The purpose of a controller is to maintain safe and efficient operation of a system. Safe and efficient operation is critical to successfully operating an SOFC system. Previous studies on hybrid systems have proposed various control strategies for meeting demand effectively. In particular, Martinez, et al. [23,63] proposed a control strategy for a locomotiveSOFC-GTsys- tem. These authors developed a cascade control strategy that involved controlling a number of variables at varying levels of priority. At the highest priority, control of the averageSOFC
temperature proceeded by manipulating the air flow (or shaft speed). At a lower priority,
1As discussed in Chapter1, microturbines (
manipulating theSOFCvoltage controlled the fuel utilization. At the lowest priority, control of system power was achieved by manipulating the inlet anode flow rate, and (on the same level) manipulating the combustor fuel flow controlled the turbine inlet temperature (thus influencing the system’s efficiency). These authors found that the hybrid system followed the power demand reasonably well, although the controlled parameters sometimes exceeded their bounds. A major benefit of such a cascade controller is the minimization of interference between control loops, as lower levels are not pursued until the higher (safety-oriented) levels have been satisfied. Such a control scheme is also amenable to development in a conven- tional programming language, such as Fortran orC, to coincide with a model written in one of these or similar languages. A major challenge, however, is avoiding oscillations between the various levels (if the control loops operate on similar timescales). Changes in one level could provoke changes in another level due to the coupled nature of physical processes inside
SOFCs.
Mueller, et al. [57] developed a control strategy that takes advantage of the synergism inherent in hybrid systems. In particular, the hybrid system manipulated the SOFC stack’s current to simultaneously alter the SOFC power and the fuel flow rate exiting the stack. Changing the fuel flow rate helped to maintain a safe recuperator inlet temperature by re- ducing the exit combustor temperature. During a load change, the stack absorbed excessive thermal energy (resulting from increased current) as the shaft speed (cooling air) ramped up. Meanwhile, the gas turbine temporarily generated greater power than intended to com- pensate for delays in fuel delivery to the stack. Thus, one prime mover’s strengths compen- sated for the other prime mover’s shortcomings. For comparison, the authors developed a non-hybrid microturbine model, which maintained a desired recuperator inlet (turbine exit) temperature by maintaining a relatively constant fuel-to-air ratio in the combustor. The authors found that the non-hybrid system followed demand at a maximum rate of approxi- mately 1 kW/s, whereas the hybrid system met an instantaneous 100 kW demand increase in only approximately 20 s. Thus, the hybrid system clearly exhibited superior performance. Roberts and Brouwer [33] developed anSOFC-GTmodel based on a proof-of-concept pro- totype developed by Siemens Westinghouse and tested at the National Fuel Cell Research Center (University of California, Irvine). The system consisted of separate power and gasi-
fier turbines, as well as multiple combustors to heat the SOFC during start-up. The system operated on natural gas, which was fed directly to theSOFC stack and combustors. Bypass valves were used to control the SOFC stack’s temperature. During start-up, the authors subjected the model and experimental system to identical control moves, including the repo- sitioning of bypass valves and adjustment of theSOFC stack’s fuel flow. The authors found that the power generated by theSOFCstack during start-up agreed well with the simulation results, as did the power generated by the turbine. The results differed slightly, however, duringSOFCstack bypass valve repositioning. The authors attributed these discrepancies to inaccurate valve measurement. The authors also compared the steady-state temperatures of the hybrid model to those of the demonstration system, again finding reasonable agreement. Discrepancies in these results were attributed to the authors’ modeling assumption of an adiabatic recuperator and adiabaticSOFC stack.
Stiller, et al. [22] developed a control strategy for a hybrid system model that involved manipulating theSOFC stack’s current to control system power, system fuel flow to control the SOFC’s fuel utilization, shaft speed (via the generator power) to control the system air flow, and the air flow setpoint to control the fuel cell’s temperature. (Leucht, et. al. [58] also controlled fuel utilization by manipulating the fuel flow.) Predefined limits prevented the fuel utilization from falling outside the range 75%–90%, as too low fuel utilization could reduce theSOFC’s efficiency significantly (potentially leading to excessively high afterburner and turbine inlet temperatures as well). Too high fuel utilization, on the other hand, could lead to harmful temperature gradients. The authors also specified a minimumSOFCvoltage of 0.52 V, corresponding to the SOFC’s maximum power output (or thereabouts). During simulation, the authors subjected the hybrid system to small (4.7%) and large (47%) step load changes. The authors found that the hybrid system responded in less than 1 min. to both types of load changes, which is relatively fast. The authors also subjected the system to various disturbances, including increased fuel cell ohmic resistance and system fuel flow overestimation, representing fuel cell degradation and sensor malfunction, respec- tively. The authors found that the average SOFC temperature remained stable following each disturbance, although slight changes in the average temperature occurred following each disturbance.
The foregoing studies, among others, have contributed substantially to the development of SOFC-MT control strategies. The present study differs from these studies, however, by focusing specifically on the open-loop response of variables in the SOFC stack. Processes within SOFCs are tightly coupled, and efficient system operation depends on proper opera- tion of theSOFCstack. Thus, the present work identifies pairs of controlled and manipulated variables that facilitate cascade control. Chapter7 further discusses possible control strate- gies that minimize interdependence, where interdependence may be defined as the inability of a manipulated variable to effectively control a targeted variable, unless control of another variable(s) is implemented. Minimizing interdependence reduces the risk of oscillations be- tween control levels in a cascade controller (see Martinez, et al. [23]). It should be reiterated that while many of the foregoing studies implemented proportional-integral-derivative (PID) controllers, the present study considers only the open-loop response of control variables. Results from this study are intended to inform control decisions at the system level.