1
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
2
Main sections of lecture:
1. Introduction.
2. Power flow direction.
3. Transformer losses
4. Method of losses reduction
5. Conclusions
3
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.
4
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
6
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
7
Fig.1 Power losses in power networks of different countries.
Netherlands
Germany
Japan
Italy
USA
France
Switzerland
Spain
Austria
Canada
New Zealand
8
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.
9
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.
10
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
11
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
14
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
15
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,
16
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
17
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
19
Source of voltage unbalance
Positive sequence Zero sequenceNegative sequenceFig. 11.
20
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
21
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
~
22
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
24
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.
25
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
26
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:
27
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.
28
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.
31
. 1.2
/ , %n
Tr TrP P
k-factor
13
Graph of transformer lossversus current harmonics
Fig. 18.
32
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…”
33
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.
34
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.
35
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;
37
.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
38
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
39
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
40