Conference Record of the 2006 IEEE International Symposium on Electrical Insulation
Effect of Harmonics on Transformers Loss of life
A. Elmoudi 1, M. Lehtonen 1, Hasse Nordman
Power Systems and HV Engineering, Helsinki Univ. of Tech., Espoo, Finland 1 ABB Transformers, Vaasa, Finland 2
Abstract - The use of non-linear (solid state) loads in power system has increased the awareness of the potential reduction of a transformer life due to the increased losses. Manufacturers and users have been applying IEEE C57.110-1989 which gives a conservative estimate of loading capability of transformers. In this paper, the effect of harmonics on transformers is discussed and a thermal model to predict a transformer hot spot temperature is presented. The model considers a time varying harmonic load cycle and ambient temperature. The model is applied on 31.5 MVA, 115±9×1.67%/6.3 KV ONAF transformer.
Winding eddy current losses, W. Other stray losses are due to losses in structures other than windings, W. The total stray losses are determined by subtracting I2R from the load losses measured during the impedance test and there is no test method to distinguish the winding eddy losses from the stray losses that occur in structural parts. A. Effect of Voltage Harmonics According to Faraday’s law the terminal voltage determines the transformer flux level. 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 is well below 5% and the magnitudes of the voltage harmonics components are small compared to the fundamental component. This is determined by the low internal impedance of most supply systems carrying harmonics. Therefore neglecting the effect of harmonic voltage and considering the no load losses caused by the fundamental voltage component will only give rise to an insignificant error . Larger transformer in powerful networks is subject to less high harmonics flux. B. Effect of Current harmonics In most power systems, current harmonics are of significance. These harmonic current components cause additional losses in the windings and other structural parts. For a transformer winding turns which consist of small strands, skin effect or the current redistribution due to internal current is usually assumed to be negligible. Conventionally, the winding eddy current losses (PEC) generated by the electromagnetic flux are assumed to vary with the square of the rms current and the square of the frequency (harmonic order h) as :
h = max
I. INTRODUCTION The widespread use of solid state controlled loads has increased the level of harmonics significantly. Increase in the transformer power losses and hence temperature rises are the primary concern of the impact of harmonics. This could lead to an increase in its insulation loss of life which is determined by the hot spot temperature reached in the winding IEEE C57-110-98 standard is developed to determine the capability of a transformer for non-sinusoidal currents based on a current harmonics spectrum and the rated pu loss density of the winding hot spot . A part from being conservative, it does not consider real load cycle and ambient temperature variation. Many researchers used the transient heat equations of the standards  to evaluate the impact of harmonics on transformer . In this paper a thermal model which considers the increased transformer temperatures due to a time varying harmonic load current and ambient temperature is proposed. The model parameters are obtained from the transformer factory test data and the estimated losses at rated load and frequency using finite element method (FEM). The model is applied on 31.5 MVA, 115±9×1.67%/6.3 KV ONAF transformer. II. EFFECTS OF HARMONICS ON TRANSFORMERS Transformer losses (PT) are divided into no load losses (PNL) and load losses (PLL) as:
PT = PNL + PLL
PEC = PEC ? R
?I h2 ? h ?I ? R
? ? ? ?
PNL are the losses due to the voltage excitation of the core. PLL is expressed as:
PLL = I 2 R + PEC + POSL
Losses due to load current and dc winding resistance, W.
where Rated eddy current losses, W. PEC-R Ih Current at harmonic order h, A. Rated current, A. IR h Harmonic order Actually, due to skin effect, the electromagnetic flux may not totally penetrate the strands in the winding at high frequencies The frequency dependence of the field penetration (δ) at harmonic frequency is given by:
1-4244-0333-2/06/$20.00 ?2006 IEEE.
ρ δ = R ?π fh h
Penetration depth at rated frequency about 10 mm for copper and 13 mm for Aluminum . Conductor resistivity. Conductor permeability. Fundamental frequency.
