DC Generator Characteristics: Understanding Voltage Generation and Equivalent Circuit

Lecture # 3 DC GENERATOR CHARACTERISTICS 1

DC GENERATOR CHARACTERISTICS o Generated voltage Eg can be calculated by: ZP 2 a NP a ZP NP Eg= = = ka ; ka = 2 a = a o Therefore, the generated voltage Eg depends on twofactors: Flux 1. Speed 2. o It is evident that generated voltage Eg varies proportionally with flux and speed at which the armature is turning. So as or increases, so doesEg. 2

DC GENERATOR CHARACTERISTICS o If the flux is held constant and the speed is changing, the new Eg: 2 Eg2 E g1 ka 2 k a 2 = = E = Eg1 g2 1 1 1 o If the speed is held constant, and the flux is varied, we get: Eg2 2 = E g1 1 2 E = Eg1 g2 1 o If both speed and flux are changed, the ratio becomes as follows: Eg2 2 2 2 2 = Eg1 Eg2 = 1 1 1 1 Eg1 3

DC GENERATOR CHARACTERISTICS Example 1: A generator rotating at 200 rad/s develops 220 V. If the fluxremains constant and the speed drops to 185 rad/s, (a) what will be the new generated voltage? (b) By how much must the flux be changed to restore the generated voltage to 220 V at the new slowerspeed? Sol. Eg2 2 2 185 (a) E = E = 220 = 203.5 ? = 1 g2 g1 Eg1 1 200 Eg2 Eg1 Eg2 2 2 2 1 220 200 220 185 = 1 = 1 2 =Eg1 2 = 1.081 1 (b) 1 1 Thus ?2 must increase by 8.1% of ?1 4

EQUIVALENT CIRCUIT OF A DC GENERATOR o The field circuit is used to generate the flux in a magnetic core as described in Chapter 1. Rf is the total resistance in field circuit and If is current in the field. Field circuit + Armature circuit The armature circuit has two parts: o 1) Symbol for the dc voltage generated by rotating armature, Eg. Vf 2) Ra is the total resistance of the armature winding and Iarepresents the armature current. Po _ o IL represents load current and Vt is the output (terminal) voltage of thegenerator. Rotor Stator o Pi: Mechanical power is fed into the generator through the rotorshaft. o Po: Electrical Power is supplied to the load via the armatureterminals. 5

SEPARATELY EXCITED GENERATOR o Unpopular type because it requires an external dc voltage source to set upa magnetic field (flux) in the field winding. o A rheostat is connected to the field winding to vary the field current If from its normal values to lower values; thus, changing the flux, . o Varying field current varies the generated voltage Eg then output voltageVt can be controlled: 1 Rf Vf If =Rf Rheostat I f Eg = ka Vf Vt = Eg - RaIa Note: Rf represents the total field resistance. Separately Excited generator 6

NO-LOAD MAGNETIZATION CURVE o Magnetization curve is used to identify the internal characteristics ofa particular generator. o Magnetization curve is a plot of Eg vs. If at a given speed . o A generator is normally operated in the saturation region (region 3 to4). o If If increases, flux increases as well as generated voltageEg. o The curve shown is due to the nonlinear behavior of a ferromagneticmaterials. o Note: Eg = ka If DC generator operatingregion 7 No-load magnetization curve

NO-LOAD MAGNETIZATION CURVE o At no-load, Ia = IL = 0 so no internal voltage drop across Ra. Therefore, Vt =Eg. Vt = Eg - RaIa= Eg@ no-load Ia= IL=0 o Because of residual magnetism, a small generated voltage Eg_residual is present although If = 0. (Point1) o As If increases, the flux, Eg increases linearly until Point 3. Then, the core becomes saturated and any further increase in If will have only a small affect on Eg. o As If decreases, we get the case of hysteresis as describedbefore. Eg_residual 8 No-load magnetization curve

VOLTAGE REGULATION o When the generator is connected to a load, IL = Ia since the armature isin series with the load. o Because Ia flows in the armature, there is a voltage drop within thearmature winding, IaRa. o Because of the internal voltage drop, the terminal voltage (Vt) is less thanthe generated voltage (Eg): Vt = Eg - RaIa Rf V f = fI Vf Rf 9 Separately Excited DC Generator

VOLTAGE REGULATION o When the generator is connected to a load IL = Ia , Vt = Eg - RaIa o At no-load (Ia = 0), Vt = Eg. o Voltage regulation (V.R.) is a measure of the change of theterminal voltage as ILincreases. o V.R. can be calculated at the rated conditions in kW or hp, and canbe found by: V %V.R. =VNL VFLx 100 =E V where g NL FL Rf Vf 10 Separately Excited DCGenerator

VOLTAGE REGULATION Example 2: A 5-KW, 120-V generator is under test. When the load is removed,the terminal voltage is found by measurement to be 138 V. Calculate the voltage regulation. Sol. VNL VFL VFL %V.R.= x100 138 120 %V.R.= x100 120 %V.R. = 15% 11

