Part-load, startup, and shutdown strategies of a solid oxide fuel cell-gas turbine hybrid system

Abstract

Current work on the performance of a solid oxide fuel cell (SOFC) and gas turbine hybrid system is presented. Each component model developed and applied is mathematically defined. The electrochemical performance of single SOFC with different fuels is tested. Experimental results are used to validate the SOFC mathematical model. Based on the simulation model, a safe operation regime of the hybrid system is accurately plotted first. Three different part-load strategies are introduced and used to analyze the part-load performance of the hybrid system using the safe regime. Another major objective of this paper is to introduce a suitable startup and shutdown strategy for the hybrid system. The sequences for the startup and shutdown are proposed in detail, and the system responses are acquired with the simulation model. Hydrogen is used instead of methane during the startup and shutdown process. Thus, the supply of externally generated steam is not needed for the reforming reaction. The gas turbine is driven by complementary fuel and supplies compressed air to heat up or cool down the SOFC stack operating temperature. The dynamic simulation results show that smooth cooling and heating of the cell stack can be accomplished without external electrical power.

Keywords

solid oxide fuel cell (SOFC) / hybrid system / part-load strategy / startup / shutdown

Introduction

High-temperature solid oxide fuel cells (SOFCs) seem to be the most efficient device to convert fuel chemical energy into electricity directly [1]. Its efficiency can further be increased through integration with a gas turbine (GT). This kind of hybrid SOFC-GT power plant is an attractive near-term option for energy generation, as it can allow efficiencies of over 60%, even for small power outputs (200-400 kW) [2].

However, to become more competitive and efficient compared with traditional energy technologies, SOFC-GT hybrid systems need to tackle a variety of significant problems. Such problems include system integration and suitable part-load, startup, and shutdown operational methods. Due to its complicated system configurations and interactive subsystems, the hybrid system may be damaged because of unsafe issues at some regimes. Thus, operational boundaries regarding safety issues must be confirmed.

The objective of this paper is to discuss a methane-based SOFC-GT hybrid system in which detailed simulation models of each component are mathematically defined. An anode-supported planar SOFC performance operating with H₂ and CH₄ are tested. The SOFC model is validated using experimental cell performance results. The GT model is based on the compressor and turbine performance map supplied by the manufacturer. Based on the simulation models, the safe operation regime of hybrid is accurately plotted and the part-load performance of the hybrid system is discussed with three different operating strategies. This study also introduces a suitable startup and shutdown strategy of the hybrid system. The responses of the hybrid system during startup and shutdown processes are acquired. Smooth cooling and heating of the SOFC stack can be accomplished without external electrical power.

System configurations

The SOFC-GT hybrid system is illustrated in Fig. 1, which mainly includes an SOFC subsystem, a GT subsystem, two exchangers, a combustor, and a pre-reformer. The working principle of the plant is described as follows.

Compressed air is preheated with two heat exchangers (HE1 and HE2) before entering the cathode of the SOFC stack. In the anode compartment, fuel is mixed with anode re-circulated stream before entering the pre-former. After being preheated and partly reformed, fuel is carried to the anode of the SOFC stack, where internal reformation occurs. This releases hydrogen, which is brought to three-phase boundaries (TPBs). Preheated compressed air is fed to the cathode of the stack, and is involved in the electrochemical reaction, occurring at the TPB of both electrodes. This produces an ionic flow through the electrolyte and electron across the electrodes [3]. Hence, electrical energy is produced, associated with heat generation during the process. The heat generated is partly used to reform the fuel, partly dissipated to the environment, and partly used to heat up feedstock gases. Excess air and un-reacted fuel are burnt within the combustor to increase stream temperature partly. HE2 and a bypass valve are placed between the combustor and the turbine to adjust turbine inlet temperature (TIT) and cathode inlet temperature. The high temperature-pressured gas then expands in the turbine and produces mechanical energy. This drives the air compressors and the directly coupled electrical generator. High temperature turbine exhaust can be used to preheat the compressed air through HE1.

Experimental studies——Single SOFC performance test

The single SOFC used in this study is an anode-supported planar electrochemical fuel cell consisting of a 15 μm 10Sc1CeSZ electrolyte fabricated by tap casting. A 1000 μm thick NiO/10Sc1CeSZ anode and a 50 μm thick La_0.6Sr_0.4CoO_3-d cathode are screen printed onto each side of the electrolyte. The cross-sectional areas of the electrolyte and each electrode are 25 cm² (5 cm × 5 cm) and 16 cm² (4 cm × 4 cm), respectively.

The single cell performance is characterized by measuring the cell potential as a function of current density. The fabricated single SOFC and IT-SOFC performance experimental system are demonstrated in Fig. 2. When the single cell is placed into the heat furnace, the anode portion of the SOFC is placed on a nickel mesh collector, while the cathode is place on a platinum mesh. A 1000 g weight is placed on top of the platinum mesh to ensure it is in good contact with the cell, which also helps reduce contact resistance between the SOFC and the current collector [4]. A highly porous alumina layer is placed between the weight and the platinum mesh. This allows air to reach the cathode reaction site uniformly underneath the weight. The cathode portion is directly exposed to ambient air for air to flow to the cell via natural convection. The entire test cell rig is contained inside a temperature-controlled furnace to ensure that it could be operated under isothermal conditions.

