Saturated core reactor for electrical power distribution networks

Description

/ 23 Saturated core reactor for electrical power distribution networks TECHNICAL FIELD

[001] The present invention is in the field of electrical engineering, more specifically to power systems and reactive power compensation devices applied to voltage regulation in distribution networks. It is an electromagnetic voltage regulator device, of the saturated core reactor type, developed for operation in overhead power distribution networks. The device comprises a Twin-Tripler type constructive configuration, composed of two three-phase cores with interconnected concentric windings, in addition to a tap system that allows adjustments in the operating range at different voltages. The invention is aimed at reactive power compensation and voltage stabilization in medium voltage networks, particularly in scenarios with high penetration of distributed generation, such as photovoltaic generation.The technology provides dynamic and passive voltage control without the need for active control systems, enabling its installation directly on poles or in benchtop arrays, with low physical impact and high operational efficiency. FUNDAMENTALS OF THE INVENTION

[002] In electrical power systems, especially in distribution and transmission networks, voltage control and reactive power compensation are often necessary to ensure the stability and quality of the supplied energy. Among the various devices used for this purpose, saturated core reactors stand out for their operation based on purely electromagnetic principles, without the need for active control systems. These devices exploit the non-linearity of the magnetization curve of ferromagnetic materials, operating Petition 870250065060, dated 07 / 28 / 2025, page 22 / 56 / 23 intentionally in the saturation region of the magnetic core. In this condition, the inductive impedance of the reactor varies as a function of the applied voltage, providing an automatic response to network fluctuations. At low voltage, the reactor has high impedance and consumes little reactive power, while at high voltage the saturation of the core reduces the impedance and it starts to consume more reactive power, helping to reduce overvoltage.

[003] The use of saturated core reactors has historically been consolidated in large-scale applications, such as transmission systems and industrial installations with high power demands, particularly since the 1950s. Classic configurations include three-phase arrangements with multiple magnetic columns and interconnected windings to optimize magnetic performance and minimize harmonic generation. Some arrangements, such as the so-called "Twin-Tripler" or "Treble-Tripler," were developed to achieve more balanced phase compensation and reduce the effects of harmonic distortion. However, despite their effectiveness, these technologies remained limited in terms of operational flexibility and adaptability to different network conditions, and were generally applied in fixed structures, such as substations.Technical and scientific literature on the subject has advanced mainly in academia, with few records of optimized applications for modern distribution networks and little incorporation of elements that allow for fine-tuning of operation according to variations in the electrical system.

[004] Document GB1194151 describes advances in voltage stabilization systems applied to alternating current networks, focusing on high-voltage applications. It is a continuation and improvement of previous technologies based on saturated core reactors, used to mitigate fluctuations and harmonic distortions in complex electrical networks. The technical objective of the document is to stabilize the voltage of Petition 870250065060, dated 07 / 28 / 2025, page 23 / 56 / 23 high-voltage systems through saturated reactor arrays configured in specific structures, such as the treble-tripler topology. The solution involves the use of segmented magnetic cores, with primary and secondary windings arranged to promote flux displacement and harmonic compensation. The systems are equipped with compensation loops, series transformers and, optionally, TAP devices, allowing refined voltage control and filtering of unwanted harmonics. The design prioritizes robustness and compatibility with high-voltage networks, with multiple variants for different operational requirements. Unlike the present invention, document GB1194151 does not address the application in medium-voltage distribution networks nor does it contemplate constructive aspects aimed at suspended installation on poles or bench arrangements.Furthermore, it does not present the use of concentric main and auxiliary windings interconnected in series, nor does it address specific strategies for minimizing electrical losses and device mass. The document's proposal focuses on robust solutions for stabilization in high-voltage networks, while the invention proposes a lighter, adjustable device adapted to the modern challenges of distribution networks with high penetration of distributed generation.

