Lec 3: Power System Components Dr. Mlbik Bsu 8/0/2009 Lesson pln 3 nd L.O. Sequence nlysis exmple ( detil fult nlysis next sem) Trnsformer model recp, tp chnge nd phse chnge, 3-phse Modeling of Synchronous Genertor Modeling of Induction motor
Blnced Opertion Of Three-Phse Circuit In the lnguge of Power Systems, three-phse circuit is sid to be blnced if the following conditions re true. If ll the sources nd lods re y-connected. There is no mutul inductnce between the phses. All neutrls re t the sme potentil. As consequence of the points (2) nd (3) bove, ll phses re decoupled. All network vribles re blnced sets in the sme sequence s the sources. If not. decouple them through symmetricl component nlysis Symmetricl Component Anlysis = c b 2 2 2 0 3 s = A - p
Symmetricl Component = 2 0 2 2 c b p = A s
Power invrince S = I * + b I b * + c I c * S = [A s ] T [AI s ] * S = 3[ I * + 2 I 2 * + 0 I 0 * ] Exmple 8., 8.2 (Glover) Trnsformer modeling Power blnce oltge, current nd impednce blnce Mmf nd flux linkge blnce ( mtching primry nd secondry voltge nd get rid of the isoltion) Power loss Exct equivlent circuit ( phsor digrm) Approximte equivlent circuit ( Power system clcultion)
Equivlent circuit of single-phse trnsformer Simplified equivlent circuit of single-phse trnsformer: () when referred to the primry side nd (b) when referred to the secondry side. 500 MA, 220/22 k with lekge rectnce of 0%. Find out the impednce in ech side.
Trnsformer exmple The A bse of the trnsformer is 500 MA nd the voltge bses in the primry nd secondry side re 200 k nd 22 k respectively. Therefore the impednce bses of these two sides re Ω Ω Assume tht the lekge rectnce is referred to the primry side. Then for 0%, i.e., 0. per unit lekge rectnce we hve Ω The bove rectnce when referred to the secondry side is Hence the per unit impednce in the secondry side is 0.0968/0.968 = 0.. Ω Trnsformer
C A c n B b Synchronous Genertor Modeling Ref: Chpter 4 Embedded Genertion By N. Jenkins et l
Schemtic digrm of synchronous genertor The schemtic digrm of synchronous genertor is shown bove. This contins three sttor windings tht re sptilly distributed. It is ssumed tht the windings re wye-connected. The winding currents re denoted by i, ib nd ic. The rotor contins the field winding the current through which is denoted by if. The field winding is ligned with the so-clled direct ( d ) xis. We lso define qudrture ( q ) xis tht leds the d -xis by 90. The ngle between the d-xis nd the -phse of the sttor winding is denoted by?d. Synch. Genertor Consists of rmture (sttor)- 3 phse, Field winding (rotor), dc The rmture develops mmf rotting t speed proportionl to the frequency (f) Field winding develops n mmf w.r.t. rotor In norml opertion, the rotor nd hence the field winding rottes synchronously with the mmf developed by the sttor with its reltive ngle, the lod ngle, determined by the torque pplied to the shft
Synch. Genertor f = PN 2*60 f = electricl frequency in Hz P = no of poles N = rotor speed in RPM fm = N/60 mechnicl frequency in r.p.s FIXED RELATIONSHIP BETWEEN SPEED AND FREQUENCY Construction of Synchronous Genertor Non-slient pole ( cylindricl rotor) Uniform irgp, big lterntor Slient pole (low speed, hydro gen)
S.S. opertion Mgnetic ckt unsturted /gp flux uniform, effect of sliency neglected /gp flux sinusoidl Rsttor negligible Three-phse equivlent circuit of synchronous genertor Single-phse equivlent circuit of synchronous genertor
Loding Cpbility Curve MA loding limit mximum MA, imposed by sttor heting MW loding limit mximum MW, imposed by turbine power rting Mx. field limit rotor current limit Stbility limit ( dynmic spect), must operte t sfe mrgin of d
Loding Cpbility Curve Governor Droop chrcteristics
Excittion control droop chrcteristics Modeling of the P.S. Consider the 50 Hz power system the singleline digrm of which is shown in Fig. The system contins three genertors, three trnsformers nd three trnsmission lines. The system rtings re Genertor G 200 MA, 20 k, X d = 5% Genertor G 2 Genertor G 3 300 MA, 8 k, X d = 20% 300 MA, 20 k, X d = 20% Trnsformer T 300 MA, 220Y/22 k, X d = 0% Trnsformer T 2 Trnsformer T 3 Three single-phse units ech rted 00 MA, 30Y/25 k, X = 0% 300 MA, 220/22 k, X = 0%
The impednce digrm of the system in single line Lods oltge nd frequency dependence Affect the behviour of P.S. Lrge no. of types of lods Differ considerbly in chrcteristics Aggregtion of lod (lump together) Types: Lighting voltge dependence Heting power nd voltge reltionship Ind. Motor P-, Q-, p.f. Synch motor
Induction Mchine modeling Next clss (Lec 4) Discussion of Assignment Further modeling concepts on sync. Mchines trnsient stte FACTS devices modeling Power Electronic Converters with genertors