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 image below a three-phase network unbalanced voltage is 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 on my website.

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 image 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.

I often use both color codes for fixed cables but does not display that clear when it comes to the Symmetrical Current Animations below.

Real-World Example – Linden Three-Phase

In this chapter, I am going to explain the data I previously sent in an Excel workbook and particularly the data in the spreadsheet called “Power Quality Data Linden”.

Based on the apparent lack of urgency on the part of City Power officials, I concluded that those who received the emails dated 15 and 17 April 2024 clearly did not understand the data nor my messages.

“In my email of 15 April 2024, I said: “The second and far more important aspect is that the summated negative sequence voltage went up to 139.37-volts with the summated zero-sequence voltages went up as high as 137.46-volts. Both these values should effectively be zero (nil). Furthermore, the highest zero-sequence as a percentage of positive sequence voltage is 100.62% and so is the negative sequence as a percentage of the positive sequence voltage. Again, these percentages should be zero or very close to zero.””

“In my email of 17 April 2024, I said: “Three days later, I have not had any response to my email from anyone at City Power and decided to send you another Excel workbook with a lot of data “redacted” so that I can point out the dangers. When you look at column H (U L31 avg. 10 min [V]) you will notice that the phase-to-phase voltage between phases 1 & 3 is less than 1 volt. The reason for that is the severity of the unbalanced voltages. That means a large three-phase delta connected electric motor would not start, or if it is running, it would be destroyed in a very short period. Your transformers and cables would also overheat and perhaps caught fire as has been happening lately.” Again, there was no apparent urgency on the part of the City Power officials.”

Since I do this kind of work for an income, I have nevertheless decided to prepare this document to explain why I specifically said, “you will notice that the phase-to-phase voltage between phases 1 & 3 is less than 1 volt”.

The following are images representing the symmetrical components of the unbalanced three-phase system such as currently exist in Linden.

With a perfectly balanced system, the magnitudes of the voltages should be the same and the phase-displacements should be 120-degrees exactly. Secondly, with a perfectly balanced system, there should ONLY be a Positive Sequence Component and NO Negative or Zero Sequence Components.

Positive-Sequence Component Vector

The image below is the positive-sequence component of the voltages as recorded at 21:20:00 on 2024-04-12.

Notice that this is rotated since the red dashed line should be on the X-axis.

Negative-Sequence Component Vector

The image below is the negative-sequence component of the voltages as recorded at 21:20:00 on 2024-04-12.

Now look at the high magnitudes of the three negative sequence components. This should be NIL and therefore absolutely NO lines at ALL. Also look at the colors of the three phases. It is not Red, Yellow, and then Blue – remember the vectors are turning anticlockwise. In this case, it is Red, Blue, and then Yellow and that is why it is called Negative.

Zero-Sequence Component Vector

The image below is the zero-sequence component of the voltages as recorded at 21:20:00 on 2024-04-12.

The reason why you only see the blue dashed line is that the Red and Yellow is hidden underneath the blue. All three are of the same magnitude. Now look at the high magnitudes of the three zero-sequence components. This should be NIL and therefore absolutely NO lines at ALL.

Cartesian Coordinates of Recorded Voltages

The question that should have been asked based on my statement “you will notice that the phase-to-phase voltage between phases 1 & 3 is less than 1 volt”, is “why”?

The voltages as recorded at 21:20:00 on 2024-04-12 between phases 1 & 2 was 414.9-volts and between phases 2 & 3 was 414.82-volts. Now look at the image and you will see that if you measure between the ends of the line 1 & 2 and 2 & 3, will get those values since the red and yellow phases are very close to in-line with each other. That is why the phase-to-phase voltage between phases 1 & 3 is less than 1 volt.

Cartesian Vector – Phase-to-Phase Voltages

The subject line of my email dated 17 April 2024 read “Possible Reason for Cable and Transformer Failures in Northern Suburbs”. I did not use that as the subject for no reason.

In my Excel workbook attached to my email dated 17 March 2024, I remove the data about the currents since it would present a distorted image. The recording was done at a house with all the appliances being single-phase with currents that can hardly be balanced. However, at the substations, it would be a completely different situation. The currents should be balanced.

With voltages represented by the solid lines of the vector as displayed in the last image, you will get a very high neutral current and very high circulating currents in the delta windings of transformers. This is what causes heat generation. The zero-sequence component is the one that produces heat in transformer and cables.