[005] Document US4058761 falls within the field of devices for voltage stabilization in alternating current networks, with emphasis on the use of saturated reactors to compensate for voltage variations caused by fluctuating loads, especially with harmonic suppression. Its technical objective is to provide a saturated reactor structure that allows for network voltage stabilization without compromising harmonic compensation, even when the system neutral is grounded, which would normally induce undesirable harmonic current components. The proposed solution consists of a saturated reactor arrangement with nine columns. Petition 870250065060, dated 07 / 28 / 2025, page 24 / 56 / 23 magnetic strips distributed in three three-phase groups, with primary windings arranged in a zigzag-duplicated star configuration, in order to reduce the zero-sequence impedance and allow grounding of the star point without compromising harmonic performance. This document does not contemplate a Twin-Tripler topology with two independent three-phase sets, nor does it use concentric main and auxiliary windings interconnected in series. Furthermore, it does not address constructive optimization issues for installation on poles or benches, nor does it address the reduction of electrical losses or total equipment mass.

[006] The increasing use of distributed generation sources, especially photovoltaic generation directly connected to medium-voltage networks, has intensified the occurrence of undesirable voltage variations in overhead distribution networks, such as overvoltages during peak generation and undervoltages during peak demand times. These disturbances affect system stability and the quality of the supplied energy, requiring efficient, robust, and easy-to-install solutions. Faced with this scenario, it becomes necessary to develop voltage regulation devices that are capable of responding automatically and passively to network variations, without depending on complex electronic systems or additional substation infrastructure.The objective of the present invention is to offer a technical solution that allows reactive compensation and voltage stabilization directly in the distribution network, with high operational efficiency, simplified installation, and flexibility for adaptation to different voltage levels, through adjustable taps in the device windings.

[007] To achieve this objective, the present disclosure defines a saturated core reactor for electrical power distribution networks, comprising: at least two structurally independent three-phase magnetic cores, configured in Twin-Tripler topology, each core consisting of three magnetic columns; windings Petition 870250065060, dated 07 / 28 / 2025, page 25 / 56 / 23 main (Np) and auxiliary (Na) concentric windings mounted on each magnetic column, electrically interconnected in series and magnetically coupled; electrical connection of the windings in a combined zigzag and star arrangement with floating neutral; and at least one winding equipped with a shunt system, with multiple switching positions for adjusting the number of active turns. BRIEF DESCRIPTION OF THE FIGURES

[008] Figure 1 shows a generic saturation curve and operating regions of different electromagnetic devices.

[009] Figure 2 shows the saturated core reactor with the topology Twin-Tripler.

[010] Figure 3A illustrates a front view of a saturated core reactor installation form in a bench arrangement on the overhead distribution network.

[011] Figure 3B illustrates a side view of a saturated core reactor installation form in a bench arrangement on the overhead distribution network.

[012] Figure 3C illustrates a top view of a saturated core reactor installation form in a bench arrangement on the overhead distribution network.

[013] Figures 4A, 4B, 4C and 4D illustrate details of the switch. Saturated core reactor taps.

[014] Figure 5 illustrates a flowchart representing the steps for the pre-dimensioning of the reactor.

[015] Figure 6 is a graphical representation of the fluxes within a 360° period.

[016] Figure 7 is an illustration of the dimensions of the cores. Petition 870250065060, dated 07 / 28 / 2025, page 26 / 56 / 23

[017] Figure 8 is a representation of the saturated core reactor core of the present invention.

[018] Figure 9 is a representation of the core with the main and auxiliary windings.

[019] Figure 10 is a top view of the core representation shown in Figure 9.

[020] Figures 11A and 11B illustrate details of the saturated core reactor assembly.

[021] Figure 12 illustrates a detail of the winding process.

[022] Figure 13 illustrates details of the assembly of the saturated core reactor windings and cores.

[023] Figure 14 illustrates details of the outer tank of the saturated core reactor.

[024] Figures 15A and 15B represent the record of the saturated core reactor voltage power test.

[025] Figure 16 illustrates the saturated core reactor installed in a bench-scale arrangement. DESCRIPTION OF THE INVENTION

[026] The following detailed description refers to the invention in such a way as to allow a person skilled in the art to reproduce its results. Other embodiments are possible and can be carried out without departing from the concept and scope of the present invention. The following detailed description should therefore not be understood in a restrictive or limiting manner.

