Effect of the GICs on magnetic saturation of asymmetric three‐phase transformer
2017; Institution of Engineering and Technology; Volume: 11; Issue: 7 Linguagem: Inglês
10.1049/iet-epa.2016.0868
ISSN1751-8679
Autores Tópico(s)Power Systems Fault Detection
ResumoIET Electric Power ApplicationsVolume 11, Issue 7 p. 1306-1314 Research ArticleFree Access Effect of the GICs on magnetic saturation of asymmetric three-phase transformer Faouzi Aboura, Corresponding Author Faouzi Aboura fouzi.aboura@g.enp.edu.dz Laboratoire de Recherche en Électrotechnique, École Nationale Polytechnique, El Harrach, 16200 Algeria Siemens-Spa Sector-Division Energy Management, 16035 Hydra, AlgeriaSearch for more papers by this authorOmar Touhami, Omar Touhami Laboratoire de Recherche en Électrotechnique, École Nationale Polytechnique, El Harrach, 16200 AlgeriaSearch for more papers by this author Faouzi Aboura, Corresponding Author Faouzi Aboura fouzi.aboura@g.enp.edu.dz Laboratoire de Recherche en Électrotechnique, École Nationale Polytechnique, El Harrach, 16200 Algeria Siemens-Spa Sector-Division Energy Management, 16035 Hydra, AlgeriaSearch for more papers by this authorOmar Touhami, Omar Touhami Laboratoire de Recherche en Électrotechnique, École Nationale Polytechnique, El Harrach, 16200 AlgeriaSearch for more papers by this author First published: 01 August 2017 https://doi.org/10.1049/iet-epa.2016.0868Citations: 12AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract The most commonly used models in geomagnetic-induced currents (GICs) studies neglect the hysteresis phenomenon. In relation to this, the authors present an approach to integrate the hysteresis phenomenon to the finite-element model (2D-FEM) for the effects of the GIC which considers the current, as an input quantity. These currents are obtained by a dynamic electromagnetic model that the authors developed, and are compared with the results obtained by experimentation. This is the first time that this phenomenon has been shown in three-phase transformers with load. They also provide other practical responses in relation to other papers in which their studies concern the imbalance GIC bias on the asymmetric three-phase transformers with no-load while the majority of the transformers operate on load. 1 Introduction Solar activity causes the geomagnetic disturbances (GMD) which are natural phenomena of a disturbance in the earth's magnetic field. This geomagnetic field gives rise to a geoelectric field, which in turn creates a geomagnetic-induced current (GIC). The GIC flowing in the lines affects the electrical network, namely transmission systems and power transformers [1-3]. The flowing of GIC on power transformers is the leading cause of almost all problems related to GMD events. This causes saturation gradually of half-cycle of the hysteresis in the power transformers, [4], which can thus induce: the increased absorption of reactive power, the generation of current harmonics, heating of the transformer and instability of the system voltage. Therefore an accurate assessment of GIC on transformers is necessary. Indeed, the electrical system sees strong increase in demand in reactive power extra for the duration of the flow of GIC [5, 6]. Besides the increase of the reactive power demand, significant amounts of current harmonics associated with GIC of order even and odd are generated due to the non-linear behaviour of the magnetising reactance of the transformers in the system [7-9]. Large magnitudes of magnetising currents and associated current harmonics produce high magnitudes of the leakage flux that is rich in harmonics. This results in much higher eddy currents losses in the windings and in the structural parts of the transformer. This also causes a corresponding increase in temperatures. Some very recent papers have focused on the heating of the various parties of the transformer [4, 10, 11]. When unipolar half-wave saturation of the transformer core occurs, a larger portion of the flux no longer passes through the core, which has the effect of creating additional eddy currents on the transformer core clamping bolts, the winding, the tie plates and the tank walls. This leads to overheating of the transformer. This additional superheating inevitably causes an accelerated aging of the insulating materials of the transformer. GIC have the ability to dangerously disrupt the operation of the power grid, especially when the current amplitude is quite high. The GIC currents can cause a collapse of the mains voltage during flow. This is what led many researchers to analyse the sensitivity and the impact of GIC on the network [12-15]. Other effects of GIC on transformers are also being observed during half-cycle saturation of the core, these are sound noise loads and large vibrations of the