Infinite Bus Calculation – Loan calculator

Infinite Bus Maximum Power Transfer Calculator

Generator Excitation Voltage (Line-to-Line, V):

Infinite Bus Voltage (Line-to-Line, V):

Total System Reactance (Per-Phase, Ohms):

Enter values and click "Calculate Maximum Power" to see the result.

function calculateMaxPowerTransfer() { var generatorVoltage = parseFloat(document.getElementById('generatorVoltage').value); var busVoltage = parseFloat(document.getElementById('busVoltage').value); var totalReactance = parseFloat(document.getElementById('totalReactance').value); var resultDiv = document.getElementById('result'); if (isNaN(generatorVoltage) || isNaN(busVoltage) || isNaN(totalReactance) || generatorVoltage <= 0 || busVoltage <= 0 || totalReactance <= 0) { resultDiv.innerHTML = 'Please enter valid, positive numbers for all fields.'; return; } // Formula for 3-phase maximum power transfer when V_gen and V_bus are line-to-line voltages // and X_total is per-phase reactance. This is a common simplification in power systems. var maxPowerWatts = (generatorVoltage * busVoltage) / totalReactance; var maxPowerMW = maxPowerWatts / 1000000; // Convert Watts to Megawatts resultDiv.innerHTML = '

Maximum Power Transfer:

' + " + maxPowerMW.toFixed(3) + ' MW' + '(' + maxPowerWatts.toLocaleString() + ' Watts)'; }

Understanding the Infinite Bus in Power Systems

The concept of an "infinite bus" is a fundamental simplification used in power system analysis. It represents an ideal, extremely large power system that can supply or absorb any amount of real and reactive power without experiencing any change in its voltage magnitude or frequency. Essentially, it acts as an unshakeable reference point in a power network.

Key Characteristics of an Infinite Bus:

Constant Voltage Magnitude: Its voltage remains fixed, regardless of the power flow.
Constant Frequency: Its frequency does not deviate from the nominal system frequency.
Zero Internal Impedance: It has no internal resistance or reactance, meaning it can theoretically supply infinite fault current.
Infinite Inertia: It has an infinitely large rotating mass, making it immune to transient disturbances.

Why Use the Infinite Bus Model?

While no real-world power system is truly infinite, the concept is incredibly useful for simplifying complex analyses. It's often used to model:

A very large interconnected grid when analyzing a small generator connected to it.
The main grid when studying the behavior of a local power plant or industrial load.
The stability of a generator connected to a much larger system.

By assuming an infinite bus, engineers can focus on the behavior of the smaller, local system without having to model the entire vast network, significantly reducing computational complexity.

Power Transfer to an Infinite Bus

One of the most common applications of the infinite bus model is in analyzing the power transfer capability of a synchronous generator connected to it. When a generator is connected to an infinite bus through a transmission line and/or transformers, the amount of power it can deliver depends on several factors, including the generator's excitation voltage, the bus voltage, and the total reactance between them.

The real power (P) transferred from a generator to an infinite bus is generally given by the formula:

P = (V_gen * V_bus / X_total) * sin(δ)

Where:

V_gen: The magnitude of the generator's excitation voltage (line-to-line).
V_bus: The magnitude of the infinite bus voltage (line-to-line).
X_total: The total equivalent per-phase reactance between the generator and the infinite bus (including generator synchronous reactance, transformer reactance, and line reactance).
δ (delta): The power angle, which is the angle difference between V_gen and V_bus.

Calculating Maximum Power Transfer

The maximum power that can be transferred occurs when the power angle (δ) is 90 degrees, because sin(90°) = 1. At this point, the system is operating at its theoretical stability limit. The formula for maximum power transfer (P_max) simplifies to:

P_max = (V_gen * V_bus / X_total)

This calculator uses this formula to determine the theoretical maximum 3-phase power that can be transferred from a generator to an infinite bus, assuming V_gen and V_bus are line-to-line voltages and X_total is the per-phase reactance.

How to Use This Calculator:

Generator Excitation Voltage (Line-to-Line, V): Enter the line-to-line voltage magnitude of the generator's internal excitation. This is often the voltage behind the synchronous reactance.
Infinite Bus Voltage (Line-to-Line, V): Input the line-to-line voltage magnitude of the infinite bus.
Total System Reactance (Per-Phase, Ohms): Provide the sum of all series reactances (synchronous reactance of the generator, transformer reactance, transmission line reactance) between the generator and the infinite bus, expressed on a per-phase basis and referred to a common voltage base if necessary.
Click "Calculate Maximum Power" to see the result in Megawatts (MW).

Example Calculation:

Consider a synchronous generator with an excitation voltage of 13,800 V connected to an infinite bus also at 13,800 V. The total equivalent per-phase reactance between the generator and the bus is 15 Ohms.

V_gen = 13,800 V
V_bus = 13,800 V
X_total = 15 Ohms

Using the formula:

P_max = (13,800 V * 13,800 V) / 15 Ohms

P_max = 190,440,000 / 15 = 12,696,000 Watts

P_max = 12.696 Megawatts (MW)

This indicates that under these conditions, the generator can theoretically transfer a maximum of 12.696 MW to the infinite bus before losing synchronism.