Study on an improved Normal Form solution and reduced-order mode reconstruction in power system

With the polynomial vector space decomposition by using Normal Form theory, the normalized analytical solutions of modal resonance are derived, which solves that the traditional Normal Form solution cannot be easily obtained under resonant condition. Based on the solution, from the viewpoint of whether the modal interaction couples and resonates or not, the nonlinear terms are decomposed into four types, i.e., uncoupled nonresonant terms, coupled nonresonant terms, uncoupled resonant terms and coupled resonant terms. The corresponding modes are categorized into 5 types, i.e., single modes, uncoupled nonresonant modes, coupled nonresonant modes, uncoupled resonant modes and coupled resonant modes. A reduced-order mode reconstruction based on least square method to estimate the coefficients of higher-order interactional modes is proposed. This might be potentially a new approach to cope with the challenge from huge amount of higher-order modes in higher-order nonlinear analysis. Two case studies are presented to analyze the types and reconstructions of the nonlinear modes, 2nd- and 3rd- order terms, which verifies the effectiveness of the proposed approach.