Enhance Week Grids

1. Stability-Enhancing Measures for
Weak Grids Study
Milestone 2 Report
June 2021
Gamini Jayasinghe
Behrooz Bahrani

2. Executive Summary
Australia’s electricity network roadmap is to replace the critical role of synchronous generator-based
plants such as coal-fired power plants with renewable, power-electronic-converter (PEC-)connected
energy resources. The generation mix from PEC-connected generators creates a power system with
low levels of native inertia leading to a weak electricity network with low system strength. Additionally,
with the majority of optimal sites for renewable energy generation (with access to high wind speed, high
solar irradiance and high capacity transmission lines) already utilised, future developments need to focus
on less favourable locations leading to the connection of newly developed solar/wind farms into weaker
parts of the grid with lower system strength.
With an increasing number of PEC-connected generators, grid locations that are distant from the
synchronous generators and close to PEC-connected ones experience low fault currents and low
system strength. This results in a number of issues for wind/solar farms, including but not limited
to post-fault instability, failure to feed in full power stably under steady-state conditions, startup
and re-synchronisation issues, control interactions and instability, failure to ride-through disturbances,
electromechanical oscillatory instability and islanding issues.
In China and the US, wind farms connected to weak parts of the network have experienced
subsynchronous oscillation (4 Hz or 30 Hz). In Australia, there are currently wind/solar farms connected
to weak parts of the network that cannot operate at their nominal power levels due to stability issues.
Additionally, some of the proposed wind/solar farms in Australia may not be developed due to stability
concerns in weak areas of the network. In some cases, regardless of physical completion of plants, they
are not able to connect to the NEM due to non-compliance with grid code mainly caused by the grid
strength at the connection point. This situation results in unnecessarily higher costs to the customers. To
address the issues related to weak grids, this project aims to:
1. Classify and describe stability issues that are likely to be expected for wind/solar farms
connected to weak grids,
2. Identify grid properties/value-range/scenarios under which the above issues are likely to be
encountered,
3. Propose add-on solutions to wind/solar farms integrated into weak grids to enable/enhance their
stability upon various contingencies in the network,
4. Propose innovative allocation, sizing, and control strategies for grid-strengthening assets such as
SynCons and grid forming inverters.
This interim report presents the findings of the study related to weak grid classification and grid
strengthening solutions. Commonly used grid strength indices such as short circuit ratio (SCR), X/R ratio
and rate of change of frequency (RoCoF) are discussed, and their inadequacy for emerging power grids
with inverter-based generation sources (IBRs) is highlighted in this report. Extensions of these indices
such as weighted SCR and voltage sensitivity are presented as recent developments. The applicability of
grid forming inverters (GFMIs) and synchronous condensers (SynCons) as grid strengthening solutions
are also discussed.
Acknowledgements
This project received funding from ARENA as part of ARENA’s Advancing Renewables Program.
Grant number 2020/ARP007.
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3. Disclaimer
The views expressed herein are not necessarily the views of the Australian Government. The
Australian Government does not accept responsibility for any information or advice contained within
this document.
List of Acronyms
ARP Advancing Renewable Program
AVR Automatic Voltage Regulator
CSCR Composite Short Circuit Ratio
DFIG Doubly-Fed Induction Machine
DFT Discrete Fourier Transform
ESCR Equivalent Circuit Based Short Circuit Ratio
GA Genetic Algorithm
GFMI Grid Forming Inverter
GFLI Grid Following Inverter
GIH Grid Innovation Hub
HSS Hyper-Spherical Search
HVDC High Voltage Direct Current
ISP Integrated System Plan
MPM Matrix Pencil Method
NEM National Electricity Market
OEM Original Equipment Manufacturer
PEC Power Electronic Converter
PLL Phase-Locked Loop
PMU Phasor Measurement Unit
PoC Point of Connection
PSCAD Power System Computer Aided Design
RMS Root Mean Square
RoCoF Rate of Change of Frequency
SCR Short Circuit Ratio
SynCon Synchronous Condenser
TNSP Transmission Network Service Provider
VSC Voltage Source Converter
VSG Virtual Synchronous Generator
WSCR Weighted Short Circuit Ratio
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4. Table of Contents
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Project Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.3 Project Outcome and Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.4 Publications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Weak Grid Classification 4
2.1 Short Circuit Ratio and X/R Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Equivalent Circuit-based Short Circuit Ratio . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Composite Short Circuit Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.4 Weighted SCR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.5 Voltage Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.6 Rate of Change of Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.7 Phase Locked Loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.8 Stability Index and Domain of Attraction . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Grid Strengthening Solutions 13
3.1 Grid Following Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3.2 Grid Forming Inverters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Comparison of grid-following and grid-forming inverters . . . . . . . . . . . 16
3.2.2 Grid Interaction Capabilities of GFLIs and GFMIs . . . . . . . . . . . . . . . 16
3.2.3 Control Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3.2.4 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.5 Energy Storage and Over-sizing . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.6 Frequency Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.7 Voltage Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.2.8 System Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.9 Regulatory Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2.10 Recent Trends in GFMI Implementations . . . . . . . . . . . . . . . . . . . . 19
3.3 SynCons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Exciter Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.3.2 Limitations of the Conventional Exciter Control Methods . . . . . . . . . . . 21
3.3.3 Further Developments Required in SynCon Exciter Control . . . . . . . . . . 22
3.3.4 Optimal Allocation and Sizing of SynCons . . . . . . . . . . . . . . . . . . . 22
4 Summary 24
References 25

