Electrochemical power systems involving batteries, ultracapacitors, fuel cells often operate under dynamic load conditions. Because of this, steady state analysis and design methods commonly used on more traditional chemical engineering systems are of limited value. Consequently, there is a demonstrated need to further improve and extend the available analytical techniques for dynamic systems. Methods for state/parameter estimation and system design are of particular importance. Several such topics have been addressed in this work and applied to the study of various electrochemical systems.; In the first, a new algorithm is proposed for tracking slow parameter drift in long-running periodic or repeated batch systems. Data regressions are performed sequentially on each cycle, assuming that the parameters of interest remain constant for the duration of each period. However, an additional term is included that penalizes large deviations of parameter values from those found in the recent past. This term adds a desirable smoothing effect to the sequence of obtained parameter values. The algorithm is demonstrated on 1500+ discharge cycles of a Sony 18650 lithium-ion battery.; The second technique revisits piecewise polynomial regression, which is widely used for fitting data that are not described well by a single functional form. Traditional approaches for performing these regressions are plagued by a number of difficulties, including the requirement of "expert user" interaction, optimizations with numerically unfavorable objective functions, and/or extensive computation times. Here, a novel method based on mixed-integer linear programming is presented which eliminates many of these previous pitfalls and is used to fit open circuit potential data of two intercalation electrodes.; The third section considers a large-scale dynamic system modeling project. A dynamic physics-based model of a packed-bed methanol reformer is derived, and a prior system-level fuel cell stack model is corrected and extended for use in system simulations. After being combined with additional plant components such as heat exchangers, a battery pack, and regulatory control loops, overall system performance is analyzed for its response to a simulated driving power profile.; Finally, an electrochemical hybrid power system design problem is formulated as a dynamic optimization problem. The chosen solution methodology has gained renewed attention recently due to increasing computing power and memory and advances in large-scale nonlinear program solution algorithms. These advances render the very large optimization problems that result from this approach tractable, while allowing for the straightforward inclusion of state path constraints.
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