Mathematical models

SOFC model

The SOFC model in Fig. 3 is based on a planar design and is developed on the following assumptions.

1) Gas flows are modeled as plug flows.

2) Laminar flow is assumed in heat transfer models.

3) Shift reaction is assumed to be always at equilibrium.

4) All heat sources and sinks derived from the reactions attack at the anode surface.

The SOFC model consists of electrochemical and thermal models. The thermodynamic model is developed, which includes convectional heat transfer equations, heat radiation equations, and heat conduction equations. Kinetics of reforming, water-gas shifting, and electrochemical reactions are included in the electrochemical model.

In the SOFC, the electric power is generated through the following reactions.

The reaction rate of the steam reforming reaction can be calculated by Eq. (1) [5]:

(1){\dot{r}}_{\mathrm{Re}\mathrm{f}(I)}=\mathrm{4274}{\mathrm{e}}^{-\frac{\mathrm{82000}}{R\cdot T_{\mathrm{P}\mathrm{E}\mathrm{A}}(x)}}{x}_{\mathrm{F}\mathrm{u}}(x,\mathrm{C}{\mathrm{H}}_{\mathrm{4}}){\displaystyle \frac{p_{\mathrm{F}\mathrm{u},\mathrm{R}\mathrm{e}\mathrm{f}}}{{\mathrm{10}}^{\mathrm{6}}\mathrm{P}\mathrm{a}}}{A}_{\mathrm{e}\mathrm{l}}\mathrm{.}

The reaction rate of the shift reaction can be calculated by:

(2){\dot{r}}_{\mathrm{S}\mathrm{h}\mathrm{i}}(x)={\mathrm{10}}^{\mathrm{4}}[x_{\mathrm{F}\mathrm{u}}(x,\mathrm{C}\mathrm{O})x_{\mathrm{F}\mathrm{u}}(x,{\mathrm{H}}_{\mathrm{2}}\mathrm{O})-{\displaystyle \frac{x_{\mathrm{F}\mathrm{u}}(x,{\mathrm{H}}_{\mathrm{2}})x_{\mathrm{F}\mathrm{u}}(x,\mathrm{C}{\mathrm{O}}_{\mathrm{2}})}{K_{\mathrm{S}\mathrm{h}\mathrm{i}}(x)}}],

where K_{\mathrm{S}\mathrm{h}\mathrm{i}} can be calculated by

(3)\ln (K_{\mathrm{S}\mathrm{h}\mathrm{i}}(x))=-{\displaystyle \frac{g^{\mathrm{0}}({\mathrm{H}}_{\mathrm{2}})+g^{\mathrm{0}}(\mathrm{C}{\mathrm{O}}_{\mathrm{2}})-g^{\mathrm{0}}(\mathrm{C}\mathrm{O})-g^{\mathrm{0}}({\mathrm{H}}_{\mathrm{2}}\mathrm{O})}{R_{\mathrm{m}}{T}_{\mathrm{P}\mathrm{E}\mathrm{A}}(x)}}.

The electrochemical reaction rate is calculated from the distributed current density:

(4){\dot{r}}_{\mathrm{E}\mathrm{l}\mathrm{c}}(x)={\displaystyle \frac{I(x)A_{\mathrm{e}\mathrm{l}}}{\mathrm{2}F}}.

For SOFC, electrochemical models are coupled with heat and mass transfer models to determine the distribution of local current density and electrode over potentials inside the SOFC.

The relationship between cell current density and voltage is written as

(5)I={\displaystyle \frac{U_{\mathrm{o}\mathrm{c}\mathrm{p}}-U_{\mathrm{o}\mathrm{p}}}{R_{\mathrm{o}\mathrm{h}\mathrm{m}}+R_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}\mathrm{e}}+R_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}\mathrm{o}\mathrm{d}\mathrm{e}}}},

where U_{\mathrm{o}\mathrm{c}\mathrm{p}} is the function of SOFC operation temperature and gas partial pressure in the anode and the cathode, which can be regulated as

(6)U_{\mathrm{o}\mathrm{c}\mathrm{p}}=U_{{\mathrm{H}}_{\mathrm{2}}}^{\mathrm{0}}+{\displaystyle \frac{RT}{\mathrm{2}F}}\ln \left({\displaystyle \frac{p_{\mathrm{f},{\mathrm{H}}_{\mathrm{2}}}{p}_{\mathrm{a},{\mathrm{O}}_{\mathrm{2}}}^{\mathrm{0.5}}}{p_{\mathrm{f},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}}}\right)+{\displaystyle \frac{RT}{\mathrm{4}F}}\ln \left({\displaystyle \frac{\mathrm{1}}{p_{\mathrm{s}\mathrm{t}\mathrm{d}}}}\right),

where

(7)U_{{\mathrm{H}}_{\mathrm{2}}}^{\mathrm{0}}=\mathrm{1.2723}-\mathrm{2.7645}\mathrm{e}-\mathrm{4}T.

U_{{\mathrm{H}}_{\mathrm{2}}}^{\mathrm{0}} is the ideal voltage for hydrogen oxidization [6] and p_{\mathrm{s}\mathrm{t}\mathrm{d}} is standard pressure.

