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HERAKLES Otomatik Avlı kalıcı sunucu. 19 Haziran'da açılıyor. Atius & Wizard güvencesiyle hemen kayıt ol, ön kayıt ödülleri aktif. HEMEN TIKLA!
Dc Load Flow Method
Because The Resistances Of Transmission Lines Are Rather Small Compared With Reactances Of Those Lines ,for Certain Types Of Operations (e.g., Fault Studies ) The Resistances Are Neglected To Simplify The Solution.
Letâs Consider The Nominal ï° Model Of A Medium Line. The Circuit Parameters Are :
A=1+ [ (1/2)yz ]
B=z+ [ (1/4)yz 2 ]
C=y
D=1+ [ (1/2)yz ]
Neglecting Line Resistance And Shunt Admittance , We Can Represent The Line With Its Inductive Reactance Only, As Shown In Figure 1.
Figure 1. Simplified Transmission Line Model
The Transmission (abcd) Parameters For This Representation Are:
A=d=1 0
B= Jxik
C= 0
And The Power Flows Through The Line ,
Ps = ï²vs Vr Cos(90 + ï¤ï©ï ï¯ï x = (vs Vr Sinï¤ï©ï ï¯ X
Pr = ï²ï vs Vr Cos(90 + ï¤) / X= (vs Vr Sinï¤ï©ï ï¯ï x (1)
For ï¤ï << 1 Radian, Sinï¤ ï¤ï®hence, In General, The Line Flows Become
Pik=(vi Vk ï¤ikï©ï ï¯ï xik (2)
Where
ï ï ï ï ï ï¤ikï ï½ï ï¤i ï²ï¤k (3)
Since All The Bus Voltages Of A Power System Are Around 1 Pu, Then Let
Vi = Vk =1 Pu
Bik =ï²1 / Xik (4)
Then Equation (3) Becomes
Pik = ï²bik ï¤ik = (ï¤i ï²ï¤k) / Xik (5)
Now, The Bus Power At Any Bus Is The Sum Of The Power Flows In The Lines Connected To That Bus. .hence ,
Pi = Pik = (ï²bik ï¤ik) I = 1, 2, ...., N (6)
Or In Matrix Form ,
P1 B11 B12 ... B1n ï¤1
P2 B21 B22 ... B2n ï¤ï²
. = . . ... . . (7)
. . . ... . .
Pn Bn1 Bn2 ... B Nn ï ï¤ N
Which Can Be Abbreviated As
[p] = [ ï¤ï ] (8)
Where
Bik = ï²1 / Xik (9)
And
Bii = (ï²bik) (10)
The Matrix Is The Imaginary Part Of Ybus . The Solution For [ï¤ïï is
[ï¤] = â1 [p] (11)
Matrix Is An (n â1) ï³ï (nï²1) Matrix Dimensionally For An N-bus System. The Diagonal And Off â Diagonal Elements Of The Matrix Can Be Found By Adding The Series Susceptances Of The Branches Connected To Bus I And By Setting Them Equal To The Negated Series Susceptance Of Branch Ik , Respectively.
Until Now , We Have Kept The System Ground As The Reference Bus. However Since We Have Dropped All Shunt Brunches In Simplifying Things , We Have Lost Our Reference. This Means That The Matrix Of Equation (7) Is Obtained By Equation (9) And (10) Will Be A Singular Matrix. Hence , ï²1 Of Equation (11) Does Not In Fact Exist.
Because The Resistances Of Transmission Lines Are Rather Small Compared With Reactances Of Those Lines ,for Certain Types Of Operations (e.g., Fault Studies ) The Resistances Are Neglected To Simplify The Solution.
Letâs Consider The Nominal ï° Model Of A Medium Line. The Circuit Parameters Are :
A=1+ [ (1/2)yz ]
B=z+ [ (1/4)yz 2 ]
C=y
D=1+ [ (1/2)yz ]
Neglecting Line Resistance And Shunt Admittance , We Can Represent The Line With Its Inductive Reactance Only, As Shown In Figure 1.
Figure 1. Simplified Transmission Line Model
The Transmission (abcd) Parameters For This Representation Are:
A=d=1 0
B= Jxik
C= 0
And The Power Flows Through The Line ,
Ps = ï²vs Vr Cos(90 + ï¤ï©ï ï¯ï x = (vs Vr Sinï¤ï©ï ï¯ X
Pr = ï²ï vs Vr Cos(90 + ï¤) / X= (vs Vr Sinï¤ï©ï ï¯ï x (1)
For ï¤ï << 1 Radian, Sinï¤ ï¤ï®hence, In General, The Line Flows Become
Pik=(vi Vk ï¤ikï©ï ï¯ï xik (2)
Where
ï ï ï ï ï ï¤ikï ï½ï ï¤i ï²ï¤k (3)
Since All The Bus Voltages Of A Power System Are Around 1 Pu, Then Let
Vi = Vk =1 Pu
Bik =ï²1 / Xik (4)
Then Equation (3) Becomes
Pik = ï²bik ï¤ik = (ï¤i ï²ï¤k) / Xik (5)
Now, The Bus Power At Any Bus Is The Sum Of The Power Flows In The Lines Connected To That Bus. .hence ,
Pi = Pik = (ï²bik ï¤ik) I = 1, 2, ...., N (6)
Or In Matrix Form ,
P1 B11 B12 ... B1n ï¤1
P2 B21 B22 ... B2n ï¤ï²
. = . . ... . . (7)
. . . ... . .
Pn Bn1 Bn2 ... B Nn ï ï¤ N
Which Can Be Abbreviated As
[p] = [ ï¤ï ] (8)
Where
Bik = ï²1 / Xik (9)
And
Bii = (ï²bik) (10)
The Matrix Is The Imaginary Part Of Ybus . The Solution For [ï¤ïï is
[ï¤] = â1 [p] (11)
Matrix Is An (n â1) ï³ï (nï²1) Matrix Dimensionally For An N-bus System. The Diagonal And Off â Diagonal Elements Of The Matrix Can Be Found By Adding The Series Susceptances Of The Branches Connected To Bus I And By Setting Them Equal To The Negated Series Susceptance Of Branch Ik , Respectively.
Until Now , We Have Kept The System Ground As The Reference Bus. However Since We Have Dropped All Shunt Brunches In Simplifying Things , We Have Lost Our Reference. This Means That The Matrix Of Equation (7) Is Obtained By Equation (9) And (10) Will Be A Singular Matrix. Hence , ï²1 Of Equation (11) Does Not In Fact Exist.
