Applying Mixed-Integer Quadratically Constrained Programming to Reduce Fuel Cell Degradation Onboard a Hybrid Ship

Abstract

New methods of ship propulsion are required to meet the targets for reducing global emissions of greenhouse gases. Hydrogen-powered fuel cells can be used to greatly reduce emissions, facilitating renewable shipping. Fuel cell durability is recognised as a large barrier to widespread fuel cell application. The goal of this graduation project is to develop a model which can be used to examine the trade-off between hydrogen consumption and degradation in the operation of a fuel cell/battery hybrid ship. The main research question is defined as follows:

”How does incorporating fuel cell degradation in the energy management system of a hybrid marine propulsion system affect the resulting fuel consumption and degradation?”

An optimisation approach is used to develop an energy management system. A quadratic mathematical model is constructed using the fuel cell’s polarisation curve as its basis. Linear relations for a fuel cell’s current-voltage relation are used to describe the fuel cell power as a quadratic current-power relation. Fuel cell degradation is included in the model by defining various operating conditions and relating them to degradation rates reported in the literature. In turn, the degradation influences the polarisation curve, thereby limiting the fuel cell’s performance. This quadratic approach to modelling the interplay between fuel cell degradation and the fuel cell’s performance is the main contribution to the literature.
The proposed energy management system is used to determine a vessel’s optimal operation, depending on the objective function applied. Two objectives are defined: minimisation of fuel consumption and minimisation of fuel cell degradation. Besides testing these single objectives, a weighted-sum approach to multi-objective optimisation is carried out using hydrogen and fuel cell system costs.
The optimal operation of the vessel is analysed based on key performance indicators such as fuel consumption, fuel cell degradation and operating costs. Incorporating fuel cell degradation in the energy management system leads to a reduction in degradation of up to 33% for the long-term simulation of the case study applied in this thesis when compared to the results for the minimisation of fuel consumption. A large increase (50%) in fuel cell lifetime can be accomplished with a very limited increase in hydrogen consumption (0.5%).
This research contributes an intuitive modelling method for the interplay between fuel cell degradation and the fuel cell’s performance. It provides insight into the considerations between fuel cell degradation and hydrogen consumption while operating a hybrid vessel, addressing a small part of a technical solution to mitigating emissions.