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Steady-state and transient response of the active power filter based on instantaneous power theory compensation method is dependent on the accurately and quickly extract the DC component of load active power. In this paper, for improving the response of this method, the numerical filter based on recursive least squares with variable forgetting factor in order to separation of DC component of load active power is proposed. Unlike conventional low-pass filters, the feature of designed numerical filter is independent of load harmonic components, quick and precision of the answer. Also, using wavelet transform the performance of active power filter under the non-ideal voltage condition is improved. Finally, the second order delta-sigma modulation is used to generate the switching pulses. Simulation results on MATLAB / SIMULINK software shows that the proposed method is properly.

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Currently, renewable energy is rapidly developing across the world in response to technical, economic, and environmental developments, as well as political and social initiatives. Moreover, the excessive penetration of distributed generation (DG) systems into electrical networks may lead to various problems and operational limit violations, such as over and under voltages, excessive line losses, overloading of transformers and feeders, protection failure and high harmonic distortion levels exceeding the limits of international standards. These problems occur when the system exceeds its Hosting Capacity (HC) limit. The HC is a transactive approach that provides a way for the distribution network to be integrated with different types of energy systems.
Distributed Generation (DG) sources are one of the important componeents of novel distribution systems, among which renewable and clean energy sources have received more attention due to the important role of these sources in reducing greenhouse pollutants.
The use of renewable sources such as wind and photovoltaic sources is expanding day by day with the increasing demand for electric energy supply. However, the limitations in the amount of the penetration of DG resources are one of the main challenges in the development of the use of these resources.
This paper is looking for a method to improve the HC of the distribution network from DG sources by using reactive power compensation and the reconfiguration of distribution systems. The results of the simulation show the advantages of using the proposed method in increasing the HC and as a result the development of the use of renewable resources.