The Effect of Harmonic Distortion on a Three phase Transformer Losses

The Effect of Harmonic Distortion on a Three phase Transformer Losses Hussein I. Zynal, Ala'a A. Yass University of Mosul Abstract-Electrical transformers are designed to work at rated frequency and sinusoidal voltage and waves. At present time the use of non linear s, such as power electronic s 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 s, transformer should work capacity less than the rated capacity given by the designer. In this research different type es in a 2KVA three phase transformer are studied linear and non linear s, also the effect of harmonics on transformer loss are evaluated. The linear s are simulated by a pure resistance but the non linear s are simulated by a three phase bridge rectifier, also a three single phase rectifiers are simulated as a non linear 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 d. 1- Introduction Transformers are usually designed for utilizing at the rated frequency and linear. Nowadays the present of nonlinear, 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 level on the transformer s. 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 linear applied in power system, such as arc furnace, electromotor s, solid state electronic devices which contain a poor power supply, solid state devices, electronic equipments that have control function and leakage at surface of polluted insulators [2]. 2-Transformer losses Transformer losses are generally classified into no or core losses and losses [3]. This can be expressed in equation form: P T = P NL + P LL (1) P NL is the no losses due to the induced voltage in the core. P LL is the loss and consist of P dc losses (I 2 R dc ) and stray losses caused by electromagnetic fields in the windings, core clamps, magnetic shields, enclosure or tank walls, etc. P dc is calculated by measuring the dc resistance of the winding and multiplying it by the square of the. The stray losses can be further divided into winding eddy losses and structural part stray losses. Winding eddy losses consist of eddy losses and circulating losses, which are all considered to be winding eddy 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]: P LL = P dc + P EC + P OSL (2) The total stray losses are determined by subtracting I 2 R dc from the 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. P TSL = P LL -P dc (3) 2-1 Eddy Current Losses in Windings: This type 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

have more eddy loss. The reason is the high electromagnetic flux intensity near the core that covers these windings. The winding eddy loss in the power frequency Spectrum tends to be proportional to the square of the 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- loss. For dry-type transformers, the windingeddy loss is assumed to be [4]: Flux Main c Eddy P EC =0.67*P TSL (4) P OSL =P TSL -P EC (5) The division of eddy- loss and other stray losses between the windings is assumed to be as follows [4] a) 60% in the low voltage winding and 40% in the high voltage winding for all transformers having a maximum 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 a maximum self cooled rating greater than 1000 A 2-1-1 Proximity effect The proximity effect contribution to the winding eddy loss is defined as follows. Consider Fig.2. The HV winding produces a flux density due to a changing. 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 s. This effect is called the proximity effect, which is caused by a -carrying conductor, or magnetic fields that induce eddy s in other conductors in close proximity to the other carrying conductor or magnetic fields. These eddy s will dissipate power, P EC, and contribute to the electrical loss in the windings in addition to those caused by normal dc losses [5].. Main Fig (2) the proximity effect on eddy. 2-1-2The computation of proximity effect parameter by using electromagnetic theory: The electromagnetic theory used to computation of proximity effect in term voltage and by using differential forms of Maxwell s equations as given below [6]: = B t (6) =+ (7) The ratio of the conduction density (J) to the displacement 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 density is neglected in case eddy s 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 x and y), then equation(10) reduces to the ordinary differential equation d E dz =σμde 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 =σμdv dt (12) The proximity effect voltage in terms of the d v dz =σμd i dt (13) After double integration of eq. (13) distance, assuming the i is not a function of distance and the flux is in one direction, the proximity effect voltage result is expressed as 256

