A New Hybrid Synchronous Machine Capable of Ultra-High Output Power.

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1 A New Hybri Synhronous Mahine Capable o Ultra-High Output ower. L.U. Anih, h.d. *, C.U. Ogbuka, M.Eng., an M. Ewelum, B.Teh. Department o Eletrial Engineering, University o Nigeria, Nsukka, Nigeria. Department o Eletronis/Eletrial Engineering, Niger State olytehni, Zungeru, Nigeria. * luanih@yahoo.om uogbuka@yahoo.om ei_mbaiwe@yahoo.om ABSTRACT This artile presents the steay-state perormane analysis o a new hybri polyphase synhronous mahine apable o ultra-high power output. The mahine omprises a roun rotor an a salient-pole rotor whih are mehanially ouple together an house in their respetive stators. Eah omponent mahine has two iential stator winings, known as the main an auiliary winings. The main winings are onnete in series an tie to an ininite busbar or generator operation, while the auiliary winings are transpose in passing rom one omponent mahine to the other an ee a variable apaitane loa. A DC iel wining spanning both setions o the mahine is mounte on the ombine rotors. t is shown that the operational value o / ratio o the mahine is epenent on the variable apaitane loa o the auiliary winings an varies rom zero to ininity an hene the output power whih is iretly proportional to it. Unlike the onventional synhronous mahines where the relutane omponent o the output power is invariably very small, ompare to the eitation omponent, the onverse is the ase in the new hybri synhronous mahine. (Keywors: ultra-high output power, transpose auiliary winings, variable / ratio, apaitane tuning NTRODUCTON The steay-state perormane o a hybri synhronous relutane mahine has been reporte in [-6], eah having two stator winings known as the main an auiliary wining. There are no rotor onutors inluing amper winings. The mahine omprises a roun rotor an salient pole rotor that are mehanially ouple together an integrally woun. The main winings are onnete in series while the auiliary winings are onnete in anti-series (transpose between the two setions o the mahine. By tuning the loa apaitane o the auiliary wining, it beomes possible to vary the operational -ais reatane ( o the mahine rom zero to ininity, while the -ais reatane ( remains onstant. Thus a variable / ratio is ahieve whih varies rom zero to ininity an hene the output power whih is iretly proportional to it. Figure shows the per phase shemati arrangement o the mahine while Figure shows the ouple iruit euivalent. Analysis o Figure assumes the ollowing: a The synhronous reatane s o the roun rotor setion o the mahine is mathe to the -ais reatane ( o the salient pole setion by esign (ie s b The main an auiliary winings o the mahine have the same pole number as the rotor poles an oupy the same slot spae an, thus peretly ouple (unity oeiient o oupling an hene mr s an ms The resistane o the wining is neglete. The aii Journal o Siene an Tehnology 83

2 mr main auiliary wg wg mr ms main auiliary wg wg j Figure : er hase Shemati Arrangement o the Hybri Synhronous Mahine. j mr j j s j s j j j ms Figure : The Couple Ciruit Euivalent o the Hybri Synhronous Relutane Mahine. For a sinusoially istribute stator wining an a salient-pole rotor struture, the wining reatane is a untion o rotor position an well known as [7]: ( ( [os δ jsinδ ] ( The mahine is analyse as a magnetially ouple iruit. Applying KL euation in the two meshes o Figure an noting the positive an negative ouplings in the respetive halves o the mahine, it an reaily be eue that: an j j( ( ( 0 j j (3 j( ( Euations ( an (3 lea iretly to the perphase steay state euivalent iruit o the mahine as shown in Figure 3. The aii Journal o Siene an Tehnology 84

