EKT 451 CHAPTER 1 Transformer

The Power Grid Diagram courtesy howstuffworks.com

Power Grid Intertie Power Plants Substation 3-phase industrial Step-down Transformer Substation Generator 0.5 – 5kV Step-up Transformer Step-down Transformer Step-down Transformer 4-15 kV Generator 0.5 – 5kV Step-up Transformer Step-down Transformer 35-70 kV 100-750 kV 120/240V residential

Transmission Tower

Substation

Utility Pole Carrying Three Phase

Figure 1.1: Block Diagrams of Transformer. 1.1 Introduction to Transformer. Transformer is a device that changes ac electrical power at one voltage level to ac electric power at another voltage level through the action of magnetic field. Figure 1.1: Block Diagrams of Transformer.

1.2 Applications of Transformer. Why do we need transformer ? (a) Step Up. Step up transformer, it will decrease the current to keep the power into the device equal to the power out of it. In modern power system, electrical power is generated at voltage of 12kV to 25kV. Transformer will step up the voltage to between 110kV to 1000kV for transmission over long distance at very low lost. (b) Step Down. The transformer will stepped down the voltage to the 12kV to 34.5kV range for local distribution in the homes, offices and factories as low as 120V (America) and 240V (Malaysia).

Figure 1.2: Core Form and Shell Form. 1.3 Types and Constructions of Transformer. Power transformers are constructed on two types of cores; (i) Core form. (ii) Shell form. Figure 1.2: Core Form and Shell Form.

Cont’d… Core form. The core form construction consists of a simple rectangular laminated piece of steel with the transform winding wrapped around the two sides of the rectangle. Shell form. The shell form construction consists of a three-legged laminated core with the winding wrapped around the center leg.

Figure 1.3: A Simple Transformer. Cont’d… Construction. Transformer consists of two or more coils of wire wrapped around a common ferromagnetic core. The coils are usually not directly connected. The common magnetic flux present within the coils connects the coils. There are two windings; (i) Primary winding (input winding); the winding that is connected to the power source. (ii) Secondary winding (output winding); the winding connected to the loads. Figure 1.3: A Simple Transformer.

Cont’d… Operation. When AC voltage is applied to the primary winding of the transformer, an AC current will result iL or i2 (current at load). The AC primary current i2 set up time varying magnetic flux f in the core. The flux links the secondary winding of the transformer.

Cont’d… Operation. From the Faraday law, the emf will be induced in the secondary winding. This is known as transformer action. The current i2 will flow in the secondary winding and electric power will be transfer to the load. The direction of the current in the secondary winding is determined by Len’z law. The secondary current’s direction is such that the flux produced by this current opposes the change in the original flux with respect to time.

1.4 General Theory of Transformer Operation. FARADAY’S LAW If current produces a magnetic field, why can't a magnetic field produce a current ? In 1831 two people, Michael Faraday in the UK and Joseph Henry in the US performed experiments that clearly demonstrated that a changing magnetic field produces an induced EMF (voltage) that would produce a current if the circuit was complete. Michael Faraday

When the switch was closed, a momentary deflection was noticed in the galvanometer after which the current returned to zero. When the switch was opened, the galvanometer deflected again momentarily, in the other direction. Current was not detected in the secondary circuit when the switch was left closed. 

An e.m.f. is made to happen (or induced) in a conductor (like a piece of metal) whenever it 'cuts' magnetic field lines by moving across them. This does not work when it is stationary. If the conductor is part of a complete circuit a current is also produced. Faraday found that the induced e.m.f. increases if (i) the speed of motion of the magnet or coil increases. (ii) the number of turns on the coil is made larger. (iii) the strength of the magnet is increased.

Faraday’s Law E = Electromotive force (emf) Φ = Flux N = Number of turn t = time Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.

Inserting a magnet into a coil also produces an induced voltage or current. The faster speed of insertion/ retraction, the higher the induced voltage.

Figure 1.4: Basic Transformer Components. According to the Faraday’s law of electromagnetic induction, electromagnetic force (emf’s) are induced in N1 and N2 due to a time rate of change of fM, Where, (1.1) e = instantaneous voltage induced by magnetic field (emf),  = number of flux linkages between the magnetic field and the electric circuit. f = effective flux

Cont’d… Lenz’s Law states that the direction of e1 is such to produce a current that opposes the flux changes. If the winding resistance is neglected, then equation (1.1) become; (1.2) Taking the voltage ratio in equation (1.2) results in, (1.3)

Cont’d… Neglecting losses means that the instantaneous power is the same on both sides of the transformer; (1.4) Combining all the above equation we get the equation (1.5) where a is the turn ratio of the transformer. (1.5) a > 1  Step down transformer a < 1  Step up transformer a = 1  Isolation Transformer

Substitute eqn(1.6) into eqn(1.2) Cont’d… According to Lenz’a Law, the direction of e is oppose the flux changes, and the flux varies sinusoidally such that (1.6) Substitute eqn(1.6) into eqn(1.2) (1.7) The rms value of the induce voltage is; (1.8)  = max sin t max

Losses are composed of two parts; (a) The Eddy-Current lost. Cont’d… Losses are composed of two parts; (a) The Eddy-Current lost. Eddy current lost is basically loss due to the induced current in the magnetic material. To reduce this lost, the magnetic circuit is usually made of a stack of thin laminations. (b) The Hysteresis loss. Hysteresis lost is caused by the energy used in orienting the magnetic domains of the material along the field. The lost depends on the material used.