[027] The saturated core reactor is an electromagnetic device whose operation is based on the nonlinear properties of ferromagnetic materials. Its operation occurs predominantly in the magnetic saturation region, a characteristic that gives the device a Petition 870250065060, dated 07 / 28 / 2025, page 27 / 56 / 23 variable impedance response as a function of applied voltage. This behavior results directly from the relationship between the magnetic field and the flux density in the core, as described by the typical magnetization curve of ferromagnetic materials. Figure 1 illustrates a generic saturation curve, highlighting the usual operating regions of different electromagnetic devices, including those that purposefully exploit the effects of saturation for the control of electrical quantities.

[028] As illustrated in Figure 1, the typical operation of a saturated core reactor begins in a linear region of the magnetization curve, where the magnetic permeability is high and the device's response to the applied voltage is predictable and stable. With increasing voltage, there is a progressive increase in the core saturation level, leading the device to operate in regions of high magnetic density. In this condition, the reactor's inductive impedance is reduced, resulting in a significant increase in the circulating current and, consequently, in the absorbed reactive power. The transition between the different saturation levels occurs gradually and continuously, allowing the device to respond dynamically to network variations with response times compatible with the electromagnetic phenomena involved.

[029] Thus, it is expected that, under operating conditions close to the nominal voltage of the electrical system, the saturated reactor will exhibit a reduced inductive current, which translates into a relatively low consumption of reactive power. However, as voltage increases in the network to which the device is connected, the magnetic core enters deeper levels of saturation, resulting in an increase in current and, consequently, in the reactive power absorbed. This behavior provides a dynamic and autonomous response to voltage variations, allowing the device itself to act on its Petition 870250065060, dated 07 / 28 / 2025, page 28 / 56 / 23 attenuation, without the need for external control mechanisms. This characteristic gives the reactor intrinsic self-regulating properties, based exclusively on its physical structure and the phenomenon of magnetic saturation.

[030] Among the topologies employed for this type of device, the present invention uses the configuration known as Twin-Tripler, characterized by the presence of two isolated three-phase magnetic cores, totaling six magnetic columns. This arrangement is designed to, under conditions of equilibrium between the phases, reduce the generation of unwanted harmonics in the system, favoring the overall electromagnetic performance. An illustrative example of this topology is shown in Figure 2.

[031] The device comprises, in its structural configuration, two three-phase magnetic cores of similar geometry, each formed by three magnetic columns. On each column are mounted two concentric windings, electrically interconnected in series and magnetically coupled. These windings are designated as the main winding (Np) and the auxiliary winding (Na), both arranged to form an integrated functional structure. This configuration results in an arrangement equivalent to that of two three-phase transformers with windings connected in series, arranged in the zigzag and star topologies with floating neutral. The combination of the number of turns in the Np and Na windings, as well as the form of their interconnections, contributes to the suppression of low-order harmonics, and, under ideal conditions of balance between the phases, reactors with this topology tend to produce harmonics of order 12k ± 1, from the 11th order.

[032] To broaden its applicability, the present configuration is directed to application in overhead distribution networks, being designed with the use of computational optimization techniques, including algorithms Petition 870250065060, dated 07 / 28 / 2025, page 29 / 56 / 23 genetic and artificial neural networks, with the aim of reducing the volume of the magnetic core. Reducing the core volume results in a decrease in the total mass of the equipment, as well as a reduction in the electrical losses associated with its operation. The decrease in volume and losses also allows for a reduction in the amount of insulating fluid needed to fill the casing, which also serves a thermal dissipation function. These constructive characteristics allow the reactor to be installed on overhead network poles or in benchtop arrangements, providing flexibility in its allocation according to the operational requirements of the electrical system. This characteristic allows its implementation at strategic points in the network, optimizing local reactive compensation without requiring additional infrastructure, such as the construction or expansion of substations.Figures 3A, 3B, and 3C illustrate one possible way to install the device in an overhead distribution environment.

[033] An additional feature that can be incorporated into the structure of the saturated core reactor is the presence of taps in the windings. This functionality allows the device to operate at different voltage levels, providing greater flexibility for adjusting the operating range according to the operating conditions of the electrical system. The inclusion of multiple tap positions, for example, up to five taps in the main and auxiliary windings of the SCR, with voltage ranges defined in the design correlated with different numbers of turns in their respective winding sets, allows the reactive power supplied by the equipment to be adjusted more precisely and in a controlled manner, optimizing performance according to the local grid voltage at the installation point.The voltage values ​​associated with each tap are predetermined to accommodate different network configurations and facilitate the adaptation of the device to systems with varying requirements. Figures 4A to 4D. Petition 870250065060, dated 07 / 28 / 2025, page 30 / 56 Figures 10 / 23 illustrate a possible constructive implementation of the tap changer in the context of a saturated core reactor. Such adaptations enable the use of the technology in the conventional overhead power distribution network of electric utilities.

