Parallel Transformer Bank Sizing Calculator – IEEE, IEC

Parallel transformer bank sizing is critical for ensuring reliable power distribution and system stability. Accurate calculations prevent overloads and optimize transformer utilization.

This article explores IEEE and IEC standards for parallel transformer bank sizing, providing formulas, tables, and real-world examples. It guides engineers through precise design and analysis.

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• Calculate parallel transformer bank capacity for 3 transformers, each 500 kVA, 11 kV primary voltage.
• Determine load sharing for two transformers in parallel with different impedance values.
• Find maximum allowable load on a transformer bank sized per IEC 60076 standards.
• Compute voltage regulation for parallel transformers under IEEE recommended practices.

Common Values for Parallel Transformer Bank Sizing – IEEE and IEC Standards

Fundamental Formulas for Parallel Transformer Bank Sizing

Transformer bank sizing involves multiple parameters including rated power, impedance, voltage, and load sharing. The following formulas are essential for accurate calculations.

1. Total Rated Power of Parallel Transformers

The total rated power (S_total) of transformers connected in parallel is the sum of individual rated powers:

• S_total: Total rated power of transformer bank (kVA)
• S_r,i: Rated power of the i-th transformer (kVA)
• n: Number of transformers in parallel

2. Load Sharing Based on Impedance

Load current sharing depends on the per-unit impedance of each transformer. The current through transformer i (I_i) is inversely proportional to its impedance:

• I_i: Load current through transformer i (A)
• I_total: Total load current (A)
• Z_i: Per-unit impedance of transformer i (pu)
• Z_base: Base impedance (pu), often 1 pu for normalization
• k: Index for all transformers in parallel

3. Per-Unit Impedance Calculation

Per-unit impedance (Z_pu) is calculated relative to a common base power (S_base) and voltage (V_base):

• Z_actual: Actual transformer impedance (Ω)
• S_base: Base power for per-unit system (kVA)
• S_r: Rated power of transformer (kVA)

4. Voltage Regulation of Parallel Transformers

Voltage regulation (VR) indicates voltage drop under load and is critical for parallel operation:

• V_no-load: Secondary voltage at no load (V)
• V_full-load: Secondary voltage at full load (V)

5. Maximum Load per Transformer in Parallel

To avoid overloading, the maximum load on each transformer should not exceed its rated capacity adjusted for load sharing:

• S_max,i: Maximum allowable load on transformer i (kVA)
• Load Factor: Typically 0.8 to 1.0 (80% to 100%)
• Safety Margin: Usually 1.1 to 1.25 depending on standards

Detailed Real-World Examples of Parallel Transformer Bank Sizing

Example 1: Sizing a Parallel Transformer Bank for a 1500 kVA Load

A power distribution system requires a total capacity of 1500 kVA at 11 kV. Two transformers are available: one rated at 1000 kVA and another at 750 kVA. Both have impedance voltages of 6% and 5.5%, respectively. Determine if these transformers can be connected in parallel and calculate the load sharing.

Step 1: Check Voltage Ratings

• Both transformers have the same primary voltage rating (11 kV) – suitable for parallel operation.
• Secondary voltages must also match (assumed 0.4 kV for this example).

Step 2: Calculate Per-Unit Impedances

Choose a common base power, typically the larger transformer rating or total load. Here, use S_base = 1500 kVA.

Step 3: Calculate Load Sharing Currents

Using the formula for load sharing:

Transformer 1 carries 55% of the load current, Transformer 2 carries 45%.

Step 4: Calculate Load in kVA for Each Transformer

Step 5: Verify Loading Limits

• Transformer 1 loading: 825 / 1000 = 82.5% (within 80-100% limit)
• Transformer 2 loading: 675 / 750 = 90% (acceptable)

Both transformers can operate in parallel safely with proper load sharing.

Example 2: Voltage Regulation Calculation for Parallel Transformers

Two 500 kVA transformers operate in parallel at 11 kV. Transformer A has an impedance voltage of 5%, Transformer B has 6%. Calculate the voltage regulation at full load with a power factor of 0.9 lagging.

Step 1: Calculate Per-Unit Impedances on Common Base

Assuming base power S_base = 1000 kVA (sum of both transformers):

Step 2: Calculate Load Sharing Currents

Step 3: Calculate Voltage Regulation for Each Transformer

Voltage regulation formula considering power factor angle (φ = cos^-1(0.9) ≈ 25.84°):

Assuming short-circuit impedance angle θ = 80° (typical for transformers):

• cos φ = 0.9
• sin φ = 0.436
• tan θ = tan 80° ≈ 5.67

Calculate VR for Transformer A:

Calculate VR for Transformer B:

Step 4: Calculate Combined Voltage Regulation

Weighted average based on load sharing:

The parallel transformer bank exhibits approximately 18.3% voltage regulation under full load.

Additional Technical Considerations for Parallel Transformer Bank Sizing

• Impedance Matching: Transformers must have similar impedance magnitudes and angles to ensure proper load sharing and avoid circulating currents.
• Tap Changer Settings: Tap positions should be coordinated to maintain voltage equality across transformers.
• Phase Displacement: Transformers must have the same vector group to prevent phase angle differences causing circulating currents.
• Thermal Limits: Continuous loading should respect temperature rise limits per IEC 60076-2 to avoid insulation damage.
• Protection Coordination: Protective devices must be set considering combined fault currents and load sharing characteristics.
• Harmonics and Non-Linear Loads: Transformers in parallel should be evaluated for harmonic currents that may cause uneven heating or losses.

References and Authoritative Standards

• IEEE Std C57.12.00 – Standard for Transformers
• IEC 60076 – Power Transformers
• IEEE Guide for Loading Mineral-Oil-Immersed Transformers
• NEMA Standards for Transformers

By adhering to these standards and applying the formulas and methods outlined, engineers can design and size parallel transformer banks that ensure operational reliability, efficiency, and safety in power systems.