transformer tank during the GMD events [3]. When the flow of the DC current is sufficiently large, the flux densities in the magnetic core span the range of pre-saturation in one hysteresis half-cycle, resulting from the base saturation for a small portion of a cycle. This is called as the partial saturation of the cycle. The B–H characteristics of the transformer core materials are strongly non-linear. For the high magnitudes of the direct current, the core provides the reluctance to the DC ampere-turns much higher and is reflected in a progressive increase of at less a quarter of the flux density. For a short time, when the core is saturated due to the flow of the GIC in a winding, a low voltage is induced in the other windings of asymmetrical three-phase transformer. This situation occurs three times per cycle and has severe consequences to the power system on which the transformer is connected. Yet all the work cited in bibliography neglects the hysteresis phenomenon in the models of the asymmetric three phase transformer. This kind of transformer is called an asymmetric transformer due to the difference in the length of the centre limb that is shorter than those of the two side limbs. Representation of the hysteresis loop is very important in view of the distribution of the magnetic flux density [16-21]. The paper [22] describes simulation model of a single-phase two winding transformer in an electromagnetic transient programme-type programme for GIC studies with hysteresis model based on the Jiles–Atherton (J–A) theory. In this paper, we present a novel approach of integrating the hysteresis in the finite-element model (FEM) for the study of GIC currents which considers the current in the winding as an input quantity. These currents can be obtained by a dynamic electromagnetic model (DEM). A comparison of experimental currents and those obtained by DEM is given in the second section. The influence of this phenomenon on the distribution of the magnetic flux density through experimental currents injected into the FEM was also highlighted. Our contribution comes from the fact that, for the first time, this phenomenon will be created in an asymmetric three-phase transformer with load. The contribution of this paper is the highlighting of the effect of geomagnetic-induced currents on magnetic saturation of asymmetric three-phase transformer with two complementary models of transformer. We also provide further answers compared with [20] for the study of the three-phase three-limb transformer with load. Laboratory results are compared with the ones of DEM. These latters are integrated in FEM on a 3 kVA/8A asymmetric three-phase transformer. In addition to what is presented above, the behaviour in load of the transformer during the flow of GIC is presented. For this purpose, several tests were performed, in balanced and unbalanced operation, by the injected of the GIC currents of 10 A. This last mode interests us the most because it gives very specific results. The influence of this phenomenon on the various elements constituting the asymmetric three-phase transformer is also studied. 2 Geomagnetic-induced currents on asymmetric three-phase transformer To simulate the GICs, we consider the circuit of Fig. 1 which comprises an asymmetric three-phase transformer operating under load balanced conditions, or in other term in our case equivalent to supply a balanced resistive load. A DC from 0 to 10 A is injected in the neutral of the transformer in order to approximate the phenomenon of GIC currents. Two cases are envisaged, namely the balanced case and the unbalanced of transmission lines. Rheostats are inserted as transmission lines into the circuit between the step up transformer (127/220 V) and the step down transformer (220/127 V). Photography of the experimental setup is presented in Fig. 2. Both asymmetric three-phase transformers are of identical type and described in Table 1. Table 1. Specification of asymmetric three-phase transformer 3 kVA, 50 HZ Three-phase transformer parameters Value rated primary voltage (V) 220 rated secondary voltage (V) 127 HV windings turns 250 LV windings turns 153 0.6566 0.72466 Fig. 1Open in figure viewerPowerPoint Scheme of three-phase transmission network subject to the GICs Fig. 2Open in figure viewerPowerPoint Experimental setup for three-phase transformer tests to measure GICs a Side view of the experimental setup b Front view of the experimental setup The DEM is used for simulation of currents of the asymmetric three-phase transformer with integration of the GICs [23]. Fig. 3 presents the diagram of the asymmetric three-phase transformer, Y–Y subjected to the GIC currents. In this section, we will use the asymmetric three-phase transformer operating in load. In this effect, load resistors will be placed