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This paper proposes an inductively active filtering (IAF) method to comprehensively improve the power quality (PQ) for not only the distribution network (public grid) but also the power-supply system (nonlinear load) connected to the network. At first, a new main-circuit topology for implementing the IAF method is presented, which consists of an inductively filtered transformer and a fully tuned branch controlled by an inverter. Its operating principle and technical features are introduced by comparing with the traditional active filtering method. Based on this, the equivalent circuit is established and by means of mathematical modeling, the unique filtering mechanism of the IAF method is revealed in theory. Further, the control strategy of the FT branch and the impedance coordination for the inductively filtered transformer are designed based on theoretical analysis. A case study is investigated in detail to illustrate the operating characteristics of the IAF method. Both the theoretical and the case studies show that the IAF method can effectively prevent harmonic components from flowing into the primary (grid) winding of the transformer. Since the harmonic components are suppressed near the harmonic source, it is good for the power-supply system and especially good for the converter transformer. Besides, since the harmonic flow is limited to near the harmonic source, the PQ of the public network can be guaranteed completely. [ABSTRACT FROM AUTHOR]

• A semi-analytical approach is developed to obtain the BESS power reserve for FFR. • The local minimum power reserve is derived to avoid UFLS under a large contingency. • The proposed method bridges the gap of the trial-and-error approaches. • The effectiveness of the proposed method is validated with an actual network model. • The methodology will advance grid services estimation and battery management. The large-scale renewable energy integration faces a challenge of frequency stability due to low inertia in weak power grids. One solution to mitigate this issue is via the fast frequency response service provided by battery storage systems so that the overall grid response during a large power outage can be improved. The battery power reserve is crucial to ensure the frequency ancillary services provision. However, grid operators currently investigate the contingency reserve of batteries through inefficient processes, such as extensive simulations or trial-and-error methods. Therefore, this paper proposes a semi-analytical methodology to quantitively determine the minimum required battery power reserve for preventing under-frequency load shedding when a severe generation trip occurs. This minimum reserve is derived from the time-variant kinetic energy of a given dispatch case. Case study results of the Mexican network demonstrate that the calculated battery power reserve can provide a cost-effective fast frequency response for a real islanded network. The research outcomes offer valuable insights for battery management and grid ancillary services requirement estimation in the transition to power networks dominated by converter-interfaced renewable energy resources. [ABSTRACT FROM AUTHOR]