Use of short-circuit resistances, method and device for monitoring the operating state of an operational three phase transformer

Abstract

The invention describes a use of short-circuit resistances, a method and a device (A) for monitoring the operating state of an operational three phase transformer (G). The effective short-circuit resistance relating to a phase of the secondary winding of the transformer is that which gives rise to charge losses when current circulates through the phase. The method comprises obtaining one or more magnitudes, such as short-circuit resistances of each harmonic, effective short-circuit resistances of each phase, charge losses of each phase, charge losses of each harmonic, total charge losses, factors of overheating and of supply of each phase, factor of supply of the transformer and factor of losses of each harmonic. The device (A) comprises a physical system for measuring and acquiring electrical signals (C); a processing system (D); and a measuring program (E).

Description

[0001] DESCRIPTION Use of short-circuit resistors, method and device for monitoring the operating status of a three-phase transformer in service TECHNICAL FIELD The present invention relates generally to the field of three-phase distribution transformers and, more specifically, to the monitoring of their operation. BACKGROUND OF THE INVENTION Short-circuit resistors are very important operating parameters of electrical transformers. In the normal operation of these machines, the short-circuit resistors determine the values ​​of the load losses and, therefore, the overheating that leads to the deterioration of their construction elements and a reduction in their useful life. Three-phase transformers in distribution networks are mostly of the Dyn11 type.In industrial practice, the following expression is widely used to calculate load losses, also known as copper losses, during the operation of these transformers: ^^^ = ^^^^ ∙ (^ ^. ^^ + ^ ^ ^^ + ^ ^ ^^ ) [1], where ^^^ are the load losses; ^^^ , ^^^ , ^^^ are the effective values ​​of the circulating currents through the phases of the secondary winding; and ^ ^^^ is the short-circuit resistance reduced or referred to the secondary, obtained as follows: 2 , [ ] being ^ ^^^ the value of the nominal pressure losses; and ^ ^^the effective value of the nominal secondary current. These quantities can be known from the catalog data provided by the transformer manufacturers, or obtained after performing a nominal short-circuit test at industrial frequency (50 - 60 Hz). The application of equation [1] provides the same results as IEEE Standard C57.110 when the transformers supply linear loads, without harmonics. This is not the usual operation of transformers in distribution networks, because the increasing presence of electronic converters in the regulation of electric motors, in lighting and photovoltaic solar energy systems, among other applications, favors the circulation of distorted currents through the windings. IEEE Standard C57.110-2018 (DOI: 10.1109 / IEEESTD.2018.8511103) establishes the expressions for the load losses of three-phase transformers supplying non-linear loads.Total pressure losses (^. ^^ ) are obtained as the sum of the direct current losses (^ ^^ ), losses due to the Skin or film effect (^ ^^ ) and the losses caused by the induced currents in the walls of the tank and other metallic parts of the transformer [3]. In these expressions, ^ ^^^^ are the nominal losses in direct current, ^ ^^^^ are the nominal losses due to the Skin effect and ^ ^^^^^ are the nominal losses caused by the phenomenon of electromagnetic induction; ^ ^ is the effective value of each harmonic of the primary currents, ℎ = ^^ / ^^ is the order of each harmonic of the primary currents (relationship between its frequency, ^^, and the fundamental frequency, = 50 − 60 ^^), ℎ^^^ is the order of the highest frequency harmonic used in the calculation, and ^ ^is the nominal value of the transformer primary current. Expression [3] gives correct results when the currents are exactly equal in the three phases of the transformer, that is, they have the same effective values ​​(^^ = ^^^ = ^^^ =^^^) and harmonics of the same frequencies (ℎ = ℎ^ = ℎ^ = ℎ^). This last equality is usually common in electrical networks; however, it is very unlikely that the effective values ​​of each harmonic of the currents are equal in the three phases of distribution transformers. Notwithstanding the above, the expressions for the load losses indicated in [3] have been used by numerous publications in the Technical Literature. As an example, the following two applications are cited, among many others: 1. Megahed, TF; Kotb, MF Improved design of LED lamp circuit to enhance distribution transformer capability based on a comparative study of various standards. Elsevier Energy Reports 2022, 8 (9), pp.445-465. https: / / doi.org / 10.1016 / j.egyr.2022.07.0272. Daniel Contreras Ramírez & Lata-García Juan. K-Factor Analysis to Increase the ActualCapacity of Electrical Distribution Transformers. Springer Communication, Smart Technologies and Innovation for Society, 2021, pp 367–379. https: / / doi.org / 10.1007 / 978-981-16-4126-8_34 However, none of these publications, nor the Standard itself, explains how to use expression [3] in the general case where the currents have different effective values ​​(^. ^) and harmonics (ℎ) in each phase of the transformer. It is also not possible to calculate the load losses of each phase of the transformer by applying equation [3], since ^^^^^ , ^^^^^ and ^^^^^^are total nominal losses, not the losses in each phase. Likewise, IEEE Standard C57.110 does not establish expressions for the calculation of the short-circuit resistance of three-phase transformers supplying non-linear loads. Nor have expressions for the short-circuit resistance of transformers supplying