[034] Figure 5 presents a flowchart representing the steps that can be followed for the definition of the physical pre-design of the magnetic and electrical units of a saturated core reactor. The process includes the logical sequence of decisions and calculations necessary for the initial dimensioning of the equipment, considering electromagnetic, geometric and operational parameters. This methodology can be adopted based on technical-scientific procedures established in research institutions or on good design practices applied to the development of electromagnetic devices. Input parameters for the physical preliminary sizing of the reactor.

[035] The preliminary information needed for the basic dimensioning of a saturated core reactor is summarized in Table 1. Among the main parameters, the following stand out: the operating voltage under no-load conditions, which corresponds to the condition of lowest reactive power consumption; the target voltage to be regulated; the reactive power required for the application; the choice of magnetic material to be used in the core; the characteristic operating points of the system; as well as construction factors, such as the stacking factor and the magnetic dispersion factor. This data provides the basis for the initial calculations of the electromagnetic and geometric design of the device. Main Data Auxiliary Data Rated operating voltage Type of magnetic core material Rated reference voltage Maximum induction (operating voltage) Reactive power (for operating voltage) Corresponding magnetic field strength Frequency Stacking factor Petition 870250065060, dated 07 / 28 / 2025, page 31 / 56 11 / 23 Dispersion Factor Table 1

[036] The stacking factor is an important quantity for the design of cores, since these are composed of thin sheets of ferromagnetic material, which are stacked. The stacking factor is the ratio between the total area of ​​the core and the area occupied by the sheets.

[037] The dispersion factor is related to the distribution of coils and magnetic flux within the transformer and is a quantity associated with constructive aspects of the equipment and is linked to magnetic fields other than the one directly established in the main magnetic core. Thus, this factor is related to the ratio between the dispersed magnetic flux and the total magnetic flux in the reactor or transformer. Formulations associated with the induced voltages in the coils and the phase voltage at the reactor terminals.

[038] Each phase that makes up the three-phase reactor, from an electromagnetic point of view, is constituted by coils subdivided into 2 main windings and 2 auxiliary windings, distributed in the two magnetic units as illustrated in Figure 2. Thus, from the perspective of a three-phase system balanced in terms of operational and constructive aspects, the following relationships can be established, which establish the correlations between the phase voltages and those induced in the set of coils that make up each electrical phase of the equipment. VL+ (1) VL - - 2 Vind^ + 2 0.367 Vind^ VL - - 2 Vind^ + 0.734 Vind^ Petition 870250065060, dated 07 / 28 / 2025, p. 32 / 56 / 23 VL 2,734^,., Vlnd(p) = 0.211 · VL(2)

[039] Considering the constructive design associated with the Twin-Tripler configuration, as well as the phase angles imposed for the induced voltages in the main and auxiliary windings, we arrive at: vmd(a) = 0.367 · Vind(p), then Knd(a) = 0.0775 · VL. Therefore, equation (2) leads to the conclusion that, in magnitude, the induced voltage in the main winding will be equal to the line voltage of the bus under regulation times the constant 0.211, while the induced voltage in the auxiliary winding will be equal to the same line voltage times the constant 0.0775.

