Direct power control (DPC) has increasingly gained attention in the last years as a robust and simple control scheme. Yet, the implications of some of the assumptions made by the original table-based DPC are not well explained in the literature. Here, a new formulation of DPC is presented, that allows to analyze the shortcomings of this kind of algorithms, mainly regarding the power limits in which table-based algorithms are valid. This is a key aspect for microgrid applications, as they require a wide range of possible active and reactive power setpoints in order to be able to control the system's voltage and frequency. A new table is then presented that allows to overcome those limitations. The proposed table is valid at any point of the inverter's power limits.Index Terms-Direct power control (DPC), power systems control, switching table, three-phase inverter.

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A naive battery operation optimization attempts to maximize short-term profits. However, it has been shown that this approach does not optimize long-term profitability, as it neglects battery degradation. Since a battery can perform a limited number of cycles during its lifetime, it may be better to operate the battery only when profits are on the high side. Researchers have dealt with this issue using various strategies to restrain battery usage, reducing short-term benefits in exchange for an increase in long-term profits. Determining this operation restraint is a topic scarcely developed in the literature. It is common to arbitrarily quantify degradation impact into short-term operation, which has proven to have an extensive impact on long-term results. This paper carries out a critical review of different methods of degradation control for short-time operation. A classification of different practices found in the literature is presented. Strengths and weaknesses of each approach are pointed out, and future possible contributions to this topic are remarked upon. The most common methodology is implemented in a simulation for demonstration purposes.