ANALYSIS OF OPERATION MODE AND PERFORMANCE INDICATORS OF A TRANSFORMER WHEN CONTROLLING ITS VOLTAGE WITH AN ALTERNATING MAGNETIC FLUX

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 10, October 2018, pp , Article ID: IJMET_09_10_020 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed ANALYSIS OF OPERATION MODE AND PERFORMANCE INDICATORS OF A TRANSFORMER WHEN CONTROLLING ITS VOLTAGE WITH AN ALTERNATING MAGNETIC FLUX Evgeniy N. Popov and Anatoliy G. Lavrov Department of Robotics and Automation of Production Systems (RAPS), Saint Petersburg Electrotechnical University LETI, Russia ABSTRACT Performance indicators of a two-winding step-down transformer that characterize its operation on completing the secondary voltage control process with a magnetic flux alternating in the range of 5-15% were analyzed. Control modes for the transformer secondary voltage with a teaser winding on the high voltage side were considered. A quantitative assessment of the control mode effect on the main performance indicators of a transformer at an alternating magnetic flux was made. The transformer parameters most and least influenced by the alternating magnetic flux were identified. Potential adverse effects of a long-term transformer operation in the control mode of the secondary voltage with the alternating magnetic flux were described. The necessity to take into account the alternating magnetic flux effect on the transformer parameters at the design and manufacturing stage was shown. The formula currently used in the scientific and technical literature, being an equation for calculating the tapping voltage ratio, that is employed to quantify the process of controlling the transformer secondary voltage, was considered and the necessity for its adjustment was shown. An alternative formula was proposed for the tapping voltage ratio calculation, which restores a physical meaning of the control process and enables its application in any control mode. Keywords: Two-Winding Transformer, Voltage Control, Alternating Magnetic Flux, Control Modes, Performance Indicators, Voltage Ratio. Cite this Article: Evgeniy N. Popov and Anatoliy G. Lavrov, Analysis of Operation Mode and Performance Indicators of a Transformer When Controlling Its Voltage with an Alternating Magnetic Flux, International Journal of Mechanical Engineering and Technology, 9(10), 2018, pp editor@iaeme.com

2 Analysis of Operation Mode and Performance Indicators of a Transformer When Controlling Its Voltage with an Alternating Magnetic Flux 1. INTRODUCTION Voltage control at power feeders or, more precisely, provision of the constancy of the effective value of this voltage is one of the most important problems in the electric power industry that ensures power supply to industrial enterprises, facilities, and complexes, since the stability of technological processes and hence the output quality largely depend thereon. Electricity is usually supplied to power consumers through step-down transformers and, therefore, in the case under consideration, the issue concerns the constant voltage provision on the secondary transformer winding. The voltage at the terminals of the secondary transformer winding during its operation under load is defined by: U2 Е2 I2r2 ji2x2 (1) while the EMF of mutual induction of its secondary winding is: E π 2f w (2) m where I2 is the secondary current; r 2, x2 are active and inductive secondary resistances; f 1 is the frequency of supply voltage; w2 is the number of serially connected secondary winding turns; m is the mutual magnetic flux amplitude in the transformer core. For the circuit of the primary winding of a transformer connected to a network with an effective voltage value U 1, we obtain the following equation: U1 E1 I1r1 ji1x1 (3) Hence, the EMF of self-induction E 1 of the transformer primary winding: Е1 U1 I1r1 ji1x1 (4) where I 1 is the primary winding current, and r 1, x 1 are the active and inductive primary resistances, respectively. In accordance with Equation (1), the effective output voltage U 2 of a transformer depends on a voltage drop at the secondary winding impedance I2r2 ji2x2, as well as on the effective range of the EMF of the mutual induction of its secondary winding E 2 In turn, the effective range of the EMF E 2, taking into account Equation (2), is determined by the amplitude m of the magnetic flux of mutual induction in the transformer core, which is proportional to the EMF effective range of the transformer primary winding self-inductance. Thus, in general, the effective secondary voltage of a transformer can change either when the load current I2 and its nature are changed, or it can be caused by a change in its effective primary voltage, and, moreover, simultaneous effect of the two above factors is possible. 2. THEORY Let us consider the physical fundamentals of control modes that have not actually been reflected in the scientific and technical literature. As indicated above, the secondary voltage deviation from the reference value can be caused by a change in the actual value U 1 of the supply voltage, that is, a change in the voltage at the terminals of the transformer primary winding, which will be accompanied by a change in the primary EMF in accordance with (4) and a closely proportional change in the editor@iaeme.com