[040] The operating voltage of the electrical network is an essential parameter in the sizing of the device, and the device architecture is designed to allow its adaptation to different voltage levels. This flexibility is made possible by adjusting the electrical quantities and insulation characteristics, respecting the dielectric limits and the regulatory requirements relevant to the voltage class considered. It is important to highlight that such adaptations do not modify the operating principle of the device, maintaining unchanged its operating logic based on the magnetic saturation of the core and the resulting effects on voltage regulation in the electrical network. Magnetic fluxes established in the core columns

[041] Generally, the mathematical relationship between induced voltages and the magnetic fluxes that produce them is consistent with equation (3). In this equation, N is the number of turns of the winding analyzed and the derivative of the magnetic flux function with respect to time. From this, the expression for the corresponding magnetic flux can be determined, as shown in equation (4). Petition 870250065060, dated 07 / 28 / 2025, page 33 / 56 / 23ν'ηά~NΈ ,1f ,. Φ = jy J Wind dt ,1T' , „ ,. = JVmax COs(ó)t) · dt φ =m^xJ cos(rnt) · dt (3) φ =max· sin(mT) ωΝ (4)

[042] In the mathematical modeling of magnetic flux, the columns of the Twin-Tripler saturated core reactor are presented by the composition of the component associated with the main winding of a given phase and that produced by the auxiliary winding, each with a difference in phase angle, as presented by equation (5). By way of example, the expression presented below contemplates the magnetic flux established in the central column of the 1st core. Vmax(pfaseB) ^max(a / asex) Φcoi2_ni =------sin(a)T - 120O)+-------sin^f) Where, ^maxÇPfaseB / Np sen(coT - 120o) is equivalent to the flux produced by the main winding; and -max^^ · sen(rnT) is equivalent to the flux produced by the auxiliary winding.

[043] Considering the electromagnetic arrangement as illustrated in Figure 2 shows that it is possible to determine the instantaneous values ​​of the magnetic fluxes over a complete cycle of the fundamental frequency of the... Petition 870250065060, dated 07 / 28 / 2025, page 34 / 56 / 23 system. Figure 6 presents, in a generic way, the waveforms of the instantaneous fluxes in each of the columns of the core, representing the three phases of the system. As expected in balanced three-phase configurations, an angular phase shift of 120° is observed between the fluxes associated with each phase, reflecting the symmetry and temporal distribution characteristic of magnetic quantities in devices of this type.

[044] Based on column 2 of core 1 (φcol2), it is possible to observe that the flux is maximum for ωt equal to 150°. This operating point corresponds to the instant when the voltages of phases A and B (whose windings make up the central column of core 1) are equal in magnitude, but with opposite signs. The corresponding currents in the three phases, neglecting the resistive part of the Twin-Tripler saturated core reactor, will consequently be 90° out of phase with their respective voltages. This implies that the currents in phases A and B have instantaneous values ​​equal to half the maximum value and have the same sign. On the other hand, phase C is at its maximum current value, with the opposite sign to the currents of the other phases.These considerations underpin the choice of magnitude and angle for the instant associated with the 150° angle at which the central magnetic column experiences a maximum flux value, as well as its corresponding magnetomotive force. Sizing the magnetic core and the number of turns of the coils.

[045] As established by equation (4), the resulting maximum magnetic flux in the central column of core 1, which occurs for ωt = 150°, can be determined by equation (6). Fmax (VfncpR} „ „ Fmax (α / ν,ςρΏ Φmax_co12= 2π f lf, ^ sin(150O— 120O) + ^ sin(150O) 7max · 0.211 Enax · 0.211 Φmax co12 = 27f N' sin(30O) + 27f Nsin(150O) _ 2π · f · Np 2π · f · Np Petition 870250065060, dated 07 / 28 / 2025, page 35 / 56 / 23 Φ max_col2 0.211 ^max 0.211 A 0.03358 · l^x 2n-f-Np^ ,+2π · f · Np' , f · Np(6)

[046] Under conditions of high saturation levels of the magnetic material, the difference between the voltage induced in the windings and the voltage at the input terminals of the equipment becomes relevant, since it is directly proportional to the density B and, consequently, to the corresponding field intensity H. This difference, as already mentioned, is mainly attributed to the leakage flux of the windings, which is dependent on the spacing between the coil and the core and the magnetic saturation of the core. In view of the above, aiming at a better adaptation to the conditions effectively imposed on the compensation process, the multiplier factor fdisp was established in equation (6) in this strategy for the pre-dimensioning of the reactor. This determines equation (7), which aims to correlate the difference between the voltage effectively used, per phase, between the induced voltage and that existing in the target busbar of the regulation. _ 0.03358 ^max· fdisp Ψmax_col2 y .(7)

