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Vinod John - One of the best experts on this subject based on the ideXlab platform.
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design of a fast response time single phase pll with dc offset rejection capability
Electric Power Systems Research, 2017Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Abstract Second-order generalized integrator (SOGI) based phase-locked loops (PLLs) are commonly used for grid voltage synchronization in single-phase grid-connected power converters. SOGI-PLLs are attractive because of their simple structure that makes them suitable for implementation even in low-end digital controllers. In this paper, an SOGI based fixed-parameter PLL structure with full dc offset rejection capability is presented. This PLL uses two cascaded SOGI structures and it is termed as cascaded generalized integrator PLL (CGI-PLL). A systematic design procedure is proposed for the CGI-PLL that minimizes the response time and Unit Vector harmonic distortion. This design achieves minimum settling time for any given worst-case frequency deviation in the grid voltage and ensures that the Unit Vector THD is less than 1%. The PLL designed using the proposed method has good harmonic attenuation capability. The steady-state and transient response of this PLL have been validated experimentally and are found to agree with the theoretical analysis.
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analysis of bandwidth Unit Vector distortion tradeoff in pll during abnormal grid conditions
IEEE Transactions on Industrial Electronics, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the Unit Vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the Unit Vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the Unit Vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of Unit Vector THD. The tuning method for SRF-PLL is also validated experimentally.
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Analysis of Bandwidth–Unit-Vector-Distortion Tradeoff in PLL During Abnormal Grid Conditions
IEEE Transactions on Industrial Electronics, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the Unit Vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the Unit Vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the Unit Vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of Unit Vector THD. The tuning method for SRF-PLL is also validated experimentally.
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A novel design method for SOGI-PLL for minimum settling time and low Unit Vector distortion
IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in grid connected systems to obtain information about the frequency, amplitude and phase of the grid voltage. In stationary reference frame control, the Unit Vectors of PLLs are used for reference generation. It is important that the PLL performance is not affected significantly when grid voltage undergoes amplitude and frequency variations. In this paper, a novel design for the popular single-phase PLL topology, namely the second-order generalized integrator (SOGI) based PLL is proposed which achieves minimum settling time during grid voltage amplitude and frequency variations. The proposed design achieves a settling time of less than 27.7ms. This design also ensures that the Unit Vectors generated by this PLL have a steady state THD of less than 1% during frequency variations of the grid voltage. The design of the SOGI-PLL based on the theoretical analysis is validated by experimental results.
Alexander Yampolsky - One of the best experts on this subject based on the ideXlab platform.
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On the intrinsic geometry of a Unit Vector field
2020Co-Authors: Alexander YampolskyAbstract:We study the geometrical properties of a Unit Vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature K, we give a description of the totally geodesic Unit Vector fields for K = 0 and K = 1 and prove a non-existence result for K 6 0,1. We also found a family �! of Vector fields on the hyperbolic 2-plane L 2 of curvature −c 2 which generate foliations on T1L 2 with leaves of constant intrinsic curvature −c 2 and of constant extrinsic curvature − c 2 4 .
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Stability of Left-Invariant Totally Geodesic Unit Vector Fields on Three-Dimensional Lie Groups
Geometry and its Applications, 2014Co-Authors: Alexander YampolskyAbstract:We consider the problem of stability or instability of Unit Vector fields on three-dimensional Lie groups with left-invariant metric which have totally geodesic image in the Unit tangent bundle with the Sasaki metric with respect to classical variations of volume. We prove that among non-flat groups only SO(3) of constant curvature + 1 admits stable totally geodesic submanifolds of this kind. Restricting the variations to left-invariant (i.e., equidistant) ones, we give a complete list of groups which admit stable/unstable Unit Vector fields with totally geodesic image.
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Invariant totally geodesic Unit Vector fields on three-dimensional Lie groups
arXiv: Differential Geometry, 2005Co-Authors: Alexander YampolskyAbstract:We give a complete list of those left invariant Unit Vector fields on three-dimensional Lie groups with the left-invariant metric that generate a totally geodesic submanifold in the Unit tangent bundle of a group with the Sasaki metric. As a result, each class of three-dimensional Lie groups admits the totally geodesic Unit Vector field. From geometrical viewpoint, the field is either parallel or characteristic Vector field of a natural almost contact structure on the group.