GENERATOR EFFICIENCY o The losses in a DC machine (generator or motor) may be divided into three classes: Input Power P i Output Power DC 1. Mechanical losses Po Generator 2. Iron or core losses Plosses 3. Copper losses Losses Power o All these losses appear as heat and thus raise the temperature of the machine. They also lower the efficiency of themachine. % =Pox100 Pi Where the efficiency: Pi = Po + Plosses and the mechanical input power: 12

GENERATOR EFFICIENCY Mechanical power losses 1. Friction losses: occurs because of the moving parts. The energy lost is in the form of heat. In DC machines, there is a brush frictions constant at any given speed, bearing friction. Windage losses: Resistance between the rotating armature and the air inside the machine. 2. These losses depend upon the speed of the machine. But for a given speed, they are practically constant. Iron or Core losses: These losses occur in the armature of a d.c. machine and are due to the rotation of armature in the magnetic field of the poles. They are of two types 1) hysteresis loss 2) eddy current loss. Note: Iron losses and mechanical losses together are called stray losses. 13

GENERATOR EFFICIENCY Hysteresis loss o Hysteresis loss occurs in the armature of the d.c. machine since anygiven part of the armature is subjected to magnetic field reversals as it passes under successive poles. o The figure shows an armature rotating in two-pole machine, consider asmall piece ab of the armature. o When the piece ab is under N-pole, the magnetic lines pass from a to b.Half a revolution later, the same piece of iron is under S-pole and magnetic lines pass from b to a so that magnetism in the iron isreversed. In order to reverse continuously the molecular magnets in the armature core, some amount of power must be spent which is called hysteresis loss.

GENERATOR EFFICIENCY Eddy current loss o In addition to the voltages induced in the armature conductors, thereare also voltages induced in the armature core. o These voltages produce circulating currents in the armature core asshown in the Figure below. o These are called eddy currents and power loss due to their flow is called eddy current loss. The eddy current loss appears as heat which raisesthe temperature of the machine and lowers its efficiency.

GENERATOR EFFICIENCY Eddy current loss o Core resistance can be greatly increased by constructing the core of thin, round. If a continuous solid iron core is used, the resistance to eddycurrent path will be small due to large cross-sectional area of thecore. o Consequently, the magnitude of eddy current and hence eddy current losswill be large. The magnitude of eddy current can be reduced by making core resistance as high as practical. The iron sheets calledlaminations. o The laminations are insulated from each other with a coating of varnish.The insulating coating has a high resistance, so very little current flows from one lamination to the other. o Also, because each lamination is very thin, the resistance to currentflowing through the width of a lamination is also quitelarge. Thus laminating a core increases the core resistance which decreases the eddy current and hence the eddy currentloss.

GENERATOR EFFICIENCY Copper Losses o If there is a current flowing through the resistance, then there is an I2Rpower loss dissipated in the form of heat and called a copperloss. o There are copper losses in the field circuits If2Rf & Is Rs and in thearmature 2 circuit Ia2Ra. o Note: There is also brush contact loss due to brush contact resistance(i.e., resistance between the surface of brush and surface of the commutator). This loss is generally included in armature copper loss. Stray Losses Iron losses and mechanical losses together are called stray losses. 17

GENERATOR EFFICIENCY Pconverted = EgIa Electrical OutputPower Po = VtIL Po = Pconv -Pcu Mechanical Input Power Pi Pi = Pst +Pconv Stray Power Losses (mechanical and core losses) Pst Copper Losses Pcu = Pcua + Pcuf +Pcus % =Po x100 Pi Pi = Po + Pst +Pcu Pi = Po +Plosses Po % = x100 Po+Plosses

GENERATOR EFFICIENCY Example 3: A 1-KW, 125-V generator requires 2 hp to supply rated output.Calculate the generator efficiency. Sol. Pi = (2 hp) (746 W/hp) = 1492W Po = 1KW % = (Po/Pi) x 100 % = (1x103 / 1492) x 100 = 67%

GENERATOR EFFICIENCY Example 4: A 2-KW, 220-V generator has constant stray power losses of 150 W.The copper losses at rated load are calculated to be 280 W. If it is driven by motor, find the power required from the motor and the efficiency of the generator, both at rated load. P Pconv Po i Sol. Pi = Po + Pst +Pcu Pi = 2000 + 150 + 280 = 2430W % = (Po/Pi) x 100 % = (2000/2430) x 100 = 82.3% Pst Pcu The input power of the generator is the output power of themotor. Usually, the motor power is in hp. Pout_motor = Pin_generator = (2430 W)(1 hp/746 W) = 3.26hp 20

SHUNT DC GENERATOR o Self-Excited DC Generator means the generator does not requirean external source to set up a magnetic field (flux). o The types of self-excited dc generators are: 1. Shunt dc generator. 2. Series dc generator. 3. Compound (shunt and series) dc generator. Field Winding Armature Winding Load Shunt DC Generator o It is called shunt-generator because the field winding shunts (in parallel) with the armature. o The residual magnetism in the core is responsible for the generation of themagnetic field; thus, a small voltage will be generated. Shunt DC Generator Eg 21