This application claims priority under 35 U.S.C. §119 to European Application No. 12180224.3 filed in Europe on Aug. 13, 2012, the entire content of which is hereby incorporated by reference in its entirety.
The present disclosure relates to synchronization with a three-phase reference signal, for example, in situations where the reference signal is unbalanced and/or subject to harmonic distortion.
In some applications, it can be desirable to be able to synchronize with a reference signal. For example, in distributed power generation, grid connected power converters can be synchronized with the phase and frequency of a utility grid.
A phase-locked loop (PLL) can be used for synchronizing with a signal. PLLs can be formed in various ways. For example, a synchronous reference frame phase-locked loop (SRF-PLL) is a PLL technique which is capable of detecting a phase angle and a frequency of a reference signal.
Different designs have been proposed based on the SRF-PLL approach. As many other designs, the SRF-PLL is based on a linearization assumption, for example, the results can be guaranteed locally. The SRF-PLL can yield a fast and precise detection of the phase angle, fundamental frequency and amplitude of the reference signal.
However, designs based on the SRF-PLL approach can be prone to fail due to harmonic distortion. The bandwidth of the SRF-PLL feedback loop can be reduced to reject and cancel out the effect of these harmonics on the output, if the reference signal is distorted with low-order harmonics, for example, harmonics close to the fundamental frequency. In some cases, however, reducing the PLL bandwidth can be an unacceptable solution as the speed of response of the PLL can be considerably reduced as well.
Further, unbalance in the reference signal can cause issues for designs based on the SRF-PLL approach.
A phase-locked loop for estimating a phase angle of a three-phase reference signal is disclosed, wherein the phase-locked loop comprises: an adaptive quadrature signal generator configured to calculate an estimated first state and an estimated second state of a model of an unbalanced three-phase system at a fundamental frequency of the reference signal on a basis of the reference signal and an estimated fundamental frequency, wherein the model includes a first state representing a sum of a positive and a negative sequence component of the reference signal at a harmonic frequency, and a second state representing a difference between the positive sequence component and the negative sequence component; a positive sequence generator configured to calculate a fundamental positive sequence component of the reference signal on a basis of the estimated first state and the estimated second state; a reference frame transformation block configured to calculate a direct component and a quadrature component in a rotating reference frame synchronous with an estimated phase angle on a basis of the fundamental positive sequence component and the estimated phase angle, and configured to determine an estimate of an amplitude of the fundamental positive sequence component on the basis of the direct component; and an estimator configured to determine estimates of the estimated fundamental frequency and the estimated phase angle on the basis of the quadrature component.
A method for estimating a phase angle of a three-phase reference signal is disclosed, wherein the method comprises: calculating an estimated first state and an estimated second state of a model of an unbalanced three-phase system at s fundamental frequency of the reference signal on the basis of the reference signal and an estimated fundamental frequency, wherein the model comprises a first state representing a sum of a positive and a negative sequence component of the reference signal at a harmonic frequency, and a second state representing a difference between the positive sequence component and the negative sequence component; calculating a fundamental positive sequence component of the reference signal on the basis of the estimated first state and the estimated second state; calculating a direct component and a quadrature component in a rotating reference frame synchronous with an estimated phase angle on the basis of the fundamental positive sequence component and the estimated phase angle; determining an estimate of an amplitude of the fundamental positive sequence component on the basis of the direct component; and determining estimates of the estimated fundamental frequency and the estimated phase angle on the basis of the quadrature component.
In the following, the disclosure will be described in greater detail by means of exemplary embodiments with reference to the attached drawings, in which
a to 3d illustrate a simulated transient response of the arrangement of
a to 4d illustrate a simulated transient response of the exemplary arrangement of
a to 5d illustrate a simulated transient response of the exemplary arrangement of
a to 6d illustrate a simulated transient response of an exemplary SRF-PLL algorithm to a change from balanced to unbalanced in a reference signal.
In accordance with an exemplary embodiment, an improved tolerance for harmonic distortion and unbalance can be achieved by using a method where a fundamental positive sequence component is first calculated from the reference signal, and the positive sequence component can be used to estimate the phase angle of the reference signal.
