Hamiltonian-Based Power Flow and Stability Analysis on a Passively Controlled Multi-Frequency Power System
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The activation of aerosol particles to form cloud droplets, a necessary first step in cloud formation, controls much of the impact that aerosols have on clouds and climate. Recently, there has been a surge of interest in extending the Köhler theory of cloud droplet activation to include surface active (typically organic) as well as water-soluble (typically inorganic) aerosol components, but a systematic framework for doing this has yet to be developed. Here, we apply a droplet stability analysis to this end. Ideal and Szyszkowski–Langmuir surfactant models are analyzed to demonstrate the new approach, but the underlying theoretical framework is fundamental and model free. A key finding is that superficial densities at the cloud activation threshold (Köhler maximum) are significantly sub-monolayer, with fractional coverage ranging from 69% to 85% for the organic compounds and mixtures studied. The result, significant for model inventories of cloud condensation nuclei, is a weakening of the surfactant effect relative to expectations based on bulk sample measurements. Analytical results are obtained for the loci of Köhler maxima and applied to aerosol mixtures containing an arbitrary number of water-soluble and surfactant components.
This document is a summary of a report prepared by the IEEE PES Task Force (TF) on Microgrid Stability Definitions, Analysis, and Modeling [1], which defines concepts and identifies relevant issues related to stability in microgrids. In this paper, definitions and classification of microgrid stability are presented and discussed, considering pertinent microgrid features such as voltage-frequency dependency, unbalancing, low inertia, and generation intermittency. A few examples are also presented, highlighting some of the stability classes defined in the paper. Further examples, along with discussions on microgrid components modeling and stability analysis tools can be found in the TF report.
As the number of inverter-interfaced distributed generators (IIDGs) increases, the decrease in the inertia of the microgrid affects the stability of microgrid voltage and current. The virtual synchronous generator (VSG) control method simulates the output characteristics of the synchronous machine to improve the inertia and damping of the microgrid. However, low-frequency oscillations can occur in systems with multi-VSGs connected in parallel, primarily when operating in island mode. Therefore, this article develops the small-signal state-space model for multi-inverters based on VSG and analyses the robust stability region (RSR) of the control parameters. Firstly, an extensible small-signal state-space model is established and simplified in the dq axis, which is a necessary preprocessing for the subsequent stability analysis. Secondly, the guardian map method based on bialternate product operation is constructed, and the RSR is established through translation mapping and rotation mapping. Therefore, the solution of RSR is transformed into the problem of identifying the Hurwitz matrix. Finally, the simulations and experiments verify that the calculated region can ensure stable operation during startup and meet the requirement to suppress low-frequency oscillations. In conclusion, the method of solving RSR proposed in this paper provides a basis for selecting controller parameters in practical engineering.
With the growing significance of renewable energy resources and energy storage systems, the number of grid-connected inverters has been rising at an increasingly rapid pace. Generally, these inverters are directly integrated with the distribution network by synchronizing with the grid voltage at the point of common coupling. However, the low grid strength and varying R/X ratios, as the common characteristics of most distribution networks or weak grids, can lead to dynamic interactions that comprise stability and limit the power transfer capacity of grid-connected inverters. To ensure stable operation of the inverters, researchers must determine the stability boundary, described as the maximum power transfer capacity of grid-connected inverters under the premise of maintaining system small-signal stability. For this purpose, we propose to formulate a state-space model of the system in the synchronously rotating dq-frame of reference and perform eigenvalue analysis to determine the stability boundary. With a detailed model of the control structure and parameters of the grid-connected inverters, the stability boundary is identified as a surface with respect to different grid strengths and R/X ratios. Case study results of proposed eigenvalue analysis are compared with those of admittance model-based stability analysis as well as time-domain simulation using a switching model in Matlab/Simulink, validating the effectiveness and accuracy of the proposed eigenvalue analysis for stability boundary identification.
