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Equivalent Circuit Parameters for Power Transformer and Implementation of Open and Short Circuit Test Simulation in Matlab (SIMULINK)

Equivalent Circuit Parameters for Power Transformer and Implementation of Open and Short Circuit... B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 Submitted: October 7, 2022 Review scientific paper Accepted: November 20, 2022 EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) 1,2 1 1 Goran Kujundžić , Vinko Kalfić , Drago Bago Abstract: This paper describes the power transformer, its basic mode of operation, parts, and construction. Equivalent circuit parameters are defined, and the methods of their determination are explained. A model of the transformer in Simulink was made and the process of its production is described. The created transformer model was then simulated through open and short circuit experiments. The values of the parameters obtained by the simulation were compared with the actual values and conclusions were drawn. The main goal of this work is to determine the precision of the operation of the transformer model in Simulink, and based on the obtained results, the same model can be used in algorithms for checking the operation of the entire power system. Keywords: transformer, Simulink, simulation, short circuit be explained. In this regard, this work aims to determine INTRODUCTION the elements of the equivalent scheme of the power transformer and to conduct simulations of the open circuit A transformer is a static electromagnetic device, which test and the short-circuit test in MATLAB (Simulink). means there are no moving parts. When transmitting electrical energy from one or more AC circuits, which To achieve this, it was considered important to give supply the primary windings of the transformer, to one or a thorough insight into the parts of the transformer, its more AC circuits, supplied from the secondary windings of construction, and the physical picture of its operation. the transformer, there are altered amounts of current and Thus, the active and passive parts of the transformer and voltage, with unchanged frequency [1]. Power transformers their role are described, as well as the construction of are the most common type of transformer and are used to the transformer - from the initial calculation, through the raise or lower the voltage level depending on the needs of construction of the core and winding of the transformer, the consumer [2]. In addition to them, depending on the the types of transformer connection and parallel operation type of application, we also distinguish between measuring of the transformer are described. The physical picture transformers and special purpose transformers, such of the operation of the transformer is explained through as welding transformers and transformers for converter the ideal and real transformer. In the case of an ideal drives [3]. Measuring transformers are used to monitor transformer, certain parameters are neglected concerning the use of electrical energy and there are two basic types the real ones. After explaining the basic characteristics of measuring transformers, namely voltage transformer of transformers, the elements of transformer equivalent and current transformer. These transformers enable the schemes will be described, models of actual conditions measurement of voltages and currents of large amounts in the device and its components will be described, as with measuring instruments of a small measuring range. well as ways to determine the elements of these schemes Voltage measuring transformers require that the difference through no-load and short-circuit experiments. between the primary voltage and the primary reduced secondary voltage be as small as possible and that the In the final part of the paper, the method of making a phase shift of the primary and secondary voltage be the model of a transformer in Simulink will be practically same, but these conditions cannot be fully met, so we are described, and experiments of no-load and short circuit talking about voltage and phase error [4]. will be performed. It will be checked whether the values of the parameters equal to the real ones will be obtained In this paper, emphasis will be placed on the power using Simulink. transformer as the most important part of transformer plants, its importance and use in the power system will Faculty of Mechanical Engineering, Computing and Electrical Engineering, University of Mostar, Bosnia and Herzegovina Correspondence email: goran.kujundzic@fsre.sum.ba © 2022 Author(s). This is an open access article licensed under the Creative Commons Attribution License 4.0. (http://creativecommons.org/licenses/by/4.0/). 11 G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) 1. FUNDAMENTALS OF ENERGY TRANSFORMER 1.1. Importance of power transformer We can say that power transformers are the basic and most widespread elements of electrical systems, and their role in the power system is especially important. The power system consists of 4 basic units. The first refers to power plants as sources of electrical energy, then we Figure 2: Main (active) parts of the transformer have the transmission grid through which electrical energy is transported from power plants to the distribution grid The iron core consists of pillars connected to the upper and large consumers and exchanges power between and lower yoke. The main role of the nucleus is to connected power systems. The third unit consists of a guide the magnetic flux forces. It is made of specially medium and low voltage distribution grid through which treated magnetic types of iron due to its good magnetic electrical energy taken from the transmission grid or conductivity and consists of sheets with a thickness of smaller power plants connected to the distribution grid is 0.3 mm to 0.5 mm. Electrical energy is transmitted by distributed to medium and small consumers connected to electromagnetic induction from primary to secondary, the distribution grid, as the fourth unit of the system. without changing the frequency. The primary is powered by an external source, and the secondary is the one Transformers are also appearing as an integral part of that creates voltage by electromagnetic induction and the electrical energy grid, within the transmission and supplies consumers [6]. The transformer core is secured distribution grid. with a cover to make it easier to insert and remove from the boiler. In order to dissipate heat, various fins, pipes, and radiators are placed on the boiler, which dissipates heat to the surrounding air or cooling water. There is an oil drain valve at the bottom. The conservator is a metal tank positioned on top of the transformer, contains a certain amount of spare oil, and allows expansion as the temperature and volume of the oil increase. In the case of transformers, the cooling system is extremely important. 1.3. Construction of power transformer 1.3.1. Transformer calculation Figure 1: Power transformer The elements for the construction of a transformer should be obtained by its calculation, and the output data are We distinguish three basic types of power transformers, usually known as output and input voltage, output current namely block, grid, and distribution transformers. Block or power, and the type of converter for which it will be used. transformers are used to connect the generator to the The size and type of core, the number of turns of individual mains, where there is a lower voltage on the generator windings, the cross-sections of their conductors, and the side [3].zThey are also called generator transformers. winding directions are the basic elements for the selection Together with the main transformers, they form a group or construction of transformers. It is also important after of large transformers [1]. Mains transformers are used all the elements are determined to check the location of to connect voltage levels in the transmission grid or to the windings because it may happen that not everything connect the transmission and distribution grid, while can fit in the available space [10]. The basic data required distribution transformers are used to connect voltage for the calculation are primary voltage (U ) and secondary levels in the distribution grid [3]. (U ), transformer power (S), core dimension (P), primary current (I ) and secondary (I ), primary wire thickness (D ), 1 2 1 1.2. Power transformer parts and secondary (D ) and current density (J). Based on the primary voltage, a constant for core sizing is determined. The basic parts of each transformer, which participate in The surface area of the core is expressed in cm and the transformation of electrical energy and without which is obtained by multiplying the sides of the coil. For the the