Download Representation of transformer, Per unit impedance , Diagram of

GANDHINAGAR INSTITUTE OF
TECHNOLOGY
Presentation
On
Representation of Power
System Components
Electrical Power System
(2150908)
Electrical Engineering
Submitted by:
Jay Kared (130120109016)
Rijay Doshi (130120109007)
Aditya Mehra (130120109001)
PRESENTATION ON :
Power System Components
Per Unit System
Complex Power
1) Components: Representation of transformer,
Per unit impedance , Diagram of power system.
2) Complex power : the steady state model of
synchronous machine power factor power control.
Power System Representation
using One Line Diagrams
• One Line Diagram or Single Line Diagram
Line Diagram of full Power System
• The following assumptions are made while
making impedance diagram of power system:• Single phase transformers are assume as ideal
transformers with their impedances indicated at
one side.
• The generators are represented as voltage sources
with series resistance and inductive reactance.
• Loads are represents by resistance and inductance
in series.
• The transmission lines are represented by pi
model.
Per Unit System
• It is usual to represent voltage , power ,
current and impedance in per unit of base or
reference values .The per unit value of any
quantity is defined as :
Actual value in any units
Base value in same units
Per-Unit Quantities
Per unit quantities are quantities that have been normalized to a base
quantity. In general
Z pu 
Z actual
Zbase
Choice of the base value Zbase is normally a rated value which is often one
of the normal full-load operations of power component in a power
network.
Let us look at two of the most common per unit formula which are widely
used when per unit calculations are involved.
(i)
Base impedance (Zbase)
For a given single-line (one-line) diagram of a power network, all
component parameters are expressed in 3- quantity whether it is the rating
(capacity) expressed as MVA or voltage as kV. Let begin with 3- base
quantity of
• (ii) Changing base impedance (Znew]
• Sometimes the parameters for two elements in the same circuit
(network) are quoted in per-unit on a different base. The
changing base impedance is given as,
2
Z NEW
 kVbase OLD 
MVAbase NEW

 pu   ZOLD 
2
MVAbase OLD
 kVbase NEW 
Complex Power
Instantaneous Power :
p (t )  v(t ) i (t ),
v(t ) = Vmax cos( t  V ),
i (t)
= I max cos( t   I ),
1
cos cos   [cos(   )  cos(   )],
2
1
p (t )  Vmax I max [cos(V   I ) 
2
cos(2 t  V   I )].
14
Complex Power, cont’d
Instantaneous Power is sum of average and varying terms :
1
p (t )  Vmax I max [cos(V   I )  cos(2 t  V   I )],
2
T
Pavg
1

p (t )dt ,

T0
1
 Vmax I max cos(V   I ),
2
 V I cos(V   I ),
Power Factor Angle =  =V   I .
15
Complex Power, cont’d
Re - interpretation of instantaneous Power :
p(t )
1
 Vmax I max [cos(V   I )  cos(2t  V   I )],
2
1
 Vmax I max [cos(V   I )  cos(2t  2V  (V   I ))],
2
1
 Vmax I max [cos(V   I )  cos(2t  2V ) cos(V   I )]
2
Instantaneous power into resistive component
1
 Vmax I max sin(2t  2V ) sin(V   I ),
2
Instantaneous power into electric and magnetic fields
16
Complex Power
S  V I  cos(V   I )  j sin(V   I ) ,
 P  jQ,
 V I *,
(Note: S is a complex number but not a phasor.)
P = Real Power (W, kW, MW),
Q = Reactive Power (VAr, kVAr, MVAr),
= magnitude of power into electric and magnetic fields,
S = Complex power (VA, kVA, MVA),
Power Factor (pf) = cos ,
If current leads voltage then pf is leading,
If current lags voltage then pf is lagging.
17
Complex Power, cont’d
Power Triangle
|S|
Q

P
2
S  P Q
2
  tan
S  P  jQ
1  Q 
 
P
pf 
P
P2  Q2
P
P
S 

cos( ) pf
18
Complex Power, cont’d
Relationships between real, reactive, and complex power:
P  S cos  ,
Q  S sin 
  S 1  pf 2 ,
Example: A load draws 100 kW with a leading pf of 0.85.
What are  (power factor angle), Q and S ?
   cos 1 0.85  31.8,
negative since
leading pf
100kW
S 
 117.6 kVA,
0.85
Q  117.6sin( 31.8)  62.0 kVAr.
Load consumes -62 kVAr, i.e. load supplies +62 kVAr  capacitive load
19
References
1. Modern Power Systems by Nagarath Kothari
2. Electrical Power Systems by V.K Mehta
3. Power System Engineering by C.L Wadhwa