Formula Sheets: Voltage & Frequency Control | Power Systems - Electrical Engineering (EE) PDF Download

 Page 1


Power S ystems F ormula Sheet: V oltage &
Frequency Control
1. Frequency Control
• Power-Frequency Relationship : Frequency deviation due to load change:
?f = -
?P
K
where ?P is change in load (p.u.), K is system frequency char acteristic (p.u.
power/Hz).
• S ystem Frequency Char acteristic :
K =
n
?
i=1
1
R
i
whereR
i
is governor droop of thei -th gener ator (Hz/p.u. power),n is number
of gener ators.
• Governor Droop Char acteristic :
R
i
=
?f
?P
i
where?P
i
is change in power output of thei -th gener ator .
• Load Damping F actor (D ):
D =
?P
load
?f
(p.u. power/Hz)
• Primary Frequency Control (Steady-state f requency deviation):
?f = -
?P
load
?
1
R
i
+D
• Area Control Error (A CE) (for interconnected systems):
A CE=?P
tie
+B?f
where?P
tie
is tie-line power deviation,B is frequency bias factor (p.u. power/Hz).
1
Page 2


Power S ystems F ormula Sheet: V oltage &
Frequency Control
1. Frequency Control
• Power-Frequency Relationship : Frequency deviation due to load change:
?f = -
?P
K
where ?P is change in load (p.u.), K is system frequency char acteristic (p.u.
power/Hz).
• S ystem Frequency Char acteristic :
K =
n
?
i=1
1
R
i
whereR
i
is governor droop of thei -th gener ator (Hz/p.u. power),n is number
of gener ators.
• Governor Droop Char acteristic :
R
i
=
?f
?P
i
where?P
i
is change in power output of thei -th gener ator .
• Load Damping F actor (D ):
D =
?P
load
?f
(p.u. power/Hz)
• Primary Frequency Control (Steady-state f requency deviation):
?f = -
?P
load
?
1
R
i
+D
• Area Control Error (A CE) (for interconnected systems):
A CE=?P
tie
+B?f
where?P
tie
is tie-line power deviation,B is frequency bias factor (p.u. power/Hz).
1
2. V oltage Control
• V oltage Drop in a Line :
?V ˜I(R cos?+X sin?)
whereI is line current,R is resistance,X is reactance,? is power factor angle.
• Reactive Power Flow (Simplified for short line):
Q=
|V
s
||V
r
|
X
sind+
|V
s
|(|V
s
|-|V
r
|)
X
whereV
s
,V
r
are sending and receiving end voltages,d is angle difference, X is
line reactance.
• V oltage Regulation with T ap-Changing Tr ansformer :
V
new
=V
nominal
·(1+t)
wheret is tap r atio change (positive or negative).
• Reactive Power Injection (b y shunt capacitor):
Q
C
= |V|
2
?C
whereV is bus voltage,C is capacitance,? =2pf .
• Shunt Reactor Compensation :
Q
L
= -
|V|
2
?L
whereL is inductance.
3. A utomatic Gener ation Control (A GC)
• A GC Objective : Minimize A CE to restore frequency and tie-line power to sched-
uled values.
• Control A ction :
?P
i
= -ß
i
· A CE
whereß
i
is participation factor for gener atori ,
?
ß
i
=1 .
• Frequency Bias F actor :
B =
1
R
+D
whereR is composite droop,D is load damping factor .
2
Page 3


Power S ystems F ormula Sheet: V oltage &
Frequency Control
1. Frequency Control
• Power-Frequency Relationship : Frequency deviation due to load change:
?f = -
?P
K
where ?P is change in load (p.u.), K is system frequency char acteristic (p.u.
power/Hz).
• S ystem Frequency Char acteristic :
K =
n
?
i=1
1
R
i
whereR
i
is governor droop of thei -th gener ator (Hz/p.u. power),n is number
of gener ators.
• Governor Droop Char acteristic :
R
i
=
?f
?P
i
where?P
i
is change in power output of thei -th gener ator .
• Load Damping F actor (D ):
D =
?P
load
?f
(p.u. power/Hz)
• Primary Frequency Control (Steady-state f requency deviation):
?f = -
?P
load
?
1
R
i
+D
• Area Control Error (A CE) (for interconnected systems):
A CE=?P
tie
+B?f
where?P
tie
is tie-line power deviation,B is frequency bias factor (p.u. power/Hz).
1
2. V oltage Control
• V oltage Drop in a Line :
?V ˜I(R cos?+X sin?)
whereI is line current,R is resistance,X is reactance,? is power factor angle.
• Reactive Power Flow (Simplified for short line):
Q=
|V
s
||V
r
|
X
sind+
|V
s
|(|V
s
|-|V
r
|)
X
whereV
s
,V
r
are sending and receiving end voltages,d is angle difference, X is
line reactance.
• V oltage Regulation with T ap-Changing Tr ansformer :
V
new
=V
nominal
·(1+t)
wheret is tap r atio change (positive or negative).
• Reactive Power Injection (b y shunt capacitor):
Q
C
= |V|
2
?C
whereV is bus voltage,C is capacitance,? =2pf .
• Shunt Reactor Compensation :
Q
L
= -
|V|
2
?L
whereL is inductance.
3. A utomatic Gener ation Control (A GC)
• A GC Objective : Minimize A CE to restore frequency and tie-line power to sched-
uled values.
• Control A ction :
?P
i
= -ß
i
· A CE
whereß
i
is participation factor for gener atori ,
?
ß
i
=1 .
• Frequency Bias F actor :
B =
1
R
+D
whereR is composite droop,D is load damping factor .
2
4. V oltage Control Devices
• S ynchronous Condenser : Provides reactive power:
Q=
|V||E| cosd-|V|
2
X
s
whereE is internal voltage,X
s
is synchronous reactance.
• Static V AR Compensator (S V C) : Reactive power output:
Q
S V C
=B
S V C
|V|
2
whereB
S V C
is susceptance (adjustable).
• On-Load T ap Changer (OL T C) : A djusts tr ansformer turns r atio to maintain
voltage.
5. Load Flow and V oltage Stability
• Power Flow Equations (for busi ):
P
i
=
n
?
k=1
|V
i
||V
k
||Y
ik
| cos(?
ik
+d
k
-d
i
)
Q
i
=
n
?
k=1
|V
i
||V
k
||Y
ik
| sin(?
ik
+d
k
-d
i
)
whereY
ik
= |Y
ik
|??
ik
is admittance matrix element.
• V oltage Stability Limit : Maximum power tr ansfer before voltage collapse:
P
max
=
|V
s
|
2
X(1+ sin?)
where? is load po wer factor angle.
3