Distribution transformers are a vital component in electrical power systems, enabling the efficient transfer of power from generation sites to end consumers. While transformers perform this important function, they also experience various types of energy losses during operation.
Core Losses (Iron Losses)
Core losses, also known as iron losses, refer to the energy dissipated in the transformer’s core due to the alternating magnetic flux. These losses are present whenever the transformer is energized, regardless of the load. The two main components of core losses are:
Hysteresis Loss
Hysteresis loss occurs due to the continuous magnetization and demagnetization of the core material as the alternating current flows through the windings. The magnetic domains in the core realign themselves with each cycle, consuming energy in the process. Hysteresis loss is proportional to the area of the hysteresis loop, which represents the magnetizing cycle of the core material.
To minimize hysteresis loss, transformer cores are typically constructed using materials with narrow hysteresis loops, such as cold-rolled grain-oriented silicon steel. The quality and grain orientation of the core material significantly impact the magnitude of hysteresis loss.
Eddy Current Loss
Eddy current loss arises from the circulating currents induced in the core material by the changing magnetic flux. These currents flow perpendicular to the direction of the magnetic flux and cause resistive heating in the core. The magnitude of eddy current loss is influenced by factors such as the thickness of the core laminations, the conductivity of the core material, and the frequency of the alternating current.
To reduce eddy current loss, transformer cores are built using thin laminations insulated from each other. The laminations are stacked in a manner that restricts the flow of eddy currents. Using materials with higher electrical resistivity, such as silicon steel, also helps to minimize eddy current loss.
Copper Losses (Winding Losses)
Copper losses, or winding losses, occur in the transformer’s electrical windings due to the resistance of the conductor material. As current flows through the windings, it encounters resistance, causing power dissipation in the form of heat. Copper losses are proportional to the square of the current and the resistance of the windings.
The resistance of the windings depends on factors such as the cross-sectional area of the conductor, the length of the windings, and the resistivity of the conductor material. Increasing the cross-sectional area of the conductor or using a material with lower resistivity can help reduce copper losses.
Copper losses are further divided into two categories:
- Load losses: These losses vary with the load current and are proportional to the square of the current. As the load on the transformer increases, the load losses increase accordingly.
- No-load losses: These losses are present even when the transformer is not supplying any load. They are caused by the current required to maintain the transformer’s magnetic field and are relatively small compared to load losses.
Other Losses
In addition to core losses and copper losses, transformers also experience other types of losses:
Stray Losses
Stray losses encompass various minor losses that occur in different parts of the transformer. These losses are caused by factors such as leakage fluxes, eddy currents in structural parts, and losses in the tank walls and clamps. Stray losses are generally small compared to core and copper losses but can still impact the overall efficiency of the transformer.
Dielectric Losses
Dielectric losses occur in the insulating materials used in transformers, such as oil and paper insulation. These losses are caused by the dissipation of energy as the insulating materials are subjected to the alternating electric field. Dielectric losses are usually negligible compared to other losses in distribution transformers.
Loss Calculation and Analysis
To quantify and analyze transformer losses, several formulas and methods are employed:
- Core loss calculation:
- Hysteresis loss = K_h × f × B_max^n × V_core
- Eddy current loss = K_e × f^2 × B_max^2 × V_core Where:
- K_h and K_e are constants specific to the core material
- f is the frequency of the alternating current
- B_max is the maximum flux density
- n is the Steinmetz exponent (typically 1.6 to 2.0)
- V_core is the volume of the core
- Copper loss calculation:
- Copper loss = I^2 × R Where:
- I is the current flowing through the winding
- R is the resistance of the winding
- Efficiency calculation:
- Efficiency = Output power ÷ (Output power + Total losses) × 100%
