Transformer Hysteresis Loss Factors

Hysteresis loss is one of the important components of iron loss (or core loss) in a transformer. It occurs due to the molecular friction within the magnetic material when the magnetic field is repeatedly applied and reversed.

The core material of the transformer is subjected to a cycle of magnetization and demagnetization as the alternating current flows through the primary winding. This process causes the magnetic domains within the core material to realign themselves, leading to energy dissipation in the form of heat. This energy loss is known as hysteresis loss.

Understanding Hysteresis Loss Dependence

The magnitude of hysteresis loss ($P_h$) in a transformer core is primarily determined by the properties of the core material and the operating conditions. It can be mathematically represented using the Steinmetz empirical formula:

$$P_h = \eta B_{max}^x f V$$

Where:

• $P_h$ is the hysteresis loss per unit volume (often multiplied by volume $V$ for total loss).
• $\eta$ (Greek letter Eta) is the Steinmetz constant, which depends on the magnetic material's properties (like its B-H curve shape).
• $B_{max}$ is the maximum flux density (in Tesla) reached in the core during the cycle.
• $x$ is the Steinmetz exponent (or hysteresis coefficient), a value typically between 1.5 and 2.5, also dependent on the material.
• $f$ is the frequency (in Hz) of the alternating magnetic field (which is the supply frequency for a transformer).
• $V$ is the volume of the magnetic core material.

From the formula, it's clear that hysteresis loss is directly proportional to the maximum flux density ($B_{max}$) and the frequency ($f$).

Analysis of Options

Let's examine the given options based on the Steinmetz formula:

• 1. flux density and frequency: This aligns perfectly with the formula ($P_h \propto B_{max}^x f$). Hysteresis loss increases with higher flux density and higher frequency.
• 2. time and thickness of lamination: Time is not a direct variable in the hysteresis loss formula. The thickness of lamination is crucial for reducing eddy current losses, not hysteresis losses.
• 3. frequency and thickness of lamination: While frequency affects hysteresis loss, the thickness of lamination primarily impacts eddy current loss.
• 4. flux density and thickness of lamination: Flux density is a factor, but the thickness of lamination is related to eddy current loss, not hysteresis loss.

Note on Lamination Thickness: Transformer cores are laminated (made of thin sheets insulated from each other) to minimize eddy current losses. Eddy current losses ($P_e$) are proportional to the square of the lamination thickness ($t^2$) and the square of the frequency ($f^2$), along with flux density ($B_{max}^2$). Hysteresis loss, however, depends on $B_{max}$ and $f$ but not directly on lamination thickness.

Conclusion

Therefore, the factors on which hysteresis loss directly depends, as indicated by the standard formula and electrical engineering principles, are the maximum flux density in the core and the supply frequency.