14th International Conference on Optimization of
Electrical and Electronic Equipment OPTIM 2014
May 22-24, 2014, Brasov, Romania
Implementation of PLL and FLL trackers for signals with high harmonic content and low
sampling frequency
L. Mathe, F. Iov, D. Sera, L. Torok, R. Teodorescu
Department of Energy Technology, Aalborg University, Aalborg, Denmark
Abstract
The accurate tracking of phase, frequency, and amplitude of different frequency components from a measured signal is an essential
requirement for many digitally controlled equipment. The accurate and robust tracking of a frequency component from a complex
signal was successfully applied for example in: grid connected inverters [1], sensorless motor control for rotor position estimation
[2], grid voltage monitoring for ac-dc converters [3] etc. Usually, the design of such trackers is done in continuous time domain.
The discretization introduces errors which change the performance, especially when the input signal is rich in harmonics [4, 5] and
the sampling frequency is close to the tracked frequency component.
In this paper different discretization methods and implementation issues, such as Tustin, Backward-Forward Euler, are discussed
and compared. A special case is analysed, when the input signal is reach in harmonics and the sampling frequency is only 10 times
larger than the tracked frequency component.
Fig. 1 and Fig. 2 presents the block scheme of a PLL respectively the QSG and the FLL. The key issue for such a
PLL is the digital implementation of the SOGI block which is used in the QSG and it can also be used in the VCO.
Fig.1 Structure of the PLL based on quadrature signal
generation
Fig.2 Diagram of the: (a) SOGI-QSG, and (b) FLL
Two discretization methods, the Backward-Forward Euler (BE-FE) and Tustin, are used in order to convert the
continuous time domain transfer function to a discrete. The BE-FE method requires less calculation power than the
Tustin method for parameter calculation of the second order transfer function. However, for applications where the
PLL is not adaptive to frequency variations these calculations can be made offline. At low sampling frequency the
BE-FE method cannot ensure the quadrature between the alpha and beta component, thus Tustin method is advised
to be used. For the case when the PLL is adaptive to frequency variation a FLL feedback is used. In this case the
parameters have to be recalculated at each sampling, which requires more calculation in case of Tustin
implementation.
References
[1]
[2]
[3]
[4]
[5]
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