ABSTRACT Transformer is very important and efficient electrical power equipment. Its ability to step-up voltages has made huge blocks of electric power transformation over long distances very economical and its ability to step-down voltages to convenient low levels has made electric power utilization safe. Depending upon application for which transformers are put in electric power industry, there are divided into power transformers, distribution transformers, grounding transformers, instrument transformers etc. The ratings and characteristics of these different transformers are therefore different and hence their design considerations, fabrications and testing procedures also different. Hence, a thorough study of above aspects and actual problems that come up at various stages in the manufacture of this important piece of electrical apparatus in a factory before being marketed is considered worth study. Currently many factories are engaged in manufacturing distribution transformers. Three phase 50 Hz distribution transformers up to 100 KVA have been designed for given ratings. This work is mainly divided into four chapters. 1
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ABSTRACT
Transformer is very important and efficient electrical power equipment. Its
ability to step-up voltages has made huge blocks of electric power transformation
over long distances very economical and its ability to step-down voltages to
convenient low levels has made electric power utilization safe. Depending upon
application for which transformers are put in electric power industry, there are
divided into power transformers, distribution transformers, grounding
transformers, instrument transformers etc.
The ratings and characteristics of these different transformers are therefore
different and hence their design considerations, fabrications and testing procedures
also different. Hence, a thorough study of above aspects and actual problems that
come up at various stages in the manufacture of this important piece of electrical
apparatus in a factory before being marketed is considered worth study.
Currently many factories are engaged in manufacturing distribution
transformers. Three phase 50 Hz distribution transformers up to 100 KVA have
been designed for given ratings.
This work is mainly divided into four chapters.
The first chapter deals with the basics of transformers construction and the
theoretical aspects behind this.
The second chapter deals with the theoretical aspects in designing of a
distribution transformer.
The third chapter deals with complete design of a three phase, 50 Hz, 100
KVA distribution transformers.
The Fourth chapter deals with the C Program illustrating problem
definitions and its results.
By giving the input parameters of a distribution transformers we can obtain
the design specification of that transformer by using a C program.
1
CONTENTS
CHAPTER 1: TRANSFORMER CONSTRUCTION
1.1 Principal of Transformer Action
1.2 Rating of transformers
1.3 Transformer on Load
1.4 Transformer with Resistance & Leakage Reactance
1.5 Transformer Tests
1.6 All-day efficiency
CHAPTER 2: DESIGN THEORY
2.1 Design of Core
2.2 Choice of Flux Density
2.3 Selection of Type of winding
2.4 Design of Insulation
CHAPTER 3: OPTIMUM DESIGN PROCEDURE
3.1 Design for minimum cost
3.2 Design for minimum loss (or) maximum efficiency
3.3 Core Design
3.4 Window Design
3.5 Yoke design
3.6 Overall Dimensions
3.7 Windings
3.8 Resistance
3.9 Leakage Reactance
3.10 Regulation
3.11 Losses
3.12 Efficiency
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3.13 All day Efficiency
3.14 No-Load Current
3.15 Tank
3.16 Cooling system
CHAPTER 4: RESULTS AND DISCUSSIONS
CHAPTER 5: CONCLUSION
CHAPTER 6: C-PROGRAM
CHAPTER 7: REFERENCES
3
TRANSFORMER CONSTRUCTION
4
CHAPTER-1
TRANSFORMER CONSTRUCTION
There are two types of general transformers, the
core type and the shell type. These two types differ from each other by the
manner in which the windings wound around the magnetic core.
The magnetic core is a stack to thin silicon-steel
laminations about 0.35 mm thick for 5o Hz transformers. In order to reduce
the eddy current losses, nearly all transformers have their magnetic core
made from cold-rolled grain-oriented sheet-steel (C.R.G.O). This material,
when magnetized in the rolling direction, has low core loss and high
permeability.
In the core-type, the windings around a considerable
part of steel core as shown in fig 1.1 (a). In the shell-type, the steel core
surrounds a major part of the windings as shown in fig 1.1 (b). For a given
output and voltage rating, core-type transformer requires less iron but
more conductor material as compared to a shell-type transformer. The
vertical portions of the core are usually called limbs or legs and the top and
bottom portions are called the yoke. This means that for single- phase
transformers, core-type has two-legged core, where as shell-type has
three legged core.
