The vector group is a fundamental characteristic of three-phase transformers that describes the phase relationships and connections of the windings. Selecting the appropriate vector group is essential for ensuring proper system operation, load compatibility, and protection coordination. This article explores the factors influencing vector group selection and provides guidance on choosing the right vector group for various applications.
Vector Group Notation
Vector group notation is a standardized method of representing the phase shift and connection arrangement of transformer windings. It consists of two main components: phase shift notation and neutral point treatment.
Phase shift notation
Phase shift notation indicates the angular displacement between the high-voltage (HV) and low-voltage (LV) windings. It uses uppercase letters for the HV side (D, Y, Z) and lowercase letters for the LV side (d, y, z), followed by numbers representing the phase shift in multiples of 30 degrees.
Some common examples include:
- Dyn11: D (delta) connected HV winding, y (star) connected LV winding, with a 30° (1 × 30°) phase shift
- YNd5: Y (star) connected HV winding with neutral point (N), d (delta) connected LV winding, with a 150° (5 × 30°) phase shift
Uppercase letters for high-voltage side
The HV side connection is denoted by uppercase letters:
- D: Delta connection, where windings are connected in a closed triangle
- Y: Star (wye) connection, where windings are connected to a common point
- Z: Zigzag (interconnected star) connection, used for creating a neutral point or reducing harmonics
Lowercase letters for low-voltage side
The LV side connection is represented by lowercase letters:
- d: delta connection
- y: star (wye) connection
- z: zigzag connection
Numbers representing the phase shift
The number following the HV and LV connection letters represents the phase shift between the windings in multiples of 30 degrees. For example:
- 1 corresponds to a 30° phase shift (1 × 30°)
- 5 represents a 150° phase shift (5 × 30°)
- 11 indicates a 330° phase shift (11 × 30°)
Neutral point treatment
The presence or absence of a neutral point on the HV and LV sides is indicated by the letters N (for HV) or n (for LV) in the vector group notation.
N or n indicating the presence of a neutral point
- If the HV side has a neutral point, the letter N is added between the HV connection letter and the phase shift number (e.g., YNd11).
- If the LV side has a neutral point, the letter n is added between the LV connection letter and the phase shift number (e.g., Dyn11).
Absence of N or n indicating no neutral point
If neither N nor n appears in the vector group notation, it means that no neutral point is present on either side of the transformer (e.g., Dd0, Yz11).
Factors Influencing Vector Group Selection
Several factors must be considered when selecting the appropriate vector group for a transformer. These include system configuration, load characteristics, parallel operation, and fault current limitation.
System configuration and grounding requirements
The vector group must be compatible with the existing system configuration and grounding requirements. The presence or absence of a neutral point on the transformer windings affects the grounding options and the flow of zero-sequence currents during asymmetrical faults.
Load characteristics and harmonic content
The load characteristics, such as the balance between phases, power factor, and harmonic content, influence the choice of vector group. Delta-connected windings can trap triplen harmonics, preventing their propagation to other parts of the system. Star-connected windings with a neutral point can supply unbalanced loads and single-phase loads.
Parallel operation of transformers
When transformers are required to operate in parallel, their vector groups must be compatible to ensure proper load sharing and avoid circulating currents. Transformers with the same vector group can be paralleled without issues, while those with different vector groups may require additional considerations or modifications.
Fault current limitation and protection coordination
The vector group affects the magnitude and distribution of fault currents in the system. Delta-connected windings can limit the flow of zero-sequence currents during earth faults, reducing the fault current levels. The vector group also influences the coordination of protection devices, such as overcurrent relays and fuses.
Common Vector Group Applications
Different vector groups are suited for various applications, depending on the specific requirements of the system. Some common applications include:
Distribution transformers
Distribution transformers often use vector groups such as Dyn11 or Dyn5. The delta-connected HV winding provides a stable neutral point for grounding and reduces the impact of harmonics, while the star-connected LV winding allows for the supply of unbalanced loads and single-phase consumers.
Generator step-up transformers
Generator step-up transformers typically employ the YNd11 vector group. The star-connected HV winding with a neutral point enables the grounding of the generator neutral, while the delta-connected LV winding blocks the flow of third-harmonic currents and provides a stable voltage reference.
Interconnecting transformers between different voltage levels
Interconnecting transformers between different voltage levels often use the YNyn0 vector group. This configuration allows for the grounding of both the HV and LV neutrals, facilitating the coordination of earth fault protection and the control of ground fault currents.
Consequences of Incorrect Vector Group Selection
Choosing an incorrect vector group can lead to various problems in transformer operation and system performance. Some of the consequences include:
Circulating currents and overheating
Incorrectly matched vector groups in parallel-connected transformers can result in circulating currents between the units, leading to overheating and reduced efficiency. This can accelerate the aging of transformer insulation and increase the risk of failures.
Voltage imbalances and phase shifts
An improper vector group selection can cause voltage imbalances and undesired phase shifts between the primary and secondary sides of the transformer. This can affect the operation of connected loads, leading to reduced efficiency, increased losses, and potential damage to equipment.
Protection coordination issues
The vector group influences the behavior of protection devices, such as overcurrent relays and fuses. An incorrect vector group can disrupt the coordination of protection schemes, leading to inadequate fault coverage, nuisance tripping, or delayed fault clearance. This can compromise the safety and reliability of the electrical system.
