Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 The Effect of Harmonic Distortion on a Three phase Transformer Losses Hussein I. Zynal, Ala'a A. Yass University of Mosul linear load applied within power system, such as arc furnace, electromotor loads, solid state electronic devices which contain a poor power supply, solid state devices, electronic equipments that have control function and leakage current at surface of polluted insulators [2]. 2-Transformer losses Transformer losses are generally classified into no load or core losses and load losses [3]. This can be expressed in equation form: PT = PNL + PLL (1) Abstract-Electrical transformers are designed to work at rated frequency and sinusoidal voltage and current waves. At present time the use of non linear loads, such as power electronic loads are increased and this leads to increase of power loss of transformer. The problem of increasing the power loss leads to several problems including increasing the temperature of the transformer, insulation damage and decrease the operational life of the transformer . To avoid these problems in case of non linear loads, transformer should work with capacity less than the rated capacity given by the designer. In this research different type of losses in a 2KVA three phase transformer are studied with linear and non linear loads, also the effect of harmonics on transformer loss are evaluated. The linear loads are simulated by a pure resistance but the non linear loads are simulated by a three phase bridge rectifier , also a three single phase rectifiers are simulated as a non linear load to obtain the effect of third harmonic . The different types of losses and capacity of a three phase transformer is then evaluated analytically and simulation in MATLAB/SIMULINK and results are compared. PNL is the no load losses due to the induced voltage in the core. PLL is the load loss and consist of Pdc losses (I2Rdc) and stray losses caused by electromagnetic fields in the windings, core clamps, magnetic shields, enclosure or tank walls, etc. 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 current losses and structural part stray losses. Winding eddy losses consist of eddy current losses and circulating current losses, which are all 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.; this can be expressed as [3]: 1- Introduction Transformers are usually designed for utilizing at the rated frequency and linear load. Nowadays with the present of nonlinear load, transformer leads to higher losses and reduction of the useful life [1]. It is one of the most important apparatus in power system operation. It maintains supply continuity to the consumers, so that transformer must be well maintained to fulfill its technical life expectation. Age of the transformer depends on its insulation condition. Degradation of transformer insulation can be caused by many factors, like increasing of transformer temperature, oxidation process of liquid or solid insulation, improper cooling system of transformer and short circuit current level on the transformer loads. Those phenomena can decrease the strength of transformer insulation and the power quality. Other phenomenon which affect to power transformer's operation is harmonic. This harmonic is driven by non PLL = P dc+ PEC + POSL (2) The total stray losses are determined by subtracting I2Rdc 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. PTSL= PLL-Pdc (3) 2-1 Eddy Current Losses in Windings: This type of loss is due to time variable electromagnetic flux that covers windings. Skin effect and proximity effect are the most important phenomenon in creating these losses. In transformers, in comparison to external windings, internal windings adjacent to core 255 Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 Main current Eddy current have more eddy current loss. The reason is the high electromagnetic flux intensity near the core that covers these windings. 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 × [4]. A portion of the stray loss is taken to be eddy-current loss. For dry-type transformers, the windingeddy loss is assumed to be [4]: PEC=0.67*PTSL (4) POSL=PTSL-PEC (5) c current Flux Main current Fig (2) the proximity effect on eddy current. 