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Considering Environmental Health and Energy Resources to Design
Transformers
Article in Current Signal Transduction Therapy · April 2019
DOI: 10.2174/1574362414666190417143157
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Current Signal Transduction Therapy, 2020, 15, 284-293
RESEARCH ARTICLE
Considering Environmental Health and Energy Resources to Design
Transformers
Hamid Davazdah-Emami1, Emad Roshandel1,* and Mohammad Nikkho2
1
Research and Development Department, Eram Sanat Mooj Gostar Company, Shiraz, Iran; 2School Electrical and
Computer Engineering, Shiraz University, Shiraz, Iran
ARTICLE HISTORY
Received: December 29, 2018
Revised: March 17, 2019
Accepted: March 21, 2019
DOI:
10.2174/1574362414666190417143157
Abstract: Background: Environmental health has become a worldwide debating issue among researchers, scientists, and governments. Although fossil fuels have been the greatest energy resources for the human, their consumption leads to injecting greenhouse gases into the air, which
can affect the existence of all living species dramatically. In fact, fossil fuels consumption pollutes
the environment because of the injection of greenhouse gases which result in global warming. On
the other hand, reductions in fossil fuel and drinking water resources have highlighted the importance of energy management and loss reduction in brand-new management strategies and manufacturing methods. Distribution transformers are one of the most used devices in power distribution networks. Hence, it seems to be logical to consider transformer losses as a definitive factor in
design and construction procedures. Furthermore, such design procedures require powerful tools
to solve complex non-linear equations and find the best solutions in the shortest time. Researchers
and scientists have always had a great challenge regarding finding the best solutions for their
analysis. In actuality, it is hard to solve complex non-linear problems by means of traditional calculation methods even if a researcher employs a powerful computer. For this reason, metaheuristic optimization algorithms have found great popularity among scientists. These algorithms
seek the best solution through a solution pool at an appropriate pace. Therefore, a researcher can
save more time and energy in solving an intricate problem.
Objective: In this paper, the authors aim to modify the conventional Teaching-Learning Based
Optimization (TLBO) algorithm to design an optimum distribution transformer by consideration
of the transformer Total Owning Cost (TOC). The TOC consists of operational and initial manufacturing costs of a distribution transformer. The used raw materials affect the manufacturing cost
and it would be decreased if the copper and iron volumes are reduced in the construction instruction. However, the operational cost that includes iron and copper losses must not be forgotten in
design analysis. Indeed, loss consideration is of great significance to keep energy from frittering
away and as a result, protects environmental resources.
Materials and Methods: A novel approach based on an optimization technique for distribution
transformer design problems is presented in this paper. The entire expenses of a transformer consist of transformer construction and operating costs. In other words, by reducing copper and iron
volumes, the initial cost of a transformer will be decreased. Due to the electromagnetic and electrical losses in transformers, the initial cost of a transformer is not its entire design problem and
the operating cost must be considered in the design algorithm. Appropriate limits on efficiency,
voltage regulation, temperature rise, no-load current and winding fill factor are the constraints on
the transformer design problems in the international standards. With respect to these constraints,
the transformer designer can minimize the volume of the core and windings. In this paper, the
Conditional Teaching-Learning Based Optimization (CTLBO) algorithm determines the appropriate transformer properties, while transformer construction cost and its operating cost are selected
as an objective function for optimization method. In order to attain a suitable voltage regulation,
transformer impedance is chosen as an optimization constraint.
Results: The result of the paper demonstrates the proposed algorithm ability in reducing the Total
Owning Cost (TOC) during transformer lifetime, which could be useful for energy distribution
companies. In addition, the result analysis proves that the total losses of the transformer are reduced by the proposed approach in comparison to conventional design techniques. Then, more energy will be saved in the power grid when the proposed transformer is utilized in the power network.
Conclusion: In this paper, a suitable method to design an optimum distribution transformer is
proposed which enables manufacturers to construct their product based on the proposed method.
In this way, it can be claimed that not only more money will be saved during the transformer operation, but also the energy consumption will be decreased drastically. Therefore, world resources
will remain for future generations.
Keywords: Energy reservoirs, environmental concerns, distribution transformer design, optimization, TLBO, total owning cost.