5. 1 Introduction
Monash University, together with project partners Australian Energy Market Operator (AEMO), AusNet
Services Pty. Ltd., Hitachi ABB Power Grids and Department of Environment, Land, Water and
Planning (DELWP) applied for and obtained funding from the Australian Renewable Agency (ARENA)
to investigate stability issues and enhancing measures for weak power grids. The project focuses on three
main areas, namely: 1) Weak grid classification, 2) Grid strengthening solutions and 3) Internal control
and interactions with other inverter-based resources in the power grid. This interim report presents the
work carried out in relation to weak grid classification and grid strengthening solutions.
1.1 Background
The National Electricity Market (NEM) interconnects the six eastern and southern states and territories
of Australia and delivers around 80% of the total electricity consumption in Australia. The NEM is
currently undergoing a major transformation where fossil fuels are being replaced by renewable energy
resources such as solar and wind. Around 8% of the total installed capacity in Australia in 2018 was
from wind power plants. If all proposed and planned wind farms go ahead, this percentage will jump to
28%. The same situation exists for solar farms. Many of these renewable resources are located in weak
areas of the grid and are prone to various stability issues. Additionally, with the current trend, strong
points in the grid are expected to be considerably weaker in five to ten years. With many optimal sites
for renewable energy farms already taken, future developments need to focus on less favourable sites
leading to the grid integration of future wind/solar farms into weaker parts of the network. This could
result in a number of stability issues as mentioned previously. Additionally, the unique peculiarities of
the Australian electricity grid, which is a very long and radial network as opposed to the meshed and
interconnected networks in other parts of the world, will intensify problems associated with weak grid
integration of renewable energy farms. One very recent example is limiting the allowable output power
of five weakly integrated solar farms in Victoria and NSW to half of their rated value by the Australian
Energy Market Operator (AEMO).
1.2 Project Outline
The project comprises the completion of three tasks. The first task focuses on the definition of a weak
grid and various measures to classify them. The other two tasks investigate different approaches by
means of which stability would be improved in weakly integrated wind/solar farms.
Task 1.Weak grids classification and test-bed development:
• Sufficient conditions for instability of weakly integrated wind and solar farms.
• Test-bed development based on northwestern victorian grid.
Task 2. Grid-strengthening solutions:
• Control, allocation and sizing of synchronous condensers.
• Control, allocation and sizing of grid-forming inverters.
Task 3. Controller interactions
• Internal Control of Wind/Solar Farms and their interactions with other PEC-connected assets.
• Wind/Solar farm Point of Connection (PoC) voltage control for damping northwestern Victoria
oscillations.
• Enhanced Phase Lock Loop (PLL) and synchronisation mechanisms
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6. 1.3 Project Outcome and Outputs
The main outputs of this project are:
• a list of the stability issues likely to arise in connection of wind/solar farms to weak grids, arranged
in a classification scheme designed to maximise understanding of the challenges and their drivers,
• list of grid properties/value-range/scenarios under which above issues are likely to be encountered,
• procedures to optimally size, allocate, and control grid forming inverters and SynCons to
strengthen the grid in weak areas leading to minimised investment cost and maximised impact
of GFMIs and SynCons on the stability of wind/solar farms upon various contingencies in the
network,
• innovative black-start capability in power-electronic-dominated areas of the grid using grid-
forming inverters,
• a list of stability issues that could happen upon the interaction of weak-grid-connected wind/solar
farms and other assets in the network such as HVDC converters, grid-forming inverters, and
SynCons.
• innovative solutions to stabilise wind/solar farms upon their adverse interaction on each other and
to damp any oscillatory behaviour.
The main outcomes of this project are:
• increased penetration of solar/wind farms in particular in weak parts of the networks unlocking
future investments,
• maximised generation capacity of existing wind/solar farms located in weaker parts of the
network,
• increased reliability/security of the grid as the renewable energy penetration grows.
1.4 Publications
1. M. Z. Mansour, S P. Me, S. Hadavi, B. Badrazadeh, A. Karimi, B. Bahrani, “Nonlinear Transient
Stability Analysis of Phased-Locked Loop Based Grid-Following Voltage Source Converters
Using Lyapunov’s Direct Method” in IEEE Journal of Emerging and Selected Topics in Power
Electronics, Feb. 2021.
2. M. Z. Mansour, S. Hadavi, B. Bahrani, “Stability Analysis and Nonlinear Control of Phase
Locked Loop of a Weak-grid Connected Voltage Source Converter” in Proc. IEEE International
Conference on Ecological Vehicles and Renewable Energies (EVER 2020), Sept. 2020.
3. S. Hadavi, M. Z. Mansour and B. Bahrani, ”Optimal Allocation and Sizing of Synchronous
Condensers in Weak Grids with Increased Penetration of Wind and Solar Farms,” in IEEE Journal
on Emerging and Selected Topics in Circuits and Systems, pp. 199-209, March 2021.
4. S. Hadavi, S. P. Me, M. Fard, A. Zadeh, B. Bahrani “Virtual Synchronous Generator Versus
Synchronous Condensers: An Electromagnetic Transient Simulation-based Comparison”, in
CIGRE Science & Engineering Journal, under review.
5. S. Hadavi, D. Rathnayake, G. Jayasinghe, A. Mehrizi-Sani, B. Bahrani, “A Data-Driven Exciter
Controller Design for Synchronous Condensers” IEEE Transactions on Power Systems, under
review.
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7. 6. D. Rathnayake, M. Akrami, C. Phurailatpam, S. Me, S. Hadavi, G. Jayasinghe, S. Zabihi, B.
Bahrani, “Grid-forming Inverter Modeling, Control and Applications” in IEEE Access, Accepted
for publication.
7. B. Bahrani, “Power-Synchronized Grid-Following Inverter without a Phase-locked Loop” in IEEE
Access, Accepted for publication.
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8. 2 Weak Grid Classification
Generally, the term ”strength” or ”weakness” at a given point in a power system is related to the ability
to transfer power in steady-state while maintaining adequate level of voltage and frequency stability.
Nevertheless, it is a relative term that should be discussed together with the system characteristics at
the given point of connection and the size of the generating system(s) to be connected. Therefore,
traditionally, several terms such as Short Circuit Ratio (SCR), X/R ratio and Rate of Change of frequency
(RoCoF) have been used to quantify the strength of a connection point. These quantities were found to
be inadequate, and thus, additional quantification methods have recently been proposed. This section
presents an overview of these methods together with a novel stability index proposed in this study. A
method to calculate the domain of attractions is also proposed in the later part of the section.
2.1 Short Circuit Ratio and X/R Ratio
In order to calculate the SCR at a given point in the network, the fault current in-feed at that location
has to be determined first. Then, the SCR is calculated as the network short circuit level in MVA at
the connection point over the nominal rating of the farm in MVA as expressed in (1) and (2). It can be
further simplified to the inverse of the per-unit impedance seen at the point of connection (3), where
VPCC and PWF are taken as base values. These equations are based on the hypothetical scenario where
a single machine is connected to the infinite bus, as shown in Figure 2.1.
SCRPCC =
Short circuit MVA at PCC
Nominal MVA of the generator
(1)
SCRPCC =
V 2
PCC
ZgPWF
(2)
SCRPCC =
1
Zg.pu
(3)
Figure 2.1: Single machine connected to an infinite bus (SMIB case)
Another commonly used index to assess the strength of a point of connection is the X/R ratio. X/R
ratio is a reflection of the impedance angle, as shown in Figure 2.2. Even though a direct or simple
relationship between SCR and X/R is not available, in weak grids, both indices are low. In order to
assess the power injection capability under various combinations of SCR and X/R ratio, a SMIB case
was simulated using the PACAD software for a 200 MW, Type 4, wind turbine connected to a 132 kV
system through a step-up transformer, as shown in 2.1. Figures 2.3 (a) - 2.3 (e) show the system response
for a step-change in the active power set point.
Typically, the SCR above five is considered as strong grids, which is evident in Figures 2.3 (a) and 2.3 (b).
The active power delivery to the grid follows the reference with some oscillations and settle in less than
half a second. Further analysis on Figures 2.3 (a) and 2.3 (b) reveals that the X/R ratio does not have a
significant effect on power delivery, oscillations or the settling time in strong grids. Connection points
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9. with SCR values between three and five are generally considered as weak points. Nevertheless, as shown
in Figure 2.3 (c) there is no significant performance degradation in terms of power delivery, oscillations
or settling time compared to Strong grids. The effects of high X/R ratios start to appear when the SCR
reaches 3. These effects have become prominent when the SCR is lower than 3, which are considered
as very weak grids. As evident in 2.3 (d), even in such very weak grid scenarios, performance is quite
similar to strong grids scenarios if the SCR is above 1.5, and the X/R ratio is very low, which means the
grid is more resistive. As the X/R ratio increases, sustained oscillations occur, leading to poor power
delivery performance. If the SCR is lowered further, it becomes impossible to reach the active power
set point, which is evident in Figure 2.3 (e).
Although there is no direct or simple relationship between the SCR and the X/R, the following
conclusions can be deduced based on the results shown in Figure 2.3. In strong grids (SCR > 5), X/R
ratio doesn’t have any significant impact on following the active power set point, oscillations or settling
time. In weak grids (3 < SCR < 5), the ability to reach the active power set point is not affected by the
X/R ratio. The effect of X/R ratio is significant in very weak grids (SCR < 3) where X/R ratio above
3 leads to longer settling times or, in the worst case, sustained oscillations. For very low SCR values
(SCR < 1.5), very low X/R ratios are preferred. Therefore, a low X/R ratio does not necessarily mean a
connected wind or solar farm will be unstable. It has to be assessed with the SCR available at the point
of connection. In summary, SCR is the primary index for assessing a connection application. X/R ratio
is the secondary index, especially if the SCR falls below 3. OEMs typically specify that the SCR at the
inverter terminals to be above 1.5 for the proper functioning of the inverter.
With the massive integration of PEC-based renewable energy resources, the calculation of SCR and X/R
ratio is not straightforward as the impedance of the connection point will be shared by more than one
generating unit. Therefore, the effective SCR available for each generating unit drops as the number
of of generating units increases. This led to the development of new indices, Equivalent Short Circuit
Ratio (ESCR), Composite Short Circuit Ratio (CSCR), and Weighted Short Circuit Ratio (WSCR), for
quantifying the strength of a given point of connection.
Figure 2.2: Impedance triangle
2.2 Equivalent Circuit-based Short Circuit Ratio
A general equivalent circuit based approach, termed equivalent circuit-based short circuit ratio (ESCR),
is proposed in [12] for assessing the impact of adjacent existing wind or solar farms on the performance
of the proposed wind or solar farm. For example, if the second wind farm, represented as G2 in Figure
2.4, is connected to the same point of connection, the effective value of the short circuit ratio can be
expressed as in (4). The effective SCR value in (4) is low compared to the SCRPCC value found in
(2). Therefore, the SCR available for existing wind farm(s) drops when new wind farms are added to
the network. The effective SCR expressed in (4) can be extended as in (5) to calculated the SCR at the
medium voltage collection bus of the wind farm, where Z11 is the transformer impedance expressed in
pu with rated power of wind farm 1 as the base power [12]. Similarly, SCR for the medium voltage
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10. 0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
50
100
150
200
Time (s)
Power
(MW)
X/R = 1.5
X/R = 3
X/R = 5
X/R = 8
X/R = 10
(a) Oscillations at SCR = 8
0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
50
100
150
200
Time (s)
Power
(MW)
X/R = 1.5
X/R = 3
X/R = 5
X/R = 8
X/R = 10
(b) Oscillations at SCR = 5
0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
50
100
150
200
Time (s)
Power
(MW)
X/R = 1.5
X/R = 3
X/R = 5
X/R = 8
X/R = 10
(c) Oscillations at SCR = 3
0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
50
100
150
200
Time (s)
Power
(MW)
X/R = 1.5
X/R = 3
X/R = 5
X/R = 8
X/R = 10
(d) Oscillations at SCR = 1.5
0.6 0.8 1 1.2 1.4 1.6 1.8 2
0
50
100
150
200
Time (s)
Power
(MW)
X/R = 1.5
X/R = 3
X/R = 5
X/R = 8
X/R = 10
(e) Oscillations at SCR = 1
Figure 2.3: Oscillations at different SCR and X/R ratio for a step-change in active power set point
collection bus of the wind farm 2 can be calculated sing (6). Z22 is the transformer impedance of the
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11. second wind farm, expressed in pu with rated power of wind farm 2 as the base power
ESCRPCC =
V 2
PCC
Zg(PWF1 + PWF2)
(4)
ESCR1 =
1
PWF1Z11 + Zg(PWF1 + PWF2)
(5)
ESCR2 =
1
PWF2Z22 + Zg(PWF1 + PWF2)
(6)
Figure 2.4: Equivalent circuit of two wind farms connected to the same point of connection
Figure 2.5: Approximate equivalent circuit assumed for the calculation of CSCR for two wind farms
connected the same point of connection
2.3 Composite Short Circuit Ratio
When wind/solar farms are connected to the same HV bus or HV busses in closed electrical proximity,
they can be approximated as a single aggregated wind/solar farm connected to the common MV bus as
shown in Figure 2.5. While the effective SCR remains the same as in (4), the SCR at the medium voltage
collection bus changes to (7), where Z1 and Z2 are transformer impedance.
CSCR =
SBase
(PWF1 + PWF2)
×
1
Zg + 1
1
Z1
+ 1
Z2
(7)
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12. 2.4 Weighted SCR
Weighted short circuit ratio (WSCR) is another index defined to assess the impact of adjacent wind/solar
farms. The general equation for calculating WSCR for fully interacting wind/solar farms is given in (8)
[12].
WSCR =
∑N
n=i SSCMV AiPWFi
(
∑N
n=i PWFi)2
(8)
where SSCMV Ai is the short circuit capacity at bus i before the connection of the wind farm i PWFi is
the MW rating of the wind farm i to be connected N is the number of wind farms fully interacting with
each other i is the wind farm index
For the two wind farm systems shown in Figure 2.4, WSCR can be calculated as (9)
WSCR =
SCR1P2
WF1 + SCR2P2
WF2
(PWF1 + PWF2)2
(9)
The WSCR calculates the short circuit ratio only at the point of connection in the HV bus. ESCR can
be used to calculate the effective SCR available for each wind/solar farm at the MV bus. CSCR also
calculates the SCR vat the MV bus. Nevertheless, it does not give SCR values for each wind/solar farm,
instead, it gives a single number for all wind/solar farms connected to the virtual MV bus. Therefore, out
of the three indices, the suitable index should be chosen based on the application. As reported in [12]
for applications with multiple WPPs, it is recommended to use the minimum value of ESCR, CSCR and
WSCR indices.
2.5 Voltage Sensitivity
The above-mentioned indices do not reflect the change of voltage at the generator terminals, MV
collection bus or the point of connection at the HV bus with the change of the active and reactive power.
Moreover, the limit of active power where voltage collapse could occur is not included in those indices.
The relationship between SCR and X/R ratio is also not clear in the above indices. This lead to the
definition of new index named as voltage sensitivity indices λ and µ, especially for weak grid scenarios
(10).
λ =
RP + XQ
V 2
∞
, µ =
XP − RQ
V 2
∞
(10)
where R and X are resistance and reactance of the transmission line, P and Q are active and reactive
power, and V∞ is the voltage at the infinite bus. More information on voltage sensitivity indices can be
found at [12].
2.6 Rate of Change of Frequency
Inverter-based resources such as wind and solar farms do not provide mechanical inertia, and thus, the
frequency stability gets affected. The rate of change of frequency (RoCoF) is a well-accepted index for
assessing frequency stability, especially in weak grid scenarios. RoCoF is high at the beginning of a
contingency event and subsequently drops as the system recovers. Weak networks with a low level of
native inertia can show RoCoFs as high as 4 Hz/s. Unfortunately, there is no industry consensus on how
to calculate/use these indices in particular for cases where several PEC-based farms are co-located. To
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13. overcome this issue, alternative indices or a mixture of the aforementioned ones are used as applicable
for a given scenario.
2.7 Phase Locked Loop
The inverters used in IBRs are generally designed to follow the grid voltages and inject current into the
existing voltage, and thus, they are known as grid following inverters (GFLIs). The common technique
used to synchronise GFLIs with the grid voltage is the use of a PLL. When integrated into weak networks,
the internal controllers of the farm, including PLL may fail to follow the grid frequency/angle, which
results in instability. Moreover, overcompensation during fault scenarios, in particular in weak grids,
could result in excessive voltage upon fault clearance, which in turn can trigger protection schemes. Thus,
to ensure optimal operation of wind/solar farms, the internal controllers and PLLs must be properly
tuned/designed to maintain stability over a wide range of scenarios and ride through faults in weak
networks. Most inverter control strategies are devised for rather strong networks such as European power
grids, and developers in Australia have utilised and are still utilising such power electronic converters
and their associated control without considering the evolving and unique characteristics of the Australian
network. Therefore, understanding the behaviour of PLLs in weak grid scenarios and their stability
regions are important to asses the performance of IBRs.
2.8 Stability Index and Domain of Attraction
The strength of a grid depends on the sensitivity of the grid voltage to active and reactive power
perturbations. The voltage of a strong grid has less sensitivity to active and reactive power changes
[12]. The basic indices used in the literature to characterise the grid strength are SCR, ECSR, CSCR
and WSCR. However, neither of these indices can predict whether a grid-following Voltage Source
Converter (VSC) is unstable as they do not take the VSC dynamics into account. The influence of the
X/R ratio on the stability of a VSC while it performs as an inverter or a rectifier is investigated in [63].
However, there is not any mathematical expression that describes the effect of the X/R ratio and SCR
on the stability of the system in previous studies.
The stability of grid-following VSCs can be assessed from two perspectives: 1) small-signal and 2)
large-signal stability. The small-signal stability analysis assesses the ability of the grid-connected VSC
to remain synchronised with the grid in the presence of small disturbances. For instance, the small-signal
stability analysis studies the effect of the injected current into the grid on the Point of Common Coupling
(PCC) voltage. This effect will be transferred to the Phase-Locked Loop (PLL); hence, a positive
feedback loop named self-synchronisation loop is formed. This positive feedback can cause instability
in the system [57], in particular, if a high-gain PLL is employed [64]. Besides, the synchronisation
instability can cause side-band oscillations in the voltage and current waveforms [56]. Two main methods
for evaluating the small-signal stability of the system are eigenvalue-based [59] and impedance-based
analysis [7, 18, 27]. Using small-signal approaches, the effect of large yet very common disturbances
such as faults and grid impedance as well as operating point changes cannot be studied.
The presence of an equilibrium point for the system in normal and faulty conditions is studied in large-
signal or transient stability studies [57]. This type of instability might occur in a system if either there
exists no stable equilibrium point, or the system does not have sufficient damping to push the states of the
system toward the equilibrium point. In transient stability analysis, given the fact that the PLL’s imposed
dynamics is much slower than the inner control loops, the converter is assumed as an ideal controllable
current source [19]. Some studies, e.g., [30], use linear a approximation of the system to assess the
stability of the system and propose stability enhancement methods. Ref. [62] solves the differential
equation related to the PLL using the averaging method and finds a time-domain expression for the PLL
operation. Although this method is effective, it is complicated. Some studies, such as [21], use Equal
9

