Download Predicting Remaining Capacity of Batteries for UAVs

Predicting Remaining Capacity of Batteries for UAVs and Electric Vehicle
Applications
Nick Williard, Wei He, Michael Osterman, Michael Pecht
The functionality and reliability of portable microelectronics systems is often limited by the ability of the
power supply to provide a continuous source of energy. In modern portable applications, lithium ion, and
lithium polymer batteries have become the choice energy system. The selection of these batteries is based
on their high volumetric and gravimetric energy densities and their ability to be scaled up or down to fit
the needs of a dynamic range of applications such as automobiles, unmanned aerial vehicles (UAV),
active RFID tags and wireless sensors. Performance of these batteries is heavily dictated by the use
conditions such as current rate of charge and discharge. In order to optimize performance of electronic
systems, the user must know the state of charge (SOC) of the battery so that periods of recharge can be
anticipated and scheduled. The user must also know the state of health (SOH) of the battery in order to
plan for the replacement of the battery.
In this paper battery design parameters and how they relate to the inherent battery capacity are discussed.
Considerations for predicting capacity under various discharge current rates are given. Also, the
hardware and software requirements of determining SOC and SOH of lithium ion batteries in portable
applications are discussed. The resulting goal of these considerations is for the implementation of a full
battery prognostics and health management (PHM) system capable of providing predictions for remaining
useful performance.
Many electronic driven military applications, such as two way radios, GPS systems, night/thermal
vision goggles, unmanned aerial vehicles, and electric vehicles require the use of portable power supplies.
In many cases these devices rely on the lithium ion or lithium polymer batteries. These battery
chemistries provide superior properties compared to the nickel-cadmium cells which were commonly
used to power rechargeable electronic systems prior to the commercialization of lithium based batteries.
Some of the advantages of lithium ion batteries include higher volumetric and gravimetric energy density
which means that more available electrical energy can be packed per unit volume or unit mass of lithium
ion battery material respectively. This characteristic helps reduce size and weight for portable
applications.
A major requirement for next generation batteries is the ability to evaluate the remaining useful
life. This is especially important in military applications such as UAVs where battery life is mission
critical information. The useful life available before the next recharge is required is often referred to as
the state of charge (SOC) and in UAVs will be directly related to the available flight time during a
particular mission. A battery’s useful cycle life before it must be replaced is referred to as the state of
health (SOH). This can be used to determine when condition based maintenance or battery replacement
should be performed. In order to determine SOC and SOH a prognostics and health monitoring (PHM)
system must be put into place to measure the battery’s capacity which is directly related to its operational
health. PHM generally combines sensing and interpretation of environmental, operational, and
performance-related parameters to assess the health of a product and predict remaining useful life.
Often batteries are designed with specific capacity requirements in mind. This abstract first
outlines some of the design parameters used to meet operational requirements, and then methods of
determining SOC and SOH are outlined.
Design for Reliability
Lithium based batteries contain an inherent design flexibility which allow them to be customized
for particular applications. For low power devices such as micro-electromechanical systems (MEMS),
and active RFID tags, anode and cathode materials can be deposited in thin films with solid electrolytes
onto substrates to provide small and compact power supplies. Cells can be flexible and designed to
operate at high temperatures due to their sold state electrolytes. Polymer electrolytes with the addition of
a zwitterionic salt have demonstrated good electrochemical properties with a thermal stability of over
300oC [1]. For larger applications, multiple battery cells can be connected in series and/or parallel to
form a battery pack which is capable of delivering a higher voltage or current than any of the single cell.
However, there are reliability concerns associated with cell imbalance which occurs when individual cells
degrade at different rates leading to a miss-match in each cell’s depth of discharge. Some work has been
done to convert models for single cell batteries into their multi-cell counterparts using an extension of the
equivalent circuit model [2].
Design flexibility is also apparent in the material processing and construction. Typically
electrodes are made by grinding the active material (graphite is used for the anode, while the cathode is a
lithium metal oxide mixed with carbon for increased conduction) into a powder of a particular particle
size. This powder is then mixed with a polymer binder for cohesion and the resulting slurry is adhered to
current collectors in order to conduct electricity from the electrodes out to the battery terminals. The
particular size of the electrode particles plays a crucial role in the cell’s performance and reliability. The
smaller the particles, the more porous the electrodes which will allow the electrolyte to be exposed to
more of the electrode surface area. This design is more conducive to high power applications but falls
short in some reliability aspects. The increased surface area exposed to lithium intercalation leads to
large electrode expansion which can cause mechanical damage in the electrodes resulting in poor cycle
life. Also the high current rate discharges, if not well controlled by a battery management system can
lead to safety problems due to large heat generation.
