Task 1 | Weak grids classification and test-bed development

This task will explore and propose new measures to classify weak networks and will identify grid scenarios and value-range under which weak-grid-connected wind/solar farms will experience instability issues. Additionally, this task will develop a testbed, based on the North-western Victorian network (in collaboration with and based on the data provided by AEMO and AusNet Services). This testbed will be used in the following tasks to validate their findings.

Task 2 | Grid-strengthening solutions

This task will propose two main grid-strengthening methods, i.e., SynCons and grid-forming inverters, and will explore their optimal allocation and sizing in weak networks. Additionally, alternative control strategies for these grid-strengthening assets with a focus on ultra-weak networks will be devised. Finally, the black-start capability of grid-forming inverters will be explored and outlined.

Task 3 | Wind/Solar farms controls and their interactions with other PEC-connected assets

In this task, two internal controllers (PoC voltage controller and PLL) for grid-following converters with a focus on ultra-weak grids (SCR less than one) will be developed to guarantee robust performance and stability over a range of grid strength scenarios and specifically when the grid is very weak. Additionally, this task will investigate the interaction of various power-electronic converter (PEC)-connected assets in the network, with a focus on the existing grid following inverters, and will identify grid scenarios and value-ranges that lead to oscillatory modes.

Grid Forming Inverter Modeling, Control, and Applications

This paper surveys the current literature on modelling methods, control techniques, protection schemes, applications, and real-world implementations pertaining to grid forming inverters (GFMIs). This paper presents a comprehensive review of GFMIs covering recent advancements in control technologies, fault ride-through capabilities, stability enhancement measures, and practical implementations. Moreover, the challenges of adding GFMIs into existing power systems, including a seamless transition from grid-connected mode to the standalone mode and vice versa, are also discussed in detail. Recently commissioned projects in Australia, the UK, and the US are taken as examples to highlight the trend in the power industry in adding GFMIs to address issues related to weak grid scenarios. Research directions in terms of voltage control, frequency control, system strength improvement, and regulatory framework are also discussed. This paper serves as a resource for researchers and power system engineers exploring solutions to the emerging problems with high penetration of IBRs, focusing on GFMIs. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper studies various aspects of these assets in detail.

Power-Synchronized Grid-Following Inverter Without a Phase-Locked Loop

This paper proposes a power-synchronized control strategy for grid-following inverters (GFLIs) to regulate their power exchange with the grid without any need for sensing/regulating the point of connection voltage. Contrary to conventional GFLIs, which rely on phase-locked loops for grid synchronization and have difficulties in weak grid conditions, the proposed strategy is power synchronized and utilizes the inverter terminal voltage for power control leading to its seamless performance in ultra-weak grids. Additionally, since the proposed approach does not require any voltage regulation at the point of connection to the grid, contrary to grid-forming inverters, it can reliably operate in stiff and/or series-compensated grids as well. The proposed approach benefits from a decoupling control structure that is tuned using a loop-shaping method. Compared to conventional GFLIs, this approach does not need any extra hardware; hence, it can easily be retrofitted into the existing large fleet of GFLIs. This paper mainly contributes to Task 2 of the project. The proposed power-synchronized GFLI is an ideal solution for incorporating the inverter-based resources in weak grids, and this paper provides a detailed description of this structure.

Optimal Allocation and Sizing of Synchronous Condensers in Weak Grids With Increased Penetration of Wind and Solar Farms

SynCons, being synchronous machines without a prime mover, provide several benefits in weak power systems, such as frequency support, system strength, and voltage regulation. Although SynCons are widely utilized to mitigate the weak grid integration challenges, their installation /operation costs make them a costly solution. Additionally, their lead-time can be more than a year, which means their initial sizing and allocation must be optimal. In this paper, a method for the optimal allocation and sizing of SynCons is proposed. The main objective of this method is maintaining Short Circuit Ratio (SCR) in the system greater than pre-defined values while the investment and operation costs of SynCons, and voltage deviation in the system are minimized. Three meta-heuristic optimization algorithms are used to implement the proposed method, and its performance is evaluated via Electromagnetic Transient (EMT) time-domain simulation in a modified IEEE 39-bus system. This paper mainly contributes to Task 2 of the project. SynCons are one of the leading solutions for grid strengthening, and this paper studies their optimal allocation and sizing, especially in weak grids with high penetration of inverter-based resources.