3 Figure 3: er hase Steay State Euivalent Ciruit o the Hybri Synhronous Relutane Mahine. From Figure 3, it an reaily be eue that the input impeane is given by is: (4 ( k os δ (4 ( k k Zin j[ k 3k ( k os δ j( k sinδ j( k (4 sin δ ] k 3k ( k os δ j( k sin δ (4 where k (5 Euation 4 an be simpliie as: [ ( a jb b a a b Z in j ] [ ( j( ] (6 ( j R e jx e j j j ( (7 Where: ( 4 ( k os δ (4 ( k k a (8 ( 4 ( k sin δ b (9 k 3k ( k osδ (0 ( k sin δ ( j AXS REACTANCES OF THE MACHNE Z in Consieration o the reative omponent o (Euation 7 leas iretly to the iret an uarature aes reatane. Thus whenδ 0, the salient pole rotor o the mahine is in the iret ais position an hene ( an when the rotor is in the uarature ais position, δ π raians (4 k k k (3 From Euation an 3, it is apparent that or a ie value o an k, etermine by the geometry o the salient pole setion o the mahine, the uarature ais reatane is epenent on the variable parameter an hene, or appropriate value o, takes values between 0 an ininity while remains onstant an thus a variable o ratio whih varies rom zero to ininity is obtaine. The loi o Z (Euation 7 as δ varies rom 0 in to π are amily o irles o raius ( an entre ( (,0 or various values o as shown in Figure 4 an all the amily o irles are tangential to the straight line passing through p.u or p. u. When, the mahine will raw or supply the same urrent irrespetive o loa. The asynhronous behavior an pull-in harateristis uner onstant urrent onitions provie an interesting stuy. The more interesting loi are probably those or whih the uarature The aii Journal o Siene an Tehnology 85

4 ais urrent has a leaing power ator. For a given output, the mahine when operating on one o suh a lous will raw less urrent than woul be the ase i the lous was with a lagging. For a onstant applie voltage, the urrent loi whih are the inverse o the impeane loi are amily o irles too, tangential to the line 0.5pu as shown in Figure 5. The straight line etening rom ± in the urrent loi whih implies ininite output power orrespons in the impeane loi to 0 as epete. The power ator is given by: os R R φ (4 e e X e Figure 6: ower Fator Loa Angle lots o the ealize Hybri Mahine. DEMERTS OF THE HYBRD SYNCHRONOUS RELUCTANCE MACHNE lots o the power ator or various values o are shown in Figure 6. One o the major emerits o the hybri synhronous relutane mahine is that the roun rotor hal o the mahine oes not ontribute to torue proution, sine there are no winings in the rotor. ts untion is essentially or impeane mathing o the iret ais reatane o the salient pole setion o the mahine to eual the synhronous reatane o the roun rotor hal s (i.e s. More importantly, the mahine annot operate as a stanalone mahine as it must be onnete to an eisting mains supply or the purpose o eriving its magnetizing urrent in a manner akin to inution generators. Figure 4: mpeane Loi o the ealize Hybri Mahine. Obe an Senjyu [8] suggeste the eploration o the possibility o embeing some permanent magnets in the roun rotor hal o the mahine with a view to making it ontribute to the output power an thus reue the loa angle δ or maimum power output o the mahine. This paper is an etension o the hybri synhronous relutane mahine reporte in [-6] to operate in the pure synhronous moe by introuing a DC iel wining spanning both setions o the mahine an mounte on the ombine rotors. Figure 5: Current Loi o the ealize Hybri Mahine. This tehniue enables the salient pole hal o the mahine to proue eitation um relutane power while the roun rotor setion ontributes eitation power only. The new hybri synhronous mahine will thus have superior output harateristis to the hybri synhronous The aii Journal o Siene an Tehnology 86

5 relutane mahine [-6] an the onventional DC iel eite synhronous mahines. DESCRTON OF THE HYBRD SYNCHRONOUS MACHNE UNDER STUDY The mahine uner stuy omprises a roun rotor an a salient pole rotor that are mehanially ouple together an house in their respetive stators. There are two iential winings on the stator sie known as the main an auiliary winings as esribe in [-6] that are appropriately interonnete an woun or the same pole numbers as the rotor poles. The only ierene between the mahine uner stuy an [-6] is that a DC eitation iel wining spanning both setions o the mahine is now mounte on the ombine rotor as shown in Figure 7. ANALYSS OF THE HYBRD SYNCHRONOUS MACHNE E The magnitue o EMF ( inue in both halves o the mahine by the rotor iel wining luφ is assume eual. The total EMF inue in the main wining is thus the sum o the EMFs E ( in both halves o the mahine an E euals. Similarly, the EMFs inue in the both halves o the auiliary wining are eual an a up to zero ue to the transposition (anti series onnetion o the auiliary winings. The euivalent iruit o the mahine is thus represente as shown in Figure 8 assuming motoring onvention. Applying the KL euation or the two meshes o Figure 8, it an reaily be shown that E j j( ( (5 0 j j( ( j (6 Euations (5 an (6 lea iretly to the euivalent iruit shown in Figure 9. The impeane o the iruit looking through the terminals o is given by: Z in ( ( j[ ] (7 Hene, ( ( E j[ ] (8 mr main auiliary wg wg mr ms main auiliary wg wg j Figure 7: er hase Shemati Arrangement o the Hybri Synhronous Mahine with Rotor Fiel Wining. The aii Journal o Siene an Tehnology 87