14. Area Criterion (EAC) for assessing the transient stability of the system. However, in this method, the
damping effect of the system is neglected; hence, the assessment is conservative. Also, a large-signal
model that includes the PLL dynamics is developed and used in [9] and [10], and it is shown that the
effect of the grid can be modeled as positive feedback. In [22], a bifurcation is found for grid-following
VSCs during the fault occurrence. Due to this bifurcation, the synchronisation might be lost and cannot
be recovered. However, similar to the EAC-based method, the damping is neglected in this study, which
is not realistic for PLL-based synchronisation units.
In some other studies, linearisation methods are employed to assess the stability of the system under
study during a fault. Additionally, phase-portrait assessment, which is a nonlinear stability analysis, is
employed for validating the stability analysis of the system conducted by other theoretical approaches
[58]. Even though this method is one of the most effective approaches for assessing the stability of
nonlinear systems, the drawback is no general rule can be introduced based on it, and the phase-portrait
study must be conducted every single time. To overcome this issue and to find the domain of attraction of
the system systematically, the only method is employing Lyapunov’s direct method for stability analysis.
Lyapunov’s direct method is used in [1] to study the stability of the power control layer of a droop-
controlled grid-following inverter based on electrostatic machine model; hence, it does not consider the
impact of the PLL on the stability of the system. This study, however, neglects the damping factor of
the system, which makes it conservative. Additionally, Lyapunov’s direct method is employed by [5, 47]
to evaluate transient angle stability of virtual synchronous generators, which do not have a PLL in their
structure.
Contrary to [1], a new method to find the equilibrium points of a PLL-synchronised grid-following
inverter is proposed. The proposed method is based on the second-order nonlinear model and state-space
model discussed in [51] and Lyapunov’s stability theorem [48]. Then, the stability of the equilibrium
points is studied, and the necessary and sufficient conditions of their stability or instability are derived.
In addition, a potential Lyapunov function is proposed for the system, and the stability analysis of the
equilibrium points is done via Lyapunov’s direct method. Using the proposed function and Lyapunov’s
direct method, the domain of attraction of the stable equilibrium points is found, and a systematic
approach for finding this domain is proposed. In the end, a dynamic and comprehensive system strength
index based on the domain of attraction of the equilibrium point is proposed. Using this index, the effect
of all of the aforementioned parameters on the transient stability of the system are considered.
The salient features of the proposed index are:
• Nonlinear stability analysis based on the second method of Lyapunov has been done. This enables
a rigorous stability analysis of a grid-following inverter, which can predict the stability of the
system upon fault clearance.
• Proposing a parametric Lyapunov function that is used for finding a domain of attraction. This
Lyapunov function is validated via simulations and experiments
.
θ =
∫
[Kpvq +
∫
Kivqdt + ω0]dt (11)
where
vq = Vgsin(−δ) + |ZL(ω)|IPCCsin(θI + ϕc(ω)) (12)
In (12), ZL(ω) is the grid impedance, ϕc(ω) is its angle, IPCC is the VSC’s output RMS current, θI is
its angle with respect to the VSC’s terminal voltage, and ω is the estimated frequency by the PLL. For
a given θg =
∫
ω0dt, in which θg is the angle of the grid voltage, and by differentiating (11) twice with
10

15. Figure 2.6: SMIB model of a grid-following VSC with its vector current control. The output filter of the
VSC is an RL filter, and the grid is modeled as an inductor and a resistor in series with an ideal voltage
source.
Figure 2.7: Block diagram of a SRF-PLL.
respect to time, the second-order nonlinear differential equation defining the dynamics of the PLL and
the grid is written as [51]
δ̈ = −KpVgδ̇cosδ+KpLLIPCCcosθIδ̈+KiRLIPCCsinθI+KiLLIPCCcosθI+KiLLIPCCcosθIδ̇−KiVgsinδ
(13)
By setting x̂1 = δ and x̂2 = δ̇, the state space model can be written as
ẋ1 = x2 and ẋ2 = B − Dsin(x1 − α) + (Acos(x1 − α) + C)x2 (14)
According to Lyapunov’s Direct Method if Lyapunov function is chosen as
V (x) = −Bx1 + D(cosα − cos(x1 + α)) +
1
2
x2
2 (15)
it can be proven that the domain of attraction’s radius can be express as
ρ = min(R1, R2) (16)
with the conditional equations
11

