Download an investigation on flux density of three phase distrubuted air

AN INVESTIGATION ON FLUX DENSITY OF THREE PHASE
DISTRUBUTED AIR-GAP 3-5 LEGGED SHUNT REACTOR
1
EMRE KURT, 2AHMETYIGIT ARABUL, 3IBRAHIM SENOL, 4FATMA KESKIN ARABUL
1,2,3,4
Yildiz Technical University
E-mail: [email protected], [email protected], [email protected], [email protected]
Abstract- Nowadays, transmission and distribution lines provide to transport energy from production area to usage area.
However, the reactive power balance on the long transmission lines do not provide, the quality of the power transmission and
the efficiency of power line is low. To achieve this situation, reactive power compensation is needed and we provide that to use
shunt reactors. The design state of shunt reactor is important to achieve this mission. It’s important to define the parameters of
shunt reactor such as yoke heights and air-gap length to set inductance value of reactor. In this study, the important parameters
of reactor is calculated and use this parameters to design a reactor. Modeled reactor isanalyzed with Finite Element Method
(FEM). Shunt reactor core’s air-gap is distributed for examine the effect of fringing by leakage flux lines and inductance
values. Shunt reactor’s main values which are used by Turkish Electricity Transmission Company (TEIAS) is selected. 3 and
5-legged core design reactors simulation results are discussed considering the TEIAS specifications.
Index Terms- Shunt reactor, core design, distributed gapped-core,fringing effect
system. This defined as Ferrati effect which is the
operating voltage increase along the transmission
lines. Shunt reactor consumed lagging reactive current
and reduces the leading capacitive charging current of
the line. Consequently, reduces the voltage rise.
Another type of over voltage is caused by the
interaction between line capacitance and any saturable
portion of system’s inductance. When switching a
transmission line which is terminated with
transformer, the voltage at the end of the line can rise
to a needed value to saturate the transformer’s
inductance. Interaction between this parameters of the
line can generate harmonics, causing over-voltage. To
reduce these negative situations, a low non-saturable
inductance can be connected parallel to transformer’s
inductance. Shunt reactors used to provide this
inductance for transmission lines [1]-[4]. Iron core
reactors, have same construction with the
transformers. It can be said shunt reactors are
transformers without secondary windings. To reduce
reactive power, magnetic circuit reluctance of shunt
reactor should be increase. To achieve this value,
distributed air-gap method have been used. Air-gap is
the dominating parameter to determine reluctance
because of core’s magnetic permeability [1].The
distributed air-gap method can be used for reduce
leakage flux. Eddy losses are decrease and
ampere-turn efficiency increase [1,3].
I. INTRODUCTION
Reactors are the most essential and supplemental
component of transmission and distribution lines such
as capacitors. According to usage purpose, reactors
can connect shunt or series to the network. Reactors
are connected either singularly or in conjunction with
other basic components. Reactors are used for many
purposes in transmission and distribution lines such as
limiting fault current, harmonic filtering, reactive
power compensation, reduction of ripple currents, load
balancing [1]-[2]. High voltage transmission lines
especially long ones, generate a lot of leading reactive
power when the line loaded lightly. Conversely, they
consume a lagging reactive power when the line
loaded weighty. As a result, if the balance of reactive
power is not provided, the voltage of line won’t be at
the rated voltage. To provide reactive power balance,
compensation procedure
must be applied at the
transmission and distribution lines for given working
conditions [2]. Reactive power balance depends on
two parameters of the line. These are charging
capacity of line and line inductance. If line inductance
is bigger than the charging capacity of line , reactive
power balance will be negative. In this case, reactive
power should be injected to the line. Conversely, if
charging capacity of the line is bigger than the line
inductance, reactive power balance will be positive
and to achieve this situation line should be
compensation. For heavy loaded lines, the reactive
power balance is negative and it needs capacitive
compensation which isprovided by shunt reactor
generally [1]-[3]. The lightly loaded transmission
systems can cause two types of overvoltage in the
system because of large inherent capacitance. That can
be controlled by using shunt reactors. The first type of
over voltage created by the leading capacitive
charging current of a lightly loaded transmission line
which flows through the inductance of the line and the
Fig. 1: Distributed Air-Gap Shunt Reactor
Proceedings of The IRES 21st International Conference, Amsterdam, Netherland, 25th December 2015, ISBN: 978-93-85832-79-6
91
An Investigation On Flux Density Of Three Phase Distrubuted Air-Gap 3-5 Legged Shunt Reactor
height (Hw) multiply we will find window area (Aw)
of reactor. In this study, Hw / Bw ratio selected 2.1. The
distance from the winding to the middle and side legs
as well as to the top and bottom yokes ( Bi, Bs, Hu, Hd)
is 60 cm. And values of 0.6, 3.2 (A/mm2) are for
windings filling factor (Ku) and current density (J).
