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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.