The influence of the stator yoke magnetic induction

The influence of the stator yoke magnetic induction
variation, Bj1, upon the geometric dimensions, cost
and efficiency of the synchronous generator
Elisabeta Spunei/ Eftimie Murgu University
Nicoleta Gillich/ Eftimie Murgu University
Faculty of Electrical Engineering and Informatics
Reşiţa, Romania
[email protected]
Faculty of Electrical Engineering and Informatics
Reşiţa, Romania
[email protected]
Ion Piroi/ Eftimie Murgu University
Faculty of Electrical Engineering and Informatics
Reşiţa, Romania
[email protected]
Abstract—In the designing of the synchronous generator, a size
that characterizes the requests magnetic is the stator yoke
induction magnetic, Bj1. The value of this size depends on the
stator yoke type (with or without ventilation channels), the stator
shape and size notch, the size of the inner diameter, D, and the
external, De one, of the stator. In this paper, we propose to
analyze the influence of the stator yoke magnetic induction
variation, Bj1, upon the geometric dimensions, the total cost and
its efficiency. This analysis is based on a classic designing
program and an optimal designing program, achieved with
MathCad software for synchronous generator of 300 kVA.
Behind the running of the optimal designing program and the
comparison of results with those obtained from the classical
designing we drew computer graphs, from which can be
extracted conclusions regarding the influence of the stator yoke
magnetic induction variation upon the dimensions, the cost and
efficiency of the synchronous generator.
Keywords-component; computer graphics; magnetic flux
density; optimization methods; costs
I.
INTRODUCTION
The current problem of designers, in the designing of
synchronous generators is to obtain a prototype generator with
high technical performance and a minimal cost.
Using the materials with improved characteristics, led to
increased performance and reduced the cost of the synchronous
generator.
Currently, trying through an optimal designing, combined
with use of the materials with the performance characteristics,
as to obtain a generator that would fulfill a specific objective
function, required by the beneficiary.
Based on these considerations, we designed a 300 kVA
synchronous generator using two methods: the classical
method and the optimal method performed using MathCad
software in two methods, having as objective function, a low
cost of the generator design.
The nominal data of the designed and analyzed
synchronous generator are: nominal power Sn = 300 kVA;
nominal voltage Un = 400 V; speed n = 1000 rot./min.; power
factor cosφ = 0.9.
In this paper we propose to analyze the influence of the
stator yoke magnetic induction variation, Bj1, upon the
geometric dimensions of the generator, upon the cost and upon
to his efficiency.
Following the comparing the results obtained from the
classical designing with those of the optimal designing, we
constructed graphs through which are analyzed, for on number
of 200 values around from classical designing, variation of
different sizes of interest [4].
II. THE ANALYSSIS OF THE STATOR YOKE
MAGNETIC INDUCTION VARIATION, BJ1, UPON THE
GEOMETRIC DIMENSIONS
The magnetic induction of the stator yoke, Bj1, is a pretty
significant size, which defines the magnetic synchronous
generator request. That size is dependent on the inner diameter,
D and the external one, De, of the stator, the existence and size
of ventilation channels, the size and shape of the notch.
The values of the stator yoke magnetic induction, Bj1, must
be between 1 ÷ 1.3 [T] for the generators without ventilation
channels, they can reach up to 1.8 [T] in the case of ventilation
channels [1], [3].
At the design stage, after determining the amounts of the
electromagnetic requests (the current blanket, A, and the air
gap magnetic induction, Bδ), the inner diameter size, D and
external, De, it is chosen the type of notch and related
isolations, it is determined the number of conductors, their
section, width, bc and height hc of notch, it is calculated the
height of the stator yoke, hj1, ant it is calculated the stator yoke
magnetic induction, Bj1, with relation [2]:
B j1 

2  k Fe  lFe1  hj1
(1)
where Φ is the magnetic flux at full load, kFe is the packing
coefficient of the core, lFe1 is the length of the stator iron, h′ j1 is
the stator yoke height calculation. For the generators without
axial ventilation channels h′j1 is equal to the height stator yoke
hj1. The calculated value within the limits specified above must
be checked.
The value of the stator yoke magnetic induction, Bj1,
resulted from the classical designing, has the value Bj1g = 1.21
[T], and following the optimal designing, it has the value
Bj1 opt = 1.569 [T], that is approximately 30% higher.
