In Article “Power and Distribution Transformers sizing calculations – part One”, we indicate that the contents of
our articles for Power and Distribution Transformers sizing calculations will
include the following points:
- Glossary of Sizing Power and Distribution Transformers,
- Power and distribution transformer components,
- Power and distribution transformer classification: construction and application,
- Three-phase power and distribution transformer connections,
- Power and Distribution Transformers sizing calculations.
The following points were
explained before (or will be explained) in our course “EP-3:Electrical Procurement – Transformers Course”:
- Power and distribution transformer components,
- Power and distribution transformer classification: construction and application,
- Three-phase power and distribution transformer connections,
So, we will not go through these points here, we will focus only on the following two points:
- Power and Distribution Transformers sizing calculations.
Also, in Article “Power and Distribution Transformers Sizing Calculations – Part Two” ,we indicate that Our study for the
Power and Distribution Transformers sizing calculations will include the
explanations of the following points:
- Resources used to calculate basic ratings of power and distribution transformers,
- Selection Factors,
- Calculations procedures For Sizing of Power and Distribution Transformers,
- Special cases.
And we explained in this article
the Resources used to calculate basic ratings of power and distribution
transformers while we explained the selection factors for the Power and
Distribution Transformers in article “Power and Distribution Transformers Sizing Calculations – Part Three”
In article “Power And Distribution Transformers Sizing Calculations – Part Four”, we indicted that the accurate sizing
calculations of Power and Distribution Transformers will include the following:
- Applicable calculations procedures for sizing of power and distribution transformers,
- Applicable procedures for calculating power and distribution transformer ratios,
- Applicable procedures for calculating power transformer efficiency,
- Applicable procedures for calculating power transformer voltage regulation.
Today we will explain the following:
- Applicable procedures for calculating power and distribution transformer ratios,
- Applicable procedures for calculating power transformer efficiency,
- Applicable procedures for calculating power transformer voltage regulation,
- Special Cases.
Note: I’d like from all of you
to review our course “EP-3: Electrical Procurement – Transformers Course” to be more familiar with the
contents of our new articles about the Power and Distribution Transformers
sizing calculations.
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2-
Applicable Procedures For Calculating Power And Distribution Transformer
Ratios.
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Step# 1:
Determine the
turns ratio.
Np/Ns
= Ep/Es = a (a:
transformer turns ratio)
Step# 2:
Determine the
volts-per-turn ratios.
volts-per-turn
(primary) = volts-per-turn (secondary)
Ep/Np
= Es/Ns
Then:
Ep = (Np/Ns)
x Es
Es = (Ns/Np)
x Ep
And:
Np = (Ep/Es)
x Ns
Ns = (Es/Ep)
x Np
Step# 3:
Determine the
ampere-turns relationships.
ampere-turns
(primary) = ampere-turns (secondary)
Ip
x Np = Is X Ns
Then:
Ip = (Ns/Np)
x Is
Is = (Np/Ns)
x Ip
And:
Np = (Is/Ip)
x Np
Ns = (Ip/Is)
x Np
Step# 4:
Determine the
volt-ampere relationships.
VAin
= VAout
Ep
x Ip = Es x Is (for single-phase transformers)
3
x Ep x Ip = 3 x Es x Is (for three-phase transformers)
Or
kVAin
= kVAout
kVp
x Ip = kVs x Is (for single-phase transformers)
3
x kVp x Ip = 3 x kVs x Is (for three-phase transformers)
Where:
Ep or KVp :
Primary Voltage,
Es or KVs:
Secondary Voltage,
Ip: Primary
Current,
Is: Secondary
Current,
Np: Primary
Turns Number,
Ns: Secondary
Turns Number.
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3-
Applicable Procedures for Calculating
Power
Transformer Efficiency.
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Note:
Efficiency is
calculated by dividing the output real power by the input real power. The
efficiency will vary depending on the amount of load because the copper
losses of a transformer vary with load.
Step# 1:
Determine the
transformer kVA, total copper losses, and total iron losses.
Step# 2:
Calculate the
output power of the transformer at the given power factor.
Pout
= kVA x 1000 x power factor (p.f.)
in watts
Step# 3:
Calculate the
required input power.
Pin
= Pout + copper losses + iron losses
Step# 4:
Calculate the
percent efficiency.
%
efficiency = (Pout/Pin) x 100
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4-
Applicable Procedures for Calculating
Power
Transformer Voltage Regulation
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Note:
As a
transformer becomes loaded, the voltage at the secondary terminals of the
transformer decreases. This decrease in voltage is caused by the voltage drop
across the internal impedance of the transformer. The higher the transformer
impedance, the higher the voltage drop.