Resistance correction due to temperature change. Rated hot spot rise over oil, K. Hot spot time constant, min. Exponent which defines non-linearity.
Other losses occur due to the stray flux, which introduces losses in the core, clamps, tank and other iron parts. When transformers are subject to harmonic load currents these losses also increase. These stray losses may increase the oil temperature and thus the hot spot temperature. 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
The thermal equations are modeled using Simulink/Matlab. The equations are solved numerically using Runge–Kutta method. The required parameters for the models are as shown in Table I. At each step the top oil temperature equation (6) is solved by inputting the variable load data and the ambient temperature with the known parameters. The calculated top oil temperature is the input ambient temperature for the hot spot model as shown in the simplified diagram Fig. 1. The implemented hot spot model block diagram is shown in Fig. 2.
I1(t) I3(t) Loss Factors (3) and (5)
2 2 h ∑ ( Ih ) h ∑( I ) R R I
POSL = POSL ? R
?I h 0.8 h
? ? ? ?I ? ? R?
All effects of harmonic currents discussed so far will increase the transformer losses. These increased losses will obviously increase the temperature rise of the transformer from its sinusoidal value. Therefore, the increased losses due to the harmonic current spectrum must be addressed. III. TRANFORMER THERMAL DYNAMIC MODEL The top oil temperature model including harmonic affects is introduced using the differential equation as :
PLL? H PNL PLL ? R PNL
∑ ( Ih ) h
∑ ( Ih )
∑ ( Ih ) h
Top-oil model (6)
Hot-spot model (7)
Fig. 1 Thermal model for hot-spot calculation.
θ O (t )
(θ H ? θ O )
dθ H dt
? ??θ O ? R ? ? ?
dθ O 1/ n + ?θ oil ? θ A ? ? dt ?
PLL ? H = P ?
I ( I h )2 R
+ PEC .
I h2 ( I h )2 R
+ POSL .
? ? ? ? (6) ? I h0.8 ( I h ) 2 ? R ?
∑ ( Ih )
Ih 2 IR
h ) ?Kθ + ∑ h 2 ( I R ) 2
I 2 2 ∑ ( Ih ) h R
PEC ? R Kθ
.[?θ H ? R ] m
1 + PEC ? R
where, PLL-H PLL-R PNL P
?θO-R τO θo θA
Increased load losses due to harmonics, W. Rated load losses, W. No load losses, W. I2R losses at rated current and frequency, W. Rated top oil rise over ambient, K. Top oil time constant, min. Top oil temperature, ° C. Ambient temperature, ° C. Exponent defines non-linearity.
Fig. 2 Block diagram of the hot spot model.
The relationship between the hot spot temperature and aging acceleration factor is given by :
? 15000 15000 ? ? ? ? ? 383 θ H + 273 ? ? e?
To estimate insulation heating effect, the loss of life factor is integrated over a given period of time. The standardized loss factors may not reflect the actual additional losses for different transformer designs as this is strongly construction dependent. The thermal model can be used to predict the additional loss factors for any given load that fits the measurement. IV. TRANSFORMER LOSSES ESTIMATION The two dimensional FEM is used to estimate the transformer losses at rated frequency and load. The transformer winding turns usually consist of copper conductors in the shape of
The hot spot temperature model including harmonic affects is presented using the differential equation as :
I 2 2 I 2 P ∑ ( I h ) ?Kθ + ∑ h ( I h ) EC ? R R R Kθ dθ H 1/ m 1/ m ? ? ?θ H ? R ? =τH + ?θ H ? θ O ? ? ? ? ? dt 1 + PEC ? R
where Hot spot temperature, ° C. pu unit eddy losses at rated load and hot spot location
small rectangular strands. The losses are found from a magneto-static solution in which the eddy current region is given zero conductivity. Figure 3 shows the transformer field solution. It can be seen that the inner low voltage (LV) winding typically has a higher attraction of the leakage flux due to the low reluctance path of the core leg. The high voltage (HV) winding divides its leakage flux with part being attached to the core and the reminder attracted to the core clamps and other structural parts. The highest local eddy losses usually occur in the end conductors where the conductors are exposed to an inclined magnetic field with two components, an axial component and a radial component. Furthermore the radial conductor dimension is usually larger than the thickness. Using the local flux density obtained from FEM the eddy current loss due to the axial and radial magnetic flux density is calculated for each disc. The eddy loss is integrated over the winding area and multiplied by the winding mean length. In order to obtain the winding losses the loss due to load current I2R must be added to the eddy losses.