1574-3624/20 $65.00+.00
©2020 Bentham Science Publishers
Considering Environmental Health and Energy Resources
1. INTRODUCTION
The distribution transformer is the most expensive component of the power distribution system. Optimum design of
this component lowers the total costs of the power distribution system. Total Owning Cost (TOC) of transformers includes the manufacturing cost (initial cost) and operating
cost. Design technique plays an important role in achieving a
sufficient transformer TOC. By making a suitable equivalency between the transformer costs, an economically efficient
transformer is obtained.
Furthermore, copper and iron are two main fundamental
materials used in the structure of the transformer [1]. Copper
is the most used type of conductor because of its conductivity capability and its lower cost in comparison to gold [2].
However, the copper mines are limited to several countries
and its high consumption will lead to increasing the copper
cost in the future [3]. On the other hand, iron and its alloys
can be found everywhere in all devices. Although the available iron mines are much greater than all other metals on
earth, this level of consumption will decrease the abundance
of the iron and bring about some challenges in the iron provision for industries [4]. Therefore, copper and iron usage
reduction not only protects the environment but also reduces
difficulties to live on earth for the next generation. On the
other hand, the optimum consumption of such valuable materials leads to saving more energy and consequently more
money.
There are some international standards and transformer
user specifications to define the transformer characteristic in
each voltage and power level [5]. Most of the available distribution transformers are designed based on these instructions. Recently, researchers present novel works of literature
to improve the transformer construction technology and
methods [6-14] to diminish the transformer TOC. Moreover,
in some pieces of literature authors have analyzed transformer lifetime, losses, and elements properties in various operating and climatic conditions [15-17]. These researches need to
optimize the transformer manufacturing and operating costs.
For instance, in [8] a high-frequency transformer has been
designed by applying fuzzy logic to decrease the manufacturing cost. A new approach which integrates multiple nonlinear constrained optimization algorithms in conjunction
with an improved heuristic algorithm has been presented in
[9]. Also, in [10], Phophongviwat by applying the genetic
algorithm as an optimization method proposed a low loss
transformer by investigation of the temperature effect. Constraints of the design problem will be maximized voltampere or minimized losses when the transformer dimensions are fixed. In these cases, design problems are formulated in Geometric Programming (GP) format, which has been
introduced in [11]. A new methodology for the inductor and
transformer designs to meet all performance requirements
and concurrently minimize the total weight has been presented in [12]. In [13], the distribution transformer cost has been
evaluated with incorporating environmental cost.
*Address correspondence to this author at the Research and Development
Department, Eram Sanat Mooj Gostar Company, Shiraz, Iran;
E-mail: e.roshandel@esmg.co.ir
Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
285
Meta-heuristic algorithms have played an eminent role in
finding suitable solutions in a large number of complex
mathematics and engineering problems [18-24]. For instance, harmony search algorithm has been exerted in [14] to
find the optimal cost for the water distribution network. Hybrid particle swarm optimization has been used to solve the
constraint problem in [19]. Power systems calculation is one
of the most intricate problems which electrical engineers
must consider in the analysis; where meta-heuristic algorithms have paved engineers’ way to find optimum solutions
in minimum time and acceptable accuracy [21-23]. Besides,
these algorithms have been applied to electrical and transformer design problems to seek optimum answers for machines elements with some constraints and uncertainties. For
example, in [24] two different optimization algorithms with
three objective functions consists of efficiency and cost have
been used to determine suitable parameters for an induction
machine design problem.
The consideration of the operating cost of a transformer
is of great importance to determine the distribution transformer characteristics during its lifetime. In this paper, the
proposed Conditional Teaching-Learning Based Optimization (CTLBO) algorithm determines the best distribution
transformer characteristics by consideration of the permissible boundary for the transformer impedance, while the
equivalency between the manufacturing cost (minimum iron
and copper masses) and operating cost (minimum electrical
and magnetic losses) of a transformer is established during
the lifetime. It must be noticed that because of the fact that
earth available resources are limited to the current mines,
any optimization in the construction of the devices will extend the opportunity of the human dwelling on the planet.
Therefore, transformer materials optimization leads to a huge
amount of iron and coppers frugality as two definitive elements in human life.
