Download Comparison of Distribution Transformer Losses and Capacity under

2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Comparison of Distribution Transformer Losses
and Capacity under Linear and Harmonic Loads
S.B.Sadati*, H.Yousefi*, B.Darvishi*, A.Tahani**
* Mazandarn Electric Power Distribution Company, Iran. Emails: [email protected], [email protected]
[email protected],
** Noshirvani Technical University of Babol, Iran. Emails: [email protected]
Abstract—The significance of harmonics in power systems
has increased substantially due to the use of solid state
controlled loads and other high frequency producing
devices. An important consideration when evaluating the
impact of harmonics is their effect on power system
components and loads. Transformers are major components
in power systems. Supplying non-linear loads by
transformer leads to higher losses, early fatigue of
insulation, and reduction of the useful life of transformer.
To prevent these problems rated capacity of transformer
supplying non-linear loads must be reduced. This paper
reviews the non linear loads effects on the transformers and
the standard IEEE procedures for derating of the
transformers which are under distorted currents. The
equivalent losses and capacity of a typical 25 KVA single
phase transformer is then evaluated using analysis and
simulations in MATLAB/Simulink-based on useful model of
transformer under harmonic condition- and results are
compared.
—
Keywords Transformer Losses and Capacity, Stray losses,
Derating of transformers, Harmonic loads
I.
INTRODUCTION
Harmonics and distortion in power systems current and
voltage waveforms emerged during the early history of ac
power systems. However, today the number of harmonic
producing devices is increasing rapidly. One result of this
is a significant increase of harmonics and distortion in
power system networks. Transformers are major
components in power systems and increased harmonic
distortion can cause excessive winding losses and hence
abnormal temperature rise. Temperature rise of
transformers due to non-sinusoidal load currents was
discussed in IEEE Transformer Committee in March
1980. This meeting Recommended providing a standard
guidance for estimation of the loading capacity of the
transformers with distorted currents. Finally, a standard
IEEE C57-110 entitled "recommended procedure for
determination of the transformer capacity under nonsinusoidal loads". The aim in publishing this standard was
providing a procedure for determination of the capacity of
a transformer under non- Sinusoidal loads. This procedure
determines the level of decreasing the rated current for
risen harmonic [1].
This paper reviews the non linear loads effects on the
transformers and the standard IEEE procedures for
derating of the transformers which are under distorted
currents. The equivalent capacity of a typical 25 KVA
transformer is then evaluated using analysis and
simulations in MATLAB/Simulink and results are
compared.
II. HARMONIC DEFINITION
Harmonic currents and voltages are created by nonlinear loads connected on the power system. Harmonic
distortion is a form of pollution in the electric plant that
can cause problems if the sum of the harmonic currents
increases above certain limits. All power electronic
converters used in different types of electronic systems
can increase harmonic disturbances by injecting harmonic
currents directly into the grid. A non-linear load is created
when the load current is not proportional to the
instantaneous voltage. Non-linear currents can be no
sinusoidal, even when the source voltage is a clean sine
wave. The principle of how the harmonic components are
added to the fundamental current is shown in Fig. 1,
where only the 5th harmonic is shown [2].
The non-linear loads that produce harmonics on the
power system are static converters, rectifiers, arc furnaces,
electronic phase control, cycloconvertors, switch mode
power supplies, pulse width modulated drives, etc.
TRANSFORMER LOSSES IN HARMONIC
LOADS
Transformer losses consist of no-load or core losses and
load losses. This can be expressed by (1).
PT = PNL + PLL
(1)
III.
where, PNL is no-load loss, PLL is load loss, PT is total
loss.
No-load loss is due to the induced voltage in core. Load
losses consist of ohmic loss, eddy current loss, and other
stray loss, or in equation form:
PLL = Pdc + PEC + POSL
(2)
where, Pdc is loss due to load current and dc resistance of
the windings, PEC is winding eddy loss, POSL is other
stray losses in clamps, tanks, etc.
Figure 1. Total current as the sum of the fundamental and 5th
Harmonic
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Pdc is calculated by measuring the dc resistance of the
winding and multiplying it by the square of the load