temperature is simulated using equations (6) and (7) by inputting the daily transformer pu loading and the ambient temperature shown in Figs. 4 and 5, respectively. Figures 6 and 7 illustrate the predicted top oil and hot spot temperatures, respectively at different harmonic cases. In the first case study, no harmonics are assumed to be present. The harmonics assumed for the second case include major harmonics 5th, 7th, 11th, 13th, 17th, 19th, 23th and 25th with total harmonic distortion (THD) 10%. The third case is with THD 22% and the same order harmonics. The increase in top oil temperature for the second and third case is 2°C and 8°C, respectively compared with no harmonics. The hot spot temperature of the HV winding shows an increase of more than 20°C for the third case. Although the hot spot temperature has increased the loss of life factor above 1.1 pu, it returns to normal loss of life at the end of the load cycle as shown in Fig. 8.
TABLE I TRANSFORMERS MODELS INPUT PARAMETERS
Transformer MVA Cooling mode Temperature base for losses No load Losses I2R winding losses Winding eddy current losses PEC Other stray losses POSL Rated pu eddy current losses at hot spot location Top oil rise over ambient Average oil to average winding Hot spot factor Top oil time constant Hot spot time constant n m
I1 I5 I7 I11 I13 I17 I19 I23 I25
31.5 ONAF 75 16100 123900 11400 11000 0.52 50.6 19.7 1.3 160 6 0.9 0.8
Load Current (pu)
Fig. 3 Transformer field solution.
The stray losses in other structural parts could then be obtained by subtracting the calculated winding eddy current losses from the total stray losses. The highest eddy losses are in the HV winding even the flux density is twice that in the LV winding. This is due to the larger radial conductor dimension used. The hot spot factor is calculated as the winding highest losses divided by the winding average losses to the power of 0.8 to predict the rated hot spot temperature rise. These calculations are important parameters used in the thermal model V. TRANSFORMER TEMPERATURE PREDICTION AND LOSS OF LIFE ESTIMATION The parameters used in the model obtained from factory test data and the FEM calculations at rated load and frequency are as illustrated in Table I. The transformer top oil and hot spot
12 Time (hrs)
Fig. 4 Daily load cycle with THD 22% (third case).
30 Loss of life (pu) 1 0.8 0.6 0.4 0.2 15 4 8 12 Time (hrs) 16 20 24 0 4 8 12 Time (hrs) 16 20 24
Ambient Temperature (
Fig. 5 Ambient temperature
Fig. 8 Insulation Loss of life.
90 C) 80 70 60 50 40 30
No harmonics with THD = 10 % with THD =22 %
Transformers subject to harmonic currents exhibit additional load losses, often experience higher winding hot spot temperature. A transformer’s expected life is intimately related to the operating temperature that it experiences during service. To correctly estimate a transformer loss of life the real load and ambient temperature variations should be considered. The thermal model proposed in this paper presents a simple method to predict the temperatures of 31.5 MVA transformer subject to a time varying loads. The loss of insulation life function is used to assess the transformer loading capability. REFERENCES
12 Time (hrs) 16 20 24
Top-oil Temperature (
Fig. 6 Predicted top oil temperature.
140 130 C)
120 110 100 90 80 70 60 50 40
No harmonics with THD =10 % with THD =22 %
8 Time (hrs)
Fig. 7 Predicted hot spot temperature.
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Hot-spot Temperature (