A. The influence of the stator yoke magnetic induction
variation, Bj1, upon the external diameter of the stator and
the total length of the generator.
The geometric dimensions of the synchronous generator is
represented by external diameter, De, of the stator and the total
length of the generator, Le, which depends on the stator iron
geometric length, lg (the package of sheet and radial ventilation
channels) and the length of the front heads, lfa, of the windings.
Because in the relation for calculating of the stator yoke
magnetic induction, Bj1, the height value of the stator yoke,
hj1, is involved it results that the value of the external
diameter, De, of the stator is influenced by the value of the
magnetic induction from the stator yoke.
decreased by 4.845% towards the value obtained by classical
design.
Following of the optimal design it results a small decrease
in the value of the stator external diameter, while its length
remains constant.
III. THE ANALYSIS OF THE STATOR YOKE
MAGNETIC INDUCTION VARIATION, BJ1, UPON THE
COSTS OF THE SYNCHRONOUS GENERATOR
The cost of the synchronous generator, Ct, consists of the
manufacturing cost, Cf, and the operating cost, Ce, throughout
its normed life.
In the manufacturing cost of the synchronous generator, the
largest share is the mass of the active materials and its total
mass. The operating cost is preponderantly influenced by the
active material losses which are the largest total losses.
A. The influence of the stator yoke magnetic induction
variation, Bj1, upon the mass of the synchronous generator
The total mass, mt, of the synchronous generator is
composed from the active mass of iron, mFe, the stator winding
copper mass, damping and excitation windings, mCu, and the
mass of the related components (bearings, roller, mounting
plates, etc.).
The influence of magnetic induction variation of the stator
yoke, Bj1, upon the active masses and the total mass is shown
in Fig. 2.
In Fig. 1 we present the influence of the stator yoke
magnetic induction variation, Bj1, upon the external diameter,
De, of the stator and upon the total length of the generator, lFe.
The values obtained are reported in units [u.rap], to the values
obtained from the classical designing.
From the analysis we found that the stator yoke magnetic
induction variation, Bj1, does not influence the length of the
synchronous generator.
Figure 2. The influence of the stator yoke magnetic induction upon the mass
of the synchronous generator
In comparison with the values obtained from the classical
designing, for the optimal designing has led to a decrease of
about 8% of the total mass, mt, of the synchronous generator.
The mass of copper, mCu, showed a slight increase (2.25%) and
the iron mass, mFe, presents a decrease with 10.67%.
For values of the stator joke magnetic induction smaller
than that resulted by classical method, the copper mass remains
aproximatively constant, while the iron and total mass increase.
Figure 1. The influence of the stator yoke magnetic induction upon the
geometric dimensions of the synchronous generator
We notice that the value obtained by induction from the
stator yoke optimal design, the external-diameter, De,
These increases are determined by the increase of the stator
external diameter, previously analyzed. In this graph the
reported units [u.rap] are used.
B. The influence of the stator yoke magnetic induction
variation, Bj1, upon the synchronous generator losses
The total losses pt, from the generator are composed by
iron losses pFe, copper losses pCu and supplementary losses in a
smaller degree.
For the optimal value of the stator yoke magnetic induction,
Bj1opt = 1.569 [T], it results a decrease of the manufacturing
cost, Cf, with 7.9%, a very small increase of the operation cost,
Ce, with 0.46% and a .decrease of the total cost, Ct, with 2.3%
over the costs result from classic design, when the stator yoke
magnetic induction value was Bj1g = 1.21 [T].
Iron losses pFe, depend on the square value of stator yoke
magnetic induction, given by relation:
1,3
 f 
p j1  k j  pst     B j12  m j1
 50 
(2)
where: kj coefficient of yoke losses increase, pst specific losses
in stator sheet plate, f real frequency and mj1 stator joke mass.
In the Fig. 3 we present the influence of the stator yoke
magnetic induction variation, Bj1, upon the iron loss, pFe, the
losses in copper, pCu, and the total losses, for the synchronous
generator, unit sizes being reported, [u.rap.] .
Figure 4. The influence of the stator yoke magnetic induction upon the costs
of the synchronous generator
For the optimal value of the stator yoke magnetic induction,
Bj1opt = 1.569 [T], it results a decrease of the manufacturing
cost, Cf, with 7.9%, a very small .increase of the operation cost,
Ce, with 0.46% and a .decrease of the total cost, Ct, with 2.3%
over the costs result from classic design, when the stator yoke
magnetic induction value was Bj1g = 1.21 [T].
