Symmetrical Component Analysis

Decompose Fundamental Currents and Voltages into Symmetrical Components

Introduction

An important aspect of Power Quality Monitoring and Analyzes is to have an insight into the complex dynamics of power systems. This is to understand why the three-phase voltages or currents are not of the same magnitudes or phase-displaced by 120-degrees.

When a three-phase circuit becomes unbalanced, the voltages and currents are no longer equal. In the picture below the three-phases as measured are displayed.

The very first step is this to decompose the unbalanced three-phase quantities into their symmetrical components. This will produce the resulting “symmetrical” components which are referred to as direct (or positive), inverse (or negative) and zero (or homopolar). Therefore, it simplifies the analysis of unbalanced three-phase power systems under both normal and abnormal conditions.

In a three-phase system, a positive-sequence set of voltages or currents produces a normal rotating field, a negative-sequence set produces a field with the opposite rotation, and the zero-sequence set produces a field that oscillates but does not rotate. This is very important to note. The zero-sequence component is the one that produces heat in transformer and cables. For a more detailed explanation, read the Negative Phase Sequencing explanations.

As shown in the figure below, the three sets of symmetrical components (positive-, negative-, and zero-sequence) add up to create the system of three unbalanced phases Va, Vb and Vc.

The imbalance between phases arises because of the difference in magnitude and phase-shift between the sets of vectors. Notice that the colors (red, blue, and yellow) of the separate sequence vectors correspond to three different phases (a, b, and c, for example).

Positive-Sequence Component

The positive-sequence component is one of the symmetrical components derived from an unbalanced three-phase system. It represents the balanced part of the system that resembles a three-phase system with equal magnitudes and 120° phase separations. See the figure below.

The positive sequence component is denoted by the subscript “1” and represented as Va₁, Vb1, and Vc1 for the three voltages respectively.

Negative-Sequence Component

The negative sequence component is another symmetrical component obtained from an unbalanced three-phase system. It represents the symmetrical imbalance caused by phasors that are equal in magnitude but have a phase sequence opposite to that of the original phasors. See the figure below.

The negative-sequence component is essential for identifying issues like unbalanced loads and diagnosing faults in the system, as it helps distinguish between symmetrical and unsymmetrical faults.

The subscript “2” denotes the negative sequence component and represents Va₂, Vb2 and Vc2 for the three voltages respectively.

Zero-Sequence Component

The zero-sequence component, the third symmetrical component, describes a unique condition where the three phasors have equal magnitudes and zero phase displacement from each other. This component primarily captures the presence of ground faults or imbalances that affect all three phases equally.

The subscript “0” denotes the zero-sequence component, represented as Va₀, Vb0 and Vc0 for the three voltages respectively.

Symmetrical Current Animation

It is important to note that different counties employ different wiring color standards. Over and above that, countries such as South Africa, have two sets of color code standards, one for flexible cable and another fixed cables.

On this web page both are being used since the color codes for fixed cables does not display that when it comes to the Symmetrical Current Animations below.

Electrical Wire Color Codes

Flexible Cable

The wire color codes from this category are extension cord, power cable, and lamp cords wiring color. South Africa uses this IEC 60446 (International Electrotechnical Commission) for flexible cable:

  • Single phase, Line (L) = brown
  • Three phase, Line 1 (L1) = brown
  • Three phase, Line 2 (L2) = black
  • Three phase, Line 3 (L3) = grey
  • Neutral (N) = blue
  • Protective earth (PE) = green-yellow

Fixed Cable

The wire color codes from this category are all of the cable behind the wall, in the wall, or on the wall.

  • Three phase, Line 1 (L1) = red
  • Three phase, Line 2 (L2) = yellow or white
  • Three phase, Line 3 (L2) = blue
  • Neutral (N) = black
  • Protective earth (PE) = green-yellow striped

To better explain the concept of Symmetrical Component Analysis, the following live demonstration, with code developed by TheOtherNeo, is used for showing how any set of unbalanced phasors in any “polyphase” system could be expressed as the sum of an equal number of symmetrical components representing a set of balanced phasors which is known as Symmetrical Components. This is known as the Fortescue Theorem.

When this webpage is opened, the current magnitudes and angles are in a balanced state. But, by changing the magnitudes or angles of the Brown (original Red), Black (original Yellow), Gray (original Blue) Phases or the Neutral in Blue (original Black) in the table below, the system will decompose the current phasor components into a set of symmetrical components that helps to analyze the system as well as visually displaying any imbalances. The fundamental currents or currents that are displayed on the ammeter are then broken down into the Positive-, Negative- and Zero-Sequence Components as explained above. As the current magnitudes and angles change, these Sequence Components changes.

On the diagram the, the fundamental currents are displayed as solid line with the Positive-Sequence currents as dashed lines with the “+” sign at the end points in brackets such as A(+), B(+) and C(+). The Negative-Sequence currents are a different style of dashed lines with the “-“ sign at the end points in brackets such as A(-), B(-) and C(-). Similarly, the Zero-Sequence currents are, once again, displayed with a different style of dashed line with the “0“ sign at the end points in brackets such as A(0), B(0) and C(0).

By changing the Neutral current magnitude and angle, the center point of the three-currents of the three-phase system will move away from the center of the X- and Y-axes.

Thus, to understand the concept of Symmetrical Component Analysis, try the following values and see what happens:

  • A-phase magnitude: 91.6, A-phase angle: -60
  • B-phase magnitude: 210.2, B-phase angle: -120
  • C-phase magnitude: 151.2, C-phase angle: -285
  • Neutral magnitude: 15, Neutral angle: 55

Decomposition of Three-phase Vector System into its Symmetrical Components

Original Vector System
Name Magnitude Angle

Conclusion

Symmetrical components are crucial in fault calculations and analysis in power systems. By decomposing an unbalanced system into positive, negative, and zero sequence components, engineers can simplify fault calculations and accurately determine fault parameters, such as fault currents and voltages.