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A. Lipsky, N. Miteva, E. Lokshin

Department of Electrical and Electronic EngineeringAriel University Center of Samaria

Israel

Electric Power Quality and Commercial Losses in Power Distribution Networks

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Main sections of lecture:

1. Introduction.

2. Power flow direction.

3. Transformer losses

4. Method of losses reduction

5. Conclusions

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1 .Introduction.

One of the main issues of the European Smart Grid

concept, which characterizes the power networks and

systems, is the profitability of the power supply.

Among other factors, it is determined by the energy

losses in electric power systems.

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Generation and transmission of electrical

energy produced by the power system

generators to its customers is characterized

by technological expenditures for its

transmission and distribution. These

technological expenditures are called technical

losses. The major share of technical losses in

power networks, about 70% , refers

to the distribution power networks (6-110 kV

network).

G ~

Line

T1

T2

Load

GW

LoadW

.1TrW

.2TrW

LW

5

G ~

Line

T1

T2

Load

GW

LoadW

.1TrW

.2TrW

LW

In addition, there are losses due to the fact that the amount of electric power transmitted to the distribution network is determined by the meters of power systems, and the electric power, which is received by consumer, is determined by the meter readings of the consumers. The last component of losses belongs to the so-called commercial losses.

Thus, the total loss of electricity W can be represented in the form of two components: technical loss WТ and non-technical or commercial loss WС:

T CW W W

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Commercial losses represent actual

imbalance in the power energy in power network,

which can be represented as:

Where WPS is energy transferred by its source to

the power network (PS - power system), W СPM

is energy, fixed by consumer meter (CPM -

consumer power meter), WТ is technical losses

of electric power.

Full power losses represent a significant

values.

C PS Т CPMW W W W

CWG ~

Line

T1

T2

Load

PSW

CPMW

.1TrW

.2TrW

LW

W

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Fig.1 Power losses in power networks of different countries.

Netherlands

Germany

Japan

Italy

USA

France

Switzerland

Spain

Austria

Canada

New Zealand

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There are several known reasons of commercial losses.

It should be noted that the error in determining of the

technical losses also relates to business losses.

One of the reasons of commercial losses is measu-

rement errors. There are known more than 30 components

of the measurement errors in power supply networks.

In spite of this, there is one more component of the

measurement error of electrical energy that is not

considered already. This component refers to the special

measurement errors of power meters, caused by

deteriorated electric power quality of a certain group of

industrial and domestic consumers.

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Let us consider for the beginning electric power

consumer, which is the source of the current harmonics.

Fig. 2. A typical scheme of power supply

Tr

L

~

AS

''S

B

AU BU

BB

LL

What measure active energy meters of consumer which

is the source of electric power quality deterioration?

50 Hz

2. Power flow direction.

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Power distortion flowing according to the previous scheme

BA

E

systZPowersystem

Loadlinear

loadZ

. 50L f HzP

. 50S f HzP

. 50LL f HzP

3 50HzPsymmetric

Fig. 4.

75f Hz

С

.50 . . 50A L Hz SYM L f HzP P P

.50 . . 50B LL Hz SYM LL f HzP P P

50 . . 50 . 50C Hz SYM L f Hz LL f HzP P P P

50 Hz

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Further let us consider the electric power consumer, which

is the source of the current fluctuations which lead to

appearance of voltage fluctuations.

Fig. 5. A typical scheme of EAF power supply

For example, let us consider only the current fluctuations

of one phase, caused by electric arc furnace.

Tr

~

AS

''S

B

AU BU

BB

LL

EAF

50 Hz

12

sec1 2 3

P

Fig. 6. The diagram of fluctuations of consumed powers

Q

S

13

p.u.

