584 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 2, MARCH 2007
Decoupled Double Synchronous Reference
Frame PLL for Power Converters Control
Pedro Rodríguez, Member, IEEE, Josep Pou, Member, IEEE, Joan Bergas, Member, IEEE,
J. Ignacio Candela, Member, IEEE, Rolando P. Burgos, Member, IEEE, and Dushan Boroyevich, Fellow, IEEE
Abstract—This paper deals with a crucial aspect in the con-
trol of grid-connected power converters, i.e., the detection of
the fundamental-frequency positive-sequence component of the
utility voltage under unbalanced and distorted conditions. Specif-
ically, it proposes a positive-sequence detector based on a new
decoupled double synchronous reference frame phase-locked loop
(DDSRF–PLL), which completely eliminates the detection errors
of conventional synchronous reference frame PLL’s (SRF–PLL).
This is achieved by transforming both positive- and negative-se-
quence components of the utility voltage into the double SRF,
from which a decoupling network is developed in order to cleanly
extract and separate the positive- and negative-sequence com-
ponents. The resultant DDSRF–PLL conducts then to a fast,
precise, and robust positive-sequence voltage detection even under
unbalanced and distorted grid conditions. The paper presents
a detailed description and derivation of the proposed detection
method, together with an extensive evaluation using simulation
and experimental results from a digital signal processor-based
laboratory prototype in order to verify and validate the excellent
performance achieved by the DDSRF–PLL.
Index Terms—Grid-connected converters, phase locked loop
(PLL), positive sequence signals detection, synchronous reference
frame (SRF).
I. INTRODUCTION
O
NE of the most important aspects to consider in the
control of grid-connected power converters is the proper
synchronization with the utility voltages. Specifically, the
detection of the positive-sequence voltage component at fun-
damental frequency is essential for the control of distributed
generation and storage systems, flexible ac transmission sys-
tems (FACTS), power line conditioners and uninterruptible
power supplies (UPS) [1], [2]. The magnitude and angle of
the positive-sequence voltage is used for the synchronization
of the converter output variables, power flux calculations, or
for the transformation of state variables into rotating reference
Manuscript received November 29, 2005; revised June 19, 2006. This paper
was presented at IEEE PESC’05, Recife, Brazil, June 12–16, 2005. This work
was supported by the Ministerio de Ciencia y Tecnologia of Spain under Grant
PR2006-0411, Project ENE2004-07881-C03-02, the Engineering Research
Center Shared Facilities supported by the National Science Foundation under
NSF Award EEC-9731677, and by the CPES Industry Partnership Program.
Recommended for publication by Associate Editor F. Blaabjerg.
P. Rodríguez, J. Bergas, and J. I. Candela are with the Department of Elec-
trical Engineering, Technical University of Catalonia (UPC), Terrassa 08222,
Spain (e-mail: prodriguez@ee.upc.edu).
J. Pou is with the Department of Electronic Engineering, Technical University
of Catalonia (UPC), Terrassa 08222, Spain.
R. P. Burgos and D. Boroyevich are with the Center for Power Electronics
Systems (CPES), The Bradley Department of Electrical and Computer Engi-
neering, Virginia Polytechnic Institute and State University (Virginia Tech),
Blacksburg, VA 24061 USA.
Digital Object Identifier 10.1109/TPEL.2006.890000
frames [3]–[5]. Regardless of the technique used in the system
detection, the amplitude and the phase of the positive-sequence
component must be fast and accurately obtained, even if the
utility voltage is distorted and unbalanced.
There are two main approaches to detect the positive sequence
component of the utility voltage. The first one assumes that the
frequency of the utility is a constant and well-known magnitude,
and is usually based on 1) instantaneous symmetrical compo-
nents (ISC) [6], 2) on space vector filters (SVF) [7], or on 3) the
recursive weighted least-square estimation algorithm (WLSE)
[8]. The second approach assumes that the utility frequency is
not constant, and uses closed-loop adaptive methods in order
to render the detection algorithm insensitive to input frequency
variations. In this sense, a frequency update algorithm can be
used in the WLSE-based approach [9]. This method however ex-
hibits long transient time intervals in the detection of frequency
changes. The most extended technique used for frequency-in-
sensitive positive-sequence detection is the three-phase phase
locked loop (PLL) based on the synchronous reference frame
(SRF–PLL) [10], although alternative structures are also pos-
sible [11]. A discussion on the behavior of the SRF-PLL under
unbalanced grid conditions will be performed in Section II.
Another possibility is to use some kind of enhanced single-phase
PLL for each phase of the system [12], [13], allowing the estima-
tion of frequency and in-phase and quadrature-phase waveforms
for each of the phase voltages. These phase voltages and their
respective 90
shifted versions can be used by the ISC method in
order to detect the positive-sequence voltages of the three-phase
system [14]. This improved version of the ISC approach uses
an additional single-phase PLL to estimate the phase-angle of
the detected positive-sequence voltage. Although this four-inde-
pendent single-phase PLL-based technique offers good results
in the estimation of the positive-sequence component in unbal-
anced power systems [15], some features can be improved by
replacing the single-phase PLLs by an enhanced three-phase
PLL structure.
This work presents an alternative detection method to be used
in unbalanced power networks, namely the decoupled double
synchronousreferenceframePLL(DDSRF-PLL).Theproposed
technique defines an unbalanced voltage vector, consisting of
bothpositive-and negative-sequencecomponents, and expresses
it on the double synchronous reference frame in order to detect
the positive-sequence component [17], [18]. This is accom-
plished by studying the relationships between the transformed
signals on the DSRF-axes, which combined with the design of
a proper decoupling system enables a fast and accurate phase
and amplitude detection of the utility voltage positive-sequence
component under unbalanced utility conditions.
0885-8993/$25.00 © 2007 IEEE
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