The output power density of SOFC can be calculated by

(8)P_{\mathrm{S}\mathrm{O}\mathrm{F}\mathrm{C}}=U\times I.

As both electrodes are normally good conductors, a constant cell operation voltage

U_{\mathrm{op}}

throughout the cell is normally considered [7].

Ohmic losses are caused by the resistance to the conduction of ions and electrons, and the contact resistance between cell components.

(9)R_{\mathrm{o}\mathrm{h}\mathrm{m}}={\rho }_{\mathrm{e}}{\delta }_{\mathrm{e}}+{\rho }_{\mathrm{c}}{\delta }_{\mathrm{c}}+{\rho }_{\mathrm{a}}{\delta }_{\mathrm{a}}.

The activation polarization terms are controlled by the electrode reaction kinetics of the respective electrodes. These represent voltage loss incurred due to the necessary activation for charge transfer. Over potentials at the cathode and anode are assumed independent of the local current density. The model derived by Achenbach is adopted in this paper [8].

Both fuel reforming and water-gas shift reactions are endothermic, and the required heat of the reactions is calculated by

(10)\mathrm{\Delta }{h}_{\mathrm{Re}\mathrm{f}}=\mathrm{3}(\mathrm{0}+h({\mathrm{H}}_{\mathrm{2}}))+(h_{\mathrm{f}}^{\mathrm{0}}(\mathrm{C}\mathrm{O})+h(\mathrm{C}\mathrm{O}))-(h_{\mathrm{f}}^{\mathrm{0}}(\mathrm{C}{\mathrm{H}}_{\mathrm{4}})+h(\mathrm{C}{\mathrm{H}}_{\mathrm{4}}))-(h_{\mathrm{f}}^{\mathrm{0}}({\mathrm{H}}_{\mathrm{2}}\mathrm{O})+h({\mathrm{H}}_{\mathrm{2}}\mathrm{O})),

(11)\mathrm{\Delta }{h}_{\mathrm{S}\mathrm{h}\mathrm{i}}=\mathrm{3}(\mathrm{0}+h({\mathrm{H}}_{\mathrm{2}}))+(h_{\mathrm{f}}^{\mathrm{0}}(\mathrm{C}\mathrm{O})+h(\mathrm{C}\mathrm{O}))-(h_{\mathrm{f}}^{\mathrm{0}}(\mathrm{C}\mathrm{O})+h(\mathrm{C}\mathrm{O}))-(h_{\mathrm{f}}^{\mathrm{0}}({\mathrm{H}}_{\mathrm{2}}\mathrm{O})+h({\mathrm{H}}_{\mathrm{2}}\mathrm{O})).

Part of the enthalpy change is turned into electric power for the electrochemical reaction.

(12)\mathrm{\Delta }{h}_{\mathrm{E}\mathrm{l}\mathrm{c}}=(h_{\mathrm{f}}^{\mathrm{0}}({\mathrm{H}}_{\mathrm{2}}\mathrm{O})+h({\mathrm{H}}_{\mathrm{2}}\mathrm{O}))-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}(h_{\mathrm{f}}^{\mathrm{0}}({\mathrm{O}}_{\mathrm{2}})+h({\mathrm{O}}_{\mathrm{2}}))-(\mathrm{0}+h({\mathrm{H}}_{\mathrm{2}}))+\mathrm{2}UF.

SOFC heat transfer model is complex. It includes convectional transfer between gas and solids as well as radiation and conduction between solid materials. Detailed thermal transfer equations are listed as follows.

Heat convection between the interconnector and the fuel:

(13)Q_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C},\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}}}[k_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}.\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}(T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}-T_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}})].

Heat convection between the interconnector and air:

(14)Q_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C},\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}}}[k_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}.\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}(T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}-T_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}})].

Heat transfer between the interconnector and the PEN by radiation:

(15)Q_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C},\mathrm{P}\mathrm{E}\mathrm{N}(R)}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}}}{\displaystyle \frac{\sigma (T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}^{\mathrm{4}}-T_{\mathrm{P}\mathrm{E}\mathrm{N}}^{\mathrm{4}})}{\mathrm{1}/{ϵ}_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}+\mathrm{1}/{ϵ}_{\mathrm{P}\mathrm{E}\mathrm{N}}-\mathrm{1}}}.

Heat conduction of the interconnector:

(16)Q_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C},\mathrm{P}\mathrm{E}\mathrm{N}(C)}={\lambda }_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}{\displaystyle \frac{{\partial }^{\mathrm{2}}{T}_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}}{\partial x^{\mathrm{2}}}}.

Heat transfer by mass transfer in the anode channel:

(17)Q_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{P}\mathrm{E}\mathrm{N}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}}{\displaystyle \sum _{i={\mathrm{H}}_{\mathrm{2}},{\mathrm{H}}_{\mathrm{2}}\mathrm{O},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{\nu }_i{R}_{\mathrm{e}\mathrm{l}\mathrm{c}}{H}_i}.

Heat transfer between the anode fuel and the PEN:

(18)Q_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{P}\mathrm{E}\mathrm{N}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}}{k}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{P}\mathrm{E}\mathrm{N}}(T_{\mathrm{P}\mathrm{E}\mathrm{N}}-T_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}).

Heat transfer between the anode fuel and the interconnector:

(19)Q_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}}{k}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}(T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}-T_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}).

