Patent Publication Number: US-10763526-B2

Title: System and method for fuel cell stack temperature control

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is related to concurrently filed and co-pending applications identified as: U.S. patent application Ser. No. 15/811,290, filed Nov. 13, 2017, entitled “System and Method for Fuel Cell Stack Temperature Control”, with named inventors Michele Bozzolo, Francesco Caratozzolo, David Silveira Erel and Alberto Traverso; and U.S. patent application Ser. No. 15/811,294, filed Nov. 13, 2017, entitled “System and Method for Fuel Cell Stack Temperature Control”, with named inventors Michele Bozzolo, Francesco Caratozzolo, David Silveira Erel and Alberto Traverso. 
     FIELD 
     The present disclosure relates to fuel cell systems. More specifically, the present disclosure relates to a system and method for controlling the temperature of the fuel cell stack. 
     BACKGROUND 
     A fuel cell is an electrochemical conversion device that produces electricity by oxidizing a fuel. A fuel cell typically includes an anode, a cathode, and an electrolyte between the anode and the cathode. A fuel cell system usually includes multiple fuel cells electrically connected to one another in series via interconnects (sometimes collectively referred to as a “fuel cell unit”) and several components configured to provide the fuel to the anodes of the fuel cells and an oxidant to the cathodes of the fuel cells. The oxygen in the oxidant is reduced at the cathode into oxygen ions that diffuse through the electrolytes into the anodes. The fuel is oxidized at the anodes, which produces electrons that flow through an electrical load. 
     Solid oxide fuel cell (SOFC) systems (and other high-temperature fuel cell systems) require a relatively high operating temperature, such as 1000 degrees Celsius, to maintain low internal electrical resistance and achieve optimal performance. Accordingly, there is a need for systems and methods for controlling high-temperature fuel cell systems to maintain a desired temperature in the fuel cell stack. 
     SUMMARY 
     Various embodiments of the present disclosure provide a fuel cell system configured to modulate the flow of oxidant through the fuel cell system to maintain a desired temperature at the fuel cell stack. The fuel cell system is configured to control the flow of oxidant to maintain the desired temperature in the fuel cell stack based on temperature measurements of fluid outside of the fuel cell stack. 
     A method is presented of operating a fuel cell system comprising a fuel cell stack comprising multiple fuel cells each comprising an anode and a cathode. The method comprises providing, by an oxidant flow control device and at a substantially constant oxidant mass flow rate, an oxidant to the cathodes; sensing, by a temperature sensor, a temperature of the oxidant upstream of the fuel cell stack and sending, by the temperature sensor, a signal representing the sensed temperature to a controller; controlling, by the controller and based on the sensed temperature, an amount of heat an oxidant heater provides to the oxidant to heat the oxidant; and providing, by a fuel flow control device and at a fuel mass flow rate, a fuel to the anodes. 
     In some embodiments the method further comprises providing, by the fuel cell stack, an electrical current to an electrical load. In some embodiments the method further comprises controlling, by the controller, the provision of the electrical current to the electrical load based on an electrical current set point. In some embodiments the method further comprises controlling, by the controller, the fuel flow control device to provide the fuel to the anodes. In some embodiments the method further comprises determining, by the controller, the fuel mass flow rate based on the electrical current set point and controlling, by the controller, the fuel flow control device to provide the fuel to the anodes at the determined fuel mass flow rate. 
     In some embodiments a first electrical current set point corresponds to a first fuel mass flow rate and a second electrical current set point that is greater than the first electrical current set point corresponds to a second fuel mass flow rate that is greater than the first fuel mass flow rate. In some embodiments the method further comprises controlling, by the controller, the oxidant flow control device to provide the oxidant to the cathodes and controlling, by the controller, the fuel flow control device to provide the fuel to the anodes. 
     In some embodiments the method further comprises controlling, by the controller and based on the sensed temperature, the amount of heat the oxidant heater provides to the oxidant to heat the oxidant by controlling, by the controller, a mass flow rate of an auxiliary fuel output by an auxiliary fuel flow control device to the oxidant heater. In some embodiments the method further comprises determining, by the controller, a difference between the sensed temperature and a temperature set point and controlling, by the controller, the mass flow rate of the auxiliary fuel provided by the auxiliary fuel flow control device to the oxidant heater to reduce the difference between the sensed temperature and the temperature set point. 
     In some embodiments determining the difference between the sensed temperature and the temperature set point comprises determining, by a proportional-integral-derivative (PID) module of the controller, the difference between the sensed temperature and the temperature set point. 
     According to another aspect of the present disclosure, a fuel cell system comprises a fuel cell stack, an oxidant control device, a fuel flow control device, a temperature sensor, an oxidant heater, and a controller. The fuel cell stack comprises multiple fuel cells each comprising an anode and a cathode. The oxidant flow control device is in fluid communication with the cathodes and configured to provide an oxidant at an oxidant mass flow rate to the cathodes. The fuel flow control device is in fluid communication with the anodes and configured to provide a fuel at a fuel mass flow rate to the anodes. The temperature sensor is configured to sense a temperature of the oxidant upstream of the fuel cell stack. The oxidant heater is configured to heat the oxidant upstream of the fuel cell stack. The controller is configured to control the oxidant flow control device to provide the oxidant to the cathodes such that the oxidant mass flow rate is substantially constant; control, based on the sensed temperature, an amount of heat the oxidant heater provides to the oxidant to heat the oxidant; and control the fuel flow control device to provide the fuel to the anodes. 
     In some embodiments the fuel cell stack is electrically connectable to an electrical load and configured to provide an electrical current to the electrical load. In some embodiments the controller is further configured to control the provision of the electrical current to the electrical load based on an electrical current set point. In some embodiments the controller is further configured to determine the fuel mass flow rate based on the electrical current set point and to control the fuel flow control device to provide the fuel to the anodes at the determined fuel mass flow rate. In some embodiments a first electrical current set point corresponds to a first fuel mass flow rate and a second electrical current set point that is greater than the first electrical current set point corresponds to a second fuel mass flow rate that is greater than the first fuel mass flow rate. 
     In some embodiments the fuel cell system further comprises an auxiliary fuel flow control device in fluid communication with the oxidant heater and configured to provide an auxiliary fuel at an auxiliary fuel mass flow rate to the oxidant heater. In some embodiments the controller is further configured to control the amount of heat the oxidant heater provides to the oxidant to heat the oxidant by controlling the auxiliary fuel mass flow rate. In some embodiments the controller is further configured to determine a difference between the sensed temperature and a temperature set point and control the auxiliary fuel mass flow rate to reduce the difference between the sensed temperature and the temperature set point. In some embodiments a proportional-integral-derivative (PID) module of the controller is configured to determine the difference between the sensed temperature and the temperature set point. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
         FIG. 1  is a block diagram of some components of one example embodiment of the fuel cell system of the present disclosure. 