in the transformer secondary to represent the load current value of 3 A per phase, as shown in Fig. 3. Fig. 3Open in figure viewerPowerPoint Diagram of the asymmetrical three-phase transformer Y–Y subjected to the GICs currents The detailed description of the subsystem comprising a step-up transformer and a step down transformer is given in [23]. The flux linkage and the fluxes are not mixed and the path of the leakage flux in air is modelled by a single-linear reluctance term obtained from the zero-sequence tests [24]. The connection with the dynamical formulation is given by the subsystems A, B and C as shown in Fig. 4, through a Matlab function that describes the (1)–(6) and the global hysteresis behaviour. The controlled MMF sources (1, 2, and 3) across the subsystems (1, 2, and 3) are used to compute (4), (5) based on (1)–(3). At every time step (t = 1 × 10−6), an 'IF statement' selects one of (4) or (5) based on the sign of the derivative of flux. Fig. 4Open in figure viewerPowerPoint Matlab/Simulink subsystem of the step up transformer and the step down transformer To take into account of core asymmetry of the three-phase transformer type, each core limb is modelled with its own customisable hysteresis non-linear. The main equations of the Tellinen model use the (λ–I) characteristics of all three limbs that are different. They are described as (1) (2) (3), are, respectively, the ascending and descending parts of the limits of hysteresis curve. is the instantaneous limb fluxes, for each phase x, dependent on the limb MMF potential . controls the width of the major hysteresis loop. is the slope of the fully saturated region along the limiting hysteresis curve. The hysteresis (4) and (5) are given by (4) If (5) If (x = 1, 2, 3) We also used the eddy current factor for the lamination in (6). This factor reflects the classical eddy current and the excess losses and is the applied dynamic current: (6) 2.1 Case 1 In this section, we will use the asymmetrical three-phase transformer with balanced load operation, the transmission lines system is . Load resistors are placed at the secondary transformer, to represent the load current value of 3 A per phase (Fig. 1). We fixed the GIC current at 10 A, and we recorded the current signals of the transformer. Fig. 5 shows the comparison between the experimental currents of the asymmetric three-phase transformer with those of DEM model. These load currents are almost sinusoidal and the spectral analysis that we will see further confirms the fact that the magnitude of the harmonics remains low compared with the fundamental one. Fig. 5Open in figure viewerPowerPoint Currents of asymmetrical three-phase transformer under balanced operation with a Current in Phase 1 b Current in Phase 2 c Current in Phase 3 2.2 Case 2 In this case, we consider balanced loads, but with the addition of different resistances to the primary of step down transformer such as , and , this creates the unbalance of phases. Fig. 6 shows the load currents of the step-down transformer for . In this case, the amplitude of the current increases and a strong deformation appears in these currents. So more the GIC current is high, the greater the deformation is significant. Fig. 6Open in figure viewerPowerPoint Load primary current of step down transformer in unbalanced conditions with a Current in Phase 1 b Current in Phase 2 c Current in Phase 3 The difference between the experimental and simulated curves with the DEM model is explained by the fact of the presence of the parasitic resistances in the measures including those cables, and by the fact of the high susceptibility of GIC currents, even at low resistance values 3 Integration of the hysteresis in FEM In our FEM model, geometry is imported from a DXF file given by AutoCAD software and exported to the software FLUX2D. It is necessary to adapt as much as possible the mesh to the physics of the problem. The mesh should not be unnecessarily fine. A fine mesh requires a longer computation time. We must find a compromise between an accurate geometrical representation of the study domain and a reasonable computation time. The mesh refinement depends on the geometrical constraints, a strong variation of the state variable requires the use of smaller elements and mesh elements located close to the infinite box can be more relaxed. Meshing is given by adaptive solver in FLUX2D. This process facilitates automatically refined mesh in the locations where the physics of the problem requires it. We have also checked the computational of domain meshed and the quality of the surface elements given in the Appendix. The post-processing is given automatically in FLUX2D by Newton–Raphson method. The formulation of classical magnetic vector potential of the FEM is adopted. The transient initialisation