non-linear loads been found in any of the consulted bibliographic references, except for the following, established very recently by L. Sima et. al.: Sima, L.; Miteva, N.; Dagan, K.J. A novel approach to power loss calculation for power transformers supplying nonlinear loads. Elsevier Electric Power Systems Research 2023,223, 109582. https: / / doi.org / 10.1016 / j.epsr.2023.109582 In this reference, L. Sima et. to the.They have established expressions for the short-circuit resistance referred to the primary (^. ^ ), based on the application of IEEE Standard C57.110, which are basically reduced to the following: where ^ ^^ is the short-circuit resistance in direct current, ^ ^^ is the resistance due to the skin effect, and ^^^^ is the resistance due to losses ^^^^; the subscript ^ indicates a parameter of the primary and the subscript ^ refers to a parameter of the secondary. ^^ = ^^^ are the total load losses defined by IEEE Standard C57.110 in equation [3] and ^ ^ is the effective value of the current of the three phases of the primary. Substitution in equation [5] of the values ​​of the load losses calculated according to equation [3] determines that ^ ^has the same values ​​in all three phases of the transformer. This result is consistent with the limitations of the use of the load loss expression included in IEEE Standard C57.110, indicated previously, and determines an equivalent model of the three-phase transformer with the same elements and values ​​in the three phases of the transformer, as represented in the single-phase equivalent circuit in Figure 1, used by L. Sima et. al. in their publication. The equivalent model of a three-phase transformer proposed by L. Sima et. al. (Figure 1), resulting from the direct application of IEEE Standard C57.110, is not physically correct, since the short-circuit resistances can have different values ​​in the three phases of the transformer when their currents are not exactly equal in each of them. This fact is confirmed by the strong dependence of the resistance values ​​on ^^ and ^ ^^^ , components of ^ ^in equation [5], of the harmonic frequencies (ℎ) and of the effective values ​​(^ ^ ) of the currents, which are usually different in the three phases of the transformer as indicated above. In short, the equivalent operating model for three-phase transformers supplying non-linear loads is closer to that represented in Figure 2, in which the short-circuit resistances have different values ​​in each phase. The short-circuit resistance developed by L. Sima et. al. (^ ^) is a purely mathematical parameter, whose only application is the calculation of the total load losses of the transformer, but it does not allow to know the real operation or the value of the losses in each of its phases. SUMMARY OF THE INVENTION In order to overcome the aforementioned drawbacks of the prior art, according to a first aspect, the present invention discloses a use of short-circuit resistors for monitoring the operating status of a three-phase transformer in service. Said resistors are effective short-circuit resistances referred to the secondary of the three-phase transformer, with the particularity that the effective short-circuit resistance referred to a phase ^ of the secondary (^^^,^) is that which gives rise to load losses dissipated in phase ^ (^^^,^) when a current circulates through phase ^, as reflected in the following expression: where: -^ generally denotes any phase of the transformer secondary, - ^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer, - ^^^,^ are the load losses dissipated in phase ^, - ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^), -ℎ^,^^^ is the order of the highest frequency current harmonic present in phase ^used in the calculation, -^^^ is the effective value of the current harmonic of order ℎ^. The use of short-circuit resistances based on the technology of the present invention makes it possible to calculate the real losses in each phase and, therefore, to know the overheatings, and the decrease in the power transmission capacity and the reduction in the useful life of the transformer. The short-circuit resistances have been applied in the present invention to the development of suitable parameters for monitoring the operating status of distribution transformers, such as, for example: an overheating factor for each phase, a supply factor for each phase, a supply factor of the transformer and a loss factor for each harmonic, as included below.According to a second aspect, the present invention also provides a method for monitoring the operating status of a three-phase transformer in service, based on the use of short-circuit resistances of the first aspect of the invention. The method comprises obtaining, by means of a monitoring device, the value of at least one magnitude of the transformer selected from the group comprising: short-circuit resistances of harmonics referred to the secondary of the transformer (^^^,^), short-circuit resistances of harmonics referred to the primary of the transformer, effective short-circuit resistances referred to the secondary of the transformer (^^^,^), component of said effective short-circuit resistances due to the Skin effect (^. ^^,^ ), component of said effective short-circuit resistances due to the phenomenon of electromagnetic induction (^ ^^^,^), effective short-circuit resistances referred to the transformer primary, load losses of each phase of the transformer secondary (^ ^^,^ ), load losses of each harmonic (^ ^^,^ ), total charge losses (^^^), superheating factor of each phase (^^^), supply factor of each phase (^^^%), transformer supply factor (^^^%), loss factor of each harmonic (^^ ^ %), according to the particularities of the following sections: a) the value of the short-circuit resistances of harmonics referred to the secondary of the transformer (^ ^^,^ ) is obtained by the expression

