In this paper we investiagte Steiner loops introduced by N.S. Mendelsohn [Aeq. Math. 6 (1991), 228–230] and provide six (seven) equivalent identities to characterize it. We also prove the power associativity of Bol loops by using closure (Hexagonal) conditions.

With the rapid increase in high penetration photovoltaic (PV) power generation systems into power systems around the world, the idea of power system oscillation mitigation with auxiliary control of PV plant has been suggested recently. In this study, the optimal control of a high penetration PV solar farm in sub-synchronous resonance (SSR) mitigation will be explored. The main contribution of the paper is designing a conventional sub-synchronous resonance damping controller (SSRDC) by properly choosing the best place in the active and reactive controllers of PV farm to place the sub-synchronous damping controller to achieve the best damping in various conditions. Also, the paper presents a complete dynamic model tailored to study via eigenvalue analysis, SSR events in the presence of a high penetration PV farm, and a systematic procedure to design a damping controller using Whale Optimization Algorithm (WOA). The results are validated through two case studies based on the IEEE first and second benchmark model for sub-synchronous resonance studies in MATLAB/Simulink and the achieved numerical results are thoroughly discussed.

Please click on PDF to view the abstract.

Studying the dynamics of magnetic plasmas in the presence of pressure gradients, gravity, and Lorentz forces is essential for understanding wave generation and propagation in the solar atmosphere and other magnetic environments. Understanding the sudden increase in the temperature of the sun’s corona is one of the challenges for solar physicists. Various solar phenomena, including sunspots, spicules, and coronal loops, are explored within these environments. We consider them to be waveguides. These waveguides are interpreted as magnetic flux tubes, providing valuable information about wave properties. For study the dissipation in the magnetic flux tubes, two key damping mechanisms are: thermal conductivity, which transfers heat within the coronal plasma, and compressive viscosity, which reveals the plasma's resistance to pressure changes and deformation.The investigation of the dissipation of magnetohydrodynamic waves in hot coronal loops is carried out using a two-dimensional Cartesian model. The findings demonstrate that there is a decrease in pulse amplitude, and dissipation or damping manifests across distinct segments of the magnetic flux tube as time progresses. We find that the considered viscosity in our model can accelerate the wave damping in the coronal loop, which is in agreement with the results reported by Ofman & Wang (2022).