IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 27, NO. 1,JANUARY 2012 321 Variable Sampling Period Filter PLL for Distorted Three-Phase Systems Ignacio Carugati, Sebastian Maestri, Patricio G. Donato, Daniel Carrica, Senior Member, IEEE, and Mario Benedetti Abstract—This paper proposes a novel variable sampling pe- riod filter phase-locked loop (VSPF-PLL) for use in the general area of three-phase systems. It is based on the concept of vari- able sampling period, which allows to automatically adjust the sampling frequency to be N PLL times the line frequency. Conven- tional three-phase PLL are based on synchronous reference frames (SRFs) to estimate the phase error between the PLL and the input signals. However, SRF transform fail when the voltage waveforms are distorted. In this paper, a sliding-Goertzel-transform- based filter is used in the loop to reject disturbances, such as unbalanced voltage and harmonics. It allows to detect the positive sequence present in the systems without errors. Characteristics of VSPF- PLL, including its mathematical model as well as steady state and dynamic responses, are discussed in this paper. The method is im- plemented in a DSP and tested using typical disturbances, such as frequency steps, unbalances, harmonics, saturation, and line-to- ground fault. Comparative simulations are performed between the proposed VSPF-PLL and some of the most common three-phase PLL described in the literature. Advantages of the proposed system over the methods analyzed are also discussed. Structural simplicity, robustness, and harmonics rejection are other attractive features offered by the proposed system. Index Terms—Grid disturbances and variable sampling period, synchronism, three-phase systems. I. INTRODUCTION T HE growing interest in renewable energy sources over fossil fuel resources has increased electricity production using distributed power generation systems (DPGS) and hence has modified the scenario of utility networks. As DPGS are com- posed of power converters and need to be connected to the grid, the information provided by the phase angle of the utility volt- age becomes necessary to perform several tasks, such as to syn- chronize the device, energize the local area, measure harmonic current, and carry out the control strategies during grid faults, among others [1]–[3]. Unfortunately, voltage unbalance, line dips, harmonics distortion, phase step, and variable-frequency environments are common conditions faced by equipment inter- facing with utility voltage. The quality of the angle information Manuscript received December 28, 2010; revised March 18, 2011; accepted April 15, 2011. Date of current version December 16, 2011. This work was supported by Consejo Nacional de Investigaciones Cient´ ıficas y T´ ecnicas under Grant PIP 01352, Universidad Nacional De Mar Del Plata under Grant 15/6263, and Ministerio de Ciencia, Tecnolog´ ıa e Innovaci´ on Productiva under Grant Red 506/10. Recommended for publication by Associate Editor D. Xu. The authors are with the Laboratorio de Instrumentaci´ on y Control, Fac- ultad de Ingenier´ ıa, Universidad Nacional de Mar del Plata, Mar del Plata 7600, Argentina (e-mail: icarugati@fi.mdp.edu.ar; somaestri@fi.mdp.edu.ar; donatopg@fi.mdp.edu.ar). Digital Object Identifier 10.1109/TPEL.2011.2149542 extracted is critical, as otherwise the converter could suffer from poor performance or even instability. Additionally, DPGS have to be able to ride through grid faults, which can be classified as symmetrical and asymmetrical. The former do not produce phase shifting and are not common. The latter, in turn, present phase shifting between phases and occur when the loads connected to each line are different, or when one or two phases are shorted to ground or to each other. Asym- metrical faults produce a negative sequence component, which appears in the phase angle and propagates in the system, affect- ing the control variables. As a consequence, the signals used to control the system have a second-order harmonics and the sys- tem response deteriorates. Therefore, the unbalanced voltage effect should be attenuated in order to obtain a proper synchro- nization signal. One of the most common strategies under grid faults is to follow the positive sequence of the utility network [1]. According to this new scenario, many standards have arisen with a view to regulate the operation of such systems. For ex- ample, regarding microgrid applications, IEEE 1547–2003 [4] standard defines, among others, the synchronization parameter limits that have to be met in order to keep the DPGS in each mode like a grid-connected mode, stand-alone (islanding) mode, and ride through between the two modes [5]. A deenergizing mode process for DPGS that does not fulfil these specifications is specified in the standard to preserve microgrid performance. A key topic in synchronization applied to DPGS is the con- trol of grid-side converters since the current injected into the utility network has to be synchronized with the grid voltage [1]. Different structures have been presented, which differ in terms of the reference frame in which they are implemented, e.g., syn- chronous, stationary, or natural frames [6]–[8]. Given the fact that several transformations in abc and dq frames are carried out in theses reference frames, the controller performance is tied to the synchronization algorithm [1]. In synchronous ref- erence frame (SRF) control, the current and voltage references are synchronized with the estimated phase angle. Conversely, in stationary and natural frame control, this does not occur as the current reference can be obtained from filtered utility volt- ages. However, the delay effect caused by the filter should be compensated. Another relevant issue in DPGS is power quality. For in- stance, the IEEE 1547–2003 standard limits the total harmonic distortion (THD) of the current injected by the DPGS to 5%. In order to determine the harmonics and interharmonics content, as well as THD, IEC 61000–4-7 [9] and IEC 61000–4-30 [10] standards define the instrumentation and power quality mea- surement methods corresponding to 50/60 Hz ac power supply 0885-8993/$26.00 © 2011 IEEE