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This article proposes the selective active, reactive, and distortion (PQD) power control strategy based on proportional-integral (PI) controllers devised in stationary $abc$ -reference frame for single-phase grid-following inverters. Its physical behavior and mathematical model are presented in detail and the system output impedance is derived. It is shown that the proposed control accurately tracks active, reactive, and selective distortion power terms. Experimental results show that the proposed control strategy effectively rejects source disturbances, achieving low values of current distortion even under heavily distorted grid voltages. Stability analysis under stiff and weak grids and dc-link voltage control for photovoltaic (PV) applications are evaluated. It is also shown that the implemented technique requires 26% less execution time in the main interruption (MI) than conventional solutions using PI plus resonant controllers.

The decarbonization of many heavy power-consuming industries is dependent on the integration of renewable energy sources and energy storage systems in isolated autonomous power systems. The optimal energy management in such schemes becomes harder due to the increased complexity and stability requirements, the rapidly varying operating conditions and uncertainty of renewable sources, the conflicting objectives across different timescales, the limited amount of reliable power sources and energy storage. The state of charge management when energy storage is used for multiple services, such as optimal scheduling and frequency support, is one of the most notorious problems in this context. To address this issue, an optimal energy management system is proposed in this paper. It co-optimizes the primary frequency control layer and the dispatch schedule of conventional generators and energy storage by taking advantage of an algorithm that provides adaptive active power demand uncertainty quantification, theoretical guarantees for frequency stability, and bounds for the reserves for frequency support assigned to the energy storage system. A pattern-based reformulation of the frequency stability constraints is derived enabling the efficient solution of the involved optimization problem, being a test case of an isolated offshore oil and gas platform presented for validation.