## 1 Introduction  
The increased integration of distributed generation (DG) into distribution network can enhance the reliability of power supply, decrease energy loss, and improve voltage profiles. However, when DG is combined with a continuously growing number of nonlinear loads, it can cause serious issues concerning the power quality aspect. Photovoltaic (PV) systems are the most widely spread DG type at the low-voltage (LV) distribution level due to their ease of installation and maintenance as well as low cost [1]. Stochastic and variable production and the pulse-width modulation (PWM) of power converters in a case of large PV integration results in the poor harmonic composition of voltage (i.e., current waveform distortion), thus deteriorating the power quality in the distribution network. Decreasing prices of other low-carbon (LC) technologies, such as battery energy storage and electric mobility, will significantly affect a higher share of LC technologies in the LV distribution network. The rising number of PV systems, electric vehicles (EVs), and battery storage systems connected to distribution networks may cause voltage and current waveform distortions. Although harmonic distortion values of distribution networks with DG and LV technologies can meet the requirements prescribed by standards, when such systems are connected to radial distribution feeders, the cumulative effect can increase the harmonic distortion level above limits set by standards [2] EN 50160 and [3] IEEE 519 [4; 5]. Modern distribution networks, in which over 70% of the generated energy is converted using power electronic converters [6], set the mitigation of harmonics as their primary goal for power quality improvement. Power quality disturbance is a phenomenon whose effects often pass unnoticed until a failure occurs, impacting both power system devices and end users [7]. Monitoring and maintaining power quality in the distribution networks, in the context of liberalization of the electricity sector, has become one of the fundamental requirements of power systems. The emphasis is undoubtedly on distribution system operators, who are obligated and responsible for ensuring adequate levels of power quality for end users [8]. To mitigate the impact of harmonics, various techniques are applied to maintain harmonic voltages and currents within recommended levels [7] such as the design of equipment, lines or transformers, optimal placement and sizing of capacitor banks, power reduction in power systems, different harmonic filters and other adaptive devices. Various factors, such as the source of harmonic, supply network parameters, or economic aspects, influence the selection of an appropriate method for mitigating harmonics [9]. Over the past fifty years, various devices for harmonic mitigation have been developed with passive filters being one of the most popular methods due to their relatively low cost and simple design. Due to passive filters' robustness and certain drawbacks, the most significant of which include the possibility of parallel resonance with the network's impedance, excessive reactive power compensation at the nominal system frequency, poor flexibility for dynamic compensation, as well as the increasing levels and variability of harmonics, some new solutions have been implemented. Active power filters are the more recent and most commonly used solutions [7; 10].  
The active power filter (APF) is presented in the most relevant literature [11; 12; 13] as a current source. The APF acts as a controlled current source when parallel connected with nonlinear unbalanced loads, and it can generate harmonic current components present in the load current [14]. The APF serves as a device that generates the compensation current \(i_{APF}\), which must satisfy [PERSON]'s current laws at the point of common coupling (PCC).