Figure 1.6: An Ideal Transformer and the Schematic Symbols. 1.5 The Ideal Transformer. An Ideal transformer is a lossless device with an input winding and an output winding. Zero resistance result in zero voltage drops between the terminal voltages and induced voltages Figure 1.6 shows the relationship of input voltage and output voltage of the ideal transformer. Figure 1.6: An Ideal Transformer and the Schematic Symbols.

The relationship between voltage and the number of turns. Cont’d… The relationship between voltage and the number of turns. Np , number of turns of wire on its primary side. Ns , number of turns of wire on its secondary side. Vp(t), voltage applied to the primary side. Vs(t), voltage applied to the secondary side. where a is defined to be the turns ratio of the transformer.

In term of phasor quantities; Cont’d… The relationship between current into the primary side, Ip(t), of transformer versus the secondary side, Is(t), of the transformer; In term of phasor quantities; -Note that Vp and Vs are in the same phase angle. Ip and Is are in the same phase angle too. - the turn ratio, a, of the ideal transformer affects the magnitude only but not the their angle.

Cont’d… The dot convention appearing at one end of each winding tell the polarity of the voltage and current on the secondary side of the transformer. 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 doted on each side of the core. If the primary current of the transformer flow into the dotted end of the primary winding, the secondary current will flow out of the dotted end of the secondary winding.

Example 1: Transformer. How many turns must the primary and the secondary windings of a 220 V-110 V, 60 Hz ideal transformer have if the core flux is not allowed to exceed 5mWb? Solution: For an ideal transformer with no losses, From the emf equation, we have

EKT 451 CHAPTER 1 Transformer 17 jan 2007

1.5 The Ideal Transformer. An Ideal transformer is a lossless device with an input winding and an output winding. where a is defined to be the turns ratio of the transformer.

Equivalent circuit of an ideal transformer 1.5 The Ideal Transformer. Equivalent circuit of an ideal transformer

1.5.1 Power in an Ideal Transformer. Power supplied to the transformer by the primary circuit is given by ; where, qp is the angle between the primary voltage and the primary current. The power supplied by the transformer secondary circuit to its loads is given by the equation; where, qs is the angle between the secondary voltage and the secondary current.

Cont’d… The output power of a transformer; - apply Vs= Vp/a and Is= aIp into the above equation gives, - The output power of an ideal transformer is equal to the input power.

Cont’d… The reactive power, Q, and the apparent power, S;

Example 2: Ideal Transformer. Consider an ideal, single-phase 2400V-240V transformer. The primary is connected to a 2200V source and the secondary is connected to an impedance of 2 W < 36.9o, find, (a) The secondary output current and voltage. (b) The primary input current. (c) The load impedance as seen from the primary side. (d) The input and output apparent power. (e) The output power factor.

Example 2: Ideal Transformer. Consider an ideal, single-phase 2400V-240V transformer. The primary is connected to a 2200V source and the secondary is connected to an impedance of 2 W < 36.9o, find, Solution:

Cont’d…Example 2 .

1.7 The Equivalent Circuit of a Real Transformer. Leakage flux in the real transformer Copper losses are resistive loses in the windings of the transformer core. Copper losses are modeled by placing a resistor Rp in the primary circuit of the transformer and a resistor Rs in the secondary circuit.

1.7 The Equivalent Circuit of a Real Transformer. The leakage flux in the windings is, Core excitation effect can be model as i) magnetization reactance, XM ii) core resistance, Rc

1.7 The Equivalent Circuit of a Real Transformer. Figure below is an exact model of a transformer.

Transferring impedances through a transformer Thévenin equivalents of transformer circuit

Transferring impedances through a transformer Equivalent circuit when secondary impedance is transferred to primary side and ideal transformer eliminated Equivalent circuit when primary source is transferred to secondary side and ideal transformer eliminated

Cont’d… To analyze practical circuits containing transformer, it is necessary to convert the entire circuit to an equivalent circuit at a single voltage level. Therefore, the equivalent circuit must be referred either to its primary side or to its secondary side in problem solving. The Transformer Model Referred to its Primary Windings

The Transformer Model Referred to its Secondary Voltage Level. Cont’d… The Transformer Model Referred to its Secondary Voltage Level.

Cont’d… The Transformer Model Referred to its Primary Windings

Cont’d… Based on the above equations and assuming a zero degree reference angle for V2, the phasor diagram is shown as

1.8 The Approximate Equivalent Circuit of a Transformer. In the Approximate model the voltage drop in Rp and Xp is negligible because the current is very small. Approximate Transformer Model Referred to the Primary Side.