transformer cannot work, are the iron core and the following calculation, we will assume that the primary primary and secondary circuit, as shown in Figure 2 [5]. voltage is 230 V with a frequency of 50 Hz, so the core sizing constant will be 45. Then it is necessary to determine 12 B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 the number of primary and secondary windings, which is for insulating reasons, the undervoltage winding is obtained from the equation: placed first up to the column of the magnetic core. By placing the upper voltage winding next to the magnetic core column, stronger insulation towards the core is N = (1) required compared to the insulation of the lower voltage winding [7]. It determines the number of turns of the wire by 1 V. The required number of windings on the primary (N ) and 1.3.4. Types of transformer connection secondary (N ) is calculated using the following equations, provided that the required number of windings on the In practice, there are two basic types of transformer secondary also depends on the required output voltage: connections, namely single-phase and three-phase transformers. Single-phase transformers can only be N = N× U ; N = N× U (2) 1 1 2 2 connected in one way. Wolf states that unlike single- phase transformers, the terminals of a three-phase The primary (I ) and secondary (I ) currents are calculated 1 2 transformer can be connected in 3 different ways, according to the equations: namely: a star connection, a triangle connection, and SS a broken star connection (zigzag connection). Each of I ; I (3) these compounds is denoted by a separate letter. The UU star designation of the junction is Y or y, the junction of If we assume that the electrical energy density is constant triangle D or d of the junction of a broken star is Z or z. The (J = 2.5 A / mm ), then the wire thickness for the primary correct transformer connection is indicated by two letters (D ) and secondary (D ) is calculated as follows: 1 2 and a number. The first letter represents the junction of the transformer primary, the second letter represents the D 0.7 ID ; 0.7 I (4) 1 12 2 junction of the transformer secondary, and the number represents the hour number. The hour number is a mark that indicates the degree of phase delay of the secondary 1.3.2. Making the core in relation to the primary. This number multiplied by 30° represents the phase angle of the secondary voltage in The iron core takes different forms and is performed degrees [8]. differently and is mostly built in a rectangular shape. It is made of a multitude of mutually insulated thin sheets. 1.4. Physical picture of transformer operation Eddy currents or Foucault currents are generated in metal conductors of electric current, which is the iron 1.4.1. Ideal transformer core of a transformer, due to the action of an alternating magnetic field. Eddy currents flow in such a way that When we assume an ideal transformer, we associate with they form a closed circle around one point inside the it negligible losses and voltage drops and ignore the ohmic conductor, so their intensity is limited by mutually resistance of the winding coils. Figure 3 schematically insulated transformer sheets [7]. When assembling, the shows the mode of operation of the transformer [9]. core is impregnated, varnished, and finally mechanically tightened with screws to prevent vibration under the influence of magnetic force. The rule also applies that increasing the power of the transformer increases the number of sheets with different widths that form the magnetic core of the transformer. 1.3.3. Transformer winding After the calculation, the winding follows. There are two Figure 3: Schematic representation of a single-phase two- basic configurations of transformers, namely the pole winding transformer (core) type and the sheathed type of transformer and According to the basic law of electromagnetic induction, they differ in the location of the windings wound on the Faraday’s law, in a bend that includes magnetic flux ( Φ) magnetic core. Thus, in the case of a column winding, the voltage of the current value (e) is induced proportional they are located on each column of the core, and in to the rate of change of current, as follows: the case of the shrouded type, they are located on the dφ central column or columns. The windings are located on eN = − (5) the columns of the magnetic cores, and the columns dt are interconnected by the yoke of the magnetic core. If the effective values are observed, it is obtained that: The space between the yokes and the pillars is called the core window and is intended to accommodate the E : E = N : N (6) windings on the magnetic core or columns. In addition, 1 2 1 2 == = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) Since the assumption of neglected voltage drops is the conductor resistance, scattering inductance, and introduced, the following holds: iron core, while the I-scheme and Γ-scheme satisfy in calculations where there are possibilities of neglecting U : U = N : N (7) certain elements, negligible values for the result [7]. In the 1 2 1 2 following, as an example, equivalent schemes of two- Power losses are also neglected, so the input power is winding and three-winding transformers will be presented, indeed equal to the output: with the corresponding equations of transformers, following the example of Goić et all [3]. U I = U I →I : I = U : U → I : I =N : N (8) 1 1 2 2 1 2 2 1 1 2 2 1 2.1. Scheme of a two-winding transformer 1.4.2. Real transformer Figure 4 shows the equivalent scheme of a two-winding Dolenc states that by introducing quantities that are transformer. The impedance of the primary side is neglected in an ideal transformer, a real transformer is denoted by Z , while the impedance of the secondary arrived at. In a real transformer, the actual properties of side is denoted by Z . Both impedances consist of the the device are taken. We assume that the primary and operating resistance (R , R ) and the scattering reactance 1 2 secondary windings have an ohmic resistance, due to (X , X ) of each transformer winding. Z denotes the so- 1σ 2σ 0 which the voltage drops with the passage of current. called transverse branch representing reactive losses The voltage drop in the primary is proportional to the due to magnetizing current (X ) and operating losses in primary current, while the voltage drop in the secondary transformer iron (R ). The voltage transformation on the (or reduced magnitude to the primary) is proportional to equivalent circuit is shown by an ideal transformer (IT). the secondary current. Due to the flow of current at ohmic resistances, losses occur, which are calculated according to the following equation: 2 2 P =P + P =I R + I R (9) cu cu1 cu1 1 1 2 2 Furthermore, with an ideal transformer, it is assumed that the magnetic forces are closed completely through the iron core. However, with a real transformer, they also close through the air because the permeability of the iron core is Figure 4: Equivalent single-phase scheme of a two-winding not infinitely large. Forces that close only around the bends transformer of the primary and secondary windings form a waste flow. The primary dissipation current and the secondary In the equivalent scheme, it is important to convert the dissipation current are in phase with the corresponding secondary values to primary or reduce the secondary currents and in the corresponding windings, they induce values to the primary side of the transformer so that all counter voltages equal to the product of the current and previously taken losses remain unchanged. By reducing the dissipative inductive resistance. These voltage drops to the primary or secondary side, multiplying (dividing) the are caused by the scattering inductance and precede impedance by the square of the transformer gear ratio, the 90° angle behind the magnetic currents that induced the transformer and the whole grid can be reduced to one them. Also, in the case of alternating magnetization of the voltage level, in which case the transformer is shown by iron core of a transformer, losses in iron occur as a result an equivalent circuit without an ideal transformer, as in of the action of eddy currents and magnetization along Figure 5 the reduction of the primary impedance to the the hysteresis loop [6]. secondary side is calculated, and the equation calculates the reduction of the secondary impedance to the primary side. 2. EQUIVALENT TRANSFORMER SCHEME NU (10) The equivalent scheme of each element represents a model NU of the actual conditions in the device and its components:   winding resistances, dissipative inductances, magnetic 1 ' '2 (11) Z = Z×= ; Z Zp× 11   2 2 circuit, and core resistances [7]. When constructing the   transformer circuit, four important physical facts