Estimation of Discharge Capacities Using Generalized Peukert’s Equation for Saft Industrial Standby Batteries
Authors: Baskaran Rajesh , Mitra Debanjan , Smollack Steve , Grewal Jagjot , Goubault Lionel , Blanchin Stephane 
Published: November 2022

Saft Industrial Standby (ISD) battery utilizes robust nickel-cadmium alkaline electrochemistry that delivers reliable performance and long life of at least 15 years over a wide range of temperature (-20 °C to 50 °C). The battery is designed with nickel based positive electrode and plastic bonded cadmium electrode in a vented prismatic cell. Typically, telecom applications used to require long duration backup power sources. With the advent of 4G/5G, the duration for backup power has been reduced to 1 hour or less. Therefore, new ISD battery was designed for power applications like 174 W/cell discharge for 1 hour and at the same time it can deliver high energy density up to 100 Wh/l. Additionally, low water consumption due to the high charge efficiency makes this battery ideal for the maintenance free remote installations. All these features render the battery aptly suitable for providing back-up power in telecom networks (4G and 5G) including remote cabinets at the lowest total cost of ownership.
The ISD battery (Tel.X-Plus) is compliant to the Telecordia GR (Generic Requirement)-3020 CORE standard, which is recommended for the secondary alkaline batteries used in the telecom back-up application. This standard requires declaration of minimum 28 discharge currents entailing different durations and end voltages for a specific battery capacity. Hence, correct estimation of deliverable capacities for any definite duration and end voltage can reduce significant number of test trials. In addition, it helps sizing the battery for different power and energy installations. There are a few analytical techniques, such as Peukert’s and Shepherd’s equations that can be used to model the discharge characteristics of batteries. There are three different forms of generalized Peukert’s equations: algebraic, hyperbolic tangent and complementary error functions. In this study, to evaluate the discharge capacities we investigated the complementary error function of the generalized Peukert’s equations described in the equation 1:
C= (Cm/erfc(-1/n)) * efrc(((i/ik)-1)/n) ... (1)
where, C is the capacity of the battery during discharge, Cm is the highest discharge capacity, i is the discharge current, ik and n are statistical parameters. We know that phase transition is key to the discharge of a battery. Therefore, we selected the equation which also defines the phase transition process. The discharge capacities were calculated between 24-hour and 0.20-hour discharge durations for 1 V/cell, 1.05 V/cell, 1.10 V/cell and 1.14 V/cell end points using the equation 1. Here, the discharge capacity that was experimentally determined at the nominal C/24 rate was used as the maximum discharge capacity, Cm. The value of the statistical parameter n is within 0 and 1 to satisfy the capacity limits when discharge current tends to infinite and zero. For example, n equals to 0.6 is used for the calculations pertaining to the 180 Ah rated battery. The other statistical parameter ik was empirically selected for each end point voltage e.g., 250 A for 1.1 V/cell. Figure 1 shows the results for the calculated discharge capacities along with the experimental values at the 1.1 V/cell cut-off. The calculated numbers closely match with the experimentally obtained values with the r2 of 0.998 (Figure 1)
Results for the other cut-off voltages (1.0 V/cell, 1.05 V/cell and 1.14 V/cell) were also obtained using the equation 1 and closely match the experimental values. Thus, the phase transition form of generalized Peukert’s equation (complementary error function) can be used for evaluating the capacities between 24-hour and 0.20-hour of discharge durations. Consequently, it enhances the test efficiency remarkably and sets the stage for battery sizing. Future studies include but not limited to the significance of n and ik, algebraic form of Peukert’s equation and Shepherd’s equation to understand the effectivity of each model with a focus on the discharge durations below 0.20-hour.

Figure 1