3) The total power delivered to a balanced Y-connected, three-phase load is 720 kW at a lagging power factor of 0.8. The line voltage at the load is 3464-V. The impedance of the transmission line is 2.5+j10.2 . What is the line voltage at the sending end of the transmission line? How much power dissipated by the transmission line? What is the total power supplied by the source? Determine the load impedance per phase.

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**Problem 3) Electrical Engineering Problem on a Y-Connected Three-Phase Load**

**Given:**
- Total power delivered to a balanced Y-connected, three-phase load: **720 kW**
- Power factor: **0.8 (lagging)**
- Line voltage at the load: **3464 V**
- Impedance of the transmission line: **2.5 + j10.2 Ohms**

**Questions:**
1. What is the line voltage at the sending end of the transmission line?
2. How much power is dissipated by the transmission line?
3. What is the total power supplied by the source?
4. Determine the load impedance per phase.

**Explanation:**
This problem involves a three-phase power system with a balanced Y-connected load, which is common in power systems analysis. A Y-connection refers to a configuration where three elements are connected in a star (Y) formation, typically used for distributing power to various loads.

The problem requires calculations involving:
- Line voltage and phase voltage relationships in a Y-connected system.
- Complex power calculations accounting for a lagging power factor (indicating inductive load).
- Power loss in transmission lines due to their impedance.
- Determining load impedance from given total power and power factor.

**Steps to Solve the Problem:**
1. **Calculate the phase currents and voltages:**
   - Convert the total power and power factor to per-phase quantities.
   - Determine the phase current using the impedance and load voltage.

2. **Determine sending end voltage:**
   - Account for voltage drop across the transmission line impedance.
   - Use calculated phase current and line impedance for this voltage drop.

3. **Compute power dissipation in the transmission line:**
   - Use the real component of the transmission line impedance and measured current.

4. **Total power supplied by the source:**
   - Add the power delivered to the load and power dissipated in transmission line.
  
5. **Load impedance per phase:**
   - Use the calculated per-phase current and the load voltage to find the impedance.

This problem tests various fundamental principles of electrical engineering pertaining to power systems, and provides a practical application of theoretical concepts in real-world power distribution.
Transcribed Image Text:**Problem 3) Electrical Engineering Problem on a Y-Connected Three-Phase Load** **Given:** - Total power delivered to a balanced Y-connected, three-phase load: **720 kW** - Power factor: **0.8 (lagging)** - Line voltage at the load: **3464 V** - Impedance of the transmission line: **2.5 + j10.2 Ohms** **Questions:** 1. What is the line voltage at the sending end of the transmission line? 2. How much power is dissipated by the transmission line? 3. What is the total power supplied by the source? 4. Determine the load impedance per phase. **Explanation:** This problem involves a three-phase power system with a balanced Y-connected load, which is common in power systems analysis. A Y-connection refers to a configuration where three elements are connected in a star (Y) formation, typically used for distributing power to various loads. The problem requires calculations involving: - Line voltage and phase voltage relationships in a Y-connected system. - Complex power calculations accounting for a lagging power factor (indicating inductive load). - Power loss in transmission lines due to their impedance. - Determining load impedance from given total power and power factor. **Steps to Solve the Problem:** 1. **Calculate the phase currents and voltages:** - Convert the total power and power factor to per-phase quantities. - Determine the phase current using the impedance and load voltage. 2. **Determine sending end voltage:** - Account for voltage drop across the transmission line impedance. - Use calculated phase current and line impedance for this voltage drop. 3. **Compute power dissipation in the transmission line:** - Use the real component of the transmission line impedance and measured current. 4. **Total power supplied by the source:** - Add the power delivered to the load and power dissipated in transmission line. 5. **Load impedance per phase:** - Use the calculated per-phase current and the load voltage to find the impedance. This problem tests various fundamental principles of electrical engineering pertaining to power systems, and provides a practical application of theoretical concepts in real-world power distribution.
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