1. Introduction1.1 V2G Background1.2 Problem Statement2. Nomenclature2.1 Symbols2.2 Common Subscripts3. PEM Hybrid Fuel Cell System Model3.1 Fuel Cell System3.1.1 Fuel Cell Stack3.1.2 Compressor3.1.3 Auxiliary Components3.2 Battery3.3 Rule-Based Control Algorithm 3.4 System Level Block Diagram3.5 Grid Power Demand Cycle4. Optimization Problem Formulation 4.1 Objective Function4.2 Design Variables4.3 Constraints4.4 Model Parameters4.5 Optimization Problem Summary5. Model Analysis5.1 Dynamic Simulation5.2 Design of Experiments Study5.3 Monotonicity Analysis5.4 Surrogate Modeling through Neural Networks6. Optimization Study6.1 Optimization Results6.2 Constraint Activity6.3 Lagrange Multipliers6.4 Interior vs. Boundary Solutions6.5 Variation of Starting Points6.6 Surrogate Model Feasibility7. Parametric Study7.1 Minimum SOC7.2 Maximum Battery Weight7.3 Maximum Fuel Cell Stack Length8. Discussion of Results8.1 Design Rules8.2 Model Limitations8.3 Future Work9. Acknowledgements 10. ReferencesME 555 – Design Optimization Winter 2007 Dongsuk KumScott Moura Plant/Control Optimization of a PEM Hybrid Fuel Cell Vehicle to Grid (V2G) System Final Report April 19th, 2007 Dongsuk Kum Scott Moura ME 555 – Winter 2007 Professor Panos Y. Papalambros Abstract Combined plant/control optimization is applied to a PEM hybrid fuel cell vehicle (HFCV) for vehicle to grid (V2G) applications. The HFCV model is developed from past control-oriented models. For the purposes of design optimization, three components (fuel cell stack, compressor, and battery) are made scalable. To construct a control scheme suitable for combined plant/control design optimization, a rule-based method is selected and framed in a manner such that several key parameters are formulated as design variables. Simulation based computations of the objective function are characterized by noise, and therefore inappropriate for gradient-based optimization algorithms. A surrogate modeling method is suggested using neural networks to approximate the physical model. Using the surrogate model, the combined design and controller HFCV model is optimized for maximum fuel economy for a given stationary power demand cycle. The solution is analyzed with respect to various optimality properties, such as constraint activity, Lagrange multipliers, interior & bounded solutions, and varying starting points. The trade-offs between optimal design solutions and constraints is observed and analyzed to analyze optimal design solutions for a PEM HFCV operating as an energy source to the power grid. Multi-objective optimization problems are formulated through parametric studies to elucidate trade offs between different design objectives. A resultant set of “design rules” are formulated to provide a physical engineering interpretation of the conclusions found. 1ME 555 – Design Optimization Winter 2007 Dongsuk KumScott Moura Table of Contents 1. Introduction................................................................................................................................. 3 1.1 V2G Background .................................................................................................................. 3 1.2 Problem Statement................................................................................................................ 3 2. Nomenclature.............................................................................................................................. 4 2.1 Symbols................................................................................................................................. 4 2.2 Common Subscripts.............................................................................................................. 4 3. PEM Hybrid Fuel Cell System Model........................................................................................ 5 3.1 Fuel Cell System................................................................................................................... 5 3.1.1 Fuel Cell Stack............................................................................................................... 6 3.1.2 Compressor .................................................................................................................... 7 3.1.3 Auxiliary Components................................................................................................... 8 3.2 Battery................................................................................................................................... 8 3.3 Rule-Based Control Algorithm........................................................................................... 10 3.4 System Level Block Diagram............................................................................................. 12 3.5 Grid Power Demand Cycle................................................................................................. 12 4. Optimization Problem Formulation.......................................................................................... 14 4.1 Objective Function.............................................................................................................. 14 4.2 Design Variables................................................................................................................. 14 4.3 Constraints .......................................................................................................................... 15 4.4 Model Parameters ............................................................................................................... 20 4.5 Optimization Problem Summary ........................................................................................ 20 5. Model Analysis......................................................................................................................... 21 5.1 Dynamic Simulation ........................................................................................................... 22 5.2 Design of Experiments Study ............................................................................................. 23 5.3 Monotonicity Analysis........................................................................................................ 26 5.4 Surrogate Modeling through Neural Networks................................................................... 28 6. Optimization