2. MATERIALS AND METHODS
2.1. Core Design Procedure of the Distribution Transformer
Electrical and magnetic investigations in a transformer
design approach are two essential aspects in the design procedure. When these parts are designed optimally, energy
losses will be decreased inherently. Sawhney presented the
distribution transformer design method in the study [25]. The
core design is the first step of the design process pursuant to
this design strategy when transformer nominal power and its
nominal primary and secondary voltages are specified.
When apparent power is defined by the consumer, the
transformer voltage per turn value is calculated by means of
the following (Eq.1):
Et = K Q
(1)
where the constant value of K is chosen from Table 1. Table
1 gives constant values of K for different types of transformers, for instance, 0.45 is the K value for a three-phase core
type distribution transformer [25]. Core flux is an indispensable value for finding the area of the core while Eq. (2) and
(3) calculate the flux and core area, respectively.
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Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
Table 1.
Davazdah-Emami et al.
Values of K coefficients For different transformer types.
Table 2.
Values of K Coefficients
Transformer Type
0.6 – 0.65
Three phase core type (power transformer)
0.45 – 0.5
Three phase core type (distribution)
1.2 – 1.3
Three phase Shell type
0.75 – 0.8
Single phase core type
1 – 1.1
Single phase shell type
Kc values for each shape of transformers.
Core Arrangement
Square
Two Stepped
Three Stepped
Four Stepped
Kc value
0.45
0.56
0.6
0.62
Et
4.44 f
Ai = ! m Bm
!m =
(2)
(3)
The diameter of the circumscribing circle is another
needed characteristic of the core in the design procedure.
This parameter calculated by (4), where Kc is a constant value. It depends on the number of core steps. There are different Kc values for each shape of the transformer which are
shown in Table 2 [25] (Eq.4).
d=
Ai
Kc
(4)
Figure 1 shows the two stepped transformer core. Following formulas determine steps dimensions, to acquire
maximum area for a given diameter (Eqs.5, 6).
a = 0.85d
(5)
b = 0.53d
(6)
Transformer output power equation that is shown in (7)
depends on the window area. So by means of (7), the area of
the window is computed. Determination of window dimensions requires window space factor (Kw) which is calculated
by (8). Current density is one of the variables in (7); international standards determine the suitable current density of the
transformer by considering its core materials and substances
(Eqs.7, 8).
(7)
Q = 3.33 fBm! ( K w Aw ) Ai " 10#3
Kw =
30 + (voltage
of
Z
HV side
in(kV ))
(8)
⎧8 ⎯⎯⎯→ Q < 20 kVA
⎪
where
Z = ⎨10 ⎯⎯
⎯→ 20 kVA < Q < 1000kVA
⎪
where
⎩12 ⎯⎯⎯→ Q ≥ 1000kVA
where
The ratio of the height to width plays an important role in
the transformer design procedure. If the ratio of height to
width in the transformers is greater than 2.5, the mechanical
Fig. (1). Two stepped core. (A higher resolution / colour version of
this figure is available in the electronic copy of the article).
strength would be decreased because of the increment in the
height of a transformer. On the other hand, the Hw/Ww reduction leads to winding expansion in the horizontal direction
which increases leakage inductance in the transformer windings. For these reasons, Transformer designers usually assume that the ratio of height to width of the window is 2.5
(Hw/Ww=2.5) [25]. Then, by applying this ratio to (9) window dimensions are achieved in the design process (Eq.9).
Aw = H wWw
(9)
In transformer using hot rolled silicon steel, the area of
the yoke is taken as 1.2 times that of the limb as follow in
(10), so maximum flux density in the yoke is computed by
(11) (Eqs.10, 11).
Ay = 1.2 Ai
(10)
Bm
1.2
(11)
By =
According to [25] stacking factor is assumed 0.9; therefore, the gross area of the yoke is calculated by (12). Assum-
Considering Environmental Health and Energy Resources
Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
287
Fig. (2). Cross sectional view of a three-phase transformer. (A higher resolution / colour version of this figure is available in the electronic copy of the article).
ing that the depth of yoke is equal to d, so the height of the
yoke can be determined as (13) (Eqs.12, 13).
