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Charge-state model for lead/acid batteries proposed as part of effort to make equivalent of fuel gage for battery-powered vehicles. Models based on equations that approximate observable characteristics of battery electrochemistry. Uses linear equations, easier to simulate on computer, and gives smooth transitions between charge, discharge, and recuperation.
The purpose of this document is to demonstrate the use of the Extended Kalman Filter as a tool for battery state estimation and the estimation of battery state of charge. The mathematical details based on the equivalent circuit model are presented followed by an electrochemical engineering model. A simplified first-order model is used to demonstrate the procedure followed by second and third-order models. Next a simplified electrochemistry model is presented along with observer development. State observability is calculated for the simpler equivalent circuit models and the simplified electrochemistry model. An outline of the battery model parameter identification method is presented, and model performance based on experimental and flight data is demonstrated.
This paper addresses the problem of building trust in online predictions of the remaining available flying time for two different electric Unmanned Aerial Vehicles (eUAVs) powered by lithium-ion-polymer batteries. Flight tests for various automation research missions for the two vehicles were monitored using two on-board battery health management applications to make predictions of the remaining flying time (RFT) for each eUAV and to predict the state of the battery. Playback of the voltage, current and temperature profiles of the battery discharge were used to assess the accuracy of the estimation of the voltage and the charge states of the models as well as the estimate of the RFT. The reference ground truth values were the observed landing time and the measured battery pack resting pack voltage 20 minutes after the flight. The predicted RFT, state of charge (SoC), and state of energy (SoE) were compared with the observed results. Noise values of one standard deviation from the mean values of the internal charge states of the battery model during a reference run were used to vary the states during simulation. One application used an equivalent circuit model of the electrical dynamics of the battery pack, and the other application used a reduced-order electrochemistry model. The variation of the model state components was compared to the variation in the estimate of the RFT and the variation in the SoE to estimate a confidence factor. Variation in the estimates caused by factors affecting the off-line laboratory parameter identification experiments is considered. Variation in the estimates due to environmental factors are discussed.
Growing interest in design and optimization of electrified aircraft propulsion concepts prompts the need for accurate, flexible, and efficient methods to model battery systems. Presented in this paper are three battery modeling methods that have been used at NASA’s Glenn Research Center, each representing different mathematical or electrical approaches. Thévenin equivalent circuit, normalization, and curve-fitting methods are compared against battery cell test data for the X-57 Maxwell electric aircraft technology demonstrator. The methods are then applied in a simple multidisciplinary optimization context using NASA’s Six-Passenger Electric Quadrotor concept to determine their applicability and performance. The normalization method achieves the highest accuracy for steady and unsteady discharge rates with a voltage mean error percentage of 0.423% and 1.186%, respectively. Optimal quadrotor mission range between the models varies up to 0.5 nmi, identifying current battery modeling methods as a potentially significant contributor to mission analysis error. A set of relevant tools and techniques for conceptual battery modeling are identified in this paper, with conclusions made on the utility of each modeling approach for various design challenges.
Recent improvements in energy densities of batteries open the possibility of using electric rather that hydraulic actuators in space vehicle systems. However, the systems usually require short-duration, high-power pulses. This power profile requires the battery system to be sized to meet the power requirements rather than stored energy requirements, often resulting in a large and inefficient energy storage system. Similar transient power applications have used a combination of two or more disparate energy storage technologies. For instance, placing a capacitor and a battery side-by-side combines the high energy density of a battery with the high power performance of a capacitor and thus can create a lighter and more compact system. A parametric study was performed to identify favorable scenarios for using capacitors. System designs were then carried out using equivalent circuit models developed for five commercial electrochemical capacitor products. Capacitors were sized to satisfy peak power levels and consequently "leveled" the power requirement of the battery, which can then be sized to meet system energy requirements. Simulation results clearly differentiate the performance offered by available capacitor products for the space vehicle applications.
