Chapter-3 POLYPHASE CIRCUITS. What is a poly-phase circuit:- A poly-phase circuit is a circuit in which there are more than one number of a. c. single phase supplies; having the same magnitude, same frequency, same phase difference successively and a conman junction point conman to all the supplies. Different poly-phase circuits are; two phase, three phase, six phase, twelve phase. .The basic poly-phase supply is the three phase supply. All other supplies are derived from that. A symmetrical three phase supply is, the supply having three phases of same magnitude, same frequency and have the same phase difference between two single phase voltages sequentially. 3.1 Advantages of three phase supply over single phase supply:- Three phase supply is advantageous over a single phase supply. Both these supplies are compared in the table below mentioning the advantages of three phase supply over single phase supply. -------------------------------------------------------------------------------------------------- Parameter 3 phase 1 phase -------------------------------------------------------------------------------------------------- (i) Voltage. high voltage is available phase to phase Low voltage. (ii) current. Low currents for the same power. high current. (iii) efficiency. High, for the same power low. machine size is smaller, hence, less losses. (iv) Machine size. Small Large for same power output. all. (v) Conductor Small. Large. cross section. (vi) Self start. Inherently possible. Not possible. Special methods are employed. (vii) Power quantity. For the same size it is higher. lower.. (viii) Out-put rating. 150 percent. . 100 percent (ix) Power quality. Smooth. Fluctuating. (x) Conductor size. Smaller. Larger. (xi) power factor. Good. Poor. 3.2 Principle of three phase generation:- As three phase supply machinery is simple in comparison to other phase supplies generation and its machinery is also simple, not complicated, symmetry of three phases can also be maintained easily; three phase generation, transmission, distribution and utilization is world wide accepted. Further the frequency of supply 50 Hz, Or 60 Hz are found convenient for above purposes. Diagram:- Three similar coils are placed in the magnetic field of a pair of N-S poles. the coils are placed at 120 degrees mechanically from each other..The sense of winding the coils is the same. The leading end of a coil is taken as phase voltage terminal and the trailing end of the coil is taken as reference voltage point. the coils are mounted on a conman shaft and the shaft is rotating at an angular speed of ω radians per second anticlockwise. The voltages are generated in all the three coils called phases. The voltage phasors are distributed 120 degrees electrically from each other. In one rotation of the shaft one cycle of each voltage is generated at phase difference of 120 degrees from each other. If the phase voltages are named sequentially say, R, Y, B then; considering R-phase voltage as a reference; the three phase voltages can be written as, vr = Vr.sinωt. vy = VySin(ωt - 2Л/3). vb = VbSin(ωt - 4Л/3) i.e. = .VbSin(ω/3).t + 2Л 3.3 Concept of Phase sequence and …:- Any particular value is atained by the different phases in magnitude and the same sense then; that sequence of attaining that value w.r.t. time by the phases is the phase sequence. If the three phases are named R, Y, B, so that,R attains the value say, positive maximum first then, Y and lastly the B phase then, R-Y-B phase voltages are in the phase sequence R-Y-B.. Positive phase sequence:- If phases are marked R,Y,B and they attain a particular instantaneous value in magnitude and sense (that either + ve or – ve ) in the same order R-Y-B, then, it is the positive phase sequence. R-Y-B, Y-B-R, B-R-Y all these represent positive phase sequence. Negative phase sequence: - If the R,Y,B, phases do not attain a particular value say + ve maximum, in magnitude and sense in the sequence of R-Y-B- ..then, the phases R,Y,B are not in positive phase sequence but, they are in negative phase sequence. R-B-Y, B-Y-R, Y-R-B, are – ve phase sequence Importance of phase sequence:- It phase sequence is reversed, the direction of rotation of the resultant magnetic field in the motor reverses and hence mechanical direction of rotation of the rotor also reverses. Thus motor rotates in reverse direction. Three phase thyristor rectifier will not work properly. Plant AVR control modules also will not work properly. Types of connections:- There are different types of three phase connections. Star connection:- Conman terminals of the three phases are connected together forming a conman point or a conman terminal called Neutral such that the phase voltages are symmetrical with 120 electrical degrees angle between any two phases of three phase supply. In the star connection again there are two types. 4 wire supply connection:- 3 phase wires and a wire from neutral is used in this system. Two voltages types are available in this supply. (1) Phase to neutral and (2) phase to phase. 