by: -E₂ N hernators are connected in parallel and supply current to a volts. Alternator A has an induced e.mf. of 13000222-6 B has an e.mf. of 12500 236-9° volts and a reactance of 3 ernator ator A is given by; -V -ZA -- 13000 222-6-10000 40 2290 5002-67-4+j5000 (2500-/1000) A 700 2-21-8"A given by: -V 12500 236-9-10000 20/7500 3290 Z 500+/0)A-2500 20 A mators A and B supply a sub-station through lines 1 and 2: 0 to neutral. If the generalors e.mf. are A, 10000 V and nd currents delivered by A and B 00 kVA, 11000 V, 10% reactance 00 kVA, 11000 V, 15 % reactance 525 A lance of line 2-419 ditions of the . 1050 A se reactances 14 10% of 11000/5 (50+)40) 2 Fig. 12.87 Referring to Fig. 12.87, we have, 1,2+1, +424 4₂2, +(1+1)Z-E Som eq. (1), we have, and Subtracti 1,-1,- E-E₂686+/1003)-(6928+/0) j5 -(200+/250) A Z₁ 13431003 js 1,-1,- (200+/250) A Adding eqs. () and (i), we have, E₁ + E₂ 2Z+Z₁ (5686+/1003)+(6928+/0) 2 (50+/40)+/S 12654 24-5 131-2240-4 12614+/1003 100+/85 -9642-35-9A-(78-1-56-6) A (78-1-56-6) A 1+1 solving eqs. (i) and (iv), we have, 169 A (M) Hello expert, I want you to explain how he got the law inside the circle. Can you explain step by step and a clear line, please?

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A
Circulating current on no-load is given by
V-(1,+1)Z-IZ
4-
2+2
enf
Example 12.57. Two single-phase alternators are connected in parallel and supply current to a
load at a terminal voltage of 10000 20 volts. Alternator A has an induced em.f. of 13000222-6⁰
volts and a reactance of 20; alternator B has an e.mf. of 12500 236-9 volts and a reactance of 3
Find the current supplied by each alternator
Solution. Current supplied by alternator A is given by;
LA
problem
;
E-VE-V
Z₁
Current supplied by alternator B is given by:
4-
F.L. current of generator A is
4-4-
F.L. current of generator Bis
E-V 13000 222-6-10000 40
2290
XA/ZA
-6500 2-67-4*+j 5000 (2500-j/ 1000) A
- 2700 2-21-8 A
Also
- (2500+/0)A-2500 20 A
Example 12.5 Two 3-phase alternators A and B supply a sub-station through lines 1 and 2.
The sub-station load is R-500;X-402 to neutral. If the generators e.mf. are A, 10000 V and
B. 12000 V and A leads B by 10 elect; find currents delivered by A and B.
: 10,000 kVA, 11000 V, 10% reactance
20,000 kVA, 11000 V, 15 % reactance
Generator A rating
Generator B rating
Reactance of line 1-3-82: Reactance of line 2-41
Solution. Fig. 12.87 shows the conditions of the
-
E-V 12500 236-9-10000 20
Z
3290
10,000x10
√3x11000
20,000x10
√3x11000
<-525 A
4-4-
<- 1050 A
Letx, and x, be the respective per phase reactances
of the generators in ohms.
A
A
525 x,
10% of 11000/5
10 11000 1
2₁
100 3
1050-15% of 11000/5
15110001
<-120
1010-090
7500
13
(50+)40)
Fig. 12.87
and
Now
2₂+41-09+41-50
Z:(5)2; Z-(50+/40) 2
10,000 210-5774 210 volts (5686+/1003) volts
√√3
E-
Referring to Fig. 12.87, we have,
and
Subtracti
1,2+(1+1)ZE
1₂ Z₁ +(1₂+1₂) Z-E
om eq. (1), we have,
E₁-E₂
12000 20-(6928+/0) volts
√√3
Adding eqs. () and (i), we have,
4, +4₂=
-
1,-1,- (200+/250) A
$686+/1003)-(6928+/0)
j5
-(200+/250) A
Z₁
12431003
js
E,+E, (5686+/1003)+(6928+/0)
-
2Z+Z₁
2 (50+/40)+/S
12654 24-5
131-2240-4
12614+/1003
100+85
96-42-35-9A-(78-1-/56-6) A
(78-1-56-6) A
1₁+1₂
solving eqs. (ii) and (iv), we have,
Hello expert, I want you to explain how
he got the law inside the circle. Can you
explain step by step and a clear line, please?
Transcribed Image Text:A Circulating current on no-load is given by V-(1,+1)Z-IZ 4- 2+2 enf Example 12.57. Two single-phase alternators are connected in parallel and supply current to a load at a terminal voltage of 10000 20 volts. Alternator A has an induced em.f. of 13000222-6⁰ volts and a reactance of 20; alternator B has an e.mf. of 12500 236-9 volts and a reactance of 3 Find the current supplied by each alternator Solution. Current supplied by alternator A is given by; LA problem ; E-VE-V Z₁ Current supplied by alternator B is given by: 4- F.L. current of generator A is 4-4- F.L. current of generator Bis E-V 13000 222-6-10000 40 2290 XA/ZA -6500 2-67-4*+j 5000 (2500-j/ 1000) A - 2700 2-21-8 A Also - (2500+/0)A-2500 20 A Example 12.5 Two 3-phase alternators A and B supply a sub-station through lines 1 and 2. The sub-station load is R-500;X-402 to neutral. If the generators e.mf. are A, 10000 V and B. 12000 V and A leads B by 10 elect; find currents delivered by A and B. : 10,000 kVA, 11000 V, 10% reactance 20,000 kVA, 11000 V, 15 % reactance Generator A rating Generator B rating Reactance of line 1-3-82: Reactance of line 2-41 Solution. Fig. 12.87 shows the conditions of the - E-V 12500 236-9-10000 20 Z 3290 10,000x10 √3x11000 20,000x10 √3x11000 <-525 A 4-4- <- 1050 A Letx, and x, be the respective per phase reactances of the generators in ohms. A A 525 x, 10% of 11000/5 10 11000 1 2₁ 100 3 1050-15% of 11000/5 15110001 <-120 1010-090 7500 13 (50+)40) Fig. 12.87 and Now 2₂+41-09+41-50 Z:(5)2; Z-(50+/40) 2 10,000 210-5774 210 volts (5686+/1003) volts √√3 E- Referring to Fig. 12.87, we have, and Subtracti 1,2+(1+1)ZE 1₂ Z₁ +(1₂+1₂) Z-E om eq. (1), we have, E₁-E₂ 12000 20-(6928+/0) volts √√3 Adding eqs. () and (i), we have, 4, +4₂= - 1,-1,- (200+/250) A $686+/1003)-(6928+/0) j5 -(200+/250) A Z₁ 12431003 js E,+E, (5686+/1003)+(6928+/0) - 2Z+Z₁ 2 (50+/40)+/S 12654 24-5 131-2240-4 12614+/1003 100+85 96-42-35-9A-(78-1-/56-6) A (78-1-56-6) A 1₁+1₂ solving eqs. (ii) and (iv), we have, Hello expert, I want you to explain how he got the law inside the circle. Can you explain step by step and a clear line, please?
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