Dynamic modeling and control methodologies are being developed to control the hybrid solid oxide fuel cell (SOFC) power system throughout its operating envelope and to develop subsystem integration processes, flow-down approaches for specifications, and corresponding analysis tools. As the aviation industry moves toward higher efficiency electrical power generation, all-electric aircraft (zero emissions), and more quiet aircraft, fuel cells are being sought as the technology that can deliver on these high expectations. The hybrid solid oxide fuel cell system combines a fuel cell with a microturbine to obtain up to 70-percent cycle efficiency and then distribute the electrical power to the loads via a power-distribution system. The challenge is to understand the dynamics of this complex multidisciplinary system, specify the subsystem interfaces, and design distributed controls that take the system through its operating scenarios in a stable and safe manner. All this needs to be accomplished while the overall system behaves much like a traditional power system in terms of its specifications and expected performance.
In this modeling and analysis approach, high-fidelity models are being developed for the distributed control designs, interface specification, and stability analysis; whereas low-fidelity models are being developed for longer time transient response analysis and to develop system control strategies. The high-fidelity models extend to frequencies that are up to the subharmonic frequency (i.e., half the switching frequency of the power processors), typically tens of kilohertz. In this regard, the power management and distribution system dictates the frequencies that need to be included in the power source models so that the hybrid fuel cell properly interfaces with the dynamics of a typical power system. A preliminary detailed SOFC model has been developed for this analysis, which includes the conservation equation dynamics, ion diffusion, charge transfer kinetics, and inherent impedances.
Hybrid SOFC power system design. PMAD, power management and distribution; BCDU, battery discharge unit; ac, alternating current; dc, direct current.
Long description of figure 1.
It has been determined that the fuel cell mathematical model needs to include the following: the fuel cell voltage relation based on the Gibbs free energy and the Nernst potential, lumped volume conservation equations modeling that includes steady-state electrochemistry and the enthalpies of formation, ion diffusion modeling, charge transfer kinetics modeling, and the inherent electron flow impedances. This mathematical model derivation can be improved and calibrated by impedance spectroscopy testing.
Nyquist stability interface impedance specification. Zo, power source output impedance; Zin, power load input impedance; G(s), transfer function (s-function of frequency).
Long description of figure 2.
The fuel cell model developed so far covers most of the modeling areas mentioned, including the development of simplified low-fidelity models. For the power system, certain key components, such as converters and inverters, are modeled with the d-q axes approach (i.e., in a stationary reference frame). So far, most of the power-distribution components that interface with the hybrid fuel cell system have been modeled. This modeling approach will allow researchers to study and specify the dynamics of these interfaces and to design system operations and control. So far, system operations and control designs have been conceived, such as (1) using a battery to temporarily divert the load current in case of a load loss (which presents a safety issue) until the fuel supply to the fuel cell can be cut off or (2) using the battery for load transients to allow time to rebalance the source power of the microturbine and the fuel cell and match it to the load demand. The microturbine model is currently based on a steady-state spreadsheet model where reduced-order dynamics are added. A high-fidelity microturbine model based on conservation equations will be developed for the hybrid fuel cell. These equations also will be used to model other auxiliary components like diffusers, heat exchangers, heaters, and humidifiers.
Turbine speed-control diagram. ω, turbine speed; Vabc, three-phase voltage; Vfd, field winding terminal voltage; Gp, speed controller transfer function.
Long description of figure 3.
The stability specification methodology calls for using the models developed, after they have been calibrated with test data, to determine the power source (fuel cell and microturbine) output impedances at the various system operating points involving voltage, temperature, and pressures. A preliminarytop-level Nyquist stability specification is in the process of being developed. On the basis of this specification and the knowledge of the source impedances, the limits on the power-distribution load impedances will be determined at the fuel cell and microturbine interfaces. This will allow the system design to be stable with quantifiable stability margins. The resulting methodology will start by modeling the hybrid system components on the basis of the individual component designs, testing to calibrate the models, designing stable power source-distributed controls, determining the source impedances, and finally (on the basis of these impedances) specifying the power-distribution components that will interface with the source at these system interfaces. In addition, the methodology will specify the closed-loop control designs and, eventually, the inrush current and the voltage/current spectral densities that limit the life of the fuel cell. Once the system is shown to be stable, the reduced-order models will be used to design and verify the system operation controls and to conduct transient analysis.
Kopasakis, George, et al.: A Theoretical Solid Oxide Fuel Cell Model for System Controls and Stability Design. Proceedings of GT2006 ASME Turbo Expo 2006: Power for Land, Sea and Air. GT2006-91247, 2006.
Glenn contact: George Kopasakis, 216-433-5327, George.Kopasakis-1@nasa.govLast updated: October 12, 2006
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