Park equations for distributed constants line

Abstract

By using the Park‐transformation the three‐phase TEM‐mode is analysed under the two different points of view: circuit and field. The first one leads, in terms of voltage and current line‐space vector, to a distributed constants active line. The second one leads, in a formal way, to the deduction of the “Maxwell‐Park equation”. The obtained result brings again, in terms of distributed constants, to the instantaneous sequence components algebra. This result allows a unified analysis, valid for any regime, of the poly‐phase travelling phenomena. This approach is particularly effective in presence of harmonics and sequence components. Under these circumstances, due to the wide spread of this kind of phenomena, the extension of the Park approach, already consolidated for the lumped constants, to the distributed constants case appears an obliged step particularly useful in a conceptual and practical path.

Analysis of three-phase transmission line radiation by means of a Park transform

“…L which in turn consent the use of the same type o f approximation seen in(6) under the same hypothesis. Evaluation of the radiated power across an infinite semi-sphere located above the ground plane implies substituting expressions (9) in (8) and calculating the appropriate Poynting vector; this results in a rather daunting expression involving the sum of the nine convolution integrals of all the possible combinations of the phase components 1.2.3.…”

Analysis of Physically Symmetrical Lossy Three-Phase Transmission Lines in Terms of Space Vectors

“…Integrating (12), 4 by inverse Laplace transform, in the distortionless lossy-line case, the following Park formulation is obtained for the voltage and current propagating waves: (13) In the general lossy line case, by introducing the -order modified Bessel function 0 (14) we obtain the following three-phase lossy transmission-line equations as shown in (15) at the bottom of the page.…”

“…In previous papers [4], [6], the authors applied the Park transformation to study the wave propagation of TEM three-phase Manuscript physically symmetrical lines. The structure of the obtained three-phase equations is similar to that of the single-phase configuration: the employed quantities, real in the single-phase two-wire case, become complex.…”

“…Due to this rotation, any vector in the coordinate system is changed into the vector in the new rotating coordinate system by (4) where the axis rotation depends on time only. It can be observed that where…”

“…In fact, the Fortescue and Lyon matrices [2] satisfy all modal analysis conditions. Furthermore, the symmetric instantaneous component method (Lyon and Park) [3], thanks to the use of the space vectors [4], is characterized by a more straightforward, versatile, and physically sound approach than the one typical of the usual modal procedure based on matrix analysis. Finally, from the application point of view, the Park approach assumes particular importance.…”