Download Variable Tap Transformer

ECE 530 – Analysis Techniques for
Large-Scale Electrical Systems
Lecture 12: Advanced Power Flow Topics
Prof. Hao Zhu
Dept. of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign
[email protected]
10/12/2015
1
Announcements
•
Midterm on Wed Oct 21, same room; 1 letter-size
formula sheet + regular calculator
•
Review session on Fri Oct 16, same room
•
Homework 4 posted, due Oct 19
2
Transformer Modeling
•
•
•
If transformers have a turns ratio (tap setting) that
matches the ratio of the per unit voltages, then they are
modeled in a manner similar to transmission lines.
However it is common for transformers to have a
variable turns ratio; this is known as an “off-nominal”
tap
Phase shifting transformers are also used sometimes, in
which there is an angle shift across the transformer
3
Transformer Representation
• The one–line diagram of a branch with a variable tap
transformer
m
k
• The network representation of a branch with off–
nominal turns ratio transformer is
t :1
Ik
k
the tap is on
the side of bus k
ykm = gkm + j bkm
Im
k
4
Transformer Representation
•
•
In the p.u. system, the transformer ratio is 1:1 if and
only if this ratio equals the system nominal voltage
ratio
For off-nominal conditions, the turns ratio is obtained
as a ratio of two p.u. quantities
5
Ideal Transformer
• An ideal transformer with t as the tap setting value
Ik = 
1
Ik
t
E k = t Ek 
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Transformer Nodal Equations
•
From the network representation

Ek 
I m  I k   y k m  E m E k   y k m  E m 

t


  y k m  E m
•
 yk m
+  
t


 Ek

Also,
 yk m 
 yk m
1
I k  I k   
 Em   2
t
t 

 t

 Ek

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Transformer Nodal Equations
•
We may rewrite these two equations as
 Ik




 Im
 ykm


2

t
  
 y

 k m



t
ykm 


t 

ykm 

Ek 








E m 
This approach is presented in F.L. Alvarado,
“Formation of Y-Node using the Primitive Y-Node
Concept,” IEEE Trans. Power App. and Syst.,
December 1982
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 –equivalent Circuit for
Transformer Branch
k
 1 1
yk m  2  
t
t
yk m
t
m
 1
y k m 1  
t

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Five Bus PowerWorld Example
With z=j0.1 between
buses 4 and 5, the
y node primitive
with t=1.0 is
  j10 j10 
 j10  j10 


If t=1.1(tap on bus 5)
then it is
PowerWorld Case: B5_Voltage
j9.09 
  j10
 j9.09  j8.26 


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Variable Tap Transformer
•
•
A transformer with a variable tap, i.e., the variable t is
not constant, may be used to control the voltage at either
the bus on the side of the tap or at the bus on the side
away from the tap
This is an example of single criterion control since we
adjust a single control variable– the transformer tap t –
to achieve a specified criterion: the maintenance of a
constant voltage at a designated bus
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Variable Tap Voltage Control
•
•
A typical power transformer may be equipped with
both fixed taps, on which the turns ratio is varied
manually at no load, and automatic on-load tap
changing (OLTC) or variable tap ratio transformers
For example, the high-voltage winding might be
equipped with a nominal voltage turns ratio plus
four 2.5% fixed tap settings to yield  5% buck or
boost voltage capability
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Variable Tap Voltage Control
•
•
•
•
In addition to this, there may be on the low-voltage
winding, 32 incremental steps of 0.625% each, giving
an automatic range of  10%
It follows from the  – equivalent model for the
transformer that the transfer admittance between the
buses of the transformer branch and the contribution to
the self admittance at the bus away from the tap
explicitly depend on t
However, the tap changes in discrete steps; there is also
a built-in time delay in how fast they respond
Voltage regulators are devices with a unity nominal
ratio, and then a similar tap range
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Ameren Champaign Test Facility
Voltage Regulators
These are connected
on the low side of a
69/12.4 kV
transformer; each
phase can be
regulated separately
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Variable Tap Voltage Control
•
•
•
OLTCs (or voltage regulators) can be directly included
in the power flow equations by modifying the
Ybus entries; that is by scaling the terms by 1, 1/t or
1/t^2 as appropriate
If t is fixed then there is no change in the number of
equations
If t is variable, such as to enforce a voltage equality,
then it can be included either by adding an additional
equation and variable (t) directly, or by doing an “outer
loop” calculation in which t is varied outside of the NR
solution
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Outer Loop Tap Control
•
•
•
The challenge with implementing tap control in the
power flow is it is quite common for at least some of
the taps to reach their limits
– Keeping in mind a large case may have thousands of LTCs!
If this control was directly included in the power flow
equations then every time a limit was encountered the
Jacobian would change
– Also taps are discrete variables, so voltages must be a range
Doing an outer loop control can more directly include
the limit impacts; usually sensitivity values are used in
the calculation
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Phase-Shifting Transformers
•
•
Phase-shifters are transformers in which the phase
angle across the transformer can be varied in order to
control real power flow
– Sometimes they are called phase angle regulars (PAR)
– Quadrature booster (British usage)
They are constructed
by include a deltaconnected winding
that introduces a 90º
phase shift that is added
to the output voltage
Image: http://en.wikipedia.org/wiki/Quadrature_booster
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Phase-Shifter Model
•
•
•
We develop the mathematical model of a phase-shifting
transformer as a first step toward our study of its
simulation
Let buses k and m be the terminals of the phase–shifting
transformer  km
The latter differs from an off–nominal turns ratio
transformer in that its tap ratio is a complex quantity,
i.e., a complex number t km e j km
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Phase-Shifter Model
•
•
For a phase shifter located on the branch (k, m), the
admittance matrix representation is obtained
analogously to that for the LTC
Note, if there is a phase shift then the Ybus is no
longer symmetric!! In a large case there are almost
always some phase shifters
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Phase-Shifter Representation
tap is on the side
of bus k
t km e
Ik
k
 km
m
k
one-line diagram of a
branch with a variable
phase shifting
transformer
j km
:1
ykm = gkm + j bkm
Im
m
network representation of a
branch with a variable
phase shifting transformer
20
Integrated Phase-Shifter Control
•
•
•
Phase shifters are usually used to control the real power
flow on a device
Similar to OLTCs, phase-shifter control can either be
directly integrated into the power flow equations
(adding an equation for the real power flow equality
constraint, and a variable for the phase shifter value), or
they can be handled in with an outer loop approach
As was the case with OLTCs, limit enforcement often
makes the outer loop approach preferred
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Two Bus Phase Shifter Example
Top line has
x=0.2 pu, while
the phase shifter
has x=0.25 pu.
1
1

cos  15   j sin  15    j5  ( j4 )(0.966  j0.259 )

j0.2 j0.25
Y12  1.036  j8.864
Y12  
PowerWorld Case: B2PhaseShifter
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Switched Shunts and SVCs
•
•
•
Switched capacitors and
sometimes reactors are
widely used at both the
transmission and
distribution levels to
supply or (for reactors)
absorb discrete amounts of reactive power
Static Var compensators (SVCs) are also used to supply
continuously varying amounts of reactive power
In the power flow SVCs are sometimes represented as
PV buses with zero real power
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Switched Shunt Control
•
The status of switched shunts can be handled in an
outer loop algorithm, similar to what is done for OLTCs
and phase shifters
– Because they are discrete they need to regulate a value to a
•
•
•
voltage range
Switched shunts often have multiple levels that need to
be simulated
Switched shunt control can interact with the OLTC and
SVC control
The power flow modeling needs to take into account the
control time delays associated with the various devices
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