Improved modified nodal analysis: a novel framework for electrical issues studies in modern power grids

• An improved modified nodal analysis (IMNA) for modern power grids is developed. • Elements of such grids that are out of the scope of MNA are easily processed by IMNA. • IMNA-based extensions of resonance analysis methods are provided. • These extensions enable resonance and stability studies in those grids to be performed. • The IMNA and the above extensions are suitable, useful and valid for such studies. Efficient electrical software is essential for analysing power system issues. Such software usually relies on nodal analysis (NA), which utilises the nodal admittance matrix to relate nodal currents and voltages. When typical elements are connected to the power system, this matrix can be systematically calculated using incidence or connection matrices, a well-established technique. However, modern power grids often incorporate non-typical elements that fall outside the scope of NA. Based on incidence matrices, modified nodal analysis (MNA) partially addresses the limitations of NA, and subsequently, modified augmented nodal analysis (MANA) further enhances this approach. This paper introduces an improved modified nodal analysis (IMNA), which employs an analytical procedure to construct the extended nodal matrix, overcoming the limitations of NA, MNA, and MANA. Additionally, the proposed IMNA extends existing resonance analysis methods and these extensions are currently the only available options for studying resonances and stability in modern power grids. One of these extensions is applied on three modified IEEE power systems and on one modified synthetic network, and the results are validated by MATLAB/Simulink simulation when possible. These results remain logical regardless of the modifications.