[047] Once the magnetic flux present is known, and that this quantity is related to the product of the induction B and the cross-section Smagdo core, equation (8) is obtained. _ 0.03358 · Vmax · fdisp ^mag · ^max y „ yy Ç mag 0.03358· Vmax· fdisp f NR™jPpumax (8)

[048] Thus, in order to properly determine the cross-section of the magnetic core, it is necessary to first establish the number of turns of the main winding, which also allows us to derive Petition 870250065060, dated 07 / 28 / 2025, page 36 / 56 / 23 the corresponding number of turns of the auxiliary winding, according to the proportion defined in the project. To make this determination feasible, the expressions involved are reformulated, replacing dependent variables with quantities previously defined in the dimensioning process, as will be detailed below. This approach allows the electromagnetic requirements to be compatible with the constructive constraints of the device.

[049] Expressions (9) and (10), which establish the correlation between the adopted magnetic saturation conditions, lead to a strategy for defining the number of turns required by equation (8). _ N · / (maxφ) ^max = i1mag (9) _ Np · / B(maxφ) Na · / A(maxφ) “max = > + j{mag maag “max = Np · / max · sin(30o) 0.367 · Np · lmax · sin(150o) ---ü-------+------ / Σ---------cmagLmag “max 0.6835 · Np · / max ( mag (10)

[050] In addition to the quantities present in equation (10), which have already been duly identified and characterized in the previous steps, the following variables stand out: / max which represents the peak value of the line current and lmnnatredlated with the physical extent of the average magnetic path / through which the flux φmax is established.

[051] From the above, equation (11) follows, which determines the number of turns Np as a function of Hmax, Imax and lmag. h Z™ _11maxLmagp= 0.6835 • / max (11) Petition 870250065060, dated 07 / 28 / 2025, page 37 / 56 / 23

[052] With regard to the magnitude lmag, this can be defined according to the constructive physical quantities of the magnetic core, as established by equation (12). image =2' (^column + ^window) + fanela (12)

[053] Figure 7 illustrates the constructive variables: Lcoluna representing the width of the column, Ljanela the width of the window and Hjanela the height of the same.

[054] Considering that manufacturers frequently adopt different strategies to correlate the geometric variables involved in the design of magnetic cores, a generalized approach is proposed that introduces degrees of freedom in the relationships between these dimensions. This strategy allows greater flexibility in constructive dimensioning, enabling the adaptation of the design to different manufacturing criteria and the optimization of electromagnetic performance according to the specifications of each application. To this end, as shown by equations (13), (14) and (15), three proportionality constants were introduced between the dimensions required for the constructive process of the device. These quantities, given the above, allow different proposals for the combination of values ​​to be adopted for the magnetic lengths set and that would lead to the same objectives regarding the operating points of the device. Hwindow column = Ci Total (13) (14) Lwindow _C13'C2 +2_ column 2^2

[055] Since the cross-section of the cores has a geometry that approximates a circle, equation (17) Petition 870250065060, dated 07 / 28 / 2025, page 38 / 56 / 23 establishes the relationship between the width of the Lcoiunae column and the geometric section. Sgeom· column „ _ columnSgeom = — J4 · Sgeom π Is ^g eom Jπ(16) (17)

[056] Given that the assembly of the device imposes a difference between the net area and the constructive physics, as already defined through the quantity “stacking factor”, it follows that: Sgeom= Smag· femp· Therefore, the width Lcoluna can be calculated as a function of Smag, according to equation (18). column ° mag •femp (18)

[057] Therefore: window = 2 Smag (19) ' femp Hwindow = 2 ' ç Smag (20) π ' femp

[058] Finally, equation (22) leads to the desired number of turns as a function of the constructive variables considered above: u^m^Smag Smag^max 2(2 Ιπ-femp ^3J^'fempl +2l^'femp (21) 1------------------------------2-------------------p0.6835-Imax

[059] Where: Petition 870250065060, dated 07 / 28 / 2025, p. 39 / 56 / 23 2-(2 + 2-^ + 61) Hmax ---------- —. , .--0.6835 / max J1umag 'femp (22)

[060] Substituting the expression for the number of turns defined by (22) into equation (8) leads to: c _o™ . λ 17 QrNS ' fdisp V Smae 820(fem„)(f ,Hm„.Bm„«(2 + 2.C3+C1))(23)

