Open circuit voltage (OCV) of the battery is the difference in potential between its positive and negative electrodes. Accurate estimation of OCV during battery usage is crucial for battery management tasks such as state of charge (SOC) estimation, state of power (SOP) estimation, etc. A vast majority of the existing approaches propose to model battery SOC estimation as a nonlinear state estimation problem; these approaches use nonlinear filtering techniques such as the extended Kalman filter (EKF) or particle filter (PF) to estimate SOC. The battery parameters in the nonlinear state-space model also need to be estimated, and are most often combined as a joint estimation problem with SOC. The drawback of using nonlinear filters is that a general solution does not exist, and only sub-optimal approximations will result. Further, nonlinear state estimators also suffers from numerical instabilities in practical applications and tend to diverge over time. The unknown nature of the model parameters makes the problem worse and may fast lead to faster divergence during the estimation process. This paper presents a novel approach to recursively estimate the OCV through a linear state-space formulation. The linearity in the state-space enables the application of the optimal Kalman filter to estimate the desired state, i.e., OCV of the battery. The model parameter estimation is derived as a constrained least-squares estimation problem by making use of the Hamiltonian function. The benefit of the proposed approach is that optimal solution is achievable for this joint state and parameter estimation problem.
A battery management system (BMS) is crucial for the safe and reliable operation of a battery pack. During use, it is important to monitor the remaining charge in the battery, known as the state of charge (SOC), to preserve battery health and lifetime. However, the SOC of a battery cannot be directly measured and it is approximated by the battery fuel gauge (BFG) using several empirical approaches. The accuracy of the SOC calculated by the BFG is affected by (i) temperature (ii) charging/usage history (iii) hysteresis and relaxation effects. Evaluating the SOC values reported by a BFG remains a challenging problem due to the fact that it is not possible to know the true SOC value. Consequently, indirect measures were developed to evaluate the SOC estimates reported by a BFG. In this paper, three BFG evaluation metrics: the Coulomb counting (CC) metric, the open circuit voltage (OCV) metric and the time-to-voltage (TTV) metric are demonstrated. The present paper is focused on demonstrating the implementation details of the above three BFG evaluation metrics. The proposed metrics are modified versions of previously reported ones to make the BFG evaluation more robust. Voltage and current data generated from a battery simulator and a BFG based on the extended Kalman filter algorithms were employed to demonstrate the proposed evaluation scheme. The battery in the simulator is set to an Rint approximation of the equivalent circuit model (ECM) and the BFG is set to assume the knowledge of the ECM model parameters. Voltage and current measurements were simulated based on a noisy model with zero mean and known standard deviation. Under these assumptions, the BFG under evaluation produced less than 1% error in SOC and less than 15 minutes in TTV error. These values, produced under the known model assumption, can be taken as a benchmark for the same voltage and current measurement noise statistics.
This paper considers the measurement extraction for a point target from an optical sensor's focal plane array (FPA) with a dead zone separating neighboring pixels. Assuming that the energy density of the target deposited in the FPA conforms to a Gaussian point spread function and that the noise mean and variance in each pixel are proportional to the pixel area (i.e., according to a Poisson noise model), we derive the Cramér-Rao lower bound (CRLB) for the covariance of the estimated target location. It is observed that that there is an optimal pixel size that minimizes the CRLB for a given dead-zone width, and the maximum likelihood estimator is shown to be efficient via Monte Carlo runs for moderate-to-large signal-to-noise ratios. The test statistic for target detection is derived and it is shown to be a matched filter at the estimated location. The distributions of the test statistic under both hypotheses are derived using some approximations. The detection probability is then obtained.
This paper is the third part of a series of papers about empirical approaches to open circuit voltage (OCV) modeling of lithium-ion batteries. The first part of the series proposed models to quantify various sources of uncertainties in the OCV models; and, the second part of the series presented systematic data collection approaches to compute the uncertainties in the OCV-SOC models. This paper uses data collected from 28 OCV characterization experiments, performed according to the data collection plan presented, to compute and analyze the following three different OCV uncertainty metrics: cell-to-cell variations, cycle-rate error, and curve fitting error. From the computed metrics, it was observed that a lower C-Rate showed smaller errors in the OCV-SOC model and vice versa. The results reported in this paper establish a relationship between the C-Rate and the uncertainty of the OCV-SOC model. This research can be thus useful to battery researchers for quantifying the tradeoff between the time taken to complete the OCV characterization test and the corresponding uncertainty in the OCV-SOC modeling. Further, quantified uncertainty model parameters can be used to accurately characterize the uncertainty in various battery management functionalities, such as state of charge and state of health estimation.
