This paper presents a Two Stage stochastic Programming (TSSP) model for the planning of Multi-Microgrids (MMGs) in Active Distribution Networks (ADNs). The model aims to minimize the total costs while benefiting from interconnections of Microgrids (MGs), considering uncertainties associated with electricity demand and Renewable Energy Sources (RESs). The associated uncertainties are analyzed using Geometric Brownian Motion (GBM) and probability distribution functions (pdfs). The model includes long-term purchase decisions and short-term operational constraints, using Geographical information Systems (GIS) to realistically estimate rooftop solar limits. The planning model is used to study the feasibility of implementing an MMG system consisting of 4 individual Microgrids (MGs) at an ADN in a municipality in the state of São Paulo, Brazil. The results show that the TSSP model tends to be less conservative than the deterministic planning model, which is based on simple and pessimistic reserve constraints, while performing faster than a simple Stochastic Linear Programming (SLP) algorithm, with higher accuracy.

A novel optimisation‐based model of the power flow (PF) problem is proposed using complementarity conditions to properly represent generator bus voltage controls, including reactive power limits and voltage recovery processes. This model is then used to prove that the Newton–Raphson (NR) solution method for solving the PF problem is basically a step of the generalised reduced gradient algorithm applied to the proposed optimisation problem. To test the accuracy, flexibility and the numerical robustness of the proposed model, the IEEE 14‐bus, 30‐bus, 57‐bus, 118‐bus and 300‐bus test systems and large real 1211‐bus and 2975‐bus systems are used, benchmarking the results of the proposed PF model against the standard NR method. It is shown that the proposed model yields adequate solutions, even in the case when the NR method fails to converge.

This paper presents an Energy Management System (EMS) for a Multi-Microgrid (MMG) system that considers power exchanges between a set of interconnected microgrids (MGs) in an Active Distribution Network (ADN), taking into account electricity demand and renewable energy generation uncertainties using an Affine Arithmetic (AA) approach. The deterministic EMS model is formulated as a cost minimization problem which includes detailed operational constraints of thermal generators and Energy Storage Systems (ESSs) within each MG, as well as power flow limits at the Point of Common Coupling (PCC), considering all power exchanges among the set of MGs and the ADN. The uncertainties are formulated in the AA domain to obtain an EMS model that is robust for a range of realizations of the uncertain parameters, with no need of statistical assumptions or repeated calculations, which can be solved with relatively low computational burden, as opposed to other approaches such as Monte Carlo Simulation (MCS). The proposed AA model is then tested and validated with data of a set of MGs in an ADN located in São Paulo, Brazil, through comparisons with the deterministic model, MCS, and a Two-Stage Stochastic Programming (TSSP) approach. Results show an execution time improvement in the AA model of approximately 70% when compared to a MCS approach, which is expected to be slower, while considering the same range of uncertainties. Furthermore, the operation cost of the overall system decreases, as expected, by approximately 63% when power exchanges are enabled, as opposed to the individual operation of each MG, demonstrating the economic benefit of MMG systems.