There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

Tensor Analysis of Networks. By Gabriel Kron. Pp. xxix, 635. 70s. 1965. (Macdonald)

Distribution System Modeling and Analysis

Ergodic theory

This paper surveys current literature on modeling methods, control techniques, protection schemes, applications, and real-world implementations pertaining to grid forming inverters (GFMIs). Electric power systems are increasingly being augmented with inverter-based resources (IBRs). While having a growing share of IBRs, conventional synchronous generator-based voltage and frequency control mechanisms are still prevalent in the power industry. Therefore, IBRs are experiencing a growing demand for mimicking the behavior of synchronous generators, which is not possible with conventional grid following inverters (GFLIs). As a solution, the concept of GFMIs is currently emerging, which is drawing increased attention from academia and the industry. 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 in 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.

/pdf/grid-forming-inverter-modeling-control-and-applications-2a4eb2edb1.pdf

Grid Forming Inverter Modeling, Control, and Applications

Historically, two similar grid-forming droop controls are widely reported in literature—the single-loop and multi-loop droop controls. Although being very similar, the authors find that the dynamic performance and stability characteristics of each control method are very different in a microgrid. Compared with the single-loop droop control, the multi-loop droop control is prone to be less damped and loses stability more easily under some circumstances. This article provides a novel insight into the different dynamic responses of the two basic controls. It points out that the two similar controls adjust the angular frequency and voltage magnitude at different locations within the inverter, resulting in different coupling reactances that impact the dynamic response and stability of microgrids differently. The use of the single-loop droop control results in a larger coupling reactance, which helps improve the dynamic response and stability. This novel insight is verified through full-order small-signal analysis, offline electromagnetic transient simulation, and real-time hardware-in-the-loop simulation experiments. The results show that the microgrid has a larger small-signal stability boundary when using single-loop droop control, and this difference increases as the value of an inverter’s inner filter inductance increases.

A Comparative Study of Two Widely Used Grid-Forming Droop Controls on Microgrid Small-Signal Stability

Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems

Higher penetration of renewable generation will increase the demand for adequate (and cost-effective) controllable resources on the grid that can mitigate and contain the contingencies locally before it can cause a network-wide collapse. However, end-use constraints can potentially lead to load unavailability when an event occurs, leading to unreliable demand response services. Sensors measurements and knowledge of the local load dynamics could be leveraged to improve the performance of load control algorithms. In the context of hierarchical frequency response using ensemble of switching loads, we present a metric to evaluate the fitness of each device in successfully providing the ancillary service. Furthermore a fitness-based assignment of control set-points is formulated which achieves reliable performance under different operating conditions. Monte Carlo simulations of ensembles of electric water heaters and residential air-conditioners are performed to evaluate the proposed control algorithm.

Prioritized Threshold Allocation for Distributed Frequency Response

In this work, we developed new Koopman operator techniques to explore the global phase space of a nonlinear system from time-series data. In particular, we address the problem of identifying various invariant subsets of a phase space from the spectral properties of the associated Koopman operator constructed from time-series data. Moreover, in the case when the system evolution is known locally in various invariant subspaces, then a phase space stitching result is proposed that can be applied to identify a global Koopman operator. A biological system, the bistable toggle switch is considered to illustrate the proposed results. The construction of this global Koopman operator is very helpful in experimental works as multiple experiments cannot be performed at the same time starting from several initial conditions.

Data-Driven Operator Theoretic Methods for Global Phase Space Learning

The proliferation of inverter-based generation and advanced sensing, controls, and communication infrastructure have facilitated the accelerated deployment of microgrids. A coordinated network of microgrids can maintain reliable power delivery to critical facilities during extreme events. Low-inertia offered by the power-electronics interfaced energy resources, however, can present significant challenges to ensuring stable operation of the microgrids. In this work, distributed small-signal stability conditions for inverter-based microgrids are developed that involve the droop-controller parameters and the network parameters (e.g. line impedances, loads). The distributed closed-form parametric stability conditions derived in this paper can be verified in a computationally efficient manner, facilitating the reliable design and operations of networks of microgrids. Dynamic phasor models have been used to capture the effects of electromagnetic transients. Numerical results are presented, along with PSCAD simulations, to validate the analytical stability conditions. Effects of design choices, such as the conductor types, and inverter sizes, on the small-signal stability of inverter-based microgrids are investigated to identify interpretable stable/unstable region estimates.

Sai Pushpak Nandanoori

Papers

A Comparative Study of Two Widely Used Grid-Forming Droop Controls on Microgrid Small-Signal Stability

Koopman Operator Methods for Global Phase Space Exploration of Equivariant Dynamical Systems

Prioritized Threshold Allocation for Distributed Frequency Response

Data-Driven Operator Theoretic Methods for Global Phase Space Learning

Distributed Small-Signal Stability Conditions for Inverter-Based Unbalanced Microgrids