Calculation of the fundamental positive sequence component can be based on a description of a three-phase signal where the signal is described by a sum of positive and negative sequences in stationary-frame coordinates. In accordance with an exemplary embodiment, the fundamental positive sequence component can be extracted even under unbalanced conditions. The calculation of the fundamental positive sequence component can also include an explicit harmonic compensation mechanism (UHCM) which can deal with a possible unbalanced harmonic distortion present in the reference signal.
In accordance with an exemplary embodiment, as a result, the calculated fundamental positive sequence component can be largely free of harmonic distortion and unbalance.
In accordance with an exemplary embodiment, the fundamental positive sequence component can then be transformed into a synchronous reference frame and a quadrature component of the positive sequence component in the synchronous reference frame can be used to estimate the fundamental frequency and the phase angle of the reference signal. The estimated fundamental frequency, for example, can be used in the calculation of the fundamental positive sequence component.
An exemplary method is disclosed, which can provide clean estimates of the phase angle and the amplitude of the fundamental positive sequence component of a three-phase reference signal, even if the reference signal is subject to unbalance and harmonic distortion. The exemplary method can also be robust against angular frequency variations.
In accordance with an exemplary embodiment, knowledge about the phase angle and the amplitude of the fundamental positive sequence component of a three-phase reference signal can be used by some applications. For example, some applications can also use additional information, such as estimates of the angular frequency, and positive and negative sequences of the fundamental component of the reference signal. This can, for example, be the case in three-phase grid connected systems, such as power conditioning equipment, flexible ac transmission systems (FACTS), power line conditioners, regenerative drives, uninterruptible power supplies (UPS), grid connected inverters for alternative energy sources and other distributed generation and storage systems.
The present disclosure discloses a method for estimating a phase angle of a three-phase reference signal. The method can provide clean estimates of the phase angle and the amplitude of the fundamental positive sequence component of a three-phase reference signal, even when the reference signal is unbalanced and/or subject to harmonic distortion.
The disclosed method is robust against angular frequency variations, and can also provide estimates of the angular frequency, and both the positive and negative sequences of the fundamental component of the reference signal.
The disclosed method can extract a fundamental positive sequence component from the reference signal. The fundamental positive sequence component can then be transformed into a synchronous reference frame where the quadrature component of the fundamental positive sequence component can be controlled to zero in order to estimate the fundamental frequency and the phase angle of the reference signal.
Extraction of the fundamental positive sequence component can be performed on the basis of a model of an unbalanced three-phase signal. For example, a signal vαβ can be seen as a sum of harmonics. Thus, a description of an unbalanced three-phase signal can involve a sum of positive and negative sequences in stationary-frame coordinates.
According to G. Escobar, S. Pettersson and C. N. M. Ho, “Phase-locked loop for grid synchronization under unbalanced operation and harmonic distortion,” in Proc. Industrial Electronics Conf. IECON11, Melbourne, November 2011, Vol. 1, pp. 623-628, the following model can describe a generator for a single unbalanced kth harmonic at a harmonic frequency kω0:
{dot over (v)}
αβ,k
=kω
0
Jφ
αβ,k,
{dot over (φ)}αβ,k=kω0Jvαβ,k. (1)
The above model includes a first state vαβ,k and a second state φαβ,k, where the states are represented in stationary αβ coordinates. Phase variables, such as phase voltages of a three-phase grid, can be transformed into αβ coordinates by using Clarke's transformation. In Equation (1), J is a transformation matrix defined as follows:
The first state vαβ,k represents a sum of a positive sequence component vαβ,kp and a negative sequence component vαβ,kn of the reference signal at the harmonic frequency kω0:
v
αβ,k
=v
αβ,k
p
+v
αβ,k
n. (3)
In accordance with an exemplary embodiment, the first state vαβ,k represents the kth unbalanced harmonic. The second state φαβ,k represents a difference between the positive sequence component and the negative sequence component:
φαβ,k=vαβ,kp−vαβ,k•n. (4)
The model of Equation (1) forms an oscillator generating an unbalanced sinusoidal signal. In this disclosure, such an oscillator is referred to as an unbalanced harmonic oscillator (UHO).