Cont’d… The voltage in the primary series impedance (r1 + jx1) is small, even at full load. Also, the no load current (I0) is so small that its effect on the voltage drop in the primary series impedance is negligible. Therefore, it matters little if the shunt branch of Rc in parallel with Xm is connected before the primary series impedance or after it. The core loss and magnetizing currents are not greatly affected by the move. Connecting the shunt components right at the input terminals has the great advantage of permitting the two series impedance to be combined into one complex impedance. The equivalent impedance referred to the primary side is;

Approximate Circuit Model of a Transformer Referred to the Secondary. Cont’d… Figure 1.11 shows the approximate equivalent circuit of transformer referred to the secondary side. Approximate Circuit Model of a Transformer Referred to the Secondary. The equivalent impedance is;

1.9 Transformer Voltage Regulation and Efficiency. Voltage regulation is a measure of the change in the terminal voltage of the transformer with respect to loading. Therefore the voltage regulation is defined as: For ideal transformer, VR = 0. It is a good practice to have as small voltage regulator as possible.

Cont’d… Transformer Efficiency, efficiency of a transformer is defined as follows; For Non-Ideal transformer, the output power is less than the input power because of losses. These losses are the winding or I2R loss (copper losses) and the core loss (hysteresis and eddy-current losses). Thus, in terms of the total losses, Plosses, the above equation may be expressed as;

Example 3: Transformer Voltage Regulation.

Cont’d…Example 3 1.11

1. 10 Open Circuit and Short Circuit 1.10 Open Circuit and Short Circuit. - Determination of transformer parameter by measurement Open Circuit Test. Provides magnetizing reactance and core loss resistance Obtain components are connected in parallel The open circuit test is conducted by applying rated voltage at rated frequency to one of the windings, with the other windings open circuited. The input power and current are measured. For reasons of safety and convenience, the measurements are made on the low-voltage (LV) side of the transformer.

Cont’d… Equivalent Circuit of the Open-Circuit Test. The secondary / high voltage (HV) side is open, the input current is equal to the no load current or exciting current (I0), and is quite small. The input power is almost equal to the core loss at rated voltage and frequency.

Open circuit test evaluation Cont’d… Open circuit test evaluation

Short Circuit Test. Cont’d… The short-circuit test is used to determine the equivalent series resistance and reactance. Provides combined leakage reactance and winding resistance One winding is shorted at its terminals, and the other winding is connected through proper meters to a variable, low-voltage, high-current source of rated frequency. The source voltage is increased until the current into the transformer reaches rated value. To avoid unnecessary high currents, the short-circuit measurements are made on the high-voltage side of the transformer.

Equivalent Circuit of the Short-Circuit Test. Cont’d… Equivalent Circuit of the Short-Circuit Test.

Equivalent circuit obtained by measurement Equivalent circuit for a real transformer resulting from the open and short circuit tests.

1.11 Three Phase Transformer. Almost all the major power generation and distribution systems in the world today are three-phase ac system. Two ways of constructing transformer of three-phase circuit; (i) Three single phase transformers are connected in three-phase bank. (ii) Make a three-phased transformer consisting of three sets of windings wrapped on a common core. The three-phased transformer on a common core (ii) is preferred because it is lighter, smaller, cheaper and slightly more efficient.

Three-Phase Transformer Connections. A three-phase transformer consists of three transformers either separate or combined on one core. combined on one core. 3 separate core

Three-Phase Transformer Connections. There are four possible connections between the secondary and primary of a three-phase transformer. (1) Wye-Wye (Y-Y). - don't use causes harmonics problems (2) Wye-Delta (Y-D). - use : high voltage transmissions (3) Delta-Wye (D-Y) - use : most common; commercial and industrial. (4) Delta-Delta (D -D). - use: industrial applications

Figure 1.15: Three-Phase Transformer Connections and Wiring Diagram. Cont’d… Figure 1.15: Three-Phase Transformer Connections and Wiring Diagram.

(1) Wye-Wye Connection. (2) Wye-Delta Connection. (3) Delta-Wye Connection. (4) Delta-Delta Connection.

Cont’d… Example 2.6: Three-Phase Transformer. What should be the ratings (voltages and currents) and turns ratio of a three-phase transformer to transform 10 MVA from 230 kV to 4160 V, if the transformer is to be connected: a) wye-delta, b) delta-wye, and c) delta-delta? Solution For both delta and wye connections, the line currents can be obtained as: .

Example 7: Voltage Regulation at Full Load. A 7200V/208V, 50kVA, three-phase distribution transformer is connected delta-wye. The transformer has 1.2% resistance and 5% reactance. Find the voltage regulation at full load, 0.8 power factor lagging. Solution

Voltage Regulation. .

Example 8: Transformer Efficiency. If the core loss of the transformer in Example 7 is 1kW, find the efficiency of this transformer at full load and 0.8 power factor. Solution .

Tutorial 1 Group Computer Group Communication Monday 22/01/07 – Makmal Komputer 1, Kg Wai Group Communication Tuesday 23/01/07 – Makmal Komputer 2, Kg Wai