A previous electrified aircraft propulsion (EAP) design space exploration study was continued to investigate the impact of mission constraints, further explore the design space of different sized aircraft, and improve the modeling process. Three aircraft were investigated, 18- and 48-passenger turboprops, and a 78-passenger turbofan. Baseline aircraft models were inherited from the earlier study and were hybridized by applying EAP technologies. A parametric study varying motor power and battery specific energy was conducted. For the 78-passenger turbofan, design range was also introduced as a parametric parameter. Key metrics for the study included equivalent lifecycle CO2 emissions and direct operating cost plus interest. Both turboprop aircraft demonstrated significant potential savings in block fuel consumption and CO2 emissions, but at increased operating costs compared to their baseline models. As the 78-passenger turbofan had shown no improvements in any metrics under reasonable technology assumptions, design range was shortened in an attempt to obtain performance benefits. When designed for a shorter range, the 78-passenger EAP vehicle showed potential improvements in block fuel when compared to a baseline with a similarly shortened design range, but not in any other metrics. Operating cost reductions were not achieved for any aircraft, but several designs came close to breaking even with their baselines. Smaller, shorter range aircraft and turboprops demonstrated larger performance benefits and smaller operating cost penalties, but a simple trade of electric energy storage in batteries for fuel is generally insufficient to produce a viable aircraft concept.
AC impedance spectra of porous nickel battery electrodes were recorded periodically during charge/discharge cycling in concentrated KOH solution at various temperatures. A transmission line model (TLM) was adopted to represent the impedance of the porous electrodes, and various model parameters were adjusted in a curve fitting routine to reproduce the experimental impedances. Degradation processes were deduced from changes in model parameters with electrode cycling time. In developing the TLM, impedance spectra of planar (nonporous) electrodes were used to represent the pore wall and backing plate interfacial impedances. These data were measured over a range of potentials and temperatures, and an equivalent circuit model was adopted to represent the planar electrode data. Cyclic voltammetry was used to study the characteristics of the oxygen evolution reaction on planar nickel electrodes during charging, since oxygen evolution can affect battery electrode charging efficiency and ultimately electrode cycle life if the overpotential for oxygen evolution is sufficiently low.
Electrochemical impedance spectra of rolled and bonded and sintered porous nickel battery electrodes were recorded periodically during charge/discharge cycling in concentrated KOH solution at various temperatures. A transmission line model (TLM) was adopted to represent the impedance of the porous electrodes, and various model parameters were adjusted in a curve fitting routine to reproduce the experimental impedances. Degradation processes for rolled and bonded electrodes were deduced from changes in model parameters with electrode cycling time. In developing the TLM, impedance spectra of planar (non-porous) electrodes were used to represent the pore wall and backing plate interfacial impedances. These data were measured over a range of potentials and temperatures, and an equivalent circuit model was adopted to represent the planar electrode data. Cyclic voltammetry was used to study the characteristics of the oxygen evolution reaction on planar nickel electrodes during charging, since oxygen evolution can affect battery electrode charging efficiency and ultimately electrode cycle life if the overpotential for oxygen evolution is sufficiently low. Transmission line modeling results suggest that porous rolled and bonded nickel electrodes undergo restructuring during charge/discharge cycling prior to failure.
For any battery-powered vehicles (be it unmanned aerial vehicles, small passenger aircraft, or assets in exoplanetary operations) to operate at maximum efficiency and reliability, it is critical to monitor battery health as well performance and to predict end of discharge (EOD) and end of useful life (EOL). To fulfil these needs, it is important to capture the battery's inherent characteristics as well as operational knowledge in the form of models that can be used by monitoring, diagnostic, and prognostic algorithms. Several battery modeling methodologies have been developed in last few years as the understanding of underlying electrochemical mechanics has been advancing. The models can generally be classified as empirical models, electrochemical engineering models, multi-physics models, and molecular/atomist. Empirical models are based on fitting certain functions to past experimental data, without making use of any physicochemical principles. Electrical circuit equivalent models are an example of such empirical models. Electrochemical engineering models are typically continuum models that include electrochemical kinetics and transport phenomena. Each model has its advantages and disadvantages. The former type of model has the advantage of being computationally efficient, but has limited accuracy and robustness, due to the approximations used in developed model, and as a result of such approximations, cannot represent aging well. The latter type of model has the advantage of being very accurate, but is often computationally inefficient, having to solve complex sets of partial differential equations, and thus not suited well for online prognostic applications. In addition both multi-physics and atomist models are computationally expensive hence are even less suited to online application An electrochemistry-based model of Li-ion batteries has been developed, that captures crucial electrochemical processes, captures effects of aging, is computationally efficient, and is of suitable accuracy for reliable EOD prediction in a variety of operational profiles. The model can be considered an electrochemical engineering model, but unlike most such models found in the literature, certain approximations are done that allow to retain computational efficiency for online implementation of the model. Although the focus here is on Li-ion batteries, the model is quite general and can be applied to different chemistries through a change of model parameter values. Progress on model development, providing model validation results and EOD prediction results is being presented.
