Electrical Power Systems

316 Electrical Power Systems
ig. 12.11: Block diagram representation of a generating unit with a reheat turbine.
The block diagram of ig. 12.11 is also applicable to a unit with non-reheat turbine.
However, in this case T r = 0.0.
12.12 STATE-SPACE REPRESENTATION
In ig. 12.11, assume Df = x 1, DP g = x 2, DP v = x 3 and DE = x 4.
Differential equations are written by describing each individual block of ig. 12.11 in terms
of state variable. (Note that S is replaced by d
dt )
x·
1 = -1 1
T x
p
x·
2 = -1 2
T x
r
x·
3 = -1 3
T x
t
x· 4 = -1
RT x
g
+ K
T x
p
HG
p
2 – K p
T
+ 1 K
T T x -
r
+ 1 4
T x
t
1
– 1 4
T x
g
I
p
D P
...(12.12)
L
r
3 +
t KJ K r
t
+ 1
T u
g
Eqns. (12.12) – (12.15) can be written in matrix form:
L
NM
• x1
• x2
• x3
• x4
O
QP
=
L
NM
-1
T
p
0
K
T
p
p
HG
-1
1 K
-
T T T
r r
0 0
I
KJ
K
T
-1
1
0 0
Tt Tt
-1-1 0 0
RT T
g g
r
t
t
r
O L
QP
NM
x
x
x
x
1
2
3
4
O
QP
+
T x
L
NM
0
0
0
1
T
g
4
O
QP
u +
L
NM
-K
T
0
0
0
p
p
O
QP
DPL ...(12.13)
...(12.14)
...(12.15)
... (12.16)