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Clarkson University
Experimental Characterization of Lithium Polymer Battery Charging Cycles during Bilateral
Energy Exchange in Power-Autonomous Systems
A Thesis Proposal by
Pushpak Jha
Electrical Engineering
Mentor: Dr. Kevin Fite
3/12/2010
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Abstract:
The goal of this research is to investigate lithium polymer batteries to better understand their capabilities, characteristics and limits. Lithium polymer batteries are widely used, especially in the hobby industry, but there is not much literature available on their performance. Of particular importance is the life time of the battery, battery capacity fade and the efficiency of recharging. Specifically we will investigate how efficiently the battery recharges during non-constant current and voltage charging conditions. In an experimental setup the batteries will be used to drive a DC motor which will spin a rotational inertia. Using computer control the system will be able to convert electrical energy into mechanical energy by discharging the battery to drive the motor. It will also be possible to convert mechanical energy back into electrical energy using the motor as a generator which will then recharge the battery. It should be noted that this research is being conducted as part of a larger project to design a powered prosthetic leg for transfemoral amputees. Lithium polymer batteries are being used as the power source for this prosthesis, and this proposal will help investigate the feasibility of energy regeneration during normal operation of the prosthesis.
Introduction:
In the last few decades many new electronic devices have been made which all rely on battery power. As a result battery technology and research have increased in an attempt to design better batteries and to better understand how to use batteries efficiently. Lithium polymer batteries are used in many applications because they are rechargeable and have high energy densities; however there are also several drawbacks. As with most rechargeable batteries, the battery capacity decreases during the life of the battery. This imposes a life time after which using the same battery is not practical because the capacity has been reduced too much. This proposal will outline a method, using an experimental setup, to characterize battery capacity fade and determine the expected life time of lithium polymer batteries.
Another major issue with batteries involves recharging the battery. Generally when a battery is recharged a constant current and constant voltage is applied which reverses the chemical reactions internally and creates stored potential energy [1]. However, in the context of a powered prosthetic limb, a portion of the recharging will occur during limb operation as the limb dissipates mechanical power.
This results in periodic and non-constant charging/discharging cycles at the battery terminals. There will be short electrical power spikes created by the actuator in the prosthetic knee, and this is the power that is returned to the battery. Unfortunately, since this energy comes in short bursts there won’t be a constant current and constant voltage so it’s unclear how much of this energy will actually by recovered by the battery. The experimental setup proposed will also be used to test how efficiently non-constant conditions recharge the lithium polymer battery. The setup will be used to characterize the efficiency of battery operation when subjected to short duration periodic power dissipation and then recharging, as it would experience during normal operation of the prosthesis.
The experimental setup will consist of a lithium polymer battery which will power a DC motor which will be used to spin a steel disk up to some speed. After steady state speed has been reached, the motor will be actively controlled for power dissipation. The disk will then begin to slow down, and in the process the DC motor will act as a generator which will recharge the battery. Since the losses in this system will be fairly small, we expect the amount of energy to be recovered from the disk slowing down to be similar to the energy needed to get it up to steady state speed initially.
The proposed research has implications for a wide range of applications even beyond the powered prosthesis. This research will help better characterize lithium polymer batteries for use in any application for which bilateral energy exchange between the actuator and power source occurs. It will provide critical information and data about capacity fade, battery lifetime and recharging capabilities.
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Background:
There has been a significant amount of research done on batteries. More specifically, battery capacity fade is a well known effect and has been researched for lithium ion batteries extensively [2-5].
Batteries tend to lose capacity due to unwanted chemical side reactions occurring inside the battery [2].
These side reactions increase the cell resistance over time and reduce the amount of lithium ions available to store potential energy. Work done by D. Zhang showed that capacity decreased by 0.04% per cycle [5]. Battery capacity fade varies depending on battery type and specific battery chemistry.
There is little information available about lithium polymer batteries, which are the type used in the powered prosthesis. It is therefore of interest to better characterize battery capacity fade of lithium polymer batteries.
As aforementioned, this project is part of a larger effort to design a powered prosthetic leg for transfemoral amputees. The power for this prosthetic leg comes from a lithium-polymer battery pack.
This electrical energy is used to drive a DC motor that is housed in the knee joint of the prosthesis. This knee joint also acts as a passive damping system when energy needs to be dissipated as part of normal walking. This prosthesis will recover part of the energy dissipated as electrical energy using the DC motor as a generator [6-7]. The amount of energy dissipated as negative work is significant, as shown in
Figure 1 below. Especially during stair descent there is a large amount of negative work done which could be converted into electrical energy for recharging the battery.
Figure 1: Averaged knee power of ten subjects at low(a), normal(b), and high(c) slopes [8].
