# Evaluation & Estimation of Load Loss for three-Phase Transformers

This article discusses the use of capacitors and its effects on the individual phase windings for the current drawal and active power measurement. The data as obtained from pattern of the transformers have analysed by comparing the values from each pattern.

Short circuit impedance and short circuit loss measurement for three-phase transformers during the testing is done by confirming the specimen under short circuiting condition to one side of the winding and application of the required voltage on the other side. This pattern of circuit condition indicates of developing the equivalent circuit of the transformer of being loaded to the extreme condition (zero-ohm load impedance). Because of this the requirement of the test supply voltage needs to be suitable for driving the load current to the winding for measurement. Due to inductive nature of coil winding, the current drawl from the supply demands higher magnitude of voltage application which becomes impractical and difficult to obtain. So, to compensation of reactive power, capacitors are used in the supply circuit. Now, use of these capacitors and effects on the individual phase windings for the current drawal and active power measurement has been discussed in this paper.

Moreover, the data as obtained from pattern of the transformers have also been analysed by comparing the values from each pattern. The mechanical design, disposition of the windings with core, clearances etc.. are the factors, which have been considered for this study. The review of the test circuit connections, parameters used for the testing are being considered also on the basis on its importance for the evaluation of the data from the testing. These factors have been mentioned below.

• Earthing of the star connected system in the circuit like (Capacitor bank, Supply Voltage source, Analyser CT/PT Circuit and the Y connected test specimen if any)
• Temperature during the time of testing
• Application of voltage/ current
• Use and calculation of capacitors for the test
• Tap position of test specimen
• Use of MF (Multifying Factor) for evaluation of loss
• Review of the formulae for equivalent calculation
• Use of connecting lead and reviews of the electrical parameters.
• Other factors like use of CT/CTR, PT/PTR for obtaining the accurate zone of measurement.

The detail study being supported by analysis, test results, data review are the main focus of this article, which may create awareness to test engineers and the utility engineers regarding the confirmation of the load loss of the specimen.

Transformer is the static electromagnetic device, works on the principle of mutual induction and transforms input electrical energy into output. First the input electrical energy is converted into magnetic energy and then re-converted to output electrical energy. During this conversion of energy, the active materials particularly electrical (Winding) and magnetic (Core) play the vital role for successful transformation of this energy without causing any storage in the device. It has two circuits, an electric circuit (that carries the current in the winding) and a magnetic circuit (that carries the magnetic flux in the core). Current in the winding and flux in the magnetic core decides the performance of parameters of the transformers. This electrical apparatus is the most efficient equipment in the electrical system, which indicates that the losses are very small as compared to the capacity of the unit. The loss is categorised of two types (No-Load Loss and Load Loss). In this article the measurement practice of load loss, its estimation and evaluation of the test results have been discussed.

Measuring Circuitry for three-phase Transformer
Every three-phase system requires the involvement of common path for the measurement of electrical parameters. Say for the star connected system, the common star terminal if so considered for the measurement circuit, then the measurement of parameters would be easier and accurate for either of the conditions i.e balanced or unbalanced. Considering this concept generally for three-phase transformer, three watt-meter method is used for measurement of load losses during testing of the transformer without the use of capacitor banks on the input side (Refer Fig-1). But in practice due to higher inductive nature of transformer coil the circuit demands higher magnitude of supply voltage, which becomes impractical to attend. So, for compensation of reactive power, capacitors are used in the supply circuit (Refer Fig-2). The star connected common terminal is taken as the reference point for per phase connection for the individual phase circuit. Load losses are normally measured with following circuit conditions.