Heat conduction of the PEN:

(20)Q_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C},\mathrm{P}\mathrm{E}\mathrm{N}}={\lambda }_{\mathrm{P}\mathrm{E}\mathrm{N}}{\displaystyle \frac{{\partial }^{\mathrm{2}}{T}_{\mathrm{P}\mathrm{E}\mathrm{N}}}{\partial x^{\mathrm{2}}}}.

Heat transfer between the anode gas and the PEN:

(21)Q_{\mathrm{P}\mathrm{E}\mathrm{N},\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{P}\mathrm{E}\mathrm{N}}}}{k}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{P}\mathrm{E}\mathrm{N}}(T_{\mathrm{P}\mathrm{E}\mathrm{N}}-T_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}).

Heat transfer between the cathode gas and the PEN:

(22)Q_{\mathrm{P}\mathrm{E}\mathrm{N},\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{P}\mathrm{E}\mathrm{N}}}}{k}_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{P}\mathrm{E}\mathrm{N}}(T_{\mathrm{P}\mathrm{E}\mathrm{N}}-T_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}).

Heat transfer through the PEN by mass transfer:

(23)Q_{\mathrm{P}\mathrm{E}\mathrm{N},\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{P}\mathrm{E}\mathrm{N}}}}\left({\displaystyle \sum _{i={\mathrm{H}}_{\mathrm{2}},{\mathrm{H}}_{\mathrm{2}}\mathrm{O},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{v}_i{R}_{\mathrm{E}\mathrm{C}}{h}_i}-{\displaystyle \sum _{i={\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{v}_i{R}_{\mathrm{E}\mathrm{C}}{h}_i}\right).

Heat transfer between the interconnector and the cathode gas:

(24)Q_{\mathrm{P}\mathrm{E}\mathrm{N},\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}(R)}={\displaystyle \frac{\mathrm{1}}{{\tau }_{\mathrm{P}\mathrm{E}\mathrm{N}}}}{\displaystyle \frac{\sigma (T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}^{\mathrm{4}}-T_{\mathrm{P}\mathrm{E}\mathrm{N}}^{\mathrm{4}})}{\mathrm{1}/{ϵ}_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}+\mathrm{1}/{ϵ}_{\mathrm{P}\mathrm{E}\mathrm{N}}-\mathrm{1}}}.

Heat transfer in the cathode channel by mass transfer:

(25)Q_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{P}\mathrm{E}\mathrm{N}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}}{\displaystyle \sum _{i={\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{\nu }_i{R}_{\mathrm{E}\mathrm{C}}{h}_i}.

Heat transfer between the cathode channel and the interconnector by convection:

(26)Q_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}}{k}_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}(T_{\mathrm{I}\mathrm{N}\mathrm{T}\mathrm{C}}-T_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}).

Heat transfer between the cathode channel and the PEN by convection:

(27)Q_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{P}\mathrm{E}\mathrm{N}}={\displaystyle \frac{\mathrm{1}}{h_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}}{k}_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},\mathrm{P}\mathrm{E}\mathrm{N}}(T_{\mathrm{P}\mathrm{E}\mathrm{N}}-T_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}).

Oxygen ions produced in the cathode are transferred to the PEN structure for the mass transfer model of SOFC. The hydrogen in the fuel channel penetrates into the PEN structure as well, where the electrochemical reaction occurs. The water steam produced from the reaction transfers to the fuel channel. Therefore, the increased mass in the fuel channel is only caused by the mass transfer of the oxygen ions. Detailed mass balance model and species balance model are listed as follows.

Mass balance equation in the fuel channel:

(28){\displaystyle \frac{\partial {\rho }_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}{\partial t}}=-{\displaystyle \frac{\partial {\rho }_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}{u}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}{\partial x}}-{\nu }_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{R}_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{M}_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{\displaystyle \frac{\mathrm{1}}{h_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}}.

Species balance equation in the fuel channel:

(29){\displaystyle \frac{\partial C_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},i}}{\partial t}}=-{\displaystyle \frac{\partial C_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d},i}{u}_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}{\partial x}}+{\displaystyle \sum _{k=\mathrm{I},\mathrm{I}\mathrm{I}}{\nu }_{i,k}{R}_k{\displaystyle \frac{\mathrm{1}}{h_{\mathrm{a}\mathrm{n}\mathrm{o}\mathrm{d}}}}},i\in \{{\mathrm{H}}_{\mathrm{2}},\mathrm{C}\mathrm{O},\mathrm{C}{\mathrm{O}}_{\mathrm{2}},{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\}.

Mass balance equation in the air channel:

(30){\displaystyle \frac{\partial {\rho }_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}{\partial t}}=-{\displaystyle \frac{\partial {\rho }_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}{u}_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}{\partial x}}+{\nu }_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{R}_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{M}_{{\mathrm{O}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}}}{\displaystyle \frac{\mathrm{1}}{h_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}}.

Species balance equation in the air channel:

(31){\displaystyle \frac{\partial C_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},i}}{\partial t}}=-{\displaystyle \frac{\partial C_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h},i}{u}_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}{\partial x}}+{\nu }_{i,(\mathrm{I}\mathrm{I}\mathrm{I})}{R}_{(\mathrm{I}\mathrm{I}\mathrm{I})}{\displaystyle \frac{\mathrm{1}}{h_{\mathrm{c}\mathrm{a}\mathrm{t}\mathrm{h}}}},i\in \{{\mathrm{N}}_{\mathrm{2}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}},{\mathrm{O}}_{\mathrm{2}}\}.

