Transformer All-Day Efficiency Calculator

A transformer can operate at substantially different loading levels through the day, while its core loss remains energized for every hour it is in service. The Transformer All-Day Efficiency Calculator estimates the energy delivered and the energy lost over the entered operating profile.

The primary result for an energy review is Total loss energy in kWh. It combines:

• Core-loss energy from the transformer’s no-load loss over all entered hours.
• Load-loss energy from winding and stray load losses, weighted by the square of each period’s Load fraction.
• Output energy delivered to the load, based on transformer rated kVA, Load fraction, Power factor, and Hours.

These values are useful for transformer-loss comparisons, operating-cost estimates, loading-profile reviews, equipment selection studies, and documentation of expected energy performance. They do not establish feeder ampacity, branch-circuit conductor size, OCPD rating, raceway fill, voltage-drop compliance, or transformer secondary conductor requirements.

Load Profile Inputs

Each Load profile rows entry represents one operating period. The rows may describe daytime occupancy, overnight standby loading, production shifts, seasonal operating modes, or any other defined interval.

Field	Electrical use in the calculation
Period label	Identifies the operating interval, such as Day or Night
Hours (h)	Sets the duration of that load condition
Load fraction (%)	Expresses transformer loading as a percentage of Transformer rated kVA
Power factor (%)	Converts apparent-power loading in kVA to output energy in kWh
Transformer rated kVA (kVA)	Establishes the transformer’s rated apparent-power base
No-load loss (W)	Represents energized core loss from manufacturer data or a test record
Full-load loss (W)	Represents load loss at rated transformer load from manufacturer data or a test record
Profile note	Records the loss test basis, tap, temperature, and source model separately

Profile hours equals the total of all entered Hours. The profile does not have to total 24 hours. If the entered rows total 10 hours, every energy result represents that 10-hour operating period; if they total 24 hours, the result represents a full day.

Peak profile load is the largest apparent-power load in the profile:

\(\displaystyle \text{Peak profile load (kVA)} = \text{Transformer rated kVA} \times \max(\text{Load fraction})\)

Power factor does not reduce the displayed Peak profile load because kVA is apparent power. Power factor affects delivered real-energy output in kWh.

Energy and Loss Formula

For each profile row, convert Load fraction and Power factor from percentages to decimal values.

\(\displaystyle L = \frac{\text{Load fraction (\%)}}{100}\)

\(PF = \frac{\text{Power factor (\%)}}{100}\)

Output Energy

Output energy is the sum of real energy delivered during each period:

\(\displaystyle \text{Output energy (kWh)} = \sum\left(\text{Transformer rated kVA} \times L \times PF \times \text{Hours}\right)\)

Because kVA multiplied by power factor produces kW, multiplying by Hours produces kWh.

Core-Loss Energy

No-load loss is treated as energized for every entered profile hour:

\(\displaystyle \text{Core-loss energy (kWh)} = \frac{ \text{No-load loss (W)} \times \text{Profile hours} }{1000}\)

Core loss does not vary with the entered Load fraction. If a transformer remains energized through a lightly loaded overnight period, its no-load loss continues through that period.

Load-Loss Energy

Full-load loss is weighted by the square of the loading fraction for each profile row:

\(\displaystyle \text{Load-loss energy (kWh)} = \sum \left( \frac{ \text{Full-load loss (W)} \times L^2 \times \text{Hours} }{1000} \right)\)

The squared loading relationship is why a transformer’s loss profile cannot be evaluated accurately by using only an average load percentage. A 50% load period contributes (0.50^2 = 0.25), or 25% of stated full-load loss. A 25% load period contributes (0.25^2 = 0.0625), or 6.25% of stated full-load loss.

Total Loss Energy

\(\displaystyle \text{Total loss energy} = \text{Core-loss energy} + \text{Load-loss energy}\)

If all-day efficiency is needed from the energy results, it can be expressed as:

\(\displaystyle \text{All-day efficiency (\%)} = \frac{\text{Output energy}} {\text{Output energy}+\text{Total loss energy}} \times 100\)

The displayed results provide the output-energy and loss-energy values used in that expression.

Calculation Example

Use the following entered profile and transformer loss data:

Input	Value
Row 1 — Period label	Day
Row 1 — Hours (h)	12
Row 1 — Load fraction (%)	50
Row 1 — Power factor (%)	100
Row 2 — Period label	Night
Row 2 — Hours (h)	12
Row 2 — Load fraction (%)	25
Row 2 — Power factor (%)	100
Transformer rated kVA (kVA)	100
No-load loss (W)	200
Full-load loss (W)	1,200

The profile contains 24 total hours. Its highest loading condition is 50% of a 100 kVA transformer:

\(\displaystyle 100 \text{ kVA} \times 0.50 = 50 \text{ kVA}\)

The resulting Peak profile load is 50 kVA.

Output Energy

Day output:

\(\displaystyle 100 \times 0.50 \times 1.00 \times 12 = 600 \text{ kWh}\)

Night output:

\(\displaystyle 100 \times 0.25 \times 1.00 \times 12 = 300 \text{ kWh}\)

\(\displaystyle \text{Output energy} = 600 + 300 = 900\text{ kWh}\)

\(\displaystyle \text{Core-loss energy} = \frac{200 \times 24}{1000} = 4.8\text{ kWh}\)

Load-Loss Energy

Day load loss:

\(\displaystyle \frac{1200 \times (0.50)^2 \times 12}{1000} = 3.6 \text{ kWh}\)

Night load loss:

\(\displaystyle \frac{1200 \times (0.25)^2 \times 12}{1000} = 0.9 \text{ kWh}\)

\(\displaystyle \text{Load-loss energy} = 3.6 + 0.9 = 4.5\text{ kWh}\)

\(\displaystyle \text{Total loss energy} = 4.8 + 4.5 = 9.3\text{ kWh}\)

The displayed result set is:

Result	Value
Profile hours	24 h
Peak profile load	50 kVA
Output energy	900 kWh
Core-loss energy	4.8 kWh
Load-loss energy	4.5 kWh
Total loss energy	9.3 kWh

Using those energy values, the calculated all-day efficiency would be approximately:

\(\displaystyle \frac{900}{900+9.3}\times100 = 98.98\%\)

Loss Data and Field Limits

Use manufacturer data or test-record values for No-load loss (W) and Full-load loss (W). The loss basis must match the transformer condition being evaluated. Record the test basis, tap position, temperature, and source model in Profile note.

The calculation assumes that:

• No-load loss remains constant during all entered profile hours.
• Full-load loss scales with the square of Load fraction.
• The transformer remains energized throughout the entered profile.
• The entered Power factor represents the real-power relationship for each load period.
• The profile represents the operating condition being evaluated, not necessarily a 24-hour calendar day.

Actual operating losses can differ when transformer temperature, tap position, harmonic loading, cooling condition, voltage condition, or manufacturer test basis differs from the entered loss data. Harmonic currents can also increase transformer heating and conductor losses without being represented by a simple Load fraction and Power factor entry.

Use separate load calculations and applicable field requirements when selecting transformer primary or secondary conductors, determining AWG or kcmil conductor size, applying ampacity adjustment factors or correction factors, checking terminal ratings and insulation temperature ratings, reviewing voltage drop, sizing overcurrent protection, or verifying equipment installation requirements with the AHJ.