2-1-2The computation of proximity effect parameter by using electromagnetic theory: The division of eddy-current loss and other stray losses between the windings is assumed to be as follows [4] The electromagnetic theory used to computation of proximity effect in term voltage and current by using differential forms of Maxwell’s equations as given below [6]: ∇ × = − ∂B⁄∂t (6) ∇ × = + ⁄ (7) The ratio of the conduction current density (J) to the displacement current density (∂D/∂t) is given by the ratio σ/(jωε), which is very high even for a poor metallic conductor at very high frequencies (where ω is frequency in rad/sec). Since this analysis is for the (smaller) power frequency, therefore the displacement current density is neglected in case eddy currents analysis in conducting parts of the transformers therefore [6]. ∇× = (8) Now, let us assume that the vector field E has component only along the x axis. ∇ E = μσ ∂E⁄∂t (9) Where the operator ∇ represent partial differential ∂ E ⁄∂ x + ∂ E ⁄∂ y + ∂ E ⁄∂ z = μσ ∂E ⁄∂t (10) Suppose, that Ex is a function of z only (does not vary with x and y), then equation(10) reduces to the ordinary differential equation d E ⁄dz = σμ dE ⁄dt (11) Now eq. (11) can be presented in terms of the proximity effect voltage induced in the conductor by the magnetic field that penetrates the conductor [5] d v!" ⁄dz = σμ dv!" ⁄dt (12) The proximity effect voltage in terms of the current d v!" ⁄dz = σμ d i⁄dt (13) After double integration of eq. (13) with distance, assuming the current i is not a function of distance and the flux is in one direction, the proximity effect voltage result is expressed as a) 60% in the low voltage winding and 40% in the high voltage winding for all transformers having a maximum current rating of less than 1000 A (regardless of turns ratio). b) 60% in the low voltage winding and 40% in the high voltage winding for all transformers having a turns ratio of 4:1 or less. c) 70% in the low voltage; winding and 30% in the high voltage winding for all transformers having a turns ratio greater than 4:1 and also having one or more windings with a maximum self cooled current rating greater than 1000 A 2-1-1 Proximity effect 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 current carrying 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 [5]. . 256 Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 V!" = σμ d i⁄dt (14) or in terms of the winding eddy current, ipe [5] %&' ()*) = 7'8 = , - . ⁄,/ - 0,- .123 ⁄,/ - 0 4123 9:;21 <- = 4123 56<>- × = , - . ⁄,/ 4123 56- the square of the rms current and the square of the frequency [4] X- PTU = PTUVW ∑GQNR n XYGQS (15) 6 (20) To obtain the true value of eddy current loss it must be multiplying by harmonic loss factor (F[\ ) when the transformer supplying nonlinear load (16) 2-2 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 [4]. 3-Effect of harmonic on transformer losses 3-1 Effect of Voltage Harmonics According to Faraday’s law the terminal voltage determines the transformer flux level [5] <@ ? <> = v(t) (17) Transferring this equation into the frequency domain shows the relation between the voltage harmonics and the flux components can be written as Nj(nw)φFG = VG (18) The flux magnitude is proportional to the voltage harmonic and inversely proportional to the harmonic order n. 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 [7]. 3-2 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 [7]. a- Current harmonic effect on I2R loss If the rms value of the load current is increased due to harmonic components, the I2R loss will be increased accordingly PI = R<K × IMNO = R <K ∑GQNR IGMNO (19) GQS b- Current harmonic effect on PEC The eddy current losses generated by the electromagnetic flux are assumed to vary with F[\V"<<] = - ^ ∑Y_`ab G- Y Y_6 ^6 ^Y ∑Y_`ab Y_6 ^6 (21) c- Current harmonic effect on other stray losses: The other stray losses are assumed to vary with the square of the rms load current and the harmonic frequency to the power of 0.8 : cOd = PcOdW ∑GQNR ne.g GQS XY X6 (22) To obtain the true value of other stray loss it must be multiplied by harmonic loss factor ([\VhiW ) when transformer supplying nonlinear load [4] [\VhiW = - ^ ∑Y_`ab Gj.k Y Y_6 - ^Y ∑Y_`ab Y_6 - ^6 (23) ^6 4- Recommended procedures for evaluating the load capability of transformers under nonlinear loads (containing harmonics) The equation that applies to linear load conditions is [4]: P\\W ()*) = 1 + PTU (pu) + Poh\ (pu) (24) PLL-R:is the loss at rated load condition with linear load. 