This paper presents a stochastic mixed-integer nonlinear programming (MINLP) model for the optimal operation of islanded microgrids in the presence of stochastic demands and renewable resources. In the proposed formulation, the microgrid is modeled as an unbalanced three-phase electrical distribution system comprising distributed generation (DG) units with droop control, battery systems (BSs) and wind turbines (WTs). The stochastic nature of the consumption and the renewable generation is considered through a scenario-based approach, which determines the optimal values of the decision variables that minimize the average operational cost of the microgrid. A set of efficient linearizations are used to transform the proposed MINLP model into an approximated convex model that can be solved via commercial solvers. In order to assess the effectiveness of the obtained solution, Monte Carlo simulations (MCS) are carried out. Results show that the proposed model considers the uncertainty while reducing the average operational costs and load curtailments, when compared with a deterministic model.@en

This paper presents a distributed strategy for the optimal dispatch of islanded microgrids, modeled as unbalanced three-phase electrical distribution systems. To set the dispatch of the distributed generation (DG) units, an optimal generation problem is stated and solved distributively based on primal-dual constrained decomposition and a first-order consensus protocol, where units can communicate only with their neighbors. Thus, convergence is guaranteed under the common convexity assumptions. The islanded microgrid operates with the standard hierarchical control scheme, where two control modes are considered for the DG units: a voltage control mode, with an active droop control loop, and a power control mode, which allows setting the output power in advance. To assess the effectiveness and flexibility of the proposed approach, simulations were performed in a 25-bus unbalanced three-phase microgrid. According to the obtained results, the proposed strategy achieves a lower cost solution when compared with a centralized approach based on a static droop framework, with a considerable reduction on the communication system complexity. Additionally, it corrects the mismatch between generation and consumption even during the execution of the optimization process, responding to changes in the load consumption, renewable generation, and unexpected faults in units.@en

In this paper, a new and generalized model for the optimal operation of microgrids is presented. The proposed mathematical model considers both the grid-connected (GC) and islanded (IS) operational modes. First, a mixed integer non-linear programming (MINLP) formulation is introduced, modeling the microgrid as an unbalanced ac three-phase electrical distribution system, comprising distributed generator (DG) units, battery systems and wind turbines. In GC mode, the frequency and the voltage magnitude references are imposed by the main grid at the point of common couple, while in IS mode, it is assumed that the DG units operate with droop control. Additionally, a set of convexification procedures are introduced in order to approximate the original MINLP model into a new convex formulation that can be solved using commercial solvers. The proposed model has been tested in a 25-bus microgrid for different scenarios, including one where a degradation of the voltage magnitude reference is observed. Results show that the proposed model is able to properly define the operational mode of the microgrid, based on the technical constraints of the system.

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In this paper, an optimal distributed approach is presented to solve the economic dispatch (ED) problem in an islanded microgrid. Active and reactive resources are taken into account in the optimization problem aiming to consider the operational requirements of the electrical system. The optimization framework is based on primal-dual constrained decomposition. Additionally, two consensus algorithms are develop to be executed in parallel by each unit, aiming to estimate locally the value of the dual variables. Convergence is guaranteed under the common convexity assumptions. Simulations were performed on the standard IEEE 30-bus system considering dispatchable and renewable generation units. The capability of the algorithm to responds in variations in load consumption, renewable generation and faults in units were assessed. Result shows the flexibility and effectiveness of the proposed approach.@en

In this paper, a generalization of the λ-Method for the economic dispatch (ED) problem in an islanded electrical distribution system (EDS) is presented. The proposed approach is based on primal-dual constrained decomposition, which allows decomposing the centralized problem into small-scale problems that can be solved in parallel and independently by each unit. Active and reactive resources are taken into account in order to consider the technical operation of the EDS. A technical implementation based on the classic droop control is also proposed, in order to reduce the communication needs of the units and the leader unit. To assess the performance of the proposed approach, simulations were performed on the IEEE 118-bus system. The capability of the algorithm to respond to unexpected changes in load consumption, non-dispatchable generation, and faults in units were assessed. Finally, the flexibility and model independence characteristics of this approach are also shown considering prohibited operational zones (POZ) for some units.@en