[0032] : where: -^^^,^ is the short-circuit resistance of a current harmonic referred to phase ^of the transformer secondary, -^ generally denotes any phase of the transformer secondary,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -^^^^, ^^^^ , ^^^^^ are a nominal short-circuit resistance referred to the secondary in direct current (^ ^^^ ), a nominal short-circuit resistance referred to the secondary by Skin effect (^ ^^^ ) and a nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer (^ ^^^^ ), respectively, which are obtained by the expressions

[0026] ^ ^ ^^^ ^ ^^^ ^ ^^^^ ^^^ = ^ 3^ ^ ^^^ = ^ ^ = 26 , ^^ 3^ ^ ^^^^^ 3^ ^ ^ ^ [ ] in which: ^^^^^ are nominal direct current load losses,^ ^^^^ are nominal Skin effect load losses,^ ^^^^^ are nominal load losses caused by the electromagnetic induction phenomenon, ^^^^ is the nominal value of the secondary current of the transformer; b) the value of the harmonic short-circuit resistances referred to the primary of the transformer is obtained by multiplying the current harmonic short-circuit resistances referred to the secondary of the transformer (^^^,^) by the square of a transformer transformation ratio ^^ = ^^ / ^^^, in which:- ^^ is the effective value of the primary voltage, and- ^^^ is the effective value of the secondary voltage in no-load condition; c) the value of the effective short-circuit resistances referred to the secondary of the transformer (^ ^^,^) is obtained by one of the following options: c1) by the expression

[0025] :^^^,^ = ^^^^ + ^^^^ ∙ ^ ^^^^ + ^^^^^ ∙ ^^ ^ ^ ^

[0025] , where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ^^^^, ^^^^ , ^^^^^ are a nominal short-circuit resistance referred to the secondary in direct current (^ ^^^ ), a nominal short-circuit resistance referred to the secondary by Skin effect (^ ^^^ ) and a nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer (^ ^^^^ ), respectively, which are obtained by the expressions

