Annals of the „Constantin Brancusi” University of TarguK...Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2017 3 TRANSFORMER’S EFFICIENCY

Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2017

36

POWER TRANSFORMERS VOLTAGE OPTIMIZATION IN ORDER TO

MINIMIZE ACTIVE POWER AND ENERGY LOSSES AND MAXIMIZE

EFFICIENCY

Georgi Tsonev Velev, Technical University of Gabrovo, Gabrovo, BULGARIA

Krasimir Marinov Ivanov, Technical University of Gabrovo, Gabrovo, BULGARIA

Adriana Foanene, University „Constantin Brȃncuşi” of Tg Jiu, ROMANIA

ABSTRACT: The paper inhere derives mathematical models for optimization of the operating

voltage of distribution power transformers in order to minimize their active power losses and

maximize their efficiency in variable loading conditions. A comparative study has been made

between oil and dry-type of power transformers. The optimization models, that are built, are

implemented in the Microsoft Excel’s module “Solver” in order to process the calculations and

present them in graphical appearance. Appropriate conclusions are made in regard with the

optimal voltage of the different power transformers in dependence on the secondary loading.

KEY WORDS: distribution power transformers, transformer power losses, transformer efficiency,

voltage optimization.

1.INTRODUCTION In the process of electrical energy

transformation, a part of the energy has been

wasted as active power loss in the power

transformer. Losses of active power and

energy in power transformers are divided into

two types – losses in the transformer’s

windings (copper losses), which are

dependent on the transformer’s loading; and

magnetic losses (iron losses of hysteresis and

eddy currents), which are independent on the

load.

Up to now many researchers have studied

the influence of the load and the power factor

upon transformers’ active power and energy

losses, neglecting the operating voltage

impact [1, 2, 3].

Operating voltage has been introduced in

the mathematical expressions for calculation

of transformer’s active power losses and

efficiency, in order to reflect its influence.

Also, operating voltage is used as an

optimization variable in the optimization

procedure for minimizing the losses and

maximizing the efficiency of the transformer.

2.ACTIVE POWER LOSSES AND

EFFICIENCY OF POWER

TRANSFORMERS, TAKING

ACCOUNT OF THE OPERATING

VOLTAGE

According to the theory, the equivalent

electrical circuit of a 2-winding distribution

power transformer could be presented in two

ways (fig.1) [4, 5].

a)

0 0S P j Q

ТR ТX

ТG ТB

ТRТX

b) Figure 1. Equivalent circuits of a power

transformer, where:


2

ТR - series resistance , ; ТX - series

reactance , ; ТG - parallel conductance , S ;

ТB - parallel susceptance , S ; 0S – complex

power losses, VA; 0P - No-load power loss,

W; Q - reactive power loss , VAr .

All parameters of the equivalent circuit can

be calculated if the specification data

parameters are known, normally they are

provided by the transformer’s manufacturer:

rS - rated apparent transformer power

(capacity), kVA;

rU - rated voltage (for each winding), kV;

Ku - short circuit voltage, %;

0I - no-load current, %;

0P - no-load power losses, kW;

kP - short-circuit power losses, kW;

According to [4], the active power losses

of a transformer are: 2

2

2 T T

SP R U G

U (1)

,where:

U - Operating voltage at the primary winding,

V; S - Apparent power of transformer’s

load, VA;

Series resistance ТR and parallel

conductance ТG of a transformer are

calculated by well-known expressions [4, 5]: 2

2, k r

Т

r

P UR

S

(2)

0

2, SТ

r

PG

U

(3)

Expressions (2) and (3) are substituted in

(1): 2

2 0

2 2 2

k r

r r

P U PSP U

U S U

22 2

02 2 2

rk

r r

US UP P P

S U U

2 22

0r

k

r r

US UP P P

S U U

(4)

The following substitutions are made in (4):

Transformer loading factor:

L

r

Sk

S (5)

Operating voltage in per-unit values:

[pu]r

UU

U (6)

In that way expression (4) will be

transformed finally into:

2 2

02

1L kP k P U pu P

U pu (7)

Equation (7) gives the dependence of the

active power losses of a transformer P on

the loading Lk and the operating

voltage U pu .

