and reactive power control
loops, here satisfactory fault ride through is shown
to be impacted by the gain of the frequency droop
controller (which measures frequency and sets output
power) . Thus, before requiring or recommending a need
Fig. 21. Frequency for fault at location 3 with nonzero K at inverter B in addition to nonzero Drp at inverter A, C, H and I
Fig. 20. Active Power for fault at location 3 with nonzero K at inverter B in addition to nonzero Drp at inverter A, C, H and I

15. ฀ ฀ ฀ ฀ ฀ ฀ ฀
76
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