Step# 1:
Determine the
voltage (E full-load) of the transformer at the secondary
terminals under full-load conditions.
Step# 2:
Calculate the
percent voltage regulation.
%
Voltage Regulation = [(E no-load – E full-load)/(E no-load)]
x 100
where E no-load
= the transformer’s rated secondary voltage
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4-
Special Cases In Transformers Sizing Calculations
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Some factors
must be taken in consideration in some cases when sizing the power and
distribution transformers these are the special cases which will be as
follows:
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1- Secondary Unit Substations
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What is the Secondary Unit
Substations?
A secondary
unit substation, sometimes called a power center, is a close-coupled assembly
consisting of three-phase power transformers, enclosed high voltage incoming
line sections, and enclosed secondary low voltage outgoing sections
encompassing the following electrical ratings:
As a result
of locating power transformers and their close-coupled secondary switchboards
as close as possible to the areas of load concentration, the secondary
distribution cables or busways are kept to minimum lengths. This concept has
obvious advantages such as:
Components of
Secondary Unit Substations:
The major
components of a unit substation are:
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Types of Secondary Unit Substations
There are two
main types of Secondary Unit Substation as follows:
1- Single-Ended
Substations:
Figure-1
shows the one-line diagram and physical layout of a secondary unit substation
that uses a radial system arrangement. This type of radial substation
arrangement is called a single-ended substation because there is only one
incoming line section at the one end (west) of the unit (prepackaged) assembly.
Fig-1:
Single-Ended Substations
2- Double-Ended
Substations:
Figure-2
shows the one-line diagram and physical layout of a secondary unit substation
that uses a secondary selective system arrangement. This type of arrangement,
the secondary selective system, overcomes the major disadvantage of the
radial system in that it provides duplicate paths of supply to the secondary
bus of each load center. This selective system has two step-down transformers,
each with its own incoming primary feeder. The secondary bus associated with
each transformer is connected through a tie breaker. Normally, the system is
operated with the tie connection open, that is, as two separate radial
systems operating independently of each other.
Fig-2:
Double-Ended Substations
With the loss
of one of the primary feeders and/or transformers, the main secondary breaker
for that circuit can be opened and the tie breaker closed, allowing the one
remaining primary feeder and transformer to energize all of the secondary
bus. The service to one-half of the load is momentarily interrupted during
this transition period.
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Factors
Must Be Taken into Consideration when Sizing Unit Substations
The selection
of kVA and impedance ratings of unit substation transformers is very critical
to the levels of available fault current on the secondary main bus side of
the substation. This available fault current on the secondary side of the
transformer, assuming that there are no other fault current sources on the
secondary side, is called The Transformer Let-Through Current.
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Procedures
For Calculating Transformer Let-Through Current
Transformer
impedance dictates how much fault current a transformer can supply to a fault
for a given kVA size. The higher the impedance, the lower the available fault
current. Sometimes transformer impedances are used to limit the let-through
current (sometimes called the infinite bus fault current calculations).
By calculating
the transformer let-through current, you can estimate the available fault
current at the secondary terminals of a transformer. Transformer let-through
current can be calculated using the following steps:
Step#1:
Calculate
rated secondary current for the transformer.
Isec
= kVA/(1.732 x kV)
Step#2:
Determine
% Z from Table-1 for single-phase transformers and Table-2 for three-phase
transformers.
% Z =
Note: Convert
%Z into decimal form
Example: 5% =
0.05
Step#3:
Calculate
the available short circuit current (Transformer Let-Through Current).
ISCA
(ILT ) = Isec/Z
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Impedance
(%Z)
Tables of
Standard Impedances for Single-Phase and Three-Phase Transformers
Table-1:
Standard Impedances for Single-Phase Power Transformers
Table-2:
Standard Impedances for Three-Phase Power Transformers
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Example:
Referring to
Figure 56, what is the transformer let-through current (ILT) at
the secondary bus? What is ILT if the impedance of the transformer
is specified at 5% versus 5.75%? What is ILT if the impedance of
the transformer is specified at 7% versus 5.75%?
Answer:
1. ILT = IFLA-sec/Z = kVA/[( 3 x kVsec)
x Z]
• Where Z is
expressed as a decimal
2. ILT
@ 5.75% = 2500/[( 3 x .48) x .0575] = 3007/0.0575 = 52.3 kA
3. ILT @
5% = 3007/0.05 = 60.1 kA
4. ILT @ 7% = 3007/0.07 = 43.0 kA
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- Paralleled Transformers,
- K-Factor Transformers,
- Transformers with Large Motor Loads.
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