Nonlinear Transient Stability Analysis of Phase-Locked Loop Based Grid-Following Voltage Source Converters Using Lyapunov’s Direct Method

In this paper, the transient stability conditions for a grid-following Voltage Source Converter (VSC) are found using Lyapunov's stability theorem. These conditions take into account both the grid specifications and the VSC dynamics. The derived conditions are based on a well-known nonlinear model of the VSC Phase-Locked Loop. To evaluate the stability of the nonlinear system, Lyapunov’s direct method is employed. To this end, a new Lyapunov function is proposed, and its characteristics are analysed. Using this Lyapunov function, the domain of attraction of the system equilibrium point is calculated. Additionally, a novel system strength index based on the domain of attraction of the system is proposed. The privilege of this index over the conventional indices are absoluteness, VSC dynamics consideration, and comparability of different VSCs with each other from a stability point of view. In the end, the correctness of the proposed stability analysis is validated via simulation in Matlab/PLECS and experiment. This paper mainly contributes to Task 1 of the project. The derived conditions and the novel system strength index for evaluation of transient stability of the grid-following VSCs are new measures for classifying weak networks and can be used for identifying grid scenarios and value ranges under which weak-grid-connected inverter-based resources experience instability issues.

A Robust Exciter Controller Design for Synchronous Condensers in Weak Grids

Weak grid scenarios and low-inertia systems are emerging issues in power systems, leading to voltage and frequency instabilities. Synchronous Condensers (SynCons) have recently drawn renewed attention as a promising solution to provide system strength and inertia support. Even though the exciter control of SynCons is a well-established technology, further developments are required to guarantee the stability of post-fault operations, particularly in weak grids. This paper proposes a data-driven approach for designing higher-order optimized exciter controllers to meet this requirement. A pseudo-random binary sequence (PRBS)-based system identification method is used to obtain frequency response data of the power system from the exciter point of view, which is then fed into the proposed optimal control design procedure. The proposed exciter controller is tested for voltage ride-through and fault scenarios in a single machine infinite bus (SMIB) case and the IEEE 39-bus test system to assess its performance compared to the conventional AC1A exciter controller. This paper mainly contributes to Task 2 of the project. SynCons are one of the leading solutions for grid strengthening, and this paper proposes a novel approach for designing SynCons' exciter controllers so that the stability of their post-fault operation, especially in weak spots of the grids is guaranteed.

H∞-based Control Design for Grid-forming Inverters with Enhanced Damping and Virtual Inertia

Grid-forming inverters (GFMIs) are identified as an important asset for achieving renewable energy-rich power grids. GFMIs are attracting significant attention due to their superior characteristics over grid-following inverters in both grid-connected (GC) and standalone (SA) scenarios. In this paper, a second-order discrete-time controller is proposed to achieve a well-damped step response for power reference commands and improved virtual inertia provision capability. In this paper, a control design method based on H∞ is proposed, which is based on the frequency response of the system, to tune the proposed controller. The proposed control design presents a methodical process to specify the desired performance indices through frequency-domain constraints. The performance of the controller is thoroughly validated analytically and through simulation results. The superior performance of the proposed controller over the virtual synchronous generator controller in terms of tracking performance and virtual inertia provision capability is verified through experimental results. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper proposes a robust control system for them to provide enhanced damping and virtual inertia.

Generalized Virtual Synchronous Generator Control Design for Renewable Power Systems

Grid-forming inverters (GFMIs) are recognized as one of the key enablers towards highly renewable energy proliferated grids. One of the pivotal characteristics of GFMIs is the ability to seamlessly switch between grid-connected (GC) and standalone (SA) modes. In this paper, a novel controller is proposed for the GFMIs to accurately follow the power reference commands in the GC mode while providing the required amount of virtual inertia in the SA mode to slow down the rate of change of frequency (RoCoF) following a disturbance. The proposed control design, where straightforward equations are given to calculate the controller gains directly, is based on the frequency response of the open-loop system. Furthermore, based on the frequency response of the controller, a condition for the placement of the poles of the controller is derived to guarantee the RoCoF relay limit compliance in the SA mode. The experimental results show that the proposed controller results in lower overshoots and shorter settling times in step responses in the GC mode than the virtual synchronous generator (VSG) controller while providing more virtual inertia than the VSG controller to slow down RoCoF in the SA mode. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper studies various aspects of these assets in detail.

