(631f) Control–Relevant Design of Electrochemical Hybrid Power Systems Using Dynamic Optimization Methods

Considerable attention is being given to the development of electrochemical hybrid power systems. These systems, comprised of a combination of fuel cells, batteries, and/or electrochemical capacitors, are being studied due to their ability to overcome performance limitations of the individual components. Depending on the size of the components used, these hybrid power systems can be designed for <1 W scale (MEMS, implantable devices) through the 10-100 W scale (man-portable power) all the way to 10-100 kW systems for vehicular applications. Fuel cells are attractive components, due to their extended operating times given an adequate fuel supply. However, they are sensitive to rapid fluctuations in load. Certain types of batteries including li-ion cells offer relatively high energy densities and respond more quickly than fuel cells, but become increasingly inefficient at higher loads. Finally, electrochemical super- or ultracapacitors have low overall energy densities, but can provide extremely high power for short durations. The addition of ultracapacitors to hybrid power systems helps smooth transient loads on the other components and can potentially prolong battery life.

Given the varying properties of the constituent components, optimal design of these hybrid power systems is largely application dependent, with weight, volume, cost, heat generation, and desired load profile/duty cycle considerations having differing relative importance. A number of studies have been conducted analyzing various hybrid systems including: i) theoretical treatment of battery?ultracapacitor hybrids [1]; ii) experimental treatment of battery?ultracapacitor hybrids [3]; and iii) experimental treatment of battery?proton exchange membrane fuel cell (PEMFC) hybrids [5, 2]. This list is meant to be a representative sample; it is by no means exhaustive.

The goal of this work is to provide a new approach to the design and characterization of hybrid power systems. Due to ever-increasing computing power and the advancement of large-scale nonlinear program (NLP) solution techniques, it is possible to address these tasks from within a dynamic optimization framework. Very recently, several promising techniques involving the discretization of system of ordinary differential equations (ODEs) or differential algebraic equations (DAEs) by orthogonal collocation have been presented in the literature for solving these large dynamic optimization problems [4]. This approach appears to offer several benefits over traditional techniques which require the integration of ODEs or DAEs at each iteration of the NLP solution. The first is that collocation procedure allows for the analytical calculation of gradients and hessians of the objective function and constraints, which allows for considerably more efficient NLP solution techniques. This results in substantial computational savings. Moreover, collocation is typically more robust to optimization or control parameters that might cause instabilities in the underlying process. This stability helps ensure satisfactory convergence of the method. Finally, the collocation approaches allow the user to specify path constraints on the state and/or control variables, which is considerably more difficult when performing a direct integration of ODEs or DAEs. These constraints are very useful for enforcing saturation of control elements or maintaining the system in a safe operating regime.

In practice, actual physical systems do not behave exactly as modeled, and the operational loads encountered by power systems often differ from the design specification to varying degrees. As a result, good control schemes must be perform satisfactorily not only for the ideal design case, but for a variety of sub-optimal plant realizations as well. The collocation-based large-scale dynamic optimization techniques should be able to optimize controller tunings over a set of perturbed plant realizations.

References

[1] R.A. Dougal, S. Liu, and R.E. White. Power and Life Extension of Battery?Ultracapacitor Hybrids. IEEE Trans. on Components and Packaging Technologies, 25(1):120?131, March 2002.

[2] L. Gao, Z. Jiang, and R.A. Dougal. An Actively Controlled Fuel Cell/Battery Hybrid to Meet Pulsed Power Demands. J. Power Sources, 130(1-2):202?207, 2004.

[3] C.E. Holland, J.W. Weidner, R.A. Dougal, and R.E. White. Experimental Characterization of Hybrid Power Systems Under Pulse Current Loads. J. Power Sources, 109:32?37, 2002.

[4] W. Hong, S. Wang, P. Li, G. Wozny, and L. Biegler. A Quasi-Sequential Approach to Large- Scale Dynamic Optimization Problems. AIChE J., 52(1):255?268, 2006.

[5] Z. Jiang, L. Gao, M.J. Blackwelder, and R.A. Dougal. Design and Experimental Tests of Control Strategies for Active Hybrid Fuel Cell/Battery Power Sources. J. Power Sources, 130(1-2):163?171, 2004.