If we consider the efficiency of a power

transformer, it is given by the expression:

2 2

1 2

P P

P P P

(8)

, where:

2P - active power at the transformer’s

secondary;

1P - active power at the transformer’s primary

side;

The active power of the secondary coil

could be expressed using the apparent power

of the load S and its power factor cos :

2 cos cosr

r

SP S S

S

2 cosL rP k S (9)

But we already have an expression for the

power losses of a transformer, according (7),

so expressions (7) and (9) are substituted in

(8):

2

2

2 2

02

cos

1cos

L r

L r L k

P

P P

k S

k S k P U pu PU pu

(10)

Equation (10) gives the dependence of the

efficiency of a transformer on the loading

Lk , the operating voltage U pu and the

power factor of the load cos .

3.MATHEMATICAL MODELS

FOR MINIMIZING THE POWER

LOSSES AND MAXIMIZING

37


3

TRANSFORMER’S EFFICIENCY

BY OPTIMIZING OPERATING

VOLTAGE

A. Optimization model for

minimizing the power losses of a

transformer An optimization model has been compiled

in order to minimize the active power losses

of a transformer, by varying transformer’s

loading Lk in the range (0,1 - 1,3) pu in equal

steps of 0,05 pu. For optimization variable

has been chosen the operating voltage at the

transformer’s primary U pu . The deviation

of operating voltage has been limited by the

range (0,9 - 1,1) pu, according to the

requirements for voltage quality of EU [9].

The mathematical model of this

optimization problem is listed below:

Objective function, according to (7) is:

2 2

02

1MinL kP k P U pu P

U pu (11)

Constraints defined for the optimization

variable i.e. the operating voltage U pu

are:

0,9 1,1U pu

B. Optimization model for

maximizing efficiency of a

transformer An optimization model has been compiled

in order to maximize the efficiency of a

transformer, by varying transformer’s loading

Lk in the range (0,1 - 1,3) pu and the power

factor of the load cos in the range (0,7 - 1)

in equal steps of 0,05 pu. For optimization

variable has been chosen the operating

voltage at the transformer’s primary U pu .

The deviation of operating voltage has been

limited by the range (0,9 - 1,1) pu, according

to the requirement for voltage quality of EU

[9].

The mathematical model of this

optimization problem is listed below:

Objective function, according to (10) is:

2 2

02

cosMax

1cos

L r

L r L k

k S

k S k P U pu PU pu

(12)

Constraints defined for the optimization

variable i.e. the operating voltage U pu

are:

0,9 1,1U pu

4.CASE STUDIES IN ORDER TO

OPTIMIZE POWER TRANSFOR-

MERS’ OPERATING VOLTAGE

BY MINIMIZING LOSSES AND

MAXIMIZING EFFICIENCY In regard with the two optimization

problems (A and B) defined in the above

chapter, a case study has been performed for

oil-immersed and dry-type distribution power

transformers 20/0,4 kV, with four rated

capacities along the gamma. The

manufacturer specification parameters of

these transformers are given in table 1,

according to the EU “Green” requirements for

production of energy efficient power

transformers, stated in [6, 7, 8]:

Table 1

rS Oil-immersed Dry-type

0P kP Ku 0P kP Ku

kVA kW kW % kW kW %

250 0,3 3,2 4,5 0,52 3,8 6

630 0,6 6,5 6 1,1 7,6 6

1600 1,2 14 6 2,2 13 6

2500 1,75 22 6,5 3,1 19 6

The performed multi-case study in regard

with the two predefined optimization models,

as stated above, have been fulfilled in the

environment of the software product

Microsoft Excel, using its add-on for solving

of optimization problems “Solver”.

In regard with minimizing transformer’s

active power losses by optimization of its

operating voltage, the following results have

been obtained and presented graphically in

fig. 2 for oil-immersed transformers and in

fig. 3 for dry-type transformers.

Analyzing figure 2, for oil-immersed

distribution transformers, minimal power

losses are obtained in the following

conditions:

38


4

Transformers with loading under 23% of

their rated capacity should operate at

minimal allowable voltage;

In the loading range of 23% - 43%,

operating voltage must be regulated to

increase linearly with load.

