France aims to deploy 45 GW of offshore wind capacity by 2050. Both ownership and maintenance of the offshore substations linking these farms to the grid are the responsibility of the French Transmission System Operator (TSO). In the event of an unscheduled substation shutdown, the TSO must pay significant penalties to producers. These penalties are proportional to the curtailed energy. A limited number of maintenance days can be declared penalty-free, provided they are scheduled in advance in accordance with contractual constraints. Failures when weather conditions prevent access to the substation can quickly snowball into huge losses. This raises a new optimization problem for the TSO: designing maintenance plans that minimize expected penalties in the presence of unexpected repairs and failures. While these substations are not yet in operation, it is already crucial to estimate the penalties associated with good maintenance strategies. This enables informed design choices and more effective management of operational risks.

Although the optimization of maintenance for onshore and offshore wind turbines has previously been studied,
the specific challenges of offshore substations highlighted above have not been dealt with. We begin by introducing a Markov Decision Process (MDP) that models the problem. Assuming that the optimal policy for this MDP can be computed, we can then simulate it to obtain an estimate of the associated costs. Two main challenges arise. First, the size of the state space makes exact dynamic programming intractable. Second, ambiguity in the degradation models stems from the lack of data on the behavior of offshore substation components. We propose methods to address each of these challenges, supported by numerical experiments on an example offshore substation comprising seven key HVDC components at the site of the future Centre Manche 1 wind farm.

The problem is modeled as a MDP, where each state reflects the asset's degradation level and ongoing maintenance, and actions correspond to maintenance decisions. Weather scenarios are incorporated to account for their impact on both power production and maintenance feasibility. The model that we introduce exhibits a particular temporal structure, with a bimonthly strategic horizon for advance planning, and a discretization with a daily time step to capture the penalty dynamics under uncertain weather conditions. Our model requires representing the substation as a set of components whose degradations are independent. For each component, a degradation model is defined as a Markov chain with a finite set of states.

A significant challenge arises from the exponential growth of the state space with the number of components, making it impossible to solve the optimization problem exactly for real-life substation models. To address this, we propose an approximate solution approach. It exploits the particular structure of our MDP, which can be decomposed into component-level MDPs. These MDPs are coupled through the cost function, which does not decompose, and through the free maintenance days that encourage the simultaneous maintenance of several components. Our approach is based on solving a linear program over an outer approximation of the polytope of reachable probabilities. We present a heuristic deduced from this approximation and numerical results showing its performance. This provides an estimate of the costs, assuming the substation's degradation model is known.

Given the novelty of these assets, there is limited information regarding the reliability of offshore substations. We only have access to a rough estimate of the Mean Time Between Failures (MTBF) of key components. Testing different degradation laws, we show that two distinct models can lead to significantly different cost outcomes despite having the same MTBF. We expect these uncertainties to persist when the substations begin operating, so we aim to incorporate them into the model. More precisely, we seek maintenance policies that remain robust to uncertainty in the transition probabilities of the degradation state. Methods do exist for robust MDPs, but the structure of the ambiguity sets in which the transition kernels lie introduces additional difficulties.