PDF Publication Title:
Text from PDF Page: 005
where Q = Q(t) is the pump flow rate (controlled input) and I = I(t) is the electrical current (treated as a measured disturbance input). Parameters k2, k3, k4 and k5 are the diffusivity coeffi- 50 cients for V 2+, V 3+, V 4+ and V 5+ across the membrane respectively. Lpe, Wpe and Hpe are the length, width and height of the porous electrode respectively and d is the thickness of membrane. Vt denotes the volume of electrolyte in each half cell, F is Faraday’s constant, n is the number of electrons transferred in the reaction, and M is the number of cells in the stack. We consider two sensors, providing measurements of the inlet and outlet open circuit cell voltage, EIN and EOUT respectively. Based on the Nernst Equation, these measurements can be OCV OCV represented as functions of the vanadium concentrations as shown below: IN ′ RT ct,2ct,5 OUT ′ RT cc,2cc,5 EOCV =E0+nFln c c , EOCV =E0+nFln c c , (4) t,3 t,4 c,3 c,4 where E0′ is the formal potential, R is the Gas constant (J mol−1 K−1) and T is the temperature. The concentrations, c, pump flow rate, Q, and electrical current, I, are considered bounded as cmin ≤c≤cmax, Qmin ≤Q≤Qmax, Imin ≤I ≤Imax. (5) 2.2. LPV Embedded State Space Model Intuitively, and without loss of generality, the dynamics of a VRB can be understood as a linear time-varying model, which is dependent on the variation of the concentrations (and hence SOC) of the system. In a practical sense, this observation motivates the following linear parameter varying approach, in which the varying parameters are naturally functions of the concentrations. To embed the nonlinear VRB model of (3) into an LPV state space description, we begin by defining the states, x(t) = (x1, x2) as x1 := ct,2ct,5 , x2 := cc,2cc,5 . (6) ct,3 ct,4 cc,3 cc,4 This particular definition for the states is attractive, since from (4) and recalling the positive, non-zero bound on the concentrations (see (5)), the states, x1, x2, in (6) can be reconstructed from the OCVs and formal potential explicitly: x =enF (EIN −E′), x =enF (EOUT−E′). (7) 1 RT OCV 0 2 RT OCV 0 Taking the derivative of each state in (6) yields d x1 = dt d x2 = dt ct,5 d ct,2 − ct,2ct,5 d ct,3 − ct,2ct,5 d ct,4 + ct,2 d ct,5, ct,3ct,4 dt c2t,3ct,4 dt ct,3c2t,4 dt cc,3cc,4 dt cc,5 d cc,2 − cc,2cc,5 d cc,3 − cc,2cc,5 d cc,4 + cc,2 d cc,5. cc,3cc,4 dt c2c,3cc,4 dt cc,3c2c,4 dt cc,3cc,4 dt 5 (8)PDF Image | Electrolyte Flow Rate Control Vanadium Redox Flow Batteries
PDF Search Title:
Electrolyte Flow Rate Control Vanadium Redox Flow BatteriesOriginal File Name Searched:
2201-12812.pdfDIY PDF Search: Google It | Yahoo | Bing
Salgenx Redox Flow Battery Technology: Salt water flow battery technology with low cost and great energy density that can be used for power storage and thermal storage. Let us de-risk your production using our license. Our aqueous flow battery is less cost than Tesla Megapack and available faster. Redox flow battery. No membrane needed like with Vanadium, or Bromine. Salgenx flow battery
CONTACT TEL: 608-238-6001 Email: greg@salgenx.com (Standard Web Page)