6 j s j mr j s j m / E j j ms j m / E Figure 8: Couple Ciruit Euivalent o the Mahine inluing the Eet o nue EMF. Figure 9: er hase Steay State Euivalent Ciruit o the Hybri Synhronous Mahine inluing the Eet o the nue EMF. Euation 8 may be represente as shown in Figure 0 or generator operation. E ( ( ( j, Figure 0: Euivalent Ciruit o the Hybri Synhronous Mahine Operating as a Generator. j j( j, E Where is the -ais reatane o the mahine ( ( impeane Z in j[ ] or o δ 0 an given by: (9 Similarly, is the -ais reatane o the mahine impeane: ( ( Z in j[ π or δ ras an given by: (4 k k k ] (0 The - omponents o the loa urrent, j an will proue omponent voltage rops an j. The phasor relations o Figure 0 using as the reerene phasor an negleting resistane is given by: The aii Journal o Siene an Tehnology 88

7 E j j ( The phasor iagram orresponing to Euation is as shown in Figure. δ φ E j δ or typial values o u E. p. u an δ rom zero to π A plot o the real output power with values o is as shown in Figure. o the mahine p., or some j Figure : hasor Diagram o Generator Moe o the Hybri Mahine. OUTUT OWER OF THE NEW HYBRD MACHNE The output power o the mahine is given by: Figure : Output ower o the Hybri Mahine or δ rom zero to π. S 3 S 3 δ ( j From the phasor iagram (Figure : ( (3 Figure 3 shows the plot o the real output power o the mahine with δ or p. u whih is hosen as an approimation to.0 p.u. E osδ (4 sin δ (5 Substituting Euations (4 an (5 into Euation (3 gives: 3 E 3 ( sinδ sinδ (6 r (7 Figure 3: Output ower o the Hybri Mahine where is the eitation power an is the relutane power. r or δ rom zero to π at p. u The aii Journal o Siene an Tehnology 89

8 For a typial value o eitation power whereas the relutane power values o is as shown in Table. o π δ 30 ra, the 6 is onstant at 0.6pu, r or some A ursory glane at Table shows that when the auiliary wining is on open iruit ( that the operational ratio is low an onseuently the output power. When the auiliary wining is short iruite ( 0 there is a small erement o the operational -ais reatane ( an a onseuent inrease in as ( is always onstant an hene an inrease output power. When a variable apaitane loa is introue into the auiliary wining, there is a marke erement o the - ais reatane ( an a orresponing inrease in the output power ue to the neutralization o the inutive reatane o the mahine by the apaitive loa. At, the inutive uarature reatane (.0 p. u o the mahine is ompletely neutralize by the apaitive reatane leaing to ininite ratio an a orresponing ininite output power., however, the apaitive reatane eees the inutive reatane, the mahine operates at leaing power ator. n omparison, the eitation power omponent is negligibly small (in the operational range.0 p. u ompare to the relutane power omponent an hene the overall output power o the mahine whih is the sum o an r is r ominant. For the relutane power.0 p. u r (an by impliation the total output power, will ten to ininity. The steay state limit o the o hybri mahine is about δ 45 unlike the onventional salient pole synhronous mahine. t is seen rom the table that or that 0.99p. u the relutane power is 7 times the ontribution ue to DC eitation. DC eitation woul nevertheless have to be reuire in orer that the mahine oul operate as a stanalone generator. r Table : Output ower Components o the Hybri Mahine or various values o at Operational alue o o δ 30 an the perentage ontributions o an to the total output power Capaitive Reatane (p.u Operational Eitation Relutane Total Output / ower ower ower Ratio r or k 3 (p.u (p.u (p.u (ininity 0.60 (ininity (ininity r % % r The aii Journal o Siene an Tehnology 90