Adaptive Virtual Resistance for Post-fault Oscillation Damping in Grid-forming Inverters

Post-fault oscillations in active power and voltage responses of grid-connected Voltage Source Converters (VSCs) have been reported in the literature. They are caused by non-ideally-tuned controllers and the implemented current limitations used for protecting the VSCs from over-currents. These oscillations become more significant when the VSC is connected to a weak grid, deteriorating the recovery process of the VSC. This paper presents a method for damping the post-fault oscillations using an adaptive virtual resistor (VR). Even though these oscillations are observed with both grid-following and grid forming inverters (GFMIs), this paper focuses on droop-based GFMIs. The proposed method dynamically integrates a VR into the VSC control and removes it in the normal operation mode of the VSC. This method is implemented in the Synchronous Reference Frame (SRF), which is commonly used due to its decoupled active and reactive power control. The amount of virtual resistance used for oscillation damping is adaptive to the recovery rate of the VSC. Hence, the proposed method is robust against changes in grid strength. Finally, the performance of the method is evaluated in PSCAD/EMTDC and also experimentally validated. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper proposes a method for damping their post-fault oscillations through an adaptive VR in their control structure.

Linear Parameter-Varying Control of A Power-Synchronized Grid-Following Inverter

This paper proposes a Linear Parameter-Varying loop-shaping controller for a power-synchronized grid-following inverter (PSGFLI). This control strategy regulates the inverter output active and reactive powers at the terminal instead of the point of connection and does not require a phase-locked loop (PLL) for extracting the voltage phase angle. Hence, the prevalent stability issues exhibited when GFLIs are connected to weak grids are not present, and the proposed PSGFLI control strategy can work under both very weak and strong grid conditions without being prone to instability. In this approach, the controller parameters are functions of the operating point and are changed during the real-time operation such that the closed-loop performance is preserved in all operating points. Furthermore, since the grid impedance is a factor in the design process, a robustness analysis against grid impedance estimation error is conducted, and it is shown that discrepancies in estimated and real grid impedances are unlikely to make the system unstable. The performance of the proposed control design is validated in MATLAB/PLECS and experiments for both strong and weak grids. This paper mainly contributes to Task 2 of the project. PSGFLI is an ideal solution for incorporating the inverter-based resources in weak grids, and this paper provides a novel control scheme for enhancing its performance.

Small-Signal Synchronization Stability Enhancement of Grid-Following Inverters via a Feedback Linearization Controller

This paper proposes a feedback linearization controller for a grid-following inverter (GFLI) that uses a conventional Phase-Locked Loop (PLL) as the synchronization unit. The proposed controller enhances the GFLI synchronization by expanding the PLL domain of attraction to the whole plane that is limited to a small region around the equilibrium point in a conventional PLL, provided that the grid impedance and voltage are known. Linearizing the overall closed-loop system, the proposed controller provides linear system attributes for the PLL, leading to an infinite domain of attraction and only one equilibrium point. Additionally, a state-feedback controller is integrated within the feedback linearization controller so that it enables the system to have an adjustable dynamic response. Finally, it is shown that the system is robust against parametric uncertainties. The performance of the proposed control design is validated in Matlab/Simulink and experiment. It is verified that the proposed controller expands the domain of attraction and enhances the system dynamic response. This paper mainly contributes to Task 2 of the project. The proposed feedback linearization controller is a good solution for stabilization of PLL-based GFLIs on weak grids.

A Planning Method for Synchronous Condensers in Weak Grids Using Semi-definite Optimization

Synchronous Condensers (SynCons) offer voltage regulation, inertia, and fault current contribution to solve the challenges of voltage and frequency instability introduced by the high penetration of renewable energy resources (RERs). However, the cost of installation and operation of a SynCon is noticeable. Furthermore, the SynCons installation can take more than a year, which means the number, size, and placement of the SynCons must be selected optimally. This paper proposes a method to formulate the optimal sizing and allocation of the SynCons via mixed-integer convex optimization. The optimization procedure aims to minimize the cost of SynCons installation, maintenance, and operation while maintaining a certain Short Circuit Ratio (SCR) at points of connection (PoCs). To ensure the SCR at the PoCs is greater than a certain threshold, the SCRs are formulated as constraints in the proposed optimization procedure. The modified IEEE 39-bus system is used to evaluate the proposed optimization method. The performance of the system with optimal SynCons is verified by electromagnetic transient time-domain simulation using PSCAD/EMTDC software. This paper mainly contributes to Task 2 of the project. SynCons are one of the leading solutions for grid strengthening, and this paper proposes a planning method for them especially in weak grids with high penetration of inverter-based resources.