16. R1 = min
√
x2
1 + x2
2 subjected to V (x) = 0, ∀x ̸= 0 (17)
and
R2 = min
√
x2
1 + x2
2 subjected to V̇ (x) = 0, ∀x ̸= 0 (18)
The domain of attraction of the equilibrium point of the system for a positive V (x1, 0) is shown in
Figure 2.8(a), where the Lyapunov function does not impose a limitation on the radius of the domain
of attraction. In Figure 2.8(b) V̇ (x1, 0) shows that there exists a ball with radius ρ = 0 : 8 around the
origin in which any initial condition necessarily is attracted to the equilibrium point. If the first state’s
initial condition (x0
1) is located inside the green area, the states ultimately converge to the origin. More
information and experimental validations can be found at [32]
Figure 2.8: The domain of attraction of the equilibrium point of the system
In contrast to the conventional system strength indices, the proposed index takes into account the
dynamics of the VSC as well and is capable of anticipating the instability of the system. Moreover, using
this index, different VSCs can be compared from the stability point of view and disturbance tolerance.
As the continuation of this work, the effect of the internal current controller will be studied; hence, the
impact of the output filter of the VSC on the stability boundary will be taken into account. Additionally,
this study will be extended beyond a single-machine infinite bus model to investigate the impact of
electrically close inverter-based resources on each other in parts of the network with low available system
strength.
12

17. 3 Grid Strengthening Solutions
A promising approach to overcome the issues related to weak grids is strengthening the grid via
installing various compensators or reinforcing the grid infrastructure. Some examples of these solutions
include transmission line reinforcement, battery energy storage technologies, synchronous condensers
(SynCons), and static compensators (STATCOMs). These solutions are very costly and are not
favourably viewed by developers. Among these solutions, however, SynCons have attracted significant
attention in recent years. SynCons are synchronous machines that do not generate electricity and only
spin freely. Via regulating its field voltage, a SynCon is capable of regulating its reactive power exchange
with the grid, leading to strengthening the network to which it is connected. Being a costly solution,
SynCons capital cost can be justified if their rating and location are optimally selected.
Grid forming inverters (GFMI) are another promising technology for grid strengthening, which are
currently gaining attention. Contrary to SynCons, GFMIs are fully controllable and may provide various
ancillary services to the grid. Although for some of those ancillary services, a large scale of energy
storage is needed, for the Grid strengthening purposes, the energy storage size can be minimised, and
so the capital cost. The inertial response and the fault capability (needed for the Grid strengthening) is
mainly relying on the capacity of power flow (provided by GFMIs ratings) rather than the energy level. In
addition, to combat weak network issues, wind/solar farm internal controllers can be optimally designed
to enhance the stability of the farm and increase its ride-through capability. These controllers include
point of connection (PoC) voltage controller, real/reactive power controllers for ancillary services, and
phase-locked loops (PLLs).
3.1 Grid Following Inverters
As discussed above, to export energy to the power grid, IBRs need to get synchronised with the grid
voltages. Their synchronisation, however, is primarily based on control algorithms and differs from
swing-equation-based synchronisation of synchronous generators. Based on their grid synchronisation,
two main categories of IBRs exist: 1) grid-following inverters (GFLIs) and 2) grid-forming inverters
(GFMIs). GFLIs mainly rely on measuring or estimating the point of connection (PoC) voltage to get
synchronised with the grid [1]–[4]. Phase-angle and frequency of the sensed/estimated PoC voltage are
extracted by a PLL, which are then used by a vector current controller. GFMIs, however, exploit active
power-frequency droop control for grid synchronisation. GFMIs regulate the PoC voltage while the
frequency and magnitude of this voltage is provided by active and reactive power control loops, which
mainly operate based on droop control. The first category is called grid-following as they follow the PoC
voltage by a PLL, while the second one is called grid-forming as they form the voltage of the PoC.
GFLIs can seamlessly operate in strong grids and export their maximum power. However, as they rely on
PLLs, their performance in weak grids deteriorates, and operation in very weak grids can lead to their
instability or side-band oscillations. These side-band oscillations are mainly due to the asymmetrical
control dynamics of synchronous reference frame PLLs. To mitigate the issues PLL face in weak grids,
several strategies are proposed. A symmetrical PLL that provides phase-angles in both d- and q-axes is
proposed in [60]. Embedding a virtual impedance in the PLL structure, the PLL is synchronised with
a remote, strong grid in [11]. Using a band-pass filter, the negative resistance of the PLL is damped by
tuning the filter. In [61], using a feed-forward loop from the PLL to the current control loop, symmetrical
dynamics in the d- and q-axes are achieved. All of these approaches, however, rely on a PLL and require
the PoC voltage measurement. GFMIs, on the other hand, face stability issues when operating in stiff
grids [57]. The main reason is regulating the PoC voltage in stiff grids is challenging as the PoC and the
grid are electronically close to each other [55].
In the recent literature, several approaches for PLL-less operation of GFLIs, mainly based on direct
power control (DPC), have been proposed. A DPC strategy without any inner current loop has been
13

18. proposed in [31]. This approach, however, does not provide mechanism to limit the current due to lack
of an inner current and also results in a variable switching frequency, causing an unexpected broadband
harmonic spectrum range. To ensure a constant switching frequency, other variants of the DPC have
been proposed that use space vector modulation, or calculate the converter voltage error in each switching
period. Model predictive control-based (MPC)-DPC approaches, which consider system constraints and
nonlinearities, are also proposed to achieve constant switching frequency. However, MPC-DPC methods
result in an excessive computational burden. A voltage-modulated DPC (VMDPC) for IBRs is proposed
in [14]. This approach does not require a PLL for its synchronisation while it has the same control
structure as the conventional vector current control approaches. As its synchronisation is not dependent
on a PLL, the VMDPC does not suffer from the shortcomings of conventional GFLIs.
However, since the VMDPC still requires the PoC voltage to control the power exchange with the
grid, its performance in weak grids deteriorates. The reason is that in weak grids, power injection by
the IBR significantly affects the PoC voltage, which in turn can destabilise the system. Although the
VMPDC, compared to other DPC-based solutions, provide superior performance, a detailed comparison
between the VMDPC and the conventional PLL-based vector current controller reveals that the VMPDC
does not provide much of improvement compared to PLL-based methods, in particular, in weak grid
conditions.
The power-synchronised control strategy proposed in this project is for grid-following IBRs. Similar to
the VMDPC, the proposed method does not rely on a PLL to get synchronised with the grid. However,
contrary to the VMDPC and many other synchronisation techniques, including conventional GFLIs and
GFMIs, the proposed method does not require PoC voltage regulation, sensing, or estimation, and it can
stably operate in both weak and stiff grids. To avoid complications caused by PoC voltage sensing, the
proposed controller utilises the inverter terminal voltage and controls the power at the terminal of the
IBR. To control the real/reactive power exchange, the proposed approach relies on a cascade control
architecture whose outer power loop provides the grid frequency and the reference of its inner current
control loop. The inner current loop is in place to ensure current limitation if needed. Hence, the main
features of the proposed power-synchronised grid-following inverter are:
• does not require a PLL,
• does not require PoC voltage sensing (unless used for fault detection) or PoC voltage regulation,
• provides decoupled real/reactive power control,
• can limit its injected current for protection purposes,
• can operate in ultra-weak/stiff grids,
• can replace the existing large fleet of conventional GFLIs.
The proposed power-synchronised inverter and its control strategy are shown in Figure 3.1 in which
an IBR is interfaced to the grid via an inductor. As the PoC voltage is not required for this control
strategy, either L or LCL filters can be utilised, i.e., a capacitor is not necessarily installed at the PoC.
The proposed controller operates in a rotating reference frame aligned with the inverter current, i.e.,
the q-component of the inverter current is zero. A power calculator block, based on the instantaneous
power theory, calculates the power delivered by the inverter. Then, using a cascade control structure,
a power control block provides the grid frequency and Id,ref for an inner inverter current control loop.
The current control loop is identical to that of the GFMI or GFLI concept. More information and
experimental validations will be provided in the next report.
14

19. Figure 3.1: The proposed power-synchronised grid-following inverter and its control block diagrams.
3.2 Grid Forming Inverters
Conventional AC power systems are dominated by synchronous generators, where the primary control
objectives of voltage and frequency regulation are achieved through exciter control and governor control,
respectively. Low output impedance, together with the automatic voltage regulation action, make
synchronous generators near-ideal voltage sources. Moreover, the inertia of the prime-mover and rotor
helps keep frequency within the operating limits during disturbances such as load changes and faults.
This ideal voltage source behaviour and high inertia are the essential features for maintaining a stable
power grid. In addition, the extensive fault current handling capability of the synchronous generators,
typically up to six times the rated current, is an essential feature in clearing faults.
With the growing demand for renewable energy technologies, mainly wind and solar, IBRs are becoming
an inevitable part of AC power systems. The inverters used in IBRs are generally designed to follow
the grid voltages and inject current into the existing voltage. This particular grid-following behaviour
resembles a current source. Almost all of the currently installed IBRs fall into this category, and thus,
voltage source behaviour is not intrinsically present in IBRs. Moreover, IBRs are not designed with
sufficiently large energy storage to emulate inertial response. The over-current ratings of the power
electronic switching devices used in inverters are also very low compared to synchronous generators.
Therefore, IBRs are considered as non-synchronous generation sources. The major challenge with
the increased penetration of non-synchronous generation sources in power systems is the voltage and
frequency regulation [28].
Microgrids, which can operate in the grid-connected mode as well as in the islanded mode, emerged as
a platform for integrating IBRs [17]. In the grid-connected mode, voltage and frequency are regulated
by the grid, and thus, IBRs simply operate as grid-following inverters. In the islanded mode, one of the
inverters, or a couple of them, should function as voltage and/or frequency regulator(s) to form a local
power grid. The concept of GFMIs originated from this particular need. Furthermore, the need for
emulating the features of the synchronous generators emerged as the concept of microgrids evolved, and
thus, energy storage elements and control solutions, including virtual synchronous generator operation,
were also developed as enhancements for GFMIs [54] [29].
Even though GFMIs were originally developed for use in islanded microgrids, the concept can be adapted
for applications in large power systems, especially in integrating wind and solar farms. Since wind and
solar farms are often located in remote sites, the line impedance tends to be high. Such sections of
the grid are termed as weaker parts of the grid. Voltage regulation at the PCC, through conventional
solutions, becomes challenging in weak grids. GFMIs provide a promising solution to this issue by
strengthening the grid.
15

