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Transformer Loss Calculation Formula


(1) Active power 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


Where: Qo - no-load reactive power loss (kvar)


Po——no-load loss (kW)


Pk——Rated load loss (kW)


Sn - transformer rated capacity (kVA)


Uk%——short circuit voltage percentage


β——load factor, which is the ratio of load current to rated current.


KT——load fluctuation loss coefficient


Qk——Rated load flux leakage power (kvar)


KQ——reactive economic equivalent (kW/kvar)



The selection conditions of each parameter in the calculation of the above formula:


(1) Take KT=1.05;


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


(3) The average load factor of the transformer is β=20% for agricultural transformers; for industrial enterprises, three shifts are implemented, and β=75% is desirable;


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


(5) Transformer no-load loss Po, rated load loss Pk, Io%, Uk%, see the product factory information.


Characteristics of Transformer Losses


Po - no-load loss, mainly iron loss, including hysteresis loss and eddy current loss;


The hysteresis loss is proportional to the frequency; it is proportional to the power of the hysteresis coefficient of the maximum magnetic flux density.


The eddy current loss is proportional to the product of frequency, maximum magnetic flux density, and thickness of the silicon steel sheet.


Pc——Load loss, mainly the loss on the 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 by the conversion value of the standard coil temperature).


The load loss is also affected by the temperature of the transformer. At the same time, the leakage flux caused by the load current will generate eddy current loss in the winding and stray loss in the metal part outside the winding.


The total loss of the transformer ΔP=Po+Pc


Transformer loss ratio = Pc /Po


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


Calculation of Variable Loss Electricity


The power loss of the transformer consists of two parts: iron loss and copper loss. The iron loss is related to the running time, and the copper loss is related to the load. Therefore, the power loss should be calculated separately.

1. Calculation of iron loss electricity: Iron loss electricity of different models and capacities, the calculation formula is: iron loss electricity (kWh) = no-load loss (kW) × power supply time (hours)


The no-load loss (iron loss) of the distribution transformer can be checked from the attached table, and the power supply time is the actual running time of the transformer, which is determined according to the following principles:

(1) For users with continuous power supply, the whole month is calculated as 720 hours.

(2) Due to power grid reasons, intermittent power supply or limited power supply, the calculation shall be based on the actual power supply hours of the substation to the user, and shall not be considered as difficult to calculate, and shall still be calculated on the basis of full-month operation. The time should be deducted when calculating the iron loss.

(3) Users who are equipped with integrated clocks on the low-voltage side of the transformer are calculated according to the accumulated power supply time of the integrated clocks.


2. Calculation of copper loss electricity: when the load rate is 40% and below, it is charged as 2% of the monthly electricity consumption (based on the reading of the electric energy meter). The calculation formula is: copper loss electricity (kWh) = monthly electricity consumption Amount (kWh) × 2%

Because the copper loss is related to the load current (electricity), when the monthly average load rate of the distribution transformer exceeds 40%, the copper loss power should be charged at 3% of the monthly power consumption. The monthly power consumption when the load rate is 40% can be checked from the attached table. The formula for calculating the load rate is: load rate = copy power/S. T. Cos ¢

In the formula: S - the rated capacity of the distribution transformer (kVA); T - the calendar time of the whole month, take 720 hours; COS¢ - power factor, take 0.80.

The variable loss of power transformer can be divided into copper loss and iron loss. Copper loss is generally 0.5%. Iron loss is generally 5~7%. The change loss of dry type transformer is smaller than that of oil invasion type. Total loss: 0.5+6=6.5 Calculation method: 1000KVA×6.5%=65KVA

65KVA × 24 hours × 365 days = 569400KWT (degrees)


The nameplate on the transformer has specific data.


Transformer no-load loss


No-load loss refers to the power absorbed by the transformer when the secondary side of the transformer is open circuit and the sine wave voltage of the primary side is equal to the rated voltage. Generally, only the rated frequency and rated voltage are paid attention to, but sometimes the tapping voltage and voltage waveform, the accuracy of the measurement system, test instruments and test equipment are not paid attention to. The calculated value, standard value, measured value, and guaranteed value of the loss are confused again.


If the voltage is added to the primary side and there is a tap, if the transformer is constant magnetic flux voltage regulation, the applied voltage should be the tap voltage of the tap position corresponding to the power supply. In the case of variable magnetic flux voltage regulation, because the no-load loss is different for each tap position, the correct tap position must be selected according to the technical requirements, and the specified rated voltage must be applied, because during variable magnetic flux voltage regulation, The primary side always applies a voltage to each tap position.