In iron-core transformers, most of the flux is confined to high
permeability core. There is, however, some flux that leaks through the core
legs and non-magnetic material surrounding the core. This flux, called
leakage flux, links one winding and not he other. A reduction in this
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leakage flux is desirable as it improves the transformer performance
considerably. Consequently, an effort is always made to reduce it. In the
core-type transformer, this is achieved by placing half of the low voltage
(L.V) winding over one leg and other half over the second leg or limb. For
the high voltage winding also, half of the winding is over one leg and the
other half over the second leg, fig 1.1(a). L.V winding is placed adjacent to
the steel core and H.V winding outside, in order to minimize the mount of
insulation required.
In the shell type transformer, the L.V and H.V windings are
wound over the central limb and are interleaved or sandwiched as shown
in fig 1.1 (b). Note that the bottom and top L.V coils are of half the size of
other coils.
In core-type transformer, the flux has a single path around the
legs or yokes, fig 1.1 (a). In the shell-type transformer, the flux in the
central limb divides equally and returns through the outer two legs as
shown in fig 1.1(b)
6
L.V. Winding
H.V-Winding
1.1 (a) CORE TYPE TRANSFORMER
Yoke
Gaps
Limb (or)leg 1.1 (b) SHELL TYPE TRANSFORMER
7
One type of laminations for the core and shell type of
transformers is illustrated in Fig 1.2 (a) and (b) respectively. The steel core
is assembled in such a manner that the butt joints in adjacent layers are
staggered as illustrated in fig 1.2 (c). The staggering of the butt joints
avoids continuous air gap and, therefore, the reluctance of the magnetic
circuit is too increased. At the same time, a continuous air gap would
reduce the mechanical strength of the core and, therefore, the staggering
of the butt joints is essential
BUTT JOINTS
1.2 (a) 1.2(b)
8
BUTTJOINTS
BUTTJOINTS
Two adjacent layers for:
(a) Core
(b) Shell type of transformers and
(c) arrangement of Butt Joints in a magnetic core
9
1.1 Principle of Transformer Action:
A transformer works on the principle of electromagnetic
induction. According to this principle, an e.m.f is induced in a coil if it links
a changing flux.
In core-type transformer, half the L.V and H.V winding is on one
limb and the other half is on the second limb. In shell-type transformer, the
L.V and H.V windings are sandwiched. However, for both these type
transformers, the schematic diagram is as shown in fig 1.3. The primary
winding P is connected to an alternating voltage source, therefore, an
alternating current I φ is connected to an alternating voltage, voltage
source, therefore, an alternating current I φ starts flowing through N1 turns.
The alternating mmf N1I sets up alternating flux φ which confined to high
permeability iron path as indicated in fig 1.3, the alternating flux induces
voltage E1 in the primary P and E2 in the secondary S. If the load is
connected across the secondary, a load current starts flowing.
In addition to the secondary winding, there may be a third
winding on the same iron core. The emf induced in the secondary winding
is usually referred to as the emf due to transformer action. Thus the
transformer action requires the existence of alternative mutual flux linking
the various windings on a common magnetic core.
During the transformer construction, first the primary and
secondary windings are wound, then the laminations are pushed through
The coil openings, layer and the steel core is prepared, the laminations are
then tightened by means of clamps and bolts.
10
Low power transformers are air cooled where as large
power transformers are immersed in oil for better cooling. In oil cooled
transformers, the oil serves as a coolant and also as an insulating medium.
For power frequency range of 25 to 400Hz, transformers
are constructed with 0.32 mm thick silicon-steel laminations. For audio
frequency range of 20 to 20,000Hz, iron core with suitable refinements is
used. For high frequencies employed in communication circuits, core is
made up of powdered ferromagnetic alloy. In special cases the magnetic
circuit of transformer is referred to as an air core transformer is primarily
used in radio devices and in certain types of measuring and testing
instruments. Cores made of soft ferrates are also used for pulse
transformers as well as for high frequency electronic transformers.