         FIG. 2  is another block diagram of some components of the fuel cell system of  FIG. 1 . 
         FIG. 3  is another block diagram of some components of the fuel cell system of  FIG. 1  during a transition from shut-down mode to standby mode. Dashed lines represent control signals while solid lines represent fluid flow paths. 
         FIG. 4  is another block diagram of some components of the fuel cell system of  FIG. 1  during a transition from standby mode to operating mode. Dashed lines represent control signals while solid lines represent fluid flow paths. 
         FIG. 5  is another block diagram of some components of the fuel cell system of  FIG. 1  during operating mode. Dashed lines represent control signals while solid lines represent fluid flow paths. 
         FIG. 6  is another block diagram of some components of the fuel cell system of  FIG. 1  during an alternative transition from standby mode to operating mode. Dashed lines represent control signals while solid lines represent fluid flow paths. 
     
    
    
     DETAILED DESCRIPTION 
     While the features, methods, devices, and systems described herein may be embodied in various forms, the drawings show and the detailed description describes some exemplary and non-limiting embodiments. Not all of the components shown and described in the drawings and the detailed descriptions may be required, and some implementations may include additional, different, or fewer components from those expressly shown and described. Variations in the arrangement and type of the components; the shapes, sizes, and materials of the components; and the manners of attachment and connections of the components may be made without departing from the spirit or scope of the claims as set forth herein. This specification is intended to be taken as a whole and interpreted in accordance with the principles of the invention as taught herein and understood by one of ordinary skill in the art. 
     Various embodiments of the present disclosure provide a fuel cell system configured to modulate the flow of oxidant through the fuel cell system to maintain a desired temperature at the fuel cell stack. The fuel cell system is configured to control the flow of oxidant to maintain the desired temperature in the fuel cell stack based on temperature measurements of fluid outside of the fuel cell stack. 
       FIGS. 1-5  illustrate one example embodiment of a solid oxide fuel cell (SOFC) system  100  of the present disclosure and components thereof. While a SOFC system is used in this example, the present disclosure may be implemented in any other suitable fuel cell system. The SOFC system  100  includes an oxidant heat exchanger  110 , a cathode ejector  112 , an oxidant heater  114 , an SOFC stack  116 , an anode ejector  118 , a pre-reformer  120 , a reformer  122 , a fuel heat exchanger  124 , an auxiliary ejector  126 , a combustor  128 , an oxidant flow control device  130 , a controller  132 , a first temperature sensor  134   a , a second temperature sensor  134   b , a third temperature sensor  134   c , a fuel flow control device  136 , and an auxiliary fuel flow control device  138 . 
     As described in detail below, the SOFC system  100  is fluidly connectable to an oxidant source  102  (such as a source of air), a fuel source  104  (such as a source of natural gas, liquefied petroleum gas, or biogas), and an auxiliary fuel source  106  (such as a source of natural gas, hydrogen, or syngas). The SOFC system  100  is operable to use oxidant from the oxidant source  102  to oxidize fuel from the fuel source  104  to generate electricity that the SOFC stack  116  supplies to an external electrical load. The SOFC system  100  is operable to use auxiliary fuel from the auxiliary fuel source  106  to heat the oxidant flowing into the SOFC stack  116 . 
     1. Components 
     The oxidant heat exchanger  110  is a suitable heat exchanger including: (1) a cold side having an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another; and (2) a hot side having a combustion byproduct inlet and a combustion byproduct outlet (not labeled) in fluid communication with one another. The oxidant heat exchanger  110  is configured to transfer heat from relatively hot combustion byproducts that flow through the hot side from the combustion byproduct inlet to the combustion byproduct outlet to relatively cold oxidant traveling through the cold side from the oxidant inlet to the oxidant outlet. The oxidant heat exchanger  110  is a counter-flow heat exchanger in this example embodiment, though the oxidant heat exchanger  110  may be any other suitable type of heat exchanger in other embodiments. 
     The cathode ejector  112  includes a motive fluid inlet  112   a , a suction fluid inlet  112   b , and a fluid outlet  112   c  in fluid communication with one another. The cathode ejector  112  is configured (such as via a convergent/divergent nozzle construction or any other suitable construction) such that when a relatively high-pressure motive fluid is introduced into the motive fluid inlet  112   a  and a relatively low-pressure suction fluid is present at the suction fluid inlet  112   b , the flow of the motive fluid through the cathode ejector  112  creates a low pressure region (a vacuum in certain instances) downstream of the motive and suction fluid inlets  112   a  and  112   b . This low pressure region sucks the suction fluid from the suction fluid inlet  112   b  and causes the suction fluid to mix with the motive fluid before flowing out of the fluid outlet  112   c.    
     The oxidant heater  114  includes an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another. The oxidant heater  114  also includes an auxiliary fuel inlet (not labeled). The oxidant heater  114  is configured to convert auxiliary fuel (received from the auxiliary fuel flow control device  138 ) into heat and to use that heat to heat the oxidant in thermal communication with the oxidant heater  114 . In this example, the oxidant heater  114  includes a gas burner, though it may be any other suitable device in other embodiments such as a catalytic start burner or electric heater. 
     The SOFC stack  116  includes multiple individual SOFCs (not shown) each including an anode and a cathode sandwiching an electrolyte. The SOFCs are electrically connected to one another in series via interconnects. The SOFC stack  116  includes a fuel inlet and a fuel outlet (not labeled) in fluid communication with one another and an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another. The SOFC stack  116  is also electrically connectable to the electrical load. Generally, in operation, as oxidant flows past the cathodes and fuel flows past the anodes of the SOFCs of the SOFC stack  116 , the oxygen in the oxidant is reduced into oxygen ions at the cathodes that then diffuse through the electrolytes to the anodes. The fuel is oxidized at the anodes, which produces electrons that flow through the electrical load. 
     The anode ejector  118  includes a motive fluid inlet  118   a , a suction fluid inlet  118   b , and a fluid outlet  118   c  in fluid communication with one another. The anode ejector  118  is configured (such as via a convergent/divergent nozzle construction or any other suitable construction) such that when a relatively high-pressure motive fluid is introduced into the motive fluid inlet  118   a  and a relatively low-pressure suction fluid is present at the suction fluid inlet  118   b , the flow of the motive fluid through the anode ejector  118  creates a low pressure region (a vacuum in certain instances) downstream of the motive and suction fluid inlets  118   a  and  118   b . This low pressure region sucks the suction fluid from the suction fluid inlet  118   b  and causes the suction fluid to mix with the motive fluid before flowing out of the fluid outlet  118   c.    