Electrical impedance spectroscopy was used to investigate the behavior of porous zinc, silver, cadmium, and nickel electrodes. State of charge could be correlated with impedance data for all but the nickel electrodes. State of health was correlated with impedance data for two AgZn cells, one apparently good and the other bad. The impedance data was fit to equivalent circuit models.
Work aimed at modeling the charge voltage and current characteristics of nickel-cadmium cells subject to taper charge is presented. Work reported at previous NASA Battery Workshops has shown that the voltage of cells subject to constant current charge and discharge can be modeled very accurately with the equation: voltage = A + (B/(C-X)) + De to the -Ex where A, B, D, and E are fit parameters and x is amp-hr of charge removed during discharge or returned during charge. In a constant current regime, x is also equivalent to time on charge or discharge.
The feasibility of electrochemical impedance spectroscopy as a method for analyzing battery state of health and state of charge was investigated. Porous silver, zinc, nickel, and cadmium electrodes as well as silver/zinc cells were studied. State of charge could be correlated with impedance data for all but the nickel electrodes. State of health was correlated with impedance data for two silver/zinc cells, one apparently good and the other dead. The experimental data were fit to equivalent circuit models.
Rotorcraft design has always been a challenging tradeoff among overall size, capabilities, complexity, and other factors based on available technology and customer requirements. Advancements in propulsion, energy systems and other technologies have enabled new vehicles and missions; complementary advances in analysis methods and tools enable exploration of these enhanced vehicles and the evolving mission design space. A system study was performed to better understand the interdependency between vehicle design and propulsion system capabilities versus hover / loiter requirements and range capability. Three representative vertical lift vehicles were developed to explore the tradeoff in capability between hover efficiency versus range and endurance capability. The vehicles were a single-main rotor helicopter, a tilt rotor, and a vertical take-off and landing (VTOL) aircraft. Vehicle capability was limited to two or three people (including pilot or crew) and maximum range within one hour of flight (100-200 miles, depending on vehicle). Two types of propulsion and energy storage systems were used in this study. First was traditional hydrocarbon-fueled cycles (such as Otto, diesel or gas turbine cycles). Second was an all-electric system using electric motors, power management and distribution, assuming batteries for energy storage, with the possibility of hydrocarbon-fueled range extenders. The high power requirements for hover significantly reduced mission radius capability. Loiter was less power intensive, resulting in about 1/2 the equivalent mission radius penalty. With so many design variables, the VTOL aircraft has the potential to perform well for a variety of missions. This vehicle is a good candidate for additional study; component model development is also required to adequately assess performance over the design space of interest.
Rotorcraft design has always been a challenging tradeoff among overall size, capabilities, complexity, and other factors based on available technology and customer requirements. Advancements in propulsion, energy systems and other technologies have enabled new vehicles and missions; complementary advances in analysis methods and tools enable exploration of these enhanced vehicles and the evolving mission design space. A system study was performed to better understand the interdependency between vehicle design and propulsion system capabilities versus hover loiter requirements and range capability. Three representative vertical lift vehicles were developed to explore the tradeoff in capability between hover efficiency versus range and endurance capability. The vehicles were a single-main rotor helicopter, a tilt rotor, and a vertical take-off and landing (VTOL) aircraft. Vehicle capability was limited to two or three people (including pilot or crew) and maximum range within one hour of flight (100-200 miles, depending on vehicle). Two types of propulsion and energy storage systems were used in this study. First was traditional hydrocarbon-fueled cycles (such as Otto, diesel or gas turbine cycles). Second was an all-electric system using electric motors, power management and distribution, assuming batteries for energy storage, with the possibility of hydrocarbon-fueled range extenders. The high power requirements for hover significantly reduced mission radius capability. Loiter was less power intensive, resulting in about 12 the equivalent mission radius penalty. With so many design variables, the VTOL aircraft has the potential to perform well for a variety of missions. This vehicle is a good candidate for additional study; component model development is also required to adequately assess performance over the design space of interest.
