per-unit system2009-3.ppt
TRANSCRIPT
-
7/22/2019 Per-Unit System2009-3.ppt
1/26
Per-Unit System
In power systems there are so many different
elements such as Motors, Generators and
Transformers with very different sizes and
nominal values. To be able to compare the performances of a
big and a small element, per unit system is
used.
-
7/22/2019 Per-Unit System2009-3.ppt
2/26
Power System Representation
Physical Components in the system arerepresented by a mathematical model.
Mathematical models of components areconnected in exactly the same way as thephysical components to obtain the systemrepresentation.
Various physical components have differentratings or basis.
It is convenient to obtain the representation with
respect to a common basis.
-
7/22/2019 Per-Unit System2009-3.ppt
3/26
Per Unit And Percent Representation
The numerical per uni tvalue of any
quantity is its ratio to the chosen base
quantity of the same dimensions.
Thus a per unit quantity is a normalized
quantity with respect to a chosen base
value.
Percent is the per unit quantity multiplied
by a 100.
-
7/22/2019 Per-Unit System2009-3.ppt
4/26
Per Unit And Per Cent Representation
Advantages
In the per-unit system of representation, deviceparameters tend to fall in a relatively fixed range,
making erroneous values prominent.
Ideal transformers are eliminated as circuit
elements. This results in a large saving in
component representation and reduces
computational burden.
The voltage magnitude throughout a given power
system is relatively close to unity in the per-unit
system for a power system operating normally.
This characteristic provides a useful check on the
-
7/22/2019 Per-Unit System2009-3.ppt
5/26
Per Unit And Percent Representation
Base Quantities
In power system calculations the nominalvoltage of lines and equipment is almost
always known, so the voltage is a
convenient base value to choose.
The apparent power (volt-ampere) is
usually chosen as a second base. In
equipment this quantity is usually knownand makes a convenient base.
-
7/22/2019 Per-Unit System2009-3.ppt
6/26
Per Unit And Percent Representation
Base Quantities
The choice of these two base quantities will
automatically fix the base of current,
impedance, and admittance.
In a system study, the volt-ampere base can
be selected to be any convenient value such
as 100 MVA, 200 MVA, etc.
-
7/22/2019 Per-Unit System2009-3.ppt
7/26
Per Unit And Percent Representation
Base Quantities
The same volt-ampere base is used in all
parts of the system. One base voltage in
a certain part of the system is selected
arbitrarily. All other base voltages mustbe related to the arbitrarily selected one
by the turns ratio of the connecting
transformers.
-
7/22/2019 Per-Unit System2009-3.ppt
8/26
Per Unit System
Power system quantities such as voltage,current and impedance are often expressed inper unit or percent of specified values.
Per unit quantities are calculated as:
ValueBaseValueActualValuePer Unit
-
7/22/2019 Per-Unit System2009-3.ppt
9/26
Per Unit Values
base
puSS
S
base
puII
I
base
puVV
V
base
puZZZ
ZZ
2
base
base
base
puV
S
ZZ
pu
base
2
base
pubase ZS
VZZ Z
Conversion of Per Unit Values
Per Unit System
-
7/22/2019 Per-Unit System2009-3.ppt
10/26
Per Unit System
Usually, the nominal apparent power (S) and
nominal voltage (V) are taken as the base
values for power (Sbase) and voltage (Vbase).
The base values for the current (Ibase) andimpedance (Z
base) can be calculated based on
the first two base values.
-
7/22/2019 Per-Unit System2009-3.ppt
11/26
Per Unit System
100%Zbase
actual%
Z
Z
The percent impedance
e.g. in a synchronous generator with 13.8 kV
as its nominal voltage, instead of saying the
voltage is 12.42 kV, we say the voltage is 0.9
p.u.
-
7/22/2019 Per-Unit System2009-3.ppt
12/26
Per Unit in 3 Circuit
Simplified:
Concerns about using phase or line voltages are
removed in the per-unit system
Actual values of R, XC and XL for lines, cables,and other electrical equipment typically phase
values.
It is convenient to work in terms of base VA (base
volt-amperes)
-
7/22/2019 Per-Unit System2009-3.ppt
13/26
Per Unit in 3 Circuit
,3
3
B
BB
BBB
VSI
IVS
B
B
B
BB
BBB
SV
IVZ
ZIV
2
3/
3
Usually, the 3-phase SB or MVAB and line-to-line VB or kVB
are selected
IB and ZB dependent on SB and VB
-
7/22/2019 Per-Unit System2009-3.ppt
14/26
Change of Base
The impedance of individual generators &
transformer, are generally in terms of
percent/per unit based on their own ratings.