20. 3.2.1 Comparison of grid-following and grid-forming inverters
The primary objective of supplying active and reactive power to the grid is common for all IBRs.
However, depending on the interaction with the grid, controller implementation and response to the
changes in the grid, they can be classified into two main groups, namely: GFLIs and GFMIs, as shown
in Fig. 3.2 (a) [35]. More information, including further subdivisions of the two categories, are given in
the following subsections.
3.2.2 Grid Interaction Capabilities of GFLIs and GFMIs
As mentioned in the introduction, applications of GFLIs are primarily focused on active power injection
into the grid with maximum power point tracking (MPPT). Therefore, the reactive power supply is
minimum and often close to zero. Such inverters are known as grid-feeding inverters (GFDIs). From a
revenue point of view, it is more attractive to run IBRs as GFDIs. Nevertheless, voltage and frequency
regulation become challenging as the number of GFDIs increases. Therefore, grid operators/regulators
have imposed strict requirements, especially on large-scale IBRs (typically above 5 MW), to support
the grid by supplying reactive power and varying active power in response to the changes in the grid.
An example P/Q response requirement is illustrated in Fig. 3.2 (b) where the reactive power response
kicks in first to support the grid [35]. If the voltage deviates further from the set-point, the active power
response has to be started. The active power response requirement may vary depending on the regulations
applied. However, the reactive power response is common in AC power systems. IBRs that operate in
the grid supporting mode are known as grid-supporting inverters (GSIs). Almost all the large-scale IBRs
work as GSIs, and small-scale IBRs, typically below 5 MW, operate as GFDIs.
The fundamental difference in grid interaction of GFMIs come from the way active and reactive power
delivery to the grid is controlled. As mentioned above, the primary objective of GFLIs is to inject
active power to the grid, and supporting the grid is the secondary objective. In contrast, in GFMIs, the
primary objective is regulating the voltage and frequency of the grid. Therefore, active and reactive
power references are continuously varied in GFMIs to achieve this objectives.
Figure 3.2: (a) Classification of grid-connected inverters and (b) P, Q control for supporting the grid
3.2.3 Control Implementation
From the control point of view, the behaviour of a GFLI can be approximated to a controlled current
source with a high impedance in parallel, as shown in Fig. 3.3 (a). A GFLI measures the voltage at the
PCC (vPCC) and derives the phase angle of the vPCC via a PLL. Then, the terminal voltage is varied such
that the desired direct- and quadrature- (d−q) line currents are achieved. The active and reactive power
support from a GFLI is achieved by controlling the injected d and q currents, respectively. In contrast
to a GFLI, a GFMI can be approximated to a voltage source with a low series impedance as shown in
Fig. 3.3 (b). Contrary to GFLIs, GFMIs do not measure the vPCC for synchronisation purposes, and
16

21. Power
Control
PLL
Current Control
vPCC
iPCC
Zg
PCC Grid
Zc
iPCC
vPCC
δ
Id Iq
* *
Id Iq
* *
Power
Control
Voltage Control
Zg
PCC Grid
iPCC
vPCC Vm δm
Vm δm
Zc
(a)
Q*
E*
ω*
(b)
P*
Q*
P*
Voltage
magnitude
& phase
Current
setpoint
Grid
Following
Grid
Forming
vPCC
iPCC
Figure 3.3: Comparison of control and approximation of (a) GFLI and (b) GFMI [44, 45].
rather form the vPCC to regulate their power output. Another major difference between the GFLI and
GFMI control is that a GFMI can operate/supply the local loads in the absence of grid connection by
establishing its own reference voltage and frequency [34, 35, 43, 45, 53]. This also leads to the difference
in synchronisation mechanism. A GFLI requires dedicated a synchronising unit to remain or operate in
synchronism with the grid and push a specific amount of active and reactive power to the grid. However,
in GFMIs, synchronisation at the beginning of the operation can be achieved in a similar manner to a
synchronous machine, and a dedicated synchronisation mechanism is not required during the normal
operation.
3.2.4 Performance Comparison
In a steady-state operating condition, depending on the control topology, power set-points and grid
conditions, both GFLIs and GFMIs can inject active and reactive power to the grid. However, one
of the main differences in performance between GFLIs and GFMIs lies in the reaction of each of these
converters to a grid disturbance in weak grids. Active and reactive power support during a disturbance,
which is also known as virtual or emulated inertia support, can be implemented in both GFLIs and GFMIs
depending on the source type. In the case of a GFLI, the disturbance is measured through voltage and
current measurements, and appropriate control actions are taken for grid support functionality. Thus, the
active or reactive power response of a GFLI is associated with some form of measurement and control
delay. However, in the case of a GFMI, the power transfer equation at the beginning of the disturbance
is given as
P =
VsVr
X
sin ∆δ (19)
where Vs is the sending end or the internal voltage, Vr is the receiving end or the grid voltage, X is
the coupling impedance, and ∆δ is the phase angle difference between the internal voltage and the grid
voltage. As the internal voltage phasor of the GFMI is not affected at the beginning of the disturbance,
an instantaneous response of power can be achieved depending on how fast the grid angle changes. Even
though the reaction of a GFMI converter is much faster compared to its GFLI counterpart, concerns on
current limitations and stability with rapid responses need to be addressed.
Another difference in the performance between GFMI and GFLI control is the small-signal stability
behaviour under weak grid conditions. With GFLIs relying on grid voltage and angle measurements
to remain synchronised to the grid, the stability margin can be greatly reduced with sudden changes
17

22. in the measured grid signals. This problem is greatly reduced in GFMIs with the possibility of self-
synchronisation and the absence of dependency on grid signals for synchronous operation.
Detailed discussions on the control methodology, performance, and limitations of the GFMIs are
provided in the following sections.
3.2.5 Energy Storage and Over-sizing
As mentioned in the introduction, GFMIs are expected to perform as synchronous generators, and thus,
it is essential to emulate the important features of synchronous generators such as the ability to supply
constant/committed power to the grid, inertial response, and fault current behaviour as much as possible.
Some form of energy storage is required to maintain committed power delivery, irrespective of the
changes in the wind or solar power input. Similarly, the inertial response requires energy storage, at
least for the duration of the required response. Therefore, the need for energy storage is another major
difference between GFLIs and GFMIs. Alternative approaches that have been proposed to manage
the energy storage requirements in GFMIs attached to wind farms are discussed below. Meeting
the fault current behaviour of the synchronous generators is challenging in GFMIs with the current
limitations in switching devices. Therefore, GFMIs have to be oversized, which makes them expensive
and commercially less attractive.
3.2.6 Frequency Control
From the above discussions, it is clearly evident that traditional frequency control approaches have to
be revisited as the share of IBRs increase in AC power systems. For GFMIs to be considered as a
promising solution, the two fundamental research questions that have to be answered are: 1) can GFMIs
achieve frequency regulation in heterogeneous systems comprising GFLIs and synchronous generators?,
and 2) are there any limitations on the share of GFMIs in power systems? [28]. Moreover, along with
the development of IBRs, another operational level question that would arise is how important it is to
regulate frequency and would the frequency tolerance band and RoCoF limits are relaxed, especially
in fully inverter-based power grids. The generation source for GFMIs is mostly wind and solar, where
frequency control pushes them to operate in non-optimal regions. In certain situations, the extracted
power might not be sufficient to meet the requirement. Energy storage is a promising solution to this issue.
Nevertheless, determining the suitable type of energy storage and optimal capacity to keep the frequency
within acceptable limits are open research questions in relation to GFMIs. The other operational concern
to be addressed is the proper load sharing mechanism between Grid Forming assets available in the
system and whether traditional droop-based techniques are still useful, or a proper communication
mechanism is needed to manage the frequency control and load sharing between isochronously controlled
Grid Forming assets.
3.2.7 Voltage Regulation
With the increase of GFMIs and GFLIs, the volt/VAR control shifts from large synchronous generators
to distributed generation sources. Therefore, it is important to understand how these distributed and local
volt/VAR control affect the voltage regulation in the entire power system. Moreover, the impact on the
exciter control of Syncons and GFMIs should be investigated. Finding the locations of GFMIs to obtain
optimal voltage regulation results is another important research area related to GFMIs. Moreover, the
suitability of traditional QV droop control and the necessity of communication-based volt/VAR control
are to be investigated, especially at increased penetration of GFMIs and GFLIs.
18