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On special types of minimal and totally geodesic Unit Vector fields
arXiv: Differential Geometry, 2005Co-Authors: Alexander YampolskyAbstract:We present a new equation with respect to a Unit Vector field on Riemannian manifold $M^n$ such that its solution defines a totally geodesic submanifold in the Unit tangent bundle with Sasaki metric and apply it to some classes of Unit Vector fields. We introduce a class of covariantly normal Unit Vector fields and prove that within this class the Hopf Vector field is a unique global one with totally geodesic property. For the wider class of geodesic Unit Vector fields on a sphere we give a new necessary and sufficient condition to generate a totally geodesic submanifold in $T_1S^n$.
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On the intrinsic geometry of a Unit Vector field
arXiv: Differential Geometry, 2005Co-Authors: Alexander YampolskyAbstract:We study the geometrical properties of a Unit Vector field on a Riemannian 2-manifold, considering the field as a local imbedding of the manifold into its tangent sphere bundle with the Sasaki metric. For the case of constant curvature K, we give a description of the totally geodesic Unit Vector fields for K=0 and K=1 and prove a non-existence result for K not equal to 0 and 1. We also found a family of Vector fields on the hyperbolic 2-plane L^2 of curvature -c^2 which generate foliations on Unit tangent bundle over L^2 with leaves of constant intrinsic curvature -c^2 and of constant extrinsic curvature -c^2/4.
Abhijit Kulkarni - One of the best experts on this subject based on the ideXlab platform.
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design of a fast response time single phase pll with dc offset rejection capability
Electric Power Systems Research, 2017Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Abstract Second-order generalized integrator (SOGI) based phase-locked loops (PLLs) are commonly used for grid voltage synchronization in single-phase grid-connected power converters. SOGI-PLLs are attractive because of their simple structure that makes them suitable for implementation even in low-end digital controllers. In this paper, an SOGI based fixed-parameter PLL structure with full dc offset rejection capability is presented. This PLL uses two cascaded SOGI structures and it is termed as cascaded generalized integrator PLL (CGI-PLL). A systematic design procedure is proposed for the CGI-PLL that minimizes the response time and Unit Vector harmonic distortion. This design achieves minimum settling time for any given worst-case frequency deviation in the grid voltage and ensures that the Unit Vector THD is less than 1%. The PLL designed using the proposed method has good harmonic attenuation capability. The steady-state and transient response of this PLL have been validated experimentally and are found to agree with the theoretical analysis.
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analysis of bandwidth Unit Vector distortion tradeoff in pll during abnormal grid conditions
IEEE Transactions on Industrial Electronics, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the Unit Vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the Unit Vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the Unit Vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of Unit Vector THD. The tuning method for SRF-PLL is also validated experimentally.
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Analysis of Bandwidth–Unit-Vector-Distortion Tradeoff in PLL During Abnormal Grid Conditions
IEEE Transactions on Industrial Electronics, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in applications which require grid synchronization. Presence of unbalance or harmonics in the grid voltage creates errors in the estimated frequency and angle of a PLL. The error in estimated angle has the effect of distorting the Unit Vectors generated by the PLL. In this paper, analytical expressions are derived which determine the error in the phase angle estimated by a PLL when there is unbalance and harmonics in the grid voltage. By using the derived expressions, the total harmonic distortion (THD) and the fundamental phase error of the Unit Vectors can be determined for a given PLL topology and a given level of unbalance and distortion in the grid voltage. The accuracy of the results obtained from the analytical expressions is validated with the simulation and experimental results for synchronous reference frame PLL (SRF-PLL). Based on these expressions, a new tuning method for the SRF-PLL is proposed which quantifies the tradeoff between the Unit Vector THD and the bandwidth of the SRF-PLL. Using this method, the exact value of the bandwidth of the SRF-PLL can be obtained for a given worst case grid voltage unbalance and distortion to have an acceptable level of Unit Vector THD. The tuning method for SRF-PLL is also validated experimentally.
