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Technical Briefs

# Determination of an Empirical Transfer Function of a Solid Oxide Fuel Cell Gas Turbine Hybrid System Via Frequency Response Analysis

[+] Author and Article Information
Alex Tsai, Larry Banta

National Energy Technology Laboratory, West Virginia University, Morgantown, WV 26506; Department of Mechanical and Aerospace Engineering, West  Virginia University, Morgantown, WV 26506

Larry Lawson, David Tucker

U.S. Department of Energy, National Energy Technology Laboratory, Morgantown, WV 26506

J. Fuel Cell Sci. Technol 6(3), 034505 (May 13, 2009) (8 pages) doi:10.1115/1.3006302 History: Received June 18, 2007; Revised December 16, 2007; Published May 13, 2009

## Abstract

This paper presents the study of the effect variations in the heat effluence from a solid oxide fuel cell (SOFC) has on a gas turbine hybrid configuration. The SOFC is simulated through hardware at the U.S. Department of Energy, National Energy Technology Laboratory (NETL). The gas turbine, compressor, recuperative heat exchanger, and other balance of plant components are represented by actual hardware in the Hybrid Performance Test Facility at NETL. Fuel cell heat exhaust is represented by a combustor that is activated by a fuel cell model that computes energy release for various sensed system states System structure is derived by means of frequency response data generated by the sinusoidal oscillation of the combustor fuel valve over a range of frequencies covering three orders of magnitude. System delay and order are obtained from Bode plots of the magnitude and phase relationships between input and output parameters. Transfer functions for mass flow, temperature, pressure, and other states of interest are derived as a function of fuel valve flow, representative of fuel cell thermal effluent. The Bode plots can validate existing analytical transfer functions, provide steady state error detection, give a stability margin criterion for the fuel valve input, estimate system bandwidth, identify any nonminimum phase system behavior, pinpoint unstable frequencies, and serve as an element of a piecewise transfer function in the development of an overall transfer function matrix covering all system inputs and outputs of interest. Further loop shaping techniques and state space representation can be applied to this matrix in a multivariate control algorithm.

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## Figures

Figure 1

Schematic of the HyPer system

Figure 2

Graphical approximation of a transfer function

Figure 3

Time series data at 0.001 Hz

Figure 4

Time series data at 0.01 Hz

Figure 5

Time series data at 0.1 Hz

Figure 6

Time series data at 1 Hz. Response is dominated by noise.

Figure 7

Bode plots of fuel cell inputs to fuel valve input

Figure 8

Bode plots of turbine inlet temperature (TIT) and turbine speed to fuel valve input

Figure 9

Generated transfer function Bode plot and experimental data Bode plot

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