Phase-split computations in an isolated system, which in general may be defined as one where the total internal energy (U), volume (V), and the number of moles (N = N 1 , N 2 ,..., N n ) of the components are fixed at some specified set of values, involves the determination of the temperature (T), pressure (P), plus the amount and composition of the various phases that constitute the system. A simpler, but analogous problem is one where T, P, and N are specified instead. In TPN space, one may first perform a stability analysis to determine whether the system is stable, meaning whether at equilibrium it will split up into multiple phases or remain in single phase. If the single-phase state is unstable, the stability analysis reliably provides a good set of initial guesses in the subsequent phase-split computations. In UVN space, however, we demonstrate that the stability analysis (which is the main subject of our earlier study [1]) may not in general provide good enough initial guesses; we offer alternative strategies for setting up good initial guesses. Furthermore, we show that a combination of successive substitution iteration (SSI) and Newton's method---two iterative methods that are prevalent in the literature in TPN space---facilitates a robust and efficient algorithm for phase-split computations in isolated systems. Finally, this combination has so far not been applied in UVN space.
Our main goals in this project are to understand: 1) the stability of the power system with very high penetration of PV or other inverter-based resources (IBR), 2) the interactions among IBRs and traditional generators, and 3) the impact of the GFM inverters on bulk power system. To achieve these goals, we took a holistic research and development approach. First, an impedance-based large system modeling and stability analysis tool was developed to aid the large IBR system small-signal stability analysis. Second, consensus-based control and transient overload ride through were developed to control and coordinate multiple GFM inverters in a large system to maintain transient stability during big grid events. Third, high fidelity electromagnetic transient (EMT) IBR models were developed and integrated into a large reduced WECC model to study the system impact from IBRs. Lastly, extensive validation tests of the GFM control which was developed in this project and implemented in two 1MW commercial solar inverters were performed using different validation platforms, e.g., control hardware-in-the-loop (CHIL) platform, power hardware- in-the-loop (PHIL) platform, and a real PV plant.
The existing impedance-based stability criterion is effective for analyzing local control interactions; however, it is difficult to scale the existing criterion to analyze wide-area control interactions among numerous IBRs through a complex power system network. The scaled version of the existing criterion requires the impedance response of each IBR in the system as well as of the network looking from all the IBRs. It is quite challenging to obtain all these impedance responses because of the computational effort and the requirement of separately scanning the impedance of the network and the IBRs. We propose a reversed criterion for the impedance-based stability analysis to address these problems. In contrast to the existing criterion, the reversed criterion analyzes the stability of a power system when an IBR is disconnected from the system. The reversed criterion estimates the impact of an IBR on the frequency and damping of power system oscillation modes using the impedance scans of only the IBR and the grid at its terminal. It can be sequentially applied at different IBRs to evaluate their impact on the power system stability. In addition to scalability, the reversed criterion gives flexibility to focus only on a few selected IBRs, depending on their rating, the magnitude of oscillations observed at their terminals, and the vendor support available for implementing stabilizing control system updates. The reversed criterion is demonstrated on a 14-bus power system with 100% IBRs.
Here, this paper considers the problem of designing a resilient distributed voltage control algorithm for distribution systems with high penetration of distributed energy resources in the presence of an unknown cyber-attack. The purpose of the attack is to force the system to violate the operating voltage limit by intercepting its communication channels and inserting exogenous signals to perturb and/or modify the information being exchanged. We first review the cooperative voltage control proposed in our previous work and provide a new stability analysis for it. Next, we present a resilient cooperative voltage control algorithm by introducing a virtual system interconnected with the original system such that the voltage can be maintained within the operational limit under unknown attacks. The resiliency of the proposed algorithm is demonstrated via simulations on the IEEE 8500-node system when subjected to an attack which consists of corrupting the data being exchanged in the communication network between two generation units.