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: P\\ ()*) = I (pu)[1 + F[\ × PTU (pu) + F[\VhiW Poh\ (pu) (25) The permissible transformers current is expressed as INR (pu) = q rsst (!u) [Svwxs ×ryz (!u)vwxs2{|t r}{s(!u) ] (26) 5- Theoretical calculation The transformer used in this paper has the parameter as given in table (1): Table (1) transformer parameter KVA V1 V2 I1R I2R Rdc1 Rdc2 2000 380 137 3.03 4.86 1.45 0.5 In this paragraph the losses of the transformer are calculated using equations given in previous sections: 1- losses with linear load a- Omic losses computation The omic loss (Pdc) calculated using equation (19), where Inrms equal rated current with linear load . Pdc= 75.24 W. 257 Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 b- Total stray losses computation using equation (3) . PTSL = 81.5 – 75.24 = 6.26 W (where PLL-R obtained from short circuit test). To separate the total stray loss to eddy current loss and other stray loss equations (4) and (5) are used: PEC = 0.67 * 6.26 = 4.194 W POSL = 0.33 * 6.26 = 2.065 W and to divided the other stray losses and winding nding eddy current losses between low voltage and high voltage windings assumptions given in article 2.1 are used [4]. PEC-LV = 0.6 * 4.194 = 2.5164 W PEC-HV = 0.4 * 4.194 = 1.677 W POSL-LV = 0.6 * 2.065 = 1.239 W POSL-HV = 0.4 * 2.065 = 0.826 W 2- Losses with nonlinear loads To calculate the losses theoretically it is assumed that the secondary current is a square wave which contain harmonic orders as given in table (2) Table (2) harmonic magnitude of secondary current Harmon ic order Seconda ry current A 1 5 7 11 13 17 19 23 4.8 6 1.0 5 0.4 7 0.3 5 0.2 3 0.1 6 0.1 2 0.0 8 a- Omic loss (Pdc ). By using equation (19)) the omic loss (Pdc) is calculated as: Pdc = 3*(3.22 * 1.45 + 5.0172 * 0.5) = 82.29 W. b- Eddy current losses By using equation (20) the eddy current loss is calculated as: PEC = 4.113 * 1.0618 = 4.36 W. To obtain the true value of eddy current loss it must be multiplied by harmonic loss factor which is evaluated by using equation (21) (2 . FHL_EC = 3.849. PEC = 16.781 W c- other stray loss By using equation (22)) the other stray loss is calculated as. POSL = 2.026 * 1.0618 = 2.152 W . To obtain the true value of other stray loss it must be multiplied by harmonic loss factor evaluated by equation (23) . FHL-OSL = 1.175 . POSL = 2.53 W. al calculated transformer losses The analytical under linear and non linear loads are tabulated in table (3) below. Table (3) analytical calculated losses value Type of losses Loss under linear load (W) Harmonic factor 40 75.36 Loss under non liner load (W) 40 82.29 Corrected losses under non linear load (W) 40 82.29 Iron Pdc PEC 4.113 4.36 3.849 16.781 POSL Total losses 2.025 121.499 2.152 1.202 2.53 141.601 By using equations (24), (25)) and ((26) the transformer capability under non linear loads is calculated as: IMax = 0.926 * 4.86 = 4.50 A. VA = 0.926 * 2000 = 1852. 6- Simulation Result In this article the three – phase 2KVA transformer is simulated with linear and non linear loads using matlab/ simulink. The eddy current loss is represented as a dependent voltage source, its voltage depend upon the second derivative of the load current and other stray losses represented as a resistance in series with the leakage inductance and dc resistance. The non linear load is a three – phase uncontrolled rectifier with resistive and high inductive loads ( with and without 5th harmonic filter ). Fig (3) show the simulation circuit. Figure (3) simulation circuit By using matlab P.S.B the losses are calculated and the results are tabulated as given in table (4). Fig(4) showss the percentage loss compared to linear load plotted against % rated load. The effect of harmonics on omic loss with different load values is given in table (5) and fig (5) shows the variation of omic loss with different load values. Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 Figure (4) shows the increase of percentage loss compared with linear load Figure (5) the omic loss for different type of loads Table (4) total losses of transformer and change of losses compare to linear load Total loss Linear load(W) Total loss under Non linear load(W) % Rated load Resistive Load rectifier with resistive load % change of loss compare with linear load rectifier with resistive load and filter % change of loss compare with linear load rectifier resistive with inductive load % change of loss compare with linear load controlled rectifier with resistive load % change of loss compare with linear load FL 122.9 139.2 13.26 129.1 5.044 138.7 12.85 141 14.72 0.75 FL 87.59 98.31 12.23 92.25 5.32 98.13 12.02 99.16 13.20 0.67 FL 73.36 81.45 11.02 77.19 5.22 81.38 10.93 82.03 11.81 0.5 FL 61.53 67.2 9.215 64.51 4.84 67.18 9.182 67.55 9.78 0.375 FL 52.17 55.72 6.8 54.36 4.19 55.72 6.80 55.93 7.20 0.25 FL 45.38 47.2 4.01 46.85 3.23 47.21 4.03 47.3 4.23 Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 Table(5)the omic loss for different type of loads %Rated load Omic loss with Linear load(W) Resistive load Omic loss with Non linear load (W) Rectifier with resistive load rectifier with resistive load and5th harmonic filter FL 77.29 82.41 0.75 FL 44.78 48.48 0.625 FL 31.65 34.6 0.5 FL 20.69 22.9 0.375 FL 11.98 13.49 0.25 FL 5.538 6.485 The eddy current loss for different type of loads are given in table (6) for different rated load and figure (6) shows the variation of