, Hz

Fig. 8. Power spectrum of the envelope current,

which modulate the impact on the fundamental

current amplitude of electric arc furnace

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In general, the modulating function describes a random

process. To clarify the essence of the phenomenon

represented modulating function as a sine wave

mod .mod cosmi I t In this case, the current in the network may be represented as

max 0( ) ( ) cosi t I t t Or

max 0( ) 1 cos cosi t I m t t

where .mod

max

mImI

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After trigonometric transforms the current can be

represented by the following components

m.modmax 0 0

m.mod0

( ) cos cos2

cos2

Ii t I t t

It

I.e. in the current there are components with frequencies

which are not generated by energy

sources of power system.

0 0,

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22 2 m.mod

max 2max

1( ) 1 0.5

T

Ii t r dt rI

T I

I.e. the additional losses in the external source to the

terminals of voltage fluctuation resistance r in p.u.

defined as

20.5 .P m

Average for the period of modulation function power

loss in the resistance r is defined as

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Power distortion flowing for voltage fluctuation source

BA

E

systZPowersystem

Loadnormal

loadZ

. 50L f HzP

. 50S f HzP

. 50LL f HzP

3 50HzPsymmetric

Fig. 9.

С

.50 . . 50A L Hz SYM L f HzP P P

.50 . . 50B LL Hz SYM LL f HzP P P

50 . . 50 . 50C Hz SYM L f Hz LL f HzP P P P

0.05 75VFf Hz Hz Besides f =50±0.05 Hz

50 Hz

2.50 . 0.5 .A L Hz SYM nomP P m P

Fig. 10. AC railway connections as examples of

asymmetrical load connections.

Source of voltage unbalance

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Source of voltage unbalance

Positive sequence Zero sequenceNegative sequenceFig. 11.

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Power distortion flowing for voltage unbalance source

BA

E

systZPowersystem

Loadnormal

3 50HzPsymmetric

Fig. 13.

С

.50 . . 2,A L Hz SYM L U UOP P P

.50 . . 2, 0B LL Hz SYM LL U UP P P

50 . . 2, 0) . 2, 0C Hz SYM L U U LN U UP P P P

. 2, 0S U UP

. 2, 0L U UP

2, 0 25U Uf Hz

Includes f =50 Hz

. 2, 0LN U UP

Source of voltage unbalance

50 Hzsymmetric

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Therefore, regardless of the type of meter, the active

energy meter errors in all cases are equal to the losses in

external, relative to the voltage distortion source terminals,

power network on the frequencies of the current harmonics,

voltage fluctuations and on frequencies of current negative

and zero sequences.

I.e. these are losses in the nearest power transformer

and power transmission lines of primary voltage of the

power transformer. T1 T2

LineG

~

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Thus, the commercial losses of the power

supply organization, are mainly determined

by the losses in power transformers, which

caused by distortion energy of particular

source of power quality deterioration (See

the next slide).

A typical scheme of power supply

Fig.14.

Therefore,

kWhmeter

50 Hz

, , 0S S Tr S SX R X X X

3. Transformer losses

''S

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Estimate the losses in power transformers due to the

asymmetry of the load, its oscillatory nature and its

generation of current harmonics.

In general case, the various types of current

distortions are not constant and vary with time. The use

of spectral methods for the calculation of losses in this

case requires the frequency separation of currents and

voltages distortions.

The following is a proposal for such a frequency

separation of different types of distortions.

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Consider the simplest methods of losses calculations in

transformers due to the distortions of currents and

voltages of different types. They allow you to evaluate the

state of the problem.

2

2.

.

( ) | ( ) |Tr k k k kIk

P G R j d

The losses in the transformer according to the various

types of current distortions on the basis of spectral

methods in general can be evaluated as:

k

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2 22 2 2 . . , ( )I I I S Cm P m P kW

are expectation value and standard deviation of

process, is transformer rated current, is s.c.

transformer loss, (kW).

2I

nomI. .S CP

2 22 2, ,I I

I Inom nom

mm

I I

Where 2 2,I Im

Considering the current distortions as random

processes, the average loss in power transformers due

to the asymmetry of the current is defined as:

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Neglecting the dependence of the transformer resistance on

the frequency for frequencies below 75 Hz, this formula can

define and the transformer losses due to the oscillatory

nature of the load.

