Transformer Impedance Calculation

Transformer Impedance Calculator

Calculate the actual impedance of a transformer in Ohms, referred to the primary side, based on its nameplate data.

function calculateTransformerImpedance() { var ratedPowerKVA = parseFloat(document.getElementById('ratedPowerKVA').value); var primaryVoltageV = parseFloat(document.getElementById('primaryVoltageV').value); var percentageImpedance = parseFloat(document.getElementById('percentageImpedance').value); var resultDiv = document.getElementById('result'); if (isNaN(ratedPowerKVA) || ratedPowerKVA <= 0) { resultDiv.innerHTML = 'Please enter a valid positive number for Transformer Rated Power.'; return; } if (isNaN(primaryVoltageV) || primaryVoltageV <= 0) { resultDiv.innerHTML = 'Please enter a valid positive number for Primary Rated Voltage.'; return; } if (isNaN(percentageImpedance) || percentageImpedance 100) { resultDiv.innerHTML = 'Please enter a valid percentage (0.1-100) for Percentage Impedance.'; return; } // Convert kVA to VA var ratedPowerVA = ratedPowerKVA * 1000; // Calculate Base Impedance (Z_base) on the primary side // Z_base = (V_rated^2) / S_rated var baseImpedanceOhms = (primaryVoltageV * primaryVoltageV) / ratedPowerVA; // Calculate Actual Impedance (Z_actual) on the primary side // Z_actual = (Percentage Impedance / 100) * Z_base var actualImpedanceOhms = (percentageImpedance / 100) * baseImpedanceOhms; resultDiv.innerHTML = '

Calculation Results:

' + 'Base Impedance (Primary Side): ' + baseImpedanceOhms.toFixed(3) + ' Ohms' + 'Actual Impedance (Primary Side): ' + actualImpedanceOhms.toFixed(3) + ' Ohms'; }

Understanding Transformer Impedance

Transformer impedance is a critical parameter that describes the internal opposition a transformer presents to the flow of alternating current. It's a measure of the voltage drop across the transformer due to its internal resistance and reactance when current flows through its windings. This value is crucial for various electrical engineering calculations, including fault current analysis, voltage regulation, and coordination of protective devices.

What is Percentage Impedance?

On a transformer's nameplate, impedance is almost always expressed as a "percentage impedance" (often denoted as Z% or u_k). This percentage represents the voltage drop across the transformer's internal impedance when full-load current flows, expressed as a percentage of the rated voltage. For example, a 5% impedance means that 5% of the rated voltage is dropped internally when the transformer delivers its full rated current.

The percentage impedance is a standardized way to compare transformers of different sizes and voltage ratings. It's particularly important for:

• Fault Current Calculation: A lower percentage impedance means the transformer will allow a higher fault current to flow during a short circuit, which impacts the sizing of circuit breakers and fuses.
• Voltage Regulation: It affects how much the secondary voltage changes between no-load and full-load conditions.
• Parallel Operation: Transformers operating in parallel must have similar percentage impedances to ensure proper load sharing.

How is Transformer Impedance Calculated?

The actual impedance of a transformer in Ohms (referred to either the primary or secondary side) can be derived from its nameplate data, specifically the rated power (kVA), rated voltage, and the percentage impedance.

The calculation involves two main steps:

1. Calculate the Base Impedance (Z_base): This is a reference impedance for the transformer's rated conditions. For the primary side, it's calculated as:
   Zbase = (Vrated2) / Srated
   Where:
   • Vrated is the primary rated voltage in Volts.
   • Srated is the transformer's rated power in VA (kVA * 1000).
2. Calculate the Actual Impedance (Z_actual): Once the base impedance is known, the actual impedance in Ohms is found by applying the percentage impedance:
   Zactual = (Percentage Impedance / 100) * Zbase

Example Calculation:

Let's consider a transformer with the following specifications:

• Rated Power: 500 kVA
• Primary Rated Voltage: 11,000 V
• Percentage Impedance: 5.75 %

Using the formulas:

1. Convert kVA to VA:
   Srated = 500 kVA * 1000 = 500,000 VA
2. Calculate Base Impedance (Primary Side):
   Zbase = (11,000 V * 11,000 V) / 500,000 VA
Zbase = 121,000,000 / 500,000 = 242 Ohms
3. Calculate Actual Impedance (Primary Side):
   Zactual = (5.75 / 100) * 242 Ohms
Zactual = 0.0575 * 242 = 13.915 Ohms

Therefore, the actual impedance of this transformer, referred to the primary side, is approximately 13.915 Ohms.