3 Evgeniy N. Popov and Anatoliy G. Lavrov amplitude m of the magnetic flux of mutual induction. In accordance with (2), the effective range of the EMF of the mutual induction E2 of the secondary winding and the secondary voltage U 2 are changed. To restore the reference value of the voltage U 2, it is necessary to change the effective range of the EMF of mutual induction E 2 of the secondary winding by means of a respective change in the amplitude m of the magnetic flux of mutual induction by adjusting the number of primary winding turns w 1. As a result, the amplitude m of the magnetic flux retains its value, control is maintained with a constant magnetic flux and the electromagnetic parameters of the transformer remain virtually unchanged after the control process is completed. Suppose that the transformer load has changed, and the effective value U 2 of its output voltage has changed in accordance with (1) (it is assumed that U1 const at the same time). To restore U 2, it is necessary to change the EMF E 2 of the secondary winding by changing the amplitude m of the mutual induction flux in the transformer core, which is achieved by adjusting the number of primary winding turns w 1. As stated in [1], a change in the amplitude m of the mutual induction flux in the process of control leads to a change in the saturation rate of the magnetic system, the no-load current, electrical and magnetic losses, the operating temperature, and the transformer winding electro-dynamic forces. Thus, in the case under consideration, the transformer secondary voltage is regulated by a change in the magnetic flux amplitude, whereby the transformer performance indicators deteriorate. This mode of control of the secondary voltage is called regulation at an alternating magnetic flux. The number of primary winding turns w 1 is to be changed until the secondary voltage U 2 regains its value with the accuracy determined by a division value of the turning number control on the transformer input side. Since modern on-load tap chargers have a nominal control range of up to 32%, in the voltage regulation mode with alternating magnetic flux, such intensive regulation can lead to severe or even emergency operating conditions. This problem is referred to in [2]: Many years of experience have shown that serious failures or series of accidents due to deficiencies in electromagnetic calculations were not related to a quantitative error or inaccuracy of the calculation, but to the fact that the phenomenon that turned out to be important had not been taken into account at all in the design. For a quantitative description of the process of the transformer secondary voltage control in the scientific and technical literature [3, 4, 5], a formula for calculating the tapping voltage ratio is used: k tap.v. Utap% U U1nom n U1nom tap 100 (5) U U 2nom 2nom where n is the number of stages included relative to the center tap; U tap % is a stage (step) of voltage control on the winding VN, as %, and the product n U tap % is voltage percentage added to the nominal primary voltage corresponding to the n-th stage [3, 4, 5] editor@iaeme.com

4 Analysis of Operation Mode and Performance Indicators of a Transformer When Controlling Its Voltage with an Alternating Magnetic Flux The use of Equation (5) for calculating the transformation ratio in the control mode with an alternating magnetic flux seems to be impossible. It is related to the fact that Equation (5) includes variable U the value of which is determined for the nominal magnetic flux in the tap transformer core, and in this control mode its value will vary directly as a change in the magnetic flux, which the proposed formula does not take into account. Considering the fact that in the classic transformer theory, the transformation ratio is defined as the ratio of the winding turn number, it seems necessary to do likewise in the case under consideration and submit the tapping voltage ratio in the form: w tap w w1 n w w 1 1 tap w1 100 tap.v. t 1 tap w2 w1 w2 w1 % k k n w (6) where w tap % is a tapping stage (step) controlling the primary winding turn number, as %, and the product n wtap is the addition of the primary winding turn number corresponding to the n-th stage in relation to the number of the principal tapping turns. Using the proposed formula reassigns to the control process its physical meaning and gives the possibility of its application in any control mode. If it is deemed necessary to calculate the control processes through known values of the tapping voltage, the authors propose to adjust Equation (5) by introducing a magnetic flux variance coefficient k : k tap.v. Utap% U1nom n U1nom k 100, U k is a coefficient that takes into account a change in the magnetic flux and is determined by the nameplate data of the on-load tap charger: 2nom 1 1 k Utap% wtap% 1n 1n In the voltage control mode with constant magnetic flux, the coefficient k must be set to unity. It seems necessary to carry out a quantitative analysis of the transformer performance factors that characterize its operation on completing the secondary voltage control process, with a magnetic flux alternating in magnitude. 3. MATERIALS AND METHODS To achieve this goal, a two-winding power transformer TDN 40000/110 was chosen. The results obtained when analyzing its performance factors can be extended to most transformers manufactured commercially, since they have the electromagnetic similarity property. The performance factors of the TDN 40000/110 transformer, as well as the normalized values of losses, impedance voltage, and no-load current are shown in Tables 1 and 2. Reduction of the net magnetic flux during the transformer secondary voltage control leads to transformer underutilization without any adverse operating conditions, therefore, this work only covers the case of voltage control by increasing the magnetic flux. Table 1 Performance factors of TDN 40000/ editor@iaeme.com