     The pre-reformer  120  includes a fuel inlet and a fuel outlet (not labeled) in fluid communication with one another. The pre-reformer  120  is a suitable device (such as an adiabatic catalytic converter) configured to remove higher hydrocarbons from unreformed fuel to convert it into pre-reformed fuel. In certain embodiments, the pre-reformer is configured to do so with no heat input other than the heat present in the fuel and/or the exhausted oxidant. In other embodiments, the SOFC system does not include a pre-reformer. 
     The reformer  122  includes: (1) a cold side including a fuel inlet and a fuel outlet (not labeled) in fluid communication with one another; and (2) a hot side including an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another. The reformer  122  is configured to transfer heat from relatively hot oxidant that flows through the hot side from the oxidant inlet to the oxidant outlet to relatively cold pre-reformed fuel traveling through the cold side from the fuel inlet to the fuel outlet. The reformer  122  is (partially) a counter-flow heat exchanger in this example embodiment, though the reformer may incorporate any other suitable type of heat exchanger in other embodiments. As the pre-reformed fuel flows from the fuel inlet to the fuel outlet, the reformer  122  is configured to reform the pre-reformed fuel via a catalyst into reformed fuel. The heating of the pre-reformed fuel aids in the catalytic conversion process. 
     The fuel heat exchanger  124  includes: (1) a cold side having a fuel inlet and a fuel outlet (not labeled) in fluid communication with one another; and (2) a hot side having an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another. The fuel heat exchanger  124  is configured to transfer heat from relatively hot oxidant traveling through the hot side from the oxidant inlet to the oxidant outlet to relatively cold reformed fuel traveling through the cold side from the fuel inlet to the fuel outlet. The fuel heat exchanger  124  is a counter-flow heat exchanger in this example embodiment, though the fuel heat exchanger may be any other suitable type of heat exchanger in other embodiments. 
     The auxiliary ejector  126  includes a motive fluid inlet  126   a , a suction fluid inlet  126   b , and a fluid outlet  126   c  in fluid communication with one another. The auxiliary ejector  126  is configured (such as via a convergent/divergent nozzle construction or any other suitable construction) such that when a relatively high-pressure motive fluid is introduced into the motive fluid inlet  126   a  and a relatively low-pressure suction fluid is present at the suction fluid inlet  126   b , the flow of the motive fluid through the auxiliary ejector  126  creates a low pressure region (a vacuum in certain instances) downstream of the motive and suction fluid inlets  126   a  and  126   b . This low pressure region sucks the suction fluid from the suction fluid inlet  126   b  and causes the suction fluid to mix with the motive fluid before flowing out of the fluid outlet  126   c.    
     The combustor  128  includes a combustion product inlet and a combustion byproduct outlet (not labeled) in fluid communication with one another. The combustor  128  is a suitable device (such as a catalytic start gas combustor) configured to receive (via the auxiliary ejector  126 , described below) and combust some or all of: (1) the fuel exhausted from the SOFC stack  116 ; (2) the oxidant exhausted from SOFC stack  116 ; and (3) fresh oxidant received from the oxidant supply  102 . While the combustor  128  and the auxiliary ejector  126  are shown as separate components in this example embodiment, in other embodiments the combustor and the auxiliary ejector are combined into a single component. 
     The oxidant flow control device  130  includes an oxidant inlet and an oxidant outlet (not labeled) in fluid communication with one another. The oxidant inlet is fluidly connectable to the oxidant supply  102  to enable the oxidant flow control device  130  to draw oxidant from the oxidant supply  102 . The oxidant flow control device  130  is any suitable device configured to (directly or indirectly) control the mass flow rate of the oxidant into the SOFC system  100 . The oxidant flow control device  130  may include, for instance, turbo-generators, turbochargers, an air compressor, a metering valve, or any other suitable system or component(s). 
     As shown in  FIG. 2 , the controller  132  includes a central processing unit (CPU) (not shown) communicatively connected to a memory (not shown). The CPU is configured to execute program code or instructions stored on the memory to control operation of various components of the SOFC system  100 . The CPU may be a microprocessor; a content-addressable memory; a digital-signal processor; an application-specific integrated circuit; a field-programmable gate array; any suitable programmable logic device, discrete gate, or transistor logic; discrete hardware components; or any combination of these. The CPU may also be implemented as a combination of these devices, such as a combination of a digital signal processor and a microprocessor, a plurality of microprocessors, or one or more microprocessors in conjunction with a digital signal processor core. 
     The memory is configured to store, maintain, and provide data as needed to support the functionality of the SOFC system  100 . For instance, in various embodiments, the memory stores program code or instructions executable by the CPU to control operation of the SOFC system  100 . The memory includes any suitable data storage device or devices, such as volatile memory (e.g., random-access memory, dynamic random-access memory, or static random-access memory); non-volatile memory (e.g., read-only memory, mask read-only memory, programmable read-only memory, erasable programmable read-only memory, electrically erasable programmable read-only memory); and/or non-volatile random-access memory (e.g., flash memory, solid-state storage). 
     As shown in  FIGS. 4-6 , the controller  132  also includes first, second, and third proportional-integral-derivative (PID) modules  132   a ,  132   b , and  132   c.    
     The temperature sensors  134   a ,  134   b , and  134   c  are thermocouples or any other suitable sensors configured to sense the temperature of the fluid or the components at locations T 1 , T 2 , and T 3 , respectively, in the SOFC system  100  (described below) and to generate and send signals that correspond to the sensed temperature to the controller  132 . 
     The fuel flow control device  136  includes a fuel inlet and a fuel outlet (not labeled) in fluid communication with one another. The fuel inlet is fluidly connectable to the fuel source  104  to enable the fuel flow control device  136  to draw fuel from the fuel source  104 . The fuel flow control device  136  is any suitable device configured to (directly or indirectly) control the mass flow rate of the fuel into the SOFC system  100 . The fuel flow control device  136  may include, for instance, a pump, a gas compressor, a metering valve, or any other suitable system or component(s). 
     The auxiliary fuel flow control device  138  includes an auxiliary fuel inlet and an auxiliary fuel outlet (not labeled) in fluid communication with one another. The auxiliary fuel inlet is fluidly connectable to the auxiliary fuel source  106  to enable the auxiliary fuel flow control device  138  to draw auxiliary fuel from the auxiliary fuel source  106 . The auxiliary fuel flow control device  138  is any suitable device configured to (directly or indirectly) control the mass flow rate of the auxiliary fuel into the oxidant heater  114 . The auxiliary fuel flow control device  138  may include, for instance, a pump, a gas compressor, a metering valve, or any other suitable system or component(s). 
     2. Connections 
     The oxidant inlet of the oxidant flow control device  130  is fluidly connectable to the oxidant source  102 . The oxidant outlet of the oxidant flow control device  130  is in fluid communication with the oxidant inlet of the cold side of the oxidant heat exchanger  110  and with the motive fluid inlet  126   a  of the auxiliary ejector  126 . 