Electrodes that are formed with larger particles and that are bounded together with high pressures
will be less porous. These cells are poor at delivering high current but have longer cycles. Because the
materials are less porous, there will be a higher density of active material contained within the cell
allowing more energy to be stored per unit volume, leading to higher capacities. Less of the electrolyte is
required to fill in the pores of the electrodes which also contribute to the overall reduction of cell volume.
These cells are better suited for low current and high capacity applications.
When designing a battery for reliability, the electrolyte must also be taken into consideration.
Decomposition of the electrolyte leads to solid precipitates which adhere to the electrodes as a surface
film. As this surface film thickens, it leads to decreased ion transport from the electrolyte into the
electrodes reducing the performance of the battery. Other decomposition products of the electrolyte’s
organic solvents are gaseous in nature and can cause an increase in the cell’s internal pressure. This
outgassing will lead to cell bulging and could cause damage to the electrodes. Electrolyte decomposition
is heavily dependent on temperature and because decomposition reactions are often exothermic, the
potential for thermal runaway is a major safety concern. Wang [3] performed calorimeter studies on a
number of different commercially used electrolytes to find the onset temperatures of exothermic behavior.
Another factor that plays a role in the reliability of the electrolyte is the polymer separator. The
separator provides electrical isolation between the anode and the cathode but is permeable by the
electrolyte. The design parameters of the separator including pore-size, thickness, and thermal properties
play an important role in battery reliability, particularly as a safety feature [4]. When the separator heats
up to a specific temperature, the material will swell and cause the pores to close. This is known as
separator shut down and it can effectively block the transport of ions through the electrolyte. This
behavior can help to prevent a thermal run-away situation in the case of overheating. These properties
along with the temperature during usage and storage must be taken into account during battery design and
electrolyte selection.
Operate for Reliability
As described above, battery design is often catered toward a particular type of usage condition.
In order to maximize reliability and performance of a battery, the effects of usage must be well
understood and controlled.
The most wide-spread characteristic used for evaluating battery reliability and performance is the
capacity. During extreme over-stress conditions such as mechanical shock or high temperatures, batteries
can experience sudden failure due to cracked casings, broken leads, or electrolyte decomposition, but
under normal operating conditions and typical usage profiles, the gradual decline in capacity over time
defines battery failure.
Capacity is a measure of electrical charge expressed in coulombs or ampere-hours (Ah) where
1Ah is equal to 3600 coulombs. Typically, a user is interested in the maximum discharge capacity (Qmax)
which is a measure of how much electrical charge a battery is capable of delivering from its fully charged
state to its fully discharged state. The manufacturer gives an estimate of what this Qmax value will be at
the beginning of life by providing the rated capacity (Qrated). This Qrated metric is typically a nominal
capacity value that pertains to a large number of batteries of a specific type or model. In reality the Qmax
value of a group of batteries will be distributed around their Qrated value. Furthermore, Qrated is usually
calculated by the manufacturer at a constant, relatively low discharge current rate. This is done by
performing a full discharge on a battery and then integrating current over time by:
t discharged
Qm ax
I (dt )
(1)
t charged
where I is the current, tcharged is the time noted at the battery’s fully charged state and tdischarge is the time
noted at the battery’s fully discharged state. What is not implicit in the definition of Qmax is the
relationship between capacity and discharge rate. In general, discharging at higher currents results in
lower observed capacities. This trend was first observed in lead acid batteries and was reported by
Peukert in a paper in 1897 [5]. It has since been shown to be applicable to lithium ion batteries and
suggests that:
I kt
Cons tan t
Q1
Q2 (
(2)
where I is current t is discharge time and k is Peukert’s constant. From this relation we can estimate the
capacity of a battery when discharged at any constant current rate by:
I2 k
)
I1
1
(3)
Capacity (Ah)
where Q2 is a known capacity when discharging at a current of I2 and Q1 is the capacity in question for a
discharge current of I1. This relation is derived in [6].
To re-validated Peukert’s relation a battery was discharged 5 times at 5 different discharge
currents. For convenience, and to normalize the current rate with respect to the battery design, the current
rate is expressed as a c-rate which is simply the discharge current divided by the rated capacity. Hence
for a battery rated 1.5Ah discharged at a current rate of 3Ampers, the c-rate would be 2C. For the battery
in this experiment, Qrated was 0.7Ah and the five discharge cycles were performed at 1C, 0.8C, 0.5C, 0.2C,
and 0.1C. The battery was discharged from a max voltage of 4.2V to a cut off voltage of 2.7V. During
each discharge cycle the capacity was calculated using equation (1). These experimental values are
shown as circles in Figure 1.