• One of the winding is shorted preferably Low Voltage winding is selected for shorting.
• Voltage as per the calculation of the impedance value is impressed on the other winding, preferably on high voltage winding. The calculation value does not become practical and feasible for application to the testing job due to inductive nature of coil winding. So, to maintain the required full load current drawl from the supply the reactive voltage due to inductance need to be compensated and accordingly capacitor of suitable values are used in the circuit.
• The rated supply frequency of sinusoidal nature shall be applied to the system.
• The measurements may be made at any current between 50 and 100 per cent, but preferably not less than 50 per cent, of the rated current (principal tapping).
• The difference in temperature between the top oil and the bottom oil shall be maintained small enough to enable the average temperature. If required oil pump could be used for this purpose.
• Derived value can be calculated by considering the temperature of the circuit, both at available and reference temperature.
• Earthing used for the circuitry shall be connected to each other and maintained at equipotential point.
• On three-winding transformers the impedance voltage/short-circuit impedances (principal tapping) and the load losses shall be measured between windings taken in pairs as shown below
a) Between winding 1 and winding 2
b) Between winding 2 and winding 3
c) Between winding 3 and winding 1
Note:- While measurement is taken for two windings, the third winding is to be taken open.
• The other factor say % impedance can also be obtained from this test.
• Calculation of load loss: – According to IEEE standards, load losses should be measured at a load current equal to the rated current for the corresponding tapping position. However, if it is not exactly equal to the rated current, the measured load-loss value will need to be corrected by the square of the ratio of the rated current to the test current (average of the measured phase current in three-phase transformers)

Load loss = I2R Loss+ Eddy Loss+ Stray Loss
While the design value is obtained, the dimension and design parameters are considered in the formula. This value under testing is compared and confirmed for the performance of the transformer. The use of correct measuring instruments with proper measuring set during the testing of load losses are highly important to achieve the value as near as the design value with allowable tolerance.

% Eddy Loss Calculation:
This loss in the transformer is developed due to the flow of eddy current in the lamination during loading condition of transformer and calculated from the dimension by the formulae as described below.
% Eddy Loss= e4 x (n2 – 0.2) x 100 / 9
Where, e= factor = (Hcu / Hel)1/2 x0.9621 x t
(Hcu / Hel) = Ratio of copper height to electrical height of winding, t= thickness of conductor
n= no. of conductors in radial direction

Stray Losses:
This loss consists of the losses due to stray magnetic flux in the windings, core, core clamps, magnetic shields, enclosure and tank wall. During loading condition, the load current in the winding develops the flux in the core and subsequent leakage flux in the iron part of the transformer. This nature of losses in the core clamps, leads etc is constituted as the stray loss and become the part of the load loss of the transformer.
Stray Loss=(%Z X Bm X CA / (a X 10000))1.7 X (2000 / hw)1/2 X ((MVA / 100)X a)1/4 X k
Where %Z= percentage Impedance
Bm= Max. Flux Density
CA = Net Core Area
a= Auto Factor ( 1= Non Auto Transformer) and less for auto transformer.
hw= Average height of winding.
MVA= MVA rating of transformer

I2R Loss:
This loss is developed in the winding of the transformer due to the flow of load current and resistance of the winding. So calculation is simple as the multiplication of square of the load current and resistance of the winding reference to the standard temperature.

Typical Test Results of Load Loss:
In this stanza the value of different transformers from test results have been mentioned for reference of the discussion.

Observations:

• The individual wattmeter reading as observed from the table is not same, but the total readings are close to the value as per the mentioned data in the GTP.
• The current drawl is also different but as not like power reading and approximately same for each phase.
• The power factor though not mentioned in this table are found of very low value in the range of ( p.f 0.01 to 0.003, angles are in minutes)
The value of loss measurement is proportional to the rating of the of the transformer.

Analysis of the Test Results
The test results under load loss measurement are very important to be analysed and interpretation for coming to the final value by the application of correction factor are also to be incorporated properly to avoid the confusion between the clients/customer and manufacturer. The reason of indifferent readings should also be reviewed before drawing any conclusion for acceptance/rejection of the test values. In this stanza the analysis of test results has been narrated for developing the awareness among all the engineers involved in this test.