should be kept in mind: that there are losses in copper caused by the passage of current through the windings of primary and secondary heated, that the iron core is heated by eddy currents and hysteresis, and that the primary and secondary windings have dissipative inductance [5]. In transformers, the T-scheme most faithfully models = = B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 In the variant of the Dyn connection group (transformers 10(20)/0,4 kV) where the secondary star is directly grounded, the zero current component can be closed from the secondary side, so the zero impedance is equal to the direct impedance of the transformer seen from the secondary, while with primary sides infinite, Figure 8. The same is true for the 10 (20) /0,4 kV transformer in the Yzn connection group. Figure 5: Equivalent Γ scheme of a two-winding transformer The parameters of the circuit can be calculated directly from the nominal data of the transformer, namely: nominal primary and secondary voltage (U and U ), rated n1 n2 apparent power of the transformer (S ), transformer short- Figure 8: Equivalent zero circuit of a transformer in a Dyn circuit voltage (u ), nominal short-circuit losses connection connection group with a directly grounded secondary star and no-load losses of the transformer (P and P ) and the k 0 percentage of the no-load current (magnetization current) 2.2. Schematic of a three-winding transformer of the transformer (i ). Three-wind power transformers in distribution grids are The following variants are most used in distribution grids: used in 110/35(30)/10 kV and 110/10(20)/10 kV variants, In the Yd or Dy group connection variant (35/10 kV i.e., as a connection to the transmission grid. In the case transformers) where the star point is not grounded, the of a three-winding transformer, there are two voltage zero current component cannot be closed on either side, transformations (primary-secondary, primary-tertiary), so the zero impedance is infinite (Figure 6). and the reduction of the impedances of the secondary and tertiary to the primary side (and vice versa) is done In the variant of the Dyn connection group (35/10 kV in the same way as in a two-winding transformer only transformers) where the secondary star is grounded via transmission ratio P (primary-secondary) and P via the Z impedance (operating resistance R or choke 1 2 (primary-tertiary): jX), the zero current component can be closed on the secondary side, so the zero impedance is equal to the sum of the direct impedance of the transformer and the N U I NU 1 12 1 1 3 PP ; (12) 3Z grounding impedances viewed from the secondary, n NU I NU I 2 2 1 2 31 while infinite from the primary side as shown in Figure 7. The equivalent scheme of a three-winding transformer with impedances reduced to the primary side is shown in Figure 9 (extended Γ scheme). Figure 6: Equivalent zero scheme of transformers in the Yd and Dy junction group Figure 9: Equivalent single-phase t scheme of a three-winding transformer Figure 7: Equivalent zero circuit of a transformer in a Dyn junction group with a secondary star point grounded across the Z impedance = = = = = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) The expressions for the impedances of individual windings into the Simulink work window with the mouse, or copy- are: paste commands are used. Z =× Z +− ZZ ( ) 3.1. Conducting experimental simulations 1 12 13 23 Z =× ZZ+ − Z ( ) (13) 2 12 23 13 The no-load test, as well as the short-circuit test, will be performed via the transformer replacement scheme shown Z =×(ZZ+ − Z ) 3 13 23 12 in Figure 11. In distribution grids, the variant of the YNynd connection group (transformers 110/35/10 kV, 110/10(20)/10 kV) is almost exclusively used, in which the primary star is directly grounded, and the secondary star is grounded via Z impedance (operating resistance R or choke jX) or is unearthed. The zero component of the currents can be closed on the primary side, and on the secondary side if the star point is grounded via the Z impedance, Figure 10. Figure 11: Alternate transformer equivalent scheme seen from the primary side In this scheme, R and X represent the resistance and 1 I1 reactance of the primary side of the transformer, and R and X the resistance and reactance of the secondary I2 side of the transformer. R is the operating resistance representing the losses in the iron, i.e., the core, X denotes the magnetization reactance which represents the main magnetic flux, and α represents the gear ratio of the transformer. The parameters can be obtained by conducting a no-load and short-circuit test, as will be shown below. 3.1.1. Performing an idle experiment The idle test is performed by connecting the primary to the rated voltage and leaving the secondary open. With the help of ammeters, voltmeters, and wattmeter’s, the input current, voltage, and power of the transformer are measured. Due to the very low no-load current, voltage drops and losses in copper are neglected. By measuring the power that the transformer at idle, at rated voltage, Figure 10: Equivalent zero circuit of the transformer in the YNynd takes from the grid, iron losses are obtained [10]. With the connection group with a directly grounded primary star and a idle test, it is possible to determine the parameters of the secondary star grounded across the Z impedance n transverse branch of the replacement circuit (R and X ), C M as well as the idle losses, the excitation current, and the idle power factor. As shown in Figure 12. 3. SIMULINK The model of the power transformer according to the existing scheme will be made for the needs of work in MATLAB (Matrix Laboratory). MATLAB is a programming language intended for technical calculations. Simulink is started from the command line with the Simulink command or using the icon in the MATLAB command window. To create a model in Simulink, you first need to Figure 12: Experimental settings for the idle test open the Library Browser window, from which we will insert the desired system components into the Simulink window. The model of the transformer that we will use is the Linear Simulink standard blocks are divided into subgroups of Transformer, which we set to the following values. The blocks. The desired block can be found in subgroups or by frequency is set to 50 Hz, the voltage of the primary side to typing the name in the search engine. The block is dragged 220 V, and the secondary to 110 V, while other values are 16 B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 left as default (R =4,3218 Ω, L =0,45856 H, R =0,7938 Ω, 1 1 2 1 (17) R 1067152,921Ω L =0,084225 H). It is possible to check other values for this transformer provided by the manufacturer. The values are shown in Table I. (18) BY sinθ 0, 000001 S M E Table I: Actual values of the transformer 1 X 900534, 2404Ω (19) R (Ω) X (Ω) R (Ω) X (Ω) C M eq eq 1080500 900380,4545 7,497 249,9011292 3.1.2. Performing a short circuit experiment Voltage Measurement and Current Measurement will be used to measure voltage and current in the primary circuit, The short-circuit test is performed in such a way that the while the measured values will be displayed on the display secondary terminals are short-circuited, and such a voltage block. To obtain the RMS value of the signal measured by is applied to the primary that the rated current flows through voltmeter and ammeter, an RMS block, which will transfer the transformer. This voltage is called the short-circuit the value to the display frame that reads these RMS values, voltage. Due to the low voltage, the magnetizing current is required, i.e., RMS values of no-load current and no-load is negligible. Since the secondary voltage is equal to zero, voltage. As the power supply on the primary side, we use all the applied voltage is spent on voltage drops. In the an AC Voltage Source, whose amplitude and frequency short-circuit test, the short-circuit voltage is 4-12% of the are set according to following values. Peak amplitude is nominal. In this case, the losses in iron can be neglected, 220 2 V, phase is 0°, frequency 50Hz and sample time 0. and the power that the transformer takes from the grid at For the frequency of the RMS block to correspond to the a rated current is equal to the losses in copper [10]. The frequency of the AC Voltage Source, it must also be set to experimental setup is shown in Figure 14. 