It is generally required that the waveform of the applied voltage must be approximately sinusoidal. Therefore, one is to use a harmonic analyzer to measure the harmonic components contained in the voltage waveform, and the other is to use a simple method to measure the voltage with an average voltmeter, but the scale is an effective value voltmeter, and compare it with the effective value voltmeter reading , when the difference between the two is greater than 3%, it means that the voltage waveform is not a sine wave, and the measured no-load loss should be invalid according to the requirements of the new standard.


For the measurement system, it is necessary to select the appropriate test line, select the appropriate test equipment and instruments. Because of the development of magnetically permeable materials, the wattage lost per kilogram has been greatly reduced. Manufacturers use high-quality high-permeability grain-oriented silicon steel sheets or even amorphous alloys as magnetically permeable materials. There are no holes in the seam and full slope, and the technology of not stacking the iron yoke is adopted in the process. The manufacturers are developing low-loss transformers, especially the no-load loss has been greatly reduced. Therefore, new requirements are placed on the measurement system. The capacity remains the same, and the decrease of no-load loss means that the power factor of the transformer decreases at no-load. The 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 class 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 will cause a power error of 2.9% when the phase difference is 1 minute. Therefore, it is necessary to correctly select the current ratio and voltage ratio of the current transformer and the voltage transformer during the actual measurement. When the actual current is much smaller than the current connected to the current transformer, the greater the phase difference and current error of the current transformer, this will lead to a larger error in the actual measurement results. Therefore, the current drawn by the transformer should be close to the rated value of the current transformer. current.


In addition, in the design, according to the prescribed procedures, the no-load loss calculated by referring to the unit loss and process coefficient of the selected silicon steel sheet 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 less than the standard value or guaranteed value, and there is no room for calculation, especially for batch-produced transformers. In addition, the calculated value is only valid for the designer or the design department, and has no legal effect. The calculated value cannot be used to judge the loss level of the product. The standard value stipulated in the standard or the guaranteed value stipulated in the contract is legally effective. 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 unqualified products. If there is a loss evaluation system, it will generally be pointed out in the contract, especially for export products, if the loss value exceeds the specified value, a fine will be imposed, and the penalty for no-load loss is the highest. For the loss evaluation values of European countries, please refer to the 11th issue of "Transformer" magazine in 1994. Thousands of dollars in fines per kilowatt. This is the legal effect and is directly linked to economic benefits.


The concept of the measured value must also be correctly understood, either the reading of the mutual meter (or the reading of the power converter) or the measured value must be converted to the rated condition, and there must be sufficient accuracy. For the measured value of no-load loss, it is mainly that the voltage waveform of the power supply should be a sine wave, and the difference between the average voltmeter reading and the effective value voltage reading is less than 3%.


Calculation of no-load loss, load loss and impedance voltage


No-load loss: When the secondary winding of the transformer is open and the primary winding is applied with a rated frequency sinusoidal waveform rated voltage, the active power consumed is called no-load loss. The algorithm is as follows: no-load loss = no-load loss process coefficient × unit loss × core

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 as follows: load loss = resistance loss of the largest pair of windings + additional loss


Additional loss = winding eddy current loss + circulation loss of parallel wire + stray loss + lead loss


Impedance voltage: When the secondary winding of the transformer is short-circuited (steady state), the voltage applied by the rated current flowing through the primary winding is called the impedance voltage Uz. Uz is usually expressed as a percentage of the rated voltage, that is, uz=(Uz/U1n)*100%


Turn potential: u=4.44*f*B*At,V


Among them: B—magnetic density in iron core, TAt—effective cross-sectional area of iron core, square meter


It can be transformed into the 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 voltages and the number of turns, the turn potential is calculated by dividing the phase voltage by the number of turns.


The no-load loss includes the hysteresis and eddy current loss in the iron core and the loss of the no-load current 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 neglected, so 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 in mathematical formulas. In the formula, Pn and Pw—represent hysteresis loss and eddy current loss kn, kw—constants

f - the frequency Hertz of the applied voltage of the transformer

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

n——Steinmetz constant. For commonly used silicon steel sheets, when Bm=(1.0~1.6) Wei/m2, n≈2. For the currently used directional silicon steel sheets, take 2.5~3. 5.


According to the theoretical analysis of the transformer, assuming that the primary induced potential is E1 (volts), then: E1=KfBm (2)


K is a proportional constant, which is determined by the number of primary turns and the cross-sectional area of the iron core, so the iron loss is:


Since the primary leakage impedance voltage drop is very small, if neglected,

E1=U1(4)


It can be seen that the no-load iron loss of the transformer has a great relationship with the applied voltage. If the voltage V is a certain value, the no-load iron loss of the transformer will not change (because f does not change), and because U1=U1N in normal operation, so No-load loss is also called constant loss. If the voltage fluctuates, the no-load loss varies. The iron loss of the transformer is related to the core material and manufacturing process, and has nothing to do with the load.


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