current. The stray losses can be further divided into
winding eddy losses and structural part stray losses.
Winding eddy losses consist of eddy current losses and
circulating current losses, which are considered to be
winding eddy current losses. Other stray losses are due to
losses in structures other than windings, such as clamps,
tank or enclosure walls, etc. The total stray losses are
determined by subtracting dc losses from the load losses
measured during the impedance test, i.e:
PTSL = PEC + POSL = PLL − Pdc .
(3)
There is no test method to distinguish the winding eddy
losses from the other stray losses [3].
A. Eddy current losses in windings
There are two effects that can cause increase in winding
eddy current losses in windings, namely the skin effect
and the proximity effect. The winding eddy current loss in
the power frequency Spectrum tends to be proportional to
the square of the load current and the square of frequency
which are due to both the skin effect and proximity effect,
i.e. [1]:
PEC ∝ I 2 × f 2 .
(4)
The impact of lower-order harmonics on the skin effect
is negligible in the transformer windings [4].
1) Proximity effect [4]
The proximity effect contribution to the winding eddy
current loss is defined as follows. Consider Fig.2. The HV
winding produces a flux density due to a changing current.
The LV winding and core cut the flux density. The flux
density that cuts the LV winding induces an emf that
produces circulating or eddy currents. This effect is called
the proximity effect, which is caused by a current-carrying
conductor, or magnetic fields that induce eddy currents in
other conductors in close proximity to the other currentcarrying conductor or magnetic fields. These Eddy
currents will dissipate power, PEC , and contribute to the
electrical loss in the windings in addition to those caused
by normal dc losses. The proximity effect loss can be
expressed as [4]:
Ppe =
µ 2 N ω 2 I 2 nd 4
Gr
128 ρ l
(5)
where, n is number of conductor strands, d is the strand
diameter, and I is maxim current. G r is proximity effect
factor and by considering δ =
1
ωµσ
,
Figure 2. Forming eddy current by proximity effect
if d / δ decreases to unity then G r → 1 ,
if d / δ is increasing beyond 4 then G r →
32 d
( − 1) .
d 4 δ
( )
δ
Below equation can be used for calculating the eddy
current loss too [3].
PTSL = PLL _ R − (R1I 12− R + R 2 I 22− R ) 
(6)
The winding eddy current loss is then calculated by
assumption 2 in 6.2 of [1] for oil-filled transformers:
PEC − R = 0.33PSTL .
(7)
B. Other stray losses in transformers
Each metallic conductor linked by the electromagnetic
flux experiences an internally induced voltage that causes
eddy currents to flow in that ferromagnetic material. The
eddy currents produce losses that are dissipated in the
form of heat, producing an additional temperature rise in
the metallic parts over its surroundings. The eddy current
losses outside the windings are the other stray losses. The
other stray losses in the core, clamps and structural parts
will increase at a rate proportional to the square of the
load current but not at a rate proportional to the square of
the frequency as in eddy current winding losses.
Experiments were done to find the change of other stray
losses with frequency. Results shown that the ac resistance
of the other stray losses at low frequencies (0–360Hz) is
equal to [5]:
0.8
f 
ROSL = 1.29  h  m Ω
(8)
 f1 
and at high frequencies (420-1200Hz) the resistance is
0.9
f 
ROSL = 9.29 − 0.59  h 
mΩ .
(9)
 f1 
Thus this loss is proportional to square of the load
current and the frequency to the power of 0.8.
Below equation can be used for calculating the other
stray loss.
POSL = PTSL − PEC
(10)
IV.
EFFECT OF HARMONIC ON NO-LOAD
LOSSES
According to Faraday’s law the terminal voltage
determines the transformer flux level, i.e.:
dϕ
= v (t ) .
(11)
dt
Transferring this equation into the frequency domain
shows the relation between the voltage harmonics and the
flux components:
Nj (h ω ).ϕh = V h .
(12)
N
This equation shows that the flux magnitude is
proportional to the voltage harmonic and inversely
proportional to the harmonic order h. Furthermore, within
most power systems the harmonic distortion of the system
voltage THD is well below 5% and the magnitudes of the
voltage harmonics components are small compared to the
fundamental component, rarely exceeding a level of 2-3%.
Therefore neglecting the effect of harmonic voltage and
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
considering the no load losses caused by the fundamental
voltage component will only give rise to an insignificant
error. This is confirmed by measurements in [6]. But if
THDv is not negligible, losses under distorted voltages can
be calculated based on ANSI-C.27-1920 standard with
(13).
2