50 Hz. Parameters on RMS block in Simulink are set as true RMS value, fundamental frequency 50Hz, initial RMS value is 0 and sample time 0,001. Figure 13 shows the implementation of the open circuit in Simulink, as follows: Figure 14: Experimental settings for a short circuit test To make a transformer model for a short-circuit test (Figure 15), we need all the same blocks to make a diagram of a transformer at idle. We set the same settings for all blocks Figure 13: Model of a transformer in Simulink for performing an as shown in the previous subchapter and set them to the idle test same values. The only difference between short circuits and idles is that the secondary terminals are no longer open The values obtained after the simulation are shown in the but short-circuited. By starting the simulation, it is possible following table: to obtain the values of voltage, current, and power of the Table II: Directly obtained values in Simulink for idling test primary side of the circuit. V (V) I (A) P (W) OC OC OC 220 0.0003197 0.04536 Determination of the parameters (resistance R and reactance X ) can be performed with the help of the obtained results in the following way: OC (14) Y =G − jB = =0, 000001453 S E C M OC OC Figure 15: Model of a transformer in Simulink for performing a PF cosθ 0, 644922796 (15) OC short circuit experiment VI OC OC GY cosθ 0, 000000937 S (16) CE == = = = = = == = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) The values obtained after the simulation are shown in connect these parts into a whole, the construction itself is Table III: always preceded by the implementation of the budget, in order to determine all the necessary elements of the future Table III: Directly obtained values in Simulink for short circuit test transformer. As for the physical picture of the operation of the transformer, in a real transformer, the real properties of V (V) I (A) P (W) the device are taken, while in the ideal certain size they are SC SC SC neglected. We assume that the primary and secondary 220 0.88 5.84 windings have an ohmic resistance, due to which the voltage drops with the passage of current, and that in a Using the previously obtained values, it is possible to real transformer the magnetic forces are closed through calculate the serial impedance of the primary circuit: the air. Also, losses in iron occur, which are neglected in SC (20) an ideal transformer, and the dependence of magnetic ZZ 250Ω eq SC induction on the strength of the magnetic field is not linear, SC but is described by a hysteresis loop. The equivalent SC (21) R R 7,541322314Ω scheme of each element represents a model of the actual eq SC SC conditions in the device and its components: winding 2 resistances, dissipative inductances, magnetic circuit, and (22) XX= = Z −= R 249,886231Ω eq SC eq eq core resistances. The elements of the equivalent scheme are determined based on the results of the no-load test and the short-circuit test and based on the calculated 3.2. Comparation of parameters quantities the equivalent scheme can be drawn. For this paper, a model of a transformer in Simulink was made, In the following, the actual transformer parameters will so the steps are described pictorially in the paper. For be compared with the parameters obtained through example, a 250 MVA, 220-110 V, 50 Hz transformer was the no-load and short-circuit experiments in Simulink. taken. Actual values were compared with the values of the The transformer on which the test was performed is a parameters obtained after the simulations of the idling and 250 MVA, 220-110 V, 50 Hz transformer. Table IV lists short-circuit experiments in Simulink. Almost equal values the transformer data and the data obtained in Simulink were obtained, so the error is negligible, and the model can through simulations. be used for further calculations. The main contribution of Table IV: Values of actual parameters and parameters obtained this paper is the description and presentation of a model in Simulink that precisely describes the behaviour of the transformer. Also, the presented model can be used for further testing (Ω) R X R X C M eq eq of transformers and operation management of the entire Actual power system in which the transformer is the main element transformer 1080500 900380,4545 7,494 249,9011292 parameters of voltage and current transformation. Parameters obtained through 1067152,921 900534,2404 7,541322314 249,886231 REFERENCES simulations in Simulink [1] D. Štefanović, Technical Encyclopedia. Zagreb, Error (%) 1,235268764 0.01708 0.6315 0.00596 Croatia: The Miroslav Krleža Institute of Lexicography, Approximately equal values, i.e., a very small error, [2] M. Krarti, Energy-Efficient Electrical Systems for show how the developed simulation models predict the Buildings, CRC Press, 2017 equivalent elements of the circuit very well. [3] R. Goić, D. Jakus and I. Penović, Electrical Energy Distribution, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture Split, 4. CONCLUSION Croatia,2008 [4] R. Židovec, MUE Measuring transformers, Accessed: This paper describes the elements of the equivalent Jun.1, 2021. [Online]. Available: https://www.scribd. scheme of the power transformer and conduct simulations com of the no-load test and the short circuit test in MATLAB [5] Z. Varga, Electrical machinery and equipment, (Simulink). Transformers, with unchanged frequency, Zagreb, Croatia: Element, 2016 change the value of voltage and current and thus, among [6] A. Dolenc, Transformers, I and II, University of Zagreb, other things, reduce losses in the transmission of electrical Croatia, 1991 energy from producers to large and small consumers. The [7] B. Skalički and J. Grilec, Electrical machines and main parts of transformers (cores and windings) actively drives, Faculty of Mechanical Engineering and Naval participate in energy conversion, but large transformers Architecture, University of Zagreb, Croatia 2011 such as energy include several passive parts. In order to = = = = = = B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 [8] R. Wolf, Fundamentals of Electrical Machines, Drago Bago graduated and completed postgraduate Školska knjiga d.d. Zagreb, Croatia 1991 PhD studies from the Faculty of Electrical Engineering [9] D. N. Mitić, Electrical Engineering 1, Petrograf, Niš, and Computing, University of Zagreb. Since 2000 he Serbia, 2007. has been employed at JP Elektroprivreda Hrvatske [10] Veleučilište u Varaždinu (VELV), Electrical machines zajednice Herceg Bosne d.d. Mostar in the Distribution - script. Accessed Jun.15, 2021. [Online]. Available: Power Division and the Development Division. Now, he https://www.scribd.com is a member of the Board and the Executive Director for Development in JP Elektroprivreda Hrvatske zajednice Herceg Bosne d.d. Mostar. He completed a professional study “Energy Efficiency” organized by the Institute of BIOGRAPHY Energy Technology in Kjeller (Oslo), Norway and the Faculty of Electrical Engineering and Computing. He Goran Kujundžić received the B.S. and Ph.D. degree is an author and a co-author of several scientific and from University of Zagreb, Croatia in 2000 and 2017 professional papers in the field of overvoltage protection respectively. He worked as a designer and project manager for medium voltage lines, the correlation of events data at the Distribution Department of Elektroprivreda HZ HB from the power system and data from the system of power utility (2000-2006) and after at Power Department professional organization IEEE. He is also a member of JP Hrvatske Telekomunikacije Mostar. His research of the Study Committee of the International Council on interests include energy storage systems and management Large Electric Systems CIGRÉ in Paris, Study Committee of microgrids that are based on renewable sources. C6 - Distribution Systems and Dispersed Generation. He is the President of the International Conference of CIRED Vinko Kalfić was born in Mostar in 1999. He received for Bosnia and Herzegovina and president of Study a BCs degree in Electrical Engineering from the Faculty Committee C6 BH K CIGRÉ - Distribution Systems and of Mechanical Engineering, Computing and Electrical Dispersed Generation. He is a member of the Board of Engineering, University of Mostar in 2021. The focus of BH K CIGRÉ and a member of the Board BAKE – BH his diploma thesis was on power transformer. During Council for Electrical Engineering. He is also a member his undergraduate study he also completed his student of the Editorial Council of the magazine B&H Electrical practice in JP ‘’Elektroprivreda HZ HB’’ d.d. Čapljina. He Engineering and a member of the Croatian Association of is currently attending the second Bologna study cycle Engineers – AMAC. at the same University. The current areas of his interests include problems in electric power systems dynamics and control, smart grids and integration of renewable energy sources. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png B&H Electrical Engineering de Gruyter

Equivalent Circuit Parameters for Power Transformer and Implementation of Open and Short Circuit Test Simulation in Matlab (SIMULINK)

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de Gruyter
