Model to design drip hose lateral line using two spacing between emitters

The use of non-pressure compensating drip hose in horticultural and annual cycle fruits is growing in Brazil. In this case, the challenge for designers is getting longer lateral lines with high values of uniformity. The objective of this study was to develop a model to design longer lateral lines using non-pressure compensating drip hose. Using the developed model, the hypotheses to be evaluated were: a) the use of two different spacing between emitters in the same lateral line allows longer length; b) it is possible to get longer lateral lines using high values of pressure variation in the lateral lines since the distribution uniformity stays below allowable limits. A computer program was developed in Delphi based on the model developed and it is able to design lateral lines in level using non-pressure compensating drip hose. The input data are: desired distribution uniformity (DU); initial and final pressure in the lateral line; coefficients of relationship between emitter discharge and pressure head; hose internal diameter; pipe cross-sectional area with the dripper; and roughness coefficient for the Hazen-Williams equation. The program allows calculate the lateral line length with three possibilities: selecting two spacing between emitters and defining the exchange point; using two pre-established spacing between emitters and calculating the length of each section with different spacing; using one emitter spacing. Results showed that the use of two sections with different spacing between drippers in the lateral line didn't allow longer length but got better uniformity when compared with lateral line with one spacing between emitters. The adoption of two spacing increased the flow rate per meter in the final section which represented approximately 80% of the lateral line total length and this justifies their use. The software allowed DU above 90% with pressure head variation of 40% and the use of two spacing between emitters. The developed model/software showed to be accurate, easy to handle and useful for lateral line design using non-pressure compensating drip hose.

A transmission line model developed directly in phase domain

The phases of a transmission line are tightly coupled due to mutual impedances and admittances of the line. One way to accomplish the calculations of currents and voltages in multi-phase lines consists in representing them in modal domain, where its n coupled phases are represented by their n propagation modes. The separation line in their modes of propagation is through the use of a modal transformation matrix whose columns are eigenvectors associated with the parameters of the line. Usually, this matrix is achieved through numerical methods which do not allow the achievement of an analytical model for line developed directly in the phases domain. This work will show an analytical model for phase currents and voltages of the line and results it will be applied to a hypothetical two-phase. It will be shown results obtained with that will be compared to results obtained using a classical model. © 2012 IEEE.

Development of a simplified transmission line model directly in the phase domain

A transmission line digital model is developed direct in the phase and time domains. The successive modal transformations considered in the three-phase representation are simplified and then the proposed model can be easily applied to several operation condition based only on the previous knowing of the line parameters, without a thorough theoretical knowledge of modal analysis. The proposed model is also developed based on lumped elements, providing a complete current and voltage profile at any point of the transmission system. This model makes possible the modeling of non-linear power devices and electromagnetic phenomena along the transmission line using simple electric circuit components, representing a great advantage when compared to several models based on distributed parameters and inverse transforms. In addition, an efficient integration method is proposed to solve the system of differential equations resulted from the line modeling by lumped elements, thereby making possible simulations of transient and steady state using a wide and constant integration step. © 2012 IEEE.

Eigenvalue analyses for non-transposed three-phase transmission line considering non-implicit ground wires

This paper presents a method for analyzing electromagnetic transients using real transformation matrices in three-phase systems considering the presence of ground wires. So, for the Z and Y matrices that represent the transmission line, the characteristics of ground wires are not implied in the values related to the phases. A first approach uses a real transformation matrix for the entire frequency range considered in this case. This transformation matrix is an approximation to the exact transformation matrix. For those elements related to the phases of the considered system, the transformation matrix is composed of the elements of Clarke's matrix. In part related to the ground wires, the elements of the transformation matrix must establish a relationship with the elements of the phases considering the establishment of a single homopolar reference in the mode domain. In the case of three-phase lines with the presence of two ground wires, it is unable to get the full diagonalization of the matrices Z and Y in the mode domain. This leads to the second proposal for the composition of real transformation matrix: obtain such transformation matrix from the multiplication of two real and constant matrices. In this case, the inclusion of a second matrix had the objective to minimize errors from the first proposal for the composition of the transformation matrix mentioned. © 2012 IEEE.