Spontaneous mitigation of giant ELMs and appearance of grassy ELMs have been observed repeatedly at low pedestal collisionality (${\nu }_{\mathrm{e},\mathrm{p}\mathrm{e}\mathrm{d}}^{{\ast}}\sim 0.15$) in the high-power (P inj > 13 MW) hybrid scenario in DIII-D. Higher β p and higher q 95 appear to be beneficial to achieving the grassy ELM regime. The grassy ELM H-mode plasma shows high energy confinement performance (H 98y2 up to over 1.5) under the conditions of high neutral beam torque and high core rotation. The pedestal width appears to exceed the EPED1.0 model prediction by more than 50%. Pedestal stability analysis performed with the ELITE code indicates that the stability against low-n kink/peeling modes is improved with increased auxiliary heating power and the operational point in the grassy ELM regime is located near the ballooning boundary. The pedestal stability characteristics during the grassy ELM crashes have been investigated in comparison with the giant ELM crashes based on plasma profiles experimentally measured with high resolution and accuracy. It has been found that the underlying mechanism for the observed small-amplitude ELM crashes is mainly the expansion of the ballooning stability boundary induced by an initial radially localized collapse in the pedestal, which helps to stop the growth of instabilities and further collapse of the pedestal. The effect of electron density pedestal on mitigating edge localized instabilities has been analyzed by numerical simulation, suggesting that the electron density pedestal characterized by high n e,sep /n e,ped and low density gradient helps to stabilize peeling-ballooning modes because of a low pressure pedestal gradient and to lower the ballooning boundary mainly because of a low ion diamagnetic frequency in the pedestal region, thus triggering ballooning instabilities and producing the intrinsic grassy ELMs. Numerical simulation of the Chinese fusion engineering test reactor (CFETR) with the SOLPS code indicates that the separatrix density might be insensitive to the electron diffusivity in the pedestal region and increase with the power flowing from the core region to the edge region. Furthermore, pedestal stability analysis suggests that the flat density pedestal with high separatrix density obtained in the high-power plasma in CFETR would make the operational point close to the ballooning boundary, which is considered to help destabilize ballooning instabilities and facilitate the access to the grassy ELM regime.
Here, we perform a gas gun experiment by shock loading tantalum samples of varying grain structures to assess the suitability of a numerical model for simulating spall behavior. The observed differences in spall strength, as well spallation and re-compression history, are not captured in uncalibrated hydrodynamic simulations. An optimization is performed on the Johnson spall model to determine the best parameters that fit the observed trends. Linear stability analysis is employed to motivate bounds on those parameters. Herein, optimized simulations agree well with the experimental results, reproducing pullback depth and recompression timescales across the different samples tested. Further, the observed pullback time of the single crystal sample was found to imply, via the stability analysis, a percolation threshold in good agreement with the theoretical value for a body centered cubic lattice. Therefore, the combined linear stability and percolation analysis shows promise and may be applied to other materials with diverse microstructures. Collectively, the findings demonstrate that the model is suitable for reproducing spall-induced free surface behavior across various microstructures, but also points to caution in using model coefficients for uncalibrated microstructures.
Deep Markov models (DMM) are generative models which are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we present a novel stability analysis method and provide sufficient conditions of DMM's stochastic stability. The proposed stability analysis is based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation function on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.
This paper proposes a distributed control method based on a consensus algorithm for distributed energy resources (DERs) using blockchain as a secure communication medium for cyber resilience. Each DER communicates with a local blockchain server that is maintained by the distributed ledger technology to allow for securely sharing local measurements among neighbouring assets to achieve the global control objectives, i.e., voltage and frequency regulation as well as accurate power sharing among the DERs, including collective grid-forming capability. To prove that the distributed control can retain system stability under a blockchain-induced variable communication delay, Lyapunov function-based stability analysis is carried out. This paper demonstrates the concept on an 11-bus test case developed in MATLAB Simulink, which has been modified from the IEEE 9-bus test case, to study dynamic operations of the five inverter-based DERs working with a blockchain-induced variable delay. The results validate the superior performance of the proposed control method, compared to heavily compromised operations of the other test cases without the security measure, affected by heavy communication delays and communication interruptions.