     The oxidant inlet of the cold side of the oxidant heat exchanger  110  is in fluid communication with the oxidant outlet of the oxidant flow control device  130 . The oxidant outlet of the cold side of the oxidant heat exchanger  110  is in fluid communication with the motive fluid inlet  112   a  of the cathode ejector  112 . The combustion byproduct inlet of the hot side of the oxidant heat exchanger  110  is in fluid communication with the combustion byproduct outlet of the combustor  128 . The combustion byproduct outlet of the hot side of the oxidant heat exchanger  110  is in fluid communication with the suction fluid inlet  126   b  of the auxiliary ejector  126  and may be vented to the atmosphere after passing through the turbine of a turbo-generator (not shown) and a recuperator (not shown). 
     The motive fluid inlet  112   a  of the cathode ejector  112  is in fluid communication with the oxidant outlet of the cold side of the oxidant heat exchanger  110 . The suction fluid inlet  112   b  of the cathode ejector  112  is in fluid communication with the oxidant outlet of the SOFC stack  116 . The fluid outlet  112   c  of the cathode ejector  112  is in fluid communication with the oxidant inlet of the oxidant heater  114 . 
     The auxiliary fuel inlet of the auxiliary fuel flow control device  138  is fluidly connectable to the auxiliary fuel source  106 . The auxiliary fuel outlet of the auxiliary fuel flow control device  138  is in fluid communication with the auxiliary fuel inlet of the oxidant heater  114 . 
     The oxidant inlet of the oxidant heater  114  is in fluid communication with the fluid outlet  112   c  of the cathode ejector  112 . The oxidant outlet of the oxidant heater  114  is fluid communication with the oxidant inlet of the SOFC stack  116 . The auxiliary fuel inlet of the oxidant heater  114  is in fluid communication with the auxiliary fuel outlet of the auxiliary fuel flow control device  138 . 
     The oxidant inlet of the SOFC stack  116  is in fluid communication with the oxidant outlet of the oxidant heater  114 . The oxidant outlet of the SOFC stack  116  is in fluid communication with the suction fluid inlet  112   b  of the cathode ejector  112 . The fuel inlet of the SOFC stack  116  is in fluid communication with the fuel outlet of the fuel heat exchanger  124 . The fuel outlet of the SOFC stack  116  is in fluid communication with the suction fluid inlets  118   b  and  126   b  of the anode ejector  118  and the auxiliary ejector  126 , respectively. 
     The fuel inlet of the fuel flow control device  136  is fluidly connectable to the fuel source  104 . The fuel outlet of the fuel flow control device  136  is in fluid communication with the motive fluid inlet  118   a  of the anode ejector  118 . 
     The motive fluid inlet  118   a  of the anode ejector  118  is in fluid communication with the fuel outlet of the fuel flow control device  136 . The suction fluid inlet  118   b  of the anode ejector  118  is in fluid communication with the fuel outlet of the SOFC stack  116 . The fluid outlet  118   c  of the anode ejector  118  is in fluid communication with the fuel inlet of the pre-reformer  120 . 
     The fuel inlet of the pre-reformer  120  is in fluid communication with the fluid outlet  118   c  of the anode ejector  118 . The fuel outlet of the pre-reformer  120  is in fluid communication with the fuel inlet of the reformer  122  and with the fuel inlet of the fuel heat exchanger  124 . 
     The fuel inlet of the reformer  122  is in fluid communication with the fuel outlet of the pre-reformer  120 . The fuel outlet of the reformer  122  is in fluid communication with the fuel inlet of the fuel heat exchanger  124 . The oxidant inlet of the reformer  122  is in fluid communication with the oxidant outlet of the fuel heat exchanger  124 . The oxidant outlet of the reformer  122  is in fluid communication with the suction fluid inlet  126   b  of the auxiliary reformer  126 . 
     The fuel inlet of the fuel heat exchanger  124  is in fluid communication with the fuel outlet of the pre-reformer  120  and the fuel outlet of the reformer  122 . The fuel outlet of the fuel heat exchanger  124  is in fluid communication with the fuel inlet of the SOFC stack  116 . The oxidant inlet of the fuel heat exchanger  124  is in fluid communication with the oxidant outlet of the SOFC stack  116 . The oxidant outlet of the fuel heat exchanger  124  is in fluid communication with the oxidant inlet of the reformer  122 . 
     The motive fluid inlet  126   a  of the auxiliary ejector  126  is in fluid communication with the oxidant outlet of the oxidant flow control device  130 . The suction fluid inlet  126   b  of the auxiliary ejector  126  is in fluid communication with: (1) the fuel outlet of the SOFC stack  116 ; (2) the oxidant outlet of the reformer  122 ; and (3) the combustion byproduct outlet of the hot side of the oxidant heat exchanger  110 . The fluid outlet  126   c  of the auxiliary ejector  126  is in fluid communication with the combustion product inlet of the combustor  128 . 
     The combustion product inlet of the combustor  128  is in fluid communication with the fluid outlet  126   c  of the auxiliary ejector  126 . The combustion byproduct outlet of the combustor  128  is in fluid communication with the combustion byproduct inlet of the hot side of the oxidant heat exchanger  110 . 
     The first temperature sensor  134   a  is positioned upstream of the suction fluid inlet  112   b  of the cathode ejector  112  and downstream of the oxidant outlet of the SOFC stack  116  such that the first temperature sensor  134   a  can sense the temperature T 1  of fluid (here, oxidant) at that location. The second temperature sensor  134   b  is positioned downstream of the combustion byproduct outlet of the combustor  128  and upstream of the combustion byproduct inlet of the hot side of the oxidant heat exchanger  110  such that the second temperature sensor  134   b  can sense the temperature T 2  of fluid (here, combustion byproducts) at that location. The third temperature sensor  134   c  is positioned upstream of the oxidant inlet of the SOFC stack  116  and downstream of the oxidant outlet of the oxidant heater  114  such that the third temperature sensor  134   c  can sense the temperature T 3  of fluid (here, oxidant) at that location. 
     As shown in  FIG. 2 , the controller  132  is communicatively connected to the first, second, and third temperature sensors  134   a ,  134   b , and  134   c  to receive the signals from the temperature sensors that correspond to the sensed temperatures. 
     The controller  132  is operatively connected to the oxidant flow control device  130  to control the oxidant flow control device  130  by providing the oxidant flow control device  130  an oxidant flow control device set point OFCD SP . The OFCD SP  corresponds to a particular output of the oxidant flow control device  130  (such as a particular quantity of revolutions per minute if the oxidant flow control device is a turbine) that itself corresponds to a particular mass flow rate of oxidant into the SOFC system  100 . The controller  132  is therefore configured to control the mass flow rate of oxidant into the SOFC system  100  via the OFCD SP  the controller  132  provides to the oxidant flow control device  130 . 