For loadings over 43 %, oil-immersed

transformers must be operated at maximal

allowable voltage.

0

0,2

0,4

0,6

0,8

1

1,2

Op

era

tin

g v

olt

ag

e

Loading factor

Sr=250kVA(oil)

Sr=630kVA(oil)

Sr=1600kVA(oil)

Sr=2500kVA(oil)

0,23 0,43Lk

Lk

, puU

Figure 2. Optimal operating voltage of oil-

immersed distribution transformers in p.u.

units as a function of transformer’s loading in

order to maintain minimal power losses.

0

0,2

0,4

0,6

0,8

1

1,2

Op

era

tin

g v

olt

ag

e

Loading factor

Sr=250kVA(dry)

Sr=630kVA(dry)

Sr=1600kVA(dry)

Sr=2500kVA(dry)

0,33 0,53Lk

Lk

, puU

Figure 3. Optimal operating voltage of dry-

type distribution transformers in p.u. units as

a function of transformer’s loading in order to

maintain minimal power losses.

Analyzing figure 3, for dry-type

distribution transformers, minimal power

losses are obtained in the following

conditions:

Transformers with loading under 33% of

their rated capacity should operate at

minimal allowable voltage;

In the loading range of 33% - 53%,

operating voltage must be regulated to

increase linearly with load.

For loadings over 53 %, dry-type

transformers must be operated at maximal

allowable voltage.

In regard with maximizing transformer’s

efficiency by optimization of its operating

voltage, the following results have been

obtained and presented graphically for oil-

immersed transformers in fig. 4 and fig. 5 and

for dry-type distribution transformers in fig.

6.

0,97

0,975

0,98

0,985

0,99

0,995

Eff

icie

ncy

Loading factor

Sr=250kVA(oil, PF=0,7)



Sr=250kVA(oil, PF=1)

Lk

Loading range with

maximum efficiency

Figure 4. Optimal loading range for

maintaining of maximal efficiency of oil-

immersed distribution transformers with rated

capacity of 250 kVA, varying load’s power

factor.

From figure 4 it is clearly obvious that a

certain power transform will have maximum

efficiency in a specific loading range, which

is independent on the load’s power factor.

Efficiency increases along with load’s power

factor but the trend of the curve remains

unchanged for the different cases.

0,97

0,975

0,98

0,985

0,99

0,995

Eff

icie

ncy

Loading factor

Sr=250kVA(oil)

Sr=630kVA(oil)

Sr=1600kVA(oil)

Sr=2500kVA(oil)

Lk

Optimal loading range

0,25 0,45Lk

0,8PF

Figure 5. Optimal loading range of oil-

immersed distribution transformers, having

different capacities, in order to maintain

maximal efficiency.

39


5

0,965

0,97

0,975

0,98

0,985

0,99

0,995Ef

fici

en

cy

Loading factor

Sr=250kVA(dry)

Sr=630kVA(dry)

Sr=1600kVA(dry)

Sr=2500kVA(dry)

Lk

Optimal loading range

0,30 0,55Lk

0,8PF

Figure 6. Optimal loading range of dry-type

distribution transformers, having different

capacities, in order to maintain maximal

efficiency.

As seen in figure 5, oil-immersed power

transformers will have maximal efficiency in

the loading range between 25 and 45 % of

their capacity, independently on their power

rating.

Considering the dry-type distribution

transformers (fig. 6), they will have maximal

efficiency in the loading range between 30

and 55 % of their capacity, independently on

their power rating. It is obvious that dry-type

transformers have optimal loading range,

wider with almost 5%, compared to oil-

immersed transformers.

