  Offshore wind farms have emerged as a popular renewable energy source that
can generate substantial electric power with a low environmental impact.
However, integrating these farms into the grid poses significant complexities.
To address these issues, optimal-sized energy storage can provide potential
solutions and help improve the reliability, efficiency, and flexibility of the
grid. Nevertheless, limited studies have attempted to perform energy storage
sizing while including design and operations (i.e., control co-design) for
offshore wind farms. As a result, the present work develops a control co-design
optimization formulation to optimize multiple objectives and identify Pareto
optimal solutions. The graph-based optimization framework is proposed to
address the complexity of the system, allowing the optimization problem to be
decomposed for large power systems. The IEEE-9 bus system is treated as an
onshore AC grid with two offshore wind farms connected via a multi-terminal DC
grid for our use case. The developed methodology successfully identifies the
Pareto front during the control co-design optimization, enabling
decision-makers to select the best compromise solution for multiple objectives.
