Degradation-conscious control for PEM fuel cells

Patent metadata

Field	Value
Publication number	US-11515553-B2
Application number	US-202016839282-A
Country	US
Kind code	B2
Filing date	Apr 3, 2020
Priority date	Apr 3, 2019
Publication date	Nov 29, 2022
Grant date	Nov 29, 2022

Abstract

A linear time varying model predictive control (LTV-MPC) framework is developed for degradation-conscious control of automotive polymer electrolyte membrane (PEM) fuel cell systems. A reduced-order nonlinear model of the entire system is derived first. This nonlinear model is then successively linearized about the current operating point to obtain a linear model. The linear model is utilized to formulate the control problem using a rate-based MPC formulation. The controller objective is to ensure offset-free tracking of the power demand, while maximizing the overall system efficiency and enhancing its durability. To this end, the fuel consumption and the power loss due to auxiliary equipment are minimized. Moreover, the internal states of the fuel cell stack are constrained to avoid harmful conditions that are known stressors of the fuel cell components.

First claim

What is claimed is:

1. A method for controlling a fuel cell having a polymer electrolyte membrane, comprising:
generating a reduced-order model for heat and water transport across the fuel cell, where water content in the membrane is modeled using only ordinary differential equations and temperature of the membrane is modeled using only ordinary differential equations;
linearizing the reduced-order model at each time step about a current operating condition of the fuel cell to form a linear model;
formulating a state-space representation of a control problem for tracking power output by the fuel cell from the linear model;
receiving, by a controller, a desired power demand for the fuel cell;
receiving, by the controller, a measurement of power output by the fuel cell;
determining, by the controller, the operating conditions of the fuel cell by solving the control problem using the desired power demand and the power measurement for the fuel cell; and
controlling, by the controller, at least one of flow rate of hydrogen into the fuel cell or delivery of air into the fuel cell based on the determined operating conditions.

2. The method of claim 1 wherein generating a reduced-order model further includes
modeling vapor concentration in a catalyst using only ordinary differential equations; and
modeling liquid saturation in the catalyst using only ordinary differential equations;
such that the reduced-order model includes vapor concentration in the catalyst and liquid saturation in the catalyst.

3. The method of claim 1 wherein the operating conditions of the fuel cell determined by the controller include anode channel relative humidity, cathode channel relative humidity, channel temperature, channel pressure and current density.

4. The method of claim 1 wherein formulating the state-space representation includes converting the continuous-time linear model to a time-discretized form using zero order hold.

5. The method of claim 1 wherein formulating the state-space representation includes representing states in the state-space representation as deviations of the state from the current operating condition and representing inputs in the state-space representation as trajectories from the current operating condition.

6. The method of claim 1 further comprises formulating the state-space representation as a linear quadratic-model predictive control problem in velocity form.

7. The method of claim 1 further comprises solving the control problem using a solver for quadratic programs.

8. The method of claim 1 further comprises formulating the control problem with constraints, where states in the state-space representation are soft-constrained with slack variables and inputs in the state-space representation are hard-constrained with strict bounds.

9. The method of claim 8 wherein the states in the state-space representation are constrained to maintain hydration and temperature of the membrane within desired bounds.

10. The method of claim 8 wherein the inputs in the state-space representation are constrained by physical properties of the fuel cell.

11. A method for controlling a fuel cell system with an air compressor, a cooling subsystem and at least one fuel cell having a polymer electrolyte membrane, wherein the air compressor delivers oxygen to cathode of the at least one fuel cell, comprising:
generating a reduced-order model for the fuel cell system, where the reduced-order model models heat and water transport across the at least one fuel cell and models operating parameters for an air compressor and cooling subsystem of the fuel cell system, where water content in the membrane is modeled using only ordinary differential equations and temperature of the membrane is modeled using only ordinary differential equations;
linearizing the reduced-order model at each time step about a current operating condition of the fuel cell system to form a linear model;
formulating a state-space representation of a control problem for tracking power output by the fuel cell system from the linear model;
receiving, by a controller, a desired power demand for the fuel cell system;
receiving, by the controller, a measurement of power output by the fuel cell system;
determining, by the controller, the operating conditions of the fuel cell system by solving the control problem using the desired power demand and the power measurement for the fuel cell system; and
controlling, by the controller, at least one of flow rate of hydrogen into the at least one fuel cell or delivery of air into the at least one fuel cell based on the determined operating conditions.

12. The method of claim 11 wherein generating a reduced-order model further includes
modeling speed of the air compressor, where the speed of the air compressor is modeled using only ordinary differential equations;
modeling pressure in supply manifold coupled to the air compressor, where the pressure in the supply manifold is modeled using only ordinary differential equations; and
modeling pressure in cathode of the at least one fuel cell, where the pressure in the cathode of the at least one field cell is modeled using only ordinary differential equations.

13. The method of claim 11 wherein generating a reduced-order model further includes modeling heat exchange between coolant of the cooling subsystem and the at least one fuel cell.

14. The method of claim 11 wherein generating a reduced-order model further includes
modeling vapor concentration in a catalyst using only ordinary differential equations; and
modeling liquid saturation in the catalyst using only ordinary differential equations;
such that the reduced-order model includes vapor concentration in the catalyst and liquid saturation in the catalyst.

15. The method of claim 11 further comprises
generating a full-order model for the fuel cell system, where diffusive mass transport and conductive heat transport are modeled using partial differential equations;
using the full-order model to obtain estimates of the fuel cell states, where measuring the internal states is not feasible.

16. The method of claim 11 wherein the operating conditions of the fuel cell system determined by the controller include anode channel relative humidity, cathode channel relative humidity, current density, coolant temperature in the cooling subsystem, coolant flow rate in the cooing subsystem and voltage applied to the air compressor.

17. The method of claim 11 wherein formulating the state-space representation includes converting the continuous-time linear model to a time-discretized form using zero order hold.

18. The method of claim 11 wherein formulating the state-space representation includes representing states in the state-space representation as deviations of the state from the current operating condition and representing inputs in the state-space representation as trajectories from the current operating condition.

19. The method of claim 11 further comprises formulating the state-space representation as a linear quadratic-model predictive control problem in velocity form.

20. The method of claim 11 further comprises solving the control problem using a solver for quadratic programs.

21. The method of claim 11 further comprises formulating the control problem with constraints, where states in the state-space representation are soft-constrained with slack variables and inputs in the state-space representation are hard-constrained with strict bounds.

22. The method o

Assignees

• Univ Michigan Regents

Inventors

• Goshtasbi Alireza
• Ersal Tulga

Classifications

• H01M8/04723

  of the coolant · CPC title

• H01M8/04753

  of fuel cell reactants · CPC title

• H01M8/04835

  of fuel cell reactants · CPC title

• H01M8/04925

  Power, energy, capacity or load · CPC title

• H01M8/04604

  Power, energy, capacity or load · CPC title