Transformer loss power is divided into iron loss and copper loss. Iron loss, also known as no-load loss, is its fixed loss, is the loss generated by the iron core (also known as iron core loss, and copper loss is also called load loss).

So do you know how the transformer loss is calculated? Today let’s approach the transformer no-load loss, understand its parameters and calculation methods.

## 1. Transformer loss calculation formula

① Active loss: ΔP = Po + KT β2 Pk

② Reactive power loss: ΔQ = Qo + KT β2 Qk

③ Comprehensive power loss: ΔPz = ΔP + KQΔQ

Qo≈Io%Sn, Qk≈Uk%Sn

In the above formula, different symbols refer to the following meanings:

Qo: no-load reactive power loss (kvar)

Sn: rated transformer capacity (kVA)

Uk%: short-circuit voltage percentage

Qk: rated load leakage power (kvar)

KQ: reactive power economic equivalent (kW/kvar)

Selection conditions for each parameter:

① Take KT=1.05;

② When the minimum load of the home solar power system is taken for the 6kV~10kV step-down transformer in the urban power grid and industrial enterprise power grid, its reactive power equivalent KQ = 0.1kW/kvar;

③ The average load factor of the transformer, for agricultural transformers, β= 20%; for industrial enterprises that implement a three-shift system, β= 75%;

④ Transformer operating hours T = 8760h, maximum load loss hours: t = 5500h;

⑤ Transformer no-load loss Po, rated load loss Pk, Io%, Uk%, please refer to the product factory information for details.

## 2. Characteristics of transformer losses

• Po:

No-load losses, mainly iron losses, include hysteresis losses and eddy current losses; Hysteresis loss is proportional to frequency, and proportional to the second power of the hysteresis coefficient of the maximum magnetic flux density;

Eddy current losses are proportional to the product of frequency, maximum flux density, and the thickness of the silicon based steel sheet.

• Pc:

Load loss, mainly the loss in resistance when the load current passes through the winding, generally called copper loss. Its size varies with the load current and is proportional to the square of the load current; (and expressed in terms of the standard coil temperature conversion value).

Load losses are also affected by the temperature of the transformer, while the leakage flux caused by the load current produces eddy current losses in the winding and stray losses in the metal part outside the winding.

The total loss of the transformer ΔP = Po + Pc

Transformer loss ratio = Pc /Po

Efficiency of the transformer = Pz/(Pz+ΔP), expressed as a percentage; where Pz is the output power of the secondary side of the transformer.

## 3. Calculation of transformer loss power

Like mentioned above, the power loss of the transformer consists of two parts: iron loss and copper loss. Iron loss is related to running time, and copper loss is related to the load size. Therefore, the lost power should be calculated separately.

① Calculation of iron loss electricity:

The calculation formula for the iron loss power of different models and capacities is: Iron loss power (kWh) = no-load loss (kW)×power supply time (hours) The power supply time is the actual operating time of the transformer and is determined according to the following principles:

• For users with continuous power supply, the whole month is calculated as 720 hours.
• Unlike off grid batteries system, due to intermittent power supply or limited power supply due to power grid reasons, the calculation shall be based on the actual number of hours of power supply provided by the substation to users. Calculate the entire month of operation. After the transformer loses power, the time for the self-falling fuse tube to be delivered to the power supply station shall be deducted when calculating the iron loss.
• For users equipped with an accumulator clock on the low-voltage side of the transformer, the calculation is based on the accumulated power supply time of the accumulator clock.

② Calculation of copper loss electricity:

When the load ratio is 40% and below, 2% of the monthly electricity consumption (in terms of meter reading) shall be charged, calculation formula: copper loss electricity (kWh) = monthly electricity consumption (kWh) x 2%

Because the copper loss is related to the size of load current (electricity), when the monthly average load ratio of distribution substation is more than 40%, the copper loss electricity shall be charged at 3% of monthly electricity consumption.

The formula for calculating the load factor is:

load factor = copy of the electricity / S. T. Cos¢

S: rated capacity of distribution substation (kVA);

T: calendar time of the whole month, take 720 hours;

COS ¢: power factor, take 0.80.

The loss of power transformer, such as 2000w inverter or 3000w inverter, can be divided into copper loss and iron loss. Copper loss is generally 0.5%. Iron loss is generally 5~7%. Transformation loss of dry-type transformer is smaller than oil-immersed one. Total transformation loss: 0.5+6=6.5 Calculation method: 1000KVA×6.5% = 65KVA 65KVA×24 hours×365 days = 569,400KWT The labels on the transformers usually contain specific data.

No-load loss refers to the secondary side of the transformer open circuit, the primary side of the rate of increase and the rated voltage sinusoidal voltage when the transformer absorbed power. If we only pay attention to the rated frequency and rated voltage, and ignore the tap voltage and voltage waveform, the accuracy of the measurement system, test instrumentation and test equipment, etc., we may confuse the loss of the calculated value, the standard value, the measured value, and the guaranteed value.

If the voltage is added to the primary side, and there is a tap, such as the transformer is constant flux regulation, the added voltage should be the tap voltage of the tap position of the corresponding power supply.

If it is variable flux regulation, because each tap position when the no-load loss is not the same, we must select the correct tap position and apply the specified rated voltage according to the technical conditions, because in the variable flux regulation, the primary side is always added to a voltage in the various tap position.

