This research aims to tackle the dual challenges of power electronic uncertainties and the intermittency of renewable energy sources by developing a comprehensive reliability model and conducting a probabilistic evaluation of VSC-MTDC-based hybrid AC/DC power systems. With a specific focus on the North Sea region, the study emphasises enhancing the reliability of these systems, which are increasingly utilised for the efficient transmission of offshore wind power. The objective is to optimise key factors such as redundancy, modularity, and maintenance costs, which are crucial for the reliable integration of these systems into existing power grids.

While Modular Multilevel Converters (MMCs) within these systems offer multiple advantages, the proliferation of power electronic components introduces substantial uncertainties, compounding reliability concerns alongside the inherent variability of renewable energy sources. To address these challenges, the proposed composite probabilistic models account for wind speed variability, turbine drivetrain reliability, and the stochastic behaviour of component failures, providing a detailed reliability model.

The findings highlight substantial opportunities for improving system performance through targeted design and maintenance strategies. By investigating the reliability of offshore wind power, MMCs, DC transmission system and the overall AC/DC system, this research provides valuable insights into optimising system performance and ensuring the efficient integration of renewable energy. The research outcomes include a composite (generation and transmission) model, reliability and cost assessment, an optimal cost-reliability strategy for MMC systems, and a constant risk-minimised cost method of substituting conventional generators with offshore wind power contributing to more resilient and cost-effective renewable energy integration.

The outcomes of this study provide crucial insights into enhancing methods for the reliability of hybrid AC/DC systems. The methodologies and results not only align with global sustainability goals but also bolster energy security by laying a strong foundation for future power grid designs that increasingly depend on sustainable energy sources and advanced power electronics.

\textbf{Keywords:} Adequacy, composite power system, multi-state model, offshore wind power, power electronics, reliability evaluation, VSC-MTDC

Differential equations are commonly solved by, first, discretising the domain and then using an iterative method on the resulting system of equations. Refining the mesh gives a more accurate solution. However, the iterative method does not necessarily converge quickly to a good approximate solution anymore. To deal with this issue, we can add a preconditioner to the system. A good preconditioner enhances the speed of convergence.

Two ways of finding a good preconditioner are known. The first uses the properties of the matrix of the system, that is an algebraic preconditioner. The second uses the properties of the differential equation that give rise to the system, which is an operator preconditioner. This thesis makes a connection between both types of preconditioning.

First, we discretise a differential equation and perform numerical test on the system to see if the
algebraic preconditioning works. Then, the domains on which the matrix and preconditioner act are defined in terms of the differential equations.

We conclude that the matrix containing the differential operators acts on H(div, Ω) × H1(Ω) and the preconditioner acts on [L2(Ω)]^2× H2(Ω). So we need to constrain the domains in such a way that the operators both act on the same domain: that is, H(div, Ω) × H2(Ω). If the function is in this domain,then we know that the algebraic preconditioner is an effective preconditioner.

The rise in renewable energy sources causes more imbalances in the power grid. These imbalances are handled on the secondary control reserve (SCR) market. The prices on the market are currently predominately determined by hydropower plants, making the market unattractive to potential market players. This thesis explores the development of a bidding strategy for these new players to enter the Swiss secondary control reserve (SCR) market. This is a sensitive matter, since bidding too high would result in the bid not being accepted, and bidding too low would mean a player could have earned more money.
Two products are traded on the SCR market: negative control reserve (NCR), activated in case of an overbalance of the grid, and positive control reserve (PCR), activated in case of an underbalance of the grid. To develop a bidding strategy, the NCR and PCR bidding prices were modelled by using an ARIMA model to forecast the next week’s maximum bid. The order of the model was selected by minimising the Akaike information criterion and the parameters were estimated by maximising the likelihood function. An ARIMA(1,2,1) model provided the lowest AIC score for both the NCR and PCR data.
The accuracy of the models was tested by examining the mean absolute error (MAE), the root mean squared error (RMSE) and the bias. To test the performance of the model on the SCR market, two additional metrics were introduced: the percentage of the bids accepted (PAB), and the percentage of the total potential revenue earned (PMR). Although the MAE, RMSE and bias of the ARIMA(1,2,1) models were low, the PAB and PMR were low as well. This is because both models tended to estimate the forecasts higher than the actual maximum prices, resulting in the bids not being accepted. By shifting the model down to the lower bound of the 95% one-step confidence interval, the PAB and PMR were more than doubled. Therefore, the forecasts of the shifted ARIMA(1,2,1) models, generated the best bidding price for the upcoming week.