Environmental Engineering Reference
In-Depth Information
1.2.2 Transmission Line
L TL
x b
di dl
dt ¼ v d4 v d3 R TL i dl þ x e L TL i ql
L TL
x b
di ql
dt ¼ v q4 v q3 R TL i ql x e L TL i dl
ð 1 : 4 Þ
C TL
x b
dv d3
dt
C TL
x b
dv q3
dt
¼ i dc þ x e C TL v q1 ;
¼ i qc x e C TL v d3
C TL
x b
dv d4
dt
C TL
x b
dv q4
dt
¼ i dc þ x e C TL v q4 ;
¼ i qc x e C TL v d4
1.2.3 Transformer
L tr
x b
di dl
dt ¼ v d2 v d1 R tr i dl þ x e L tr i ql
L tr
x b
di ql
dt ¼ v q2 v q1 R tr i ql x e L tr i dl
ð 1 : 5 Þ
C o
x b
dv d1
dt
C o
x b
dv q1
dt
¼ i dl þ x e C o v q1 ;
¼ i ql x e C o v d1
1.2.4 Cable
L ca
x b
di dl
dt ¼ v d3 v d2 R ca i dl þ x e L ca i ql
L ca
x b
di ql
dt ¼ v q3 v q2 R ca i ql x e L ca i dl
ð 1 : 6 Þ
C ca
x b
dv d2
dt
C ca
x b
dv q2
dt
¼ i dc þ x e C ca v q2 ;
¼ i qc x e C ca v d2
1.2.5 RL Load
The RL load in the dq-domain can be described as
L load
x b
di dL
dt ¼ v d4 R load i dL þ x e L load i qL
L load
x b
di qL
dt ¼ v q4 R load i qL x e L load i dL
ð 1 : 7 Þ
C o
x b
dv d4
dt
C o
x b
dv q4
dt
¼ i dL þ x e C o v q4 ;
¼ i qL x e C o v d4
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