Comprehensive Modeling, Analysis, and Comparison of State-Space and Admittance Models of PLL-Based Grid-Following Inverters Considering Different Outer Control Modes

The phase-locked loop (PLL)-based grid-following inverters have been widely used as the interface between renewable energy resources (e.g., wind and solar power) and the utility grid. To provide the small-signal stability analysis community with handy both state-space and admittance models and investigate the effects of various outer control loops on the small-signal models, this article presents a comprehensive and systematic small-signal modeling, analysis, and comparison framework of the PLL-based grid-following inverters, where the state-space and dq-domain admittance models of eleven control modes are derived step by step in a completely followable style. All of these derived small-signal models are verified by the time-domain step responses and frequency-domain dq-domain admittance measurement. The insights into the effects of these outer control modes on the poles and residues of the dq-domain admittance model are also explored, which help to understand how these outer control modes contribute to the dq-domain admittance shaping. By paving the way for studying the interactions between different IBRs, this paper mainly contributes to Task 3 of the project.

Output Impedance Derivation and Small-Signal Stability Analysis of a Power-Synchronized Grid Following Inverter

In recent years, grid-following inverters (GFLIs) and grid-forming inverters (GFMIs) have established their position as the mainstream synchronization techniques for the grid integration of inverter-based resources into power systems. However, both of these integration techniques have their shortcomings in weak, strong, and/or series-compensated grids. Recently, in the literature, a power synchronized GFLI has been proposed that does not suffer from the issues exhibited in GFLIs and GFMIs. This article provides an analytical output impedance of this power-synchronized GFLI that uses a linear parameter-varying controller (LPV-PSGFLI). This impedance is then used for impedance-based stability analysis via the Nyquist stability criterion. In addition, the derived impedance is validated via system identification, and a comparison between a conventional GFLI and an LPV-PSGFLI is made under various system strengths. It is seen that the LPV-PSGFLI can inject power into the grid, whereas the conventional GFLI fails when both are integrated into a very weak grid. Finally, the accuracy of the impedance-based stability analysis using the derived output impedance is validated in Matlab/PLECS and in experiments in various scenarios. This paper mainly contributes to Task 2 of the project. PSGFLI is an ideal solution for incorporating the inverter-based resources in weak grids, and this paper studies the small-signal stability of this inverter.

Comparison of PLL-Based and PLL-Less Control Strategies for Grid-Following Inverters Considering Time and Frequency Domain Analysis

This article presents a comprehensive comparison of three control strategies used for grid-following inverters (GFLIs). The first strategy is the phase-locked loop (PLL)-based vector current control (VCC), and the other two PLL-less controllers are the voltage-modulated direct power control (VMDPC) and the linear-parameter-varying power-synchronized control (LPV-PSC). The VCC relies on the PLL to synchronize with the grid frequency to control the exchanged real and reactive power with the grid, which may result in instability issues under weak grid conditions. To prevent this, the VMDPC and LPV-PSC are proposed recently as PLL-less approaches to overcome the difficulties of the VCC in weak grid conditions. The performances of the VCC, VMDPC, and LPV-PSC are comprehensively reviewed in this article, considering the operations of the GFLIs under both strong and weak grids. In addition to evaluating the three controllers in the time-domain, the frequency-domain impedance-based stability analysis based on the generalized Nyquist criterion is also considered, which confirms the time-domain findings in terms of accurate predictions of the stable/unstable operations of the GFLIs that are equipped with these controllers. It is found that, compared to the conventional VCC and the VMDPC, the LPV-PSC has promising performance under various test conditions in both strong and weak grids, which may be a future solution for weak-grids connection of the GFLIs. This paper mainly contributes to Task 2 of the project by focusing on the stability of different types of grid-following inverters.

