Shankar Mohan

The estimation of temperature distribution in cylindrical battery cells under unknown cooling conditions

The estimation of temperature inside a battery cell requires accurate information about the cooling conditions even when the battery surface temperature is measured. This paper presents a model-based approach for estimating temperature distribution inside a cylindrical battery under unknown convective cooling conditions. A reduced-order thermal model using a polynomial approximation of the temperature profile inside the battery is used. A dual Kalman filter (DKF), a combination of a Kalman filter and an extended Kalman filter, is then applied for the identification of the convection coefficient and the estimation of the battery core temperature. The thermal properties are modeled by volume averaged lumped-values under the assumption of a homogeneous and isotropic volume. The model is parameterized and validated using experimental data from a 2.3 Ah 26650 lithium-iron-phosphate battery cell with a forced-air convective cooling during hybrid electric vehicle drive cycles. Experimental results show that the proposed DKF-based estimation method can provide an accurate prediction of the core temperature under unknown cooling conditions by measuring battery current and voltage along with surface and ambient temperatures.

Maximum Power Estimation of Lithium-Ion Batteries Accounting for Thermal and Electrical Constraints

Enforcement of constraints on the maximum deliverable power is essential to protect lithium-ion batteries from over-charge/discharge and overheating. This paper develops an algorithm to address the often overlooked temperature constraint in determining the power capability of battery systems. A prior knowledge of power capability provides dynamic constraints on currents and affords an additional control authority on the temperature of batteries. Power capability is estimated using a lumped electro-thermal model for cylindrical cells that has been validated over a wide range of operating conditions. The time scale separation between electrical and thermal systems is exploited in addressing the temperature constraint independent of voltage and state-of-charge (SOC) limits. Limiting currents and hence power capability are determined by a model-inversion technique, termed Algebraic Propagation (AP). Simulations are performed using realistic depleting currents to demonstrate the effectiveness of the proposed method.Copyright

Estimating the Power Capability of Li-ion Batteries Using Informationally Partitioned Estimators

Enforcing constraints on the maximum deliverable power is essential to protect lithium-ion batteries and to maximize resource utilization. This paper describes an algorithm to address the estimation of power capability of battery systems accounting for thermal and electrical constraints. The algorithm is based on model inversion to compute the limiting currents and, hence, power capability. The adequacy of model inversion significantly depends on the accuracy of model states and parameters. Herein, these are estimated by designing cascading estimators whose structure is determined by quantifying the relative estimability of states and parameters. The parameterized battery model and the estimation algorithms are integrated with a power management system in a model of a series hybrid electric vehicle to demonstrate their effectiveness.

Convex computation of the reachable set for hybrid systems with parametric uncertainty

To verify the correct operation of systems, engineers need to determine the set of configurations of a dynamical model that are able to safely reach a specified configuration under a control law. Unfortunately, constructing models for systems interacting in highly dynamic environments is difficult. This paper addresses this challenge by presenting a convex optimization method to efficiently compute the set of configurations of a polynomial hybrid dynamical system that are able to safely reach a user defined target set despite parametric uncertainty in the model. This class of models describes, for example, legged robots moving over uncertain terrains. The presented approach utilizes the notion of occupation measures to describe the evolution of trajectories of a nonlinear hybrid dynamical system with parametric uncertainty as a linear equation over measures whose supports coincide with the trajectories under investigation. This linear equation with user defined support constraints is approximated with vanishing conservatism using a hierarchy of semidefinite programs each of which is proven to compute an outer approximation to the set of initial conditions that can reach the user defined target set safely in spite of uncertainty. The efficacy of this method is illustrated on a pair of systems with parametric uncertainty.

Optimal power management for a series hybrid electric vehicle cognizant of battery mechanical effects

This paper presents an optimal power management strategy for a series hybrid electric vehicle (SHEV) with the consideration of battery bulk mechanical stress. The relation between mechanical stress and state-of-charge (SOC) is characterized first. Then, this relation is used to penalize the battery usage leading to capacity fade due to particle fracture in the negative electrode. The optimal power management strategy is found using Dynamic Programming (DP) not only for maximizing fuel economy but also for minimizing the battery cumulative bulk mechanical stress. DP results suggest that battery SOC needs to be regulated around a lower value for prolonged battery life. Moreover, it is found that the cumulative bulk mechanical stress can be significantly reduced at a small expense of fuel economy.