AyG =
Hy =
Ay
0.9
AyG
Dy
TLV =
VLV
Et
(17)
I LV
(18)
(12)
a LV =
(13)
When the bare conductor dimensions are clear, dimensions of the insulated conductor are obtained by referring to
the table of conductor dimensions. After that, conductor layers are determined by considering the constraint of the window dimension. The distance between the winding and core,
which is called an oil duct, must be considered to provide
appropriate conditions for the oil circulation and transformer
cooling process. The thermal constraints are solved by
choosing 6mm distance for oil ducts in the construction of
the distribution transformers [25]. The height of the LV
winding can be calculated by (19), where rond is the rounding operator (Eq.19).
Height, width, and depth of frame are calculated in (14),
(15) and (16), respectively. Figure 2 shows the crosssectional view of the three-phase core type transformer. The
transformer winding design method will be explained in the
following part (Eqs.14-16).
H = 2H y + H w
(14)
W = 2D + a = 2(Ww + d ) + a
(15)
D = Dy
(16)
Figure 2 shows the cross-sectional view of the threephase core type transformer. The transformer winding design
method will be explained in the following part.
2.2. Winding Design of a Distribution Transformer
Most of the commonly used conductors for transformer
windings are constructed with copper and aluminum. To
determination of suitable conductor in different conditions
for distribution transformers, a comprehensive comparison
of distribution transformers built either with copper or with
aluminum windings has been presented in [44].
The winding design procedure is started by the design of
low voltage (LV) conductors. The number of turns for the
LV side is calculated by (17). If the value is not an integer in
the first calculation, the designer must round it to an upper
integer number and find a new value of the electromotive
force per turn. According to (18), to calculate the area of a
bare conductor, LV nominal current, and current density are
required (Eq.17, 18).
δ
hLV = [rond(
(height of
TLV
) + 1] !
number of layers
insulated conductor )
(19)
Calculation of radial depth of LV winding is necessary to
find the inside and outside diameters of the LV winding. By
applying the following formulas, these characteristics are
determined (Eq.20-22).
bLV = ([number
[radial depth
of
layers ] ×
of
conductor ]) +
(20)
([thickness of insulation between layers ] ×
[number of layers − 1])
DiLV = d + 2[the thickness of insulation between
(21)
LV winding and core]
DoLV = DiLV + 2[bLV ]
(22)
The design of the LV winding leads to determine the
high voltage (HV) winding characteristics. Like LV design
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Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
Davazdah-Emami et al.
stage, determination of HV turns is the first step in the HV
design stage (Eq.23).
THV = VHV !
TLV
VLV
(23)
DLV =
DiLV + DoLV
2
(30)
DHV =
DiHV + DoHV
2
(31)
In order to make coils voltage less than 1500V in HV
side, quantified numbers of winding coils were assumed and
also due to using multiple layers, winding turns can be calculated.
lmtlv = πDLV
(32)
lmthv = πDHV
(33)
The nominal HV side current and area of bare conductors
are calculated by means of following formulas. By referring
to the standard table of conductor dimensions, diameter and
the characteristics of insulated conductors are attained
(Eqs.24-29).
rLV =
TLV ρlmtlv
a LV
(34)
rHV =
THV ρlmthv
a HV
(35)
I HV =
Q
3VHV
(24)
I HV
!
(25)
aHV =
h = [ Number of coils ] ×
hv
[ Number of turns per layers] ×
[ Diameter of insulated conductor ] +
(26)
[( Number of coils ) − 1] ×
[ spacer used between nearly coils ]
bHV = ([number of
layers ] ×
[ Diameter of insulated conductor ]) +
(27)
([thickness of insulation between layers ] ×
[number of layers − 1])
DiHV = DoLV + 2[thi ]
(28)
DoHV = DiHV + 2[bHV ]
(29)
The standard distances between high and low voltage
windings and distances between windings and core are of
great importance for insulation clearance. To meet the standard distances, designers can calculate the core dimensions
after calculating the winding characteristics. With regard to
design formulas, core and windings calculations are independent. So if the core dimensions change, these changes
after meeting insulation standards will be introduced as new
core dimensions. There is another way to achieve exact core
dimensions for designers. They can calculate the winding
characteristics and determine the core dimensions accordingly.