23. 3.2.8 System Strength
Even though virtual Synchronous Generators (VSGs), as an advanced form of GFMIs, have demonstrated
their merit in effectively contributing to the system strength of high renewable-penetrated networks, the
role of each VSG components such as virtual inertia, synthetic impedance, damper winding’s, and flux
model or their combined effect has not been fully worked out yet. Clarifying this can lead to identifying
key players of the system strength enhancement and help with the improvement of stability through the
allocation of sufficient factors.
3.2.9 Regulatory Framework
The implementation of GFMIs require demonstration of the above-mentioned key functionalities, mainly
frequency and voltage regulation, and developing confidence among the grid operators and regulators.
Since GFMI is relatively a new technology, grid integration should take a gradual approach where
its frequency and voltage regulation capabilities should be demonstrated in microgrids at early stages
[28]. Adding GFMIs into larger power systems should take place at gradually increasing power levels.
Moreover, it is essential to establish technical standards and commissioning procedures, and amend
other relevant regulatory frameworks to reflect capabilities and limitations of GFMIs, especially fault
ride-through and fault current levels.
3.2.10 Recent Trends in GFMI Implementations
Dalrymple Battery Energy Storage System (BESS) - ABB: ElectraNet’s 30 MW / 8 MWh, BESS at
Dalrymple substation in South Australia, is a utility-scale implementation with GFMIs carried out by
Hitachi ABB Power Grids. The Dalrymple BESS is the first large-scale grid-forming BESS connected
to the Australian National Electricity Market (NEM) and is built on Virtual Synchronous Generator
technology, which strengthens the grid by replicating the behaviour and performance of a synchronous
machine, providing synthetic inertia and high fault current to allow higher levels of renewable energy
resources to connect and operate. The system also provides reliability and flexibility services such as
fast power injection, seamless islanding and black-start of the local distribution network. When faults
occur on the upstream feeder, the system seamlessly islands in co-ordination with the nearby 91 MW
Wattle Point Wind Farm and distributed solar PV, to continue operating a local islanded power system to
ensure continuity of supply to the local customers. This makes the Dalrymple BESS more than an energy
storage system, but the largest autonomous microgrid in the world. The project’s results and operation
have demonstrated for the first time on the NEM the critical role grid-forming inverters, as opposed
to grid-following inverters, can play in strengthening the grid and enabling high renewable targets to be
met. In addition to this, the Dalrymple BESS offers competitive market services to the NEM, providing a
commercial return to the operator, which isn’t possible currently with comparable power system support
technology such as synchronous condensers. [6, 49].
Hornsdale BESS - Tesla: The 150 MW / 193.5 MWh power reserve located in Jamestown, South
Australia, is situated next to the 315 MW Hornsdale wind farm. The battery has already shown its
immense value for the grid in a number of ways, largely through grid stabilisation services and savings
[20]. The pre-existing grid-following control has recently been updated to grid-formingcontrol through
a software update [42].
Alinta Energy BESS - ABB: Alinta Energy’s BESS implemented by ABB interfaced through a 30 MW
VSG provides a spinning reserve for off-grid mining operations in Newman, Western Australia. The
BESS is also capable of energising long capacitive lines and black-starting the mine [49].
General Electric: GE has had multiple implementations of GFMI that are tailor-made for specific
applications. The 30 MW / 22 MWh BESS at Imperial Ignition District, California, is used for black-
19

24. starting a gas turbine. Another recent implementation is located at the Perryville generating station with a
rating of 7.4MW / 6.6 MWh, commissioned in 2019. Recently, GE research secured 4.2 million dollars
funding from U.S. Department of Energy Solar Energy Technologies Office (SETO) to develop grid-
forming solar inverter control technologies [4]. GE aims to develop grid-forming controls to allow wind
and solar inverters to improve the transient stability of systems with high renewable energy resources
penetration.
Dersalloch Windfarm - National Grid UK, Scottish Power Renewables: The 69 MW farms with 23 units
of Siemens Gemesa Turbines is the first large-scale implementation of GFMI control by a wind farm.
The project is commissioned, and the black-start capability was demonstrated in November 2020 [8].
The wind farm is able to regulate the local frequency and voltage, forming a stable network island before
connecting to the rest of the grid.
AusNet Services GESS: The Grid Energy Storage Systems (GESS) commissioned by ABB in 2014 consists
of a 1 MWh 1C lithium battery system that interfaces to the microgrid through a 1 MVA VSG inverters
and a 1 MVA diesel generator connected to the grid through a 3 MVA three-winding transformer. The
system is located at an end-of-line distribution feeder in an industrial estate situated in the northern
suburbs of Melbourne. AusNet Services aimed to test a non-network option to manage peak demand
with the potential to defer network augmentation, and GESS proved to be a suitable candidate. It is
demonstrated that such an embedded generation source can also provide peak load support by reducing
the upstream feeder requirements during peak consumption periods by supplying the loads locally.
Given the capabilities of the GESS with regards to power system quality, AusNet Services also planned
to investigate the effect on local system quality and stability that the GESS provides, such as power
factor, voltage support, harmonics, flicker, and negative sequence voltage. Additionally, the islanding
capabilities of the GESS have been investigated by AusNet Services to improve system supply and
stability in the case of larger network faults. In the event of a fault, the GESS islands the downstream
feeder, creating an islanded microgrid which the GESS would supply until its energy reserves are depleted
or the fault is cleared. When the fault is cleared, the GESS would reconnect to the grid and transfer the
supply back to the network and begin recharging the batteries on a scheduled, preset programmed time
of day [3].
3.3 SynCons
Wind/Solar farms are generally located in remote areas, and they often require long transmission lines to
connect to the main power grid. This increases the line impedance that could lead to weak grid scenarios
with a low X/R ratio and a low short circuit ratio (SCR). Voltage regulation at the point of connection
(PoC), generally carried out with reactive power control, becomes challenging in such scenarios since
the voltage becomes sensitive to the active power as well. From the wind or solar farm perspective, the
main objective is to maximise the active power delivery, and thus, they require additional resources to
supply reactive power [41, 52]. Therefore, it is essential to provide reactive power support with modified
control to regulate the PoC voltage and strengthen the transmission line [12].
Reactive power can be supplied using either static VAR devices (capacitor banks) or dynamic VAR
devices such as static synchronous compensators (STATCOMs) and synchronous condensers (SynCons).
Voltage regulation is challenging with static VAR solutions due to their step-change nature of the reactive
power supply. STATCOMs, however, overcome this limitation through the continuous change of reactive
power. Nevertheless, owing to the power converter limitations, STATCOMs cannot provide reactive
power beyond their capacity under grid faults, which is a requirement for clearing the faults. SynCons,
which are under/over-excited synchronous generators operated without a prime mover, have the ability
to change the reactive power smoothly and also provide reactive power up to six times the rated capacity
under grid faults. Therefore, SynCons are becoming the popular choice for reactive power supply in wind
20

25. and solar farms [25, 36, 38]. Moreover, it is possible to use the rotor inertia for short term frequency
support, which is an added benefit of SynCons, especially at higher levels of penetration of asynchronous
generation sources [2, 41]. This may require adding inertia plates to the rotor and making alterations to
the active power control, which is beyond the scope of this study [13, 39]. STATCOM/SynCon hybrid
solutions are also being tested to employ their complementary behaviours for suppressing overshoots in
fault recovery [50, 52].
The PoC voltage regulation through reactive power control of the SynCon is achieved by varying the
exciter current. Conventional exciter controllers are based on low-order controllers, and therefore,
stability cannot be guaranteed, especially under large disturbances such as faults in weak grids. Controller
tuning is often used to extend the operating range and keep the SynCon stable for large disturbances [46].
Nevertheless, due to the absence of knowledge on the frequency response of the system and the controller
not being optimised for the given system, large-signal stability cannot be guaranteed. Therefore, higher-
order controllers, designed based on the frequency response and optimised for the given system, are
required to minimise the voltage sensitivity. As a solution, this paper proposes to identify the frequency
response of the system and then develop an optimised higher-order controller to guarantee both small-
signal and large-signal stability.
The pseudo-random binary sequence (PRBS) signal injection and observation of the system response
are used in this study for system identification. Once the frequency response of the system is identified
through PRBS, an optimised controller is designed using a fixed-structure controller. The convex
optimisation approach is used to minimise the sensitivity to high-frequency noise. The developed
controller is then tested for a single machine infinite bus (SMIB) case and the IEEE 39-bus test system
under three-phase symmetrical faults to assess the fault recovery performance. Simulation results show
that the proposed exciter controller is able to recover and regulate the PoC voltage after faults, whereas
the conventional AC1A controller results in large oscillations in the PoC voltage.
The main contribution of this study is proposing a control strategy for SynCons that, unlike the
conventional AC1A, can maintain its stability in very weak grids, does not interact with other controllers
in the system, and does not introduce subsynchronous oscillations. The proposed controller is an H∞-
based robust controller that maintains the system’s stability and damps the sub-synchronous oscillations.
The proposed controller design procedure is essentially based on the following contributions:
• Apply identification method to identify a system from a SynCon’s exciter point of view (it is the
base of the proposed controller).
• Select the best order for the controller in terms of the sensitivity function.
• Obtain controller gains by convex optimisation.
3.3.1 Exciter Control
Exciter produces the rotor magnetic field, which in turn induces emfs in the stator winding of a SynCon.
The magnitude of the induced voltage depends on the exciter current, and higher currents in the exciter
(an over-excited SynCon) induce more voltage in the stator mimicking a capacitive reactive power
generator. Similarly, an under-excited SynCon absorbs reactive power. Therefore, with the appropriate
control of the exciter current, the reactive power injected into the PoC can be controlled. Hence, the
exciter current reference is derived from the reactive power requirement to restore the PoC voltage.
3.3.2 Limitations of the Conventional Exciter Control Methods
The source of electrical power for the exciter could be a separate DC source connected through slip rings
or an AC generator and a rotating rectifier embedded into the rotor. Conventional exciter controllers
21