1.2 Rating Of Transformers:
The manufacturer of transformers fixes a name plate
on the transformers, on which are recorded the rated output, the rated
voltages, the rated frequency etc. of a particular transformer. A typical
name plate rating of a single phase transformer is as follows: 20 KVA,
3300/220V,50Hz. Here 20KVA is the rated output at the secondary
terminals. Note that rated output is expressed in Kilo-volt-amperes(KVA)
rather than in Kilowatts(KW).This is due to the fact that rated transformer
output is limited by heating and hence by the losses in the transformer.
These losses depend on transformer voltage (core loss) and current loss
and are almost unaffected by the load power factor. Consequently the
transformer rated output is expressed in KVA and not in KW. At zero p.f
11
load, a transformer can be made to operate at rated KVA output while
delivering zero power
For any transformer
(Rated input in KVA at the primary terminals)(Cos θ1)
= (Rated output in KVA at the secondary terminals)(Cos θ2)+Losses
Since the transformer at a very high efficiency, losses may
be ignored. Further, the primary p.f.Cos θ2 are nearly equal. Therefore, the
rated KVA marked on the name plate of a transformer, refers to both the
windings, i.e. the rated KVA of the primary winding and the secondary
winding are equal.
1.3 Transformer on Load:
When the secondary is loaded, the secondary current I2
with respect to V2 is determined by the characteristics of the load. Current
I2 is in phase with V2 if load is non-inductive, it lags if load is inductive and it
leads if load is capacitive.
The secondary current set up its own m.m.f (=N2
I2) and hence its own flux Ф2 which is in opposition to the main primary flux
Ф which is due to I0. The secondary flux Ф2 weakens the primary flux Ф
momentarily, hence primary back e.m.f. E 1 tends to be reduced. For a
moment V1 gains the upper hand over E1 and hence causes more current
to flow in primary.
Let the additional primary current be I2’.It is know as load
Component of primary current. This current is antiphase with I2.The
additional primary m.m.f N1I2’ sets up its own flux Ф2’ which is in opposition
to Ф2 (but is in the same direction as Ф) and is equal to it magnitude.
Hence, the two cancel each other out. So, we find that the magnetic effects
of secondary current I2 are immediately neutralized by the additional
12
primary current I2’ which is brought into existence exactly at the same
instant as I2.
Hence, wherever the load conditions, the net flux passing
thought the core is approximately the same at no-load. An impartment
deduction is that due to the constancy of core flux at all loads, the core
loss is also practically the same under all load conditions.
As Ф2= Ф2 N2I2=N1I2
I2=(N2/N1)I2 = KI2
13
Hence, when transformer is on load, the primary winding has
two currents in it; one is I0 and the other is I2’ which is anti-phase with I2
and K time in magnitude. The total primary current is the vector sum of I0
and I2’.
In fig1.3(a) are show the vector diagrams for a load
transformer when load is non-inductive and when it is inductive (a similar
diagram could be drawn for capacitive load).Voltage transformation ratio of
unity is assumed so that primary vectors are equal to the secondary
vectors. With reference to fig 1.3(a), I2 is secondary current in phase with
E2 (strictly speaking it should be V2). It causes primary current I2 which is
anti-phase with it and equal to it in magnitude (k=1). Total primary current
I1 is the vector sum of I0 and I2 and lags behind v1 by an angle Ф1.
In fig 1.3 (b) vectors are drawn for an inductive load. Here, I2
lags E2 (actually V2) by Ф2. Current I2 is again anti phase with I2 and equal
14
to it in magnitude. As before I1 is the vector sum of I2 and I0 and lags
behind V1by Ф1.
It will be observed that Ф1 is slightly greater than Ф2 But if we
neglect I0as compared to I2 as in fig 1.3(c) then Ф1= Ф2 more over, under
this assumption. N1I2=N2I1=N1I2; I2/I1=I1/I2=N2/N1=K.
It shows that under full-load conditions, the ratio of primary
and secondary current is constant. This impartment relationship is made
15
the basis of current transformer. A transformer which is used with a low-
range ammeter for measuring currents in circuits where the direct
connection of the ammeter is impracticable.
1.4 Transformer with Resistance and Leakage Reactance:
16
The above figure 1.4 shows the primary and secondary windings of a
transformer with reactance taken out of the windings. The primary
impedance is given by
Z1=√ (R12+X1
2)
Similarly second impedance is given by Z2=√ (R22+X2
2)
The resistance and leakage reluctance of each winding is
responsible for some voltage drop in each winding. In primary, the leakage
reactance drop is I1X1(usually 1 or 2%)
Hence V1 = E1 + I1(R1 +j X1) = E1 + I1 Z1
Similarly, there are I2 R2 and I2 X2 drops in secondary which combine with V2
to give E2.