5 Evgeniy N. Popov and Anatoliy G. Lavrov Performance Factor Value Nameplate power, kilovolt-ampere Number of branches, pcs 3 Frequency, hz 50 High voltage, kilovolt 115 Low voltage, kilovolt 38.5 Winding circuit and phase displacement group Un/D 11 On-load tap changer type neutral mode HV 16; 9 stages Cooling oil natural/air forced cooling (D) Installation type outdoor Winding conductor copper Temperature class of insulation А Magnetic system design flat rod-type magnetic system with concentric winding Type of load continuous Transformer Type Table 2 Losses, impedance voltage, and no-load current No-Load Losses, kilowatt Short-Circuit Short-Circuit Voltage for HV-LV Windings, as % No-Load Current, as % TDN 40000/ During the analysis, the methodology proposed in [6] was used and the transformer performance factors were considered with a reduction by 5%, 10%, and 15% in the primary winding turn number, which leads to a proportional increase in the transformer magnetic flux. 4. RESULTS AND DISCUSSION Table 3 shows the results of quantitative analysis in the form of absolute and relative values of the transformer performance factors, where w hv is the number of the transformer primary winding (higher voltage) turn number. Table 3 Performance factors of the TDN 40000/110 transformer whv abs. value 0.95w hv 0.9w hv 0.85w hv abs. rel. abs. rel. abs. rel. value unit value unit value unit rel. unit HV coil losses, kilowatt Short-circuit losses, kilowatt Short-circuit voltage relative value, as % Sustained short-circuit current in HV winding, kiloampere Average specific radial force in HV winding, kilonewton Average specific radial force in LV winding, kilonewton Mean tensile stress in HV winding, megapascal Mean compressive stress in LV editor@iaeme.com

6 Analysis of Operation Mode and Performance Indicators of a Transformer When Controlling Its Voltage with an Alternating Magnetic Flux winding, megapascal Relative effective value ХХ, as % ХХ losses, kilowatt Overall losses, kilowatt Efficiency output, as % LV winding temperature over ambient air temperature, С HV winding temperature over ambient air temperature, С The change in the primary winding turn number stands for connecting, with the help of an on-load tap-changer, regulating tapping coil turns cumulative or opposing to the high voltage winding. The connection of additional turns to the primary winding entails a change in the voltage drop across the complex impedance of the HV winding due to an increase in the active resistance and an increase (in the case of accordant connection) or a reduction (in case of opposite connection) of inductive resistance. As can be seen from Table 3, the main losses in the HV winding of the transformer increase in proportion to the increase in the net magnetic flux, which entails an increase in overall short-circuit losses by 2-7%, respectively. When calculating the short-circuit losses, the change in supplementary losses in the windings and taps of the eddy currents closing in separate wires and the circulating currents closing in the parallel winding paths were not taken into account, since the supplementary losses normally constitute 1-2% of the overall short-circuit losses and their changes in the case under consideration are small to negligible. Reducing the number of the primary winding turns by 5%, 10%, and 15% leads to a change in the short-circuit impedance and, therefore, the short-circuit voltage drops by 9%, 17% and 24%, and the short-circuit current increases by 13%, 21% and 32%, respectively, which reduces the overall resistance of the transformer in the event of a fault. A fold increase in the short-circuit current leads to an increase in the specific radial force in the HV and LV transformer windings by a factor of times, which accordingly leads to a proportional increase in the average tensile and compressive stresses in the winding wires. The radial forces arising from the axial component of a stray magnetic field cause the external windings to stretch and the internal ones to constrict [7]. According to the calculations, even with an increase in magnetic flux by 10%, the average tensile stress in the VN winding conductors exceeds the permissible value of 60 MPa [6]. Radial forces have different effects on the external and internal windings. They are most dangerous for the internal winding wires experiencing compression and bending subject to radial forces in the spans between the rails the winding is coiled around. Balance disturbance of the winding and its destruction are possible as a result of the wire bending in the spans between the rails, or because of a buckling failure. A significant increase in the radial force can lead to the winding destruction, deformation or rupture, or the collapse of support structures [7]. When the magnetic flux of the transformer is increased by 15%, the no-load current increases by a factor of 7, and the idling loss increases by a factor of 1.7. However, these increases in the current and idling losses, in fact, do not have a significant effect on the transformer efficiency, because the no-load current is less than one percent of the editor@iaeme.com