Battery life is also affected by the depth of discharge [9]. The depth of discharge (DoD) is a percentage which represents what percent of the total energy in a battery has been consumed. In general the higher the DoD the shorter the battery life [9]. For most batteries the optimal DoD during repeated cycles is between 20-40% and a repeated DoD of 80% results in a 5 times shorter battery life. In the use of the powered prosthesis the DoD may be below 0.1% and there will be a discharge/charge cycle during every step taken. It is unclear how such low DoDs and high numbers of cycles affect battery life.
Another important issue is the efficiency of the battery in storing the regenerated electrical energy. Rechargeable batteries are usually charged by applying a constant current and constant voltage
[10]. In the powered prosthesis, the regenerated energy will not be constant. Since every step we take is slightly different, and since every locomotive function is different, the amount of power recovered per step will never be the same. More importantly, the electrical energy that is generated will not be constant; it will be a function of the actuator’s operating conditions. Depending upon limb requirements,
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the motor may generate large charging currents that are undesirable from the standpoint of battery life
[10]. It is also not clear how much of this generated energy will recharge the battery. Furthermore, the efficiency of electrical generation also depends upon the lower-level approach for motor control during mechanical power dissipation [11].
Capacitors are being considered as a possible method of auxiliary energy storage. Capacitors have several advantages including short charge/discharge times, high cycle life and high efficiency [12].
They are also unaffected by the depth of discharge and capacitors can be charged using non-constant current easily and efficiently. The main disadvantage is capacitors have a much lower energy density compared to batteries. This means one would need a larger, heavier and possibly more expensive capacitor to store the same amount of energy as a lithium polymer battery. There is also the possibility of using a battery and capacitor together to create an energy storage system that would work better than either by itself [12]. This system could store regenerated energy more efficiently and it would improve battery life by lowering the overall impedance of the system and letting the capacitor handle components of the load that exhibit fast transients.
Research Methodology:
Subsection 1: Objectives
There are several main objectives we are trying to accomplish with this proposed research. First, lithium polymer battery properties need to be better characterized and understood. These characteristics include battery performance, battery life, max number of cycles till the battery is unusable and capacity fade. Specifically, we are interested in the case where the batteries are discharged to a low depth of discharge (DoD < 0.1%) and then recharged. Most batteries life times are between 400-1000 cycles if the DoD is between 20%-40%. In our case, each “cycle” will be one stride of the person wearing the prosthesis. Within one stride the battery will be discharged to power the motor and then recharged when the motor acts as a passive damper. As a result the batteries will have to last a very high number of cycles, upwards of 500,000, but a very low DoD. One main objective is learning how a low DoD and a high number of cycles affect battery performance and battery life.
Another objective is to learn how efficiently lithium polymer batteries recharge under periodic but non-constant charging conditions. The passive regenerative damping system will produce spikes of energy during the regenerative portions of the stride. Since batteries are normally recharged with constant current and voltage, it’s unclear how efficiently these spikes of energy can be stored within the battery.
The last objective is to determine if using capacitors can improve the systems efficiency. Using capacitors by themselves or with a battery has potential to increase battery life and energy storage efficiency. This will be explored in detail especially if either of the other two objectives cannot be adequately resolved or if they result in conclusions that show lithium polymer batteries perform poorly under such charging conditions.
Subsection 2: Experimental Setup
A proposed experimental setup has been designed to accomplish the objectives. The setup consists of a lithium polymer battery pack (Thunder Power model TP2000-35PL) connected to a PWM servo amplifier (Advanced Motion Controls model Z12A8) and a brushed DC motor (Maxon model
Re40), which are the same type used in the powered prosthesis. The motor will be connected, possibly via a belt drive, to a steel disk. The steel disk will act as a rotational load inertia which will be sped up by the motor initially and when the motor is switched to a damping mode, the disk will begin to decelerate and will in turn drive the motor producing electricity. In this way this setup can be used to simulate both the battery being discharged to drive a load and recharged by electrical power generated by slowing the rotational load. By making simple changes to the setup it will be possible to simulate many different conditions of interest.
The system will be controlled using a real-time MATLAB/Simulink control scheme. This will allow the process of data gathering to be automated and precise. There will be a virtual control panel
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which will turn the system on and off and gather data such as load speed, motor speed, motor torque, and the currents and voltages on the battery and motor. Using this data we will be able to determine the capacity fade of the battery over repeated trials, and the efficiency of the battery at storing non-constant low magnitude electrical power. The system can also be easily modified to include a capacitor/battery system to do further research.
Subsection 3: Preliminary Research
In preparation for the oncoming research some preliminary work has been done. This work involves literature reviews to gain a better understanding of prior work in the field. A model of the system has been created in Simulink and MATLAB code has been written to do several basic modeling calculations.