26. +
KA
1+sTA
LV
Gate
AC
Rotating
Exciter
VOEL
VUEL
HV
Gate
_
VRmax
VRmin
VR
IFD
EFD
VSet
VF
VC
sKF
VA
Main Controller
1+sTC
1+sTB
1+sTF
Figure 3.4: The AC1A exciter diagram.
recommended by IEEE are broadly categorised into three groups as DC, AC, and STATIC, based on
the powering method mentioned above. The complete list of exciter controllers and IEEE recommended
practices can be found in [16, 23, 37]. Out of these IEEE exciter control models, AC1A, AC4A, and
AC7B are the popular choices for exciter control in SynCons [39, 40]. The IEEE AC1A exciter controller
is shown in Fig. 3.4, where VSet, VUEL, VOEL, EFD, and IFD are reference voltage, under-excitation limit,
over-excitation limit, field voltage, and field current. The parameters that can be tuned in the main
controller are regulator gain, KA, and the time constant, TA. The other two parameters, TB and TC, are
time constants inherent to the voltage regulator, which are small enough to be neglected in most cases.
Therefore, AC1A is in fact a typical first-order controller.
Conventional IEEE exciters are low-order controllers, and they are tuned to suit the given application
and thereby maintain adequate performances. Nevertheless, large-signal stability, especially during and
post-fault recovery in weak grids, cannot be guaranteed even with optimally tuned controllers. This
is because the conventional exciter controllers do not take the frequency response of the given system
into account. Hybrid control methods, adding non-linear control into the linear controllers, have been
proposed to enhance post-fault recovery and stability [26]. Nevertheless, they still lack knowledge on
the frequency response of the system, and thus, robust control cannot be guaranteed. Therefore, it is
essential to know the frequency response of the system to design a robust controller.
3.3.3 Further Developments Required in SynCon Exciter Control
The impact of exciter control of SynCons on weak grid integration of renewable energy sources,
especially during the fault recovery phase, is not well explored. This paper sheds some light on this
area by proposing a data-driven exciter control design approach and comparing the performance of
the proposed exciter controller against a conventional AC1A exciter controller. The PSCAD/EMTDC
simulation results verify the stable operation of the proposed exciter controller in a SMIB case and a
modified IEEE 39-bus system for high voltage ride-through and fault ride-through scenarios. Voltage
sensitivity analysis shows that low-order controllers fail to perform under these scenarios in weak grids,
and therefore, higher-order controllers are needed. The proposed controller design approach addresses
this requirement by identifying the frequency response of the system and then using convex optimisation
to find the optimum higher-order controller for the given system. Thus, the stable operation of the
SynCon is achieved with the proposed controller. For future studies, other conventional exciters such
as static exciters can be taken into account. Additionally, the SynCon reactive power limits may be
incorporated into the proposed control design procedure.
3.3.4 Optimal Allocation and Sizing of SynCons
Being a costly solution, SynCons capital cost can be justified if their rating and location are optimally
selected. There are a limited number of studies on the optimal operation of SynCons and their impacts
in weak grids. For example, in [24], a method to find the optimal location based on increasing impacts of
22

27. SynCons in a power system and voltage stability is introduced. However, the SynCon installation cost and
the effect of wind/solar farms penetration are not considered in this method. In [33], the post-retirement
planning of existing synchronous machines is proposed to enhance the SCR and frequency response in a
power system. The SynCons’ location and size are based on the retired synchronous machines’ capacity
and location. If a retired synchronous machine’s location is far from a new PEC-connected generator
or the size of the retired synchronous machine is lower than a required value, it does not have sufficient
impacts on the stability of the system. In this project, an optimisation method to determine an optimal
number, allocation, and sizing of SynCons is explored to enhance the system strength and stability in
a large weak power system in the presence of wind and solar farms. The proposed method minimises
investment, operation, and maintenance costs of SynCons, and also voltage deviation in a system while
the system’s SCR is maximised at different nodes. Two different approaches are taken into account for
the SCR calculation to ensure that the system strength is maximised. Since the SCR calculation based on
SynCon allocation and sizing is a nonlinear problem, linear programming optimisation approaches such
as convex optimisation are not applicable. Therefore, in this paper, three meta-heuristic optimisation
algorithms are adopted to implement the proposed optimisation method with the lowest complexity
and without any linearisation. As the proposed method is simple and not time-consuming, it can be
used for the system planning stage. The results are verified with Electromagnetic Transient (EMT)
simulation in PSCAD/EMTDC software. The Australian grid code is considered as a reference to
examine the interaction of SynCons with wind and solar farms in a weak grid. Moreover, the optimised
allocation/sizing of SynCons is compared with a random allocation/sizing. The main contributions of
this study are as follows:
• A comprehensive optimisation method to minimise the SynCons overall cost and the system’s
voltage deviation at different buses,
• Consideration of grid codes standards in the optimisation method,
• Consideration of PEC-connected generators and SynCons in the SCR calculation,
• Maintaining system strength in a large power system above a minimum requirement with minimum
contribution of SynCons,
• Applying three different meta-heuristic algorithms for optimisation.
More information and results of the study can be found in [15].
23

28. 4 Summary
This report presents the work carried out and outcomes produced in relation to the Weak grid
classification and grid strengthening solutions. The conventional weak grid classification indices, SCR,
X/R ratio and RoCoF are introduced, and their inadequacy in power grids with IBRs are discussed.
The recently introduced indices, including ESCR, CSCR, WSCR, and voltage sensitivity, are explained,
and their strengths and limitations are discussed. Considering limitations of the existing indices, a novel
index that is based on calculating the domain of attraction has been proposed in this report as a promising
solution. The use of Syncons and grid-forming inverters as grid strengthening solutions and their optimal
allocation are discussed in detail. A novel control strategy for the syncon exciter control is proposed to
achieve enhanced post-fault stability under weak grid scenarios. The proposed controller is based on
grid impedance estimation and determining the best-suited order of the controller.
Future work includes understanding controller interactions in wind/solar farms and exploring the
possibilities of using grid-forming inverter solutions to mitigate controller interaction issues.
24

29. References
[1] Andrade, Fabio et al. “Study of large-signal stability of an inverter-based generator using a
Lyapunov function”. In: IECON 2014-40th Annual Conference of the IEEE Industrial Electronics
Society. IEEE. 2014, pp. 1840–1846.
[2] Aziz, A., Oo, A. M. T., and Stojcevski, A. “Issues and Mitigations of Wind Energy Penetrated
Network: Australian Network Case Study”. In: Jour. of Modern Power Systems & Clean Energy
6.6 (Nov. 2018), pp. 1141–1157.
[3] Battery/diesel grid-connected microgrids: a large-scale, industry-based case study of future
microgrid capabilities. Report. Accessed: May 4, 2021. ABB, 2015. URL: https://library.e.
abb.com/public/0dd8532d75d14c49a6bc92cb91d71b30/%20Ausnet%5C%20Services%
5C%20GESS%5C%20white%5C%20paper.pdf.
[4] Bellini, Emiliano. General Electric works on grid-forming inverter controls. PV Magazine
International. Accessed: May 4, 2021. Apr. 2020. URL: https://www.pv-magazine.com/
2020/04/06/%20general-electric-works-on-grid-forming-inverter-controls/.
[5] Cheng, Huijie et al. “Transient angle stability of paralleled synchronous and virtual synchronous
generators in islanded microgrids”. In: IEEE Transactions on Power Electronics 35.8 (2020),
pp. 8751–8765.
[6] Cherevatskiy, S. et al. “Grid Forming Energy Storage System addresses challenges of grids with
high penetration of renewables (A case study)”. In: CIGRÉ Session (2020).
[7] Chou, Shih-Feng, Wang, Xiongfei, and Blaabjerg, Frede. “Two-port network modeling and
stability analysis of grid-connected current-controlled VSCs”. In: IEEE Transactions on Power
Electronics 35.4 (2019), pp. 3519–3529.
[8] Djunisic, Sladjana. ScottishPower Completes Black Start Project Using 69-MW Wind Farm.
Renewables Now. Accessed: May 4, 2021. Nov. 2020.
[9] Dong, Dong et al. “Analysis of phase-locked loop low-frequency stability in three-phase grid-
connected power converters considering impedance interactions”. In: IEEE Transactions on
Industrial Electronics 62.1 (2014), pp. 310–321.
[10] Dong, Dong et al. “Frequency behavior and its stability of grid-interface converter in distributed
generation systems”. In: 2012 Twenty-Seventh Annual IEEE Applied Power Electronics Conference
and Exposition (APEC). IEEE. 2012, pp. 1887–1893.
[11] Fang, Jingyang et al. “Stability improvement for three-phase grid-connected converters through
impedance reshaping in quadrature-axis”. In: IEEE Transactions on Power Electronics 33.10
(2017), pp. 8365–8375.
[12] Group B4.62, Working. “Connection of Wind Farms to Weak AC Networks”. In: Cigre Technical
Brochure 671. CIGRE. December 2016.
[13] Gu, H., Yan, R., and Saha, T. K. “Minimum Synchronous Inertia Requirement of Renewable
Power Systems”. In: 33.2 (March 2018), pp. 1533–1543.
25

30. [14] Gui, Yonghao et al. “Control of grid-connected voltage-source converters: The relationship
between direct-power control and vector-current control”. In: IEEE Industrial Electronics
Magazine 13.2 (2019), pp. 31–40.
[15] Hadavi, Sajjad, Mansour, Milad Zarif, and Bahrani, Behrooz. “Optimal Allocation and Sizing of
Synchronous Condensers in Weak Grids With Increased Penetration of Wind and Solar Farms”.
In: IEEE Journal on Emerging and Selected Topics in Circuits and Systems 11.1 (2021), pp. 199–
209.
[16] Hajagos, LM and Basler, MJ. “Changes to IEEE 421.5 Recommended Practice for Excitation
System Models for Power System Stability Studies”. In: IEEE Power Engineering Society General
Meeting. 2005, pp. 334–336.
[17] Han, H. et al. “Review of Power Sharing Control Strategies for Islanding Operation of AC
Microgrids”. In: IEEE Transactions on Smart Grid 7.1 (2016), pp. 200–215.
[18] Harnefors, Lennart et al. “Passivity-based stability assessment of grid-connected VSCs—An
overview”. In: IEEE Journal of emerging and selected topics in Power Electronics 4.1 (2015),
pp. 116–125.
[19] He, Xiuqiang, Geng, Hua, and Ma, Shaokang. “Transient stability analysis of grid-tied converters
considering PLL’s nonlinearity”. In: CPSS Transactions on Power Electronics and Applications 4.1
(2019), pp. 40–49.
[20] Hornsdale Power Reserve: Year 2 Technical and Market Impact Case Study. Report. Accessed: May
4, 2021. Aurecon, 2019. URL: https://hornsdalepowerreserve.com.au/wp-content/
uploads/2020/07/Aurecon-Hornsdale-Power-Reserve-Impact-Study-year-2.pdf.
[21] Hu, Qi et al. “Large signal synchronizing instability of PLL-based VSC connected to weak AC
grid”. In: IEEE Transactions on Power Systems 34.4 (2019), pp. 3220–3229.
[22] Huang, Meng et al. “Bifurcation and large-signal stability analysis of three-phase voltage source
converter under grid voltage dips”. In: IEEE Transactions on Power Electronics 32.11 (2017),
pp. 8868–8879.
[23] IEEE Standard. “IEEE Recommended Practice for Excitation System Models for Power System
Stability Studies”. In: IEEE Std 421.5. IEEE. 2016, pp. 1–207.
[24] Igbinovia, Famous O et al. “Optimal location of the synchronous condenser in electric-power
system networks”. In: 2016 17th International Scientific Conference on Electric Power Engineering
(EPE). IEEE. 2016, pp. 1–6.
[25] Jia, J. et al. “Investigation on the Combined Effect of VSC-Based Sources and Synchronous
Condensers Under Grid Unbalanced Faults”. In: 34.5 (Oct. 2019), pp. 1898–1908.
[26] Jiang, DC. et al. “Hybrid Excitation Control Strategy of The Synchronous Condenser Using
Differential Geometry Principle Assisted with a PI Controller”. In: Proc. IEEE Conference on
Industrial Electronics and Applications. Xi’an, China, 2019, pp. 1033–1038.
[27] Liao, Yicheng and Wang, Xiongfei. “Impedance-based stability analysis for interconnected
converter systems with open-loop RHP poles”. In: IEEE Transactions on Power Electronics 35.4
(2019), pp. 4388–4397.
26