A Lithium-Ion Cell Low-Earth-Orbit Verification Test Program is being conducted by NASA Glenn Research Center to assess the performance of lithium-ion (Li-ion) cells over a wide range of low-Earth-orbit (LEO) conditions. The data generated will be used to build an empirical model for Li-ion batteries. The goal of the modeling will be to develop a tool to predict the performance and cycle life of Li-ion batteries operating at a specified set of mission conditions. Using this tool, mission planners will be able to design operation points of the battery system while factoring in mission requirements and the expected life and performance of the batteries. Test conditions for the program were selected via a statistical design of experiments to span a range of feasible operational conditions for LEO aerospace applications. The variables under evaluation are temperature, depth-of-discharge (DOD), and end-of-charge voltage (EOCV). The baseline matrix was formed by generating combinations from a set of three values for each variable. Temperature values are 10 C, 20 C and 30 C. Depth-of-discharge values are 20%, 30% and 40%. EOCV values are 3.85 V, 3.95 V, and 4.05 V. Test conditions for individual cells may vary slightly from the baseline test matrix depending upon the cell manufacturer s recommended operating conditions. Cells from each vendor are being evaluated at each of ten sets of test conditions. Cells from four cell manufacturers are undergoing life cycle tests. Life cycling on the first sets of cells began in September 2004. These cells consist of Saft 40 ampere-hour (Ah) cells and Lith ion 30 Ah cells. These cells have achieved over 10,000 cycles each, equivalent to about 20 months in LEO. In the past year, the test program has expanded to include the evaluation of Mine Safety Appliances (MSA) 50 Ah cells and ABSL battery modules. The MSA cells will begin life cycling in October 2006. The ABSL battery modules consist of commercial Sony hard carbon 18650 lithium-ion cells configured in series and parallel combinations to create nominal 14.4 volt, 3 Ah packs (4s-2p). These modules have accumulated approximately 3000 cycles. Results on the performance of the cells and modules will be presented in this paper. The life prediction and performance model for Li-ion cells in LEO will be built by analyzing the data statistically and performing regression analysis. Cells are being cycled to failure so that differences in performance trends that occur at different stages in the life of the cell can be observed and accurately modeled. Cell testing is being performed at the Naval Surface Warfare Center in Crane, IN.
A work envelope has been defined for weightless Extravehicular Activity (EVA) based on the Space Shuttle Extravehicular Mobility Unit (EMU), but there is no equivalent for planetary operations. The weightless work envelope is essential for planning all EVA tasks because it determines the location of removable parts, making sure they are within reach and visibility of the suited crew member. In addition, using the envelope positions the structural hard points for foot restraints that allow placing both hands on the job and provides a load path for reacting forces. EVA operations are always constrained by time. Tasks are carefully planned to ensure the crew has enough breathing oxygen, cooling water, and battery power. Planning first involves computers using a virtual work envelope to model tasks, next suited crew members in a simulated environment refine the tasks. For weightless operations, this process is well developed, but planetary EVA is different and no work envelope has been defined. The primary difference between weightless and planetary work envelopes is gravity. It influences anthropometry, horizontal and vertical mobility, and reaction load paths and introduces effort into doing "overhead" work. Additionally, the use of spacesuits other than the EMU, and their impacts on range of motion, must be taken into account. This paper presents the analysis leading to a concept for a planetary EVA work envelope with emphasis on lunar operations. There is some urgency in creating this concept because NASA has begun building and testing development hardware for the lunar surface, including rovers, habitats and cargo off-loading equipment. Just as with microgravity operations, a lunar EVA work envelope is needed to guide designers in the formative stages of the program with the objective of avoiding difficult and costly rework.
