Fast Frequency Control Scheme through Adaptive Virtual Inertia Emulation

This paper presents a novel virtual inertia controller for converters in power systems with high share of renewable resources. By combining the analytical study of system dynamics and a Linear-Quadratic Regulator (LQR)-based optimization technique, the optimal state feedback gain is determined, adapting the emulated inertia constant according to the frequency disturbance in the system. The optimality is achieved through trade-off between the critical frequency limits and the required control effort, i.e. utilization of the internal energy storage. The proposed controller is integrated into a state-of-the-art converter control scheme and verified through EMT simulations. The results show a significant improvement in the frequency response compared to an open-loop system, while also preserving drastically more DC-side energy than a non-adaptive controller

Stability Analysis of Converter Control Modes in Low-Inertia Power Systems

This paper deals with the small-signal stability analysis of converter control modes in low-inertia power systems. For this purpose, a detailed differential-algebraic equation model of the voltage source converter and its control scheme is developed. Both grid-forming and grid-feeding concepts have been considered, as well as different active power controllers based on traditional droop and virtual inertia emulation. An eigenvalue analysis of the linearized state-space system is conducted and the performance of different control configurations is compared. Furthermore, various bifurcation studies have been completed and conclusions on stability margins have been drawn with respect to control sensitivity and robustness

Interval-Based Adaptive Inertia and Damping Control of a Virtual Synchronous Machine

This paper presents a novel virtual synchronous machine controller for converters in power systems with a high share of renewable resources. Using an interval-based approach, the emulated inertia and damping constants are adaptively adjusted according to the frequency disturbance in the system, while simultaneously keeping the frequency within prescribed limits. Furthermore, the sufficient stability conditions for control tuning are derived. The proposed design is integrated into a state-of-the-art converter control scheme and tested through time-domain simulations. A comparative study against the existing approaches in the literature verifies the control effectiveness

Partial Grid Forming Concept for 100% Inverter-Based Transmission Systems

With the current trends in renewable energy integration, the concept of a 100% inverter-based power system is becoming more of a reality. However, the existing Voltage Source Converter (VSC) control schemes for such systems focus mostly on the operation of low-voltage microgrids, which have different requirements from the transmission system perspective. This paper proposes a new classification of VSC control strategies depending on their mode of operation. Then, the concept of partial grid forming VSC is introduced and it is shown that a system with zero rotational inertia can operate without a dedicated grid-forming VSC unit, but rather with partial forming of key system characteristics distributed across different VSC units. The performance of this approach is tested on detailed VSC models developed in both MATLAB Simulink and virtual Hardware-In-the-Loop (vHIL) platforms. Furthermore, an investigation towards necessary converter and network criteria for providing a stable system under the proposed control concepts is presented

Robust Converter Control Design under Time-Delay Uncertainty

This paper deals with the converter control design under time delay uncertainty in power systems with high share of converter-based generation. Two approaches for time delay modeling are proposed using linear fractional transformations and linear parameter-varying systems, respectively. Subsequently, two output-feedback synthesis methods are implemented based on H∞ control theory, and formulated using linear matrix inequalities: (i) a norm-bounded parametric H∞ controller; and (ii) a gain-scheduled H∞ control. These robust control principles are then employed to improve the performance of Voltage Source Converters (VSCs) under varying measurement delays. Three novel control strategies are proposed in order to redesign the conventional inner control loop and improve converter performance when dealing with measurement uncertainty. Finally, the controllers are integrated into a state-of-the-art VSC model and compared using time-domain simulations

LQR-Based Adaptive Virtual Synchronous Machine for Power Systems with High Inverter Penetration

This paper presents a novel virtual synchronous machine controller for converters in power systems with a high share of renewable resources. Using a linear quadratic regulator-based optimization technique, the optimal state feedback gain is determined to adaptively adjust the emulated inertia and damping constants according to the frequency disturbance in the system, while simultaneously preserving a tradeoff between the critical frequency limits and the required control effort. Two control designs are presented and compared against the open-loop model. The proposed controllers are integrated into a state-of-the-art converter control scheme and verified through electromagnetic transient (EMT) simulations

A Stochastic-Robust Approach for Resilient Microgrid Investment Planning Under Static and Transient Islanding Security Constraints

When planning the investment in Microgrids (MGs), usually static security constraints are included to ensure their resilience and ability to operate in islanded mode. However, unscheduled islanding events may trigger cascading disconnections of Distributed Energy Resources (DERs) inside the MG due to the transient response, leading to a partial or full loss of load. In this paper, a min-max-min, hybrid, stochastic-robust investment planning model is proposed to obtain a resilient MG considering both High-Impact-Low-Frequency (HILF) and Low-Impact-High-Frequency (LIHF) uncertainties. The HILF uncertainty pertains to the unscheduled islanding of the MG after a disastrous event, and the LIHF uncertainty relates to correlated loads and DER generation, characterized by a set of scenarios. The MG resilience under both types of uncertainty is ensured by incorporating static and transient islanding constraints into the proposed investment model. The inclusion of transient response constraints leads to a min-max-min problem with a non-linear dynamic frequency response model that cannot be solved directly by available optimization tools. Thus, in this paper, a three-stage solution approach is proposed to find the optimal investment plan. The performance of the proposed algorithm is tested on the CIGRE 18-node distribution network

Gravitational Collapse: Expanding and Collapsing Regions

We investigate the expanding and collapsing regions by taking two well-known spherically symmetric spacetimes. For this purpose, the general formalism is developed by using Israel junction conditions for arbitrary spacetimes. This has been used to obtain the surface energy density and the tangential pressure. The minimal pressure provides the gateway to explore the expanding and collapsing regions. We take Minkowski and Kantowski-Sachs spacetimes and use the general formulation to investigate the expanding and collapsing regions of the shell.Comment: 12 pages, 4 figures, accepted for publication in Gen. Relativ. Gra

Constraining warm dark matter with cosmic shear power spectra

We investigate potential constraints from cosmic shear on the dark matter particle mass, assuming all dark matter is made up of light thermal relic particles. Given the theoretical uncertainties involved in making cosmological predictions in such warm dark matter scenarios we use analytical fits to linear warm dark matter power spectra and compare (i) the halo model using a mass function evaluated from these linear power spectra and (ii) an analytical fit to the non-linear evolution of the linear power spectra. We optimistically ignore the competing effect of baryons for this work. We find approach (ii) to be conservative compared to approach (i). We evaluate cosmological constraints using these methods, marginalising over four other cosmological parameters. Using the more conservative method we find that a Euclid-like weak lensing survey together with constraints from the Planck cosmic microwave background mission primary anisotropies could achieve a lower limit on the particle mass of 2.5 keV.Comment: 26 pages, 9 figures, minor changes to match the version accepted for publication in JCA