Among distributed energy resources, solar photovoltaic (PV) generation has the largest penetration in the distribution networks. Serving electric vehicles (EV) with renewable resource generation would further reduce the carbon footprint of the energy supply chain for electric vehicles. However, the integration of solar PV and EVs in the unbalanced distribution network introduces several challenges including voltage fluctuations, voltage imbalances, reverse power flow, and protection devices’ malfunctions. The uncertainties associated with solar PV integration and electric vehicles operation require significant effort to develop accurate optimization methodologies in the unbalanced distribution systems operation. In this thesis, in order to cope with the uncertainties, we first developed a two-stage optimization problem, to identify the feasible dispatch margins of photovoltaic generation considering the distribution network operation constraints. The dispatch margins of photovoltaic generation are quantified considering the worst-case realization of demand in the distribution network. The linear and the second-order cone mathematical problem formulation is procured to solve the optimal power flow problem. Second, a data-driven distributionally robust optimization framework is proposed for the operation of the unbalanced distribution network considering the uncertainties associated with the interconnected EV fleets and solar PV generation, and the proposed framework leverages the column-and-constraint generation approach. Moreover, to minimize the operation cost and improve the ramping flexibility, a continuous-time optimization problem, is developed and reformulated to a linear programming problem using Bernstein polynomials. Here, a generalized exact linear reformulation of the data-driven distributionally robust optimization is used to capture the worst-case probability distribution of the net demand uncertainties. Furthermore, in this thesis, an interconnection of multi microgrids (MGs) technology is considered a promising solution to handle the variability of the distributed renewable energy resources and improve the energy resilience in the distribution network. The coordination among the microgrids in the distribution network could improve the operation cost, reliability, and security of the distribution network. Therefore, an adaptive robust distributed optimization framework is developed for the operation of a distribution network with interconnected microgrids considering the uncertainties in demand and solar PV generation.

Degree Date

Spring 2022

Document Type


Degree Name



Electrical and Computer Engineering


Mohammad E. Khodayar

Number of Pages




Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License