### Problem 3.22A balanced Y-connected voltage source with \( E_{ag} = 277 \angle 0^\circ \) volts is applied to a balanced-Y load in parallel with a balanced-Δ load where \( Z_Y = 20 + j10 \) and \( Z_Δ = 30 - j15 \) ohms. The Y load is solidly grounded. Using base values of \( S_{\text{base}1ϕ} = 10 \) kVA and \( V_{\text{base},LN} = 277 \) volts, calculate the source current \( I_a \) in per-unit and in amperes.#### Explanation:- **Y-connected voltage source:** This means that the power source and loads are connected in a star configuration.- **Balanced-Y and Δ Load:** These are specific configurations of electrical loads, where \( Z_Y \) and \( Z_Δ \) are their impedances given in complex form.- **Solidly Grounded Y Load:** Indicates that the Y load has a direct connection to the ground, eliminating potential unbalances.- **Base Values:** Used for per-unit system calculations where the apparent power base is \( 10 \) kVA and the line-to-neutral voltage base is \( 277 \) volts.### ObjectiveCalculate the source current \( I_a \) in two formats:1. **Per-unit system:** A normalized value of electrical quantities.2. **Amperes:** The standard unit of electric current.

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A balanced Y-connected voltage source with E = 277/0° volts is applied to a balanced-Y load in parallel with a balanced-A load where Zy = 20 + j10 and ZA = 30 – j15 ohms. The Y load is solidly grounded. Using base values of Spasels = 10 kVA and V naseLN = 277 volts, calculate the source current I, in per-unit and in amperes.

A balanced Y-connected voltage source with E = 277/0° volts is applied to a balanced-Y load in parallel with a balanced-A load where Zy = 20 + j10 and ZA = 30 – j15 ohms. The Y load is solidly grounded. Using base values of Spasels = 10 kVA and V naseLN = 277 volts, calculate the source current I, in per-unit and in amperes.

Power System Analysis and Design (MindTap Course List)

6th Edition

ISBN:9781305632134

Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma

Chapter3: Power Transformers

Section: Chapter Questions

Problem 3.25P: Consider a single-phase electric system shown in Figure 3.33. Transformers are rated as follows:...

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Question

### Problem 3.22

A balanced Y-connected voltage source with \( E_{ag} = 277 \angle 0^\circ \) volts is applied to a balanced-Y load in parallel with a balanced-Δ load where \( Z_Y = 20 + j10 \) and \( Z_Δ = 30 - j15 \) ohms. The Y load is solidly grounded. Using base values of \( S_{\text{base}1ϕ} = 10 \) kVA and \( V_{\text{base},LN} = 277 \) volts, calculate the source current \( I_a \) in per-unit and in amperes.

#### Explanation:
- **Y-connected voltage source:** This means that the power source and loads are connected in a star configuration.
- **Balanced-Y and Δ Load:** These are specific configurations of electrical loads, where \( Z_Y \) and \( Z_Δ \) are their impedances given in complex form.
- **Solidly Grounded Y Load:** Indicates that the Y load has a direct connection to the ground, eliminating potential unbalances.
- **Base Values:** Used for per-unit system calculations where the apparent power base is \( 10 \) kVA and the line-to-neutral voltage base is \( 277 \) volts.

### Objective
Calculate the source current \( I_a \) in two formats:
1. **Per-unit system:** A normalized value of electrical quantities.
2. **Amperes:** The standard unit of electric current.

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