The system model consists only of the DC motor and load inertia. The modeling has been done in order to design and build an efficient and operational experimental setup. The Simulink environment allows us to modify many parameters, such as applied voltage or current to the motor and the size of the load inertia, which helps us design an optimal system. The system is modeled by two differential equations which are shown below as eqns. 1 and 2 and a relationship shown in eqn. 3. Alternatively if we include a belt drive in the system model we use eqn. 4 instead of eqn. 2. If the belt drive is included, the motor velocity is no longer equal to the load velocity but they are related as shown in eqn. 5.
[1]
[2]
[3]
[4]
[5]
Parameters Description
Motor inductance
Motor terminal resistance
Applied voltage
Current
Motor torque constant
Rotational velocity
Mechanical time constant
Gear ratio
Radius of gear at the motor
Motor inertia
Motor friction
Radius of gear at the load
Load inertia
Table 1: Explanation of parameters
The Simulink modeling has given us guidelines on building the experimental setup. Motor data supplied by the manufacturer of the motor we are using was used in the model. The other parameters were varied to determine the best possible setup. The load in these simulations is based on a steel disk we currently have, which has an inertia of J load
=
0.093 kg∙m 2
. The servo amp will be used to control the current and
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it will be fixed at i = 3 A. Using these conditions along with the motor data supplied, it has been determined that using a gear ratio of N = 0.8 gives us one possible operating condition. With this operating condition the load will take about 90 seconds to achieve steady state speed and will store about 85 J of rotational potential energy. A second operating condition where N = 0.55 will take about
50 seconds to get up to speed and will store about 40 J of energy. Further work will have to be done to determine which operating condition is best. It might also be possible to build a setup where changing the gear ratio is simple and this would be ideal.
In conclusion, the proposed research will expand current knowledge about lithium polymer battery characteristics. It will explore specific topics about batteries which are either undocumented or unknown. After reading previous literature and doing some preliminary work an experimental setup has been designed. By gathering and analyzing the data from the proposed setup we will be able to learn more about lithium polymer batteries. While this research is being done as part of a larger effort, it will also fill a gap in general battery knowledge.
Timeline:
The expected timeline for this project is shown in Figure 2 below.
Duration in months
Item
1
Description
Literature review and preliminary work
1 2 3 4 5 6 7 8
2 Building the experimental setup
3 Data gathering
4 Data analysis
5 Writing the thesis
Figure 2: Expected timeline
References:
1) Cope, Richard C. "The Art of Battery Charging." IEEE (1999): 233-35.
2) Arorat, Pankaj, and Ralph E. White. "Capacity Fade Mechanisms and Side Reactions in Lithium-
Ion Batteries." Journal of The Electrochemical Society (1998): 3647-667.
3) Aurbach, Doron, Boris Markovsky, and Alexander Rodkin. "An Analysis of Rechargeable
Lithium-ion Batteries after Prolonged Cycling." Electrochimica Acta (2002): 1-13
4) Liaw, Bor Yann, and Rudolph Jungst. "Modeling Capacity Fade in Lithium-Ion Cells." Journal of Power Sources (2005): 157-61.
5) Zhang, D., and B.S. Haran. "Studies on Capacity Fade of Lithium-ion Batteries." Journal of
Power Sources (2000): 122-29.
6) Andrysek, Jan, Tony Liang, and Bryan Steinnagel. "Evaluation of a Prosthetic Swing-Phase
Controller With Electrical Power Generation." IEEE Transactions on Neural Systems and
Rehabilitation Engineering (2009): 390-96.
7) Andrysek, Jan, and Gilbert Chau. "Electromechanical Swing-Phase-Controlled Prosthetic Knee
Joint for Conversion of Physiological Energy to Electrical Energy: Feasibility Study." IEEE
Transactions on Biomedical Engineering (2007): 2276-283.
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8) Riener, R., and M. Rabuffetti. "JOINT POWERS IN STAIR CLIMBING AT DIFFERENT
SLOPES." Proc. of The First Joint BMESEMBS Conference Serving Humanity, Georgia,
Atlanta. 13-16.
9) Thaller, Lawrence H. "Expected Cycle Life Vs. Depth of Discharge Relationships of Well-
Behaved Single Cells and Cell Strings." Journal of The Electrochemical Society (1983): 986-90.
10) Seth, B., and W.C. Flowers. "Generalized Actuator Concept for the Study of the Efficiency of
Energetic Systems." Journal of Dynamic Systems, Measurement, and Control (1990): 233-38.
11) Tucker, Michael R., and Kevin B. Fite. "Mechanical Damping with Electrical Regeneration for a
Powered Transfemoral Prosthesis." (2010).
12) Schneuwly, Adrian, Gianni Sartorelli, Juergen Auer, and Bobby Maher. Ultracapacitor
Applications in the Power Electronic World . Publication. Maxwell Technologies.
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