Environmental Engineering Reference
In-Depth Information
Appendix E
OLTC derivatives
The partial derivatives for an on-load tap-changer (OLTC) element are extensive.
However, they can be derived from the following general expressions [243,244].
Taking (4.8) as a reference, the incremental form regarding the active power of
OLTC element occurring in direction
km
can be expressed as:
∂P
km
∂θ
k
∂P
km
∂θ
m
∂P
km
∂τ
P
km
=
θ
k
+
θ
m
+
τ
∂P
km
∂
∂P
km
∂
∂P
km
∂
+
|
V
k
| +
|
V
m
| +
|
t
|
(E.1)
|
V
k
|
|
V
m
|
|
|
t
Taking (4.9) as a basis equation, the incremental form regarding the reactive
power of OLTC element occurring in direction
km
can be expressed as:
∂Q
km
∂θ
k
∂Q
km
∂θ
m
∂Q
km
∂τ
Q
km
=
θ
k
+
θ
m
+
τ
∂Q
km
∂
∂Q
km
∂
∂Q
km
∂
+
|
V
k
| +
|
V
m
| +
|
t
|
(E.2)
|
V
k
|
|
V
m
|
|
t
|
Taking (4.13) as a reference, the incremental form regarding the active power in
OLTC element occurring in direction
mk
can be expressed as:
∂P
mk
∂θ
m
∂P
mk
∂θ
k
∂P
mk
∂τ
P
mk
=
θ
m
+
θ
k
+
τ
∂P
mk
∂
∂P
mk
∂
∂P
mk
∂
+
|
V
m
| +
|
V
k
| +
|
t
|
(E.3)
|
V
m
|
|
V
k
|
|
t
|
Taking (4.14) as a basis equation, the incremental form regarding the reactive
power of OLTC element occurring in direction
mk
can be expressed as:
∂Q
mk
∂θ
m
∂Q
mk
∂θ
k
∂Q
mk
∂τ
Q
mk
=
θ
m
+
θ
k
+
τ
∂Q
mk
∂
∂Q
mk
∂
∂Q
mk
∂
+
|
V
m
| +
|
V
k
| +
|
|
t
(E.4)
|
V
m
|
|
V
k
|
|
|
t
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