It is generally required that the waveform of the applied voltage must be an approximate sinusoidal waveform. Therefore, one is a harmonic analyser to measure the harmonic component contained in the voltage waveform, the second is a simple method, with an average voltmeter, but the scale for the rms voltmeter to measure the voltage, and the rms voltmeter readings compared to the difference between the two is greater than 3%, indicating that the voltage waveform is not sinusoidal, measured no-load losses, according to the requirements of the new standard should be invalidated.

For the measurement system, it is necessary to select the appropriate test line, select the appropriate test equipment and instrumentation. Because of the development of permeability materials, the wattage per kilogram loss in a substantial decline in manufacturing plants are selected high-quality high permeability grain-oriented silicon steel sheet or even select amorphous alloys as permeability materials, structure and the development of such as stepped seams and the full slope of the non-porous.

The process of using non-stacking on the iron yoke process, manufacturers are in the development of low-loss transformers, especially the no-load loss has been a substantial decline. Therefore, new requirements are placed on the measurement system. The capacity remains unchanged and the no-load loss decreases, which means the power factor of the transformer decreases when it is no-load.

A small power factor requires the manufacturer to change and transform the measurement system. It is advisable to use the three-wattmeter method for measurement, choose a 0.05-0.1 level transformer, and choose a wattmeter with a low power factor. Only in this way can the measurement accuracy be guaranteed.

When the power factor is 0.01, the phase difference of the transformer is 1 minute, which will cause a power error of 2.9%. Therefore, in actual measurement, the current ratio and voltage ratio of the current transformer and voltage transformer must be correctly selected.

When the actual current is much smaller than the current connected to the current transformer, the phase difference and current error of the current transformer will be larger, which will lead to larger errors in the actual measurement results. Therefore, the current drawn by the transformer should be close to the rated current transformer.

In addition, the no-load loss calculated by referring to the unit loss and process coefficient of the selected silicon steel sheet according to the prescribed procedures in the design is generally called the calculated value. This value should be compared with the standard value specified in the standard or with the standard value or guaranteed value specified in the contract. The calculated value must be smaller than the standard value or guaranteed value, and there must be no margin in calculation, especially for mass-produced transformers.

In addition, the calculated value is only valid for designers or design departments and has no legal effect. The calculated value cannot be used to judge the loss level of the product. The standard value specified in the standard or the guaranteed value specified in the contract has legal effect.

Products that exceed the standard value plus the allowable deviation, or the guaranteed value (the guaranteed value is equal to the standard value plus the allowable deviation), are considered unqualified products. If there is a loss evaluation system, it will generally be pointed out in the contract. Especially for export products, fines will be imposed if the loss value exceeds the specified value, and the fine for no-load loss is the highest.

The concept of actual measured value must also be understood correctly. Either the reading of the mutual meter (or the reading of the power converter) or the actual measured value must be converted to rated conditions, and must have sufficient accuracy.

For the actual measured value of no-load loss, it is mainly that the voltage waveform of the power supply must be sinusoidal, and the difference between the average voltmeter reading and the effective voltage reading is less than 3%.

When the secondary winding of the transformer is open-circuited and the primary winding applies a rated voltage with a sinusoidal waveform of rated frequency, the active power consumed is called no-load loss.

When the secondary winding of the transformer is short-circuited (steady state), the active power consumed when the primary winding flows through the rated current is called load loss.

The algorithm is: load loss = resistance loss of the largest pair of windings + additional loss

Additional loss = winding eddy current loss + circulating current loss of parallel-wound wires + stray loss + lead loss

• Impedance voltage:

When the secondary winding of the transformer is short-circuited (steady state), the voltage applied when the primary winding flows through the rated current is called impedance voltage Uz.

Usually Uz is expressed as a percentage of the rated voltage, that is, uz=(Uz/U1n)*100%

• Turn potential:

u=4.44*f*B*At,V

B: magnetic density in the core

TAt: effective cross-sectional area of the core, square meters

It can be converted into a commonly used formula for transformer design calculation: When f=50Hz: u=B*At/450*10^5,V

When f=60Hz: u=B*At/375*10^5,V

If you already know the phase voltage and the number of turns, the turn potential is equal to the phase voltage divided by the number of turns. Transformer no-load loss calculation - the no-load loss component of the transformer.

No-load losses include hysteresis and eddy current losses in the core and no-load current losses on the primary coil resistance. The former is called iron loss and the latter is called copper loss. Since the no-load current is very small, the latter can be ignored. Therefore, the no-load loss is basically the iron loss. ​

There are many factors that affect the no-load loss and iron loss of the transformer, which are expressed by mathematical formulas.

Pn, Pw: represents hysteresis loss and eddy current loss kn, kw constants;

f: frequency of the external voltage applied to the transformer Hertz;

Bm: Maximum magnetic flux density in the iron core Wei/m2;

n: Steinmetz constant. For commonly used silicon steel sheets, when Bm=(1.0~1.6) Wei/m2, n≈2. For currently used directional silicon steel sheets, it takes 2.5~3.5. ​

According to the theoretical analysis of the transformer, assuming that the primary induced potential is E1 (volt), then: E1=KfBm; K is the proportionality constant, which is determined by the number of primary turns and the core cross-sectional area.

Since the primary leakage resistance voltage drop is very small, if it is ignored, then E1=U1

It can be seen that the no-load loss iron loss of the transformer has a great relationship with the external voltage. If the voltage V is a certain value, the no-load loss iron loss of the transformer remains unchanged (because f does not change), and because U1=U1N during normal operation, so no-load loss is also called constant loss. If the voltage fluctuates, the no-load losses change.

The iron loss of the transformer is related to the core material and manufacturing process, and has nothing to do with the load size.