What is the sum of hysteresis loss and eddy current loss?
2 Answers
The sum of hysteresis loss and eddy current loss in electrical systems is known as **core loss** or **iron loss**. Both hysteresis and eddy current losses occur in the core material of electrical machines like transformers and motors. Let’s break down each component and then combine them to understand their total impact.
### 1. Hysteresis Loss
Hysteresis loss arises due to the repeated magnetization and demagnetization of the core material as the magnetic field within it changes. This process causes the core material to lose energy in the form of heat. The magnitude of hysteresis loss depends on:
- **Material properties:** Different core materials have different hysteresis loss characteristics. For instance, silicon steel has lower hysteresis loss compared to pure iron.
- **Frequency of magnetic field changes:** Higher frequencies lead to higher hysteresis losses.
- **Magnetic flux density:** Greater flux density increases hysteresis loss.
The hysteresis loss \( P_h \) can be estimated using the formula:
\[ P_h = \eta B_{max}^n f \]
where:
- \( \eta \) is the hysteresis loss coefficient of the material,
- \( B_{max} \) is the maximum flux density,
- \( n \) is the Steinmetz exponent (usually between 1.5 and 2.5),
- \( f \) is the frequency of the alternating magnetic field.
### 2. Eddy Current Loss
Eddy current loss is caused by circulating currents induced in the core material by changing magnetic fields. These currents create their own magnetic fields, which oppose the original magnetic field and cause energy loss in the form of heat. The magnitude of eddy current loss depends on:
- **Material properties:** Core materials with higher electrical conductivity have higher eddy current losses.
- **Frequency of magnetic field changes:** Higher frequencies increase eddy current losses.
- **Core thickness:** Thicker cores have higher eddy current losses.
The eddy current loss \( P_e \) can be estimated using the formula:
\[ P_e = \frac{B_{max}^2 f^2 d^2}{\rho} \]
where:
- \( B_{max} \) is the maximum flux density,
- \( f \) is the frequency,
- \( d \) is the thickness of the core material,
- \( \rho \) is the electrical resistivity of the core material.
### 3. Core Loss (Iron Loss)
The total core loss is the sum of hysteresis loss and eddy current loss:
\[ P_{core} = P_h + P_e \]
### Summary
In practical terms, engineers aim to minimize core losses by using materials with lower hysteresis and eddy current loss characteristics. For example, silicon steel with its high electrical resistivity and low hysteresis loss is commonly used in transformer cores to reduce these losses. Understanding and managing these losses is crucial for designing efficient electrical machines and transformers.
### 1. Hysteresis Loss
Hysteresis loss arises due to the repeated magnetization and demagnetization of the core material as the magnetic field within it changes. This process causes the core material to lose energy in the form of heat. The magnitude of hysteresis loss depends on:
- **Material properties:** Different core materials have different hysteresis loss characteristics. For instance, silicon steel has lower hysteresis loss compared to pure iron.
- **Frequency of magnetic field changes:** Higher frequencies lead to higher hysteresis losses.
- **Magnetic flux density:** Greater flux density increases hysteresis loss.
The hysteresis loss \( P_h \) can be estimated using the formula:
\[ P_h = \eta B_{max}^n f \]
where:
- \( \eta \) is the hysteresis loss coefficient of the material,
- \( B_{max} \) is the maximum flux density,
- \( n \) is the Steinmetz exponent (usually between 1.5 and 2.5),
- \( f \) is the frequency of the alternating magnetic field.
### 2. Eddy Current Loss
Eddy current loss is caused by circulating currents induced in the core material by changing magnetic fields. These currents create their own magnetic fields, which oppose the original magnetic field and cause energy loss in the form of heat. The magnitude of eddy current loss depends on:
- **Material properties:** Core materials with higher electrical conductivity have higher eddy current losses.
- **Frequency of magnetic field changes:** Higher frequencies increase eddy current losses.
- **Core thickness:** Thicker cores have higher eddy current losses.
The eddy current loss \( P_e \) can be estimated using the formula:
\[ P_e = \frac{B_{max}^2 f^2 d^2}{\rho} \]
where:
- \( B_{max} \) is the maximum flux density,
- \( f \) is the frequency,
- \( d \) is the thickness of the core material,
- \( \rho \) is the electrical resistivity of the core material.
### 3. Core Loss (Iron Loss)
The total core loss is the sum of hysteresis loss and eddy current loss:
\[ P_{core} = P_h + P_e \]
### Summary
In practical terms, engineers aim to minimize core losses by using materials with lower hysteresis and eddy current loss characteristics. For example, silicon steel with its high electrical resistivity and low hysteresis loss is commonly used in transformer cores to reduce these losses. Understanding and managing these losses is crucial for designing efficient electrical machines and transformers.