3wire supply connection:- Only 3 phase wires are used. Phase to phase voltages are available. This type of supply is also available in delta connection. Diagram:- Please see the next page. Balanced and Unbalanced load:- Balanced Load:- Balanced load in 3 phase system is that load in which all the 3 phase load current and the voltages are equal in magnitude with each other respectively and their phasors are distributed 1200 electrically apart from each other in the plane of their rotation, all rotating in anticlockwise direction at an uniform speed ω = 2Лf where f is rotational frequency in revolutions per sec. This condition is existed when R, L, C circuit elements of same value are in each phase. Unbalanced load:- The 3 phase load in which the values of R, L, C differ from phase to phase is an unbalanced load. In an symmetrical system of supply also this type of load draws phase currents unequal in magnitude and they are not distributed 120 degrees electrically from each other. Therefore, an unbalanced load gives rise to different voltage components and corresponding current components in each phase; those are having multiple frequencies that of the system frequency. This introduces harmonic voltages and currents in the whole system. 3.4 Relation between phase and line quantities in Star/Delta(Y/) system:- Star Connection:- In star connection, Line Voltage, VL = √3.Vph And IL = Iph. Star connection. Delta connection. 3.5 Calculation of current, power, power factor in 3 system. Power in a phase = Vph.Iph.CosΦ. Power in 3 phases = 3.Vph.Iph.CosΦ = . VL IL. CosΦ. (cosΦ is the p.f.) in both star and delta connected load. Because, VL=√3.Vph and IL=Iph in star connection. Similarly, VL=Vph and IL=√3.Iph. In three phase connection the p.f. does not change between the line and phase Numericals on above:- See Appendix B Chapter 4 TRANSFORMER 4.1 Working principle of transformer…:- There are two numbers of coils or windings wound on the same laminated iron core-closed iron path. One winding is called primary. The second winding is called secondary. The primary is given a. c. supply. The primary draws the supply current and produces varying magnetic field in the core. The varying magnetic flux induces voltages in both the coils so as to oppose the cause. The cause is the applied voltage and the current flowing in the primary due to the applied voltage. In primary, self induced voltage appears because of induction due to self generated flux and in the secondary winding mutually induced voltage appears due to alternating flux of the primary. That is, the magnetic flux produced by the primary passes through the secondary and induces voltage in the secondary. The direction of self induced voltage in primary and mutually induced voltage in the secondary, is the same. In each turn of the primary and also that of secondary. Same voltage is induced because, the rate of change of magnetic flux is the same for both the windings. Hence and is the same for each coil. The minus sign indicates that, the induced voltages are in opposite directions to the primary applied voltage. Here there is no load on the transformer. Under this condition small amount of current flows through the primary, That current is called magnetizing current. When load is connected across secondary, current f lows through the secondary. That current flow produces magnetic flux in opposite direction to that of primary. This load current opposes the magnetic flux in the core due to magnetizing current. Therefore, primary current increases till it becomes capable to oppose the flux developed by the secondary current. Thus, in the primary magnetizing current plus equivalent load current flows. The equivalent load current in primary is I2’ = where, I2' is the secondary equivalent current component, I2 is the secondary current flowing due to the load and N2, N1 are the secondary and primary windings’ turns. A transformer does not generate energy it transmits electrical energy from one circuit to another circuit by changing the voltage and current magnitudes. In doing so it consumes a very small percent of input energy which is called losses of the transformer. Classification:- On construction basis:- 1.Core type:- Each winding primary and secondary is on iron core. The core is laminated. That is the core is made from thin sheets of iron. They are mounted on the different limbs of the core in single phase transformer and on the same core, such that, one winding is inside the other winding in three phase transformer. In core type construction the winding encloses the core. 2. Shell type:- Each winding is mounted on the same central core. In shell type transformer parallel magnetic paths are existing. That reduces the reluctance of magnetic path. Reluctance is the property of a magnetic material that opposes magnetic flux. 3. Berry type:- In berry type special attention is given to distribute the flux in maximum parallel paths. Both the windings are on the same core. It may be either shell type of core type. Based on transformation of V and I:- ( i) Step up transformer:- The supplied voltage to primary is increased in secondary by proving higher number of turns in secondary. (ii) Step down transformer:- The primary supply voltage is reduced in magnitude in the secondary. Based on use:- a) Generation transformer:- It is used to step up generator voltage for primary transmission. b) Transmission transformer:- It is used to transmit generated power for use. It may be step up or step down transformer. c) Distributiontransformer:- It is used to step down the voltages further for use by the consumers at his premises. Based on power:- Power transformer:- It transmits power. It runs the electrical machines Instrument transformers:- They are used in measuring instruments to measure voltage and current for different purposes like measuring current and voltage, providing voltage or current signals to system control and protection etc. Based on number of windings:- Two winding transformer:- Two different windings for primary and secondary are provided to each phase. Auto transformer:- Primary and secondary windings are obtained from a single winding. Three winding transformer:- In delta winding there is not neutral. To provide a neutral for three phase delta connected winding, tertiary star connected winding is provided to obtain neutral..In ungrounded star delta tertiary winding is provided for providing closes circulation path for harmonics. Based on supply system: - (1) Single or one phase transformer:- It works in one phase system. (2) 3 Phase transformer:- It works in three phase system, Parts and their material:- Windings:- There are two windings. (1) Primary and (2) Secondary. They are enameled copper insulated and wound on a former, put on the core. They are insulated from the core. The windings carry current. Core:- It provides closed magnetic path for the flux. It is constructed from laminated silicon steel. It is the assembly of the plates. The plates are varnished to provide a thin coat of insulation on each plate. 