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Angular Symmetrical Components

            Conventional Symmetrical components are divided into three categories such as Positive, negative and Zero Sequence Components. Now I proposed the different analysis of the symmetrical components using polar coordinate theory which we used in Vector fields namely Cylindrical coordinate system and Spherical Coordinate system.

            First we represent the three sequence voltages in three coordinate (Cartesian) system. I just name the space for representation of the magnitudes of symmetrical components as "Symmetical Component Space(SCS)". Alternatively, we may call the Space as "ZPN Space".

        The main purpose of this analysis is to simplify the voltage unbalance analysis, and factor estimation. Cartesian coordinate system of ZPN components are converted into two polar coordinate system.

A. Cylindrical Angular Symmetrical Components (CASC) 

        Line voltages are divided into positive and negative sequence components only. Zero sequence components are absent in line voltages. So the sequence voltages of line voltages will be represented in 2D plane (PN Plane). 


Fig 1. Cylindrical Coordinate representation/Polar coordinate of line voltages

        Effective magnitude of Positive and Negative Sequence Components is referred as "Delta Effective Line Voltage (DEL Voltage)". This voltage is equal to Quadratic mean of unbalanced line voltages. The power in unbalanced system of these line voltages will be equal to the same delivered by balanced three phase system of "DEL Voltage".

        The Geometric angle (as ahown in figure) between Positive sequence component and DEL Voltage (Not phase angle) is referred as "Tangent Angle of Unbalance (TAU)". It is determined as Tangent Inverse of Voltage Unbalance Factor which is the ratio between Negative Sequence and Positive Sequence. Negative Sequence in per unit is similar to the TAU in radians for smaller values. So the TAU is represented as Angular form of Negative Sequence Voltage.

B. Spherical Angular Symmetrical Components (SASC)

        Phase voltages are divided into three components namely, Positive, Negative and Zero sequence voltages. Spherical coordinate system is used for the representation of sequence components. Already the DEL voltage and TAU will represent the Positive and Negative sequence components. Zero sequence component will be represented in Polar form by converting it into spherical coordinate system as shown in figure below.

Fig 2: Spherical Angular Symmetrical Components (SASC)
        Effective magnitude of all Sequence Components is referred as "Star Effective Line Voltage (SEL Voltage)". This voltage is equal to the effective magnitude of all Phase Voltages. . The power in unbalanced star connected system will be equal to the same delivered by balanced three phase system of "SEL Voltage".

        The Geometric angle (as ahown in figure) between SEL Voltage and DEL Voltage is referred as "Zero Sequence Tangent Angle (ZESTA)". It is determined as Cosine Inverse of the ratio between DEL Voltage and SEL Voltage. It is represented as the Angular form of Zero Sequence Component.

        The four components from CASC and SASC is collectively referred as "Angular Symmetrical Components". 

1. Star Effective Line Voltage (SELV)

2. Delta Effective Line Voltage (DELV)

3. Zero Sequence Tangent Angle (ZeSTA)

4. Tangent Angle of Unbalance (TAU)

Conversion Table is given below:

        SELV, DELV, and ZeSTA will be easily determined by the magnitudes of phase voltages and line voltages. But the Tangent Angle of Unbalance is typical to estimate. TAU is depends on the sequence either positive or negative. Sequence dependent TAU will ranges from zero to 90 degree. Absolute TAU estimated from line voltage magnitudes irrespective of phase angles will ranges only from zero to 45 degrees.

The Estimation of TAU will be published Soon...

References:

1. Research Article: Click Here

2. Research Thesis: Click Here

http://hdl.handle.net/10603/564562







        



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   I am Dr.V.Arivumani working as Assistant Professor in Department of Electrical and Electronics Engineering, at Government College of Engineering, Bargur, Krishnagiri District (Since April 2013). UG - EEE - 2003 | PG - Power System - 2006 | PhD - 2024 Teaching service from 2006 - GKM, SAACE, DCE, Vels University, and GCE Bargur (Present) State-level  Second Rank in TRB Exam for Assistant Professors in Government Engineering Colleges I have the World's Shortest Email address:  v@co1.in  (8 characters). Currently, I own the domain  Co1.in  (Co One dot in) PPPs Publications      Programs        Patents

My Article: Angular symmetrical components-based anti-islanding method for solar photovoltaic-integrated microgrid

This article examines how an innovative Angular Symmetrical Components of Voltages be applied to islanding detection and voltage unbalance factor estimation at a photovoltaic inverter-based distribution unit. Positive and Negative Sequence Components are converted into a polar form such as Line Aggregate RMS (LARMS) Voltage and Tangent Angle of Unbalance (TAU) which are determined from two line voltage signals. Three voltage relays are replaced with a single relay which compares the LARMS voltage and TAU with threshold limits to identify the condition of balance. ASCOV relay does not generate the trip signal in a non-islanding situation such as linear load switching and nonlinear load switching. The Non-Detection Zone (NDZ) of this ASCOV relay is very low compared to other relays. The proposed anti-islanding method is tested in a SPV powered microgrid using MATLAB/SIMULINK and the performance was studied under islanding and non-islanding events. Consequently, the simulation outcome ind