E2= V2+ I2(R2 +j X2)= V2+ I2 Z2
It may be noted that leakage reactance’s can also transferred from
one winding to the other in the same way as resistance.
X2’= X2/K2 and X1’= K2 X1
And X01= X1+ X2’= X1+ X2/K2 and X02= X2+ X1’= X2+ K2 X1
It is obvious that total impedance of the transformer as referred primary is
given by
Z01 =√ (R012+X01
2)
Z02 =√ (R022+X02
2)
17
1.5 Transformer Tests
The transformer constants or parameters can be easily determined by two tests (i)
pen-circuit test and (ii) the short-circuit test. These tests are very economical and
convenient, because they furnish the required information without actually loading the
transformer. In fact, the testing of every large a.c.machinary consists of running two tests
similar to the open and short – circuit test of a transformer.
Open – circuit or No-load Test
The main purpose of this test is to determine on-load losses. One winding of the
transformer – whichever is convenient but usually high voltage winding – is kept open
the other is connected to a supply of normal voltage and frequency (Fig.21-29). A
wattmeter W, voltmeter V and ammeter A are connected in the low-voltage winding i.e.
primary winding in the present case. Fig.21-29.
Shows the simplified diagram whereas, Fig.21-30 shows actual connections. With
normal voltage applied to the primary, normal flux will be set up in the core, hence
normal iron losses will occur which are recorded by the wattmeter. As the primary no
load current Io (as measured by ammeter) is small (usually 2 to 10% of rated
load current) Cu loss is negligibly small in primary and nil in secondary (being open).
18
Hence, the wattmeter reading represents practically the core-loss under no-load
conditions (and which is the same for all loads as pointed out in Art.21-8).
Sometimes a high resistance voltmeter is connected across the secondary. The
reading of the voltmeter gives the induced e.m.f. in the secondary winding. This helps in
finding the transformation ration K.
Short-circuit or Impedance Test
This is an economical method for determining the following:
(i) Equivalent impedance (Zo1 or Zo2), leakage reactance (Xo1 or Xo2) and resistance
(Rol or Ro2) of the transformer as referred to the winding in which the measuring
instruments are placed.
(ii) Cu loss at full-load (and at any desired load). This loss is used in calculating the
efficiency of the transformer.
(iii) Knowing Zo1 or Z02, the total voltage drop in the transformer as referred to primary
or
secondary can be calculated and hence regulation of the determined.
In this test, one winding – usually the low- voltage winding, is solidly short-
circuited by a thick conductor ( or through an ammeter which may serve the additional
purpose of indicating rated load current) as shown in Fig. 21-31.
A low voltage (usually 5 to 10% of normal primary voltage) at correct frequency
(though for Cu losses it is not essential) is applied to the primary and is cautiously
increased till full-load currents are flowing both in primary and secondary (as indicated
by the respective ammeters).
Since, in this test, the applied voltage is a small percentage of the normal voltage,
the mutual flux Ө produced in the core is also a small percentage of its normal value
(because flux is proportional to the voltage as shown in the e.m.f. equation of the
transformer in Art.21-6). Hence, core losses are very small with the result that the
19
wattmeter reading represents the full-load Cu loss or I2 R loss for the whole transformer
i.e. both primary Cu loss and secondary Cu loss. If Vsc is the voltage required to
calculate rated load current on short circuit, then
Also
1.6 All day Efficiency:
The ordinary or commercial efficiency of transformer is given by
the ratio of output in watts and input in watts. But there are certain types of
transformers whose performance cannot be judged by this efficiency.
Transformers used for supplying lighting and general network i.e.
distribution transformers have their primaries energized all twenty-four
hours, although their secondary’s supply little or no load much of the time
during the day except during the house lighting period. It means that where
as core loss occurs throughout the day, the copper loss occurs only when
the transformer is loaded. Hence, it is considered a good practice to design
such transformers so that core losses are very low. The copper losses are
relatively less important, because they depend on the load. The
performance of such transformer should be judged by all-day efficiency
which is computed on the basis of energy consume during a certain time
period, usually a day of 24 hours.