IV. THE ANALYSIS OF THE STATOR YOKE
MAGNETIC INDUCTION VARIATION, BJ1, UPON THE
COSTS OF THE SYNCHRONOUS GENERATOR
Figure 3. The influence of the stator yoke magnetic induction upon the losses
of the synchronous generator
Compared to the classical value of the stator yoke magnetic
induction (Bj1g = 1.21 [T]), following the optimal design (Bj1 opt
= 1.569 [T]), the iron losses, pFe, increased by approximately
18.2 %, so it is a substantial increase.
In comparison with the same reference data, the copper
losses, pCu, increased by 1.36% and the total losses, pt,
increased by 2.9%.
The main performance of the synchronous generator the
efficiency is calculated with the relation [2]:

S N  cos 
S N  cos   pt
(3)
where Sn is the generator apparent power, cos φ is the power
factor and pt are the total losses of generator.
The values of the stator yoke magnetic induction, Bj1,
smaller than those result from classic design lead to a
significant decrease of the iron losses and a lower decrease of
the total losses of the synchronous generator.
C. The influence of the stator yoke magnetic induction
variation, Bj1, upon the costs of the synchronous
generator
Because after the optimal design, the total mass of the
generator decreased, we expect that the manufacturing costs,
Cf, to be lower than the results of the classical designing.
The influence of the stator yoke magnetic induction
variation, Bj1, upon the cost of manufacturing, Cf, the operating
cost, Ce, and the total cost, Ct, is shown in Fig. 4, The values
are in reported units, [u.rap.], reported to the values resulted
from the classical design.
Figure 5. The influence of the stator yoke magnetic induction upon the
efficiency the synchronous generator
Fig. 5 presents the influence of the stator yoke magnetic
induction variation Bj1, upon synchronous generator relative
efficiency the values are in reported units [u.rap.] calculated as
ratio between that obtained by the proposed method and the
classical one.
For the optimal magnetic induction value of stator joke,
Bj1opt = 1.569 [T], occurs a diminished efficiency diminish with
0.165% comparing to the one obtained by classic design, Bj1g =
1.21 [T].
V.
CONCLUSION
Analyzing the graphs presented in this paper it can be
concluded that the stator yoke magnetic induction, Bj1, as
main input variable in the design process, influence the
geometric dimensions, cost and efficiency of the synchronous
generator.
Hence, higher values of the stator yoke magnetic
induction, lead to a constant maintaining of synchronous
generator length and a reduction of stator’s external
diameter De.
Considering as analysis domain for the stator yoke
magnetic induction, the interval 1÷1.569 [T], decreases of the
external diameter, De, of the stator, is of approximative 9%.
Thus, for the domain of analysis 1 ÷ 1.569 [T] of the stator
yoke magnetic induction, Bj1, the iron losses pFe, increase
approximately 30%, the total losses, pt, increase approximately
4.2%, while the copper losses, pCu, have an insignificant
increase.
The optimal value of the stator yoke magnetic induction,
Bj1, led to a lower decrease of the total cost of the generator,
and on the entire range of analysis, the decrease is
approximately 4.1%.
The increase of the value of the stator yoke magnetic
induction, Bj1, leads to lower efficiency, but the decrease is
insignificant (0.165 %).
It follows that, to achieve the chosen objective function
(cost of the synchronous generator as small) the value of the
stator yoke magnetic induction must be large.
Through this analysis, we contribute to restricting the range
of variation of the stator yoke magnetic induction in the range
1.2 ÷ 1.57 [T], the maximum values ensuring the successful
achievement of the objective function.
REFERENCES
The decrease of stator’s external diameter De, leads to a
significant decrease, especially of the iron mass.
[1]
However, an important mass reduction for the whole
assemble is attended (8%).
[2]
[3]
On the entire domain of analysis above mentioned, the
mass of iron, mFe, presents a decrease of approximately with
20%, the total mass, mt, decreas approximately with 16.2%,
while the mass of copper, mCu, increases with 2.26%.
But the increase of stator joke magnetic induction value Bj1
has negative influence upon losses, conducting to increased
values especially for iron losses.
[4]
[5]
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