V =σμd i dt (14) or in terms of the winding eddy, i pe [5] ()= = (15) = (16) 2-2 Other Stray Losses in Transformers: Each metallic conductor linked by the electromagnetic flux experiences an internally induced voltage that causes eddy s to flow in that ferromagnetic material. The eddy s produce losses that are dissipated in the form of heat, producing an additional temperature rise in the metallic parts over its surroundings. The eddy 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 but not at a rate proportional to the square of the frequency as in eddy 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)φ =V (18) The flux magnitude is proportional to the voltage harmonic and inversely proportional to the harmonic order n. Furthermore, in most power systems the harmonic distortion of the system voltage is well below 5% and the magnitudes of the voltage harmonics components are small d 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 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, harmonics are of significance. These harmonic components cause additional losses in the windings and other structural parts [7]. a- Current harmonic effect on I 2 R loss If the rms value of the is increased due to harmonic components, the I 2 R loss will be increased accordingly P =R I =R I (19) b- Current harmonic effect on P EC The eddy losses generated by the electromagnetic flux are assumed to vary the square of the rms and the square of the frequency [4] P =P n (20) To obtain the true value of eddy loss it must be multiplying by harmonic loss factor (F ) when the transformer supplying nonlinear F = (21) c- Current harmonic effect on other stray losses: The other stray losses are assumed to vary the square of the rms and the harmonic frequency to the power of 0.8 : =P (22) To obtain the true value of other stray loss it must be multiplied by harmonic loss factor ( ) when transformer supplying nonlinear [4] = n.. (23) 4- Recommended procedures for evaluating the capability of transformers under nonlinear s (containing harmonics) The equation that applies to linear conditions is [4]: P ()=1+P (pu)+p (pu) (24) P LL-R :is the loss at rated condition linear. As the effect of harmonic on losses of transformer evaluated in pervious sections, a general equation for calculating es when transformer supplying a harmonic can be defined as fallow: P ()=I (pu)[1+f P (pu)+ F P (pu) (25) The permissible transformers is expressed as I (pu)= () [ () () ] (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 I 1R I 2R R dc1 R dc2 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 linear a- Omic losses computation The omic loss (P dc ) calculated using equation (19), where I nrms equal rated linear. P dc = 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). P TSL = 81.5 75.24 = 6.26 W (where P LL-R obtained from short circuit test). To separate the total stray loss to eddy loss and other stray loss equations (4) and (5) are used: P EC = 0.67 * 6.26 = 4.194 W P OSL = 0.33 * 6.26 = 2.065 W and to divided the other stray losses and winding eddy losses between low voltage and high voltage windings assumptions given in article 2.1 are used [4]. P EC-LV = 0.6 * 4.194 = 2.5164 W P EC-HV = 0.4 * 4.194 = 1.677 W P OSL-LV = 0.6 * 2.065 = 1.239 W P OSL-HV = 0.4 * 2.065 = 0.826 W 2- Losses nonlinear s To calculate the losses theoretically it is assumed that the secondary is a square wave which contain harmonic orders as given in table (2) Table (2) harmonic magnitude of secondary Harmon ic order Seconda ry A 1 4.8 6 5 1.0 5 7 0.4 7 11 0.3 5 13 0.2 3 a- Omic loss (P dc ). By using equation (19) the omic calculated as: 17 0.1 6 P dc = 3*(3.2 2 * 1.45 + 5.017 2 * 0.5) = 82.29 W. b- Eddy losses By using equation (20) the eddy loss is calculated as: P EC = 4.113 * 1.0618 = 4.36 W. To obtain the true value of eddy loss it must be multiplied by harmonic loss factor which is evaluated by using equation (21). F HL_EC = 3.849. P EC = 16.781 W c- other stray loss By using equation (22) the other stray loss is calculated as. P OSL = 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). F HL-OSL = 1.175. P OSL = 2.53 W. The analytical calculated transformer losses under linear and non linear s are tabulated in table (3) below. Table (3) analytical calculated losses value 19 0.1 2 23 0.0 8 loss (P dc ) is Type of losses Loss under linear (W) Loss under non liner (W) Iron 40 40 P dc 75.36 82.29 Harmonic factor P EC 4.113 4.36 3.849 P OSL 2.025 2.152 1.202 2.53 Total 121.499 141.601 losses By using equations (24), (25) and (26) the transformer capability under non linear s is calculated as: I Max = 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 linear and non linear s using matlab/ simulink. The eddy loss is represented as a dependent voltage source, its voltage dependd upon the second derivative of the and other stray losses represented as a resistance in series the leakage inductance and dc resistance. The non linear is a three phase uncontrolled resistive and high inductive s ( and out 5 th harmonic filter ). Fig (3) show the simulation circuit. Figure (3) simulation circuit Corrected losses under non linear (W) 40 82.29 16.781 By using matlab P.S.B the losses are calculated and the results are tabulated as given in table (4). Fig(4) shows the percentage loss d to linear plotted against % rated. The effect of harmonics on omic loss different values is given in table (5) and fig (5) shows the variation of omic loss different values.