The states of a kth harmonic in the reference signal can be estimated using, for example, the following estimator:
{circumflex over ({dot over (v)}
αβ,k
=k{circumflex over (ω)}
0
J{circumflex over (φ)}
αβ,1+γk{tilde over (v)}αβ,k,
{circumflex over ({dot over (φ)}αβ,k=k{circumflex over (ω)}0J{circumflex over (v)}αβ,k, (5)
where {circumflex over (v)}αβ,k and {circumflex over (φ)}αβ,k are estimates of the first and the second state at the fundamental frequency, and {tilde over (v)}αβ,k is a difference between the reference signal vαβ and the unbalanced first harmonic, e.g., the first state {circumflex over (v)}αβ,k. γk is a design parameter which introduces damping.
The model of Equation (1) and the estimator of Equation (5) can be used to extract the fundamental positive sequence component, e.g., the positive sequence component vαβ,1p of the first harmonic. However, in order to apply an estimator of Equation (5), an estimate {circumflex over (ω)}0 of the fundamental frequency has to be known. Estimating the fundamental frequency will be discussed later in this disclosure.
On the basis of the reference signal vαβ and the estimated fundamental frequency {circumflex over (ω)}0, the disclosed method can calculate (e.g., via a processor) an estimated first state {circumflex over (v)}αβ,1 of the model and an estimated second state {circumflex over (φ)}αβ,1 of the model at the fundamental frequency of the reference signal vαβ.
When values of the two estimated states are known, a fundamental positive sequence component {circumflex over (v)}αβ,1p of the reference signal vαβ can be calculated on the basis of the estimated first state {circumflex over (v)}αβ,1 and the estimated second state {circumflex over (φ)}αβ,1. A fundamental negative sequence component {circumflex over (v)}αβ,1n of the reference signal can also be calculated on the basis of the estimated first state {circumflex over (v)}αβ,1 and the estimated second state {circumflex over (φ)}αβ,1 of the model of an unbalanced three-phase system.
In accordance with an exemplary embodiment, a synchronous reference frame approach can then be used with the fundamental positive sequence component {circumflex over (v)}αβ,1p as the new reference. On the basis of the fundamental positive sequence component {circumflex over (v)}αβ,1p and an estimated phase angle {circumflex over (θ)}0, a direct component {circumflex over (ν)}d,1p and a quadrature component {circumflex over (ν)}q,1p in a rotating reference frame synchronous with the estimated phase angle can be calculated.
An estimate of an amplitude of the fundamental positive sequence component {circumflex over (v)}αβ,1p can be determined on the basis of the direct component {circumflex over (ν)}d,1and estimates of the estimated fundamental frequency {circumflex over (ω)}0 and the estimated phase angle {circumflex over (θ)}0 can be determined on the basis of the quadrature component vq,1p.
The estimated phase angle {circumflex over (θ)}0 can be determined by integrating the estimated fundamental frequency {circumflex over (ω)}0. When the estimated phase angle {circumflex over (θ)}0 follows the actual phase angle of the fundamental positive sequence component {circumflex over (v)}αβ,1p in synchrony, the magnitude of the quadrature component {circumflex over (ν)}q,1p is zero. According to an exemplary embodiment, the method can adjust the estimated fundamental frequency {circumflex over (ω)}0, that is, the change rate of the estimated phase angle {circumflex over (θ)}0, in order to minimize the magnitude of the quadrature component {circumflex over (ν)}q,1p.
In order to deal with harmonic distortion in the reference signal vαβ, the disclosed method can also include extracting harmonic contents {circumflex over (v)}αβ,h of the reference signal at least at one harmonic frequency other than a fundamental harmonic frequency of the reference signal. The harmonic distortion of the reference signal can be compensated for on the basis of the extracted harmonic content {circumflex over (v)}αβ,h. In a manner similar to that in connection with the first harmonic, the extraction can be performed on the basis of the reference signal vαβ, the estimated fundamental frequency {circumflex over (ω)}0, and the model of an unbalanced three-phase system.
The adaptive quadrature signal generator 11 can act as a means for calculating an estimated first state {circumflex over (v)}αβ,1 of the model and an estimated second state {circumflex over (φ)}αβ,1 of the model at the fundamental frequency. In
The positive sequence generator 12 can act as a means for calculating the fundamental positive sequence component {circumflex over (v)}αβ,1p. The positive sequence generator 12 calculates the fundamental positive sequence component {circumflex over (v)}αβ,1p of the reference signal vαβ on the basis of the estimated first state {circumflex over (v)}αβ,1 and the estimated second state {circumflex over (φ)}αβ,1. In
The apparatus can also include a means for calculating a fundamental negative sequence component {circumflex over (v)}αβ,1n of the reference signal on the basis of the estimated first state {circumflex over (v)}αβ,1 and the estimated second state {circumflex over (φ)}αβ,1 of the model of an unbalanced three-phase system. The fundamental negative sequence component {circumflex over (v)}αβ,1n can, for example, be calculated by dividing a difference between the estimated first state {circumflex over (v)}αβ,1 and the estimated second state {circumflex over (φ)}αβ,1 by two.