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© 2022 Goran Kujundžić et al., published by Sciendo
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2566-3151
DOI
10.2478/bhee-2022-0013
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Abstract

B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 Submitted: October 7, 2022 Review scientific paper Accepted: November 20, 2022 EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) 1,2 1 1 Goran Kujundžić , Vinko Kalfić , Drago Bago Abstract: This paper describes the power transformer, its basic mode of operation, parts, and construction. Equivalent circuit parameters are defined, and the methods of their determination are explained. A model of the transformer in Simulink was made and the process of its production is described. The created transformer model was then simulated through open and short circuit experiments. The values of the parameters obtained by the simulation were compared with the actual values and conclusions were drawn. The main goal of this work is to determine the precision of the operation of the transformer model in Simulink, and based on the obtained results, the same model can be used in algorithms for checking the operation of the entire power system. Keywords: transformer, Simulink, simulation, short circuit be explained. In this regard, this work aims to determine INTRODUCTION the elements of the equivalent scheme of the power transformer and to conduct simulations of the open circuit A transformer is a static electromagnetic device, which test and the short-circuit test in MATLAB (Simulink). means there are no moving parts. When transmitting electrical energy from one or more AC circuits, which To achieve this, it was considered important to give supply the primary windings of the transformer, to one or a thorough insight into the parts of the transformer, its more AC circuits, supplied from the secondary windings of construction, and the physical picture of its operation. the transformer, there are altered amounts of current and Thus, the active and passive parts of the transformer and voltage, with unchanged frequency [1]. Power transformers their role are described, as well as the construction of are the most common type of transformer and are used to the transformer - from the initial calculation, through the raise or lower the voltage level depending on the needs of construction of the core and winding of the transformer, the consumer [2]. In addition to them, depending on the the types of transformer connection and parallel operation type of application, we also distinguish between measuring of the transformer are described. The physical picture transformers and special purpose transformers, such of the operation of the transformer is explained through as welding transformers and transformers for converter the ideal and real transformer. In the case of an ideal drives [3]. Measuring transformers are used to monitor transformer, certain parameters are neglected concerning the use of electrical energy and there are two basic types the real ones. After explaining the basic characteristics of measuring transformers, namely voltage transformer of transformers, the elements of transformer equivalent and current transformer. These transformers enable the schemes will be described, models of actual conditions measurement of voltages and currents of large amounts in the device and its components will be described, as with measuring instruments of a small measuring range. well as ways to determine the elements of these schemes Voltage measuring transformers require that the difference through no-load and short-circuit experiments. between the primary voltage and the primary reduced secondary voltage be as small as possible and that the In the final part of the paper, the method of making a phase shift of the primary and secondary voltage be the model of a transformer in Simulink will be practically same, but these conditions cannot be fully met, so we are described, and experiments of no-load and short circuit talking about voltage and phase error [4]. will be performed. It will be checked whether the values of the parameters equal to the real ones will be obtained In this paper, emphasis will be placed on the power using Simulink. transformer as the most important part of transformer plants, its importance and use in the power system will Faculty of Mechanical Engineering, Computing and Electrical Engineering, University of Mostar, Bosnia and Herzegovina Correspondence email: goran.kujundzic@fsre.sum.ba © 2022 Author(s). This is an open access article licensed under the Creative Commons Attribution License 4.0. (http://creativecommons.org/licenses/by/4.0/). 11 G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) 1. FUNDAMENTALS OF ENERGY TRANSFORMER 1.1. Importance of power transformer We can say that power transformers are the basic and most widespread elements of electrical systems, and their role in the power system is especially important. The power system consists of 4 basic units. The first refers to power plants as sources of electrical energy, then we Figure 2: Main (active) parts of the transformer have the transmission grid through which electrical energy is transported from power plants to the distribution grid The iron core consists of pillars connected to the upper and large consumers and exchanges power between and lower yoke. The main role of the nucleus is to connected power systems. The third unit consists of a guide the magnetic flux forces. It is made of specially medium and low voltage distribution grid through which treated magnetic types of iron due to its good magnetic electrical energy taken from the transmission grid or conductivity and consists of sheets with a thickness of smaller power plants connected to the distribution grid is 0.3 mm to 0.5 mm. Electrical energy is transmitted by distributed to medium and small consumers connected to electromagnetic induction from primary to secondary, the distribution grid, as the fourth unit of the system. without changing the frequency. The primary is powered by an external source, and the secondary is the one Transformers are also appearing as an integral part of that creates voltage by electromagnetic induction and the electrical energy grid, within the transmission and supplies consumers [6]. The transformer core is secured distribution grid. with a cover to make it easier to insert and remove from the boiler. In order to dissipate heat, various fins, pipes, and radiators are placed on the boiler, which dissipates heat to the surrounding air or cooling water. There is an oil drain valve at the bottom. The conservator is a metal tank positioned on top of the transformer, contains a certain amount of spare oil, and allows expansion as the temperature and volume of the oil increase. In the case of transformers, the cooling system is extremely important. 1.3. Construction of power transformer 1.3.1. Transformer calculation Figure 1: Power transformer The elements for the construction of a transformer should be obtained by its calculation, and the output data are We distinguish three basic types of power transformers, usually known as output and input voltage, output current namely block, grid, and distribution transformers. Block or power, and the type of converter for which it will be used. transformers are used to connect the generator to the The size and type of core, the number of turns of individual mains, where there is a lower voltage on the generator windings, the cross-sections of their conductors, and the side [3].zThey are also called generator transformers. winding directions are the basic elements for the selection Together with the main transformers, they form a group or construction of transformers. It is also important after of large transformers [1]. Mains transformers are used all the elements are determined to check the location of to connect voltage levels in the transmission grid or to the windings because it may happen that not everything connect the transmission and distribution grid, while can fit in the available space [10]. The basic data required distribution transformers are used to connect voltage for the calculation are primary voltage (U ) and secondary levels in the distribution grid [3]. (U ), transformer power (S), core dimension (P), primary current (I ) and secondary (I ), primary wire thickness (D ), 1 2 1 1.2. Power transformer parts and secondary (D ) and current density (J). Based on the primary voltage, a constant for core sizing is determined. The basic parts of each transformer, which participate in The surface area of the core is expressed in cm and the transformation of electrical energy and without which is obtained by multiplying the sides of the coil. For the the transformer cannot work, are the iron core and the following