     The controller  132  is operatively connected to the fuel flow control device  136  to (in certain operating modes) control the fuel flow control device  136  by providing the fuel flow control device  136  a fuel flow control device set point FFCD SP . The FFCD SP  corresponds to a particular output of the fuel flow control device  136  (such as a particular quantity of liters per minute if the fuel flow control device is a pump) that itself corresponds to a particular mass flow rate of fuel into the SOFC system  100 . The controller  132  is therefore configured to control the mass flow rate of fuel into the SOFC system  100  via the FFCD SP  the controller  132  provides to the fuel flow control device  136 . 
     The controller  132  is operatively connected to the auxiliary fuel flow control device  138  to (in certain operating modes) control the auxiliary fuel flow control device  138  by providing the auxiliary fuel flow control device an auxiliary fuel flow control device set point AFFCD SP . The AFFCD SP  corresponds to a particular output of the auxiliary fuel flow control device  138  (such as a particular quantity of liters per minute if the auxiliary fuel flow control device is a pump) that itself corresponds to an amount of heat the oxidant heater  114  provides to the oxidant. The controller  132  is therefore configured to control the amount of heat the oxidant heater  114  provides to the oxidant via the AFFCD SP  the controller  132  provides to the auxiliary fuel flow control device. 
     3. Operation 
     The SOFC system  100  is operable in an operating mode and a standby mode. Shut-down mode as used herein refers to a state in which the SOFC system  100  is not operating and is at ambient temperature. 
     When the SOFC system  100  is in operating mode, the SOFC stack  116  is at an operating temperature within a range of operating temperatures, such as between about 800 degrees centigrade and 1000 degrees centigrade, and the SOFC system  100  provides the oxidant to the cathode side of the SOFC stack  118  and fuel to the anode side of the SOFC stack  118 . The ensuing reactions generate electricity that is provided to the electrical load  300 . 
     When the SOFC system  100  is in standby mode, the SOFC stack  116  is at a standby temperature that may be within the range of operating temperatures (or below the range of operating temperatures), and the SOFC system  100  provides the oxidant to the cathode side of the SOFC stack  116  but does not provide fuel to the anode side of the SOFC stack  116 . This means that the SOFC stack  116  does not provide electrical power to the electrical load  300  in standby mode. To ensure the SOFC stack  116  remains at the operating temperature when in standby mode, the SOFC system  100  supplies auxiliary fuel to the oxidant heater  114  to heat the oxidant flowing into the SOFC stack  116 . 
     Generally, when oxidant flows through the SOFC system  100 , it does so as follows. The controller  132  is configured to control the oxidant flow control device  130  to draw oxidant from the oxidant source  102  and deliver the oxidant to the oxidant inlet of the cold side of the oxidant heat exchanger  110 . As the oxidant flows from the oxidant inlet to the oxidant outlet, relatively hot combustion byproducts (or oxidant, depending on the mode of operation) traveling through the hot side of the oxidant heat exchanger  110  (described below) heat the oxidant. The oxidant exits the oxidant outlet of the cold side of the oxidant heat exchanger  110  and flows into the motive fuel inlet  112   a  of the cathode ejector  112 . 
     The oxidant flows through the cathode ejector  112 , mixes with oxidant received at the suction fluid inlet  112   b , and flows out of the fluid outlet  112   c  to the oxidant inlet of the oxidant heater  114 . If the auxiliary fuel flow control device  138  is providing auxiliary fuel to the oxidant heater  114 , the oxidant heater  114  heats the oxidant as the oxidant flows from the oxidant inlet of the oxidant heater  114  to the oxidant outlet of the oxidant heater  114 . 
     The oxidant flows past the third temperature sensor  134   c  to the oxidant inlet of the SOFC stack  116 . The oxidant flows from the oxidant inlet of the SOFC stack  116  to the oxidant outlet of the SOFC stack  116 . The oxidant flows from the oxidant outlet of the SOFC stack  116 : (1) past the first temperature sensor  134   a  and to the suction fluid inlet  112   b  of the cathode ejector  112 ; or (2) to the oxidant inlet of the fuel heat exchanger  124 . As described above, the oxidant that flows to the suction fluid inlet  112   b  of the cathode ejector  112  mixes with oxidant received at the motive fluid inlet  112   a  and flows back to the oxidant heater  114 . 
     The oxidant that flows to the oxidant inlet of the fuel heat exchanger  124  flows through the fuel heat exchanger  124 , exits the oxidant outlet of the fuel heat exchanger  124 , and flows to the oxidant inlet of the reformer  122 . The oxidant flows through the reformer  122 , exits the oxidant outlet of the reformer  122 , and flows to the suction fluid inlet  126   b  of the auxiliary ejector  126 . 
     If fuel is not also flowing through the SOFC system  100 , the oxidant mixes with oxidant received from the oxidant heat exchanger  110  and is sucked through the auxiliary ejector  126  by oxidant received from the oxidant flow control device  130  at the motive fluid inlet  126   a . The oxidant flows out of the fluid outlet  126   c  to the combustion products inlet of the combustor  128 . Since no fuel is present in the oxidant, the oxidant flows through the combustor  128  without being ignited and past the second temperature sensor  134   b  and to the combustion byproducts inlet of the hot side of the oxidant heat exchanger  110 . As this relatively hot oxidant flows through the oxidant heat exchanger  110 , it heats the fresh oxidant flowing from the oxidant flow control device  130  to the cathode ejector  112 , as described above. After exiting the combustion byproducts outlet of the hot side of the oxidant heat exchanger  110 , some of the oxidant flows back to the suction fluid inlet  126   b  of the auxiliary ejector  126  and some of the oxidant is exhausted to atmosphere. 
     If fuel is also flowing through the SOFC system  100 , the oxidant at the suction fluid inlet  126   b  of the auxiliary ejector  126  mixes with combustion byproducts received from the oxidant heat exchanger  110   b  and is sucked through the auxiliary ejector  126  by oxidant received from the oxidant flow control device  130  at the motive fluid inlet  126   a . The oxidant/combustion byproducts mixture—referred to as combustion products—flows out of the fluid outlet  126   c  to the combustion products inlet of the combustor  128 . The combustor  128  ignites the combustion products to produce heated combustion byproducts, which flow from the combustion byproducts outlet of the combustor  128  past the second temperature sensor  134   b  and to the combustion byproducts inlet of the hot side  110   b  of the oxidant heat exchanger  110 . As these relatively hot combustion byproducts flow through the oxidant heat exchanger  110 , they heat the fresh oxidant flowing from the oxidant flow control device  130  to the cathode ejector  112 , as described above. After exiting the combustion byproducts outlet of the hot side  110   b  of the oxidant heat exchanger  110 , some of the combustion byproducts flow back to the suction fluid inlet  126   b  of the auxiliary ejector  126  and some of the combustion byproducts are exhausted to atmosphere. 