Micro GT model

The selected micro GT is a C30 from CAPSTONE. This is a single-shaft turbine equipped with a centrifugal compressor and a radical turbine. The major parameters of the C30 GT are summarized in Table 1. The compressor and turbine models provide the standard thermodynamic equations for the input-output relationship of the working fluid, based on pressure ratio and isentropic efficiency, listed as follows.

Compressor outlet pressure

(32)P_{\mathrm{o}\mathrm{u}\mathrm{t}}=ϵP_{\mathrm{i}\mathrm{n}}.

Compressor outlet temperature

(33)T_{\mathrm{C},\mathrm{o}\mathrm{u}\mathrm{t}}=T_{\mathrm{C},\mathrm{i}\mathrm{n}}+T_{\mathrm{C},\mathrm{i}\mathrm{n}}({\mathrm{\pi }}^{(k-\mathrm{1})/k}-\mathrm{1})/{\eta }_{\mathrm{C}}.

Compressor consumed power

(34)W_{\mathrm{C}}=\mathrm{4.18}{c}_{\mathrm{p}}{G}_{\mathrm{k}}{T}_{\mathrm{C},\mathrm{i}\mathrm{n}}({ϵ}^{(k-\mathrm{1})/k}-\mathrm{1})/{\eta }_{\mathrm{C}}.

Turbine outlet temperature

(35)T_{\mathrm{T},\mathrm{o}\mathrm{u}\mathrm{t}}=T_{\mathrm{T},\mathrm{i}\mathrm{n}}{\left({\displaystyle \frac{P_{\mathrm{T},\mathrm{o}\mathrm{u}\mathrm{t}}}{P_{\mathrm{t},\mathrm{i}\mathrm{n}}}}\right)}^{(K_{\mathrm{T}}-\mathrm{1})/K_{\mathrm{T}}}.

Turbine output power

(36)W_{\mathrm{C}}=\mathrm{4.18}{c}_{p,R}{G}_{\mathrm{T}}{T}_{\mathrm{T},\mathrm{i}\mathrm{n}}\left[\mathrm{1}-{\left({\displaystyle \frac{P_{\mathrm{t},\mathrm{o}\mathrm{u}\mathrm{t}}}{P_{\mathrm{t},\mathrm{i}\mathrm{n}}}}\right)}^{(K_{\mathrm{T}}-\mathrm{1})/K_{\mathrm{T}}}\right]{\eta }_{\mathrm{t}}.

The latter values are determined by a performance map, which describes the compressor and the turbine by introducing pressure and efficiency as a function of mass flow rate and shaft speed. The performance maps of the compressor are presented in Fig. 4.

The generator efficiency in this paper is assumed constant. The power output from the GT can be calculated by:

(37)W_{\mathrm{G}\mathrm{T}}={\eta }_{\mathrm{g}\mathrm{e}\mathrm{n}}({\eta }_{\mathrm{t}}{W}_{\mathrm{t}}-W_{\mathrm{c}}),

where {\eta }_{\mathrm{g}\mathrm{e}\mathrm{n}} is the generator efficiency, {\eta }_{\mathrm{t}} is the turbine mechanical efficiency, and W_{\mathrm{t}}, W_{\mathrm{c}} are the turbine output power and the compressor consumed power, respectively.

The shaft model includes the acceleration or deceleration of the shaft through a moment of inertia of the moving parts:

(38){\displaystyle \frac{\mathrm{d}\omega }{\mathrm{d}t}}={\displaystyle \frac{P_{\mathrm{B}}}{I\omega }},

where \omega is the angular shaft speed, I is the moment of inertia, and P_{\mathrm{B}} is the power balance.

Combustor models

Assume all residual combustible compounds such as C₂H₅OH, CH₄, CO, and H₂ formed in the fuel cell stack could be fully oxidized in the combustor. The associated chemical reactions are

(39){\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}\mathrm{O}\mathrm{H}+\mathrm{3}{\mathrm{O}}_{\mathrm{2}}=\mathrm{2}\mathrm{C}{\mathrm{O}}_{\mathrm{2}}+\mathrm{3}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{\Delta }{H}_{\mathrm{r}\mathrm{x}\mathrm{n},\mathrm{C}{\mathrm{H}}_{\mathrm{4}}}

(40)\mathrm{C}{\mathrm{H}}_{\mathrm{4}}+\mathrm{2}{\mathrm{O}}_{\mathrm{2}}=\mathrm{C}{\mathrm{O}}_{\mathrm{2}}+\mathrm{2}{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{\Delta }{H}_{\mathrm{r}\mathrm{x}\mathrm{n},\mathrm{C}{\mathrm{H}}_{\mathrm{4}}}

(41)\mathrm{C}\mathrm{O}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{O}}_{\mathrm{2}}=\mathrm{C}{\mathrm{O}}_{\mathrm{2}}+\mathrm{\Delta }{H}_{\mathrm{r}\mathrm{x}\mathrm{n},\mathrm{C}\mathrm{O}}

(42){\mathrm{H}}_{\mathrm{2}}+{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}{\mathrm{O}}_{\mathrm{2}}={\mathrm{H}}_{\mathrm{2}}\mathrm{O}+\mathrm{\Delta }{H}_{\mathrm{r}\mathrm{x}\mathrm{n},{\mathrm{H}}_{\mathrm{2}}}

The temperature of the product gas (T_{\mathrm{p}}) can be calculated based on a simple energy balance on the combustor control volume.