calculation, we will assume that the primary primary and secondary circuit, as shown in Figure 2 [5]. voltage is 230 V with a frequency of 50 Hz, so the core sizing constant will be 45. Then it is necessary to determine 12 B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 the number of primary and secondary windings, which is for insulating reasons, the undervoltage winding is obtained from the equation: placed first up to the column of the magnetic core. By placing the upper voltage winding next to the magnetic core column, stronger insulation towards the core is N = (1) required compared to the insulation of the lower voltage winding [7]. It determines the number of turns of the wire by 1 V. The required number of windings on the primary (N ) and 1.3.4. Types of transformer connection secondary (N ) is calculated using the following equations, provided that the required number of windings on the In practice, there are two basic types of transformer secondary also depends on the required output voltage: connections, namely single-phase and three-phase transformers. Single-phase transformers can only be N = N× U ; N = N× U (2) 1 1 2 2 connected in one way. Wolf states that unlike single- phase transformers, the terminals of a three-phase The primary (I ) and secondary (I ) currents are calculated 1 2 transformer can be connected in 3 different ways, according to the equations: namely: a star connection, a triangle connection, and SS a broken star connection (zigzag connection). Each of I ; I (3) these compounds is denoted by a separate letter. The UU star designation of the junction is Y or y, the junction of If we assume that the electrical energy density is constant triangle D or d of the junction of a broken star is Z or z. The (J = 2.5 A / mm ), then the wire thickness for the primary correct transformer connection is indicated by two letters (D ) and secondary (D ) is calculated as follows: 1 2 and a number. The first letter represents the junction of the transformer primary, the second letter represents the D 0.7 ID ; 0.7 I (4) 1 12 2 junction of the transformer secondary, and the number represents the hour number. The hour number is a mark that indicates the degree of phase delay of the secondary 1.3.2. Making the core in relation to the primary. This number multiplied by 30° represents the phase angle of the secondary voltage in The iron core takes different forms and is performed degrees [8]. differently and is mostly built in a rectangular shape. It is made of a multitude of mutually insulated thin sheets. 1.4. Physical picture of transformer operation Eddy currents or Foucault currents are generated in metal conductors of electric current, which is the iron 1.4.1. Ideal transformer core of a transformer, due to the action of an alternating magnetic field. Eddy currents flow in such a way that When we assume an ideal transformer, we associate with they form a closed circle around one point inside the it negligible losses and voltage drops and ignore the ohmic conductor, so their intensity is limited by mutually resistance of the winding coils. Figure 3 schematically insulated transformer sheets [7]. When assembling, the shows the mode of operation of the transformer [9]. core is impregnated, varnished, and finally mechanically tightened with screws to prevent vibration under the influence of magnetic force. The rule also applies that increasing the power of the transformer increases the number of sheets with different widths that form the magnetic core of the transformer. 1.3.3. Transformer winding After the calculation, the winding follows. There are two Figure 3: Schematic representation of a single-phase two- basic configurations of transformers, namely the pole winding transformer (core) type and the sheathed type of transformer and According to the basic law of electromagnetic induction, they differ in the location of the windings wound on the Faraday’s law, in a bend that includes magnetic flux ( Φ) magnetic core. Thus, in the case of a column winding, the voltage of the current value (e) is induced proportional they are located on each column of the core, and in to the rate of change of current, as follows: the case of the shrouded type, they are located on the dφ central column or columns. The windings are located on eN = − (5) the columns of the magnetic cores, and the columns dt are interconnected by the yoke of the magnetic core. If the effective values are observed, it is obtained that: The space between the yokes and the pillars is called the core window and is intended to accommodate the E : E = N : N (6) windings on the magnetic core or columns. In addition, 1 2 1 2 == = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) Since the assumption of neglected voltage drops is the conductor resistance, scattering inductance, and introduced, the following holds: iron core, while the I-scheme and Γ-scheme satisfy in calculations where there are possibilities of neglecting U : U = N : N (7) certain elements, negligible values for the result [7]. In the 1 2 1 2 following, as an example, equivalent schemes of two- Power losses are also neglected, so the input power is winding and three-winding transformers will be presented, indeed equal to the output: with the corresponding equations of transformers, following the example of Goić et all [3]. U I = U I →I : I = U : U → I : I =N : N (8) 1 1 2 2 1 2 2 1 1 2 2 1 2.1. Scheme of a two-winding transformer 1.4.2. Real transformer Figure 4 shows the equivalent scheme of a two-winding Dolenc states that by introducing quantities that are transformer. The impedance of the primary side is neglected in an ideal transformer, a real transformer is denoted by Z , while the impedance of the secondary arrived at. In a real transformer, the actual properties of side is denoted by Z . Both impedances consist of the the device are taken. We assume that the primary and operating resistance (R , R ) and the scattering reactance 1 2 secondary windings have an ohmic resistance, due to (X , X ) of each transformer winding. Z denotes the so- 1σ 2σ 0 which the voltage drops with the passage of current. called transverse branch representing reactive losses The voltage drop in the primary is proportional to the due to magnetizing current (X ) and operating losses in primary current, while the voltage drop in the secondary transformer iron (R ). The voltage transformation on the (or reduced magnitude to the primary) is proportional to equivalent circuit is shown by an ideal transformer (IT). the secondary current. Due to the flow of current at ohmic resistances, losses occur, which are calculated according to the following equation: 2 2 P =P + P =I R + I R (9) cu cu1 cu1 1 1 2 2 Furthermore, with an ideal transformer, it is assumed that the magnetic forces are closed completely through the iron core. However, with a real transformer, they also close through the air because the permeability of the iron core is Figure 4: Equivalent single-phase scheme of a two-winding not infinitely large. Forces that close only around the bends transformer of the primary and secondary windings form a waste flow. The primary dissipation current and the secondary In the equivalent scheme, it is important to convert the dissipation current are in phase with the corresponding secondary values to primary or reduce the secondary currents and in the corresponding windings, they induce values to the primary side of the transformer so that all counter voltages equal to the product of the current and previously taken losses remain unchanged. By reducing the dissipative inductive resistance. These voltage drops to the primary or secondary side, multiplying (dividing) the are caused by the scattering inductance and precede impedance by the square of the transformer gear ratio, the 90° angle behind the magnetic currents that induced the transformer and the whole grid can be reduced to one them. Also, in the case of alternating magnetization of the voltage level, in which case the transformer is shown by iron core of a transformer, losses in iron occur as a result an equivalent circuit without an ideal transformer, as in of the action of eddy currents and magnetization along Figure 5 the reduction of the primary impedance to the the hysteresis loop [6]. secondary side is calculated, and the equation calculates the reduction of the secondary impedance to the primary side. 2. EQUIVALENT TRANSFORMER SCHEME NU (10) The equivalent scheme of each element represents a model NU of the actual conditions in the device and its components:   winding resistances, dissipative inductances, magnetic 1 ' '2 (11) Z = Z×= ; Z Zp× 11   2 2 circuit, and core resistances [7]. When constructing the   transformer circuit, four important physical facts should be kept in mind: that there are losses in copper