A novel control scheme based on a new stochastic equivalent model of the power system, which provides flexible inertia constant to enable high penetration levels of Microgrid (MG) generation is proposed. The approach combines an adaptive Energy Storage System (ESS) dispatch strategy with an MG controlled islanding scheme to provide frequency support for the host power grid. First, a Center-of-Gravity (COG) formulation of the inertia-control scheme is proposed, in which the unbalance torques between the control areas and the COG are used to reduce frequency deviations. An application example-based equivalent model of ESSs as seen from the grid side is then proposed that takes advantage of the ESS special attributes to contribute to inertial response. Simulation results on two test systems demonstrate the efficiency of the proposed control scheme to increase the host grid ability to efficiently integrate multiple MGs. Numerical tests suggest that the proposed control scheme increases system penetration level at least by 12%, which justifies the use of inertia emulation techniques to accommodate higher levels of distributed generation.

The inclusion of higher-order terms in Small-Signal (Modal) analysis has been an intensive research topic in nonlinear power system analysis. Inclusion of 2nd order terms with the Normal Form method has been well developed and investigated, overcoming the linear conventional small-signal methods used in the power system control and stability analysis. However, application of Normal Form methods has not yet been extended to include 3rd order terms in an efficient manner. Due to a growing inclusion of renewable energy- based generators and the increase of energy exchanges trough long distance, modern grids exhibit predominant nonlinear oscillations and existing tools have to be upgraded to cope with this new situation. In this paper, fundamentals of Normal Form Theory along with a review of existing tools based on this theory is firstly presented. Secondly, a new formulation of Normal Dynamics based on a third-order transformation of the system's dynamic approximation is proposed and the induced benefits are compared to existing Normal Form methods. Finally, the proposed method is applied to a standard test system, the IEEE 2-area 4-generator system, and results given by the conventional linear small-signal and 2nd Normal Form analysis are compared to the proposed approach. The applicability of the proposed MNF to larger networks with more complex models has been evaluated on the New England New York 16 machine 5 area system.

This paper presents a measurement-based under-frequency load shedding scheme that considers time delays, measurement uncertainties, and communication network faults. Using a moving first-degree polynomial function, an iterative approach to estimate the frequency nadir and the associated frequency nadir time is proposed. Then, a novel method to simultaneously estimate the power imbalance and the system inertia constant is developed. According to an analytical basis, a base system is selected from a set of pre-defined base systems to guarantee accurate power imbalance estimation. Finally, a mathematical index is investigated to calculate a threshold for the generation-load power imbalance beyond which loads should be shed. Further, a systematic approach for specifying the amount of load to be shed in each transmission bus of the system is proposed. The effectiveness of the proposed methodologies is examined on both simulated and actual measured data from 9 historical power system disturbances in a national power grid.

A new model-based framework for studying nonlinear dynamic behavior of stressed power systems that combines Koopman mode analysis and perturbation theory is proposed. First, a sys-tematic approach to deriving high-dimensional representations of nonlinear dynamical systems based on perturbation theory is presented. Nonlinear behavior is interpreted as a projection of the Koopman operator eigenfunctions of an extended coordinate system onto the physical variables of the system. Analytical for-mulations are then obtained for the construction of the extended coordinate system based on perturbation theory. The analysis methodology is demonstrated on three test systems: a Single-Machine, Infinite-Bus (SMIB) system, a three-machine test sys-tem, and the IEEE 50-machine test system.

The inclusion of higher-order terms in small-signal (modal) analysis augments the information provided by linear analysis and enables better dynamic characteristic studies on the power system. This can be done by applying Normal Form theory to simplify the higher order terms. However, it requires the preliminary expansion of the nonlinear system on the normal mode basis, which is impracticable with standard methods when considering large scale systems. In this paper, we present an efficient numerical method for accelerating those computations, by avoiding the usual Taylor expansion. Our computations are based on prescribing the linear eigenvectors as unknown field in the initial nonlinear system, which leads to solving linear-only equations to obtain the coefficients of the nonlinear modal model. In this way, actual Taylor expansion and associated higher order Hessian matrices are avoided, making the computation of the nonlinear model up to third order and nonlinear modal analysis fast and achievable in a convenient computational time. The proposed method is demonstrated on a single-machine-infinite-bus (SMIB) system and applied to IEEE 3-Machine, IEEE 16- Machine and IEEE 50-Machine systems.