Doing after all calculations, parameters of designing
reactor are founded. Additionally, the yoke is a
rectangular with a width (dy) equal to the outer
diameter of the leg (Doc) and a thickness (Hy) of 80 cm,
window width (Bw) and window height (Hw) are 330
cm and 693 cm.
Similar with transformers, the flux density at the rated
voltage depends on the winding turns.Laminated
yokes provide an extra path for leakage flux and limit
the level of leakage flux which passing through the
reactor’s core. At the present time, shunt reactors are
designing with distributed air-gaps. To decrease
fringing flux which are enter and exit moves along the
air-gap, these air-gaps distributed along legs [1].
To determine air-gaps, we need values of reactor’s
reactive power, maximum flux density, frequency,
inductance value which is increased cause of fringing
effect, number of turns and stored energy between
air-gaps. In this study, we simulated reactor which is
changed air-gap numbers and observe how this change
effect reactor [5].
II. STRUCTRE OF MODELING REACTOR
(1)
K = 4.44 ⋅ f ⋅ 103 ⋅ K t
(2)
Φm
Kt = (
)
I e⋅N
(3)
r ly 0
r ay 0
=
d
y
L
Ag
μ0 ⋅( )
lg
L ol
=
(11)
2 ⋅ r lyw
r ly0
(12)
Fig. 2: Dimensions of 5-legged Reactor Core
The parameters of the reactor are calculated according
to the equations given above. Table 1 shows the
parameters of the 3 phase shunt reactors.
Q
(5)
After calculation these parameters, section area of the
leg (Ai) and diameter of the leg can be find.
d 2
Ai = π ⋅ ( )
2
Sy
(4)
π 2
( ⋅B ⋅ f )
μ0 m
Bm
(10)
rly0 and ray0 that given parameters in equation 10 and
11 are ratios for 5 legged core and generally select
between 2-3. Values of d0, dy, S0, Sy are shown in Fig.
2.
To calculate Ag and lg values, we use max magnetic
flux (Bm), frequency and magnetic permeability of air
(μ0) in the formula given below.
Φm
=
S0
Rated voltage (Ve), rated current (Ie), frequency (f),
equivalent maximum magnetic flux (Φm), integers
which are depend on transformers structure (Km and
K), number of turns (N) as defined in equations given
above. Winding turns can be calculate from value of
reactor’s inductance and Ag / lg ratio. Ag is air-gap area
and lg is total air-gap length. In this study, this ratio
selected as 1.1 considering energy density values.
Ai =
(9)
d0
V ⋅2e
L =
ω ⋅Q
Ag ⋅ l g =
(8)
I e⋅ N
Aw =
K u⋅J
In Turkey's transmission lines standards, reactor's core
must be 5-legged. For this reason, 5 legged core design
is done and essential equations for this are given in
Equation 10 and 11.
In this study, three phase shunt reactor designed for the
values of rated voltage value as 420 kV and rated
reactive power as 250 MVAr. Iron’s reluctance and
copper losses are neglected. Equations which are used
to calculate reactor modeling are given below.
N =
Aw = H w ⋅ B w
Table I : Parameters of modeled reactor
(6)
(7)
When reactor’s window width (Bw) and window
Proceedings of The IRES 21st International Conference, Amsterdam, Netherland, 25th December 2015, ISBN: 978-93-85832-79-6
92
An Investigation On Flux Density Of Three Phase Distrubuted Air-Gap 3-5 Legged Shunt Reactor
air-gap and there are many leakage flux. These
leakage flux creates extra losses in the core. To
observe these situations andsee mesh operations
clearly, modeled reactor is simulated as shown in Fig.
4.
III. MODELING OF THE REACTOR
Three-dimensional FEM using for investigate a
reactor which is modeled in section two and using
assumptions given below:
1) Entire model of reactor is designed in Maxwell.
2) This study does not investigate Eddy losses, these
losses neglected. Magnetostatic equations is used for
the inductance calculation.
Accuracy and validity of FEM is proven by recent
projects [6]-[11]. According to this validity and
accuracy, a three-dimensional model is created. , The
Poisson Vector Equation (Eq.12) is solved to meshing
the space of the problem and presuming linearity [12].
⎛1
ur ⎞ ur
∇ × ⎜ μ ⋅ μ ∇× A ⎟ = J
⎝ 0 r
⎠
Fig. 4: Meshed Model of 3-Legged Reactor Core Model
(13)
After mesh operations, rated current (Ie) is applied to
reactor coil and the model is simulated. As a result of
applied current through the coil, magnetic flux lines
and leakage flux are shown in Fig. 5. These leakage
fluxes cause additional losses on the reactor.
In Eq. 13,A is the magnetic potential vector and µr is
the relative permeability.After the simulation,
parameters such as flux density, magnetic flux density
and magnetic potential vector are calculated easily. By
the Eq.14,15,16which are given below, the density of
the energy in the problem spaceand the inductance of
the winding can be calculated.
wm =
1 uur ur
H⋅B
2
Wm =
∫∫∫ Wmdv
L =
2⋅Wm
Im
(14)
(15)
(16)
Where Wm, wm, B and H represent the magnetic
energy, the density of the energy per volume, flux
density vector, and magnetic field strength. During the
FEM, the maximum current is applied, and in order to
achieve accuracy, smaller meshes are used in every
part of running program [9].