V
 
(13)
P = PM  Ph + Pec  hrms  

 V rms  
where Vhrms and Vrms are the RMS values of distorted and
sinusoidal voltages, PM and P are no-load losses under
distorted and sinusoidal voltages , Ph and Pec are hysteresis
and eddy current losses, respectively [7].
V.
EFFECT OF HARMONIC ON LOAD LOSSES
[1]
In most power systems, current harmonics are of more
significance. These harmonic current components cause
additional losses in the windings and other structural parts.
A. Effect of harmonics on dc losses
If the rms value of the load current is increased due to
harmonic components, then these losses will increase with
the square of the current.
 hmax

PΩ = R dc × I A2 = R dc ×  ∑ I h2, rms 
 h =1

(14)
B. Effect of harmonics on eddy current losses
The eddy current losses generated by the
electromagnetic flux are assumed to vary with the square
of the rms current and the square of the frequency:
h = max
∑
Pec = Pec − R
h2(
h =1
Ih 2
)
IR
(15)
The harmonic loss factor for winding eddy currents is
derived as:
2
I 
h2  h 
∑
∑
h =1
 I1  .
FHL = hh==1max
=
(16)
2
h
=
max
2
 Ih 
I
∑
h
 
∑
h =1
h =1  I 1 
Therefore under harmonic loads, eddy current losses in
winding must be multiplied in harmonic losses factor.
h = max
h = max
h 2 I h2
C. Effect of harmonics on other stray losses
The other stray losses are assumed to vary with the
square of the rms current and the harmonic frequency to
the power of 0.8:
h = max
∑
POSL = POSL − R
h 0.8 (
h =1
Ih 2
) .
IR
FHL −STR =
POSL
POSL − R
2
Ih 
∑
I 
= h =1  
h = max
Ih
∑