     Generally, when fuel flows through the SOFC system  100 , it does so as follows. The fuel flow control device  136  is configured to draw unreformed fuel from the fuel source  104  and deliver the unreformed fuel to the motive fluid inlet  118   a  of the anode ejector  118 . The unreformed fuel flows through the anode ejector  118 , mixes with fuel that is recycled from the fuel cell stack exhaust and received at the suction fluid inlet  118   b , and flows out of the fluid outlet  118   c  to the fuel inlet of the pre-reformer  120 . 
     The pre-reformer  120  removes higher hydrocarbons from the unreformed fuel to convert it into pre-reformed fuel. The reformed/pre-reformed fuel mixture flows out of the fuel outlet of the pre-reformer  120 , at which point some of the mixture flows into the fuel inlet of the cold side of the reformer  122  and some of the mixture bypasses the reformer  122  and flows directly to the fuel inlet of the fuel heater  124 . 
     As the mixture flows through the cold side of the reformer  122  from the fuel inlet to the fuel outlet, the relatively hot oxidant flowing through the hot side of the reformer  122  heats the mixture and the reformer  122  reforms the pre-reformed fuel portion of the mixture into reformed fuel via a catalyst. The reformed fuel flows from the fuel outlet of the reformer  122  and joins the pre-reformed fuel/reformed fuel mixture that bypassed the reformer  122  before flowing to the fuel inlet of the cold side of the fuel heater  124 . As the mixture flows through the cold side of the fuel heater  124 , the relatively hot oxidant flowing through the hot side of the fuel heater  124  heats the mixture before it exits the fuel outlet of the fuel heater  124  and flows to the fuel inlet of the SOFC stack  116 . 
     The pre-reformed/reformed fuel mixture flows through the SOFC stack  116  and from the fuel outlet of the SOFC stack  116  to: (1) the suction fluid inlet  118   b  of the anode ejector  118 ; and (2) the suction fluid inlet  126   b  of the auxiliary ejector  126 . The pre-reformed/reformed fuel mixture received at the suction fluid inlet  126   b  forms part of the combustion products the combustor  128  ignites, as described above. 
     Described below are methods for transitioning the SOFC system  100  from shut-down mode to standby mode, for transitioning the SOFC system  100  from standby mode to operating mode, and for operating the SOFC system  100  at operating mode. 
     3.1 Transitioning from Shut-Down Mode to Standby Mode 
     As shown in  FIG. 3 , upon initial startup of the SOFC system  100  from shut-down mode (and ambient temperature) to standby mode, the controller  132  is operable to raise the temperature T 3  to a standby temperature at a desired rate. The controller  132  is configured to do so by: (1) controlling the oxidant flow control device  130  to control the flow of oxidant into the SOFC system  100 ; and (2) controlling the auxiliary fuel flow control device  138  to control the flow of auxiliary fuel to the oxidant heater  114  and thus the amount of heat applied to the oxidant. Since fuel is not flowing through the SOFC system  100  during startup, the SOFC stack  116  does not supply electricity to the electrical load. 
     More specifically, the controller  132  is configured to provide an oxidant flow control device set point (OFCD SP ) (which may be stored in the memory of the controller  132 ) to the oxidant flow control device  130  to control the oxidant flow control device  130  to provide a corresponding mass flow rate of oxidant into the SOFC system  100 . The oxidant flows through the SOFC system  100  as generally described above. The controller  132  is also configured to provide an auxiliary fuel flow control device set point (AFFCD SP ) (which may be stored in the memory of the controller  132  or determined according to a predetermined function or using a PID feedback loop tied to T 3 ) to the auxiliary fuel flow control device  138  to control the auxiliary fuel flow control device  138  to increase the mass flow rate of the auxiliary fuel to the oxidant heater  114  (and thus the amount of heat applied to the oxidant in thermal communication with the oxidant heater  114 ) over time to enable controlled heating of the SOFC stack  116  to the operating temperature. 
     Once the temperature T 3  reaches the standby temperature (with no fuel flowing through the SOFC system  100 ), the SOFC system  100  is in standby mode, and the controller  132  is configured to control the oxidant flow control device  130  and the auxiliary fuel flow control device  138  to maintain the temperature T 3  at the standby temperature (such as via a PID feedback loop tied to T 3 ). 
     3.2 Transitioning from Standby Mode to Operating Mode 
     To transition the SOFC system  100  from standby mode to operating mode, the controller  132  is configured to ramp up the amount of fuel flowing through the SOFC system  100 , ramp up the amount of electricity provided to the electrical load, and taper off the amount of auxiliary fuel supplied to the oxidant heater while achieving and maintaining a temperature T 3  within the range of operating temperatures. 
     To do so, the controller  132  is configured to: (1) control the oxidant flow control device  130  to control the flow of oxidant into the SOFC system  100 ; (2) control the auxiliary fuel flow control device  138  to control the flow of auxiliary fuel to the oxidant heater  114  and thus the amount of heat applied to the oxidant; and (3) control the fuel flow control device  136  to control the flow of fuel into the SOFC system  100 . 
     More specifically, the controller  132  is configured to provide a generally constant OFCD SP  to provide a constant mass flow rate of oxidant into the SOFC system  100 . The oxidant flows through the SOFC system  100  as generally described above. 
     The controller  132  is also configured to determine the AFFCD SP  based on a PID feedback loop. In this embodiment, the controller  132  is configured to receive (via user input or via a lookup table stored on the memory of the controller  132 ) an SOFC stack inlet temperature set point T 3   SP , which represents a desired temperature of the oxidant just upstream of the oxidant inlet of the SOFC stack  116  and downstream of the oxidant outlet of the oxidant heater  114 . 
     The controller  132  is communicatively connected to the third temperature sensor  134   c  to receive a signal corresponding to the temperature T 3 , which represents the measured temperature of the oxidant just upstream of the oxidant inlet of the SOFC stack  116  and downstream of the oxidant outlet of the oxidant heater  114 . The controller  132  is configured to calculate the arithmetic mean, the median, or another average temperature T 3   MEAS  from multiple measured temperatures over a particular period of time (though in other embodiments T 3   MEAS  represents an instantaneous temperature reading). 
