Appliance Design - March 2009 - (Page 23)

POWER 1.5 15 1.49 ( D , .4s) ( D , 4s) ( D , 40s) ( D , 400s) 10 vo ( t) 1.48 5 1.47 1.46 0 10 20 30 40 0 0 0.2 0.4 0.6 0.8 1 t (s) Fig. 6. Battery voltage for pulse-duty ratio, D, of 0.1. D Fig. 7. Power multiplier for hybrid system with various periods as a function of pulse-duty ratio. Φ(t) is the Heaviside function. Solving the circuit for the external voltage, vo, yields Equations 3 and 4. Once one has solved for the external voltage, it is relatively straightforward to obtain the battery and capacitor currents with Equations 5 and 6. A detailed description of these equations can be found in the article: Power and Life Extension of Battery – Ultracapacitor Hybrids by R.A. Dougal, Shengyi Liu, and Ralph E. White, IEEE Transactions on Components and Packaging Technologies, Vol. 25, No. 1, March 2002, pp 120-131. The article serves as the basis for much of SolRayo’s battery/capacitor modeling work at frequencies lower than 1 kHz. By plotting Equations 1, 5 and 6, one can see in Fig. 4 the load current and the current supplied by the battery and the electrochemical capacitor. The figure shows the results for: D = 0.1, T = 10 s, C c = 40 F, R b = 0.15 Ω, and R c = 0.0125 Ω. For this combination of parameters, most of the pulsed load is being met by the electrochemical capacitor. If we increase the pulse-duty ratio, D, to 0.25, the electrochemical capacitor still meets a significant part of the pulsed load, as seen in Fig. 5. The battery voltage for the initial conditions with the pulse-duty ratio, D, of 0.1 is shown in Fig. 6. The battery voltage drops during the load pulse and then recovers as the battery charges the electrochemical capacitor. The figures show that, by incorporating an electrochemical capacitor into the circuit, the battery current is reduced to a fraction of the load peak current. This substantially reduces the internal voltage drop in the battery. Simplifying the design so that the output voltage is constant, which is reasonable in light of Fig. 6, one can assume that the peak power drawn from the battery occurs at the same time the battery current is at its maximum value. As the figures show, the maximum battery current occurs at t = (k+D)T. The previous equations can be used to estimate the peakRbattery ecurrent, as seen in DT (1 D )T Io 1 be Ib, peak = I 1 Equationso 7, 8,b and 9. e T = Io (1 c ) = R + Rc 1 Assuming that the battery maximum operating current is equal to its rated current (I b, peak = I rated ) then Equation 10 is also true. Thus, γ is a multiplier that reveals how much more current the hybrid system can deliver than the battery alone can deliver. In a similar fashion, the power which can be delivered by the hybrid system is shown in Equation 11, where Prated is the rated power of the battery. Fig. 7 shows the calculation of γ for a variety of periods as a function of pulse duty ratio (D). As the figure shows, the peak power delivered by the hybrid system can be more than 10 times the rated battery power. The plot also shows that the hybrid system will perform better for systems with a smaller duty cycle. Many battery applications having high-current pulse loads can)Tgreatly ben-Io Rb e DT 1 e (1 D Ib, peak = Io 1 = Io (1 c ) = Rb + Rc e electrochemiefit from the addition1 of T cal capacitors. As this modeling demonstrates, the incorporation of an electrochemical capacitor into a battery application can result in a 10-fold increase in maximum power, thereby allowing for significant reductions in size, weight, and cost for battery/electrochemical capacitor hybrid systems. < For more information, email: Io = Irated contactsolrayo@solrayo.com Ib, peak = Io 1 Rb e DT 1 e (1 D)T = Io (1 Rb + Rc 1 e T c )= Io Ppeak = Irated Vb = Prated Equation 9. Equation 11. Equation 7. Io = Irated Equation 8. www.applianceDESIGN.com Equation 10. Ppeak = Irated Vb = Prated applianceDESIGN March 2009 23 http://www.appliancedesign.com

Table of Contents Feed for the Digital Edition of Appliance Design - March 2009

Appliance Design - March 2009 Contents Editorial Shipments/Forecasts News Watch Transmitting Power Wirelessly Promises to Reduce the Ever-Growing Tangle of Cords and Cables Found in the Modern Home. There Are Different Technological Approaches for Achieving this Goal, and Some Are Already on the Market. Electrochemical Capacitors Can Provide an Extra Peak-Power Boost in Battery-Operated Appliances, Allowing Product Designs to Have Smaller Battery Packs. Metallic Foams Put the Properties of Metals into Lightweight Packages. Applications for this Emerging Technology Include Gas Burners, Heat Exchangers, and Electronics Housings. Hall-Effect Switches Are Compact and Provide a High Degree of Reliability and Durability as They Virtually Eliminate Mechanical Wear, Shock, and Contact Oxidation. Blowing Agents for Polyurethane Foam Insulation Face Increased Scrutiny Due to Global Warming Concerns, but Alternatives with Lower GWP Values May Provide Solutions to Meet These Challenges. Design Marts Association Report: AHAM Advertisers' Index

Appliance Design - March 2009

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