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Electric Power Quality and CommercialLosses in Power Distribution Networks

A.M. Lipsky N.V. Miteva E.. Loks!in

Ariel "niversity Center o# amaria$ %srael

Abstract — Some study results about commercial losses in electrical supply networks withnonlinear loads are presented in the paper. It is shown that the power losses in power supplynetworks and transformers, which are caused by current distortions, represent commercialpower losses of power supply companies. These losses are fundamentally different from thetechnological or technical power losses associated with power supply of the electricityconsumers of various types. Technological losses cannot in principle be reduced to zero, whilethe commercial losses associated with electric power quality distortions may, in principle, be

reduced to a value close to zero. For instance, energy distortion caused by current harmonicshas been estimated by the magnitude of such losses in the power transformer that depend onthe magnitude of the current T! and the "#factor value. It is found that in many cases theselosses significantly e$ceed the accuracy class of the power and energy meters used in powernetworks. Thus, in order to improve the efficiency of power system operations and to reducecommercial losses, it is proposed to consider these losses when evaluating the balance ofgenerated and consumed electric power by calculating such losses when energy meters areinstalled on the secondary side of transformers which connect consumers to the powersystem.

Key words—commercial losses$ trans#ormer losses and !i&!er current !armonics.

%. Introduction'!e mart (rid concept$ related to t!e power networks and systems re)uire

pro#itability o# t!e power supply *+,. Amon& ot!er t!in&s$ t!is means correct

measurement o# t!e produced and consumed active ener&y )uantities$ i.e.$ correct

meter readin& o# t!e active ener&y meters or active power meters. '!e active power

produced to supply a particular consumer may be presented as #ollows- PPP c& += /+0

w!ere Pc is t!e consumed active power1

∆P is t!e active power losses associated wit! t!e power supply o# a particular

consumer.

'!e active power losses ∆P consists o# tec!nical losses and non2tec!nical or

commercial losses *3$4 and ot!ers,. '!e tec!nical losses are associated wit!

transmission and distribution o# produced ener&y$ w!ile t!e commercial losses are

related to t!e imbalance o# t!e amount o# ener&y transmitted to t!e consumer and

t!e amount o# ener&y w!ic! is metered by t!is consumer *5$ 6,. 7nly commercial

losses are considered #urt!er on.

7ne o# t!e components o# commercial losses is t!e loss associated wit! t!e

incorrectness o# t!e system electrical ener&y or active power meterin&. '!e meterin&

values are in#luenced by various #actors$ includin& t!e presence o# current and

volta&e !armonics into power systems *8$ 9$ :$ ; and ot!ers,.

'!e present study analy<es t!e measurement results o# active power and ener&yas well as t!e correspondin& commercial losses in t!e power networks supplyin&

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only consumers w!ic! are sources o# current !armonics. '!e ot!er #actors t!at a##ect

t!e measurement readin&s o# t!e active and ener&y meters are not taken into

consideration.

A typical sc!eme o# power supply o# a consumer t!at is a source o# current

!armonics is s!own in =i&.+. %n t!is #i&ure P is t!e e)uivalent power supply system

t!at trans#ers electrical ener&y to t!e trans#ormer 'r. A nonlinear load L$ w!ic! is asource o# current !armonics$ is supplied by t!is trans#ormer. '!e points A and > are

t!e possible meter locations in t!e power network. ? is t!e s!ort circuit power at

point A. %t is assumed t!at L is t!e only source o# current !armonics in t!e power

system P. '!e load consumes #rom t!e power system electric ener&y only o# t!e

main #re)uency. '!e nonlinear load &enerates t!e current !armonics into t!e power

supply network *+@,.

'!e readin& o# t!e active power meters installed at t!e points A and > /=i&.+0 are

determined by t!e #ollowin& epressions-

∑=

−+=

n

3!

B'.!L.+'r.+ A PP PP /30

∑∑==

−−=

n

3!

B'.!

n

3!

