Lecture Name #14

Electric Machinery BProf. Dr. Juan Segundo Ramrez

Synchronous Machine ModelLecture #2Synchronous Machine ModelTwo-axis ModelLesson SummaryIntroduction to two-axis modelParks transformationVoltage equation in dq0 frameEquivalent Circuit for two-axis modelSub-transient and transient reactanceInstructional ObjectiveOn completion of this lesson a student should be able to:

Explain the concept of two-axis model of a synch. Develop the two-axis Eq. circuit model of a synch machineExplain the concept of sub-transient and transient reactance in a synch.

Cross section of and elementary stator and salient-pole rotor.

Stator- rotor mutual inductances

Called parks transformation, where

Voltage equations: salient-pole machine

Parks Transformation; AdvantagesA direct-axis circuit which rotates with the field circuit and is mutually coupled to itA quadrature-axis circuit which is displaced 90 from the d-axis, and thus has no mutual inductance with the field or other d-axis circuit although it rotates in synchronism with them.A stationary stand-alone o-coil with no coupling to any other circuit, and thus is not shown in Fig.

Transient and subtransient effects

ExampleThe single-line diagram of an unloaded power system is shown in Fig. 3.22. Reactances of the two sections of the transmission line are shown on the diagram. The generators and transformers are rated as follows:

Generator 1: 20 MVA, 13.8 kV, Xd=0.20 per unitGenerator 2:30 MVA, 18 kV, Xd=0.20 per unitGenerator 3:30 MVA, 20 kV, Xd=0.20 per unitTransformer T1:25 MVA, 220Y/13.8 kV, X=10% Transformer T2 :single- phase units, each rated 10 MVA, 127/18 kV, X=10 %Transformer T3 : 35 MVA, 220Y/22Y kV , X=10%A) Draw the impedance diagram with all reactances marked in per unit and with letters to indicate points corresponding to the single-line diagram. Choose a base of 50 MV A, 13.8 kV in the circuit of generator 1.Suppose that the system is unloaded and that the voltage throughout the system is 1.0 per unit on bases chosen in part a. If a three-phase short circuit occurs from bus C to ground, find the phasor value of the short-circuit current ( in amperes) if each generator is represented by its sub transient reactance.Find the megavoltamperes supplied by each generator under the conditions of part (b).ABCEF1DT1T2j 100 j 80 32Generator 1; Xd=0.250/20=0.50 pu3 rating T2: 220/18 kV,30 MVABase in trasmission line: 220 kV, 50 MVABase for generator 2: 18 kVGenerator 2; Xd=0.250/30=0.33 puBase for generator 3: 22 kVGenerator 3; Xd=0.2(20/22)250/30=0.275 puT1; X=0.150/25=0.2 puT2; X=0.150/30=0.167 puT3; X=0.150/35=0.143 puBase Z=2202/50=968 Line B-C; Z=80/968=0.826 puLine C-E; Z=100/968=0.1033 pu123j0.2j0.5j0.0826j0.1033j0.167j0.333j0.143j0.275ABCEDFA)

B)E1E2E3X1=j0.5+j0.2+j0.0826X2=j0.333+j0.167+j0.1033X3=j0.143+j0.275S/C

C)

Mutual inductance

Rotor

Mutual indictances

Armature/D-winding

S Sq-axisd-axis

D-damper windingd-axis armatureequivalentwinding

Field winding

d-axis armatureequivalentwinding

Q-damper winding