caused by the passage of current through the windings of primary and secondary heated, that the iron core is heated by eddy currents and hysteresis, and that the primary and secondary windings have dissipative inductance [5]. In transformers, the T-scheme most faithfully models = = B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 In the variant of the Dyn connection group (transformers 10(20)/0,4 kV) where the secondary star is directly grounded, the zero current component can be closed from the secondary side, so the zero impedance is equal to the direct impedance of the transformer seen from the secondary, while with primary sides infinite, Figure 8. The same is true for the 10 (20) /0,4 kV transformer in the Yzn connection group. Figure 5: Equivalent Γ scheme of a two-winding transformer The parameters of the circuit can be calculated directly from the nominal data of the transformer, namely: nominal primary and secondary voltage (U and U ), rated n1 n2 apparent power of the transformer (S ), transformer short- Figure 8: Equivalent zero circuit of a transformer in a Dyn circuit voltage (u ), nominal short-circuit losses connection connection group with a directly grounded secondary star and no-load losses of the transformer (P and P ) and the k 0 percentage of the no-load current (magnetization current) 2.2. Schematic of a three-winding transformer of the transformer (i ). Three-wind power transformers in distribution grids are The following variants are most used in distribution grids: used in 110/35(30)/10 kV and 110/10(20)/10 kV variants, In the Yd or Dy group connection variant (35/10 kV i.e., as a connection to the transmission grid. In the case transformers) where the star point is not grounded, the of a three-winding transformer, there are two voltage zero current component cannot be closed on either side, transformations (primary-secondary, primary-tertiary), so the zero impedance is infinite (Figure 6). and the reduction of the impedances of the secondary and tertiary to the primary side (and vice versa) is done In the variant of the Dyn connection group (35/10 kV in the same way as in a two-winding transformer only transformers) where the secondary star is grounded via transmission ratio P (primary-secondary) and P via the Z impedance (operating resistance R or choke 1 2 (primary-tertiary): jX), the zero current component can be closed on the secondary side, so the zero impedance is equal to the sum of the direct impedance of the transformer and the N U I NU 1 12 1 1 3 PP ; (12) 3Z grounding impedances viewed from the secondary, n NU I NU I 2 2 1 2 31 while infinite from the primary side as shown in Figure 7. The equivalent scheme of a three-winding transformer with impedances reduced to the primary side is shown in Figure 9 (extended Γ scheme). Figure 6: Equivalent zero scheme of transformers in the Yd and Dy junction group Figure 9: Equivalent single-phase t scheme of a three-winding transformer Figure 7: Equivalent zero circuit of a transformer in a Dyn junction group with a secondary star point grounded across the Z impedance = = = = = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) The expressions for the impedances of individual windings into the Simulink work window with the mouse, or copy- are: paste commands are used. Z =× Z +− ZZ ( ) 3.1. Conducting experimental simulations 1 12 13 23 Z =× ZZ+ − Z ( ) (13) 2 12 23 13 The no-load test, as well as the short-circuit test, will be performed via the transformer replacement scheme shown Z =×(ZZ+ − Z ) 3 13 23 12 in Figure 11. In distribution grids, the variant of the YNynd connection group (transformers 110/35/10 kV, 110/10(20)/10 kV) is almost exclusively used, in which the primary star is directly grounded, and the secondary star is grounded via Z impedance (operating resistance R or choke jX) or is unearthed. The zero component of the currents can be closed on the primary side, and on the secondary side if the star point is grounded via the Z impedance, Figure 10. Figure 11: Alternate transformer equivalent scheme seen from the primary side In this scheme, R and X represent the resistance and 1 I1 reactance of the primary side of the transformer, and R and X the resistance and reactance of the secondary I2 side of the transformer. R is the operating resistance representing the losses in the iron, i.e., the core, X denotes the magnetization reactance which represents the main magnetic flux, and α represents the gear ratio of the transformer. The parameters can be obtained by conducting a no-load and short-circuit test, as will be shown below. 3.1.1. Performing an idle experiment The idle test is performed by connecting the primary to the rated voltage and leaving the secondary open. With the help of ammeters, voltmeters, and wattmeter’s, the input current, voltage, and power of the transformer are measured. Due to the very low no-load current, voltage drops and losses in copper are neglected. By measuring the power that the transformer at idle, at rated voltage, Figure 10: Equivalent zero circuit of the transformer in the YNynd takes from the grid, iron losses are obtained [10]. With the connection group with a directly grounded primary star and a idle test, it is possible to determine the parameters of the secondary star grounded across the Z impedance n transverse branch of the replacement circuit (R and X ), C M as well as the idle losses, the excitation current, and the idle power factor. As shown in Figure 12. 3. SIMULINK The model of the power transformer according to the existing scheme will be made for the needs of work in MATLAB (Matrix Laboratory). MATLAB is a programming language intended for technical calculations. Simulink is started from the command line with the Simulink command or using the icon in the MATLAB command window. To create a model in Simulink, you first need to Figure 12: Experimental settings for the idle test open the Library Browser window, from which we will insert the desired system components into the Simulink window. The model of the transformer that we will use is the Linear Simulink standard blocks are divided into subgroups of Transformer, which we set to the following values. The blocks. The desired block can be found in subgroups or by frequency is set to 50 Hz, the voltage of the primary side to typing the name in the search engine. The block is dragged 220 V, and the secondary to 110 V, while other values are 16 B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 left as default (R =4,3218 Ω, L =0,45856 H, R =0,7938 Ω, 1 1 2 1 (17) R 1067152,921Ω L =0,084225 H). It is possible to check other values for this transformer provided by the manufacturer. The values are shown in Table I. (18) BY sinθ 0, 000001 S M E Table I: Actual values of the transformer 1 X 900534, 2404Ω (19) R (Ω) X (Ω) R (Ω) X (Ω) C M eq eq 1080500 900380,4545 7,497 249,9011292 3.1.2. Performing a short circuit experiment Voltage Measurement and Current Measurement will be used to measure voltage and current in the primary circuit, The short-circuit test is performed in such a way that the while the measured values will be displayed on the display secondary terminals are short-circuited, and such a voltage block. To obtain the RMS value of the signal measured by is applied to the primary that the rated current flows through voltmeter and ammeter, an RMS block, which will transfer the transformer. This voltage is called the short-circuit the value to the display frame that reads these RMS values, voltage. Due to the low voltage, the magnetizing current is required, i.e., RMS values of no-load current and no-load is negligible. Since the secondary voltage is equal to zero, voltage. As the power supply on the primary side, we use all the applied voltage is spent on voltage drops. In the an AC Voltage Source, whose amplitude and frequency short-circuit test, the short-circuit voltage is 4-12% of the are set according to following values. Peak amplitude is nominal. In this case, the losses in iron can be neglected, 220 2 V, phase is 0°, frequency 50Hz and sample time 0. and the power that the transformer takes from the grid at For the frequency of the RMS block to correspond to the a rated current is equal to the losses in copper [10]. The frequency of the AC Voltage Source, it must also be set to experimental setup is shown in Figure 14. 