Multivariable Control Design for Grid-forming Inverters with Decoupled Active and Reactive Power Loops

In Grid-forming inverters (GFMIs), dynamic control of the magnitude ( Vc ) and angle ( θ ) of the point of common coupling (PCC) voltage is used to achieve active ( P ) and reactive ( Q ) power transfer across a line. However, independent control of P and Q via Vc and θ becomes challenging due to the coupling between P and Q loops. The coupling becomes severe as the resistance-to-reactance ratio of the grid impedance and the power angle between the GFMI and the grid voltages are increased. This paper proposes a novel multivariable controller to completely decouple P and Q loops in GFMIs. The proposed multivariable controller could be designed based on the prevalent control structures for GFMIs such as droop controller, swing equation-based virtual synchronous generator (VSG) controller, zero steady-state error reactive power controller, and fixed steady-state error reactive power controller. The additional cross-channel decoupling controllers in the proposed multivariable controller provide superior decoupling action over the existing decoupling methods, such as the virtual inductor-based method. An H∞ -based method is adopted to tune the proposed multivariable controller parameters, where the straightforward formulation of the desired closed-loop dynamics based on the open-loop system is clearly shown. The decoupling performance of the controller is experimentally validated extensively. The experimental results show that the proposed controller results in superior performance over the prevalent decoupling methods, such as the virtual-inductor decoupling method. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper proposes a novel control method for them.

Online Grid Impedance Estimation-Based Adaptive Control of VSGs Considering Strong and Weak Grid Conditions

The conventional virtual synchronous generator (VSG) is normally designed to meet certain operational and control requirements in the islanded mode. However, once the VSG is switched to grid-connected mode (GCM), the robust operation cannot be guaranteed under different grid conditions. It can lead to, especially in strong grids, poor dynamic performance such as significant oscillation, long settling time, and high overshoot. In order to improve the VSG performance in the GCM, this article first analyses in depth the inherent coupling between the active and reactive power and its dependence on the grid conditions, such as the short circuit ratio, grid impedance ratio Xg/Rg, and the wide grid impedance variations. Afterwards, an online grid impedance estimation-based adaptive VSG (AVSG) control strategy is proposed to ensure the robust operation of the VSG considering both strong and weak grid conditions. This technique allows the operator to specify the desired settling time of output power and damping ratio. To estimate the grid impedance in real time without extra hardware and reduce the associated impacts on power quality, an online event-based grid impedance estimation algorithm is embedded into the control loop of the AVSG. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper proposes an adaptive controller tuning technique to improve the performance of the VSG-based GFMIs.

Impact of Voltage-Loop Feedforward Terms on the Stability of Grid-Forming Inverters and Remedial Actions

This paper reveals the impact of voltage control loop feedforward terms on the stability of grid-forming inverters (GFMIs) connected to a grid. By deriving a mathematical model, this paper shows that unless the GFMI current control loop is fast enough, the feedforward terms in the voltage control loop may threaten the GFMI small-signal stability. To this end, a necessary and sufficient condition for GFMI stability is proposed, provided that the grid impedance at the point of connection is known. Furthermore, two easy-to-implement yet effective remedial actions are proposed to enhance stability. Aiming to preserve the control structure, the first remedial action re-tunes the voltage controller to satisfy the obtained stability condition, while the second remedial action incorporates simple gains to attenuate the feedforward terms. Moreover, to demonstrate the effectiveness of the second remedial action, the obtained necessary and sufficient stability condition is modified to include the proposed attenuation gain. Eventually, the accuracy of the stability analysis and the effectiveness of the proposed remedial actions are evaluated in simulation and experiment. This paper mainly contributes to Task 2 of the project. GFMIs are one of the leading solutions for grid strengthening, and this paper discusses the stability of GFMIs considering their inner control loops.

Near-optimal Storage Strategies in Electricity Markets

Storing electricity is completely essential to the energy transition. It also deeply disrupts the manner in which electricity markets operate, for it introduces delay. In this paper, we consider a dynamic model of an oligopolistic market with demand shocks, in which a storage unit buys and sells energy subject to a capacity constraint. To make progress in this stochastic game, we restrict attention to simple heuristics, and we can characterise the optimal policy of a storage unit in this restricted class of heuristics.

Dr Behrooz Bahrani

Ms Jacqueline Bridge

Dr Babak Badrzadeh

Dr Sasan Zabihi

Dr Reza Razzaghi

Professor Tony Marxsen

Dr Mohammad Hasan Ravanji

Postdoctoral research fellow

Dr Nabil Mohammed

Postdoctoral research fellow

Dr Weihua Zhou

Postdoctoral research fellow

Dr Gamini Jayasinghe

Postdoctoral research fellow

Dr Milad Zarif Mansour

PhD student

Dr Sajjad Hadavi

PhD student

Mr Dayan Rathnayake

PhD student

Mr Si Phu Me

PhD student