It is much more difficult to determine the losses in the

power transformer due to current harmonics generated by

the nonlinear loads.

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It is known that load losses of the current

harmonics in power transformers are determined as:

Ll DC EC OSLP P P P

Where is loss due to resistance of winding

for dc current, is winding eddy current loss,

is other stray losses in structural parts of

transformer such as tank, clams and so on.

DCP

ECP

OSLP

Some the results of losses calculations taking into

 consideration these components are shown below.

LlP

Liquid filled transformer

Transformer data

The power losses due to harmonics are calculated according to С57.110-2008 standard

Fig. 16.

Some results of power losses calculations

. 1.2

/ , %n

com Tr TrP P P

1.1%

1.1%

I Fig. 17.

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. 1.2

/ , %n

Tr TrP P

k-factor

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Graph of transformer lossversus current harmonics

Fig. 18.

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Estimate of losses magnitude

Estimated transformer population in the world (February 2005)

“… Nowadays, over 50% of load is non-linear. For

example the are computers, energy saving lights,

office equipment, variable speed drives…”

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For example, Japan's commercial losses as losses in

transformers only due to current harmonics can be

estimated as (cos φ ≈ 1):

= 900 GW × (0.5×0.01×0.7) = 3.5 GW.

When load factor is equal to 0.7 .

It is power of two good power stations.

In general, commercial losses of power supply

organization due to only the current harmonics can

be estimated as:

co .0.35%m TRP P

comP

Measurement and taken into account of the commercial losses.

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The carried out analysis of the commercial losses allows

to conclude, that one of the ways to reduce these losses

(may) can be the reduction of current harmonic levels

generated by their sources in the supply network. This

can be accomplished in many ways, including using

current harmonic filters.

4. A method for commercial losses reduction

Reducing power losses of current harmonics in power

transformers of consumers’ networks and external

power supply network also reduces technical losses in

power networks. I.e. losses at a frequency of 50 Hz.

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Consider the expression of the energy balance for

produced and consumed in a power network with a

source of the current harmonics in the following form:

cons.50Hz cons.50Hz dis.50 HzgenW W W W

genWHere is energy produced by generators to supply a

specific consumer except of own energy producer needs,

cons.50HzW is energy consumed by this customer at 50 Hz,

cons.50HzW is technical loss associated with electricity

supply of consumers, which has equivalent just the same

power and that it is not a source of current harmonics,

dis.50HzW is an equivalent value of the energy distortion,

which must produce the energy source at 50 Hz

frequency.

.50 .50 .dis Hz dis Hz disW W W

.50 .dis Hz disW and W are loss of energy at 50 Hz

frequency, associated with the transportation equivalent

value of the distortion energy at 50 Hz to the consumer, and

the loss of energy due to their generation of current

harmonic source;

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.50 .50 . .50 .dis Hz dis Hz line dis Hz TrW W W

. . . . .dis dis line dis TrW W W

These energy losses are presented as:

Thus

cons.50Hz cons.50Hz

.50 . .50 .

. . . .

gen

dis Hz line dis Hz Tr

dis line dis Tr

W W W

W W

W W

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Thus, the power system total losses for power supply

of the power consumer, which is current harmonic

source, by more than 2 times higher than the power

transformer losses due to current harmonics.

Reducing the levels of the current harmonics in the

limit up to zero, i.e. assuming one can

reduce the amount of commercial and technical losses

at least by twice to the losses in the power transformer

and the external network users due to harmonics.

. 0,disW

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1. The power transformer losses of consumers, worsening

the electric power quality, are commercial losses of power

supplying organizations.

2. Reducing of these losses is possible by reduction of the

levels of current harmonic, current unbalance and

smoothing the load curve of specific consumers.

3. Reduction of this type of commercial losses leads to a

technical losses decrease.

4. There are relatively simple methods of calculation and

taking into consideration of this kind of commercial losses .

5 .Conclusion

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