Output in KWH
All day efficiency= ----------------------------- (for 24 hours)
Input in KWH
20
This efficiency is always less than the commercial efficiency of a
transformer.
To find this all day efficiency, we have to know the load cycle
on the transformer i.e. how much and how long the transformer is loaded
during 24 hours. Practical calculations are facilitated by making use of
load factor
21
DESIGN THEORY
22
CHAPTER-2
DESIGN THEORY
2.1 Design of core:
The cross section for core type of transformers may be
rectangular, square or stepped. Shell type transformers use cores with
rectangular cross section.
2.1.1 Rectangular core:
For core type distribution transformers and small power
transformers for moderate and low voltage, the rectangular stepped core
section may be used. The ratio of depth to width of core varies between
1.4 to 2. Rectangular shaped coils are used for rectangular cores.
For shell type transformer width of central limb is 2 to 3
times the depth of the core.
2.1.2 Square and stepped cores:
When circular coils are required for high voltage
distribution and power transformers square and stepped cores are used.
Circular coils are preferred because of the superior mechanical
characteristics. A transformer coil, under mechanical stresses produced by
excessive leakage flux due to short circuit, tend to assume a circular from .
On circular coils, these forces are radial there is no tendency for the coil to
change its shape; on
23
rectangular coils the forces are perpendicular to the conductors and tend
to give the coils a circular form, thus deforming it.
With core type transformers of small sizes, simple rectangular core can
be used with either square or rectangular coils. For this purpose the cores
are squares shaped. This circle is know as the circumscribing circle being
large in comparison giving rise to higher copper loss and conductor cost.
With larger transformer cruciform cores which utilize the
space better are used. As space utilization is better with cruciform cores.
The diameter of circumscribing circle is smaller than with square
cores of the same area. Thus the length of mean turn of copper is reduced
with consequent reduction in cost of copper. It should be kept in mind that
two different sizes of laminations are used in cruciform cores, the large
transformers further steps are introduced to utilize the core space which
reduces the length of mean turn with consequent reduction in both cost of
copper and copper loss.
It would seen that we can go on introducing steps with resultant
reduction in cost of winding . However with larger number of steps a large
numbers of sizes
24
of laminations have to be used. This results in higher labour charges for
shearing and assembling different types of laminations.
Thus the reduction in winding costs with a certain numbers of
steps has to be balanced with the extra labour cost. The numbers of steps
to be used for particular transformers have to be decided by the about
considerations.
2.2 Choice of Flux Density:
The value of flux density in the core determines the core area.
Higher values of flux density give smaller core area and therefore there is
a saving in cost of iron. Also with the reduction in core area the length of
mean turn of windings is also reduced. Thus there is saving in conductor
costs also. But with higher flux densities the iron loss become high,
resulting in considerable temperature gradient across the core.
High flux density necessitates a large magnetizing current which
contains objectionable harmonics.
The value of flux density to be chosen also depends upon the
service conditions of the transformers. As a distribution transformer has to
e designed for a high all day efficiency, and there fore the value of flux
density should be low in order to keep down the iron loss.
25
The usual values of maximum flux density BM for transformers using hot
rolled silicon steel are:
Distribution transformer-----------1.1to1.35 wb/m2
Power transformer------------------1.25to1.45 wb/m2
Lower values should be used for small rating transformers.
2.3 Selection of Type of Winding:
It is first necessary it select proper types of windings to be used in
the transformer. The design of the winding chosen must be such that the
desired electrical characteristics and adequate mechanical strength is
obtained.
The high voltage winding are usually of the following types;
1) Cylindrical winding with circular conductor
2) Cross over winding with either circular or small rectangular
conductors
3) Continuous disc type winding with rectangular conductors
The cylindrical and the cross-over winding are used for
transformers of ratings upto 1000 KVA and 33 KV. The disc type winding
is used for transformers of higher rating ranging from 200K VA to tens of
MVA and Voltages from 11KV upwards.
26
The low voltage are usually of the following two types:
1) cylindrical winding
2) Helical winding(usually double helical)
But these windings employ rectangular conductors. Cylindrical
windings are used for KVA rating up to 800 and voltages up to 15KV and
sometimes up to 33KV.