Energy-Conscious Warm-Up of Li-Ion Cells From Subzero Temperatures

Lithium (Li)-ion battery cells suffer from significant performance degradation at subzero temperatures. This paper presents a predictive control-based technique that exploits the increased internal resistance of Li-ion cells at subzero temperatures to increase the cells temperature until the desired power can be delivered. Specifically, the magnitude of a sequence of bidirectional currents is optimized such as to minimize total energy discharged. The magnitude of current is determined by solving an optimization problem that satisfies the battery manufacturers voltage and current constraints. Drawing bidirectional currents necessitates that a temporary energy reservoir for energy shuttling, such as an ultracapacitor or another battery, be available. When compared with the case when no penalty on energy withdrawn is imposed, simulations indicate that reductions of up to 20% in energy dispensed as heat in the battery as well as in the size of external storage elements can be achieved at the expense of longer warm-up operation time.

Control synthesis for nonlinear optimal control via convex relaxations

This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional linear program over the space of measures. To generate approximations to this infinite-dimensional program, a sequence of Semi-Definite Programs (SDP)s is formulated in the instance of polynomial cost and dynamics with semi-algebraic state and bounded input constraints. A method to extract a polynomial control function from each SDP is also given. This paper proves that the controller synthesized from each of these SDPs generates a sequence of values that converge from below to the value of the optimal control of the original optimal control problem. In contrast to existing approaches, the presented method does not assume that the optimal control is continuous while still proving that the sequence of approximations is optimal. Moreover, the sequence of controllers that are synthesized using the presented approach are proven to converge to the true optimal control. The performance of the presented method is demonstrated on three examples.

On Improving Battery State of Charge Estimation Using Bulk Force Measurements

Lithium-ion (Li-ion) batteries undergo physical deformation as their state-of-charge (SOC) changes. The physical deformation causes changes in the pressure (equivalently, force) applied at the end-plates of a constrained battery pack or module. This paper proposes the fusion of bulk force and battery voltage measurements to estimate the SOC in Li-ion battery packs. In this paper, using discrete Linear Quadratic Estimators (dLQEs), the advantage of using force measurements in addition to voltage measurement to improve SOC estimates is quantitatively studied through simulations. It is observed that including force measurements can decrease the mean and standard deviation of SOC estimation error by 50% in some SOC intervals.Copyright

Temperature Estimation in a Battery String Under Frugal Sensor Allocation

In electric vehicle applications, batteries are usually packed in modules to satisfy the energy and power demand. To facilitate the thermal management of a battery pack, a model-based observer could be designed to estimate the temperature distribution across the pack. Nevertheless, cost target in industry practice drives the number of temperature sensors in a pack to a number that is not sufficient to yield observability of all the temperature states. This paper focuses on formulating the observer design and sensor deployment strategy that could achieve the optimal observer performance under the frugal sensor allocation. The considered observer performance is the estimation errors induced by model and sensor uncertainty. The observer aims at minimizing the worst-case estimation errors under bounded model and sensor uncertainty.Copyright

The estimation of radial temperature distribution in cylindrical battery cells under unknown cooling conditions

The estimation of temperature inside a battery cell requires accurate information about the cooling condition even when the battery surface temperature is measured. This paper presents a model-based approach for estimating the temperature distribution inside a cylindrical battery under the unknown convective cooling condition. A reduced order thermal model using a polynomial approximation of the temperature profile inside the battery is used. A Dual Extended Kalman Filter (DEKF) is then applied for the identification of the convection coefficient and the estimation of the battery core temperature. Experimental results show that the proposed DEKF-based estimation method can provide an accurate prediction of the core temperature under the unknown cooling condition by measuring the battery current and voltage along with surface and ambient temperatures.