Operating characteristics (winding resistance and reactance) are two essential parameters to decrease transformer
losses in optimization procedures. If DHV and DLV are the
mean value of LV and HV winding diameter respectively
and length of the mean turn of HV and LV windings are
shown by lmtlv and lmthv respectively, the resistance of
each side is determined by (34) and (35). In addition the
mean diameter of windings, their mean lengths and heights
are calculated by (37), the leakage reactance of windings
referred to HV side is obtained by (38) (Eqs.30-38).
T
RHV = rHV + (rLV ) × ( HV ) 2
TLV
⎧
DiLV + DoHV
⎪ Dm =
2
⎪⎪
⎨lmt = πDm
⎪
h + hHV
⎪hc = LV
2
⎩⎪
l
b + bHV
2
X HV = 2πfµ 0THV
( mt )[(thi ) + LV
]
hc
3
(36)
(37)
(38)
Per unit value of resistance and reactance of windings is
calculated by (39) and (40), respectively. Also, (41) shows
the per unit impedance of a transformer (Eqs.39-41).
R p.u =
RHV I HV
VHV
(39)
X p.u =
X HV I HV
VHV
(40)
ε = ( X p.u ) 2 + ( R p.u ) 2
(41)
3. OPTIMIZATION ALGORITHM
By applying a suitable optimization approach, the appropriate characteristics of a transformer will be acquired for
designers, which results in transformer cost reduction. A
large number of optimization methods have been introduced
to solve such problems so far [26-43]. TLBO is one of the
widely used algorithms which have been applied to various
optimization problems. It uses two main parts called student
and teacher phases while the best student of the first phase is
chosen to work in the teacher phase. In this paper, CTLBO
method is proposed to find the optimum transformer parameters.
Initialize section, teacher phase, and student phase are
three essential parts of conventional Teaching-Learning
Based Optimization (TLBO) algorithm which is proposed in
the study [45]. Solution pool initializes randomly in the first
section. Teacher phase is the second part of TLBO algorithm
by applying (42), minimum cost candidates from solution
space are selected in this section (Eq.42).
Considering Environmental Health and Energy Resources
Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
(42)
X inew = X i + R ⊗ (T − rM )
Initialize number of population, termination criterion
where  is Hadamard product, which is used when the elements of two similar size matrices are multiplied with each
other and i,j element of the resulted matrix is the product of
elements i,j of the original two matrices. T is the best solution, M is the mean vector of whole solutions and R, r are
random vector and a random number, respectively. Finally
Xinew will be substituted by Xi for all those Xis satisfying
cost(Xi)> cost(Xinew).
Evaluate the initial population No
Is this population convincing consditions?
Yes
Calculate the mean of each design variable
The last section of this procedure is the student phase.
Random selection and modification of solutions are accomplished by using (43) and (44) in this part (Eqs.43, 44).
s = Sign(Cost ( X r ) − Cost ( X i ))
(43)
= X + sR ⊗ ( X − X )
(44)
X
new
i
i
i
r
Select the best solution Calculate the Difference_Mean and modify the solutions based on best solution
Keep the previous solution
Where Sign(x) function is 1 if x is - and -1 if x is positive. R
is the random vector, Xr is a random solution selected from
solution space and r is a random number. Finally, Xinew will
be substituted by Xi for all those Xis satisfying cost(Xi)>
cost(Xinew).
CTLBO investigates some conditions on variables in
each step of conventional TLBO. In this method, each variable is determined randomly, while all of them comply with
problem conditions. Figure 3 shows a population with D
variables and P groups. If determined values of variables
convince conditions, these values are selected as a first group
in the first step, otherwise, random selection must be continued to find the suitable values for variables. Figure 4 shows
the flowchart of CTLBO algorithm.
289
No
Is new solution better than existing
Yes
Accept Is this population convincing consditions?
Yes
No
No
(K1Xnew+K2Xold)/(K1+k2)
Select the solutions randomly and modify them by comparing with each other Keep the previous solution
No
Is new solution better than existing
Is termination criterion fulfilled?
Yes
Yes
Accept Is this population convincing conditions?
Yes
No
Final value of solution
(K1Xnew+K2Xold)/(K1+k2)
Fig. (4). Proposed CTLBO algorithm flowchart. (A higher resolution / colour version of this figure is available in the electronic
copy of the article).
to Xold, in this condition, K2 has been chosen to be greater
than K1 (K2>K1).
