A key motivator for wider deployment of microgrids (small electric networks with distributed generation connected that operate either connected at low and medium voltage levels or isolated mode) is to bring about the decentralization of the generation. This goal is because microgrids use renewable power sources and storage energy systems. However, the microgrids operation represents various challenges for grid-connected microgrids about the power interchanges with the distribution network. If the operation is performed under optimal conditions, there are benefits for microgrid investment. This paper proposes a detailed formulation to operate microgrids with photovoltaic systems and storage. The model can be used with multiple microgrids interconnected considering electricity prices and tariffs. The model corresponds to an optimal power flow approach for microgrids considering some energy storage systems. The mathematical model considers explicitly electricity tariffs. Illustrative results indicate the optimal operation of microgrids considering a load curve; specifically, the microgrid is designed to operate at different operational circumstances. A case includes multiple microgrids interconnected at different electricity prices. The electricity tariffs determine the power interchanges between the distribution network and the microgrid. Such insights about the optimal operation of microgrids provide a wide range of applications, particularly in operation and feasibility of projects.

This paper utilizes convex optimization to implement a day-ahead scheduling strategy for operating a photovoltaic distribution static compensator (PV-STATCOM) in medium-voltage distribution networks. The nonlinear non-convex programming model of the day-ahead scheduling strategy is transformed into a convex optimization model using the second-order cone programming approach in the complex domain. The main goal of efficiently operating PV-STATCOMs in distribution networks is to dynamically compensate for the active and reactive power generated by renewable energy resources such as photovoltaic plants. This is achieved by controlling power electronic converters, usually voltage source converters, to manage reactive power with lagging or leading power factors. Numerical simulations were conducted to analyze the effects of different power factors on the IEEE 33- and 69-bus systems. The simulations considered operations with a unity power factor (active power injection only), a zero power factor (reactive power injection only), and a variable power factor (active and reactive power injections). The results demonstrated the benefits of dynamic, active and reactive power compensation in reducing grid power losses, voltage profile deviations, and energy purchasing costs at the substation terminals. These simulations were conducted using the CVX tool and the Gurobi solver in the MATLAB programming environment.

This study makes a revision of the most recent investigations that have implemented the wavelet transform by analyzing the electrical and mechanical variables of the induction motors. The investigations can be grouped into three main topics: diagnosis and detection of faults, control and detection systems and the classification of electromagnetic disturbances.