8. Transformer Sizing and Efficiency

Principle: Transformer sizing involves selecting a transformer with sufficient kVA rating to supply the expected loads plus a margin for future growth or contingencies, while also considering the transformer’s efficiency and losses. A transformer is rated in kVA (not kW) because it must handle apparent power (including reactive power) without overheating.

Key aspects:

  • Capacity (kVA): Sum up all loads (kW or kVA), apply diversity (since not all loads are on simultaneously), and ensure the chosen transformer kVA exceeds the maximum demand. Common practice is to add a safety margin (e.g., select the next standard size above the calculated demand or include ~10–20% spare capacity).
  • Impedance and Fault Level: The transformer’s impedance (expressed as a percentage) affects the fault current on the secondary side and voltage regulation. Sizing from an impedance perspective might mean ensuring that the percentage voltage drop (%VD) under full load is acceptable, which is related to the transformer’s %Z and the load power factor.
  • Efficiency: Transformers incur two main losses: no-load (core) losses, which occur whenever the transformer is energized, and load (copper) losses, which vary with the load current (I²R losses in the windings). Efficiency is typically highest at the load point where core and copper losses are equal. Modern designs aim for high efficiency even at partial loads, driven by energy cost considerations and regulatory requirements.

Sizing Calculations

  1. Load Aggregation: List all loads that the transformer will feed (motors, lighting, HVAC, etc.). Convert each load to kVA (using kW/PowerFactor for AC loads) and sum them, or perform a load flow/diversity study if the peak demands do not coincide. This may result in an after-diversity maximum demand (ADMD).
  2. Select kVA: Choose a standard transformer rating above the calculated demand. For example, if the calculation indicates 420 kVA, a 500 kVA unit might be selected (standard sizes might be 400, 500, 630 kVA, etc.). It is generally unwise to run a transformer at more than 80–90% of its capacity continuously, both for longevity and future growth.
  3. Check Loading: If a transformer is expected to run near full load frequently, consider a fan-cooled (ONAN/ONAF) rating or even paralleling transformers to split the load. Also, verify that inrush currents from large motors do not saturate the transformer, causing voltage dips.
  4. Efficiency and Loss Evaluation: Determine the annual energy throughput and calculate losses. For instance, if the no-load loss is 1 kW and the load loss is 5 kW at full load, and if on average the transformer operates at 50% load, then the core loss is always 1 kW while the copper loss at 50% load is (0.5)² × 5 = 1.25 kW, totaling ~2.25 kW of losses on average. Over a year (~8760 hours), this equates to ~19.7 MWh lost, costing approximately $1970/year (at $0.1/kWh). Efficiency at 50% load is calculated as output/(output + loss) = (250 kW)/(251.25 kW) ≈ 99.5%. Note that efficiency drops at very low loads (where core loss dominates) or at very high loads (where copper loss dominates). Manufacturers provide efficiency curves or a Peak Efficiency Index for EcoDesign compliance. Designers might select a slightly larger transformer to improve efficiency by operating in the 50–70% load range rather than at 90–100%.
  5. Voltage and Impedance: Confirm the required primary and secondary voltages (e.g., 11 kV to 415 V), the number of phases, and any tap changer requirements for voltage adjustment. The transformer’s impedance (e.g., 5% or 6%) influences the internal voltage drop under load. Although it is not usually a sizing criterion, it is an important performance consideration.

Niche Applications

  • High-efficiency transformers (Amorphous core): For energy conservation, low-loss transformers with amorphous metal cores may be chosen, especially when the load is low most of the time, to reduce no-load losses. This option typically involves a higher initial cost in exchange for long-term energy savings.
  • K-factor transformers: In environments with significant harmonic currents (such as data centers), special transformers with lower losses at harmonic frequencies and the ability to handle higher neutral currents may be specified. These transformers may be sized larger due to the additional heating caused by harmonics.
  • Inrush current: Large transformers can draw magnetizing inrush currents that are 5–10 times the rated current for a few cycles when energized. Although this is not directly a sizing issue, the upstream breaker must accommodate this inrush, and in installations with multiple transformers, staggered energization might be necessary.
  • Parallel transformers: Instead of one large transformer, two smaller transformers may be connected in parallel for redundancy or due to physical constraints. Care must be taken to ensure they share the load properly (matched impedance) and that each can carry the full load if the other fails (N-1 criterion).
  • Transformer overheating due to overloads: Standards sometimes permit short-duration overloads, particularly in cooler ambient conditions or when prior load was low, given the transformer’s thermal time constant (see IEC 60076-7 on loading guides).

Industry Relevance

Transformers are a critical and expensive component of electrical systems. Correct sizing avoids undercapacity—which can lead to overload and failure—as well as overcapacity, which results in unnecessary capital expenditure and increased core losses. In utility distribution, transformers are often available in standard sizes, but industrial and commercial projects require careful calculation based on the expected load. Transformer efficiency has become increasingly important, with regulations such as the EU’s EcoDesign Regulation and the US Department of Energy’s rules (10 CFR Part 431) driving improvements. A well-sized, efficient transformer can operate reliably for decades with minimal losses and provide capacity for future expansion.

Standards

  • IEC 60076 series: Governs power transformers, covering rating definitions, temperature rise limits (typically 65 K for oil-cooled or 55 K for some other types), impedance tolerance, and more. IEC 60076-12 deals with loading beyond the nameplate rating, while IEC 60076-1 ensures a transformer can continuously deliver its rated kVA under specified conditions.
  • BS EN 50464 / 50588: European standards that align with EcoDesign requirements for distribution transformers, specifying maximum losses. A “Tier 2” compliant 1000 kVA transformer, for instance, will have significantly lower losses than older designs.
  • ANSI/IEEE C57 series: In North America, standards such as C57.12.00 and C57.12.90 apply to dry-type and liquid-filled transformers, specifying standard kVA sizes and providing guidelines for overload and life expectancy. IEEE C57.91 offers guidance on loading mineral-oil transformers.
  • NEC/CEC: While installation codes set rules for transformer overcurrent protection (e.g., sizing primary fuses), they do not dictate how to size the transformer’s kVA; that is determined by engineering practice.
  • Energy codes: Standards such as ASHRAE 90.1 require that transformers in certain buildings meet DOE efficiency levels, and green building standards may encourage the selection of higher efficiency units even if they are physically larger.

Software Tools

  • Load Analysis Software: Tools such as ETAP and similar load scheduling programs can aggregate loads and recommend transformer sizes based on calculated maximum demand.
  • Manufacturer Selection Tools: Many transformer vendors provide online tools where you input parameters such as primary and secondary voltage, phase, and required kVA, and the tool outputs a list of suitable models. Some tools also allow you to input desired loss parameters to choose between standard and low-loss models.
  • Loss Evaluation Software: Utilities may use software to evaluate the net present value of transformer losses. By comparing the cost of core and copper losses over the transformer’s life, an optimal design can be selected.
  • Thermal Modeling Tools: For large power transformers, simulation tools can model cooling requirements (e.g., whether fans are needed), although standard distribution transformers typically rely on empirical design methods.
  • Short-Circuit Calculation Tools: These tools automatically use the transformer’s %Z to calculate secondary fault levels, ensuring that the chosen transformer provides stiff voltage for motor starts.

In practice, transformer sizing is often straightforward – choose a size somewhat above the calculated load – but efficiency and regulatory compliance add depth to the decision-making process. A well-sized, efficient transformer will operate reliably for decades, minimizing losses and accommodating future growth.