Fig. (3). Variable selection in CTLBO algorithm.
When a new random variable did not satisfy the conditions, CTLBO must find another variable. CTLBO can select
a new variable that is established between the old variables
by using (Eq.45).
k1 X new + k2 X old
(45)
k1 + k2
Where k1 and k2 are the constant values that determine the
convergence dimension. For example, if k1 is bigger than k2,
CTLBO finds the new variable near to the Xnew and viceversa. Assuming Xnew does not convince the constraints of
the problem and it is possible for a new variable to be closer
X inew =
4. CASE STUDY
A three-phase transformer is designed in this section. The
proposed method works as an optimizer to minimize the
transformer costs by considering different constraints such as
transformer volume, weight, and short circuit impedance.
Table 3 shows the characteristics of the studied transformer.
The short circuit impedance (%IZ or ɛ) range is the essential
constraint of the optimization problem, which must be limited among 0.07 to 0.14.
The transformer TOC minimization is the objective of
the optimization algorithm, which is defended as follow
(Eq.46):
n
CF = ∑ (clCui + clFi ) + CI
i =0
(46)
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Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
Table 3.
Davazdah-Emami et al.
Specification of studied distribution transformer.
Values
Table 4.
Nominal Power
250 kVA
Nominal Voltages
20 kV/400v
Nominal frequency
50 Hz
Type
Core Type
Connection type
Wye-Delta
Number of winding layers in LV side
2
Number of winding layers in HV side
24
Optimization results for transformer in different energy costs.
Parameters
Case 1
Case 2
Rp (Ohm)
189.63
42.4561
ɛr (p.u)
0.0395
0.0088
Xp (Ohm)
557.22
425.0926
ɛx (p.u)
0.1161
0.0886
ɛ (p.u)
0.1226
0.089
Hw (m)
0.5556
0.7189
Ww (m)
0.0606
0.289
Hf (m)
0.9271
1.2165
Wf (m)
0.8301
1.5276
Df (m)
0.2488
0.3332
Initial cost ($)
3655.89$
9212.52$
Cost of ohmic losses ($)
25908.43$
7585.56$
Cost of core losses ($)
22599.76$
15920.66$
Total price ($)
52150.73$
32719.07$
Bm (Tesla)
1.4999
0.8306
δ (A/mm2)
5.9586
1.2734
In order to analyse the effects of energy cost on transformer TOC, two different energy costs are assumed in this
section, which is shown in Table 4. In Table 4, the total price
shows the transformer cost, during its lifetime when the energy cost is 17¢/Kwh. In addition, in the design procedure of
case 1, the cost of energy is not considered while in case 2,
the cost of energy is assumed 17¢/Kwh. Furthermore, the
supposed copper and iron price is 5.24$/kg in design calculation. The proposed optimization algorithm is executed by a
laptop equipped by 2.4GHz Core i7 processor and 8GB
RAM on the explained problem. The laptop finds the optimum solutions in less than 5 minutes.
According to the optimization results, when the energy
cost is not considered in the transformer design procedure,
the initial cost of the transformer is less than in other cases.
In fact, when designers select maximum values for current
and flux densities in order to determine the transformer characteristics, the initial transformer cost is decreased inherently.
In this condition, due to the operating costs of the transformer, the total owning cost will be increased. If energy
cost is considered as a limiting factor, the operating costs
will become dominant. So, designers will try to decrease the
current and flux densities by choosing the suitable values of
them to determine the optimum values for transformer characteristics during its lifetime. In the latter case, the initial
cost rises as a result of the raw materials increment. However, the total owning cost will be decreased in the long run,
owning to the optimization of transformer characteristics.
Considering Environmental Health and Energy Resources
Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
291
In the traditional transformer design problems, the initial
cost and operating cost have been two segregated parameters
throughout the design procedure. Although the designed
transformers are satisfied with the consumers’ constraint by
consideration of the initial cost, the total owning cost of the
transformer during its lifetime is high. On the other hand, in
some problems, transformer efficiency is assigned as a constraint for the designer. In this condition, the initial cost of
the transformer will not set on the optimum value [25]. On
the contrary, according to the results, the proposed algorithm
enables distribution companies to design a transformer with
the optimum values of the operating cost and initial cost,
simultaneously.