Figure (4) shows the increase of percentage loss d linear Figure (5) the omic loss for different type of s Table (4) total losses of transformer and change es to linear Total loss Linear (W) Total loss under Non linear (W) % Rated Resistive Load rectifier resistive linear rectifier resistive and filter linear rectifier resistive inductive linear controlled resistive linear 122.9 139.2 13.26 129.1 5.044 138.7 12.85 141 14.72 0.75 87.59 98.31 12.23 92.25 5.32 98.13 12.02 99.16 13.20 0.67 73.36 81.45 11.02 77.19 5.22 81.38 10.93 82.03 11.81 0.5 61.53 67.2 9.215 64.51 4.84 67.18 9.182 67.55 9.78 0.375 52.17 55.72 6.8 54.36 4.19 55.72 6.80 55.93 7.20 0.25 45.38 47.2 4.01 46.85 3.23 47.21 4.03 47.3 4.23

%Rated Table(5)the omic loss for different type of s Omic loss Linear (W) Resistive Rectifier resistive 77.29 82.41 0.75 44.78 48.48 0.625 31.65 34.6 0.5 20.69 22.9 0.375 11.98 13.49 0.25 5.538 6.485 The eddy loss for different type of s are given in table (6) for different rated and figure (6) shows the variation of eddy loss different rated Omic loss Non linear (W) resistive and5th harmonic filter 78.3 46.03 32.9 21.87 13.03 6.476 Rectifier resistive and inductive 82.05 48.3 34.48 22.83 13.46 6.473 controlled resistive α=30 82.7 48.63 34.7 22.96 13.53 6.5 Table (6) the effect of harmonics on eddy loss different values %Rated 0.75 0.625 0.5 0.375 0.25 Eddy loss Linear (w) Resistive 3.782 1.885 1.15 0.563 0.131 0.038 resistive 14.12 8.215 5.693 3.524 1.769 0.501 Eddy loss Non linear (w) resistive and5th harmonic filter 8.426 4.829 3.295 1.981 0.930 0.177 resistive and inductive 13.98 8.219 5.733 3.569 1.808 0.521 controlled resistive α=30 15.52 8.919 6.161 3.811 1.951 0.586 Figure (6) change of eddy loss percentage of rated The other stray loss for different type of s is given in table(7)for different values. Fig (7) shows the variation of other stray loss different values. Figure (7) change of other stray loss percentage of rated 7- Practical Result A three phase 2KVA 380/137volt star delta transformer is connected in laboratory linear and non linear s. The nonlinear s are a three phase bridge resistive and high inductive s. By using (3

Phase Power Quality (3945-B powepad) the input, output powers were measured. Also the waveform were recorded and analyzed. Fig (8) shows the practical waveform of the for high inductive. Figure(8) waveform for rectifier high inductive. The result obtained as The total power loss linear is equal to 121.34 W. The total power loss non linear is equal to 146.7 W. The maximum permissible secondary non linear is 4.423 A. The maximum permissible VA non linear 1818. Table (8) gives the comparison between analytical simulation and practical results for non linear. Table (8) comparison between analytical simulation and practical results. Analytical simulation practical Total 141.6 139.2 146.7 Losses (W) VA 1852 1878 1818 rating I max (A) 4.5 4.56 4.423 8-Conclusion In this paper the effect of harmonics upon transformer losses based on(ieee standard c57-110) have been analyzed and evaluated. The equivalent KVA and maximum ratings of a three phase transformer for supplying harmonic s are evaluated. The analytical simulation and experimental results shows that losses increase increase of total harmonic distortion of the transformer and rated capacity decreases. when transformer supplying non linear the percentage increase es at full was 13.26% d case of linear, but when 5 th 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 loss was 63.4% and increase of other stray loss was 5.2% d the case of linear s. When the transformer ed three single phase rectifier ( the secondary contains third harmonic as well as the other harmonics) the percentage increase was 28% at full d linear 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 19-23,2009, Harbin, China. [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 s, 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. 261