'r.!L.+> P PPP /40

w!ere ∆P'r.+ is t!e trans#ormer loss due to t!e basic current !armonic1

PL.+ is t!e active power consumed by t!e nonlinear load1

∆P'r.! is t!e sum o# t!e trans#ormer losses due to t!e current !armonics$

w!ere t!e !armonic number ! c!an&es #rom 3 up to n1

∆PB'.! 2is t!e sum o# t!e losses in t!e e)uivalent resistance o# t!e power

system due to t!e current !armonics$ w!ere ! c!an&es #rom 3 up to n.

'!e di##erence in t!e readin&s o# t!e active ener&y meters at points A and >

&ives t!e value o# active power losses and de#ines active power losses in t!e

trans#ormer due to t!e basic and t!e !i&!er !armonics$ i.e.-

∑=

+==

n

3!

'r.!'r.+> A P PP2P P /50

'!e value o# active power o# t!e trans#ormer losses at t!e basic !armonic is

associated wit! t!e losses due to t!e transmission o# t!e produced ener&y to t!e

consumer$ i.e.$ t!e tec!nical losses are uni)uely determined by t!e passport data o#

t!e trans#ormer$ takin& into consideration its load #actor *++$+3 and ot!ers,. '!is

component o# t!e di##erence between t!e meter readin&s is not analy<ed #urt!er on.

%n t!e case under consideration$ t!e value o# t!e power losses in t!e trans#ormer

due to t!e current !armonics is determined by t!e distortion power *8,$ w!ic! is not

produced by t!e power system but a##ects t!e meter readin& and causes ener&y

imbalance in power networks. '!ere#ore$ t!e losses related to t!e distortion powers!ould be included into t!e commercial losses.

=i&. +- A typical sc!eme o# power supply

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%n practice$ t!e commercial losses eit!er cannot be measured or it is very di##icult

to do t!is. owever$ in order to obtain t!e amount o# commercial losses to be taken

into account$ some o# t!eir types may be calculated wit! a certain de&ree o#

accuracy.

>elow$ t!e commercial losses o# t!e power system associated wit! t!e current

!armonics$ &enerated to t!e network by t!e nonlinear load L /=i&.+0 are calculated.=or t!is purpose$ t!e amount o# t!e trans#ormer losses due to t!e current !armonics

∆P'r.! t!at is one o# t!e components o# t!e commercial losses is determined takin&

into account *:$ +4,.

&. ' (hysical )etwork *odel

A p!ysical model o# a power network wit! a nonlinear load t!at corresponds to

t!e typical sc!eme o# power s!own in =i&.+ is considered /=i&. 30. '!e resistance L

is used as a load. 'o avoid t!e in#luence o# t!e e)uivalent system impedance o# t!e

34@V power supply system on t!e measurement results$ an additional resistance '

is connected as a virtual trans#ormer resistance. %ts value eceeds many times t!eresistance value o# a real trans#ormer and o# t!e 34@V power system connected to

t!e sc!eme input terminals A+2A3. '!is allows avoidin& t!e noticeable measurement

error in real conditions /=i&.+0. %n order to avoid t!e p!ase s!i#t between t!e volta&e

and current o# eac! !armonic #re)uency$ includin& t!e basic #re)uency$ and in t!is

case t!e arisin& FnonG2active powers *+5,$ a power re&ulator e& /=i&.30$ based on

t!e M7=E' transistor is connected between t!e load and point >.

%dentical types o# watt2meters H+ and H3 used in t!e sc!eme are di&ital devices

o# @.3 accuracy class$ accordin& to t!e %EC 83@64233 standard *+6,.

4. +$perimental esults

=our sets o# measurements are carried out$ w!ere t!e durations o# t!e current

conduction intervals are as #ollows 2 3 ms$ 5 ms$ 8 ms and : ms. '!is allows us to

compare t!e in#luence o# currents wit! a di##erent distortion #actor 'D%-

( ) +@@I%'D%n

3!