[061] The number of turns of the main coil can be obtained using equations (8) and (11). For the purposes of defining the methodology established for this invention, the relationship below is used, which leads to the required expression (24). The result thus obtained leads to the value of Np and Na, since they are in a proportion of 0.367. _ 0.03358 •Vmax^fdisp _ 0.03358 •Vmax^fdispmaaf NB ^pf SB J Pp ^max J °magumax

[062] The formulation set out above assumed that the core has a circular cross-section, therefore its thickness would correspond to the width of the column (Lcolumn). However, for the prediction of the weight of the magnetic units, the cross-section is considered rectangular and, therefore, the thickness of the core (ecore) is determined by equation (25). enucleo = ç____ ç fugeom mnag Jemp column ç .Jmag Iπ·femp = 0 8862 · V™ f3 / 2 u ,υυυζ. mmag Jemp (25) Computational Modeling of the Element-Based Saturated Core Reactor Finite Petition 870250065060, dated 07 / 28 / 2025, page 40 / 56 / 23

[063] Based on the construction data obtained in the project, an equivalent computational model of the device was developed using ANSYS software, in order to evaluate its performance and electromagnetic behavior through simulations based on the Finite Element Method. The modeling was conducted meticulously, fully considering the physical configuration of the equipment, including the double magnetic core structure and the arrangement of the associated windings, in order to faithfully represent the real operating conditions.

[064] A piece of data of extreme importance for the representation of the core is the saturation curve of the material used in the project. This data is responsible, among other parameters, for the saturation values ​​of the equipment. It is worth noting, once again, that the equipment in question operates in the saturation region. Thus, for the purposes of this modeling, the saturation data of the saturated core reactor were entered into the finite element software in accordance with the data provided by the manufacturer.

[065] Figure 8 illustrates the arrangement of the two magnetic cores of the device, positioned side by side, according to the configuration foreseen in the project. The image allows visualization of details of the stacking of the ferromagnetic laminations that make up each core, highlighting the constructive structure adopted. In the computational modeling, the cross-sectional area was inserted with precision, considering both the total physical area and the area effectively occupied by the magnetic material, in order to correctly reflect the relationship between the geometry and the electromagnetic performance of the system, in accordance with the parameters defined in the project.

[066] Figures 9 and 10 show the detailed modeling of the saturated core reactor windings. In Figure 9, a Petition 870250065060, dated 07 / 28 / 2025, page 41 / 56 / 23 front view in which the main windings are positioned in the outermost region of the magnetic columns (represented in red), while the auxiliary windings are located in the inner part (represented in blue), both organized by phase. This concentric arrangement reflects the structure adopted in the physical design of the device and was fully considered in the construction of the computational model.

[067] It is important to highlight that the windings, including the taps positioned in the lower region, were modeled with polygonal geometry instead of circular, in order to optimize the computational cost of the simulation process. Each winding was represented by a 24-sided structure, which provides a satisfactory approximation of the real shape with a significant reduction in processing time. The main winding was modeled in multiple layers, according to the construction specifications established in the project, and the spacing between layers was rigorously respected, as evidenced in Figure 9. Evidence and tests

[068] Details of the core assembly can be seen in the Figures Figures 11A and 11B show the silicon steel sheets, preferably 27QG100, which were properly cut and stacked according to the design. The winding process is shown in Figure 12.

[069] In Figure 13, all the interconnections made in the windings to form the saturated core reactor in Twin-Tripler format can be seen. The two cores positioned side by side are also highlighted in this figure.

[070] Figure 14 shows construction details of the external tank of the saturated core reactor, which will house the cores and Petition 870250065060, dated 07 / 28 / 2025, page 42 / 56 / 23 windings and will be filled with vegetable oil, providing the necessary insulation for this voltage regulation equipment.

[071] After the saturated core reactor was manufactured, several initial tests were carried out in order to commission the equipment at the factory. The following tests were highlighted: routine test, heating test and surge test. Figures 15A and 15B show the photographic record of the test carried out to obtain the power-voltage curve of the saturated core reactor.