Impedance of transmission line in ohmic value When pieces of equipment with various
different ratings are connected to a system, it
is necessary to convert their impedances to a
per unit value expressed on the same base.
-
7/22/2019 Per-Unit System2009-3.ppt
15/26
Z
VS
ZZZ
old
B
old
Bold
B
oldpu 2
Z
V
S
Z
ZZ
new
B
new
B
new
B
new
pu 2
new
B
new
B
Vbasevoltagenew&
Sbasepowernewon theimpedanceunitpernewthebenewpuZ
old
B
old
B
Vbasevoltage&
Sbasepoweron theimpedanceunitperthebeoldpuZ
1
2
Change of Base
-
7/22/2019 Per-Unit System2009-3.ppt
16/26
2
newB
old
B
old
B
new
Bold
pu
new
puV
V
S
SZZ
old
B
new
Bold
pu
new
puS
SZZ
From (1) and (2), the relationship between the
old and the new per unit value
If the voltage base are the same,
Change of Base
-
7/22/2019 Per-Unit System2009-3.ppt
17/26
General Relations Between Circuit
Quantities
3
2
3
3
3
2
3
3033*303
303
3
30
3
30
303
*3
30
S
V
S
VV
I
V
I
VZ
V
S
Z
VII
Connection
S
V
S
VV
I
V
Z
ConnectionY
o
LLLLo
LL
L
o
LL
D
LL
D
LL
o
D
LL
o
LD
o
LLLL
o
LL
L
LN
Y
-
7/22/2019 Per-Unit System2009-3.ppt
18/26
Base Conversion
2
)(
2
)(
)(
)(
)()( **
newbase
oldbase
oldbase
newbase
oldpunewpu
KV
KV
MVA
MVAZZ
-
7/22/2019 Per-Unit System2009-3.ppt
19/26
Example One: Base Conversion
A 50-MVA, 34.5:161 kV transformer with 10%
reactance is connected to a power system where all
the other impedance values are on a 100 MVA, 34.5
or 161 kV base. The reactance of the transformerunder new base is:
2.0*50
100*1.0
2
)(
2)(
)( newbase
oldbase
newpuKV
KVZ
-
7/22/2019 Per-Unit System2009-3.ppt
20/26
Example Two: Base Conversion
A generator and transformer, as shown below, are to
be combined into a single equivalent reactance on a
100 MVA, 110 kV (high voltage side) base.
-
7/22/2019 Per-Unit System2009-3.ppt
21/26
Advantages
More meaningful when comparing different voltagelevels
The per unit equivalent impedance of the transformer
remains the same when referred to either the primaryor the secondary side
The per unit impedance of a transformer in a three-phase system is the same, regardless the winding
connection The per unit method is independent of voltage
changes and phase shifts through transformers
-
7/22/2019 Per-Unit System2009-3.ppt
22/26
Advantages
Manufacturers usually specify the impedance of the
equipment in per unit or percent on the base of its
nameplate ratings
The per unit impedance values of various ratings ofequipment lie in a narrow range
-
7/22/2019 Per-Unit System2009-3.ppt
23/26
Advantages
Transformer equivalent circuit can besimplified by properly specifying basequantities.
Give a clear idea of relative magnitudes ofvarious quantities such as voltage, current, powerand impedance.
Avoid possibility of making serious calculationerror when referring quantities from one side of
transformer to the other.
-
7/22/2019 Per-Unit System2009-3.ppt
24/26
Advantages
Per-unit impedances of electrical equipment ofsimilar type usually lie within a narrownumerical range when the equipment ratingsare used as base values.
Manufacturers usually specify the impedances ofmachines and transformers in per-unit or percentin nameplate rating.
-
7/22/2019 Per-Unit System2009-3.ppt
25/26
Advantages
The circuit laws are valid in per unit systems,
and the power and voltage equation are
simplified since the factor 3 and 3 are
eliminated in the per-unit systems. Ideal for the computerized analysis and
simulation of complex power system problems.
-
7/22/2019 Per-Unit System2009-3.ppt
26/26