Synchronous Power Of Power Angle Curve Calculator

Synchronous Power Formula:

\[ P_{syn} = \frac{|E_g| \cdot |V|}{X_s} \cdot \cos(\delta) \]

EMF of Generator (E_g):

Volt

Voltage of Infinite Bus (V):

Volt

Synchronous Reactance (X_s):

Ohm

Electrical Power Angle (δ):

Radian

Synchronous Power (P_syn):

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1. What is Synchronous Power?

Synchronous Power is defined as the electrical power output of a synchronous generator that is influenced by the power angle. It represents the real power transfer capability between the generator and the infinite bus in a power system.

2. How Does the Calculator Work?

The calculator uses the Synchronous Power formula:

\[ P_{syn} = \frac{|E_g| \cdot |V|}{X_s} \cdot \cos(\delta) \]

Where:

\( E_g \) — EMF of Generator (Volt)
\( V \) — Voltage of Infinite Bus (Volt)
\( X_s \) — Synchronous Reactance (Ohm)
\( \delta \) — Electrical Power Angle (Radian)

Explanation: The formula calculates the maximum power that can be transferred between a synchronous machine and an infinite bus system, considering the voltage magnitudes, synchronous reactance, and the power angle between them.

3. Importance of Synchronous Power Calculation

Details: Accurate synchronous power calculation is crucial for power system stability analysis, generator capability assessment, and determining the maximum power transfer limits in electrical grids.

4. Using the Calculator

Tips: Enter EMF of Generator and Voltage of Infinite Bus in volts, Synchronous Reactance in ohms, and Electrical Power Angle in radians. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the significance of the power angle δ?
A: The power angle δ represents the phase difference between the rotor position and the rotating magnetic field, which determines the amount of power that can be transferred between the generator and the grid.

Q2: Why is synchronous reactance important in this calculation?
A: Synchronous reactance represents the internal impedance of the synchronous machine and determines how much the terminal voltage drops under load conditions, affecting the power transfer capability.

Q3: What is an infinite bus in power systems?
A: An infinite bus is an idealized concept representing a power system with constant voltage and frequency, unaffected by changes in the connected generator's operation.

Q4: How does the power angle affect synchronous power?
A: Synchronous power varies sinusoidally with the power angle. Maximum power transfer occurs at δ = 90° (π/2 radians), and power decreases as the angle moves away from this optimal value.

Q5: What are typical values for synchronous reactance?
A: Synchronous reactance values typically range from 0.8 to 2.0 per unit for most synchronous machines, depending on the machine size and design characteristics.