eddy current loss with different rated load 78.3 46.03 32.9 21.87 13.03 6.476 Rectifier with resistive and inductive load 82.05 48.3 34.48 22.83 13.46 6.473 controlled rectifier with resistive load α=30 82.7 48.63 34.7 22.96 13.53 6.5 Table (6) the effect of harmonics on eddy current loss with different load values %Rated load Eddy loss with Linear load(w) Resistive load FL 0.75 FL 0.625 FL 0.5 FL 0.375 FL 0.25 FL 3.782 1.885 1.15 0.563 0.131 0.038 Eddy loss with Non linear load (w) rectifier with resistive load 14.12 8.215 5.693 3.524 1.769 0.501 Figure (6) change of eddy current loss with percentage of rated load The other stray loss for different type of loads is given in table(7)for different load values. Fig (7) shows the variation of other stray loss with different load values. rectifier with resistive load and5th harmonic filter 8.426 4.829 3.295 1.981 0.930 0.177 rectifier with resistive and inductive controlled rectifier with resistive load α=30 13.98 8.219 5.733 3.569 1.808 0.521 15.52 8.919 6.161 3.811 1.951 0.586 Figure (7) change of other stray loss with percentage of rated load 7- Practical Result A three phase 2KVA 380/137volt star – delta transformer is connected in laboratory with linear and non linear loads. The nonlinear loads are a three phase bridge rectifier with resistive and high inductive loads. By using (3 Canadian Journal on Electrical and Electronics Engineering Vol. 3, No. 5, May 2012 Phase Power Quality (3945-B powepad) the input, output powers were measured. Also the current waveform were recorded and analyzed. Fig (8) shows the practical waveform of the current for high inductive load. 28% at full load compared with linear load case. Reference [1] D.M. Said, K.M. Nor, “Simulation of the Impact of Harmonics on Distribution Transformers”, 2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia. [2] Sumaryadi, Harry Gumilang, Achmad Susilo, “Effect of Power System Harmonic on Degradation process of Transformer Insulation System”, Proceedings of the 9th International Conference on Properties and Applications of Dielectric Materials, July 1923,2009, Harbin, China. Figure(8) current waveform for rectifier with high inductive load. The result obtained as The total power loss with linear load is equal to 121.34 W. The total power loss with non linear load is equal to 146.7 W. The maximum permissible secondary current with non linear load is 4.423 A. The maximum permissible VA with non linear load 1818 . Table (8) gives the comparison between analytical simulation and practical results for non linear load. Table (8) comparison between analytical simulation and practical results. Total Losses (W) VA rating Imax (A) Analytical 141.6 simulation 139.2 practical 146.7 1852 1878 1818 4.5 4.56 4.423 [3] Asaad A. Elmoudi, " Evaluation of Power System Harmonic Effects on Transformers Hot Spot Calculation and Loss of Life Estimation", Ph. D. Thesis, Helsinki University of Technology, 2006. [4] IEEE Std C57.110-1998, “IEEE Recommended Practice for Establishing Transformer Capability When Supplying Nonsinusoidal Load Currents”. [5] S. B. Sadati, A. Tahani, B.Darvishi, M. Dargahi, H.yousefi, “ Comparison of Distribution Transformer Losses and Capacity under Linear and Harmonic loads”, 2nd IEEE International Conference on Power and Energy (PECon 08), December 1-3, 2008, Johor Baharu, Malaysia . [6] S.V. Kulkarni, S. A. Khaparde, ”Transformer Engineering Design and Practice", Indian Institute of Technology, Bombay Mumbai, India, Marcel Dekker. Inc. 2004 .(Book) [7] A. Elmoudi, M. Lehtonen, Hasse Nordman, “Effect of Harmonics on Transformers Loss of life”, Conference Record of the 2006 IEEE International Symposium on Electrical Insulation. 8-Conclusion In this paper the effect of current harmonics upon transformer losses based on(IEEE standard c57-110) have been analyzed and evaluated. The equivalent KVA and maximum current ratings of a three – phase transformer for supplying harmonic loads are evaluated. The analytical simulation and experimental results shows that losses increase with increase of total harmonic distortion of the transformer current and rated capacity decreases. when transformer supplying non linear load the percentage increase of losses at full load was 13.26% compared with case of linear load, but when 5th harmonic filter is connected the percentage increase of the losses reduced to 5.04%. The percentage increase of omic loss was 31.4% while the increase of eddy current loss was 63.4% and increase of other stray loss was 5.2% compared with the case of linear loads. When the transformer loaded with three single phase rectifier ( the secondary current contains third harmonic as well as the other harmonics) the percentage increase of loss was 261