     The third PID module  132   c  is configured to calculate the difference (if any) between T 3   SP  and T 3   MEAS , and controls the output of the auxiliary fuel flow control device  138  to reduce the difference between T 3   SP  and T 3   MEAS . The third PID module  132   c  is configured to do so by using the difference between T 3   SP  and T 3   MEAS  to determine an AFFCD SP  that corresponds to an output of the auxiliary fuel flow control device  138  that will (via operation of the oxidant heater  114 ) reduce the difference between T 3   SP  and T 3   MEAS . In this embodiment, the controller  132  is therefore configured to modulate the output of the auxiliary fuel flow control device  138  to converge T 3   MEAS  to T 3   SP . The controller  132  is configured to provide the AFFCD SP  to the auxiliary fuel flow control device  138  to control the heat provided by the oxidant heater  114 . Generally, AFFCD SP  decreases over time as the SOFC stack  116  heats up because the chemical reactions in the SOFC stack  116  generate heat. 
     The controller  132  is also configured to determine and provide an FFCD SP  to the fuel flow control device  136  to control the fuel flow control device  136  (and therefore the mass flow rate of fuel into the SOFC system  100 ). The FFCD SP  varies in accordance with a current set point I SP  that corresponds to the amount of current the SOFC stack  116  is desired to supply to the electrical load. The I SP  and the FFCD SP  are related via a direct relationship such that the higher the I SP , the higher the FFCD SP . The fuel flows through the SOFC system  100  as generally described above. 
     Once the mass flow rate of the auxiliary fuel reaches zero, fuel is flowing through the SOFC system  100 , and the SOFC unit  116  is at the operating temperature, the SOFC system  100  is in the operating mode. 
     In other embodiments, the controller  132  determines T 3   SP  based on the I SP . That is, in these embodiments a relationship exists between T 3   SP  and the I SP . 
       FIG. 6  shows an alternative embodiment of the SOFC system employing a different way of transitioning from standby mode to operating mode. In this embodiment, the controller  132  is configured to determine the OFCD SP  based on a PID feedback loop. The third PID module  132   c  is configured to calculate the difference (if any) between T 3   SP  and T 3   MEAS , and controls the output of the oxidant flow control device  130  to reduce the difference between T 3   SP  and T 3   MEAS . The PID module  132   c  is configured to do so by using the difference between T 3   SP  and T 3   MEAS  to determine an OFCD SP  that corresponds to an output of the oxidant flow control device  130  that will reduce the difference between T 3   SP  and T 3   MEAS . In this embodiment, the controller  132  is therefore configured to modulate the output of the oxidant flow control device  130 —and therefore the mass flow rate of oxidant into the SOFC system  100 —to converge T 3   MEAS  to T 3   SP . 
     In this embodiment, the controller  132  is configured to determine (such as via a look-up table) and provide an FFCD SP  to the fuel flow control device  136  to control the fuel flow control device  136  (and therefore the mass flow rate of fuel into the SOFC system  100 ). The FFCD SP  varies in accordance with the I SP . The I SP  and the FFCD SP  are related via a direct relationship such that the higher the I SP , the higher the FFCD SP . Additionally, the controller  132  is configured to determine (such as via a look-up table) and provide an AFFCD SP  to the oxidant heater  114  to control the oxidant heater  114 . The AFFCD SP  varies in accordance with the I SP . The I SP  and the AFFCD SP  are related via a direct relationship such that the higher the I SP , the higher the AFFCD SP . 
     3.3 Operating Mode 
     When in the operating mode, the controller  132  is configured to maintain the temperature of the SOFC stack  116  at the operating temperature (or within a range of operating temperatures). The controller  132  is configured to do so by: (1) controlling the oxidant flow control device  130  to control the flow of oxidant into the SOFC system  100 ; and (2) controlling the fuel flow control device  136  to control the flow of fuel into the SOFC system  100 . 
     The controller  132  is configured to determine (such as via a look-up table) and provide an FFCD SP  to the fuel flow control device  136  to control the fuel flow control device  136  (and therefore the mass flow rate of fuel into the SOFC system  100 ). The FFCD SP  varies in accordance with the I SP . The I SP  and the FFCD SP  are related via a direct relationship such that the higher the I SP , the higher the FFCD SP . Regardless of the mass flow rate of the fuel, the fuel travels through the SOFC system  100  as generally described above for the transition operating mode. 
     The controller  132  is also configured to determine and provide an OFCD SP  to the oxidant flow control device  130  to control the oxidant flow control device  130  (and therefore the mass flow rate of oxidant into the SOFC system  100 ). In the operating mode, the controller  132  is configured to determine the OFCD SP  based on a PID feedback loop tied to T 1  and T 2  (described below). 
     With other factors held constant (as they generally are in the operating mode), the mass flow rate of the oxidant into the SOFC system  100  controls the temperature of the SOFC stack  116 . So in the operating mode, the controller  132  is configured to control the temperature of the SOFC stack  116  via controlling the output of the oxidant flow control device  130 . Generally, the higher the mass flow rate of the oxidant into the SOFC system  100 , the more the oxidant imparts a cooling effect on the SOFC stack  116  and the lower the temperature of the SOFC stack  116 . Conversely, the lower the mass flow rate of oxidant into the SOFC system  100 , the less the oxidant imparts a cooling effect on the SOFC stack  116  and the higher the temperature of the SOFC stack  116 . So if the temperature of the SOFC stack  116  is higher than desired, the controller  132  is configured to control the oxidant flow control device  130  to increase the mass flow rate of the oxidant into the SOFC system  100  to increase its cooling effect and lower the temperature of the SOFC stack  116 . Conversely, if the temperature of the SOFC stack  116  is lower than desired, the controller  132  is configured to control the oxidant flow control device  130  to decrease the mass flow rate of the oxidant into the SOFC system  100  to decrease its cooling effect and increase the temperature of the SOFC stack  116 . 
     In the operating mode, the controller  132  is configured to determine the OFCD SP  based on a PID feedback loop. The first PID module  132   a  is configured to receive a cathode ejector temperature set point T 1   SP , which represents a desired temperature of the oxidant upstream of the suction fluid inlet  112   b  of the cathode ejector  112  and downstream of the oxidant outlet of the SOFC stack  116 . The first PID module  132   a  may receive T 1   SP  via user input or via a lookup table stored on the memory of the controller  132 . In certain embodiments the controller determines T 1   SP  based on the I SP . 
     The first PID module  132   a  is communicatively connected to the first temperature sensor  134   a  to receive a signal corresponding to the temperature T 1 , which is the measured temperature of the oxidant upstream of the suction fluid inlet  112   b  of the cathode ejector  112  and downstream of the oxidant outlet of the SOFC stack  116 . The controller  132  is configured to calculate the arithmetic mean, the median, or another average temperature T 1   MEAS  from multiple measured temperatures over a particular period of time (though in other embodiments T 1   MEAS  represents an instantaneous temperature reading). 
     The first PID module  132   a  is configured to calculate the difference (if any) between T 1   SP  and T 1   MEAS  and to calculate T 2   SP  based on that difference. T 2   SP  represents a desired temperature of the combustion byproducts downstream of the combustion byproducts outlet of the combustor  128  and upstream of the combustion byproducts inlet of the hot side of the oxidant heat exchanger  110 . The first PID module  132   a  is configured to send T 2   SP  to the second PID module  132   b.    
