Model for evaluating the electric power output of Pressure Retarded Osmosis generation plants

Abstract

In this work a mathematical model is assembled to evaluate the electric complex power and electric current output of pressure retarded osmosis (PRO)- based generation plants. Unlike other works already reported in the literature, the assembled model allows performing that evaluation in the abc reference frame based on the salinity concentrations of the salty and fresh water bodies entering the membrane modules and the phasor voltages at the terminals of the generation plant. The induction generator is selected as the power transductor. The assembled model also collects main phenomena affecting the PRO process efficiency: internal concentration polarization, external concentration polarization and spatial variations. A numerical example is presented where the model is used to evaluate the electric complex power output of the PRO generation plant. The numerical results obtained suggest that reactive power compensation may be needed for the selected power transductor. These results also confirm that the main phenomena affecting the PRO process efficiency substantially affect the active power production, but not the reactive power consumption. In this way, the assembled model may be used to analyse the steady state performance of electric networks under the integration of PRO generation plants.

Pressure Retarded Osmosis Power Units Modelling for Power Flow Analysis of Electric Distribution Networks

“…The coefficients of (65) are given by (66). The general guidelines to Formulates (65) and (66) are given in [19]. The solution of (65) for R L1 is directly obtained from (67), which yields the values R L1a and R L1b .…”

“…Bearing in mind the expectations for integrating PRO power units as DG and the importance of the power flow analysis for the planning and operation of distribution systems, this paper comprehensively addresses the modelling of PRO power units into the power flow analysis of three-phase radial distribution networks. For this purpose, the model of PRO power units reported in [19], assembled by authors of the present work from the basic principles to estimate electric power production [2,20], is adapted and embedded within the formulation of the power flow problem of distribution networks reported in [21]. The resulting power flow problem considering embedded PRO units is directly solved by using the forward-backward sweep (FBS) method [21].…”

“…For this purpose, the phasors V n abc_D of the line-to-line voltages must be obtained from transforming the line-to-ground voltages V n abc according to (16), where D V is the transformation matrix given by (17). Then, the phase currents components I n abc_ZD , I n abc_ID , and I n abc_PD can be assessed from ( 18), (19), and (20), respectively, where the per-phase load is considered as constant impedance Z ∆ , constant current magnitude I n ∆ , and constant power S n ∆ , respectively. The per-phase constant impedance Z ∆ and constant current magnitude I n ∆ are evaluated from ( 21) and (22), respectively, by considering the initial condition (nominal value) V n ∆_0 of the magnitude of the line-to-line voltage, the known per phase complex power S n ∆ , and the load apparent power S n ∆ (for ∆ = ab, bc, ca).…”