A Simple but Comprehensive Lead-Acid Battery Model for Hybrid System Simulation

Transcription

1 Presentation from visit site for current author contact info A Simple but Comprehensive Lead-Acid Battery Model for Hybrid System Simulation Michael Ross - GPCo inc Workshop on Photovoltaic Hybrid Systems - PV Horizon, September 10, 2001, Montréal, Canada

2 Types of Battery Models Energy models: Σ (energy out) = ησ (energy in) very simple, adequate for basic simulations no voltage information, therefore hybrid system control strategy must be expressed in terms of SOC gassing, water loss, heat evolution, PV array voltage unknown Voltage-Current/SOC models: V batt =V(I, SOC, T, etc) relatively simple, adequate for investigating system control ignores stratification, different conditions at different locations in the battery Physical models: system of differential equations complex, useful for evaluating actual conditions in battery can show how control strategy affects stratification and the effect that this has on battery ageing

3 Voltage-Current/SOC Relation: Discharge V = DV I DK T OC V + T OC DP1 1+ ( I) ( T 25) DV ( 1 AhR) DP 2 + DP AhR 3 DP 4 slope + ( 1 DaTr( T 25) ) Base potential......minus overpotential based on: Shepherd model (1965) updated by Copetti (1993) fit to measured curves using Matlab s non-linear least squares curve fitting p c) (V ge ta o l v Flooded vented tubular battery, Constant current discharge at 25C Fit curve time (hours)

4 V Voltage-Current/SOC Relation: Charge VOC = CVOC + ( T 25) + CV T I CP1 CP3 + CP2 CP4 CK 1+ I 1 AhC slope AhC + ( 1 CaTr( T 25) ) Base potential......minus overpotential I gas AhD = V diff τ 3 = CK τ 1 e (this is linearized just above onset of gassing) ( I max( I gas, I SD ) dt + AhD0 (the actual charge current is the current at the terminals minus gassing current) p c) (V ge ta o l v "Monitored" data above 2.5 V is actually manufactured based on the literature Flooded, vented tubular battery, constant current charge at 25ºC time (hours)

5 Improvements on Copetti (1993) State of charge not used-- this is an ambiguous term rather, state variable is the remaining dischargeable active material Gassing calculated from voltage based on Tafel equation if we assume all coulombic inefficiencies due to gassing, we do not need to assume a battery efficiency curve, unlike Copetti Copetti uses a separate, empirical voltage curve during gassing because we use I charge = I terminals - I gas, the characteristic end-of-charge plateau appears automatically Resulting model is: simpler (one equation for voltage instead of two) more accurate (transition from charge to gassing region is smooth) physically interpretable (no invented efficiency or gassing curves)

6 Heat Evolution 1) Joule : P heat = I terminal V overpotential 2) Reversible : P heat =d/dt(h reaction -W) (charging reaction) -heat liberated on charge, absorbed on discharge 3) Gassing : P heat =d/dt(h reaction -W) (electrolysis reaction) -heat absorbed for all gasses not recombined Voltage (V), Gas (L/hr), Heat (W) Gassing heat dominated by Joule heat of Reversible heat dominates gassing reaction Joule heat dominates A -4A OC 5A 2A time (h) Voltage Heat Gas

7 Lifetime limited by cycling and shelf-life Battery Life: 30 Cycles at 50% SOC 1 year float at 25ºC Cycle life catches up with float life SOC, Lives Used State of Charge Lives Used Cycle life drops due to deeper cycling 25ºC 60ºC 25ºC time (hours) At high temperature, difficult to fully charge battery so SOC drops At high temperatures, float life is limiting

8 Use in PV Hybrid System Simulation 5 St. Hubert, Québec, April 11th and 12th 100 Ah battery + 82 Wp array Absorption Charging Bulk Charging Float Charging Battery Voltage SOC, Current (Amps) 2 1 SOC Voltage (V) 0 PV Array Current Battery Current 9-2 Load of 1 A No load Load of 1 A No load Load of 1 A time (hours) 8

9 Implemented in Simulink Also calculates water loss and self-discharge Link with PV array, weather, charge controller, genset, etc.

10 Acknowledgements Work done under contract to Natural Resources Canada CEDRL Hybrid System Simulation Program Program on Energy Research and Development (PERD) Dave Turcotte, Farah Sheriff, Lucie Nolin References Bader, C. A New Battery State-of-Charge Indicator Especially for Use in Electric Vehicles. Proceedings of the 9th Internation Symposium, Brighton, September D.H. Collins, ed. London: Academic Press. pp (1975). Copetti, J.B., E. Lorenzo, and F. Chenlo. A General Battery Model for PV System Simulation. Progress in Photovoltaics. Vol. 1, pp (1993). Sauer, D. U. Modelling of Local Conditions in Flooded Lead-Acid Batteries in PV Systems. Journal of Power Sources (1997). Shepherd, C.M. Design of Primary and Secondary Cells-- II. An Equation Describing Battery Discharge. Journal of the Electrochemical Society.Vol. 112, no. 7, pp (1965). Spiers, David J. and Asko A. Rasinkoski. Limits to Battery Lifetime in Photovoltaic Applications. Solar Energy. Vol. 58, pp (1996). Vinal, George Wood. Storage Batteries (4 th edition). New York: John Wiley & Sons, Watsun Simulation Laboratory. Watsun-PV 6.0 User s Manual and Program Documentation. Waterloo, Ontario: University of Waterloo, 1997.

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