     The second PID module  132   b  is communicatively connected to the second temperature sensor  132   b  to receive a signal representing the temperature T 2 , which is the measured temperature of the combustion byproducts downstream of the combustion byproducts outlet of the combustor  128  and upstream of the combustion byproducts inlet of the hot side of the oxidant heat exchanger  110 . The controller  132  is configured to calculate the arithmetic mean, the median, or another average temperature T 2   MEAS  from multiple measured temperatures over a particular period of time (though in other embodiments T 2   MEAS  represents an instantaneous temperature reading). 
     The second PID module  132   b  is configured to determine the difference (if any) between T 2   SP  and T 2   MEAS  and to calculate the OFCD SP  based on that difference. The OFCD SP  corresponds to a particular mass flow rate of oxidant into the SOFC system  100  required to bring T 2   MEAS  to T 2   SP  and T 1   MEAS  to T 1   SP , thereby bringing the temperature of the SOFC stack  116  to the desired temperature. The controller  132  is configured to provide the OFCD SP  to the oxidant flow control device  130  to control the oxidant flow control device  130  to draw oxidant from the oxidant source  102 . Regardless of the mass flow rate of the oxidant, the oxidant travels through the SOFC system  100  as generally described above for the startup operating mode. 
     The controller  132  is therefore configured to modulate the output of the oxidant flow control device  130  based on fluid temperature measurements taken outside of the SOFC stack  116  to maintain the temperature of the SOFC stack  116  at a desired temperature (or within a desired temperature range). This is more beneficial than using temperature measurements taken at the SOFC stack  116  to determine how to modulate the output of the oxidant flow control device  130  to achieve a desired temperature in the SOFC stack because it provides a quicker response time. The SOFC stack  116  is slow to respond to thermal changes as compared to the oxidant at T 1  and T 2 . 
     According to aspects of the present disclosure, a method is presented of operating a fuel cell system comprising a fuel cell stack comprising multiple fuel cells each comprising an anode and a cathode. The method comprises providing, by an oxidant flow control device and at a substantially constant oxidant mass flow rate, an oxidant to the cathodes; sensing, by a temperature sensor, a temperature of the oxidant upstream of the fuel cell stack and sending, by the temperature sensor, a signal representing the sensed temperature to a controller; controlling, by the controller and based on the sensed temperature, an amount of heat an oxidant heater provides to the oxidant to heat the oxidant; and providing, by a fuel flow control device and at a fuel mass flow rate, a fuel to the anodes. 
     In some embodiments the method further comprises providing, by the fuel cell stack, an electrical current to an electrical load. In some embodiments the method further comprises controlling, by the controller, the provision of the electrical current to the electrical load based on an electrical current set point. In some embodiments the method further comprises controlling, by the controller, the fuel flow control device to provide the fuel to the anodes. In some embodiments the method further comprises determining, by the controller, the fuel mass flow rate based on the electrical current set point and controlling, by the controller, the fuel flow control device to provide the fuel to the anodes at the determined fuel mass flow rate. 
     In some embodiments a first electrical current set point corresponds to a first fuel mass flow rate and a second electrical current set point that is greater than the first electrical current set point corresponds to a second fuel mass flow rate that is greater than the first fuel mass flow rate. In some embodiments the method further comprises controlling, by the controller, the oxidant flow control device to provide the oxidant to the cathodes and controlling, by the controller, the fuel flow control device to provide the fuel to the anodes. 
     In some embodiments the method further comprises controlling, by the controller and based on the sensed temperature, the amount of heat the oxidant heater provides to the oxidant to heat the oxidant by controlling, by the controller, a mass flow rate of an auxiliary fuel output by an auxiliary fuel flow control device to the oxidant heater. In some embodiments the method further comprises determining, by the controller, a difference between the sensed temperature and a temperature set point and controlling, by the controller, the mass flow rate of the auxiliary fuel provided by the auxiliary fuel flow control device to the oxidant heater to reduce the difference between the sensed temperature and the temperature set point. 
     In some embodiments determining the difference between the sensed temperature and the temperature set point comprises determining, by a proportional-integral-derivative (PID) module of the controller, the difference between the sensed temperature and the temperature set point. 
     According to another aspect of the present disclosure, a fuel cell system comprises a fuel cell stack, an oxidant control device, a fuel flow control device, a temperature sensor, an oxidant heater, and a controller. The fuel cell stack comprises multiple fuel cells each comprising an anode and a cathode. The oxidant flow control device is in fluid communication with the cathodes and configured to provide an oxidant at an oxidant mass flow rate to the cathodes. The fuel flow control device is in fluid communication with the anodes and configured to provide a fuel at a fuel mass flow rate to the anodes. The temperature sensor is configured to sense a temperature of the oxidant upstream of the fuel cell stack. The oxidant heater is configured to heat the oxidant upstream of the fuel cell stack. The controller is configured to control the oxidant flow control device to provide the oxidant to the cathodes such that the oxidant mass flow rate is substantially constant; control, based on the sensed temperature, an amount of heat the oxidant heater provides to the oxidant to heat the oxidant; and control the fuel flow control device to provide the fuel to the anodes. 
     In some embodiments the fuel cell stack is electrically connectable to an electrical load and configured to provide an electrical current to the electrical load. In some embodiments the controller is further configured to control the provision of the electrical current to the electrical load based on an electrical current set point. In some embodiments the controller is further configured to determine the fuel mass flow rate based on the electrical current set point and to control the fuel flow control device to provide the fuel to the anodes at the determined fuel mass flow rate. In some embodiments a first electrical current set point corresponds to a first fuel mass flow rate and a second electrical current set point that is greater than the first electrical current set point corresponds to a second fuel mass flow rate that is greater than the first fuel mass flow rate. 
     In some embodiments the fuel cell system further comprises an auxiliary fuel flow control device in fluid communication with the oxidant heater and configured to provide an auxiliary fuel at an auxiliary fuel mass flow rate to the oxidant heater. In some embodiments the controller is further configured to control the amount of heat the oxidant heater provides to the oxidant to heat the oxidant by controlling the auxiliary fuel mass flow rate. In some embodiments the controller is further configured to determine a difference between the sensed temperature and a temperature set point and control the auxiliary fuel mass flow rate to reduce the difference between the sensed temperature and the temperature set point. In some embodiments a proportional-integral-derivative (PID) module of the controller is configured to determine the difference between the sensed temperature and the temperature set point. 
     Various modifications to the embodiments described herein will be apparent to those skilled in the art. These modifications can be made without departing from the spirit and scope of the present disclosure and without diminishing its intended advantages. It is intended that such changes and modifications be covered by the appended claims.