[072] In the aforementioned test, each of the taps was evaluated individually by gradually applying voltage values ​​and measuring the corresponding reactive power absorbed by the device. The results obtained are consolidated in Table 2, allowing the analysis of the equipment's behavior under different operating conditions. TAPE 1 TAPE 2 TAPE 3 TAPE 4 TAPE 5 Applied Voltage [kV] Reactive Power [kVAr] Applied Voltage [kV] Reactive Power [kVAr] Applied Voltage [kV] Reactive Power [kVAr] Applied Voltage [kV] Reactive Power [kVAr] Applied Voltage [kV] Reactive Power [kVAr] 30.149 3.3 30.270 4.2 30.129 5.1 30.675 7.2 30.372 8.4 31.038 4.2 31.018 5.1 31.382 6.9 31.220 8.4 31.281 10.8 32.049 5.4 32.655 8.1 32.190 8.7 32.231 11.1 32.008 13.2 33.322 7.8 33.807 11.1 33.423 12.3 33.039 13.8 33.201 18.6 34.312 9.9 34.272 12.6 34.150 15.0 34.090 18.9 34.433 30.0 35.161 12.6 35.302 16.5 35.201 20.1 35.181 27.9 35.100 41.7 36.272 17.1 36.393 22.8 36.050 27.6 36.050 42.6 35.524 53.4 37.424 23.7 37.282 32.7 37.060 45.0 36.616 56.7 36.070 72.6 38.192 32.7 38.151 49.8 37.525 56.7 37.202 80.1 36.252 81.3 39.000 48.6 38.515 60.3 38.030 76.8 37.606 102.6 36.515 94.2 39.505 62.4 39.000 80.1 38.252 86.7 37.767 114.0 36.696 107.1 40.071 85.8 39.242 92.1 38.333 91.2 37.889 124.8 36.797 114.9 40.273 97.2 39.424 102.3 38.576 106.2 37.949 127.2 36.919 123.6 40.334 99.3 39.626 114.9 38.636 111.0 38.010 132.6 36.979 127.5 40.394 103.5 39.707 120.3 38.677 112.8 38.151 144.3 37.040 134.7.

[073] Figure 16 illustrates a representative installation of the device in an operating electrical power distribution network. The equipment operated for more than a month, in accordance with the conditions foreseen in the project and meeting the technical parameters established for its application. This Petition 870250065060, dated 07 / 28 / 2025, page 43 / 56 / 23 installation serves as evidence of the practical feasibility and performance of the device in a real network environment. Petition 870250065060, dated 07 / 28 / 2025, pages 44 / 56

Claims

1 / 2 CLAIMS 1. Saturated core reactor for electrical power distribution networks, characterized by comprising: at least two structurally independent three-phase magnetic cores, configured in Twin-Tripler topology, each core consisting of three magnetic columns; concentric main (Np) and auxiliary (Na) windings mounted on each magnetic column, electrically interconnected in series and magnetically coupled; electrical connection of the windings in a combined zigzag and star arrangement with floating neutral; and at least one winding equipped with a shunt system, with multiple switching positions for adjusting the number of active turns.

2. Saturated core reactor, according to claim 1, characterized in that the windings of each phase are arranged concentrically around the magnetic columns of each core.

3. Saturated core reactor, according to claim 1, characterized in that it is installed in a suspended manner in a station or in a bench arrangement.

4. Saturated core reactor, according to claim 1, characterized in that the main windings are arranged in multiple layers, with uniform spacing between the layers.

5. Saturated core reactor, according to claim 1, characterized in that the auxiliary winding is positioned internally to the main winding in each phase. Petition 870250065060, dated 07 / 28 / 2025, page 45 / 56 2 / 2 6. Saturated core reactor, according to claim 1, characterized in that the number of turns is calculated according to the equation: NP = 2-(2 + 2-C3 + Ci) Hmax 0.6835 max ^mag ' femp Where, Np: Number of turns of the main winding; Ci: Dimension of the base of the central column of the magnetic core; C3: Dimension of the base of the side columns of the magnetic core; Hmax: Maximum magnetic field intensity in the core; Imax: Maximum electric current of the main winding; : Effective cross-sectional area of ​​the magnetic core; femP: Stacking factor of the magnetic core. Petition 870250065060, dated 07 / 28 / 2025, pp. 46 / 56

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