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A novel design method for SOGI-PLL for minimum settling time and low Unit Vector distortion
IECON 2013 - 39th Annual Conference of the IEEE Industrial Electronics Society, 2013Co-Authors: Abhijit Kulkarni, Vinod JohnAbstract:Phase-locked loops (PLLs) are necessary in grid connected systems to obtain information about the frequency, amplitude and phase of the grid voltage. In stationary reference frame control, the Unit Vectors of PLLs are used for reference generation. It is important that the PLL performance is not affected significantly when grid voltage undergoes amplitude and frequency variations. In this paper, a novel design for the popular single-phase PLL topology, namely the second-order generalized integrator (SOGI) based PLL is proposed which achieves minimum settling time during grid voltage amplitude and frequency variations. The proposed design achieves a settling time of less than 27.7ms. This design also ensures that the Unit Vectors generated by this PLL have a steady state THD of less than 1% during frequency variations of the grid voltage. The design of the SOGI-PLL based on the theoretical analysis is validated by experimental results.
David Mitra - One of the best experts on this subject based on the ideXlab platform.
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Two Characterizations of the Standard Unit Vector Basis of l1
Positivity, 2003Co-Authors: David MitraAbstract:We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the Unit Vector basis of l 1. We show that a normalized unconditional basic sequence in l 1 that is semi-normalized in l ∞ is equivalent to the standard Unit Vector basis of l 1.
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Two characterizations of the standard Unit Vector basis of $l_1$
arXiv: Functional Analysis, 2000Co-Authors: David MitraAbstract:We show that for a sequence in a Banach space, the property of being stable under large perturbations characterizes the property of being equivalent to the Unit Vector basis of $l_1$. We show that a normalized unconditional basic sequence in $l_1$ that is semi-normalized in $l_\infty$ is equivalent to the standard Unit Vector basis of~$l_1$.
Lieven Vanhecke - One of the best experts on this subject based on the ideXlab platform.
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Energy and volume of Unit Vector fields on three-dimensional Riemannian manifolds
Differential Geometry and Its Applications, 2002Co-Authors: Jc Gonzalez-davila, Lieven VanheckeAbstract:Abstract We study the stability and instability of harmonic and minimal Unit Vector fields and the existence of absolute minima for the energy and volume functional on three-dimensional compact manifolds, in particular on compact quotients of unimodular Lie groups.
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harmonic and minimal Vector fields on tangent and Unit tangent bundles
Differential Geometry and Its Applications, 2000Co-Authors: Eric Boeckx, Lieven VanheckeAbstract:Abstract We show that the geodesic flow Vector field on the Unit tangent sphere bundle of a two-point homogeneous space is both minimal and harmonic and determines a harmonic map. For a complex space form, we exhibit additional Unit Vector fields on the Unit tangent sphere bundle with those properties. We find the same results for the corresponding Unit Vector fields on the pointed tangent bundle. Moreover, the Unit normal to the sphere bundles in the pointed tangent bundle of any Riemannian manifold always enjoys those properties.
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Minimal and Harmonic Unit Vector Fields in and Its Dual Space
Monatshefte für Mathematik, 2000Co-Authors: Kazumi Tsukada, Lieven VanheckeAbstract:The complex two-plane Grassmannian carries a Kahler structure J and also a quaternionic Kahler structure ?. For we consider the classes of connected real hypersurfaces (M, g) with normal bundle such that and are invariant under the action of the shape operator. We prove that the corresponding Unit Hopf Vector fields on these hypersurfaces always define minimal immersions of (M, g), and harmonic maps from (M, g), into the Unit tangent sphere bundle with Sasaki metric . The radial Unit Vector fields corresponding to the tubular hypersurfaces are also minimal and harmonic. Similar results hold for the dual space .
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Invariant Minimal Unit Vector Fields on Lie Groups
Periodica Mathematica Hungarica, 2000Co-Authors: Kazumi Tsukada, Lieven VanheckeAbstract:We provide a new characterization of invariant minimal Unit Vector fields on Lie groups and use it to construct some new examples. In particular, we determine all these Vector fields on three-dimensional Lie groups.
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examples of minimal Unit Vector fields
Annals of Global Analysis and Geometry, 2000Co-Authors: J C Gonzalezdavila, Lieven VanheckeAbstract:We provide a series of examples of Riemannian manifoldsequipped with a minimal Unit Vector field.