Modern medicine is undergoing a revolution in the application of new sensor capabilities for aiding in diagnosis of specific conditions and monitoring a variety of informative vital signs. In the past, many of the measurements were limited by what could be accomplished externally. A shift toward in-vivo monitoring for both diagnostic and therapeutic sensing and actuation [1] has created a need for low power electronics, high energy density batteries and methods to successfully power devices embedded in the body. For a review of the field and sensing capabilities see [2]. Recent studies suggest that charging with ultrasound is more efficient at longer transmission distance (> 10cm) than inductive charging [3]. In this manuscript, we discuss the modeling and experimentation that we have accomplished and demonstrate in ultrasonic charging of sensors having the form and fit of in-vivo sensors. The task goal has been to use piezoelectric transducers for wireless communication and powering of sensors internal to the human body with a goal to transmit power levels of 100 W a receiver with receiving area of 3x3 mm2 over a distance of 16 cm equivalent to human body interior. The results suggest that we can transmit power levels that exceed this baseline requirement.
The Radiation and Technology Demonstration (RTD) Mission is under joint study by three NASA Centers: the NASA Johnson Space Center, the NASA Goddard Space Flight Center, and the NASA Glenn Research Center at Lewis Field. This Earth-orbiting mission, which may launch on a space shuttle in the first half of the next decade, has the primary objective of demonstrating high-power electric thruster technologies. Secondary objectives include better characterization of Earth's Van Allen trapped-radiation belts, measurement of the effectiveness of the radiation shielding for human protection, measurement of radiation effects on advanced solar cells, and demonstration of radiation-tolerant microelectronics. During the mission, which may continue up to 1 year, the 2000-kg RTD spacecraft will first spiral outward from the shuttle-deployed, medium-inclination, low Earth orbit. By the phased operation of a 10-kW Hall thruster and a 10-kW Variable Specific Impulse Magneto-Plasma Rocket, the RTD spacecraft will reach a low-inclination Earth orbit with a radius greater than five Earth radii. This will be followed by an inward spiraling orbit phase when the spacecraft deploys 8 to 12 microsatellites to map the Van Allen belts. The mission will conclude in low Earth orbit with the possible retrieval of the spacecraft by the space shuttle. A conceptual RTD spacecraft design showing two photovoltaic (PV) array wings, the Hall thruster with propellant tanks, and stowed microsatellites is presented. Early power system studies assessed five different PV array design options coupled with a 120-Vdc power management and distribution system (PMAD) and secondary lithium battery energy storage. Array options include (1) state-of-the-art 10-percent efficient three-junction amorphous SiGe thin-film cells on thin polymer panels deployed with an inflatable (or articulated) truss, (2) SCARLET array panels, (3) commercial state-of-the-art, planar PV array rigid panels with 25-percent efficient, three-junction GaInP2/GaAs/Ge solar cells, (4) rigid panels with 25-percent efficient, three-junction GaInP2/GaAs/Ge solar cells, in a 2 -concentrator trough configuration, and (5) thin polymer panels with 25-percent efficient, three-junction GaInP2/GaAs/Ge solar cells deployed with an inflatable (or articulated) truss. To assess the relative merits of these PV array design options, the study group developed a dedicated Fortran code to predict power system performance and estimate system mass. This code also modeled Earth orbital environments important for accurately predicting PV array performance. The most important environmental effect, solar cell radiation degradation, was calculated from electron-proton fluence input from the industry standard AE8/AP8 trapped radiation models and the concept of damage equivalence. Power systems were sized to provide 10 kW of thruster power and approximately 1 kW of spacecraft power at end of life. Of the five PV array design options, the option 1 (thin-film cells) power system was the most massive 590 kg, whereas the option 4 (trough concentrator) power system was the lightest 260 kg. Arguably, the lowest cost would come from the option 3 (commercial array panels) power system with an acceptable, albeit greater, system mass of 320 kg. Predicted power system performance during the spiral-out mission phase is shown the preceding graph for the option 5 (flexible-panel) array. From the results, the radiation-induced power loss over time is evident as the spacecraft slowly spirals outward through the trapped proton belt. The importance of the spiral trip time is also evident in the two curves representing 74-day and 182-day spiral-out periods. The longer spiral time introduces a beginning-of-life power oversizing penalty greater than 1 kW. Future studies will analyze power system performance and mass with a 50-Vdc power management and distribution architecture favorable to the VASIMR thruster and longer missions.