• The reasons of power and current asymmetry during this test are mainly due to the following points.
a. Load loss is the constituent of Loading Stray loss, eddy current loss and I2R loss. But the value of stray and eddy loss under loading condition is flux dependent, particularly the leakage flux linkage to the supporting structures like tank, frame and other metallic parts of the transformer.
b. For the three-phase three limb transformer, the leakage flux distribution on the tank is more for the middle limb than that of the side limbs, because of the asymmetrical limb structure.
c. The other factors like the compactness of the core assembly, clamping design etc also decides the magnitude of leakage flux.
d. The asymmetrical magnetic couplings, the reason of asymmetrical mutual impedance along with effective AC resistance of the winding are also the factor of asymmetrical reading value of individual phases.
• The value of current flow from the source is mainly dependent on the electrical parameters of the winding and these values do not change much. The variation of winding resistance and reactance is quality supply dependent. Resistance value changes due to availability of DC and AC component factor and reactance is frequency factor of the supply source.
• The reason and effect of Low Power factor for the load loss measurement of the transformer can be summated as follows.
a. The load loss measurement is done by short circuiting one side of the winding with application of voltage on other side of the transformer. The electrical circuit of this shorting is represented as a low resistive load on the system. This way equivalent circuit of both sides get reflected to the supply end and the short circuit impedance is measured by the calculation of voltage applied and the current drawn from it.
b. During this test the inductive reactance of the transformer compared to resistance is more and the equivalent circuit to the supply system becomes inductive in nature with larger phase angle and lower power factor.
c. Effects:- As the power factor is very small, the phase angle is nearer to 900. Load loss at low power factor is very sensitive to its calculation. Because any small error in comparison to the actual low power factor is considerable and results with serious error in the load loss value. Phase-angle error of 1 minute in the voltage or current will result in approximately 3% error in loss measurement for a transformer with a load-loss power factor of 0.01. So Phase-angle uncertainty is one of the many uncertainties associated with measurement of the transformer load losses at low power factor ( Refer Fig-3 and 4)

Use of Correction Factor
As discussed above in the measuring circuitry of the load loss, the role of measuring instruments are very sensitive for the calculation and evaluation of load loss. We use CT for correct transformation, PT for voltage transformation and power analyser for correct recording of the value. Every parameter replica into the display recording is important and its effect on the measuring set up is now discussed.

