Approximation of stability boundary of a power system using the real normal form of vector fields

Abstract

iii 3. APPROXIMATION OF STABILITY BOUNDARY 3.1 Linear Analysis around the UEP 3.2 Coefficient of Curvature 23 3.3 Approximation of the Manifold of the UEP 25 3.4 Display of Boundary 3.5 Potential Energy 3.6 Computation of Distance 27 3.7 Computational Steps 2S 3.8 Summary 4. NUMERICAL RESULTS 4.1 11 Generator Test System 31 4.2 Simulation of Stress in a System 33 4.3 UEP Angles and System Eigenvalues 4.3.1 Effect of loading of critical generators 4.3.2 Effect of fault location and postfault network 35 4.4 Nonlinear Interaction Coefficients, h2r 4.4.1 Effect of loading of critical generators 4.5 r Coefficients 4.5.1 Effect of loading of critical generators 4.5.2 Effect of fault location and postfault network 4.6 Shape of Manifold Near the UEP and Size of the Region of Stability. 4.6.1 Effect of loading of critical generators 4.7 Trajectory Behavior Near the Boundary of the Region of Stability. . 4.7.1 Behavior of system trajectory near the UEP iv 4.7.2 How the faulted trajectory leaves the boundary 4.8 Potential Energy and Distance of Manifold from the Postfault SEP. 53 4.8.1 Effect of loading of critical generators 4.8.2 Effect of fault location 4.9 Equilibrium Points When System is Stressed 4.10 Summary 5. MODE OF SYSTEM INSTABILITY

Stability analysis of Riccati differential equations related to affine diffusion processes

“…But, we will not discuss this problem in this paper. An interested reader can consult [4] or [24], for example.…”

“…The techniques used in this area vary according to a specific problem of interest: for example, [22,27] for polynomial systems and [4,24] for power systems to name a few. On the other hand, the escape of a solution to infinity, or the blow-up of a solution in finite time has also been widely studied.…”

Nonlinear dynamic singularity analysis of two interconnected synchronous generator system with 1:3 internal resonance and parametric principal resonance

“…Therefore, we can let a 1 = 0 in (21), which yields (22) can be transformed into the following form:…”

“…Therefore, for a better understanding of the underlying cause of the complex behavior of a stressed power system, many researchers have turned to seek new methods. Many scientists have made great efforts on applying the method of normal forms to quantify nonlinear modal interaction in power systems [21][22][23][24] and strong modal resonance analysis [25] , as similar to the most widely considered ones for studying the normal mode bifurcation in nonlinear mechanical systems [26][27][28][29] .…”

On expansion of estimated stability region: Theory, methodology, and application to power systems

“…Refs. [6][7][8][9][10] used the normal form transformation to convert the original system to a linear system in a neighborhood of the CUEP. Because the stable and unstable sub-manifolds of the linear system can be obtained easily, the approximation of stability region boundary can be determined by converting the obtained stable manifold to the original coordinate.…”