Performance analysis of solid oxide fuel cell and micro gas turbine top-level cycle

. First, a simulation model of the SOFC-MGT top-level combined cycle was established through Matlab/Simulink, and then the effect of different methane flow rates on the performance of the stack and the SOFC-MGT system was analyzed. The research results show that with the increase of methane flow, the power of the stack and SOFC-MGT system gradually increases, but the efficiency of the SOFC-MGT system gradually decreases with the increase of methane flow.


Introduction
The efficiency of traditional gas turbines is limited by the "Carnot cycle", and the fuel utilization rate is only about 30%. Most of the energy is lost in the form of heat. How to improve the efficiency of gas turbines has always been the focus of research. A fuel cell is a device that directly converts the chemical energy of hydrogen energy and other fuels into electrical energy. It has many advantages such as noiseless, high efficiency, and pollution-free [1,2] . Solid oxide fuel cell (SOFC) is a medium-high temperature fuel cell. Its stack working temperature is about 600 ℃~1000 ℃ , and the exhaust gas emission temperature is about 600℃, and it has high quality can be reused [3] . Because fuel cells are not restricted by the "Carnot cycle", their energy utilization rate is much higher than that of traditional heat engines, usually between 60% and 80%. Therefore, if the two can be effectively combined to form a fuel cell and gas turbine combined cycle system, the operating efficiency of the gas turbine will be greatly improved. The solid oxide fuel cell and micro gas turbine (SOFC-MGT) combined cycle has two main structures: one is the bottom cycle mode; the other is the top cycle mode.
Lv [4] established an IT-SOFC-MGT top-level cycle simulation model to analyze the influence of water vapor content on system performance. Zhan [5] established a dualreactor SOFC-MGT bottom cycle simulation model, and analyzed the impact of different SOFC reactor connection methods on system performance. Zhu [6] established a SOFC-MGT top-level loop simulation model based on Matlab /Simulink software, and analyzed the impact of high back pressure (1.7kg/cm2) on system performance. Saisirirat [7] used MATLAB simulation software to establish a detailed thermodynamic model of the SOFC-GT hybrid system, and proposed two structures of the SOFC-GT hybrid cycle.
At present, scholars have conducted many researches on SOFC anode catalysts, electrolytes and other materials, but there are few studies on the combination of SOFC-MGT. Therefore, this article combines the existing 1kW SOFC in the laboratory to carry out the top-level circulation structure of SOFC-MGT. The analysis and research provide theoretical support for the industrial application of SOFC-MGT.

Assumptions
In this paper, the following assumptions are made when modelling the SOFC-MGT dynamics.
-All gases are ideal -The heat exchange between the system and the outside world is ignored -The reforming reaction and the water-gas replacement reaction are in equilibrium -The temperature, gas components and pressure in the system are uniformly distributed.
-The system is modelled using centralised parameters. The SOFC-MGT top cycle structure is shown in Figure  1.

Pre-reformer model
In the pre-reformer, which mainly consists of the reforming reaction of methane and the water-gas replacement reaction, the chemical reaction equations are as follows [8] . 4 2 2 (2) From the equation for conservation of mass we get [5] In the above equation, 1 P is the average pressure inside the pre-reformer, re V is the volume of the prereformer, 5 T is the average temperature of the prereformer, R is the universal gas constant x is the molar mass fraction of the exit gas, Assuming that both the reforming and water-gas replacement reactions have reached equilibrium, the equilibrium constants can be expressed as [9] respectively：   In the above equations, r K and s K are the equilibrium constants for the reforming and water-gas replacement reactions respectively.

Electrochemical model
The actual voltage of a fuel cell monolith can be represented by the following equation. T is the temperature of the stack.

Temperature model
According to the above assumptions, neglecting the heat exchange between the reactor and the outside world, the conservation of energy equation yields [11] In the above equations, Q is the heat of water-gas replacement reaction, 3 Q is the heat of electrochemical reaction.

Pressurised gas turbine model
Compressor pressure ratio  is： The compressor outlet temperature can be expressed as:

Turbine model
The micro gas turbine uses a centripetal turbine, which has the advantages of simple structure, large enthalpy drop in a single stage and wide operating range [12] . The turbine expansion ratio is: The turbine efficiency characteristics can be expressed as: In the above equation, 9 G is turbine inlet flow, 9 p is turbine inlet pressure, 9 T is turbine inlet temperature, T  is turbine speed. So far, the mathematical model of the SOFC-MGT combined cycle system has been established, and the simulation model of the new SOFC-MGT bottom cycle system has been obtained through Matlab/Simulink simulation.

Performance analysis
The laboratory has an existing 1kW solid oxide fuel cell experimental system, as shown in Fig.2. Through simulation and experimental testing, the voltampere characteristic curve of SOFC is shown in Fig.3:   Fig.3 Volt-ampere characteristic curve of SOFC As can be seen from the figure, the simulation model built in this paper is in good agreement with the experimental test data. When the output current is less than the rated output current of 43A, the maximum error between the simulation model and the experimental test data is 4.7%.
Through simulation, the volt-ampere characteristic curve and fuel cell power characteristic curve of the fuel cell under different methane flow rates are obtained, as shown in Figs 4 and 5: It can be seen from Fig.4 and Fig.5 that with the increase of methane flow, the output voltage and power of SOFC have increased. The larger the output current of SOFC, the increase of methane flow will greatly improve the output performance of the stack. However, the increase of methane flow will increase the internal pressure of the stack, which puts forward higher requirements on the sealing performance of the stack.
The system power characteristic curve of the SOFC-MGT top-level cycle is shown in Fig.6 under different methane flow rates obtained through simulation. It can be seen from Fig.6 that with the increase of methane flow, the power of the SOFC-MGT system has increased. At the same time, the larger the output current of the stack, the greater the impact of the increase of methane flow on the output performance of the SOFC-MGT system.
The system efficiency characteristic curve of the SOFC-MGT top-level cycle is shown in Fig.7 under different methane flow rates obtained through simulation. The greater the methane flow rate, the lower the efficiency of the system. This is because with the increase of methane flow, the maximum power of the stack gradually increases, and the maximum discharge current corresponding to the stack gradually increases, which makes the losses of the stack gradually increase, resulting in a gradual decrease in the efficiency of the system.

Conclusions
Through the simulation analysis of the SOFC-MGT combined cycle structure designed in this paper, the following conclusions are obtained: • The SOFC-MGT simulation model established in this paper is correct, and the SOFC-MGT top-level combined cycle structure is feasible.
• As the methane flow rate increases, the output performance of the SOFC gradually increases. The larger the methane flow rate, the better the output performance.
• The greater the output current of the stack, the more obvious the effect of the increase in methane flow on the performance of the stack.
• With the increase of methane flow, the output performance of the SOFC-MGT system gradually increases, but the efficiency of the SOFC-MGT system gradually decreases.