is given by a static computation because the zero initialisation in FLUX2D is not carried out in accordance with the physical reality. The starting is accompanied then by a numeric transient, which distorts the solving process. To prevent from this problem, it is possible in FLUX2D to take into account initials conditions of the static computation initialisation type and the boundary conditions are then assigned automatically by FLUX2D on the infinite box (the magnetic potential at infinity is null). The infinite domain is modelled by infinite box technique. The exterior domain (infinite) is linked to an image domain (called the infinite box) through a space transformation. For FLUX2D, the infinite box is described by two superimposed discs in crown shaped. The external circle represents the image of the infinite. The use of this infinite box implicitly assumes a null field at infinity in our study. We choose to take internal radius equal to 1400 mm and external to 1750 mm for a length of the transformer that is 350 mm as shown in Fig. 7. The inverse J–A vector hysteresis model is chosen for the FEM. We have integrated the hysteresis in 2D time-domain solver FLUX [25], by using external user function named User subroutines. User subroutines are written in Groovy, this is name of an object oriented programming language intended to the Java platform which implements the inverse J–A vector hysteresis model. The detailed description of the FEM model is given in [23], and the parameters of the J–A model are given in Table 2. The bolts used to maintain the core and their relative permeability was assigned. Table 2. Specification of asymmetric three-phase transformer 3 kVA, 50 HZ J–A model parameters Value 22.05 10.62 1,810,000 c 0.15 Fig. 7Open in figure viewerPowerPoint 2D-FEM of the asymmetric three-phase transformer a 2D-FEM of the asymmetric three-phase transformer b Meshing of the 2D-FEM of the studied domain In this section, we showed the influence of GIC currents on the asymmetric three-phase transformer through a study of the 2D-FEM as shown in Fig. 7. The hysteresis is integrated in the 2D-FEM, and we consider the experimental current in the winding as an I/O (input/output) parameter by using a current source in the electrical circuit of the 2D-FEM. An I/O parameter is a variable quantity in our study. The variations are defined by I/O parameter defined by means of a table of values dependents of time obtained by the DEM. First, the magnetic flux density of the asymmetric three-phase transformer, with load and the transmission lines balanced is represented. Tests are carried out with and without GIC current of 10 A. Next, we consider the case of the imbalanced transmission lines to show the maximum value of average flux density reached and the different parts subjected to the maximum flux density. Following this, we determine the current harmonics in the asymmetrical three-phase transformer subject to GIC currents of 10 A. All the results are observed on our personal computer with the following configuration: Windows 7, CPU: Intel(R) Core(TM) i5-2410M @ 2.3 GHz and RAM: 6 GB and the time duration to obtain one period of current signal (20 ms) is 128 min. 3.1 Harmonic calculation 3.1.1 Case 1 The current harmonics of the transformer under load condition and without GIC current are determined. Resistors are placed at the secondary of test transformer, to represent the load current value of 3 A per phase (Fig. 8). The magnetic flux in the transformer core is nearly sinusoidal (Fig. 9a). Fig. 8Open in figure viewerPowerPoint Magnitude and rank of current harmonics with a Current in Phase 1 b Current in Phase 2 c Current in Phase 3 Fig. 9Open in figure viewerPowerPoint Magnetic flux in the core of the asymmetric three-phase transformer a Magnetic flux in the core without GIC b Magnetic flux in the core with in the case of balanced operation c Magnetic flux in the core with in the case of unbalanced operation The total harmonic distortion (THD) is the ratio of the root mean square (RMS) of the harmonic content to the RMS value of the fundamental quantity, expressed as a per cent of the fundamental. The THD measures the effective value of harmonic distortion and it is defined as (7) (8) is the RMS value of the harmonic content and is the fundamental component of the RMS value [26]. The THDs of the three phases are: THDI1 = 9.86, THDI2 = 5.094 and THDI3 = 7.17% 3.1.2 Case 2 The current harmonics of the transformer with phases balanced and with application a GIC current are determined. The THDs of the three phases are: THDI1 = 11.82, THDI2 = 7.24 and THDI3 = 8.52%. In Fig. 10, the even-order harmonics observed are low, they indicate small components of DC fluxes causing a unipolar saturation, and also show a small increasing of the THD of