• Use of CT and current element:- For Current transformer, secondary rating of higher range say 5 A than to 1 A may contribute comparative more error with of same accuracy class. Because the current being the RMS is recorded in the logarithm cramped scale for higher range. So any error becomes significant for the measurement. Moreover the CTR should also be of proportionate with minimum error. If any correction factor is mentioned should be used during calculation of the load loss for the composite error (combination of phase angle and ratio error). Measurement of losses at lower range of supply current could cause error more. So it is recommended to use at least 50 % of the rated current and correction can be done by the multiplication of square of the ratio of rated current to the applied current under testing.
• Use of PT and Voltage element:- Similarly the voltage transformer should be of electromagnetic type with allowable limit of ratio and phase angle error for all the range of voltage recording condition. This effect does not carry that much of impact on the measurement of the load loss as compared to the current factor due to the application of a particular range of voltage supply for testing of load loss. If any correction factor is mentioned should also be used during calculation for both ratio and phase angle error.
Note:- The use of Instrument transformer below 70 % of the rated operation value contributes considerable higher error for measurement. So it preferable to apply the value more than 70 %. ( Refer fig- 5, 6 ).
• Correction due to use of connection leads:- The wire/lead used for the connection of the equipment also plays role to affect the measurement of load loss. The wires used from the secondary side of the instrument transformers (CT, PT) should be of suitable size to avoid considerable loss of measurement parameters. Particularly for the PT, the secondary lead connection should be of minimum of 4 Sq.mm size with distance of testing control room being less than 20 meters. The primary connecting leads for shorting the winding becomes the part of the winding and its connection to the bushings should have proper contact with minimum contact resistance. It is advised that if the shorting connection losses exceed 5% of the total load losses, the shorting connection should be replaced by one that of a larger cross section and that the joints be made tighter to minimise contact resistance at the joints. The circuit including the shorting connection could be introduced with special instrument connection to auto deduct the loss due to this shorting. The connection for the single phase circuit is shown in fig-5. Similarly for three-phases winding the corresponding circuit can be taken. However this type of the use of circuit is generally not used. Rather suitable size of the shorting connection is taken in the circuit.
• Correction factor for temperature and total time period of measurement: – Temperature during measurement is one of the most important factors for correction of the load loss. Because the winding resistance changes of its value due to change of temperature and affects the recording of the losses. Moreover, the testing time should also be minimum as possible to avoid considerable rise of winding temperature.
• Use of display meters (Power analyser):- The digital scale used in the power analyser should be at least of 4- ½ digit for better accuracy for all used range of measurement and should be of better quality with optimum range operating range at minimum allowable error. The use of multiplication factor should be avoided and the reading directly obtained should be reported in the form final value of the load loss.
• Use of CT and current element:- For Current transformer, secondary rating of higher range say 5 A than to 1 A may contribute comparative more error with of same accuracy class. Because the current being the RMS is recorded in the logarithm cramped scale for higher range. So any error becomes significant for the measurement. Moreover the CTR should also be of proportionate with minimum error. If any correction factor is mentioned should be used during calculation of the load loss for the composite error (combination of phase angle and ratio error). Measurement of losses at lower range of supply current could cause error more. So it is recommended to use at least 50 % of the rated current and correction can be done by the multiplication of square of the ratio of rated current to the applied current under testing.
• Use of PT and Voltage element:- Similarly the voltage transformer should be of electromagnetic type with allowable limit of ratio and phase angle error for all the range of voltage recording condition. This effect does not carry that much of impact on the measurement of the load loss as compared to the current factor due to the application of a particular range of voltage supply for testing of load loss. If any correction factor is mentioned should also be used during calculation for both ratio and phase angle error.
Note:- The use of Instrument transformer below 70 % of the rated operation value contributes considerable higher error for measurement. So it preferable to apply the value more than 70 %. ( Refer fig- 5, 6 ).
• Correction due to use of connection leads:- The wire/lead used for the connection of the equipment also plays role to affect the measurement of load loss. The wires used from the secondary side of the instrument transformers (CT, PT) should be of suitable size to avoid considerable loss of measurement parameters. Particularly for the PT, the secondary lead connection should be of minimum of 4 Sq.mm size with distance of testing control room being less than 20 meters. The primary connecting leads for shorting the winding becomes the part of the winding and its connection to the bushings should have proper contact with minimum contact resistance. It is advised that if the shorting connection losses exceed 5% of the total load losses, the shorting connection should be replaced by one that of a larger cross section and that the joints be made tighter to minimise contact resistance at the joints. The circuit including the shorting connection could be introduced with special instrument connection to auto deduct the loss due to this shorting. The connection for the single phase circuit is shown in fig-5. Similarly for three-phases winding the corresponding circuit can be taken. However this type of the use of circuit is generally not used. Rather suitable size of the shorting connection is taken in the circuit.
• Correction factor for temperature and total time period of measurement: – Temperature during measurement is one of the most important factors for correction of the load loss. Because the winding resistance changes of its value due to change of temperature and affects the recording of the losses. Moreover, the testing time should also be minimum as possible to avoid considerable rise of winding temperature.
• Use of display meters (Power analyser):- The digital scale used in the power analyser should be at least of 4- ½ digit for better accuracy for all used range of measurement and should be of better quality with optimum range operating range at minimum allowable error. The use of multiplication factor should be avoided and the reading directly obtained should be reported in the form final value of the load loss.

Conclusion

The load loss measurement during the routine test of the transformer is considered as one of the important techno-commercial test upon which the performance of the transformer depends upon. The client and manufacturer insist for the correctness of the test practice and its methodology for measurement of the load loss. This test and obtained value is also referred for financial calculation for the case of any deviation from the declared value in the GTP/ specification. So, the described concepts can develop the awareness among the testing engineers to be cautious for the measurement of Load Loss in the transformer.

Er. P.K.Pattanaik,
Asst. General Manager (Elect) in E & MR Division,
OPTCL Bhubaneswar