EET 103 Transformer Chapter 5 1

A transformer is a device that changes ac electric energy at one voltage level to ac electric energy at another voltage level through the action of a magnetic field. Introduction to Transformer 2

Transformers are constructed of two coils or more placed around the common freeomagnetic core so that the charging flux developed by one will link to the other. The coil to which the source is applied is called the primary coil. The coil to which the load is applied is called the secondary coil. Introduction to Transformer 3

The most important tasks performed by transformers are: Changing voltage and current levels in electric power systems. Matching source and load impedances for maximum power transfer in electronic and control circuitry. Electrical isolation (isolating one circuit from another or isolating DC while maintaining AC continuity between two circuits). 4

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Mutual Inductance Mutual inductance exits between coils of the same or different dimensions. Mutual inductance is a phenomenon basic to the operation of the transformer. 6

Mutual Inductance A transformer is constructed of 2 coils placed so that the changing flux developed by one will link the other. The coil to which the source is applied is called primary The coil which the load is applied is called secondary. 7

Mutual Inductance (Cont…) 8

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An ideal transformer is a lossless device with an input winding and output winding. Ideal Transformer a = turns ratio of the transformer 10

Power in ideal transformer Where  is the angle between voltage and current 11

Impedance transformation through the transformer The impedance of a device – the ratio of the phasor voltage across it in the phasor current flowing through it 12

Non-ideal or actual transformer Mutual flux 13

Losses in the transformer Copper (I 2 R) losses: Copper losses are the resistive heating in the primary and secondary windings of the transformer. They are proportional to the square of the current in the windings. Eddy current losses: Eddy current losses are resistive heating losses in the core of the transformer. They are proportional to the square of the voltage applied to the transformer. 14

Hysteresis losses: Hysteresis losses are associated with the arrangement of the magnetic domain in the core during each half cycle. They are complex, nonlinear function of the voltage applied to the transformer. Leakage flux: The fluxes Φ LP and Φ LS which escape the core and pass through only one of the transformer windings are leakage fluxes. These escaped fluxes produce a self inductance in the primary and secondary coils, and the effects of this inductance must be accounted for. Losses in the transformer 15

Transformer equivalent circuit E p = primary induced voltageE s = secondary induced voltage V p = primary terminal voltageV s = secondary terminal voltage I p = primary currentI s = secondary current I e = excitation currentI M = magnetizing current X M = magnetizing reactance I C = core current R C = core resistanceR p = resistance of primary winding R s = resistance of the secondary windingX p = primary leakage reactance X s = secondary leakage reactance Ie ImIc 16

Dot convention 1.If the primary voltage is positive at the dotted end of the winding with respect to the undotted end, then the secondary voltage will be positive at the dotted end also. Voltage polarities are the same with respect to the dots on each side of the core. 2.If the primary current of the transformer flows into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding. 17

Exact equivalent circuit the actual transformer a.The transformer model referred to primary side b.The transformer model referred to secondary side 18

Approximate equivalent circuit the actual transformer a.The transformer model referred to primary side b.The transformer model referred to secondary side 19

Exact equivalent circuit of a transformer refer to primary side E p = primary induced voltageE s = secondary induced voltage V p = primary terminal voltageV s = secondary terminal voltage I p = primary currentI s = secondary current I e = excitation currentI M = magnetizing current X M = magnetizing reactance I C = core current R C = core resistanceR p = resistance of primary winding R s = resistance of the secondary windingX p = primary leakage reactance X s = secondary leakage reactance 20

Primary side Secondary side The Equation: 21

Exact equivalent circuit of a transformer referred to primary side Exact equivalent circuit of a transformer referred to secondary side 22

Approximate equivalent circuit of a transformer referred to primary side Approximate equivalent circuit of a transformer referred to secondary side V p /a aIpaIp + - R eqs IsIs jX eqs R c /a 2 jX M /a 2 VsVs + - R eqs =R p / a 2 +R s X eqs =X p / a 2 +X s VpVp IpIp + - R eqp I s /a jX eqp RcRc jX M aVsaVs + - R eqp =R p +a 2 R s X eqp =X p +a 2 X s 23

Open circuit test Provides magnetizing reactance and core loss resistance Obtain components are connected in parallel Parameter determination of the transformer 24

Experiment Setup In the open circuit test, transformer rated voltage is applied to the primary voltage side of the transformer with the secondary side left open. Measurements of power, current, and voltage are made on the primary side. Since the secondary side is open, the input current I OC is equal to the excitation current through the shunt excitation branch. Because this current is very small, about 5% of rated value, the voltage drop across the secondary winding and the winding copper losses are neglected. 25

Admittance Open circuit Power Factor Open circuit Power Factor Angle Angle of current always lags angle of voltage by  26

Short circuit test –Provides combined leakage reactance and winding resistance –Obtain components are connected in series 27

Experiment Setup In the short circuit test, the secondary side is short circuited and the primary side is connected to a variable, low voltage source. Measurements of power, current, and voltage are made on the primary side. The applied voltage is adjusted until rated short circuit currents flows in the windings. This voltage is generally much smaller than the rated voltage. 28

Impedances referred to the primary side Power Factor of the current Angle Power Factor Therefore 29

The equivalent circuit impedances of a 20-kVA, 8000/240-V, 60-Hz transformer are to be determined. The open circuit test and the short circuit test were performed on the primary side of the transformer and the following data were taken: Find the impedances of the approximate equivalent circuit referred to the primary side and sketch that circuit Open- circuit test (on primary) Short- circuit test (on primary) Voc = 8000 V Vsc = 489 V Ioc = A Isc = 2.5 A Poc = 400 W Psc = 240 W 30

Voltage Regulation (VR) The voltage regulation of a transformer is defined as the change in the magnitude of the secondary voltage as the current changes from full load to no load with the primary held fixed. At no load, 31

Phasor Diagram Lagging power factor Unity power factor 32

Leading power factor 33

Efficiency The efficiency of a transformer is defined as the ratio of the power output (P out ) to the power input (P in ). P core = P eddy current + P hysteresis P cu = P copper losses 34

35 P cu = Copper losses are resistive losses in the primary and secondary winding of the transformer core. They are modeled by placing a resistor R p in the primary circuit of the transformer and resistor R s in the secondary circuit. P CORE = Core loss is resistive loss in the primary winding of the transformer core. It can be modeled by placing a resistor R c in the primary circuit of the transformer.

Example A 15 kVA, 2400/240-V transformer is to be tested to determine its excitation branch components, its series impedances and its voltage regulation. The following test data have been taken from the primary side of the transformer Open- circuit test Short- circuit test Voc = 2400 V Vsc = 48 V Ioc = 0.25 A Isc = 6.0 A Poc = 50 W Psc = 200 W 36

The data have been taken by using the connections of open circuit test and short circuit test a.Find the equivalent circuit of this transformer referred to the high voltage side. b.Find the equivalent circuit of this transformer referred to the low voltage side. c.Calculate the full load voltage regulation at 0.8 lagging power factor and 0.8 leading power factor. d.What is the efficiency of the transformer at full load with a power factor of 0.8 lagging? 37