the three phases compared with the case without GIC. The current harmonics being low that means that the magnetic flux of the core is almost sinusoidal (see Fig. 9b). Fig. 10Open in figure viewerPowerPoint Magnitude and rank of current harmonics with in the case of balanced operation a Current in Phase 1 b Current in Phase 2 c Current in Phase 3 3.1.3 Case 3 By against, in the case of the phases imbalance of the transformer, and for a GIC of 10 A, there are appearance of even-order harmonics and an increase in the magnitude of odd harmonics (Fig. 11). In addition, a large distortion appears in the flux of the core of asymmetric three-phase transformer (Fig. 9c). Fig. 11Open in figure viewerPowerPoint Magnitude and rank of current harmonics with . In the case of unbalanced operation a Current in Phase 1 b Current in Phase 2 c Current in Phase 3 The THDs of the current of three phases are THDI1 = 25.10, THDI2 = 56.44 and THDI3 = 17.18%. 3.2 Maximum values of the magnetic induction in the case of balanced and unbalanced phases In this section, the maps of the average magnetic induction are presented for visualising the maximum saturation values and relevant areas of the transformer. The real value of maximum average magnetic flux density in each region of the transformer can be obtained by their colour in accordance to the shades. The highest values of the magnetic flux density are located in areas near the inner corners of the limbs of the transformer and the magnetic induction of the core bolt is also high in the localised region at the surface of the core bolt and can be >2.5 T [16]. These values of the magnetic flux density produce a warm-up in these regions. However, the value of the maximum average magnetic flux density without GIC is 1.81 T (Fig. 12a). With the GICs in balanced operation its value is 3.15 T (Fig. 12b). It becomes equal to 2.04 T for unbalanced operation with the presence of GIC (Fig. 12d). In addition, the distribution of the magnetic flux density is changed; this peculiarity is due to the load current that influences on the magnetic flux density. The distribution of the flux density in the core section, surrounding the bolt (c) (see Fig. 12b), reveals that the leakage flux into the bolt during the core saturation is concentrated at the outer surface, demonstrating thus the skin effect and a portion of the magnetic flux in the core disappears, due to the situation of the phases imbalance. Fig. 12Open in figure viewerPowerPoint Field map of the magnetic flux density a In the case of balanced operation with b In the case of balanced operation with c In the case of balanced operation with in the core bolt c d In the case of unbalanced operation with 4 Conclusion In this paper, we treated the effects of GICs of high amplitude on the asymmetric three-phase transformer. FEM and DEM have been developed for this purpose. Our main contributions are as follows. In FEM, we managed to introduce the hysteresis which has been neglected in all the works encountered in the bibliography. The results of the DEM have been then integrated in FEM to simulate the subjected transformer to the GICs, with load. Furthermore, other important points are to be reported in this work. In balanced operation, the asymmetrical three-phase transformer is not very affected by the current GIC, and the harmonic 2, characteristic of phenomena of GIC, does not appear in the current signals while the magnetic flux density in the transformer core increases only slightly. This is due to the fact that there is no way back DC flux which is forced of circulate in the air, characterised by a path of high reluctance magnetic flux. Thus, the magnetic flux passing becomes low. However, once the phases are not anymore balanced, then we find the presence of the even-order harmonics in the current signals. The transformer can also be subject to change in the distribution of the magnetic flux density. The obtained results by the FEM allowed us to see that the magnetic flux density increases with the GIC and decreases in parts of the transformer when the phases are unbalanced, thus highlighting a change of the distribution of the magnetic flux density for a transformer operating with load. 6 Appendix The computational domain meshed and the quality of the surface elements is given as follows: Number of nodes: 21,267 Number of line elements: 2108 Number of surface elements: 9958 Mesh order: seconnd order Number of elements not evaluated: 0% Number of excellent quality elements: 99.3% Number of good quality elements: 0.69% Number of average quality elements: 0.01% Number of poor quality elements: 0%.' 5 References 1 IEEE: ' Guide for establishing power transformer capability while under geomagnetic disturbances', IEEE Std. 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