3J! ⋅= ∑

=

/60

and K2#actor-

( )∑=

⋅=−

n

+!

33J! !%#actor K

/80

on t!e watt2meters readin& values$ and t!e in#luence o# t!ese coe##icients values on

t!e amount o# commercial losses. %n epressions /60 and /80 %!J is per unit values o#

current !armonics. '!e values c!aracteri<in& commercial losses ∆Pcom.A and ∆Pcom.>$

w!ic! determine t!e imbalance between t!e amount o# produced active power and

t!e active power measured by t!e consumer$ may be presented respectively as#ollows-

=i&. 3. A p!ysical model #or t!e investi&ation o# t!e meter re&istrations

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+

n

3!

B'.!

C7M.AP

P

P

∑==

/90

+

n

3!

B'.!'r.!

C7M.>P

0 P/

P ∑=+

= /:0

w!ere ∆PB'.! and ∆P'r.! are t!e losses due to current !armonics in t!e

e)uivalent system resistance /at 34@V0 and in t!e virtual trans#ormer resistance1

P+2 is t!e active power at t!e basic !armonic received #rom t!e electrical

network.

ome investi&ation results are s!own in 'able + and 'able 3 w!en B'+9.: Ω

and L:9.3;Ω. '!e 'D% #actor and K2#actor are calculated #or eac! o# above

investi&ated current durations respectively be#ore /point A0 and a#ter t!e trans#ormer

/point >0. '!e calculated results are s!own in 'able 4.

'able +- Measured results at point A

∆t *ms, P A *H, P+ *H, ∆PB'. *H, PC7M.A *I,

3 +:5.3 +:8.; 23.9 2+.59

5 449.6 44:.8 2+.+ 2@.44

8 5+5.9 5+5.6 @.3 @.@6

: 59+.; 59+.3 @.9 @.@3

'able 3- Measured results at point >

∆t *ms, P> *H, P+ *H, /∆PB'. ∆P'. 0 *H, PC7M.> *I,

3 +65.: +95.9 2+;.; 2+3.:8

5 3:4.@ 3;;.8 2+8.8 26.:98 458.; 464.6 28.8 2+.;@

: 4;5.@ 4;5.6 2@.6 2@.+4

'able 4- Measured and calculated results at points A and >

∆t *ms, 3 5 8 :

k2#actor *p.u., 3@.6 :.8 5.8 +.;

'D *I, ++; 83 44 +3

PC7M.A *I, +.59 @.44 @.@6 @.@3

PC7M.> *I, +3.:8 6.:9 +.; @.+4

'!e meter readin&s at point > /'able 30 can di##er si&ni#icantly #rom t!e active

power value P+ supplied to t!e consumer by a power network o# 34@V. H!en t!eimpulse duration is 3 ms$ w!ic! corresponds to 'D% o# ++;I and to K2#actor o#

3@.6$ t!e di##erence in t!e meter readin&s$ i.e.$ t!e imbalance o# active power and

respectively o# active ener&y$ reac!es up to +3.:8I /'able 40. H!en t!e impulse

duration is : ms$ w!ic! corresponds to 'D% value e)ual to +3I and to K2#actor

value e)ual to +.;$ t!e imbalance o# active power and respectively o# active ener&y is

very small$ about @.+I /'able 40.

'!e results o# watt2meter readin&s at point A /'able +0 s!ow t!at in t!e worst

case$ w!en t!e duration o# t!e current conduction is 3 ms /'D% ++;I and K2#actor

3@.60$ t!e active power and ener&y imbalance is about +.59I. '!ere#ore$ in t!is

case$ t!e measured commercial losses at point A$ related to t!e power supply o# t!enonlinear load$ are about ten times less t!an t!e correspondin& commercial losses

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measured at point >.