(43){\displaystyle \sum _i{h}_{\mathrm{r},i}}+\mathrm{\Delta }{h}_{\mathrm{r}\mathrm{x}\mathrm{n},{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}\mathrm{O}\mathrm{H}}+\mathrm{\Delta }{h}_{\mathrm{r}\mathrm{x}\mathrm{n},\mathrm{C}{\mathrm{H}}_{\mathrm{4}}}+\mathrm{\Delta }{h}_{\mathrm{r}\mathrm{x}\mathrm{n},\mathrm{C}\mathrm{O}}+\mathrm{\Delta }{h}_{\mathrm{r}\mathrm{x}\mathrm{n},{\mathrm{H}}_{\mathrm{2}}}={\displaystyle \sum _j{n}_j{\displaystyle {\int }_{T_{\mathrm{r}}}^{T_{\mathrm{p}}}{c}_{\mathrm{p},j}\mathrm{d}T}}.

Heat exchanger model

The heat exchanger model is simulated based on the ϵ-\mathrm{N}\mathrm{T}\mathrm{U} method [9], implementing temperature-dependent specific heat.

An iterative procedure is implemented to assess the outlet temperature based on the average hot and cold fluid-specific heat calculations. These parameters depend on the unknown HE outlet temperature. Thus, estimated values for the temperature are selected, allowing average specific heat to be calculated. Consequently, the outlet temperature is re-calculated through the ϵ-\mathrm{N}\mathrm{T}\mathrm{U} method. The procedure is stopped when the convergence criterion on such temperature is satisfied.

Results and discussion

Model validation

SOFC experimental results and model validation

During the SOFC performance testing process, the fuel flow rate is kept constant at 500 ml/min. The air flow rate is 2000 mL/min. The gas inlet temperatures are 673 K at the fuel and air sides. The current-voltage (I-V) curves of the cell tested with H₂ and CH₄ at 750°C and 850°C are displayed in Figs. 5 and 6, respectively.

To validate the SOFC model, the polarization curves generated by the simulation model is compared with the experimental ones for different operating temperatures with CH₄ and H₂, respectively. The developed model can achieve errors lower than 3%. Unfortunately, SOFC stack experimental data have not been acquired, thus validating stack performance is not yet possible.

Micro GT model validation

The micro GT model was validated using available data from the manufacturer. Figure 7 compares compressor efficiency and pressure ratio at different operating conditions between the experimental data and simulation model. Fig. 8 compares turbine efficiencies between the experimental data and simulation model, both of which show good agreement. This proves the validity of the GT model.

Steady-state performance

System performance at design point

The design objectives and parameters are displayed in Table 2. The efficiency of the entire plant is calculated as the ratio between the net power produced and the LHV of the feeding fuel. The SOFC stack efficiency is the ratio between the power supplied by the SOFC stack and the LHV of the fuel supplied to the cell. Considering all losses, the hybrid system and SOFC stack have net LHV-based electric efficiency of 62.3% and 49.8% at the design point, respectively. Most values of hybrid system efficiency in previous studies range between 53% and 66.5%, respectively [10-12].

Limitations for steady-state operation

Varying the arbitrary air and fuel flow rates is impossible because unsafe issues would occur [13]. In this paper, the steady-state simulation with the designed system detected the following unsafe issues at certain regimes, as shown in Fig. 9.

1) Overheating: This appears for high fuel flow rate and low air flow rate, which can damage different components. In SOFC, high temperatures may cause irreversible changes in the electrode structure such as recombination of the nickel catalyst. For metallic components with high thermal load, such as the heat exchanger and GT, high temperatures may lead to material failure. This inevitably leads to system breakdown.

2) Cooling of SOFC stack: For the opposite case of high air flow rate and low fuel flow rate, the SOFC stack is strongly cooled down. Therefore, the voltage is low. Operating in this regime is not recommended due to low efficiency and possible risk of thermal cracking.

3) Compressor surge: Pressure generally runs into a surge if the compressor ratio is too high for its current GT rotational speed. This can cause violent oscillations in the gas path of the system where the compressor is connected to, and can thus damage the whole system.

4) Low fuel flow rate: If the fuel flow rate is too low, the ejector pressure difference will become negative. Hence, the nozzle flow may change to subsonic. This results in ejector malfunction.

Part-load operation strategies

Control strategies for partial load operating conditions have been investigated in the past few years [14,15]. In this paper, part-load operation is obtained by only varying air and fuel flow rates. The following control strategies are described in detail and are shown in Fig. 10.

Strategy A: Varying the fuel flow rate while air flow rate is constant

Strategy B: Varying the fuel flow rate and adjusting the air flow rate to keep the SOFC stack operating temperature constant

Strategy C: Varying the fuel flow rate and adjusting the air flow rate to keep the air-to-fuel flow rate ratio constant

In each strategy, a flow control valve regulates the fuel flow rate while the GT rotational speed controls the air flow rate. Two bypass valves adjust the TIT as shown in Fig. 11.

