System modeling and temperature control for a fuel cell system based on local model networks

ABSTRACT

Fuel cells have been studied for use in stationary power generation and vehicle propulsion systems. The fuel cell thermal management subsystem is coupled and nonlinear, posing challenges for modeling and temperature control. This paper aims to integrate the physical models of the fuel cell stack, pump, thermostat, and other components combined with intelligent algorithms into an efficient system-level thermal management model framework and develop a model predictive controller to solve the temperature control problem. First, a physics-based nonlinear model of the fuel cell system is developed and used as a basis to identify the linearized model for different operating points. Then, the global model is obtained by fusing the local models with Gaussian validity functions using the local linear model tree method. Third, a multi-step prediction model is derived based on the local model networks, and a parameterized linear state space form is obtained and used for controller design. Furthermore, an online correction method is developed to reduce the model discrepancy. Finally, the accuracy of the system model and the performance of the proposed controller are verified by open-loop experimental data and a series of closed-loop simulation cases.

KEYWORDS:

• Fuel cell
• thermal management data-driven methods
• renewable energy systems
• model predictive control

Nomenclature

Abbreviations	=
MPC	=	Model Predictive Control
ANN	=	Artificial Neural Network
SVR	=	Support Vector Regression
KNN	=	K-nearest neighbor
PEMFC	=	Proton Exchange Membrane Fuel Cell
CHP	=	Combined heat and power
BP	=	Bipolar plate
MEA	=	Membrane Electrode Assembly
LMN	=	Local model network
NARX	=	Nonlinear auto-regression with exogenous input
NFIR	=	Nonlinear Finite Impulse Response
MISO	=	Multi-input single-output
LoLiMoT	=	Local Linear Model Tree
Symbols	=
Cst	=	Heat capacity of the fuel cell stack
ΔH	=	Heat value of hydrogen
nst	=	Cell number
Ist	=	Load current
F	=	Faraday constant
${\dot{m}}_{\mathrm{col}}$	=	Flow rate of coolant
Vcell	=	Output voltage of a single cell
PH2	=	Partial pressure of hydrogen
PO2	=	Partial pressure of oxygen
Dpump	=	Diameter of pump
Npump	=	Pump speed
ρcol	=	Coolant density
Ppump,out	=	Outlet pressure of pump
Ppump,in	=	Inlet pressure of pump
${\dot{m}}_{\mathrm{major}}$	=	Coolant flow rate of the major-cycle
${\dot{m}}_{\mathrm{minor}}$	=	Coolant flow rate of the minor-cycle
α	=	Thermostat opening
Tminor	=	Coolant temperature of the minor-cycle
Cminor	=	Heat capacity of the minor-cycle
Pptc	=	Power of PTC
Tm	=	Mixing temperature of minor-cycle and major-cycle
Tex	=	Heat exchanger outlet temperature
Φi	=	Validity function
φ	=	Scheduling vector
r	=	Input variable of the local model
Llm	=	Number of the local models
θi.	=	Parameter vector
C	=	Control horizon
P	=	Prediction horizon
Q	=	The weight of cost function
${\dot{Q}}_{\mathrm{hydrogen}}$	=	Energy generated by the chemical reaction
${\dot{Q}}_{\mathrm{elec}}$	=	Electrical energy
${\dot{Q}}_{\mathrm{loss}}$	=	Heat lost to the environment
${\dot{Q}}_{\mathrm{col}}$	=	Heat removed by the cooling water

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [91848111].