Scott J. Moura

A Stochastic Optimal Control Approach for Power Management in Plug-In Hybrid Electric Vehicles

This paper examines the problem of optimally splitting driver power demand among the different actuators (i.e., the engine and electric machines) in a plug-in hybrid electric vehicle (PHEV). Existing studies focus mostly on optimizing PHEV power management for fuel economy, subject to charge sustenance constraints, over individual drive cycles. This paper adds three original contributions to this literature. First, it uses stochastic dynamic programming to optimize PHEV power management over a distribution of drive cycles, rather than a single cycle. Second, it explicitly trades off fuel and electricity usage in a PHEV, thereby systematically exploring the potential benefits of controlled charge depletion over aggressive charge depletion followed by charge sustenance. Finally, it examines the impact of variations in relative fuel-to-electricity pricing on optimal PHEV power management. The paper focuses on a single-mode power-split PHEV configuration for mid-size sedans, but its approach is extendible to other configurations and sizes as well.

Battery-Health Conscious Power Management in Plug-In Hybrid Electric Vehicles via Electrochemical Modeling and Stochastic Control

This paper develops techniques to design plug-in hybrid electric vehicle (PHEV) power management algorithms that optimally balance lithium-ion battery pack health and energy consumption cost. As such, this research is the first to utilize electrochemical battery models to optimize the power management in PHEVs. Daily trip length distributions are integrated into the problem using Markov chains with absorbing states. We capture battery aging by integrating two example degradation models: solid-electrolyte interphase (SEI) film formation and the “Ah-processed” model. This enables us to optimally tradeoff energy cost versus battery-health. We analyze this tradeoff to explore how optimal control strategies and physical battery system properties are related. Specifically, we find that the slope and convexity properties of the health degradation model profoundly impact the optimal charge depletion strategy. For example, solutions that balance energy cost and SEI layer growth aggressively deplete battery charge at high states-of-charge (SoCs), then blend engine and battery power at lower SoCs.

Velocity Predictors for Predictive Energy Management in Hybrid Electric Vehicles

The performance and practicality of predictive energy management in hybrid electric vehicles (HEVs) are highly dependent on the forecast of future vehicular velocities, both in terms of accuracy and computational efficiency. In this brief, we provide a comprehensive comparative analysis of three velocity prediction strategies, applied within a model predictive control framework. The prediction process is performed over each receding horizon, and the predicted velocities are utilized for fuel economy optimization of a power-split HEV. We assume that no telemetry or on-board sensor information is available for the controller, and the actual future driving profile is completely unknown. Basic principles of exponentially varying, stochastic Markov chain, and neural network-based velocity prediction approaches are described. Their sensitivity to tuning parameters is analyzed, and the prediction precision, computational cost, and resultant vehicular fuel economy are compared.

Integrated Optimization of Battery Sizing, Charging, and Power Management in Plug-In Hybrid Electric Vehicles

This brief presents an integrated optimization framework for battery sizing, charging, and on-road power management in plug-in hybrid electric vehicles. This framework utilizes convex programming to assess interactions between the three optimal design/control tasks. The objective is to minimize carbon dioxide (CO2) emissions, from the on-board internal combustion engine and grid generation plants providing electrical recharge power. The impacts of varying daily grid CO2 trajectories on both the optimal battery size and charging/power management algorithms are analyzed. We find that the level of grid CO2 emissions can significantly impact the nature of emission-optimal on-road power management. We also observe that the on-road power management strategy is the most important design task for minimizing emissions, through a variety of comparative studies.

Adaptive Partial Differential Equation Observer for Battery State-of-Charge/State-of-Health Estimation Via an Electrochemical Model

This paper develops an adaptive partial differential equation (PDE) observer for battery state-of-charge (SOC) and state-of-health (SOH) estimation. Real-time state and parameter information enables operation near physical limits without compromising durability, thereby unlocking the full potential of battery energy storage. SOC/SOH estimation is technically challenging because battery dynamics are governed by electrochemical principles, mathematically modeled by PDEs. We cast this problem as a simultaneous state (SOC) and parameter (SOH) estimation design for a linear PDE with a nonlinear output mapping. Several new theoretical ideas are developed, integrated together, and tested. These include a backstepping PDE state estimator, a Pade-based parameter identifier, nonlinear parameter sensitivity analysis, and adaptive inversion of nonlinear output functions. The key novelty of this design is a combined SOC/SOH battery estimation algorithm that identifies physical system variables, from measurements of voltage and current only.

