• To study the practical transformer, the effect of assumptions, made for ideal transformer, will be taken up one by one under following cases.
Case-1: All Features of ideal Transformer Expect:
μ ≠ ∞
On No-load Condition:
• As there is no core loss, hence magnetizing current and no load current will equal and flux ϕ will be in phase with no load current because flux is generated by load current.
On Load Condition:
• No load current is also known s exciting current.
μ ≠ 0 and Core Loss Exists:
• The core losses are always present in the ferromagnetic core of the transformer, since the transformer is an ac-operated magnetic device.
• The hysteresis loss in the core can be minimised by using high grade material such as CRGO steel and eddy current loss can be minimised by using thin laminations for the core.
• Because of hysteresis the no-load current of exciting current I0 leads the magnetic flux ø by an angle α, called angle of hysteretic advance.
Iø = I0 sin ø0
• The component lø along ø is called the reactive or magnetizing current and the second component lc along V1 is called core loss component or power component.
• In an ideal transformer, core-loss current lc = 0 and no-load current l0 = magnetizing current lø.
Effect of Leakage Flux:
• The magnetic potential difference is necessary for the establishment of flux in a magnetic circuit.
• This magnetic potential difference establishes.
• The mutual flux Ø linking both the windings.
• This magnetic potential difference establishes:
- The mutual flux Ø linking both the windings.
- The primary leakage flux fl1, which links only the primary winding.
• The inductor is the suitable element for showing the leakage flux element.
• Ø l1 and Øl2 are in phase with l1 and l2 respectively because these flux are created by load current.
• El1 and El2 are the induced emf caused by leakage fluxes in primary and secondary respectively.
• x1 and x2 are the leakage reactances of primary and secondary respectively.
Complete phasor Diagram:
• We are using convention that all induced emfs, and currents directly satisfy, Lenz's law (by opposing the flux).
Basic Equation for Transformers:
Equivalent circuit is a circuit representation of the equation describing the performance of the device.
Exact Equivalent Circuit:
• All the prime quantities are referred to primary side.
Equivalent Circuit Referred to Secondary Side:
Testing of Transformed:
• The following test are performed to find the performance parameters of transformers.
• In determining the relative polarity of the two windings of a transformer the two windings are connected in series across a voltmeter while one of the winding is excited from a suitable voltage source as shown in figure.
• If the polarities of the windings are as marked on the diagram, the voltmeter should read E=(E1–E2). If it reads (E1 + E2), then it is called additive polarity. We don't want additive polarity because these are subjected to high voltage stresses.
• On account of these reasons, the polarity markings of one of the windings must be interchanged then after interchanging polarity voltmeter reads (E1 – E2) is called subtractive polarity. Subtractive polarity. Subtractive polarity is preferable to additive polarity.
Open-circuit (OC0 or no load test):
• The open circuit test given the following information:
• Core-loss at rated voltage voltage and frequency
• The shunt branch parameters of the equivalent circuit, i.e. Rc and Xm
• Turns ratio of the transformer.
• A voltmeter, wattmeter and an ammeter are connected in the low voltage side of the transformer. Readings are recorded when e applied rated frequency voltage to the L.V. side and kept high voltage side open circuited.
• The ammeter records the no-load current or exciting current l0. Since l0 is quite small (2 to 6%) of rated current, so primary leakage impedance drop is negligible.
• The wattmeter recorded input power which consist of core loss and ohmic loss.
• The ohmic loss during open circuit test is negligible in composition with the normal core loss.
• Parameters of shunt branch can be find out by following sequence of equations.
Where Voc ,Poc and lo are instruments reading.
• The short circuit test gives the following information:
- Ohmic loss at rated current and frequency.
- The equivalent resistance and equivalent leakage reactance.
- Voltage regulation of a transformer.
• For efficiency, all data is necessary which are obtained from both test, open circuit test and short circuit test.
• In short circuit test, all the instruments are placed on the high voltage side and low voltage side of transformer is short circuited.
• The applied voltage is adjusted by auto transformer to circulate rated current in the high voltage side.
This circulated rated current achieved by only 2 to 12% of its rated value of primary voltage.
• In this test, the wattmeter records the core-loss and the ohmic loss in both the windings but core loss and shut branch parameter ignored because only 2 to 12% of rated voltage voltage is applied.
• To find different parameters of transformers the sequence of equations.
Back to Back or Sumpner's test or load Test:
• While open circuit test and short circuit tests on a transformer yield its equivalent circuit parameters, these cannot be used for the 'heat run' test where in the purpose is to determine the steady temperature rise if the transformer was fully loaded continuously; this is so because under each of these tests the power loss to which transformer is subjected is either the core-loss or copper-loss but not both.
• In order to determine the maximum temperature rise, it is necessary to conduct a full-load test on a transformer or back to back test. It is also called Regenerative test or sumpner's test. The back to back test on single phase transformers requires two identical transformers.
• The primary windings of the two transformers are connected in parallel and supplied at rated voltage and rated frequency.
• The secondaries are connected in series with their polarities in phase opposition which can be checked by the voltmeter V2. If the voltmeter Vab across a, b point reads zero, the secondaries are in series opposition and terminal a and be are use for test.
• If voltmeter Vab =sum of the two secondaries voltages. It means these are in the same phase. In order to bring them in phase opposition, terminals ad should be joined together to result in zero voltage across terminals bc.
• The total voltage across the two secondaries in series will be zero. There will be no current in the secondary windings. The transformers will behave as if their secondary windings are open circuited Hence, the reading of wattmeter W1 gives the iron losses of both the transformers.
• Now a small voltage is injected in the secondary circuit by a regulating transformer excited by the main supply. The magnitude of the injected voltage is adjusted till the ammeter A2 reads full load secondary current, this current produces full load current to flow through the primary windings and will follow a circulatory path through the main bus bar.
• The reading of wattmeter W2 will not be not affected by this current. This wattmeter W2 given the full load copper losses of the two transformers.
• The Ammeter A1 given total no-load current of the two transformers. Thus in this method we have loaded the two transformers to full load but the power taken from the supply is only that necessary to supply the losses of both transformers.
• The temperature rise of transformers can be determined by operating these transformers back to back for a long time and measuring the temperature of the oil at the periodic intervals of time.