### **Step 1: Introduction to the Concept** This problem involves an industrial low-voltage power distribution system with multiple motors and a general load. The focus is on: - Power factor correction using capacitors, - Sizing cables and protection devices, - Ensuring the overall system meets regulatory requirements for power factor to avoid utility penalties. The questions guide us through the steps needed in designing such a system: - **a)** Sizing the power factor correction capacitors for each motor (receiver). - **b)** Calculating appropriate cable cross-sections and overcurrent protection ratings. - **c)** Determining the additional required system-wide capacitor power to meet minimum power factor requirements. --- ### **Step 2: Part (a) — Individual Capacitor Power Calculation** #### **Power Factor Correction for Each Receiver** **Formula:** To correct the power factor (`cosφ1`) to the target power factor (`cosφ2`, usually 0.98 or 1), the required reactive power of the capacitor (`Qc`) is: \[ Q_c = P \times (\tan \phi_1 - \tan \phi_2) \] where: - \( P \) = Active power of the load (in kW) - \( \phi_1 = \cos^{-1}(\text{initial power factor}) \) - \( \phi_2 = \cos^{-1}(\text{target power factor}) \) **Steps:** 1. **Determine the active power (P) for each motor**. - M1 = (last two digits of student number) kW. - M2 = M1 + 1, M3 = M2 + 1, etc. (if the result is 0, use 1). 2. **Find the initial power factor for each motor** (given in the table). 3. **Choose a target power factor** (commonly 0.98). 4. **Calculate φ1 and φ2**. 5. **Compute Qc for each motor**. --- ### **Step 3: Part (b) — Cable Cross-Section and Overcurrent Protection** #### **Cable Selection** - Use the full-load current for each receiver: \[ I = \frac{P}{\sqrt{3} \cdot V \cdot \eta \cdot \cos\phi} \] - P = Active Power (W) - V = Line-to-line voltage (400 V) - η = Efficiency - cosφ = Power Factor - Use standard tables (e.g., IEC or local code) to select a cable with a current-carrying capacity above the calculated current, considering installation conditions and voltage drop limits. #### **Protection Device Selection** - Overcurrent protection (fuse or MCB) rating should be: \[ I_{\text{protection}} \geq I_{\text{full load}} \] - Select the next standard rating above the full-load current. --- ### **Step 4: Part (c) — System-wide Capacitor Power Calculation** #### **System-wide Power Factor Correction** - Calculate **total active power** (sum all receivers + general load). - Calculate **initial system power factor** (weighted average if needed). - **Target system power factor** (usually ≥0.90 or 0.95 to avoid penalties). - Use the same formula as in (a) with total active power. --- ### **Step 5: Final Short Answer** **In summary:** - Calculated the required capacitor (kVAR) for each receiver based on their power and initial power factor. - Determined the cable cross-section and overcurrent protection device rating for each receiver using their full-load current. - Computed the total required system capacitor size to meet the target power factor and avoid utility penalties. --- ### **Step 6: Step-by-Step Summary** 1. **Introduced the key concepts**: Power factor correction, cable and protection sizing. 2. **Calculated individual capacitors**: Used each motor’s power and power factor to find needed kVAR for target PF. 3. **Sized cables and breakers**: Used current from each motor to select correct cable and protection. 4. **Calculated system-wide capacitor**: Summed all loads, checked total PF, and computed additional kVAR for compliance. 5. **Final short answer**: Summarized that we sized capacitors, cables, and protection for each load and system-wide. --- **To proceed with numerical answers, please provide the last two digits of your student number!**