Question

What is the relationship between current and voltage in star delta connection?

Answer 1

In a star-delta (or wye-delta) connection, commonly used in three-phase electrical systems, the relationships between current and voltage in the star (wye) and delta configurations are crucial for understanding how these systems function. Here’s a detailed breakdown:

### Star (Wye) Connection

In a star connection:

- **Phase Voltage (\(V_{ph}\))**: This is the voltage across each phase of the motor or load. It’s the voltage from any one phase to the neutral point.
- **Line Voltage (\(V_{L}\))**: This is the voltage between any two lines in the system.

For a star connection:
- **Phase Voltage** is related to **Line Voltage** by the formula:
  \[
  V_{L} = \sqrt{3} \times V_{ph}
  \]
  This relationship comes from the geometry of the triangle formed by the line voltages and phase voltages.

- **Phase Current (\(I_{ph}\))**: This is the current flowing through each phase of the load.
- **Line Current (\(I_{L}\))**: This is the current flowing through each line.

For a star connection:
- **Phase Current** is equal to the **Line Current**:
  \[
  I_{L} = I_{ph}
  \]

### Delta Connection

In a delta connection:

- **Phase Voltage (\(V_{ph}\))**: This is the voltage across each phase winding.
- **Line Voltage (\(V_{L}\))**: This is the voltage between any two lines in the system.

For a delta connection:
- **Line Voltage** is equal to **Phase Voltage**:
  \[
  V_{L} = V_{ph}
  \]

- **Phase Current (\(I_{ph}\))**: This is the current through each phase winding.
- **Line Current (\(I_{L}\))**: This is the current flowing through each line.

For a delta connection:
- **Line Current** is related to **Phase Current** by the formula:
  \[
  I_{L} = \sqrt{3} \times I_{ph}
  \]

### Key Points:

- **In Star Connection**:
  - Voltage relationship: \(V_{L} = \sqrt{3} \times V_{ph}\)
  - Current relationship: \(I_{L} = I_{ph}\)

- **In Delta Connection**:
  - Voltage relationship: \(V_{L} = V_{ph}\)
  - Current relationship: \(I_{L} = \sqrt{3} \times I_{ph}\)

### Conversion Between Star and Delta:

When converting a system from star to delta or vice versa, the following relationships apply for the impedances:

- **In Star**: The impedance of each phase is \(Z_{ph}\).
- **In Delta**: The impedance of each phase is \(Z_{ph} / 3\).

To summarize, the star-delta connections affect how voltage and current are distributed within the system, impacting how the system is designed and operated. The star configuration tends to be used for systems where neutral is required or for lower voltage applications, while the delta configuration is often used for high-voltage systems and can be used to balance loads and reduce harmonics.

Answer 2

In electrical engineering, particularly in three-phase systems, the relationship between current and voltage in star (Y) and delta (Δ) connections is crucial for understanding how these configurations affect power distribution and load sharing. Here’s a detailed explanation of these relationships:

### Star Connection (Y-Connection)

In a star connection, the three phases are connected to a common neutral point. The key relationships in a star connection are:

1. **Line Voltage (V_L) and Phase Voltage (V_Ph):**
   - The line voltage is the voltage measured between any two of the three phase lines.
   - The phase voltage is the voltage measured across each phase winding and the neutral point.
   - The relationship is:  
     \[ V_L = \sqrt{3} \times V_Ph \]

2. **Line Current (I_L) and Phase Current (I_Ph):**
   - The line current is the current flowing through each of the three phase lines.
   - The phase current is the current flowing through each phase winding.
   - In a star connection, the line current is equal to the phase current:  
     \[ I_L = I_Ph \]

### Delta Connection (Δ-Connection)

In a delta connection, the three phases are connected in a loop, forming a triangle. The key relationships in a delta connection are:

1. **Line Voltage (V_L) and Phase Voltage (V_Ph):**
   - In a delta connection, the phase voltage is the voltage across each winding.
   - The line voltage is the voltage measured between any two of the three phase lines.
   - The relationship is:  
     \[ V_L = V_Ph \]

2. **Line Current (I_L) and Phase Current (I_Ph):**
   - The line current is the current flowing through each of the three phase lines.
   - The phase current is the current flowing through each winding of the delta.
   - The relationship is:  
     \[ I_L = \sqrt{3} \times I_Ph \]

### Conversion Between Star and Delta

When converting between star and delta connections, the relationships for voltage and current change due to the different ways the windings are configured. This is often used in transformer connections and motor starters. Here are the conversion formulas:

1. **Star to Delta Conversion:**
   - Phase Voltage in Delta (V_Ph,Δ) = Phase Voltage in Star (V_Ph,Y)
   - Phase Current in Delta (I_Ph,Δ) = \(\frac{I_Ph,Y}{\sqrt{3}}\)

2. **Delta to Star Conversion:**
   - Phase Voltage in Star (V_Ph,Y) = \(\frac{V_Ph,Δ}{\sqrt{3}}\)
   - Phase Current in Star (I_Ph,Y) = \(\sqrt{3} \times I_Ph,Δ\)

### Summary

- **Star Connection:**
  - Line Voltage = \(\sqrt{3}\) × Phase Voltage
  - Line Current = Phase Current

- **Delta Connection:**
  - Line Voltage = Phase Voltage
  - Line Current = \(\sqrt{3}\) × Phase Current

Understanding these relationships helps in designing and analyzing three-phase systems, ensuring that the voltage and current are correctly managed for efficient power distribution and load balancing.