Uncertainty sources affect the planning and operation of energy systems. Different system operators need proper alternatives to cope with these uncertainties and improve the operation of their systems from technical and economical viewpoints. This thesis focuses on the risk-averse planning, operation, and coordination of energy systems including the transmission systems, distribution systems, and stand-alone renewable energy-based microgrids. We develop the existing uncertainty modeling methods and propose new mathematical models, pricing strategies, and operational coordination frameworks to enhance the ability of system operators to cope with uncertainties in the real-time operation of the energy systems and the electricity markets.  

From the uncertainty modeling viewpoint, when it comes to planning and operation of power systems with high penetration of renewable energy, since enough flexibility sources may not be available to cope with the uncertainties in the real-time operation, effective uncertainty sources need to be predicted accurately in the planning stage. Consequently, Bayesian statistics and a stochastic-probabilistic method based on Metropolis-coupled Markov chain Monte Carlo simulation are developed to predict the stochastic behavior of uncertainty sources in different energy systems. We utilized our proposed methods to model the stochastic behavior of wind speed, solar radiation, the water flow of a river, electrical load consumption, the behavior of electric vehicle customers, and the harmonic hosting capacity calculation in different case studies. A novel data classification and curve fitting methods are also proposed for deriving appropriate probability distribution functions (PDFs) based on long-term historical data. We consider demand response programs (DRPs), renewable energy sources, and the dynamic line rating as the embedded resources to prepare flexibility services in the ancillary service market. When it comes to utilizing DRPs, the uncertainty in customers' participation and responsiveness profoundly affects the real-time operation of power systems. Therefore, the risk associated with the utilization of uncertain DR is investigated. Moreover, we evaluate the eligibility conditions for risk-averse utilization of DRPs and apply the risk management cost to the pricing policy of DRPs. 

There are several flexibility service buyers in the power system that aim to activate flexibility services based on their objectives. Consequently, there are conflicts between the interest of different buyers that affect the system operation and pay-off mechanism in the electricity market. Accordingly, proper mathematical structures, coordination frameworks, decomposition techniques, and pay-off mechanisms are needed to be introduced to enhance the coordination between different buyers of the flexibility services. Therefore, we propose a look-ahead multi-interval framework for the TSO-DSO operational coordination problem. We develop the logic-based Benders decomposition technique for our large-scale optimization problem, which is a bilevel mixed-integer linear programming (MILP) problem. 

Finally, the results verify that the proposed uncertainty modeling techniques positively affect the planning and operation of different energy systems, especially stand-alone renewable energy-based microgrids. It is shown that the uncertainty of DRPs highly affected the operation of the power system and the ancillary service market. The ramping capability of reserves is introduced as an eligibility condition for risk-averse utilization of DRPs. Dynamic line rating can be used as a reliable flexibility source in the real-time operation of the power system. Furthermore, the results show that the proposed TSO-DSO coordination scheme can properly manage the conflict between the objectives of different flexibility service buyers. Finally, the Logic-based Benders decomposition (LBBD) can properly solve a large-scale bilevel MILP problem. The LBBD method also improves the execution time of MILP problems.