Open AccessAnalysis of Hopf bifurcation with forecast uncertainties in load/generation
Author(s) -
Krishan Ram,
Verma Ashu,
Mishra Sukumar,
Bijwe Pradeep R.
Publication year - 2017
Publication title -
iet generation, transmission and distribution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.92
H-Index - 110
eISSN - 1751-8695
pISSN - 1751-8687
DOI - 10.1049/iet-gtd.2016.1316
Subject(s) - eigenvalues and eigenvectors , hopf bifurcation , range (aeronautics) , boundary (topology) , electric power system , stability (learning theory) , mathematics , control theory (sociology) , boundary value problem , power (physics) , bifurcation , computer science , nonlinear system , engineering , mathematical analysis , physics , control (management) , quantum mechanics , machine learning , artificial intelligence , aerospace engineering
Eigenvalue analysis is a very essential technique for power system small‐signal stability (SSS) determination. Uncertainties in load/generation forecast are very common in power systems due to its geographical spread, size and complexity. These uncertainties can be divided into two types: (a) statistical (b) non‐statistical. It is observed from the literature that the effects of non‐statistical uncertainties in eigenvalue analysis are discussed comparatively less. In this study, a boundary eigenvalue analysis is developed based on boundary power flow to handle the non‐statistical uncertainties in loads and solar photovoltaic generation (SPVG) forecasts. First, mathematical model for evaluation of boundary of the critical eigenvalues for SSS analysis of dynamic power system (DPS) is developed. Then, the upper/lower boundary of a particular eigenvalue for a given range of uncertainties in load/SPVG at various buses is investigated. The boundary eigenvalue analysis predicts the worst‐case scenario for a given range of uncertainty in forecasted data which may help for secure operation of DPS. Second, Hopf bifurcations which may lead in highly stressed DPS is evaluated with increasing load/generation in the system in the presence of non‐statistical uncertainties. Results for two standard test systems are taken to demonstrate the potential of the proposed approach.