Battery management systems (BMS) are important for ensuring the safety, efficiency and reliability of a battery pack. Estimating the internal equivalent circuit model (ECM) parameters of a battery, such as the internal open circuit voltage, battery resistance and relaxation parameters, is a crucial requirement in BMSs. Numerous approaches to estimating ECM parameters have been reported in the literature. However, existing approaches consider ECM identification as a joint estimation problem that estimates the state of charge together with the ECM parameters. In this paper, an approach is presented to decouple the problem into ECM identification alone. Using the proposed approach, the internal open circuit voltage and the ECM parameters can be estimated without requiring the knowledge of the state of charge of the battery. The proposed approach is applied to estimate the open circuit voltage and internal resistance of a battery.
In this paper, we present a novel SOC tracking algorithm for Li-ion batteries. The proposed approach employs a voltage drop model that avoid the need for modeling the hysteresis effect in the battery. Our proposed model results in a novel reduced order (single state) filtering for SOC tracking where no additional variables need to be tracked regardless of the level of complexity of the battery equivalent model. We identify the presence of correlated noise that has been so far ignored in the literature and use this for improved SOC tracking. The proposed approach performs within 1% or better SOC tracking accuracy based on both simulated as well as HIL evaluations.
In this paper, we consider the problem of state of charge estimation for rechargeable batteries. Coulomb counting is one of the traditional approaches to state of charge estimation and it is considered reliable as long as the battery capacity and initial state of charge are known. However, the Coulomb counting method is susceptible to errors from several sources and the extent of these errors are not studied in the literature. In this paper, we formally derive and quantify the state of charge estimation error during Coulomb counting due to the following four types of error sources: (i) current measurement error; (ii) current integration approximation error; (iii) battery capacity uncertainty; and (iv) the timing oscillator error/drift. It is shown that the resulting state of charge error can either be of the time-cumulative or of state-of-charge-proportional type. Time-cumulative errors increase with time and has the potential to completely invalidate the state of charge estimation in the long run. State-of-charge-proportional errors increase with the accumulated state of charge and reach its worst value within one charge/discharge cycle. Simulation analyses are presented to demonstrate the extent of these errors under several realistic scenarios and the paper discusses approaches to reduce the time-cumulative and state of charge-proportional errors.
In this paper, the problem of online anomaly detection in multi-attributed, asynchronous data from a large number of individual devices is considered. It has become increasingly common for many services, such as video-on-demand (VOD), to have connected customers where hundreds of millions of subscribers access a cluster of content servers for online services. It is important to monitor these transactions online, in order to ensure acceptable quality of experience to the customers as well as for detecting any abnormal or undesirable activities. Our proposed anomaly detection strategy works in two phases: First we perform intermittent anomaly detection in space, using data from the entire set of devices for a short duration in time. This phase employs principal component analysis (PCA) for data reduction and captures models of normal and abnormal features. Then, these identified models are used to monitor each subscriber's devices online in order to quickly detect any abnormalities. The proposed approach is demonstrated on Comcast's Xfinity video streaming data.
This paper presents an approach to real-time battery capacity estimation by combining the advantages of the opportunistic zero-current states in the dynamic current profile of the battery and the knowledge of the open circuit voltage (OCV)-state of charge (SOC) curve of the battery. With the knowledge of OCV parameters, the SOC can be estimated through OCV lookup using the OCV-SOC curve. The difference in SOC between two different points is the change in Coulombs normalized by the battery capacity - this relationship is exploited to estimate the battery capacity. In the capacity estimation using the OCV-SOC curve, there are two existing approaches to OCV estimation. In the first approach, the battery is completely rested and the terminal voltage is measured; in a rested battery, the terminal voltage is treated as the OCV. In the second approach, the voltage drop is computed by estimating the equivalent circuit model (ECM) parameters of the battery; the OCV is then computed by subtracting the voltage drop from the measured terminal voltage. Both of these approaches have limitations: it takes a long time to fully rest a battery and ECM parameter estimation problem suffers form non-linearities and sub-optimal solutions as a result of that. In this paper, we propose an approach to estimate the battery capacity without the wait for complete rest of the battery or for the estimation of ECM parameters. Rather than waiting for battery rests, it is proposed to make OCV measurements whenever the current through the battery is zero. It is hypothesized in this paper that, the resulting OCV error, due to both the hysteresis and relaxation effect, can be considered zero-mean when sufficient number of measurements are taken. The proposed approach, when tested using real world battery data, show significantly accurate estimation of battery capacity. Further, it is observed that the amount of rest time before taking the OCV measurement positively correlated with capacity estimation accuracy. The standard deviation of the computed capacities immediately after zero current and after one hour of rest, relative to true capacity is 0. 3Ah and 0. 2Ah respectively.
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