Energy losses in a transformer occur because it is not a 100% efficient machine; a portion of the incoming electrical energy is inevitably converted into heat and dissipated.

These losses are generally divided into two main categories: Copper Losses (Load Losses), which directly relate to the electrical current passing through the system, and Iron Losses (Core Losses), which relate to the magnetic field.

1. Copper Loss / Winding Loss (Current-Dependent)

Copper loss occurs because the electrical conductors (usually copper or aluminum) used for the primary and secondary windings have inherent electrical resistance.

• The Cause: When electrical current flows through the windings, it encounters resistance, generating heat.
• The Formula: Copper loss is proportional to the square of the current multiplied by the winding resistance (I²R).
• Behavior: Because it depends on the load current, these losses are dynamic. They are near zero when the transformer is idle (no load) and increase exponentially as the electrical load and current draw increase.

2. Iron Loss / Core Loss (Voltage-Dependent)

Iron losses happen inside the transformer's magnetic core and occur continuously as long as the transformer is energized, regardless of whether a load is connected. It consists of two sub-components:

• Hysteresis Loss: Caused by the continuous energy required to magnetize, demagnetize, and reverse the magnetic domains within the core material with every cycle of the alternating current (AC).
• Eddy Current Loss: Caused by circulating, induced electrical currents swirling within the core steel body due to the changing magnetic flux, which generates localized heat.
• Behavior: These losses remain relatively constant 24/7 as long as the primary side is connected to voltage.

Key Takeaway: Transformer efficiency peaks when copper losses equal iron losses. Managing these losses is critical for modern power distribution efficiency.

Summary Comparison

Loss Type	Primary Driver	Varies With Load?	Manifestation / Result
Copper Loss	Electrical Current (I2R)	Yes (increases with heavier loads)	Heat in the coils/windings
Iron Loss	Alternating Magnetic Flux	No (constant 24/7 when energized)	Heat in the core structure

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Total power loss (P_loss) in a transformer is the sum of Copper Losses (which depend on the electrical current) and Iron Losses (which depend on the core voltage and magnetic flux).

P_loss = P_cu + P_fe

1. Copper Loss (P_cu) Formula

Copper loss is primarily a function of the load current passing through the winding resistances of both the primary and secondary coils.

P_cu = I₁² R₁ + I₂² R₂

Alternatively, referred entirely to the secondary or primary side:

P_cu = I₂² R_equivalent

Where:

• I₁ = Primary current
• I₂ = Secondary current
• R₁ = Resistance of the primary winding
• R₂ = Resistance of the secondary winding
• R_equivalent = Total equivalent resistance referred to one side

Note on Load Factor (x): If the transformer is operating at a fraction of its full load, the copper loss at that specific load can be calculated using the full-load copper loss (P_cu,full):

P_cu(x) = x² × P_cu,full

(Where x is the loading factor, e.g., 0.75 for 75% load).

2. Iron Loss / Core Loss (P_fe) Formula

Iron loss consists of hysteresis loss and eddy current loss, both derived from the maximum magnetic flux density (B_max) and supply frequency (f).

P_fe = P_h + P_e

Expanding the components:

P_fe = (K_h × f × B_maxⁿ) + (K_e × f² × B_max²)

Where:

• K_h = Hysteresis constant (based on core material)
• K_e = Eddy current constant
• f = Supply frequency (e.g., 50 Hz or 60 Hz)
• B_max = Maximum magnetic flux density in the core
• n = Steinmetz exponent (typically ranging between 1.5 and 2.5 depending on the core steel)