Fig. 5: Magnetic Flux Lines
To reduce leakage fluxes and losses, total air-gap
length distributed along the core legs equally. In this
study, six different numbers of air-gaps as 1, 10, 20,
30, 40, 50 applied and simulated to see the effects of
air-gap number on the flux distribution in the reactor.
Air-gaps cause to reduce leakage fluxes and
inductance value. As a result of this simulation, the
relation between the number of air-gaps and the
inductance value is shown in Fig.6. These results are
expected such as mentioned above.
IV. SIMULATION
A. 3-Legged Core Design
According to calculations in section 2 and 3, 3-legged
modeled reactor is shown at Fig.3.
6.5
6
Inductance value
5.5
5
4.5
4
3.5
3
2.5
0
Fig. 3: 3-Legged Modeled Shunt Reactor
5
10
15
20
25
30
Number of air-gaps
35
40
45
50
Fig. 6: Inductance Values of 3-Legged Reactor
Air-gaps are used to calibrate magnetic circuit
reluctance and inductance value. However, these
air-gaps cause some disadvantages. In non-distributed
air-gap models, a lot of energy accumulate in the
In Fig.7 includes magnetic flux lines at six different
values of air-gaps and see clearly how to reduce
leakage fluxes at the air gaps and legs edges.
Proceedings of The IRES 21st International Conference, Amsterdam, Netherland, 25th December 2015, ISBN: 978-93-85832-79-6
93
An Investigation On Flux Density Of Three Phase Distrubuted Air-Gap 3-5 Legged Shunt Reactor
Fig. 8: Meshed Model of 3-Legged Reactor Core Model
In Fig.8, 5-legged reactor core is shown which is
meshed. 5-legged core creates from 3-legged core how
add two additional legs on sides. These additional legs
provides an extra path for flux lines and fluxes that
through in these paths reduce density at the main legs.
As a result, leakage and losses are reduced. Inductance
value is decreased as expected and this variation is
shown at Fig.10.
Fig. 7: Magnetic FluxDensity Changes of 3-Legged Reactor
B. 5-Legged Core Design
Turkish Electricity Transmission Company (TEIAS)
is the authorized company to operate transmission
lines in Turkey. According to TEIAS's specifications,
reactor's core must be 5-legged. For this reason,
5-legged core design is done.
Fig. 9: Magnetic Flux Density Changes of 5-Legged Reactor
Fig.9 include flux lines which are different values of
air-gap. When the Fig. 6 and Fig.10 analyzed, it is
observed that 5-legged cores inductance values a bit
more than 3-legged core. However, leakage fluxes a
bit less than 3-legged core.
9
Inductance value
8
7
CONCLUSION
6
In this study, design and simulation progress of shunt
reactors that is the most essential and supplemental
part of transmission and distribution lines are studied.
Shown the effect of air-gaps numbers change on the
reactor is purposed. Simulations shows that air-gaps
directly affectsthe inductance value and magnetic
circuit reluctance. And also it is observed in some
results that core design affects the leakage fluxes and
5
4
3
0
5
10
15
20
25
30
Number of air-gaps
35
40
45
50
Fig. 10: Inductance Values of 5-Legged Reactor
Proceedings of The IRES 21st International Conference, Amsterdam, Netherland, 25th December 2015, ISBN: 978-93-85832-79-6
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An Investigation On Flux Density Of Three Phase Distrubuted Air-Gap 3-5 Legged Shunt Reactor
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the inductance values of reactor.
Difference between 3 and 5-legged cores are leakage
flux and inductance value. 3-legged core has better
inductance value than 5-legged core but 5-legged core
has small leakage fluxes than 3-legged core. For these
reasons, TEIAS would rather 5-legged core shunt
reactors in Turkey power transmission systems. As a
result, 3 or 5-legged cores will select application
specifications.
For future study, cost function of reactor will calculate
according to reactor dimensions, using materials and
reactor’s losses. By calculate cost function, efficiency
of reactor will be increase. Conversely, losses of
reactor will be decreased.
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M. Heatcote , '' J&P Transformer Book '' , 2007
Tao Zheng,Zhao, Y.J.; Ying Jin; Chen, P.L.; Zhang, F.F.,
“Design and Analysis on the Turn-to-Turn Fault Protection
Scheme for the Control Winding of a Magnetically Controlled
Shunt Reactor”, IEEE Transactions, Volume:30, Issue:2, April
2015
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Turan,
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HavaAralığıBulunanReaktörÇeşitlerininİrdelenmesiveBirProt
otipiçinUygulamaÖrneği”, KocaeliUniversitesi, 2010
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Proceedings of The IRES 21st International Conference, Amsterdam, Netherland, 25th December 2015, ISBN: 978-93-85832-79-6
95