Iron loss and Copper loss in electrical machine {ss and oc test}

Core Loss (Iron Loss) in Transformers and Electrical Machines 

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What is Core Loss (Iron Loss)?

Core loss, also called iron loss, occurs in the magnetic core of electrical machines such as transformers, motors, and generators. This loss is caused by alternating magnetic fields in the core material when the machine is energized.

Core loss consists of two main components:

1. Hysteresis Loss

2. Eddy Current Loss

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1. Hysteresis Loss

Definition:
Hysteresis loss occurs due to the lagging of the magnetic flux behind the magnetizing force in the core material as it undergoes repeated magnetization and demagnetization cycles.

Cause:
Each time the magnetic field reverses, some energy is lost in realigning the magnetic domains within the core material.

Formula:

$$P_h = \eta \cdot B_{max}^{1.6} \cdot f \cdot V$$

Where:

• $P_h$: Hysteresis loss (W)

• $\eta$: Steinmetz hysteresis coefficient (depends on material)

• $B_{max}$: Maximum flux density (T)

• $f$: Frequency (Hz)

• $V$: Volume of the core (m³)

How to Reduce:

• Use materials with low hysteresis loss (like silicon steel)

• Annealing to reduce internal stresses

• Use of amorphous or nanocrystalline materials

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2. Eddy Current Loss

Definition:
Eddy current loss is caused by circulating currents induced within the core due to changing magnetic fields (Faraday’s law). These currents flow in loops inside the conductive core, producing I²R losses.

Cause:
Alternating magnetic field induces voltages in the core itself, which causes circulating currents.

Formula:

$$P_e = K_e \cdot B_{max}^2 \cdot f^2 \cdot t^2 \cdot V$$

Where:

• $P_e$: Eddy current loss (W)

• $K_e$: Eddy current coefficient

• $t$: Thickness of the lamination (m)

• Other symbols as before

How to Reduce:

• Laminating the core to break up current paths

• Using thinner laminations

• Insulating laminations

• Using materials with high electrical resistivity

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Total Core Loss

$$P_{core} = P_h + P_e$$

In practice, core losses are measured experimentally and often specified in manufacturer datasheets in W/kg at certain values of frequency and flux density.

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Significance of Core Loss

• Occurs even under no-load condition (unlike copper loss)

• Affects efficiency and temperature rise of machines

• Important in design of transformers and high-frequency devices (e.g., switch-mode power supplies)

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Materials Used to Minimize Core Loss

Material	Characteristics
CRGO Silicon Steel	Common in transformers; low core loss
Amorphous Steel	Very low hysteresis and eddy current loss
Ferrites	High resistivity; used in high-frequency devices
Nanocrystalline alloys	Excellent for high-efficiency applications

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Core Loss in Transformers Example

Suppose a transformer core made of silicon steel has the following data:

• Frequency = 50 Hz

• Volume = 0.01 m³

• $B_{max}$ = 1.2 T

• $\eta$ = 0.01

• $K_e = 1.5 \times 10^{-5}$, $t = 0.5 \text{ mm} = 0.0005 \text{ m}$

Hysteresis Loss:

$$P_h = 0.01 \cdot (1.2)^{1.6} \cdot 50 \cdot 0.01 \approx 0.007 W$$

Eddy Current Loss:

$$P_e = 1.5 \times 10^{-5} \cdot (1.2)^2 \cdot (50)^2 \cdot (0.0005)^2 \cdot 0.01 \approx 3.375 \times 10^{-10} W$$

Here, hysteresis dominates due to low eddy loss (thanks to lamination).

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Conclusion

Core loss (iron loss) is a key efficiency factor in electrical machines, particularly under no-load conditions. Understanding and minimizing both hysteresis and eddy current losses is crucial in the design of energy-efficient devices, especially transformers and high-speed machines.

• Copper Loss – 

  Copper loss, also called I²R loss, is a type of electrical power loss that occurs in the windings of electrical machines and devices like transformers, motors, and generators. It is caused by the resistance of the copper (or sometimes aluminum) wires used in the windings.

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  🔧 What Is Copper Loss?

  Definition:
  Copper loss refers to the energy dissipated as heat due to the resistance in the electrical windings when current flows through them. It follows Joule’s Law, which states:

  $$P = I^2R$$

  Where:

  • $P$ = power loss (watts)

  • $I$ = current (amperes)

  • $R$ = resistance of the winding (ohms)

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  📍 Where Does It Occur?

  Copper loss primarily occurs in:

  • Transformer windings

  • Motor stator and rotor windings

  • Generator windings

  • Inductors and coils

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  🧮 Calculation Example

  If a transformer winding has a resistance of 0.5 ohms and carries 10 A current:

  $$\text{Copper Loss} = I^2 \cdot R = 10^2 \cdot 0.5 = 100 \cdot 0.5 = 50 \text{ watts}$$

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  🔁 Dependence on Load

  Copper loss is load-dependent:

  • Increases with load because current increases

  • At no-load, copper loss is minimal

  • At full-load, copper loss is maximum

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  📉 Effects of Copper Loss

  • Reduces efficiency of the machine

  • Causes heating, which may affect insulation and lifespan

  • May require additional cooling systems

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  ⚙️ How to Minimize Copper Loss

  1. Use low-resistance conductors: Higher purity copper or silver reduces resistance.

  2. Increase conductor cross-section: Thicker wires have lower resistance.

  3. Optimize design: Shorter winding lengths, better layout.

  4. Use superconductors: In advanced applications, though not practical for most.

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  🆚 Copper Loss vs. Iron Loss

  Feature	Copper Loss	Iron Loss
  Occurs in	Windings	Core (iron/steel)
  Depends on	Load current	Voltage and frequency
  Type	Variable loss	Constant loss
  Formula	$I^2 R$	Hysteresis + Eddy Loss

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  📚 Applications Where It Matters

  • Power transformers

  • Electric motors

  • Transmission lines

  • Inductive heating systems

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  ✅ conclusion

  Copper loss is a critical factor in the performance and efficiency of electrical machines. It is proportional to the square of the current and the resistance of the conductors. Engineers strive to reduce copper loss through material selection and design optimization to enhance efficiency and durability.

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  🔄 Determine Core loss and Copper: Open Circuit vs Short Circuit Test

  Feature	Open Circuit Test (OC Test)	Short Circuit Test (SC Test)
  Purpose	To measure core (iron) loss	To measure copper (I²R) loss
  Transformer Side Energized	Low Voltage (LV) side	Low Voltage (LV) side
  Other Side Condition	High Voltage (HV) side open	High Voltage (HV) side shorted
  Input Voltage	Rated voltage (full voltage)	Very low voltage (5–10% of rated)
  Current Drawn	Small (no-load current)	Rated current
  Wattmeter Reading Represents	Iron loss only	Copper loss only
  Loss Considered	Core (hysteresis + eddy current losses)	Copper loss (primary + secondary winding resistance)
  Copper Loss Significance	Negligible (due to low current)	Major (due to rated current flow)
  Core Loss Significance	Major (due to rated voltage applied)	Negligible (due to low voltage)
  Instruments Used	Voltmeter, Ammeter, Wattmeter	Voltmeter, Ammeter, Wattmeter
  Power Factor	Low (magnetizing current lags voltage)	High (resistive circuit)
  Parameters Determined	No-load current, iron loss, magnetizing impedance	Equivalent impedance, copper loss, resistance, reactance
  Side for Measurement	Usually done on LV side for safety and ease	Usually done on LV side, shorting HV side

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