Based on the conclusions: (a) Peak power capability of the battery pack degrades more rapidly with cycle life than does the three-hour constant- current capacity. This peak power degradation determines the useful life under driving profile conditions. Consequently, the useful life with driving profiles that have a high peak power demand is much less than the life with profiles having a low peak power requirement. (b) Rest periods of up to eight hours between discharge and charge has little effect on battery life. (c) The three-step constant current (CI1/CI2/CI3) charge method produces a lower temperature rise but does not yield increased cycle life over the constant-current, constant voltage (CI/CV) charge method recommended by the battery manufacturer. (d) Cooling of sealed starved-electrolyte lead-acid batteries is more difficult than for flooded-electrolyte batteries, particularly in those designs where the elec- trode battery assembly is not in contact with the battery casing walls.
This is due to the greater heat generation and poorer thermal conduc- tion in the sealed battery. (e) The design of the battery pack thermal management system can be significantly improved to improve the volumetric energy density of the system. (f) The most promising short-range approach to increasing the battery utilization of the active BATTERY CYCLE LIFE VERSUS PEAK POWER AND REST PERIOD 173
material in VRLA batteries is by the use of forced electrolyte circu- lation through the battery electrodes.
Modeling NiMH Batteries
A mathematical model for the NiMH cell was recently developed by Paxton and Newman. However, the model analysis was limited to the discharge behavior of the NiMH cell. While predicting an end-to-end performance of a battery pack in vehicle testing, it is important to account for the charge and overcharge reactions.
As part of the mathematical model development, it is important to incorporate the gassing phase of the NiMH battery. The NiMH cell can be broken down into the cathode (metal hydride) and anode (porous NiOOH), a separator and an electrolyte. The reaction at the anode is
NiOOH +H2O +e-´Ni(OH)2+OH- With side reactions as
1/2O2+H2O +2e-´2OH- At the cathode the reaction is
MH +OH-´M +H2O +e- With the side reaction as
2OH-´1/2O2+H2O +2e-
When the equations for the anode and the cathode are combined they yield the overall NiMH reaction
NiOOH +MH ´Ni(OH)2+M
The side reactions at the anode and the cathode represent the oxygen recirculation reaction occuring inside the NiMH cell. During the charge phase, O2 is generated at the Ni/electrolyte interface. The generated oxygen dissolves into the electrolyte. Once the electrolyte is saturated, the O2 evolves in to the gas phase. This process of liguid to gas phase transition forms an internal oxygen cycle for the NiMH cell. The accu- mulation of oxygen in the gas phase results in pressure build up in the NiMH cell.
Some of the assumptions made include:
174 TESTING AND MODELING OF ELECTRIC VEHICLE BATTERIES
• The NiMH electrode consists of porous, cylinder with a substrate inside the electrode.
• The MH electrode consists of a uniform size, porous substrate.
• There is a continuous gas flow network with a uniform and a con- stant volume inside the NiMH cell.
• There is no contact between the active material and the oxygen gas phase as the electrolyte forms the bridge between the active mater- ial and the gas phase.
• Effects of convection of the electrolyte and the oxygen gas are neg- ligible. Thus the movement of free O2occurs through the diffusion process.
Charge Acceptance of a cell is defined as the ratio of partial charge used by the electrochemical reaction to reverse the active materials to the total charge applied to the cell. The equation for charge acceptance may be expressed as
Charge acceptance = SaNiin1d ¥dt ÚIdt
where in1is the transfer current density, A/cm2, I is the current density, A/cm2. The charge acceptance is a function of the SOC and time.
Similarly SOC may be defined as
SOC = SaNiin1d ¥dt/Qmax
where Qmax is the maximum theoretical charge capacity of the nickel electrode per unit projected area, C/cm2. And DOD is expressed as
DOD =1 + SaNiin1d ¥dt/Qmax =1 +SOC Cell Pressure is expressed as
P =P0+(PO2-P0O 2)
where P0is the initial (reference) cell pressure and is set to be zero. In the case of a sealed NiMH battery, the cell pressure results from the balance of oxygen generation, transport, and recombination. The cell pressure increases when the oxygen generation rate is higher than the oxygen recombination rate. This is a condition that occurs during battery charging and overcharging.
BATTERY CYCLE LIFE VERSUS PEAK POWER AND REST PERIOD 175
Polarization Resistance Model of NiMH Batteries
Polarization resistance associated with the NiMH battery is linear in nature at lower temperatures. The polarization resistance depends upon the SOC and is time dependent. This resistance is affected by electrode material composition, electrolyte level, electrode density, and electrode particle size. The polarization characteristic on discharge and the limit- ing current depends on the SOC of the electrode. The polarization resis- tance increases and the limiting current decreases as the SOC of the electrode decreases. Present at the hydride electrode, this resistance is ohmic in nature. The polarization resistance in the starved cell depends upon the amount of electrolyte in the cell. The resistance value decreases with increasing electrolyte quantity and the limiting current becomes lower. The polarization curve approaches a limiting current at higher current density.
Assuming an equivalent circuit for the interface consists of a double layer capacitor and a reaction resistance connected in parallel to the capacitance can also be calculated. The surface area of the electrode can be derived from the capacitance value. NiMH battery pack voltage (Vpack) maybe defined as
Vpack=OCV -IR - DV
where the OCV is the open circuit voltage of the battery pack under no- load condition, I is the battery pack discharge current (A).
The polarization model for the NiMH may be defined as DRC ¥dDV/dt + DV =I DR
since I =I0+(dDI/dt) ¥t
Therefore, DV = DR [(I0- DRC ¥(dDI/dt)(1 -exp(-t/DRC)) + (dDI/dt) ¥t]
For example, assume that the battery pack is at 7% DOD and the OCV for the NiMH cell is 1.359 V/cell, Rbattis 0.225W, DR is 0.059W. There- fore, using the above equation, DRC =21.3 seconds.
The polarization resistance increases with decreasing temperature.
The temperature dependence indicates that it may be associated with the resistance of the KOH electrolyte. Thus making the polarization resistance time dependent and SOC dependent.