The sum of hysteresis loss and eddy current loss is referred to as the **core loss** in electrical engineering, particularly in the context of transformers and other magnetic devices.
### **Core Loss**
Core loss (or iron loss) represents the total power lost in the core of a magnetic device due to the alternating magnetic field. This loss is crucial because it affects the efficiency of transformers, inductors, and motors.
#### **1. Hysteresis Loss**
Hysteresis loss occurs due to the lag between the magnetization and demagnetization of the core material as the magnetic field changes. This lag is a result of the energy needed to realign the magnetic domains in the core material with each cycle of the alternating current (AC).
- **Formula:** \( P_h = \eta \cdot B_{\text{max}}^n \cdot f \cdot V \)
Where:
- \( P_h \) is the hysteresis loss.
- \( \eta \) is the hysteresis constant (depends on the material).
- \( B_{\text{max}} \) is the maximum flux density.
- \( n \) is the Steinmetz exponent (typically between 1.6 and 2.5).
- \( f \) is the frequency of the alternating current.
- \( V \) is the volume of the core material.
#### **2. Eddy Current Loss**
Eddy current loss arises from the circulating currents induced in the core material by the changing magnetic field. These currents flow in loops within the core and generate heat due to the resistance of the material.
- **Formula:** \( P_e = \frac{B_{\text{max}}^2 \cdot f^2 \cdot V \cdot k_e}{\rho} \)
Where:
- \( P_e \) is the eddy current loss.
- \( B_{\text{max}} \) is the maximum flux density.
- \( f \) is the frequency of the alternating current.
- \( V \) is the volume of the core material.
- \( k_e \) is a constant related to the shape and thickness of the core.
- \( \rho \) is the electrical resistivity of the core material.
### **Core Loss Formula**
The total core loss is the sum of hysteresis and eddy current losses:
\[ P_{\text{core}} = P_h + P_e \]
In summary:
- **Hysteresis Loss**: Energy lost due to the magnetic properties of the core material being cycled with each AC cycle.
- **Eddy Current Loss**: Energy lost due to currents induced within the core material by the changing magnetic field.
Both types of losses contribute to the inefficiency and heating of the magnetic core, and minimizing them is crucial for improving the performance and efficiency of magnetic devices.
### **Core Loss**
Core loss (or iron loss) represents the total power lost in the core of a magnetic device due to the alternating magnetic field. This loss is crucial because it affects the efficiency of transformers, inductors, and motors.
#### **1. Hysteresis Loss**
Hysteresis loss occurs due to the lag between the magnetization and demagnetization of the core material as the magnetic field changes. This lag is a result of the energy needed to realign the magnetic domains in the core material with each cycle of the alternating current (AC).
- **Formula:** \( P_h = \eta \cdot B_{\text{max}}^n \cdot f \cdot V \)
Where:
- \( P_h \) is the hysteresis loss.
- \( \eta \) is the hysteresis constant (depends on the material).
- \( B_{\text{max}} \) is the maximum flux density.
- \( n \) is the Steinmetz exponent (typically between 1.6 and 2.5).
- \( f \) is the frequency of the alternating current.
- \( V \) is the volume of the core material.
#### **2. Eddy Current Loss**
Eddy current loss arises from the circulating currents induced in the core material by the changing magnetic field. These currents flow in loops within the core and generate heat due to the resistance of the material.
- **Formula:** \( P_e = \frac{B_{\text{max}}^2 \cdot f^2 \cdot V \cdot k_e}{\rho} \)
Where:
- \( P_e \) is the eddy current loss.
- \( B_{\text{max}} \) is the maximum flux density.
- \( f \) is the frequency of the alternating current.
- \( V \) is the volume of the core material.
- \( k_e \) is a constant related to the shape and thickness of the core.
- \( \rho \) is the electrical resistivity of the core material.
### **Core Loss Formula**
The total core loss is the sum of hysteresis and eddy current losses:
\[ P_{\text{core}} = P_h + P_e \]
In summary:
- **Hysteresis Loss**: Energy lost due to the magnetic properties of the core material being cycled with each AC cycle.
- **Eddy Current Loss**: Energy lost due to currents induced within the core material by the changing magnetic field.
Both types of losses contribute to the inefficiency and heating of the magnetic core, and minimizing them is crucial for improving the performance and efficiency of magnetic devices.