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An optimization and fast load-oriented control for current-based solid oxide fuel cell system

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Journal of Solid State Electrochemistry Aims and scope Submit manuscript

Abstract

One of the key problems for a solid oxide fuel cell (SOFC), which is a high-temperature power-generation plant, is the cooperative control of safe operation and system efficiency during load tracking. Within the constraints of thermal safety, the SOFC plant should have the maximum output efficiency under various static conditions. Moreover, the SOFC system can switch between different static working conditions smoothly, safely, and quickly when the external load power changes. To achieve cooperative thermoelectric control, taking a 5-kW stand-alone SOFC system as the research object, according to the optimal static strategy designed based on the optimal operating curves (OOCs), a sliding mode controller (SMC) is designed and the closed-loop responses are discussed for SOFC system power switching during load tracking. The identification results demonstrate that the electrical coupling dynamic model can depict and predict accurately the electrical characteristics of SOFC stacks. And based on the obtained OOCs, the thermoelectric control can be achieved and thermal safety ensured using the designed SMC.

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Abbreviations

AR :

air excess ratio [−]

BP :

bypass valve opening ratio [−]

C :

specific heat capacity [kJ kmol−1 K−1]

△E 0 :

standard electrode potential (V)

FU :

fuel utilization [−]

F :

Faraday’s constant [96,485 C mol−1]

h :

convective heat transfer coefficient [kW cm−2 K−1]

I :

current [A]

LHV :

low heat value [kJ]

Max. |ΔT PEN|:

maximum PEN temperature gradient [K cm−1]

Max. T PEN :

maximum PEN temperature [K]

N :

control volume mole number [kmol]

\( \dot{N} \) :

molar flow rate [kmol s−1]

N 0 :

number of fuel cells [−]

p :

pressure [bar]

k :

thermal conductivity [kW cm−1 K−1]

P :

power [kW]

\( \dot{Q} \) :

heat transfer [kW]

R :

universal gas constant [8.314 kJ kmol−1 K−1]

A :

surface area [cm2]

T :

temperature [K]

U :

voltage [V]

\( \dot{W} \) :

work [W]

X :

species mole fraction

L :

distance between control volume [cm]

C D :

current density [A cm−2]

i 0 :

exchange current [A cm−2]

S node :

area of each node [cm2]

LSM:

lanthanum strontium manganate

j :

the index of discretization units of the cell

J :

the user-defined number of cell nodes

τ :

effectiveness

γ :

specific heat ratio, 1.4

δ :

number of electrons participating in the electro-chemical reaction

α :

charge transfer coefficient, 0.5

ε :

specified tolerance constant, 1e−5

η :

efficiency [%]

amb:

ambient

act:

activation

B:

burner

bl:

blower

by:

bypass

con:

concentration

dl:

diagonal line

i :

species

in:

inlet

out:

outlet

net:

system net output power

s:

stack

v:

volume

so:

solid control volume

ga:

gas control volume

ca:

cathode

an:

anode

PEN:

positive electrode-electrolyte-negative electrode

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Funding

The work was supported by the open fund project of Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System (No. znxx2018ZD02), the basic research project of Shenzhen (JCYJ20170307160923202), and the National Natural Science Foundation of China (61573162).

Author information

Authors and Affiliations

  1. Air Force Early Warning Academy, Wuhan, 430010, China

    Lin Zhang, Shaoying Shi, Feng Wang, Hongtu Xie & Hong Chen

  2. School of Automation, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jianhua Jiang & Xi Li

  3. Research institute of Huazhong University of Science and Technology, Shenzhen, 518057, China

    Xi Li

  4. College of Computer Science and Technology, Hubei Province Key Laboratory of Intelligent Information Processing and Real-time Industrial System, Wuhan University of Science and Technology, Wuhan, 430065, China

    Xiaowei Fu

Authors
  1. Lin Zhang
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  2. Shaoying Shi
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  3. Jianhua Jiang
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  4. Feng Wang
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  6. Hong Chen
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  8. Xi Li
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Corresponding author

Correspondence to Xi Li.

Appendix

Appendix

Detailed expressions of SOFC operating parameters, thermal temperature constraints, and electrical outputs.

Operating parameters

$$ {\displaystyle \begin{array}{c} FU=\frac{N_0\times {I}_s}{2F\times {\dot{N}}_{H_2}}\\ {} AR=\frac{4F\times {X}_{O_2}{\dot{N}}_{air}}{N_0\times {I}_s}\\ {} BP=\frac{4F\times {X}_{O_2}{\dot{N}}_{air, by}}{N_0\times {I}_s\times AR}\end{array}} $$

Thermal temperature constraints

$$ {\displaystyle \begin{array}{c}\mathit{\operatorname{Max}}.\left|{\varDelta T}_{PEN}\right|=\mathit{\max}\left\{{T}_{PEN}\left(j+ 1\right)-{T}_{PEN}(j)\right\},\kern1.25em \left\{j= 1, 2,\dots N- 1\right\}\\ {}\mathit{\operatorname{Max}}.{T}_{PEN}=\mathit{\max}\left\{{T}_{PEN}(j)\right\},\kern1.5em \left\{j= 1, 2,\dots N- 1\right\}\\ {}{\varDelta T}_{inlet}=\left|{T}_{HE, air}-{T}_{HE, fuel}\right|\end{array}} $$

Electrical outputs

$$ {\displaystyle \begin{array}{c}{P}_{bl}=-{\frac{1}{\tau_{bl}}}^{\ast}\frac{{\gamma RT}_{amb}}{\gamma - 1}\left[{\left(\frac{p_{out}}{p_{amb}}\right)}^{\left(\gamma - 1\right)/\gamma }- 1\right]{\dot{N}}_{air}\\ {}{P}_{net}={U}_s{I}_s-{P}_{bl}\\ {} SE=\frac{U_s{I}_s-{P}_{bl}}{{\dot{N}}_{H_2}\ast {LHV}_{H_2}}\times 100\%\end{array}} $$

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Zhang, L., Shi, S., Jiang, J. et al. An optimization and fast load-oriented control for current-based solid oxide fuel cell system. J Solid State Electrochem 22, 2863–2877 (2018). https://doi.org/10.1007/s10008-018-3996-x

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