3. Transformer oil :- It is insulating synthetic suitable oil. It provides insulation to transformer parts from earth and provides cooling. Transformer core wound with windings is put dip on wooden rafters in transformer oil in a closed tank. Conservator: - At the top of transformer body an expansion chamber for oil, connected to tank is provided. Oil is filled in transformer up to half level in conservator. Breather: - To provide dry air for respiration of transformer silica jell breather is connected to conservator at its top. On load the transformer oil heats up. Hence it expands and drives out air from conservator. On no load the oil cools down to atmospheric temperature. Hence it contracts and sucks air from atmosphere through silica jell breather. Silica jell absorbs moisture from the air and gives dry air. Buchholz relay:- It is mounted on transformer main tank in between the tank and the conservator in the oil pipe connecting them. Obviously, it is full of transformer oil. In case of an internal short circuit inside the tank, the gases and vapors formed in oil are entrapped in the relay. They are visually seen through its glass window. An electrical monitoring contact pair for alarm and tripping is provided in the relay. Comparison of core type and shell type single phase transformers:- Core type transformer Shell type transformer 1. window in core. 2 Windows in the core. 2.Winding encircles the core Core encircles the windings. 3.Winding easy to repair. Difficult. 4.Better Cooling to winding. Less cooling. 5.Less mechanical protection to winding More protection. 6.Magnetic path reluctance higher. It is lower. 4.2 EMF Equation:- The supply voltage and hence the supply current are sinusoidal. Therefore the magnetic flux Φ is sinusoidal. Hence, = m sin(wt), where, Φ is the instantaneous flux, Φm is the maximum flux during its variation. ω is angular velocity in degrees per sec. or rad./s The sinusoidally changing flux w.r.t. time induces emfs in transformer windings given by, E = = -N.d[Φmsin(ωt)/dt = - N m.ω.cos(ωt), where, N is the number of turns of the winding. The maximum induced e.m.f. is Emax = N. m.ω volts. volts. Thus, induced voltages are directly in proportion to the frequency f, maximum flux density and number of turns of the coil. Factor affecting induce emf are, f the frequency, Φm the maximum value of flux during its sinusoidal variation and N the number of turns of the coil. In the range of very high frequencies and in magnetic saturation of the core this relation does not hold good. Imp: Statements 1. If d.c supply is given to transformer no induced emfs. are produced in the transformer windings, as there is not varying flux in the core. The resistance of the winding is small. Hence the d.c source is short circuited by the transformer winding. Hence, it is said that the transformer acts as short circuit in d.c. circuit. 2. Induced emf in any winding of transformer is function of magnetic flux variation w.r.t time. Therefore ideally the transformation ration of the transformer remains constant at different frequencies. Small variation in transformation ratio may occur due to increase in leakage flux at high frequencies and in case of saturation of core. 4.3 Voltage ratio: - The primary voltage E1 = 4.44 m f N1. The secondary voltage E2 = 4.44 m f N2. Hence the voltage ratio is = , the impedance drops are neglected for practical applications. E represents the generated emf. It causes current to flow through the concerned circuit. The emf is generated in the winding. Winding has its self resistance. It causes voltage drop. In the winding. The generated voltage has to over come this internal voltage drop. Therefore, voltage at the coil terminals is reduced by that amount and it is V. Current ratio: - In an ideal transformer, as the windings are not having any resistance, Input power = output power i.e. V1 I1 cos = V2 I2 cos the phase difference between voltage and current called power factor angle, is constant. It is the same on primary and secondary. V1 I1 cos = V2 I2 cos = Primary and secondary currents are inversely proportional to turns of winding. k is called transformation ratio. In case of high frequencies like MHz the voltage transformation ratio does not equals the turns ratio. It is less. 4.4 KVA rating: - Transformers are rated on volt ampere basis. KVA, MVA are the higher units. VA rating consists apparent power i.e a8ctive and reactive power. Electrical design’s limiting factor is temperature. High temperature damages insulation. Therefore, winding- conductor Section is so chosen that it gives winding-insulation temperature rise within its limits. System voltage are fixed. Hence, Rated current of transformer multiplied by supply voltage gives volt-ampere rating of a single phase transformer. The total current in primary or secondary winding of a transformer consists