Virtual inertia is an effective control approach to attenuate sudden voltage changes during transient events in low-inertia dc grids. While methods have been proposed implement virtual inertia, its impact on grid stability the presence of constant power loads (CPLs) remains unclear. In this letter, we perform a rigorous analysis for grids with CPLs powered by virtual-inertia-enhanced converters...

In the N-body problem, it is a simple observation that relative equilib-ria (planar solutions for which the mutual distances between the particles remain constant) have constant moment of inertia. In 1970, Don Saari conjectured that the converse was true: if a solution to the N-body problem has constant moment o f inertia, then it must be a relative equilibrium. In this note, we connrm the conj...

This paper proposes an efficient method to solve the optimal power flow problem in power systems using Particle Swarm Optimization PSO . The objective of the proposed method is to find the steady-state operating point which minimizes the fuel cost, while maintaining an acceptable system performance in terms of limits on generator power, line flow, and voltage. Three different inertia weights, a...

To improve the primary frequency response in future low-inertia hybrid power system a fuzzylogic based frequency controller (FFC) for wind farms augmented with energy storage systems(wind-storage system) and intelligent PV farms for the frequency stabilization is proposed inthis paper. Using system frequency deviations the proposed controller provides bidirectionalreal p...

This paper presents an alternative and efficient method for solving the optimal control of single-stage hybrid manufacturing systems which are composed with two different categories: continuous dynamics and discrete dynamics. Three different inertia weights, a constant inertia weight (CIW), time-varying inertia weight (TVIW), and global-local best inertia weight (GLbestIW), are considered with ...

This paper proposes a design method of optimal H2 integral servo controller. The optimal H2 integral controller is to establish a way to find the admissible controller such that the controlled plant is stabilized and guarantee to track a constant reference signal while minimizing the close-loop system H2 norm from the disturbance to the controlled output. In this paper the derivative state cons...

The Wilberforce pendulum provides an important qualitative demonstration of coupled harmonic oscillators, but quantitative measurements are not typically performed. The present work examines the dynamics of a simple pendulum comprising a steel spring with attached mass using an ultrasonic motion detector. A series of measurements allowed determination of the coupling constant between the longit...

The five relative equilibria of the three-body problem give rise to solutions where the bodies rotate rigidly around their center of mass. For these solutions, the moment of inertia of the bodies with respect to the center of mass is clearly constant. Saari conjectured that these rigid motions are the only solutions with constant moment of inertia. This result will be proved here for the planar...

In this paper, an adaptive virtual inertia-damping system based on model predictive control (MPC) is proposed to enhance the frequency dynamic performance of islanded microgrids (MGs) considering a high penetration level renewable energy sources (RESs). Recently, large amount RESs replacing traditional generating units, causing undesirable effect MG stability and inertia, thus weakening MG. The...