-. erification of +$perimental results

'!e sc!eme in =i&.+ corresponds to t!e real sc!eme o# power supply. '!is

sc!eme is analy<ed wit! t!e real parameters o# t!e consumed power and o# t!e

trans#ormer. '!e resistance$ eternal to t!e load /t!e point >$ =i&.+0$ is a sum o# t!e

trans#ormer resistance ' and t!e resistance o# t!e power system . '!e power

system resistance depends on t!e value o# t!e s!ort circuit power ? at t!e primary

volta&e o# t!e trans#ormer.

(enerally$ t!e power o# t!e trans#ormer in industrial power systems is

si&ni#icantly smaller t!an t!e s!ort circuit power at t!e point w!ere t!e system is

connected to t!e trans#ormer primary side. '!at is w!y$ 'OO and t!us$ t!e

value in t!e #ollowin& calculation can be ne&lected.

%t is assumed t!at t!is load o# t!e trans#ormer is a resistance$ supplied t!rou&!

t!e power re&ulator o# t!e same type described above. %t is also assumed t!at t!e

re&ulation is carried out in t!e same ran&e as it was done in t!e investi&ation model-t!e durations o# t!e current impulses are 3$ 5$ 8 and : ms.

'!e trans#ormer losses are calculated by t!e met!od described in t!e 69.++@2

3@@: standard *+8,. As an eample$ t!e li)uid #illed trans#ormer w!ose tec!nical data

are &iven in *++, is considered- 36@@ kVA$ "+"345.63.5kV$ Dye$ ".C.8I$

P@6+@@H$ P.C. 3+;5+H$ +5.@58R$ 3@.@+88R$ %+2 5+.:A$ %32 8@+.5A. '!e

value o# t!e trans#ormer losses w!en t!e trans#ormer is #ully loaded and in t!e

absence o# t!e current !armonics is +.@8I.

ome calculation results about commercial losses$ obtained durin& t!e

measurements o# active power values and t!e correspondin& active ener&y values at

point > /'able 30$ are s!own in 'able 5. Analy<in& t!ese results$ it is evident t!at t!ecommercial losses can reac! lar&e values$ si&ni#icantly eceedin& t!e accuracy class

o# t!e meter w!en t!e consumed active power and t!e correspondin& active ener&y

at t!e secondary side o# t!e trans#ormer are measured #or values o# 'D% lar&er t!an

36I and o# K2#actor lar&er t!an 5.6. '!ere are a lot o# consumers w!ic! are sources

o# current !armonics and are c!aracteri<ed by 'D% e)ual or lar&er t!an :62+3@I

and by K2#actor e)ual or lar&er t!an +423@ *+9,. =or suc! consumers t!e commercial

losses measured at t!e secondary side o# t!e trans#ormer are +2+.8I.

'able 5- Calculated results in real trans#ormer 36@@ kVA

∆t *ms, 3 5 8 :

k2#actor *p.u., 3@.6 :.8 5.8 +.;'D *I, ++; 83 44 +3

PC7M.> *I, +.: @.69 @.3+ @.@5

/. 0onclusions

'!e concept o# mart (rid assumes t!e use o# smart active ener&y meters.

H!en suc! meters are installed at t!e secondary side o# t!e supplyin& trans#ormer$

t!e power losses due to t!e current !armonics in t!e trans#ormer may be calculated

accordin& to t!e met!od described in %EEE C69.++@23@@: standard *+8, and taken

into consideration w!ile workin& out t!e balance between t!e produced and

consumed active power. '!e investi&ations carried out !ave s!own t!at w!en t!eamount o# consumed electrical ener&y o# t!e a#orementioned loads is measured on

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t!e primary side o# t!eir power trans#ormers$ t!e commercial losses caused by

current !armonics are reduced about ten times. '!e power losses at t!e #undamental

#re)uency may be obtained in t!e simplest way usin& t!e passport data o# t!e

trans#ormer *++$ +3,.

Ener&y losses in power networks and in &rid trans#ormers o# t!e power

consumers &eneratin& current !armonics are t!e commercial power losses o# t!epower system. '!ey c!aracteri<e t!e ne&ative electric ener&y balance in power

networks wit! nonlinear loads.

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