Feedforward-Feedback Control of a SOFC Power System: A Simulation Study

Smooth and timely control actions improve the efficiency and durability of solid oxide fuel cell (SOFC) power systems. In this paper a systematic feedforward-feedback approach to control design for SOFC power systems is proposed. The control aim is to regulate the temperature of and the temperature difference over the stack by manipulating the air flow, air inlet temperature and fuel flow. The feedforward part responds to the demanded electrical current and stoichometry of reforming and electrochemical processes. It gives the fuel flow rate needed to achieve the required stack current with a given fuel utilization. The air flow rate is then calculated according to the oxygen consumption in fuel cells and a given air utilization. Feedforward control is combined with the feedback control to adjust the manipulated variables based on the measured system output. Relative gain array (RGA) analysis (Shinskey, 1988) is performed over the system inputs and outputs (I/O) to determine optimal I/O pairing for control. The RGA is calculated from the static gain matrix of the SOFC stack model (Sorrentino et al., 2008). The strongest interactions are found between the cathode outlet temperature and the cathode inlet temperature, the stack temperature difference and the air flow rate, and the stack voltage and the fuel flow rate. Fuel flow rate has a strong influence also on the stack temperature and can be in some situations used to support temperature control. Based on the RGA analysis, two individual PI control loops are determined. In the first loop, the cathode outlet temperature is controlled by the proportional-integral (PI) controller that uses the cathode inlet temperature as the manipulated variable. In the second loop, the stack temperature difference is controlled by the PI controller with the air flow rate as the manipulated variable (see Figure 1). Altogether the control system consists of two PI control loops, making it feasible for practical implementation. The control target is similar as in (Pohjoranta et al., 2015) but it is obtained here with a significantly simpler approach. Anti-windup protection is included in the PI controllers to avoid long settling times caused by the limits on the manipulated variables (Peng et al, 1999). Parameters of the PI controllers are tuned from the open-loop step response experiments by applying the Magnitude Optimum Multiple Integration (MOMI) method (Vranèiæ et al., 1999). The feedforward-feedback control is evaluated on the SOFC stack model (Sorrentino et al., 2008) over a one-day operation cycle using the standard load profile of residential houses (Knight and Ribbering, 2007). The proposed feedforward-feedback control provides good control of the stack temperatures (see Figure 2). Relatively high stack voltage changes are caused by the significant load changes, however, but these can be reduced by combining a SOFC power system with an energy buffer. References Knight, I., Ribbering, H. (eds.) (2007). European and Canadian non-HYAC Electric and DHW Load Profiles for Use in Simulating the Performance of Residential Cogeneration Systems. A Report of Subtask A of FC+COGEN-SIM: The Simulation of Building-Integrated Fuel Cell and Other Cogeneration Systems. Peng Y., Vrancic D., Hanus R. (1996). Anti-windup, bumpless, and conditioned transfer techniques for PID controllers. Control syst. mag., 16, 48-57. Pohjoranta, A., Halinen, M., Pennanen, J., Kiviaho, J. (2015). Model predictive control of the solid oxide fuel cell stack temperature with models based on experimental data. Journal of Power Sources, 277, 239-250. Shinskey, F.G. (1988). Process control systems. 3rdedition. McGraw-Hill, New York. Sorrentino, M., Pianese, C., Guezennec, Y.G. (2008). A hierarchical modeling approach to the simulation and control of planar solid oxide fuel cells. Journal of Power Sources, 180, 380-392. Vrancic, D., Peng, Y., Strmcnik, S. (1999). A new PID controller tuning method based on multiple integrations, Control Engineering Practice, 7(5), 623-633. Figure 1

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