0,97

0,975

0,98

0,985

0,99

0,995

Ma

xim

al

eff

icie

ncy

Loading factor

Sr=630kVA(oil, PF=0,7)Sr=630kVA(dry, PF=0,7)

Lk

Efficiency difference 0,4%

a)

0,976

0,978

0,98

0,982

0,984

0,986

0,988

0,99

0,992

0,994

Ma

xim

al

eff

icie

ncy

Loading factor


Lk


b)

0,98

0,982

0,984

0,986

0,988

0,99

0,992

0,994

Ma

xim

al

eff

icie

ncy

Loading factor


Lk


c)

0,984

0,986

0,988

0,99

0,992

0,994

0,996

Ma

xim

al

eff

icie

ncy

Loading factor


Lk


d)

Figure 7. Maximal efficiency difference

between oil-immersed and dry-type

distribution transformers.

a) 630 kVArS , cos 0,7 ; b) 630 kVArS ,

cos 0,9 ; c) 2500 kVArS , cos 0,7 ; d)

2500 kVArS , cos 0,9 ;

If contemporary oil-immersed and dry-type

power transformers are compared in regard

with their efficiency, the following

conclusions can be made (fig.7):

Oil-immersed transformers have always

higher energy efficiency than dry-type

transformers;

In the low capacity range gamma, the

maximal efficiency difference is around

0,4 – 0,5 % in favor of oil transformers,

independently of the power factor(fig. 7 a,

b);

In the high capacity range, the maximal

efficiency difference decreases and is

around 0,2 – 0,3 %, again in favor of oil

transformers;

40


6

CONCLUSIONS

Dry-type distribution transformers have

wide application and are preferred more and

more in urban areas, small companies, public

buildings etc., because of their fire and

explosion proof safety. Also they can be

installed directly inside the buildings saving

space and additional expenses.

However, dry transformers have higher

noise levels and operating temperature, higher

active power and energy losses, and lower

efficiency than oil-immersed transformers.

All this causes increased long-term expenses

for covering of their losses.

In order to decrease power losses and

increase transformers’ efficiency, the

following conclusions can be made in regard

with the optimal operating parameters of oil-

immersed and dry-type distribution

transformers:

A. By regulation of operating voltage at

the primary of the transformer:

Oil transformers with loading under 23%

of their rated capacity should operate at

minimal allowable voltage. In the loading

range of 23% - 43%, operating voltage

must be regulated to increase linearly with

load. For loadings over 43 %, oil-

immersed transformers must be operated at

maximal allowable voltage.

Dry-type transformers with loading under

33% of their rated capacity should operate

at minimal allowable voltage. In the

loading range of 33% - 53%, operating

voltage must be regulated to increase

linearly with load. For loadings over 53 %,

dry-type transformers must be operated at

maximal allowable voltage.

Operating voltage can be regulated

successfully in industrial electrical

distribution networks mostly and is hardly

applicable for public distribution power

networks;

B. By choosing the optimal rated

capacity and the correct type of power

transformer:

Oil-immersed transformers have always

better energy efficiency than dry-type

transformers;

Oil-immersed power transformers have

maximal efficiency in the loading range

between 25 and 45 % of their capacity,

independently on their power rating;

Dry-type distribution transformers have

maximal efficiency in the loading range

between 30 and 55 % of their capacity,

independently on their power rating.

Dry-type transformers have optimal

loading range, wider with almost 5%,

compared to oil-immersed transformers.

In the low capacity range gamma, the

maximal efficiency difference is around

0,4 – 0,5 % in favor of oil transformers,

independently of the power factor;

In the high capacity range, the maximal

efficiency difference decreases and is

around 0,2 – 0,3 %, again in favor of oil

transformers;

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Ahn, Distribution Transformer Losses

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No. 2, May 2009;

2. Hulshorst, W.T.J., J.F. Groeman, Energy

saving in industrial distribution transformers

KEMA, 2002

3. Kennedy, B. W., Energy-efficient

Transformers, Mc Graw Hill, 1998;

4. Petrenko, L. I., Electrical Power Networks.

Handbook with problems, Publisher house

“Higher School”, Kiev, 1976, UDK

621.311(07);

5. Kirchev, V., K. Yanev, M. Georgiev,

Electrical Power Networks – Medium and

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6. ABB, Technical guide. MV/LV transformer

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548/2014 of 21 May 2014 on implementing

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41

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Annals of the „Constantin Brancusi” University of TarguK...Annals of the „Constantin Brancusi” University of Targu Jiu, Engineering Series , No. 2/2017 3 TRANSFORMER’S EFFICIENCY