Part-load performance of hybrid system

The fuel and air flow rates of the hybrid system in different control strategies are displayed in Fig. 11. The fuel flow rate to the SOFC stack decreases in all cases, which is the main cause of the reduced power output of the hybrid system. This is because the SOFC stack is the main power output source. The fuel flow rate in Strategy A is slightly more reduced than that in Strategies B and C due to the lower system part-load efficiency. The air flow rate is adjusted depending on different control strategies.

The TIT and the SOFC operating temperature at part-load operation are important parameters because they determine the performance of the entire system. TIT and the SOFC mean operating temperature in different control strategies are shown in Figs. 12 and 13, respectively. In Strategy A, at partial load operation, the fuel flow rate reduces with constant air flow rate. Hence, the fuel-to-air flow rate ratio decreases, which determines the reduction of TIT and SOFC stack temperature. In Strategy B, SOFC stack operating temperature is constant. The reduction in fuel flow rate determines the reduction of fuel concentration in the cathode exhaust, and similarly, the reduction of the combustor. The latter causes TIT to decrease. In Strategy C, the air-to-fuel ratio is constant. In contrast to Strategy A, stack temperature and TIT increase rapidly with the net power reduction.

The SOFC stack performance is affected by its operating temperature and current density, even at partial load operation. Figure 14 exhibits the SOFC stack electrochemical performances at part-load conditions. The cell voltage is dependent on the current density and stack operating temperature [16]. In Strategy A, the reduction of its operating temperature is so high that the decrease in cell voltage approaches 0.56 V. The effect of temperature decrease is dominant with respect to current density reduction. In Strategy B, although the SOFC operating temperature is constant, less voltage losses cause the voltage to increase slightly with the reduction in current density. In contrast to Strategy A, a rapid increase in cell voltage is obtained in Strategy C as a consequence of current density reduction (determined by the reduction of fuel flow rate) and stack temperature growth.

Figure 15 shows the dimensionless output power of the GT and the SOFC stack at part-load conditions. Air mass flow rate and TIT mainly determine GT output power, while the SOFC stack output power is the function of cell voltage and current density. In Strategy A, the gas flow rate is constant but TIT rapidly decreases. This causes the GT power to decrease. Similarly, the high value reduction of the SOFC overvoltage and current density results in the rapid decrease of the SOFC stack output power. In Strategy B, the gas flow rate and TIT decrease slightly, causing a decrease in GT output power. However, this increase is smaller than that in Strategy A. For the SOFC stack, the output power slightly decreases although operating temperature is constant due to the lower current density. In Strategy C, TIT increases rapidly, but GT output power decreases even more rapidly than those in Strategies A and B. This is because of the rapid reduction of the air flow rate as shown in Fig. 11. For the SOFC stack, SOFC output power slightly decreases although its operating temperature increases at part-load operation due to the rapid decrease of current density.

Figure 16 shows the hybrid system net efficiency at part-load operation. In Strategy A, the net electric efficiency of the system is 62.6% at design point and decreases to 43% at minimum load. The compressor isentropic efficiency is constant because there is no variation in air flow rate and rotor speed. Meanwhile, turbine efficiency decreases with the reduction in dimensionless net power due to TIT reduction. Moreover, the high values of the SOFC stack over-voltages cause higher SOFC stack efficiency defects with respect to full-load operation. Finally, the overall plant net efficiency rapidly decreases. In Strategy B, the net electric efficiency in steady-state ranges from 58.8% at minimum load to a maximum of 65.8% at intermediate load (59%), and back to 62.6% at full load. Due to the constant operating temperature and less current densities, the efficiency of the SOFC stack slightly increases at part-load operation. On the other hand, GT efficiency decreases with the reduction in output power based on the turbo-machinery performance maps as shown in Fig. 6. While the system net power varies from 59% to 100%, the increase in the SOFC stack net efficiency is dominant. The GT reduction performance dominates from a load of 21% to 59% of the hybrid system. Consequently, the system overall efficiency slightly increases with an output power reduction between a load of 100% to 59%, and then decreases with an output power reduction to a load below 59%. The best part-load performance is achieved in Strategy C, which increases slightly from 62.6% at design point to a load of 65.1% at 85% power reduction. Although the variation of the air flow rate and TIT determines the efficiency of the GT reduction, high voltages versus the full-load operation consequently lower the efficiency defects of the SOFC stack. The reduction in GT efficiency is small while SOFC stack efficiency increases. Thus, system efficiency rapidly increases. However, Strategy C shows a small operating range, which does not allow a reduction of more than 82% of the nominal value of the plant net electrical power. This is restricted by the high temperature of the SOFC stack and the system TIT.

Startup and shutdown strategies

A suitable startup and shutdown strategy should be available with as few extra auxiliaries as possible. Moreover, no external power is required to drive the GT during the process. During startup, the SOFC must be heated smoothly and slowly to a temperature high enough to introduce fuel and start the SOFC operation (SOFC ignition). The shutdown phase must take the system to a state where it can be left alone without risk.

During the startup and the shutdown phases, the components of the hybrid system must be protected from critical incidents. Issues that appear only during the startup and the shutdown process, and the proposed methods to deal with these issues, are discussed as follows.

