Abstract—This paper presents the small-signal model for a derivative hybrid power filter. The derivative hybrid filter consists of a combination of an active and a passive filter in a single structure. The small-signal model will describe how the line current interacts with the active filter inverter duty- cycle and how the DC link voltage interacts with the line current. The steps to obtain the small-signal model will be presented. The controllers will be designed based on the obtained small-signal model. Pre-established requirements for controlling the derivative hybrid filter will be stated. Moreover, stability analysis will also be made from the small-signal model. Experimental results will show that the obtained small-signal model describes truly the derivative hybrid filter. Index Terms—active filters, harmonic filters, modeling. I. INTRODUCTION Tuned passive filters (TPF) are widely used in electrical system to mitigate harmonic currents produced by nonlinear loads. Their advantages as robustness, design simplicity and low initial cost make them an attractive solution for energy quality improvement. However, their performances are quite deteriorated due to some unpredictable behavior. Voltage distortion in the electrical grid may cause a high series-resonant current level in the system. Consequently, some TPF protection devices will operate unsuitably. As an attempt to avoid such undesirable happening the IEEE1531 guide [1] recommends to tune the TPF at a frequency short lower than the desired one. Nevertheless, the TPF efficiency is compromised. Electrical systems which have a 5 th harmonic TPF installed as a solution to improve energy quality guarantees that the 5 th harmonic from the load does not flow through it. But, all other load harmonic currents from load pass almost totally through the system. As standardizations and regularizations for harmonic current injected into the system and for distortion level limits for distorted grid voltages have been imposed in some countries, electrical scenarios like that described must be adapted. Harmonic currents with frequencies higher than the TPF frequency are not allowed to flow through the system. Also, the system should be able to hold a likely series-resonant current caused from distorted voltages into the TPF without changing the normal operation. This work was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – CAPES, by CNPq and by Fapesp. Brazil. The most simplified solution is to replace the TPF to a shunt active filter (SAF) [2][3]. This action makes the electrical system to deliver a sinusoidal current waveform and to prevent any possibility of series-resonant current. However, its relatively high cost and the TPF wastage make it unattractive. Another solution is to maintain the TPF installed and place a SAF in parallel with it. This solution makes a short reduction into the cost due to the unnecessary SAF to hold the harmonic current at the same frequency than that the TPF. Nevertheless, series-resonant current is still prone to happen. In order to aim a solution with low cost and no series- resonant current and keeping the TPF installed, hybrid filters (HF) were developed. Hybrid Filters combine a TPF and active filter (AF) in a single structure. A common HF topology is the connection of the AF in series with the TPF [4][6]. This solution reduces the cost due to the reduced voltage hold by the AF, but it must hold all filtered current. Another HF topology is the connection of the AF in parallel with the TFP inductor [7], known as Derivative Hybrid Filter (DHF). This solution processes less power electronically compared to those already described due to the voltage and current holding by the AF. The reduction occurs due to the AF holds low voltage and low current, where the filtered current is shared between the AF and the TPF inductor. The DHF analysis and dimensioning were presented in [8][9]. However, the authors did not use a mathematical model to design the line harmonic current controller and did not show the DHF behavior during step loads. Also, the electrical system behavior when the grid voltages present distortion was not investigated. Renewable energy penetration into the electrical system increased along the last years [10]. As result, the impedance characteristic of the electrical grid begins to be influenced by their inverters output impedance [11]. The energy quality is deteriorated due to a likely series resonance formed by the inverter output capacitance and the grid inductance. The DHF is an attractive solution to solve quality issues in electrical system containing renewable sources connected through inverters. The mathematical model of a DHF may describe precisely its dynamic behavior. Designing a controller without modeling the system is not suited when loads change their apparent power consumption. Even more, in Small-Signal Model for a Derivative Hybrid Power Filter Tiago Davi Curi Busarello 1 , Newton da Silva 2 , Edson Adriano Vendrusculo 1 and José Antenor Pomilio 1 1: School of Electrical and Computer Engineering. University of Campinas – UNICAMP. Av. Albert Einstein, 400 13083-852 - Campinas -SP Brazil. 2: University of Londrina – UEL - Londrina – PR Brazil E-mail: tiago201@dsce.fee.unicamp.br, newton.silva@uel.br, adriano@dsce.fee.unicamp.br, antenor@dsce.fee.unicamp.br.