Modal decoupling of overhead transmission lines using real and constant matrices: Influence of the line length
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The Clarke's matrix is a well-known real and constant transformation matrix used for modal transformation in three-phase transmission lines modeling. Although modal analysis has been widely discussed in the technical literature on power system modeling, a new content is approached in this research proving that the approximation using an exact and constant modal transformation matrix depends on both the frequency-dependent parameters and transmission line's length. As an important conclusion, the approach using the Clarke's matrix leads to more accurate results considering long transmission lines. There are two methods for modal decoupling in power systems modeling. The first uses only a single constant and real transformation matrix during the entire modeling/simulation routine. The second uses the frequency-dependent transformation matrix for parameters decoupling into the propagation modes and the Clarke's matrix for mode-to-phase transformation of voltage and current values during simulations. The accuracy of these two modeling/simulation processes are evaluated, in the time and frequency domains, based on results obtained from a reference routine that employs the exact frequency-dependent matrix in modal transformations and numerical transforms for simulation in the time domain. The proposed analysis proves that the accuracy of both methods varies with the line length during electromagnetic transient simulations that leads to peak errors up to approximately 10%. The influence of the line length in modal analysis techniques was not approached in previous references on power system modeling, which represents the original contribution of this paper.