A leading motorcycle manufacturer wanted to include a realistic battery model in its MapleSim powertrain model. The challenge of this project was to create an electrical and thermal model of a lead-acid automotive battery. The behavior of lead-acid batteries is extremely nonlinear and depends on numerous factors, including the temperature, rate of charge or discharge, and the state of charge. Far from being a simple constant voltage source, a battery’s voltage will change under these varying operating conditions.
The battery’s state of charge can be thought of as a “gas tank” function that is one when the battery is full and zero when the battery is empty. When the state of charge is zero, the battery will not deliver any charge and must be recharged. As the battery recharges, the state of charge increases from zero to one. If the battery is recharged beyond its capacity, the excess energy is lost in the form of heat through various processes that are detrimental to the battery’s longevity.
The open-circuit voltage is measured at the terminals of the battery when no load is attached. The open-circuit voltage is itself a function of the state of charge and battery temperature. The equivalent series resistance (ESR) of the battery is the apparent resistance internal to the battery and is a complicated function of the state of charge and rate of charge or discharge.
Typically, the manufacturer will provide a variety of charge/discharge curves and parameters that give information on the dynamic behavior of a battery. The challenge for engineers is to model the dynamic behavior of a battery and fit the manufacturer data to the chosen model. Many of the available models are circuit-based and rely on dynamic components like resistors and capacitors whose values change in response to the operating conditions. However, purely circuit-based implementations do not implement the thermal characteristics of the battery, and very few circuit simulators allow for dynamic components with such complicated governing equations. Consequently, existing models are inadequate predictors of battery behavior, and are therefore ill-suited for use in engine models where heat loss must be taken into account or in studies of overall energy efficiency.
Figure 1 - The battery model connected to a variety of loads.
The multiphysics and parametric nature of MapleSim makes it especially well-suited to implementing a realistic battery model. The model created was based on a third-order model selected from published research. The resulting battery model, shown in Figure 1, is connected to a variety of loads. It has positive and negative electrodes, a temperature port, and a state of charge port. It is connected to a resistor and a motor to demonstrate that it can power both static and dynamic loads, respectively. Current sources are also used to facilitate charging and discharging of the battery model.
The battery model was divided into a thermal component and an electrical component that were connected, as seen in Figure 2. The thermal component takes the amount of power lost by the battery and converts that to heat. The heat capacity of the battery is specified by the manufacturer. Next, the battery loses heat based on the temperature difference between it and its surroundings through body radiation heat loss.
The electrical model uses MapleSim custom components to directly specify the governing equations of the active circuit elements. Instead of a mess of functions blocks, the complicated governing equations are specified directly in an attached Maple worksheet. The net result is a clean and intuitive schematic that exposes the model to the user. The simulated dynamic response of the battery accurately matches the behavior of real batteries, as shown in the simulation results in Figure 3.
MapleSim allows a complex multi-domain analytical model of a lead-acid battery to be implemented in a straightforward way that provides realistic results. By connecting the battery model to a MapleSim powertrain model, the customer can efficiently analyze options for components such as starters and alternators, and investigate the results under a variety of operating conditions.
Figure 2 - The thermal and electrical characteristics of the battery are easily separated and connected in MapleSim.
Figure 3 - The output of a MapleSim simulation of the dynamic response of the battery model. The battery current is shown in the top left plot. First, 65 A is drawn from the battery, the battery rests, then is recharged with 10 A. The dynamic response of the voltage (top right), temperature (bottom left) and state of charge (bottom right) are shown.
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