31. [28] Lin, Yashen et al. Research Roadmap on Grid-Forming Inverters. Tech. rep. National Renewable
Energy Lab.(NREL), Golden, CO (United States), 2020.
[29] Liu, J. et al. “Enhanced Virtual Synchronous Generator Control for Parallel Inverters in
Microgrids”. In: IEEE Transactions on Smart Grid 8.5 (2017), pp. 2268–2277.
[30] Liu, Yuan et al. “Transient Stability Enhancement Control Strategy Based on Improved PLL for
Grid-Connected VSC during Severe Grid Fault”. In: IEEE Transactions on Energy Conversion
(2020).
[31] Malinowski, Mariusz, Jasinski, Marek, and Kazmierkowski, Marian P. “Simple direct power
control of three-phase PWM rectifier using space-vector modulation (DPC-SVM)”. In: IEEE
Transactions on Industrial Electronics 51.2 (2004), pp. 447–454.
[32] Mansour, Milad Zarif et al. “Nonlinear Transient Stability Analysis of Phased-Locked Loop
Based Grid-Following Voltage Source Converters Using Lyapunov’s Direct Method”. In: IEEE
Journal of Emerging and Selected Topics in Power Electronics (2021).
[33] Masood, Nahid-Al et al. “Post-retirement utilisation of synchronous generators to enhance
security performances in a wind dominated power system”. In: IET Generation, Transmission
& Distribution 10.13 (2016), pp. 3314–3321.
[34] Matevosyan, Julia et al. “Grid-forming inverters: Are they the key for high renewable
penetration?” In: IEEE Power and Energy magazine 17.6 (2019), pp. 89–98.
[35] Mirafzal, Behrooz and Adib, Aswad. “On Grid-Interactive Smart Inverters: Features and
Advancements”. In: IEEE Access 8 (2020), pp. 160526–160536.
[36] Mohanan, Vishnu Arayamparambil Vinaya et al. “Stabilising Influence of a Synchronous
Condenser in Low Inertia Networks”. In: IET Gen., Trans. & Dist. 14.17 (Sept. 2020), pp. 3582–
3593.
[37] NEPLAN. “EXCITER MODELS Standard Dynamic Excitation Systems in NEPLAN Power
System Analysis Tool”. In: NEPLAN Technical Document. NEPLAN. V555, pp. 1–186.
[38] Nguyen, H. T. et al. “Applying Synchronous Condenser for Damping Provision in Converter-
Dominated Power System”. In: Journal of Modern Power Systems and Clean Energy Early Access
(Sept. 2020), pp. 1–9.
[39] Nguyen, H. T. et al. “Combination of Synchronous Condenser and Synthetic Inertia for Frequency
Stability Enhancement in Low-Inertia Systems”. In: 10.3 (July 2019), pp. 997–1005.
[40] Nguyen, H. T. et al. “Hardware- and Software-in-the-Loop Simulation for Parameterizing the
Model and Control of Synchronous Condensers”. In: 10.3 (July 2019), pp. 1593–1602.
[41] Nguyen, H. T. et al. “Talega SynCon - Power Grid Support for Renewable-based Systems”. In:
Proc. IEEE Southeastcon. Huntsville, AL, USA, 2019.
[42] Parkinson, Giles. Tesla Big Battery at Hornsdale Delivers World Record Output of 150MW. Renew
Economy, Australia. Accessed: May 4, 2021. July 2020. URL: https://reneweconomy.com.
au/tesla-big-battery-at-hornsdale-delivers%20-world-record-output-of-
150mw-26392/.
27

32. [43] Pattabiraman, Dinesh, Lasseter, RH, and Jahns, TM. “Comparison of grid following and grid
forming control for a high inverter penetration power system”. In: 2018 IEEE Power & Energy
Society General Meeting (PESGM). IEEE. 2018, pp. 1–5.
[44] Rocabert, Joan et al. “Control of Power Converters in AC Microgrids”. In: IEEE transactions on
power electronics 27.11 (2012), pp. 4734–4749.
[45] Rosso, R. et al. “Grid-Forming Converters: an Overview of Control Approaches and Future
Trends”. In: 2020 IEEE Energy Conversion Congress and Exposition (ECCE). 2020, pp. 4292–
4299.
[46] Sajnekar, DM, Deshpande, SB, and Moharil, RM. “Efficient PID Controller Tuning Method
Selection to be Used in Excitation System of Brushless Synchronous Generator”. In: International
Conference on Computation of Power, Energy Information and Commuincation. 2016, pp. 413–
418.
[47] Shuai, Zhikang et al. “Transient angle stability of virtual synchronous generators using Lyapunov’s
direct method”. In: IEEE Transactions on Smart Grid 10.4 (2018), pp. 4648–4661.
[48] Slotine, Jean-Jacques E, Li, Weiping, et al. Applied nonlinear control. Vol. 199. 1. Prentice hall
Englewood Cliffs, NJ, 1991.
[49] Sproul, Stephen, Cherevatskiy, Stanislav, and Klingenberg, Hugo. Grid Forming Energy Storage:
Provides Virtual Inertia, Interconnects Renewables and Unlocks Revenue. Accessed: May 4, 2021.
July 2020. URL: https://go.hitachi-powergrids.com/grid-forming-webinar-2020.
[50] Stiger, A, Rivas, RA, and Halonen, M. “Synchronous Condensers Contribution to Inertia and
Short Circuit Current in Cooperation with STATCOM”. In: IEEE PES GTD Grand International
Conference and Exposition Asia (GTD Asia). 2019, pp. 955–959.
[51] Taul, Mads Graungaard et al. “An overview of assessment methods for synchronization stability of
grid-connected converters under severe symmetrical grid faults”. In: IEEE Transactions on Power
Electronics 34.10 (2019), pp. 9655–9670.
[52] Tzelepis, D. et al. “Enhancing Short-Circuit Level and Dynamic Reactive Power Exchange in GB
Transmission Networks under Low Inertia Scenarios”. In: Proc. IEEE International Conference on
Smart Energy Systems and Technologies (SEST 2019). Porto, Portugal, Sept. 2019, pp. 1–6.
[53] Unruh, Peter et al. “Overview on Grid-Forming Inverter Control Methods”. In: Energies 13.10
(2020), p. 2589.
[54] Vandoorn, T.L. et al. “Review of Primary Control Strategies for Islanded Microgrids with Power-
Electronic Interfaces”. In: Renewable and Sustainable Energy Reviews 19 (2013), pp. 613–628.
[55] Wang, Shike et al. “Small-signal modeling and stability prediction of parallel droop-controlled
inverters based on terminal characteristics of individual inverters”. In: IEEE Transactions on Power
Electronics 35.1 (2019), pp. 1045–1063.
[56] Wang, Xiongfei, Harnefors, Lennart, and Blaabjerg, Frede. “Unified impedance model of grid-
connected voltage-source converters”. In: IEEE Transactions on Power Electronics 33.2 (2017),
pp. 1775–1787.
28

33. [57] Wang, Xiongfei et al. “Grid-synchronization stability of converter-based resources—An
overview”. In: IEEE Open Journal of Industry Applications 1 (2020), pp. 115–134.
[58] Wu, Heng and Wang, Xiongfei. “Design-oriented transient stability analysis of PLL-synchronized
voltage-source converters”. In: IEEE Transactions on Power Electronics 35.4 (2019), pp. 3573–
3589.
[59] Yang, Dongsheng and Wang, Xiongfei. “Unified modular state-space modeling of grid-connected
voltage-source converters”. In: IEEE Transactions on Power Electronics 35.9 (2020), pp. 9702–
9717.
[60] Yang, Dongsheng et al. “Symmetrical PLL for SISO impedance modeling and enhanced stability
in weak grids”. In: IEEE Transactions on Power Electronics 35.2 (2019), pp. 1473–1483.
[61] Zhang, Xueguang et al. “A symmetrical control method for grid-connected converters to suppress
the frequency coupling under weak grid conditions”. In: IEEE Transactions on Power Electronics
35.12 (2020), pp. 13488–13499.
[62] Zhao, Jiantao et al. “Nonlinear and transient stability analysis of phase-locked loops in grid-
connected converters”. In: IEEE Transactions on Power Electronics 36.1 (2020), pp. 1018–1029.
[63] Zhou, Jenny Z and Gole, Aniruddha M. “VSC transmission limitations imposed by AC system
strength and AC impedance characteristics”. In: (2012).
[64] Zhou, Jenny Z et al. “Impact of Short-Circuit Ratio and Phase-Locked-Loop Parameters on the
Small-Signal Behavior of a VSC-HVDC Converter”. In: IEEE Transactions on Power Delivery
29.5 (2014), pp. 2287–2296.
29