Modelling and solution methods for renewables-driven energy markets

Responding to the alarming climate change consequences, many countries are paying significant attention to the energy systems' transition towards environmental sustainability. As an example, European Union established an ambitious goal to become climate-neutral by 2050 compared to 10 levels, and South Korea aims to reduce greenhouse gas emissions by 37% below business-as-usual by 2030. Considering the essential role of energy markets in modern economies such targets pose a fundamental challenge to finding a potential solution that would ensure furthering human-kind well-being and decarbonisation. One of the commonly exploited crucial tools for planning energy systems transition and understanding its effect on the economy and social welfare is energy systems modelling. However, modelling techniques undergo criticism regarding the insufficient level of precision provided for police makers. In particular, two of the main challenges are associated with i) a limited number of attempts to integrate multiple energy-sector stakeholders into a single-model formulation and ii) a trade-off between the model complexity and its numerical tractability. This dissertation addresses both of these challenges. First, it formulates a modelling framework allowing one to represent energy systems operations involving multiple generation companies and transmission system planning. Additionally, the energy system models formulated in this dissertation allow for the consideration of renewable supporting policies such as carbon tax and investment subsidies. These models provide insights into how a welfare-maximising unit may impact the increase of renewable share in the generation mix without harming the total welfare. Such a study was conducted for Nordic and Baltic countries. Second, this dissertation provides a solution method formulation that can be applied to solving proposed mathematical models. The solution algorithm was developed in two stages: i) combining Lagrangian decomposition with mixed-integer relaxation allowing one to obtain an arbitrary precise solution in case of duality gap absence and ii) embedding these techniques within a duality-based branching strategy that would ensure solving to optimality even in the presence of duality gap. The models in this dissertation serve as a support for decision-makers trying to understand how and to which extent they can exploit the influence of the transmission system operator on the energy system with or without other supportive policies in the context of decarbonising the energy system. The solution algorithms proposed in this dissertation are generally applicable to a wide range of two-stage stochastic mixed integer problems appearing in such sectors as, for example, the design of water networks, modelling refinery processes and transportation systems.