VHV
=
Nominal voltage of high voltage side
(V)
VLV
=
Nominal voltage of low voltage side
(V)
Et
=
emf per turn (V)
Ai
=
net core area (m2) = stacking factor *
Agi
Aw
=
Area of window (m2)
Ac
=
Area of copper in the window (m2)
D
=
distance between core centres (m)
A large number of conventionally designed transformers
are worked in the power distribution systems which impose
significant expense to the system. Therefore, the power distribution system cost will be reduced immensely, if designers
decrease transformer prices in the systems. In other words, a
little reduction in construction and operating costs of the
transformers results in impressive power distribution system
cost diminution. Moreover, the loss reduction helps saving
more energy and prevents energy dissipation through the
power systems. In this condition, the next generation of human beings will have more chance to benefit from energy
resources.
d
=
Diameter of circumscribing circle (m)
Kw
=
Window space factor
f
=
Nominal frequency (Hz)
TLV, THV
=
Number of turns in primary and secondary winding, respectively
I p, I s
=
Current in primary and secondary
windings, respectively (A)
ap, as
=
Area of conductors of primary and secondary windings respectively (m2)
CONCLUSION
li
=
Mean length of flux path in iron (m)
In this paper, the CTLBO algorithm determined the appropriate transformer properties when the transformer TOC
was the objective function for the optimization method. In
addition, suitable transformer impedance has been selected
as an optimization constraint to prepare the suitable voltage
regulation for the transformer. Optimization results demonstrated the merits of the CTLBO algorithm and the novel
design strategy for transformer design.
Lmt
=
Length of mean turn of transformer
windings (m)
Gi
=
Weight of active iron (Kg)
Gc
=
Weight of copper (Kg)
pi
=
Loss in iron per weight (w)
pc
=
Loss in copper per weight (w)
Furthermore, the proposed method can make a big difference in transformer design approach in comparison to the
traditional methods. By applying the proposed method, the
initial cost of the transformer will increase. However, by
investigating the operating cost and energy cost during the
transformer lifetime, the total cost of the transformer will be
decreased. Hence, it would help distribution companies, if
they consider this issue in their design procedure.
Ay
=
Net yoke area (m2)
AyG
=
Gross area of yoke (m2)
Ww
=
Width of window (m)
Hw
=
Height of window (m)
H
=
Height of frame (m)
W
=
Width of frame (m)
lv
=
Radial depth of LV winding (m)
bhv
=
Radial depth of HV winding (m)
In brief, the paper not only proposes an appropriate approach to decrease the total owing costs of distribution transformers but also suggests a way to reduce transformer energy dissipation during operation in a power grid. For this reason, the construction of the transformers based on the proposed approach presented in this paper helps energy reservoirs to remain more for human beings.
LIST OF ABBREVIATIONS
Q
=
Rated apparent power (kVA)
φm
=
Flux (wb)
Bm
=
Maximum flux density (wb/m2)
δ
=
Current density (A/m2)
T
=
Number of turns per phase
b
LV
Di , DiHV =
inside diameter of LV and HV windings, respectively (m)
DoLV, DoHV
=
outside diameter of LV and HV windings, respectively (m)
RHV
=
Total resistance referred to HV side
(ohm)
thi
=
The thickness of insulation between LV
and HV windings (m)
ETHICS APPROVAL AND CONSENT TO PARTICIPATE
Not applicable.
292
Current Signal Transduction Therapy, 2020, Vol. 15, No. 3
HUMAN AND ANIMAL RIGHTS
No animals/humans were used for studies that are basis
of this research.
Davazdah-Emami et al.
[13]
[14]
CONSENT FOR PUBLICATION
Not applicable.
[15]
AVAILABILITY OF DATA AND MATERIALS
The authors confirm that the data supporting the findings
of this research are available within the article.
[16]
[17]
FUNDING
None.
CONFLICT OF INTEREST
The authors declare no conflict of interest, financial or
otherwise.
[18]
[19]
[20]
ACKNOWLEDGEMENTS
This research was supported by the Eram Sanat Mooj
Gostar (ESMG) company. Authors thank colleagues from
the ESMG company who provided insight and expertise that
greatly assisted the research.
[21]
[22]
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