h =1  I
h



2
2
 I h  0.8
∑
  h
h =1  I 1 
(18)
=
2
h = max
Ih 
∑
 
h =1  I 1 
h = max
0.8
VI. VALUATION OF LOSSES AND CAPACITY OF
TRANSFORMER UNDER HARMONIC LOADS [1]
The equation that applies to linear load conditions is:
PLL − R ( pu ) = 1 + PEC − R ( pu ) + POSL − R ( pu ) (19)
where, PLL-R is rated load losses, 1 is dc losses, PEC-R is
rated winding eddy current loss, POSL-R is rated other stray
losses at rated current.
As the effect of harmonic on losses of transformer
evaluated in pervious sections, a general equation for
calculating of losses when transformer supplying a
harmonic load can be defined as fallow:
PLL ( pu ) = I 2 ( pu ) × [1 + FHL × Pec − R ( pu )
+ FHL − STR × POSL − R ( pu )]
(20)
The permissible transformers current is expressed as:
I max ( pu ) =
(21)
PLL − R ( pu )
1 + [ FHL × Pec − R ( pu ) ] + [ FHL − STR × POSL − R ( pu ) ]
Using above mentioned equation, the permissible current
and derating of the transformer can be derived.
VII. CALCULATION OF LOSSES AND CAPACITY
OF TRANSFORMER UNDER HARMONIC LOADS
In this section, calculation and simulation of losses and
capacity of transformer under harmonic loads will
perform. Then results are compared with each other.
A.
analytical Method
The generic parameters of a 25KVA single phase
transformer that designed in Irantransfo manufactory are
summarized in table I.
The total stray loss, PTSL, can be calculated as follows:
PTSL = PSC − Pdc = 670 − 531.854 = 138.1467 w
The winding eddy current loss and other stray loss are:
PEC = 0 . 33 (138 . 146 ) = 45 . 589 w
Posl = 0 . 67 (138 . 146 ) = 92 . 557 w
If transformer supplying a load with specification in
table II losses on harmonic load calculated as fallow:
The harmonic loss factor for eddy current winding and
other stray losses are:
FHL = 3.734
FHL −STR = 1.202
(17)
The harmonic loss factor for other stray losses is
expressed in a similar form as for the winding eddy
currents:
h = max
Therefore under harmonic loads, other stray losses
must be multiplied in harmonic losses factor.
TABLE I.
TRANSFORMER PARAMETERS
V1(V)
V2(V)
I1(A)
I2(A)
Po(W)
Psc(W)
20000
231
1.25
108.5
150
670
TABLE II.
HARMONIC LOAD SPECIFICATION [8]
Harmonic order
1
5
7
11
13
magnitude
1
0.192
0.132
0.073
0.0057
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
Table III shows losses under harmonic load. Total
losses increase about 28% under harmonic load. This
increase in total losses results from significant increase in
eddy current losses in winding. Thus, the rms value of the
maximum permissible non-sinusoidal load current with
the given harmonic composition from equation 21 is:
Figure 3. Proposed equivalent transformer model referred to primary
side
1.262
= 0.906 pu
1.53774
= 0.906 × 108.2 = 98.03 A
I max ( pu ) =
I max
TABLE IV.
Equivalent KVA=25 × 0.906= 22.65 KVA
7-2- Simulation method
Basically, transformers model consist of ordinary
parameters such as the leakage inductances and dc
resistances, magnetizing inductances and core resistance
that obtain from no-load test, short circuit test and dc test.
In this model, stray losses that consist of eddy current
losses in windings and other stray losses don’t considered.
When transformer supplying harmonic loads these losses
that are proportional with frequency is more considerable.
Fig. 3 shows the proposed transformer model with the
proximity effect loss represented as a potential difference
defined as the second derivative of the load current and
the other stray losses represented as a resistor in series
with the leakage inductance and dc resistance [9].
For Simulation of the obtained transformer model,
MATLAB/Simulink is used. Fig. 4 shows the proposed
model of transformer in MATLAB/Simulink. Current
sources with different frequencies are put in parallel to
model the harmonic load, as in Table 2. Load power
losses are determined through simulations and
summarized in table IV. Thus, the rms value of the
maximum permissible non-sinusoidal load current with
the given harmonic composition from equation 21 is:
1.251
= 0.916 pu
1.4916
= 0.916 × 108.2 = 99.12 A
I max ( pu ) =
I max
Type of losses
Rated losses (w)
PLL Losses under
rms harmonic
load current(w)
No-load
dc
Winding eddy
current
