Lossless Power Delivered In Synchronous Machine Calculator

Formula Used:

\[ \text{Lossless Power Delivered} = \text{Maximum Power} \times \sin(\text{Electrical Power Angle}) \] \[ P_l = P_{\text{max}} \times \sin(\delta) \]

Lossless Power Delivered (P_l):

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1. What is Lossless Power Delivered in Synchronous Machine?

Lossless Power Delivered by Synchronous Machine is the power that is converted from electrical to mechanical power without any electrical loss. It represents the ideal power transfer in a synchronous machine system.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_l = P_{\text{max}} \times \sin(\delta) \]

Where:

\( P_l \) — Lossless Power Delivered (Watt)
\( P_{\text{max}} \) — Maximum Power (Watt)
\( \delta \) — Electrical Power Angle (Radian)

Explanation: The formula calculates the power delivered by a synchronous machine based on the maximum power capability and the electrical power angle (load angle) between rotor and stator positions.

3. Importance of Lossless Power Calculation

Details: Accurate calculation of lossless power is crucial for power system stability analysis, machine performance evaluation, and determining the optimal operating conditions for synchronous machines in electrical power systems.

4. Using the Calculator

Tips: Enter maximum power in watts and electrical power angle in radians. Both values must be positive numbers for valid calculation.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the electrical power angle?
A: The electrical power angle (δ) represents the angular displacement between rotor and stator positions and determines the power transfer capability in synchronous machines.

Q2: What is the typical range for maximum power?
A: Maximum power varies significantly based on machine size and design, ranging from kilowatts to megawatts for different synchronous machine applications.

Q3: Why is this considered "lossless" power?
A: This calculation assumes ideal conditions without electrical losses such as copper losses, iron losses, or stray losses that occur in practical machines.

Q4: How does the power angle affect power delivery?
A: Power delivery increases with the sine of the power angle up to 90 degrees (π/2 radians), reaching maximum at this point, then decreases for larger angles.

Q5: What are practical applications of this calculation?
A: This calculation is essential for power system planning, machine design, stability studies, and determining safe operating limits for synchronous generators and motors.