PDE estimation techniques for advanced battery management systems — Part II: SOH identification

A critical enabling technology for electrified vehicles and renewable energy resources is battery energy storage. Advanced battery systems represent a promising technology for these applications, however their dynamics are governed by relatively complex electrochemical phenomena whose parameters degrade over time and vary across material design. Moreover, limited sensing and actuation exists to monitor and control the internal state of these systems. As such, battery management systems require advanced identification, estimation, and control algorithms. In this paper we examine state-of-health (SOH) estimation, framed as a parameter identification problem for parabolic PDEs and nonlinearly parameterized output functions. Specifically, we utilize the swapping identification method for unknown parameters in the diffusion partial differential equation (PDE). A nonlinear least squares method is applied to the output function to identify its unknown parameters. These identification algorithms are synthesized from the single particle model (SPM). In a companion paper we examine a new battery state-of-charge (SOC) estimation algorithm based upon the backstepping method for PDEs.A critical enabling technology for electrified vehicles and renewable energy resources is battery energy storage. Advanced battery systems represent a promising technology for these applications, however their dynamics are governed by relatively complex electrochemical phenomena whose parameters degrade over time and vary across manufacturer. Moreover, limited sensing and actuation exists to monitor and control the internal state of these systems. As such, battery management systems require advanced identification, estimation, and control algorithms. In this paper we examine a new battery state-of-charge (SOC) estimation algorithm based upon the backstepping method for partial differential equations (PDEs). The estimator is synthesized from the so-called single particle model (SPM). Our development enables us to rigorously analyze observability and stability properties of the estimator design. In a companion paper we examine state-of-health (SOH) estimation, framed as a parameter identification problem for parabolic PDEs and nonlinearly parameterized output functions.

Dynamic Traffic Feedback Data Enabled Energy Management in Plug-in Hybrid Electric Vehicles

Recent advances in traffic monitoring systems have made real-time traffic velocity data ubiquitously accessible for drivers. This paper develops a traffic data-enabled predictive energy management framework for a power-split plug-in hybrid electric vehicle (PHEV). Compared with conventional model predictive control (MPC), an additional supervisory state of charge (SoC) planning level is constructed based on real-time traffic data. A power balance-based PHEV model is developed for this upper level to rapidly generate battery SoC trajectories that are utilized as final-state constraints in the MPC level. This PHEV energy management framework is evaluated under three different scenarios: 1) without traffic flow information; 2) with static traffic flow information; and 3) with dynamic traffic flow information. Numerical results using real-world traffic data illustrate that the proposed strategy successfully incorporates dynamic traffic flow data into the PHEV energy management algorithm to achieve enhanced fuel economy.

Air flow control in fuel cell systems: An extremum seeking approach

This paper examines the problem of maximizing net power output in a polymer electrolyte membrane (PEM) fuel cell system. The net power production depends heavily on the oxygen excess ratio in the cathode. However, the time-varying parameters and complex nonlinear dynamics of the system present many challenges to regulating oxygen excess ratio under all operating conditions. A constrained extremum seeking control architecture is presented to effectively regulate oxygen excess ratio about an optimum value that maximizes net power output over a broad range of operating conditions. Simulation results demonstrate that this control technique improves fuel cell system performance and our constrained optimization approach enables faster convergence rates for an admissible level of overshoot.

Optimal Control of Film Growth in Lithium-Ion Battery Packs via Relay Switches

Recent advances in lithium-ion battery modeling suggest unequal but controlled and carefully timed charging of individual cells by reduce degradation. This paper compares anode-side film formation for a standard equalization scheme versus unequal charging through switches that are controlled by deterministic dynamic programming (DDP) and DDP-inspired heuristic algorithms. A static map for film growth rate is derived from a first-principles battery model adopted from the electrochemical engineering literature. Using this map, we consider two cells that are connected in parallel via relay switches. The key results are the following: 1) optimal unequal and delayed charging indeed reduces film buildup, and 2) a near-optimal state feedback controller can be designed from the DDP solution and film growth rate convexity properties. The simulation results indicate that the heuristic state feedback controller achieves near optimal performance relative to the DDP solution, with significant reduction in film growth compared to charging both cells equally, for several film growth models. Moreover, the algorithms achieve similar film reduction values on the full electrochemical model. These results correlate with the convexity properties of the film growth map. Hence, this paper demonstrates that unequal charging may indeed reduce film growth, given certain convexity properties exist, lending promise to the concept for improving battery pack life.

Charge trajectory optimization of plug-in hybrid electric vehicles for energy cost reduction and battery health enhancement

This paper examines the problem of optimizing the charge trajectory of a plug-in hybrid electric vehicle (PHEV), defined as the timing and rate with which the PHEV obtains electricity from the power grid. Two objectives are considered in this optimization. First, we minimize the total cost of fuel and electricity consumed by the PHEV over a 24-hour naturalistic drive cycle. We predict this cost using a previously-developed stochastic optimal PHEV power management strategy. Second, we also minimize total battery health degradation over the course of the 24-hour cycle. This degradation is predicted using an electrochemistry-based model of anode-side resistive film formation in Li-ion batteries. The paper shows that these two objectives are conflicting, and trades them off using a non-dominated sort genetic algorithm, NSGA-II. As a result, a Pareto front of optimal PHEV charge trajectories is obtained. The effects of electricity price and trip schedule on the Pareto front are analyzed and discussed.