Other stray
Total
152.54
529.45
40.23
152.54
566.23
168.25
93.26
815.48
116.58
1003.60
Figure 4. Proposed model in Simulink
TABLE V.
COMPARISON BETWEEN ANALYTICAL AND SIMULATION
METHOD
CONCLUSION
Equivalent KVA=25 × 0.916= 22.9 KVA
The comparison between two steps (table V) shows that
the predicted values using analytical and simulation
methods are similar but simulation shows smaller losses
than the analytical method. The reason is that in the
analytical method it is assumed that the eddy current
losses are proportional with the square of the harmonic
orders that is a pessimistic assumption. In [10] a corrected
winding eddy current loss factor is presented which
confirms this.
TABLE III.
LOSSES UNDER HARMONIC LOAD BY
SIMULATION
LOSSES UNDER HARMONIC LOAD
Type of
losses
Rated
losses
(w)
Losses under
rms harmonic
load
current(w)
Harmo
nic
losses
factor
No-load
dc
Windin
g eddy
current
Other
stray
Total
150
531.854
45.589
150
565.36
48.461
3.734
Corrected
losses
under
harmonic
load(w)
150
565.36
180.96
92.557
98.389
1.202
118.27
820
862.21
-
1014.59
Loss under liner
load(watt)
Loss under harmonic
load(watt)
percent of increase losses
Capacity under
harmonic load(KVA)
percent of decrease
capacity
Based on
analytical
method
820
Based on
simulation
method
815.48
1014.59
1003.60
23.73%
22.65
23.07%
22.90
9.4%
8.4%
VIII. CONCLUSION
Effects of non-linear loads upon the transformer losses
based on the conventional method (IEEE standard C57110) have been studied for derating purpose. The
harmonic losses factor for eddy current winding and other
stray losses has been computed in order to evaluate the
equivalent KVA of the transformer for supplying nonlinear loads. A useful model of transformer was presented
for calculating losses and capacity under harmonic
condition. Then losses and capacity of a transformer were
evaluated with analytical and simulation methods. The
result shows that losses increase in harmonic load and
therefore decrease the rated capacity. Assumption of
increase of the winding eddy current losses with the
square of the frequency in the analytical methods and the
available standards is somehow less accurate. So every
2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia
changing in current harmonic leads to change in harmonic
losses factor and thus cause to change losses and capacity
of transformer. For power systems with transformer, it is
better to carry out monitoring on voltage and current, to
reach to useful capacity of transformer based on available
standards and the proposed model, if harmonic
components exist.
REFERENCES
[1]
IEEE Std C57.110-1998, IEEE Recommended Practice for
Establishing Transformer Capability when Supplying Non
sinusoidal Load Currents.
[2] Odendal, E.J, Prof., “Power Electronics Course notes”, Durban,
University of Natal, pg. 8.36.
[3] L. W. Pierce, “Transformer design and application consideration
for non Sinusoidal load currents,” IEEE Trans, on Industry
Applications, vol.32, no.3, 1996, PP.633-645
[4] Butterworth, S, “Effective resistance of inductance coils at radio
frequencies”, Exp, Wireless.
[5] Yildrim, D, Fuchs, E, “Transformer derating and comparison with
Harmonic Loss Factor Approach”, IEEE Trans. PD, Vol 15, no. 1,
January 2000.
[6] A Girgis, E. Makram, J. Nims,“ Evaluation of temperature rise of
distribution transformer in the presence of harmonic distortion,”
Electric Power Systems Research, vol. 20, no.1, Jan 1990, pp.1522
[7] D.S. Takach, “Distribution Transformer No Load Losses”, IEEE
Trans. on PAS, Vol. 104, No. 1, 1985, pp. 181-193
[8] IEEE Std. 519-1992, IEEE Recommended Practices and
Requirements for Harmonic Control in Electrical Power Systems,
IEEE Publications, 445 Hoes Lane, P.O. Box 1331, Piscataway,
NJ 08855 1331, USA.
[9] S.B.Sadati, A.Tahani, M.Jafari, M.Dargahi, “Derating of
transformers under Non-sinusoidal Loads”, Proc. of the 11th
International Conference on Optimization of Electrical and
Electronic Equipment OPTIM 2008, Brasov, Romania
[10] S. N. Makarov, A. E. Emanuel, “Corrected Harmonic Loss Factor
For Transformers supplying Non-sinusoidal Load current” Proc.
of the 9th International conference on Harmonics and Power
Quality, vol. 1, Oct.2000, pp.87-90.