50 Hz. Parameters on RMS block in Simulink are set as true RMS value, fundamental frequency 50Hz, initial RMS value is 0 and sample time 0,001. Figure 13 shows the implementation of the open circuit in Simulink, as follows: Figure 14: Experimental settings for a short circuit test To make a transformer model for a short-circuit test (Figure 15), we need all the same blocks to make a diagram of a transformer at idle. We set the same settings for all blocks Figure 13: Model of a transformer in Simulink for performing an as shown in the previous subchapter and set them to the idle test same values. The only difference between short circuits and idles is that the secondary terminals are no longer open The values obtained after the simulation are shown in the but short-circuited. By starting the simulation, it is possible following table: to obtain the values of voltage, current, and power of the Table II: Directly obtained values in Simulink for idling test primary side of the circuit. V (V) I (A) P (W) OC OC OC 220 0.0003197 0.04536 Determination of the parameters (resistance R and reactance X ) can be performed with the help of the obtained results in the following way: OC (14) Y =G − jB = =0, 000001453 S E C M OC OC Figure 15: Model of a transformer in Simulink for performing a PF cosθ 0, 644922796 (15) OC short circuit experiment VI OC OC GY cosθ 0, 000000937 S (16) CE == = = = = = == = = G. Kujundžić, V. Kalfić, D. Bago: EQUIVALENT CIRCUIT PARAMETERS FOR POWER TRANSFORMER AND IMPLEMENTATION OF OPEN AND SHORT CIRCUIT TEST SIMULATION IN MATLAB (SIMULINK) The values obtained after the simulation are shown in connect these parts into a whole, the construction itself is Table III: always preceded by the implementation of the budget, in order to determine all the necessary elements of the future Table III: Directly obtained values in Simulink for short circuit test transformer. As for the physical picture of the operation of the transformer, in a real transformer, the real properties of V (V) I (A) P (W) the device are taken, while in the ideal certain size they are SC SC SC neglected. We assume that the primary and secondary 220 0.88 5.84 windings have an ohmic resistance, due to which the voltage drops with the passage of current, and that in a Using the previously obtained values, it is possible to real transformer the magnetic forces are closed through calculate the serial impedance of the primary circuit: the air. Also, losses in iron occur, which are neglected in SC (20) an ideal transformer, and the dependence of magnetic ZZ 250Ω eq SC induction on the strength of the magnetic field is not linear, SC but is described by a hysteresis loop. The equivalent SC (21) R R 7,541322314Ω scheme of each element represents a model of the actual eq SC SC conditions in the device and its components: winding 2 resistances, dissipative inductances, magnetic circuit, and (22) XX= = Z −= R 249,886231Ω eq SC eq eq core resistances. The elements of the equivalent scheme are determined based on the results of the no-load test and the short-circuit test and based on the calculated 3.2. Comparation of parameters quantities the equivalent scheme can be drawn. For this paper, a model of a transformer in Simulink was made, In the following, the actual transformer parameters will so the steps are described pictorially in the paper. For be compared with the parameters obtained through example, a 250 MVA, 220-110 V, 50 Hz transformer was the no-load and short-circuit experiments in Simulink. taken. Actual values were compared with the values of the The transformer on which the test was performed is a parameters obtained after the simulations of the idling and 250 MVA, 220-110 V, 50 Hz transformer. Table IV lists short-circuit experiments in Simulink. Almost equal values the transformer data and the data obtained in Simulink were obtained, so the error is negligible, and the model can through simulations. be used for further calculations. The main contribution of Table IV: Values of actual parameters and parameters obtained this paper is the description and presentation of a model in Simulink that precisely describes the behaviour of the transformer. Also, the presented model can be used for further testing (Ω) R X R X C M eq eq of transformers and operation management of the entire Actual power system in which the transformer is the main element transformer 1080500 900380,4545 7,494 249,9011292 parameters of voltage and current transformation. Parameters obtained through 1067152,921 900534,2404 7,541322314 249,886231 REFERENCES simulations in Simulink [1] D. Štefanović, Technical Encyclopedia. Zagreb, Error (%) 1,235268764 0.01708 0.6315 0.00596 Croatia: The Miroslav Krleža Institute of Lexicography, Approximately equal values, i.e., a very small error, [2] M. Krarti, Energy-Efficient Electrical Systems for show how the developed simulation models predict the Buildings, CRC Press, 2017 equivalent elements of the circuit very well. [3] R. Goić, D. Jakus and I. Penović, Electrical Energy Distribution, Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture Split, 4. CONCLUSION Croatia,2008 [4] R. Židovec, MUE Measuring transformers, Accessed: This paper describes the elements of the equivalent Jun.1, 2021. [Online]. Available: https://www.scribd. scheme of the power transformer and conduct simulations com of the no-load test and the short circuit test in MATLAB [5] Z. Varga, Electrical machinery and equipment, (Simulink). Transformers, with unchanged frequency, Zagreb, Croatia: Element, 2016 change the value of voltage and current and thus, among [6] A. Dolenc, Transformers, I and II, University of Zagreb, other things, reduce losses in the transmission of electrical Croatia, 1991 energy from producers to large and small consumers. The [7] B. Skalički and J. Grilec, Electrical machines and main parts of transformers (cores and windings) actively drives, Faculty of Mechanical Engineering and Naval participate in energy conversion, but large transformers Architecture, University of Zagreb, Croatia 2011 such as energy include several passive parts. In order to = = = = = = B&H Electrical E g n e i g, Volume 16, Issue 2, 2022:11-19 n i e r n ISSN:2566-3143, eISSN:2566-3151, DOI: 10.2478/bhee-2022-0013 [8] R. Wolf, Fundamentals of Electrical Machines, Drago Bago graduated and completed postgraduate Školska knjiga d.d. Zagreb, Croatia 1991 PhD studies from the Faculty of Electrical Engineering [9] D. N. Mitić, Electrical Engineering 1, Petrograf, Niš, and Computing, University of Zagreb. Since 2000 he Serbia, 2007. has been employed at JP Elektroprivreda Hrvatske [10] Veleučilište u Varaždinu (VELV), Electrical machines zajednice Herceg Bosne d.d. Mostar in the Distribution - script. Accessed Jun.15, 2021. [Online]. Available: Power Division and the Development Division. Now, he https://www.scribd.com is a member of the Board and the Executive Director for Development in JP Elektroprivreda Hrvatske zajednice Herceg Bosne d.d. Mostar. He completed a professional study “Energy Efficiency” organized by the Institute of BIOGRAPHY Energy Technology in Kjeller (Oslo), Norway and the Faculty of Electrical Engineering and Computing. He Goran Kujundžić received the B.S. and Ph.D. degree is an author and a co-author of several scientific and from University of Zagreb, Croatia in 2000 and 2017 professional papers in the field of overvoltage protection respectively. He worked as a designer and project manager for medium voltage lines, the correlation of events data at the Distribution Department of Elektroprivreda HZ HB from the power system and data from the system of power utility (2000-2006) and after at Power Department professional organization IEEE. He is also a member of JP Hrvatske Telekomunikacije Mostar. His research of the Study Committee of the International Council on interests include energy storage systems and management Large Electric Systems CIGRÉ in Paris, Study Committee of microgrids that are based on renewable sources. C6 - Distribution Systems and Dispersed Generation. He is the President of the International Conference of CIRED Vinko Kalfić was born in Mostar in 1999. He received for Bosnia and Herzegovina and president of Study a BCs degree in Electrical Engineering from the Faculty Committee C6 BH K CIGRÉ - Distribution Systems and of Mechanical Engineering, Computing and Electrical Dispersed Generation. He is a member of the Board of Engineering, University of Mostar in 2021. The focus of BH K CIGRÉ and a member of the Board BAKE – BH his diploma thesis was on power transformer. During Council for Electrical Engineering. He is also a member his undergraduate study he also completed his student of the Editorial Council of the magazine B&H Electrical practice in JP ‘’Elektroprivreda HZ HB’’ d.d. Čapljina. He Engineering and a member of the Croatian Association of is currently attending the second Bologna study cycle Engineers – AMAC. at the same University. The current areas of his interests include problems in electric power systems dynamics and control, smart grids and integration of renewable energy sources.

Journal

B&H Electrical Engineeringde Gruyter

Published: Dec 1, 2022

Keywords: transformer; Simulink; simulation; short circuit

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