The reference frame transformation block 13 can then calculate a direct component {circumflex over (ν)}d,1p and a quadrature component {circumflex over (ν)}q,1p in a rotating reference frame synchronous with the phase angle (dq coordinates). In
In
When the magnitude of the quadrature component {circumflex over (ν)}q,1p is zero, the fundamental positive sequence component {circumflex over (v)}dq,1p in the rotating reference frame coordinates includes only the direct component {circumflex over (ν)}d,1p. Thus, the magnitude of the fundamental positive sequence component {circumflex over (v)}αβ,1p can be represented by the direct component {circumflex over (ν)}d,1p. In accordance with an exemplary embodiment, the reference frame transformation block 13 can also act as means for determining an estimate of an amplitude of the fundamental positive sequence component {circumflex over (v)}αβ,1p on the basis of the direct component {circumflex over (ν)}d,1p.
In
In order to deal with harmonic distortion, the exemplary phase-locked loop 10 of
The unbalanced harmonic compensation mechanism 15 in
The harmonic contents {circumflex over (v)}αβ,h can be extracted on the basis of the reference signal vαβ, the fundamental frequency {circumflex over (ω)}0, and the above model of the unbalanced three-phase system, e.g., a model that includes a first state representing a sum of a positive and a negative sequence component of the reference signal at the harmonic frequency in question, and a second state representing a difference between the positive sequence component and the negative sequence component of the reference signal at the harmonic frequency in question.
of harmonic components extracted by the UHOs can be fed back to the arrangement of
In
An exemplary simulation of the implementation of
First, in the time frame of t=0 to 1 s, the setup was simulated under balanced conditions. The reference signal was formed only by a fundamental positive sequence of 100 V of amplitude. The fundamental frequency was 314.16 rad/s (50 Hz), with a zero phase shift.
Second, in the time frame of t=1 s to 2 s, the setup was simulated under unbalanced conditions. The reference signal included positive and negative sequence components. The positive sequence had an amplitude of 100 Vat 314.16 rad/s (50 Hz) and a zero phase shift. For the negative sequence, an amplitude of 30 V and a phase shift of 1 rad were used.
Third, in the time frame of t=2 s to 3 s, the setup was simulated under unbalanced conditions with harmonic distortion. 3rd and 5th harmonics were added to the unbalanced signal of the second simulation step in order to create a periodic distortion. Both harmonics had also negative sequence components in order to have unbalance in the added harmonics as well.
Fourth, the setup was simulated with a frequency variation. A step change in the fundamental frequency of the reference signal was introduced at time t=3 s, changing from 314.16 rad/s (50 Hz) to 219.9 rad/s (35 Hz).
a to 3d show a simulated transient response of the exemplary arrangement of
a to 4d show the simulated transient response of the exemplary arrangement of
In
a to 5d show a simulated transient response of the exemplary arrangement of
For comparison, a SRF-PLL scheme as disclosed in V. Kaura and V. Blasco, “Operation of a phase locked loop system under distorted utility conditions,” IEEE Trans. on Ind. Appl., Vol. 33, Issue 1, pp. 58-63, January/February 1997 was also simulated. The SRF-PLL was tuned to avoid excess of ripple, while still allowing for an acceptable dynamical response.
a to 6d illustrate that the SRF-PLL scheme lacked means for dealing with the unbalanced operation. Similar results were obtained when harmonic distortion was added on top of the unbalance.
Thus, it will be appreciated by those skilled in the art that the present invention can be embodied in other specific forms without departing from the spirit or essential characteristics thereof. The presently disclosed embodiments are therefore considered in all respects to be illustrative and not restricted. The scope of the invention is indicated by the appended claims rather than the foregoing description and all changes that come within the meaning and range and equivalence thereof are intended to be embraced therein.
Number | Date | Country | Kind |
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12180224.3 | Aug 2012 | EP | regional |