1) The anode should be flushed with N₂ to ensure an inert atmosphere to avoid oxidation of the anode while SOFC is not active.

2) During the startup process, steam and heat are not enough for fuel reforming reaction. Therefore, H₂ is chosen as the fuel instead of CH₄ for the SOFC startup because H₂ does not need to re-form.

3) In the early phase of the shutdown, GT delivers a net power output based on the heat stored in the SOFC system. To dissipate this power, variable throttle is introduced into the turbine exhaust stream. Throttling the exhaust gas decreases the pressure reduction in the turbine. Hence, net power can be controlled to zero by manipulating the throttle opening.

4) Auxiliary fuel is chosen to drive the GT without extra power during late shutdown and during startup, and to heat the system. The fuel facilitates control of the shaft speed and air flow accordingly, due to the quick response of the GT system to the TIT.

5) In the late phase of shutdown, the recuperation of the turbine exhaust heat to compressed air should be omitted to cool down the cell stack to a lower temperature. To solve this problem, a bypass of the turbine exhaust gas around HE1 is used to facilitate low SOFC air inlet temperature

6) In the late phase of startup, before the SOFC is ignited, auxiliary fuel is used to supply high temperature gas to preheat the SOFC stack to the design temperature.

The layout of the system, including the auxiliaries for startup and shutdown, is shown in Fig. 17. Additional ducts are painted in blue. The proposed and simulated startup and shutdown sequences are explained in Tables 3 and 4, respectively.

Before the hybrid system startup, the system initial state is as follows.

1) The SOFC stack is at a temperature of 400 K.

2) The GT is rotating at 80% of its design speed when the startup sequence is initiated.

3) The auxiliary valve is manipulated to control the air flow rate to 80% of the design value. The required auxiliary fuel flow rate is approximately 35% of the design value.

4) The fuel channel is flushed with nitrogen.

Figure 18 shows the flow rate of various gases during the startup process. The responses of the system in terms of temperature and power are shown in Figs. 19 and 20, respectively.

The SOFC heats up slowly until the reactions are started with hydrogen at 16200 s. At this point, the turbine outlet temperature reaches a maximum of 1040 K because throttling provokes only a small temperature decrease in the turbine. If this is critical for the HE1 used in practice, SOFC ignition, cessation of auxiliary, and exhaust throttling should be advanced to an earlier time. Hence, the heat exchangers operating temperature decreases.

The LHV of the methane used as auxiliary fuel for heating the SOFC stack (excluding the ordinary fuel flow after 19400 s) is 550 kWh. This corresponds to the fuel needed for 1.55 h of full load operation. The amount of hydrogen consumed during the startup sequence is 57 kWh.

After the startup initiation, GT could be used to supply the power at 2000 s. Thus, at this time, the hybrid system could deliver approximately 20% of its design output power. SOFC begins to produce electrical power at 16500 s after startup initiation. First, power slowly increases to a value of 38% of the design power until the load change operation is started. Then it can follow a load.

Before initiating the shutdown sequence of the hybrid system, the system is assumed to be operated at steady-state full load condition. Figure 21 shows the gas flow rate during the shutdown process while Fig. 22 shows the temperature response of the system.

The temperature of the SOFC stack decreases slowly and smoothly without sharp breaks or high thermal gradients. The assumed power requires the control and stand-by to be systems be supplied by GT using the remaining heat of the SOFC stack. The system output power reaches zero 25 s after the shutdown sequence is initiated. At about 2800 s, the SOFC temperature is sufficient to drive the GT at a desired air flow. From this point on, auxiliary fuel is required to maintain air flow. After approximately 7200 s, the SOFC operating temperature reaches an uncritical regime. The system can then be switched off. For the entire shutdown sequence, the consumed amount of methane corresponds to approximately 0.43 h of full load operation.

Conclusions

The performance of SOFC and GT hybrid system is presented. The electrochemical performance of single SOFC operating with H₂ and CH₄ is experimentally tested. Simulation and experimental results are in good agreement. Based on the simulation model, the safe operation regime of the hybrid system is accurately plotted.

In the safe regime of the system, three different part-load strategies are introduced, and the part-load performance of the hybrid system is analyzed. The fuel-only control method (Strategy A) is the simplest strategy. However, it has the lowest efficiency at part-load conditions mainly due to the rapid decrease of the TIT and stack operating temperature. Strategy B enlarges the operation range (21%-100%) with a slight efficiency decrease (59.6%-65.8% throughout the entire load range). The best part-load performance is obtained with Strategy C, which has a constant air-to-fuel flow rate ratio. However, the operation range is very narrow, from a load of 82% to its design point.

Another major objective of this paper is to introduce a suitable startup and shutdown strategy for the hybrid system with as few additional components as possible. The sequences for startup and shutdown are proposed. System responses to the execution of these sequences are acquired using the simulation model. The startup strategy uses H for the ignition phase of the SOFC instead of externally generated steam for reforming reactions. The shutdown strategy uses auxiliary fuel to drive the GT to supply compressed air to cool the stack. Smooth cooling and heating of the cell stack can be accomplished without using external electrical power. However, such system is not suited for frequent startup and shutdown due to the long time required and since the thermal cycling reduces SOFC lifetime.

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