of active current component and reactive current component. The vector sum of these two gives total current. For safe working of transformer i.e. operation of the transformer within its temperature limits, maximum continuous current allowed is this total current. Whole of it can be drawn as an active current also. It depends on the type of load as how much it is reactive. The manufacturer does not know , what type of load a consumer will apply on its transformer. Therefore, kva rating is specified for a transformer. It is defined by VA, KVA, MVA. A consumer may use various types of p.f. loads maintaining total current equal to transformer’s rated current. Losses: In a transformer there are two types of losses. Constant losses/Iron losses:- They are (i) hysterisis losses and (ii) eddy current losses. Both are due to alternating magnetizing flux in the transformer core. Hysterisis losses are due to recidual magnetism in the core. That opposes the cyclic periodical variation of magnetic flux. Hence, hysteresis losses take place. Alternating magnetic flux induces voltages in the core material. These voltages flow currents in the core. Core offer resistance to flw of the currents. Hence losses take place these losses are called eddy current losses, The magnetic flux remains constant from no load to full load of a transformer. Hence hysteresis and eddy current losses remain constant through out the range of operation of the transformer. These losses are combinely called iron losses or constant losses. Copper/Variable losses:- Transformer windings have resistance, what so ever small value it may be. Currents flow through the windings. The winding resistance causes I2R losses. They are proportional to the currents flowing in the transformer windings. Hence, they vary as the load vary. These losses are called copper losses. They are variable losses. They vary at square of the current. Concept of Maximum Efficiency: - when maximum power is transferred from input to output by a transformer then the transformer will have max efficiency. When constant losses and cu-losses are equal to each other then the transformer will have maximum. Definition of efficiency:- It is the capability of a m/c (transformer) to transfer maximum of input power. Regulation:- When a transformer is put on load its voltage at the load terminals drops.The drop in voltage at full load with respect to no load voltage is called the regulation of the transformer. There are two trends in finding out regulation. Some manufacturers quote the voltage dop with respect to no load voltage and others quote it with respect to full load voltage, at the load terminals. Regulation up:- (Voltage at no load – voltage at full load)/ (Voltage at full load) It multiplied by 100 gives percentage regulation. Regulation down:- (Voltage at no load – voltage at full load)/ (Voltage at no load) 4.5 numericals based on 4.2 to 4.4:- 4.6 Auto transformer:- Construction:- Single phase autotransformer has only one winding in which both the primary and secondary are specified. Full winding turns form the primary and part of turns from the conman end terminal between primary and secondary forms the secondary. The secondary draws load current and part of primary exclusive of the secondary, draws the primary plus secondary current. The movable wiper terminal point is the phase terminal of the secondary. Variable current and voltage ratios are available in autotransformer. Generally it operates as step down transformer. Step up Autotransformer:- If the Primary phase winding is extended beyond the primary phase terminal then higher than primary voltage is obtained at secondary terminals. Comparison with two wind transformer:- It is as given below. Points Two Windings Autotransformer Windings separation Yes No Movable contact No Yes Type Either step up Both, step or step down down conman Cu-saving No Yes Variable secondary voltage adjust No Yes Isolation Yes No Size Large Small Cost high low Losses high low Low high Regulation poor better Applications: power supply, variable A.C. industrial applications, isolation starter for 1phase a.c. Motor, dimmerstat to control stage lighting 4.7 Isolation Transformer:- It has primary and secondary winding for each phase. Primary and the secondary windings are electrically separated from each-other. There is not any physical connection between the two. It isolates primary and secondary circuits electrically. 3 Transformer:- When 3 single phases are connected in star or delta fashion and their voltages are separated by 120 electrical degrees from each other in positive phase sequence; then it is three phase transformer. Connections: - There are following different connections Star/star-Y/Y , Delta/delta/, Y/, /Y, V/V, T/T open scott 3 phase auto connected transformer. 6.Line and phase value relations:- Y-connection -connection VL = VL = Vph IL = Iph IL = P = VL IL cos P = VL IL cos Application: - power circuit Distribution Instrumentation Functional Industrial Polarity marketing:- When the primary terminal is having applied instantaneous + ve of –ve voltage; the secondary terminal is indicating similar voltage polarity; then both the terminals have same polarity. Same polarity marking is done by providing colored dots. For R,Y,B phases, red, yellow, blue colors are used respectively. Large dot for primary and small dot for secondary is used for a phase. The polarity is also denoted by A,B,C for R,Y,B phases on primary and a, b, c on secondary respectively. The polarity is also denoted by R,Y,B on primary and r, y, b, on secondary respectively. The polarity marking should be in positive phase sequence. Figures:-