A set of three Y-connected sources produce a balanced set of 3-phase voltages delivered to the A-connected load. All the given voltages are peak phasors. Assume a positive sequence. (Hint: combine the parallel impedance as one impedance first) (Internal source impedances and the line impedances are zero) 20020° V A 30 2 2002-120° V 140 2 +B -j40 2 30 Ω n b -40Ω 30 2 200/120° V (a) Draw the equivalent 'a-phase' circuit. (b) Find the phase voltages at the load. (c) Find the phase currents at the load.

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### Transcription for Educational Website

#### Three-Phase System with Y-Connected Sources and Δ-Connected Load

This image illustrates a three-phase system where three Y-connected sources produce a balanced set of three-phase voltages. These voltages are delivered to a Δ-connected load. All given voltages are considered peak phasors, and the sequence is positive.

**Key Parameters:**

- **Source Voltages:** 
  - \(200 \angle 0^\circ \, V\)
  - \(200 \angle -120^\circ \, V\)
  - \(200 \angle 120^\circ \, V\)

- **Load Impedance:**
  - Each phase consists of a series combination of a 30 Ω resistor and an impedance of \(-j40 \, \Omega\).

**Instructions:**

(a) **Draw the Equivalent 'a-phase' Circuit:**
   - Simplify the circuit to represent a single phase ('a-phase') for further analysis. This involves calculating the equivalent series and parallel impedances.

(b) **Find the Phase Voltages at the Load:**
   - Determine the voltages across each load impedance in the Δ-connected configuration.

(c) **Find the Phase Currents at the Load:**
   - Calculate the currents flowing through each load impedance using Ohm's Law and the given voltages.

(d) **Find the Total Complex Power Delivered to the Load:**
   - Compute the total complex power, considering both real power (P) and reactive power (Q).

**Diagram Explanation:**

- **Components:**
  - Three neutral connections (n) from the Y-connected sources to the a, b, and c phase lines.
  - Δ-connected load consisting of three identical branches, each with a resistor and inductor in series:
    - **Resistor:** 30 Ω
    - **Reactive Impedance:** \(-j40 \, \Omega\)

- **Circuit Flow:**
  - Each phase voltage from the Y-connection applies across one series branch of the Δ-connected load.
  - The references A, B, and C represent the connection points at the load, corresponding to each phase.

This setup exemplifies the principles of three-phase power systems, balancing and combining impedances, and the analysis of complex power.
Transcribed Image Text:### Transcription for Educational Website #### Three-Phase System with Y-Connected Sources and Δ-Connected Load This image illustrates a three-phase system where three Y-connected sources produce a balanced set of three-phase voltages. These voltages are delivered to a Δ-connected load. All given voltages are considered peak phasors, and the sequence is positive. **Key Parameters:** - **Source Voltages:** - \(200 \angle 0^\circ \, V\) - \(200 \angle -120^\circ \, V\) - \(200 \angle 120^\circ \, V\) - **Load Impedance:** - Each phase consists of a series combination of a 30 Ω resistor and an impedance of \(-j40 \, \Omega\). **Instructions:** (a) **Draw the Equivalent 'a-phase' Circuit:** - Simplify the circuit to represent a single phase ('a-phase') for further analysis. This involves calculating the equivalent series and parallel impedances. (b) **Find the Phase Voltages at the Load:** - Determine the voltages across each load impedance in the Δ-connected configuration. (c) **Find the Phase Currents at the Load:** - Calculate the currents flowing through each load impedance using Ohm's Law and the given voltages. (d) **Find the Total Complex Power Delivered to the Load:** - Compute the total complex power, considering both real power (P) and reactive power (Q). **Diagram Explanation:** - **Components:** - Three neutral connections (n) from the Y-connected sources to the a, b, and c phase lines. - Δ-connected load consisting of three identical branches, each with a resistor and inductor in series: - **Resistor:** 30 Ω - **Reactive Impedance:** \(-j40 \, \Omega\) - **Circuit Flow:** - Each phase voltage from the Y-connection applies across one series branch of the Δ-connected load. - The references A, B, and C represent the connection points at the load, corresponding to each phase. This setup exemplifies the principles of three-phase power systems, balancing and combining impedances, and the analysis of complex power.
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