9 CONCLUSON n this paper, it is shown that when a ylinrial rotor mahine is mehanially ouple to a salient pole mahine, with the synhronous reatane s o the roun rotor mahine mae eual to the iret ais reatane o the salient pole setion (i.e ; on the -ais, the eetive - ais reatane o the mahine is an the eetive -ais reatane is, giving a ratio k. s k k k For a ie mahine geometry ( k where, the eetive salieny ator,, an be raise i a seon set o stator (auiliary winings whose oil sies are isplae 80º eletrial (transpose between the two setions o the mahine are installe an ee a balane variable apaitane loa. By varying the apaitane loaing, will vary rom zero to ininity while k remains unaete an a variable ratio whih is iretly proportional to the relutane power omponent is ahieve at goo power ators an normal urrents. The new hybri synhronous mahine will have a higher output power to size ratio ompare to the onventional salient pole synhronous mahine, beause the eitation power has a ator o whih ompensates or oupling two mahines. Furthermore, the relutane omponent is very large an ar eees the eitation omponent. Construtionally, the stator o the new hybri synhronous mahine will have eeper slots in orer to aommoate the two sets o winings (main an auiliary. The output voltage o the auiliary wining oul be sense an use in the ontrol o the mehanial governing or ajustment o the iel eitation when there is nee to improve stability o operation. The mahine is epete to have a relatively better asynhronous run-up harateristi than a onventional salient pole synhronous mahine beause the apaitane o the auiliary wining an be tune suh that the ierene between the eetive rotor -ais reatane an the eetive uarature ais reatane will not be so pronoune. The pull-in torue, as a ratio o the pull-out torue will thereore be greater. The stability o the mahine on loa an be raise by inreasing the auiliary wining apaitane loa ater the mahine has been brought to synhronism. The new hybri synhronous mahine is being stuie or bulk power supply in view o its ultrahigh power output potential. REFERENCES. Agu, L.A. an L.U. Anih A ariable Synhronous Relutane Mahine. roeeing o the Eletri ower Engineering Conerene (EEC. Nsukka, Nigeria Agu, L.A. an L.U. Anih. 00. Enhanement o the Output Synhronous Relutane Mahines by Capaitane njetion Tehniue. Tehnial Transation o the Nigerian Soiety o Engineers. 37(: Agu, L.A. an L.U. Anih. 00. olyphase Relutane Mahines without Rotating Winings. Tehnial Transations o the Nigerian Soiety o Engineers. 37(4: Anih, L.U. an L.A. Agu A Novel Strategy or Raising the Unit Output o Large Synhronous Mahines. Nigerian Journal o Tehnology (NJOTECH. (: Agu, L.A. L.U. Anih, J.O. Ojo, an A.A. Aisa Novel Synhronous Relutane Mahine with Capaitane njetion. Marthinusen Rotating Mahine Conerene 5th-7th July 005, ilansberg Conerene Centre, South Aria Anih, L.U The erormane Charateristis o Couple Roun Rotor an Salient ole Synhronous Mahine. Unpublishe h.d. Thesis o the University o Nigeria, Nsukka. 7. Lawrenson,.J. an L.A. Agu Theory an erormane o olyphase Relutane Mahines ro. O EE. 3(8: The aii Journal o Siene an Tehnology 9

10 8. Obe, E.S. an T. Senjyu Analysis o olyphase Synhronous Relutane Motor with Two ential Stator Winings. Eletri ower System Researh. 76: ABOUT THE AUTHORS Engr. Dr. Anih, Linus Uhehukwu h.d. (Nig. is a Senior Leturer in the Department o Eletrial Engineering, University o Nigeria, Nsukka. He was a ormer Hea o Department o Eletrial Engineering ( He is a registere member o EEE ( His urrent researh interest is in Couple Relutane Mahines. Engr. Ogbuka, Cosmas Uhenna reeive his B.Eng Degree (First Class Honours an M.Eng Degree (Distintion in 004 an 009 respetively in the Department o Eletrial Engineering University o Nigeria, Nsukka where he presently works as a Leturer/Researh Stuent. His researh interests are in Ajustable Spee Drives o Eletrial Mahines: (DC an AC Eletri Mahine Torue/Spee Control with Converters an nverters an ower Eletronis. Engr. Ewelum, Mbaiwe is a Grauate Researh Stuent in the Department o Eletrial Engineering, University o Nigeria, Nsukka an a Senior Leturer in Niger State olytehni Zungeru Niger State Nigeria. His researh interest is in Eletrial Mahines. SUGGESTED CTATON Anih, L.U., C.U. Ogbuka, an M. Ewelum A New Hybri Synhronous Mahine Capable o Ultra-High Output ower. aii Journal o Siene an Tehnology. 0(:83-9. aii Journal o Siene an Tehnology The aii Journal o Siene an Tehnology 9

Chapter 2: One-dimensional Steady State Conduction

Chapter 2: One-dimensional Steady State Conduction 1 Chapter : One-imensional Steay State Conution.1 Eamples of One-imensional Conution Eample.1: Plate with Energy Generation an Variable Conutivity Sine k is variable it must remain insie the ifferentiation