Virtual Test Bed for Electrochemical Power Sources

This paper introduces the Virtual Test Bed (VTB) for modeling, dynam and virtual-prototyping of power sources in the system context. Typical ele power sources such as battery, fuel cell and supercapacitor are first mod environmen and the capability of advanced visualizations of simulation results, make quite powerful. el cell, resistive-c INTRODUCTION The Virtual Test Bed (VTB) [1] provides a unique capability for virtual p advanced power systems. The philosophy of the VTB environment is consi of the VHDL-AMS language [2] that defines several forms of connect simulation objects – those in which power flow is conserved at points between simulation objects, and those in which only signals or data a between objects. The VTB embraces multi-disciplinary systems and combination thus providing a comprehensive and efficient system-modeling environmen great value to the power source community by encapsulating knowledge of performance in the form of models, which allows others to build and ex simulations with those models but without having to know the d electrochemistry. In this paper, we will first describe VTB modeling of several typical el components including battery, fuel cell and super capacitor, then do applications of system simulation using these models, including hybrid batt capacitor power sources, p MODELING OF ELECTROCHEMICAL POWER SOURCES his approach story of each parameter on is desired to s at points of tion to other objects. In this section, we will describe models of several electrochemical components including a lithium-ion battery, a PEM fuel cell and a super Native VTB models are coded in resistive-companion (RC) format [3]. T considers the fully coupled equations for all processes, yielding the hi process, the interactions between different processes, and the effect of each the dynamic system response. This model formulation is useful where it connect together simulation objects that must obey natural conservation law connec capacitor. Lithium-ion battery modeling Many detailed physics-based models been built to study the internal dy lithium-ion battery [4,5,6,7,8,9], but generally these models are not suitab level design exercises. On the other hand, simple dynamic mode capacitor/resistor networks [10,11], that can be used in a circuit simulato too simplified. The battery model described in this paper i namics of the le for system ls based on r are generally s based on reference [12], and is sui ony US18650 temperatu esponse to transient power demand. Fig. 1 shows the battery model equivalent circuit. The battery consists of a nonlinear voltage source in series with an internal resistance, and an RC network that represents the first order transient response of the battery. table for virtual-prototyping of battery-powered system. The model (S is used as example) accounts for nonlinear equilibrium potentials, rateand redependencies, thermal effects and r Fig. 1. Battery equivalent circuit The equilibrium potential the tery (open-circuit voltage) dep temperature and the amount of active material ava ref ref ( ) T β nd temperatures. are obtained by curve-fitting to a group of curves measured at different rates a The expressions for the potential, the terminal voltage and the state of discharge are given by equations ( 1), ( 2) and( 3). of bat ends on the ilable in the electrodes, which can be of the battery e d sch e r te and the temperature. For a typical discharge curve, the equilibrium potential as a function of the state of discharge is found by excluding the internal (ohmic) potential losses. The rate factor specified in terms of the state of discharge (SOD). The discharge capacity depends on th i arg a ( ) i α , and temperature factor ( ) T β unity for Iref and Tref respectively, ( ) i α and ( ) ( ) [ ] ( ) ( ) [ ] ( ) t i R t t T t i v t t T t i E int , , , , − = ( 1) ( ) ( ) [ ] ( ) ( ) [ ] ( ) T E t t T t i SOD c t t T t i v n k k k ∆ + ∑ ⋅ = =0 , , , , ( 2) ( ) ( ) [ ] ( ) [ ] ( ) [ ] ( ) ∫ ⋅ ⋅ = t dt t i t T t i t t T t i SOD 1 , , β α r Q 0 Battery current and heat generation are calculated from equations ( 4) an the current and temperature are obtained fr ( 3) d ( 5). When om these two equations in every time step during simulation, they will affect the coefficients ( ) i α and ( ) T β in the next time step, and the battery potential and SOD are affected further. ( ) ( ) ( ) ( ) [ ] ( ) [ ] ( ) ( ) ( ) [ ] ( ) [ ] t i R t t T t i E t v dt d C t i R t t T t i E t v R t i 1 1 2 , , , , 1 − − + − − = ( 4) ( ) ( ) ( ) ( ) ( ) [ ] ( ) [ ] ( ) ] ng rate dependence of potential when the batte is tested under constant current discharge at several currents from 2.8 A to 0.28 A, wh keeping the battery temperature constant at room temperature (23°C). Fig. 3 sho battery temperature dependent characteristics when the battery is discharged at 0.7A under different temperatures from –20°C to 45°C. [ a c T t T A h R t i t t T t i E t v R R t i t t dT c m − − − − + ⋅ = ⋅ ⋅ 2 1 2 1 2 , , 1 Comparison between model simulation result and manufacture’s data are shown in Fig. 2 and Fig. 3. Fig. 2 shows the resulti ry ile ws p d ( 5) Fig. 2 Rate dependence of potential Fig. 3 Characteristics of temperature dependence PEM fuel cells modeling As with the Lithium battery model, there are many highly detailed polymer electrolyte, or proton exchange, membrane fuel cell availa models of a ble in literatu e [13,14,15,16,17,18]. From a macroscopic view point the level of detail is beyond the requirement of system level designers. A model that encompasses basic fuel cell voltage current characteristics [19] with attention paid to stack pressure and temperature [20] and conservation of mass and heat power [21] would suit the system level model ideally. r Fig. 4 Pictorial Representation To this end the potential of each cell of a fuel cell stack is determin b I n o cell e m I r I b E E ⋅ ⋅ − ⋅ − ⋅ − = ) log( ed y equation ( 6).