What is the formula for Delta and Star connected system?
2 Answers
In electrical engineering, Delta (Δ) and Star (Y) configurations are used to connect three-phase electrical systems. The formulas to convert between these two configurations are as follows:
### From Delta (Δ) to Star (Y)
If you have a Delta-connected system with impedances \( Z_{AB}, Z_{BC}, Z_{CA} \), the equivalent Star-connected impedances \( Z_A, Z_B, Z_C \) are given by:
\[
Z_A = \frac{Z_{AB} \cdot Z_{CA}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
\[
Z_B = \frac{Z_{AB} \cdot Z_{BC}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
\[
Z_C = \frac{Z_{BC} \cdot Z_{CA}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
### From Star (Y) to Delta (Δ)
For a Star-connected system with impedances \( Z_A, Z_B, Z_C \), the equivalent Delta-connected impedances \( Z_{AB}, Z_{BC}, Z_{CA} \) are given by:
\[
Z_{AB} = \frac{Z_A \cdot Z_B}{Z_A + Z_B} + Z_C
\]
\[
Z_{BC} = \frac{Z_B \cdot Z_C}{Z_B + Z_C} + Z_A
\]
\[
Z_{CA} = \frac{Z_C \cdot Z_A}{Z_C + Z_A} + Z_B
\]
### Summary
These conversions help analyze three-phase systems more conveniently depending on the requirements of the circuit. If you need more specific examples or explanations, feel free to ask!
### From Delta (Δ) to Star (Y)
If you have a Delta-connected system with impedances \( Z_{AB}, Z_{BC}, Z_{CA} \), the equivalent Star-connected impedances \( Z_A, Z_B, Z_C \) are given by:
\[
Z_A = \frac{Z_{AB} \cdot Z_{CA}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
\[
Z_B = \frac{Z_{AB} \cdot Z_{BC}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
\[
Z_C = \frac{Z_{BC} \cdot Z_{CA}}{Z_{AB} + Z_{BC} + Z_{CA}}
\]
### From Star (Y) to Delta (Δ)
For a Star-connected system with impedances \( Z_A, Z_B, Z_C \), the equivalent Delta-connected impedances \( Z_{AB}, Z_{BC}, Z_{CA} \) are given by:
\[
Z_{AB} = \frac{Z_A \cdot Z_B}{Z_A + Z_B} + Z_C
\]
\[
Z_{BC} = \frac{Z_B \cdot Z_C}{Z_B + Z_C} + Z_A
\]
\[
Z_{CA} = \frac{Z_C \cdot Z_A}{Z_C + Z_A} + Z_B
\]
### Summary
These conversions help analyze three-phase systems more conveniently depending on the requirements of the circuit. If you need more specific examples or explanations, feel free to ask!
In electrical engineering, particularly in the analysis of three-phase electrical systems, the terms "Delta" (Δ) and "Star" (Y) refer to two different types of connections for three-phase circuits. Each configuration has its own set of formulas for calculating various parameters, such as impedances, voltages, and currents. Here's a detailed explanation of the formulas associated with Delta and Star connected systems:
### Star (Y) Connection
1. **Impedance Conversion:**
If you have the impedance values in the Star (Y) connection and need to convert them to Delta (Δ) connection, or vice versa, you use the following formulas:
- **From Star (Y) to Delta (Δ):**
\[
Z_{\Delta} = 3 \cdot Z_{Y}
\]
- **From Delta (Δ) to Star (Y):**
\[
Z_{Y} = \frac{Z_{\Delta}}{3}
\]
Here, \( Z_{\Delta} \) is the impedance in Delta connection, and \( Z_{Y} \) is the impedance in Star connection.
2. **Voltage and Current Relations:**
- **Line Voltage (V_L) to Phase Voltage (V_Ph):**
\[
V_L = \sqrt{3} \cdot V_{Ph}
\]
- **Line Current (I_L) to Phase Current (I_Ph):**
\[
I_L = I_{Ph}
\]
### Delta (Δ) Connection
1. **Impedance Conversion:**
As noted above, to convert impedances between Delta and Star connections:
- **From Delta (Δ) to Star (Y):**
\[
Z_{Y} = \frac{Z_{\Delta}}{3}
\]
- **From Star (Y) to Delta (Δ):**
\[
Z_{\Delta} = 3 \cdot Z_{Y}
\]
2. **Voltage and Current Relations:**
- **Line Voltage (V_L) to Phase Voltage (V_Ph):**
\[
V_{Ph} = V_L
\]
- **Line Current (I_L) to Phase Current (I_Ph):**
\[
I_L = \frac{I_{Ph}}{\sqrt{3}}
\]
### Summary of Key Relationships:
- **Star (Y) Connection:**
- Line Voltage \( V_L \) is related to Phase Voltage \( V_{Ph} \) by \( V_L = \sqrt{3} \cdot V_{Ph} \).
- Line Current \( I_L \) is the same as Phase Current \( I_{Ph} \).
- **Delta (Δ) Connection:**
- Phase Voltage \( V_{Ph} \) is the same as Line Voltage \( V_L \).
- Line Current \( I_L \) is related to Phase Current \( I_{Ph} \) by \( I_L = \frac{I_{Ph}}{\sqrt{3}} \).
Understanding these relationships is crucial for analyzing and designing three-phase electrical systems, ensuring that components operate correctly and efficiently.
### Star (Y) Connection
1. **Impedance Conversion:**
If you have the impedance values in the Star (Y) connection and need to convert them to Delta (Δ) connection, or vice versa, you use the following formulas:
- **From Star (Y) to Delta (Δ):**
\[
Z_{\Delta} = 3 \cdot Z_{Y}
\]
- **From Delta (Δ) to Star (Y):**
\[
Z_{Y} = \frac{Z_{\Delta}}{3}
\]
Here, \( Z_{\Delta} \) is the impedance in Delta connection, and \( Z_{Y} \) is the impedance in Star connection.
2. **Voltage and Current Relations:**
- **Line Voltage (V_L) to Phase Voltage (V_Ph):**
\[
V_L = \sqrt{3} \cdot V_{Ph}
\]
- **Line Current (I_L) to Phase Current (I_Ph):**
\[
I_L = I_{Ph}
\]
### Delta (Δ) Connection
1. **Impedance Conversion:**
As noted above, to convert impedances between Delta and Star connections:
- **From Delta (Δ) to Star (Y):**
\[
Z_{Y} = \frac{Z_{\Delta}}{3}
\]
- **From Star (Y) to Delta (Δ):**
\[
Z_{\Delta} = 3 \cdot Z_{Y}
\]
2. **Voltage and Current Relations:**
- **Line Voltage (V_L) to Phase Voltage (V_Ph):**
\[
V_{Ph} = V_L
\]
- **Line Current (I_L) to Phase Current (I_Ph):**
\[
I_L = \frac{I_{Ph}}{\sqrt{3}}
\]
### Summary of Key Relationships:
- **Star (Y) Connection:**
- Line Voltage \( V_L \) is related to Phase Voltage \( V_{Ph} \) by \( V_L = \sqrt{3} \cdot V_{Ph} \).
- Line Current \( I_L \) is the same as Phase Current \( I_{Ph} \).
- **Delta (Δ) Connection:**
- Phase Voltage \( V_{Ph} \) is the same as Line Voltage \( V_L \).
- Line Current \( I_L \) is related to Phase Current \( I_{Ph} \) by \( I_L = \frac{I_{Ph}}{\sqrt{3}} \).
Understanding these relationships is crucial for analyzing and designing three-phase electrical systems, ensuring that components operate correctly and efficiently.