2.4 Design of Insulation:
During the processes of power transfer from one circuit to
another; electrical, mechanical and thermal phenomenon take place in a
transformer., the winding voltage produce an electrostatic field in the
dielectric and therefore stress the insulation, the current in the windings
and to mechanical stressing of insulation, finally the losses. In the
transformer produce temperature rise which produce thermal stresses.
Hence, the fundamental considerations in the design of
insulation of transformers may be described as those of arranging core,
windings and insulation to obtain satisfactory electrical and thermal
characteristics during the steady state as well as transient conditions. The
three basic considerations in the design of insulation are various
conditions.
2.4.1 Electrical considerations:
The basic insulation structure is primarily determined from
consideration of the magnitude and nature of voltage which appears
between different parts of the transformer i.e., voltages between individual
27
turns, between coil or layers, between windings and from winding to core
and tank.
The electrical design should also take care of the eddy current losses
in conductors and leakage reactance of windings.
a) Eddy current losses:
The winding should be designed that the stray load losses
small. The stray load loss includes eddy current loss in conductor and also
in tank walls and clamping structure. The conductor should be split into
small strips to reduce eddy current losses in conductor.
b) Leakage Reactance:
A given arrangement of core and winding determines the
leakage reactance of the windings. The leakage reactance is adjusted by
changing the winding configuration and brought within desired limits.
2.4.2 Mechanical Considerations:
The basic mechanical considerations in the design of insulation
are of two types:
a) The insulation must be capable of withstanding the mechanical stresses
imposed on it during manufacturing processes.
b) The insulation must be able to withstand the mechanical stresses which
are developed in the winding due to electromagnetic forces and
mechanical stresses produced under normal conditions of operation are
28
quite small and ordinarily are of minor importance .However, under fault
conditions, particularly dead short circuit, the electromagnetic forces may
be increased several hundred times.
2.4.3 Thermal considerations:
The thermal aspects of design of insulation are determine from
the consideration of insulating materials used, selection of maximum
operating temperatures and types of cooling method employed.
The transformer structures should be such that the losses developed in
the core and winding produce temperature rises in the various parts which
no where exceed the permissible limit both under normal over load/fault
conditions and which, in the interest of economy, approved those limits as
early as possible. The insulation of a transformer is divided into four types:
a) Major insulation
b) Minor insulation
c) Insulation relative to tank
d) Insulation between the phases
a) Major Insulation:
The insulation between windings and grounded core
and insulation between the windings of the same phase is called major
insulation.
b) Minor insulation:
Insulation between different parts of one winding i.e.
insulation between turns, coils and layers etc is called Minor insulation.
c) Insulation relative to tank:
The insulation relative to the tank is called oil barrier
insulator in oil immersed transformers. This insulation consists of oils
29
ducts, barriers and coverings. Partitions of solid insulating materials placed
inside oil ducts are called barriers
d) Insulation between the phases:
There must be provided relative insulation between the
phases to avoid the short circuit between the phases
30
DESIGN PROCEDURE
31
CHAPTER 3
DESIGN PROCEDURE
OPTIMUM DESIGN:
Transformers may be designed to make of following qualities
as minimum.
1) Total volume
2) Total weight
3) Total cost
4) Total losses
Фm
All these qualities vary with r= --------
AT
Thus we say r is a controlling factor for all these qualities.
3.1 Design for minimum cost:
Let us consider a single transformer, whose KVA output is,
Q = 2.22fBmAiKwAwδ X 10-3
=2.22fBmAiAcδ X 10-3
Assuming flux and current densities are constant, the product
Ac Ai is constant for a given transformer.
Let,
Ac Ai = M2
Фm
Now r = --------
AT
32
Фm = BmAi
AT = KwAwδ / 2 = δ / 2
r = 2 BmAi / δ Ac
=> Ai = δ * r / 2 Bm =β (say)
Where β is a function of only as Bm and δ are constants.
From above
Ai = M √ β, Ac = M / √ β
Let Ct = Total cost of transformer active materials
Ci = Total cost of Iron
Ct = Cc+ Ci
Cc = Total cost of conductor
Ct = CI gi li Ai + Cc gc lmt Ac
Where Ci & Cc are specific costs of iron & copper.