Experimental values
Peukert relation
0.76
0.75
O
0.74
0.73
0.72
0.71
0
0.4
0.8
1.2
C-rate
Figure 1 Experimental results for capacity vs. C-rate and the
predicted results by Peukerts equation
From the data k was found to be 1.013. Figure1 compares test results with those predicted by
equation (3).
In order to evaluate the amount of charge that is contained within a battery at any given time or
its state of charge (SOC), Qmax should be known. A PHM system should be implemented that can monitor
and analyze data in order to determine Qmax. This value can be determined by performing a full discharge
and applying equation (1), however if usage requirements prevent a full discharge from being performed,
other methods of estimating Qmax are available and they are discussed in the next section. The state of
charge can then be evaluated by monitoring the current or number coulombs that enter or leave the battery
between two prescribed cut-off voltage levels. Current and voltage monitoring can be done with a small
integrated circuit, which is low volume and a relatively simple hardware requirement. This method is
typically known as coulomb counting and was demonstrated by Ng [10]. This method may be further
improved by applying Peukert’s equation to adjust the Qmax value during varying current discharges.
Cycle life considerations
Evaluating battery performance and reliability becomes increasingly complex due to the changes
in the voltage profile and Qmax with cycle life. In order to understand how these parameters change and
also to understand the level of battery degradation, state of health (SOH) should be monitored. SOH is
directly related to capacity fade which happens when Qmax decreases over repeated charge/discharge
cycles due to complex chemical side reactions as well as mechanical damage suffered over a battery’s
lifetime. SOH can be defined as:
SOH (c)
c
Qmax
Qrated
where the SOH at any cycle c is equal to the Qmax value at that cycle over Qrated which gives an
approximation of the Qmax value at the beginning of life. Capacity fade has been found to follow slow
reduction followed by a more pronounced drop. To avoid the pronounced drop in capacity, end of useful
life has been defined to occur when SOH reaches 80%. From this point a failure criteria can be drawn
such as, the battery should be considered failed when the SOH reaches 80%.
A major problem in determining SOH is finding the value of Qmax at every cycle. As we
described, this value can be discovered by performing a full discharge, but in real applications a full
discharge may not always be applied to the battery. To solve this problem, complex filtering techniques
such as extended Kalman filter [11] may be applied. However, these algorithms require physical
measurements as inputs that can then be related to Qmax. Deriving a model that can accurately predict
Qmax based on a given set of readily measured inputs is one of the most fundamental challenges in battery
health monitoring. Among some of the popular inputs to measure include, current, voltage, casing
thickness, internal resistance, and internal impedance.
When a model has been established that gives good capacity prediction results and a filtering
algorithm has been fine tuned to account for uncertainty, capacity predictions can be made. This requires
the model and the associated uncertainty to be projected into the future toward some failure threshold.
Predicting the end of remaining useful performance in an integral part of a complete PHM system because
it can help to make decisions regarding maintenance and operation. Typically, the longer a particular
battery has been operating, the more information can be gathered which will improve predictions as time
goes on.
Conclusions
Battery design and how it relates to performance and reliability was discussed. The design parameters
that influence the final capacity rating of batteries were outlined. Because battery performance is so
depend on individual design parameters, they must be properly characterized before being put into use. In
order to characterize the current output as it relates to capacity, a 5 cycle discharge test was proposed.
These results were fit to Peukert’s equation to help predict battery capacity at different discharge rates.
An overview for predicting capacity as it applies to SOC and SOH was discussed. In order for these
predictions to be useful in real life applications, predictions must take into account many environmental
and usage variables. This abstract focused on the effect of different discharge current rates on the
maximum capacity of a battery. It was found that Peukert’s law was a good model to fit the relationship
between C-rate and the observed battery capacity. This law can be applied to adjust for discharge current
rate when predicting the maximum capacity during cycling.
With the ability to predict Qmax both SOC and SOH can be estimated. A general overview on the
requirements for determining SOC and SOH for batteries was given. This included some of the hardware
and software tools necessary for making parameter measurements. This overview was based on the
assumption that an in situ determination of Qmax at every cycle could be made.
ACKNOWLEDGMENTS
The authors would like to thank the Center for Advanced Life Cycle Engineering (CALCE) at the
University of Maryland and the more than 100 companies and organizations that support its research
annually.
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