7 Evgeniy N. Popov and Anatoliy G. Lavrov nominal one, and the idling current losses are almost 1/6 times as much as the short-circuit loss. The increase in overall losses in the transformer leads to an increase in the winding temperature by 5 C, and the rate of thermal insulation wear is known to be doubled at each temperature change by 6 C. Consequently, voltage control within 15% nearly halves the service life of the insulation, and, accordingly, of the transformer itself. 5. CONCLUSION Conclusions from the presented material can be broadly divided into three groups. The first group includes proposals for changing the formulas used in the educational and instructional materials. The second includes conclusions from the analysis of voltage control modes of the transformer secondary winding. The third group consists of conclusions from the quantitative analysis of the transformer performance factors that characterize its operation on completing the process of controlling the secondary voltage with an alternating magnetic flow. 1. It is necessary to introduce the formula for determining the tapping voltage ratio expressed through a respective number of turns in the training literature and educational materials (6), and to exclude an analogous one (5) represented as a function of voltages and voltage additions, applied at this time [5, 6, 7]. The formula applied presently distorts the meaning of the control process, while its application is impossible without the necessary correction factors in the voltage control mode with an alternating magnetic flux. 2. The analysis of the transformer secondary winding voltage control modes has shown that if the secondary voltage deviation is caused bya change in the supply network voltage, the control action is provided with a constant magnetic flux. On completing the control process, the transformer continues to operate with the previous electromagnetic parameters. 1) If the secondary voltage is changed under the action of a load, the control is performed with an alternating magnetic flux. This control mode leads to a change in the saturation rate of a magnetic system, the no-load current, electrical and magnetic losses, the operating temperature and the electro-dynamic forces acting on the transformer windings. After the control process is completed, the transformer starts to operate with parameters different from the initial values. 2) From the analysis of physical processes of voltage control it follows that the control mode of the secondary voltage depends solely on the cause of the secondary voltage deviation. On a case-by-case basis, this will depend on the operation modes for the voltage of the supply and secondary distribution mains. 1. The quantitative analysis of the transformer performance factors characterizing its operation on completing the secondary voltage control process with an alternating magnetic flux in the range of 5-15% has shown that: despite the increase in overall losses by 20%, the transformer efficiency decreases insignificantly, by 0.1%; there are significant radial forces in the windings that can lead to the destruction of a transformer, which must be taken into account when designing and manufacturing transformers; an increase in overall losses caused by a change in the magnetic flux leads to an increase in the temperature of the windings and oil of a transformer, whereby its service life is almost halved; editor@iaeme.com

8 Analysis of Operation Mode and Performance Indicators of a Transformer When Controlling Its Voltage with an Alternating Magnetic Flux Voltage control with alternating magnetic flux exertsthe greatest negative effect on the step-down distribution transformers having higher relative values of current and no-load losses. A significant increase in steel losses can lead to overheating and breakdown in the insulation of their sheets, which should be given special attention in their design. REFERENCES [1] Lavrov, A. G. and Popov, Ye. N. Analysis of Control Modes of the Transformer Secondary Voltage with On-Load Tap Chargers. Saint Petersburg Electrotechnical University LETI, 5, 2017, pp [2] Leites, L. V. Electromagnetic Calculations of Transformers and Reactors. Moscow: Energiya, 1981, pp [3] Gerasimenko, A. A. and Fedin, V. T. Transmission and Distribution of Electricity: A Tutorial, 4th Edition. Moscow: Knorus, 2014, pp [4] Tatarov, Ye. I. Power Supply Systems and Electrical Networks: A Set of Learning and Teaching Aids. Nizhny Novgorod: Nizhny Novgorod State Technical University, 2013, pp [5] Pospelov, G. Ye. and Fedin, V. T. Electrical Systems and Networks. Design, 2nd Edition. Minsk: Vysshaya Shkola, 1988, pp [6] Tikhomirov, P. M. Transformer Calculation, 2nd Edition. Moscow: Energiya, 1986, pp [7] Lure, A. I. Short-Circuit Electrodynamic Withstand of Transformers and Reactors. Moscow: Znak, 2005, pp editor@iaeme.com