[0026] ^ ^ ^^^ ^ ^^^ ^ ^^^^ ^^^ = ^ 3^ ^ ^^^ = ^ ^ 3 ^ ^^^^ = ^ 26 , ^ ^ ^^ 3^ ^^ [ ]where: ^^^^^ are nominal load losses in direct current,^ ^^^^ are nominal load losses due to the Skin effect,^ ^^^^^ are nominal load losses caused by the electromagnetic induction phenomenon, ^^^^ is the nominal value of the secondary current of the transformer; - ^ ^ ^^^ , ^ ^ ^^^ are a factor of phase losses ^ due to the skin effect (^^ ^ ^ ^ ), and a phase loss factor ^ due to electromagnetic induction in the metallic parts of the transformer (^ ^ ^ ^ ^ ), respectively, which are obtained by the expressions

[0027] in which: ^ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^), ^ℎ^,^^^ is the order of the highest frequency current harmonic present in phase ^ used in the calculation,^ ^^^ is the effective value of the current harmonic of order ℎ^;c2) by means of the expression

[0029] where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ^^^,^ is the short-circuit resistance of a current harmonic referred to phase^ of the secondary of the transformer,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in phase ^ used in the calculation, - ^^^ is the effective value of the current harmonic of order ℎ^; d) the value of the component due to the Skin effect (^^^,^) of the effective short-circuit resistances of each phase referred to the secondary (^ ^^,^), is obtained by the expression [28.1] ^^^,^ = ^^^^ ∙ ^^ ^ ^ ^ [28.1], where: -^^^^ are the nominal load losses due to the Skin effect, - ^^ ^ ^ ^ is the loss factor of phase z due to the Skin effect; e) the value of the component due to the electromagnetic induction phenomenon (^^^^,^) of the effective short-circuit resistances of each phase referred to the secondary (^ ^^,^ ), is obtained by the expression [28.2] ^^^^,^ = ^^^^^ ∙ ^^ ^ ^ ^ [ 28.2 ] , where: -^^^^^ is the nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer, - ^ ^^^^ is the loss factor of phase ^ due to electromagnetic induction in the metallic parts of the transformer; f) the value of the effective short-circuit resistances referred to the primary of the transformer is obtained by multiplying the effective short-circuit resistances referred to the secondary of the transformer (^^^,^) by the square of a transformation ratio of the transformer ^^ = ^^ / ^^^, in which: - ^^ is the effective value of the voltage of the primary, and - ^^^ is the effective value of the voltage of the secondary in no-load condition; g) the value of the load losses of each phase of the secondary of the transformer (^^^,^) is obtained by one of the following options: g1) by the expression

[0030] where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in phase ^ used in the calculation, - ^^^ is the effective value of the current harmonic of order ℎ^;g2) by means of the expression

[0034] where: -ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the highest frequency current harmonic present in phase ^ used in the calculation,- ^^^,^ is the short-circuit resistance of a current harmonic referred to phase^ of the transformer secondary,- ^^^ is the effective value of the current harmonic of order ℎ^;h) the value of the load losses of each harmonic (^^^,^) is obtained by means of the expression

[0033] : ^^^,^ = ^^^,^ ∙ ^ ^^ ^ ^

[0033] , ^^^,^,^ where: -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^ is the effective value of the current harmonic of order ℎ^, - ^^^,^ is the short-circuit resistance of a current harmonic referred to phase ^of the transformer secondary; i) the value of the total load losses (^^^) is obtained by one of the following options: i1) by means of expression

[0031] : where: -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^,^ are the load losses of each phase of the transformer secondary; i2) by means of the expression

[0035] : where: -ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in the phase ^ used in the calculation, - ^^^,^ are the load losses of each harmonic; j) the value of the superheating factor of each phase (^^^) is obtained by the expression

[0036] : where: -^^^ is the overheating factor of each phase ^, which defines the increase in losses in each phase ^ in relation to the losses that would occur in the transformer operating without non-linear loads, -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer, - ^^^,^ is the short-circuit resistance of a harmonic (^^^,^) at the fundamental frequency, that is, of the harmonic of order ℎ=1;k) the value of the supply factor of each phase (^^^%) is obtained by means of the expression

[0037] :100

[0037] , where: -^^^% is the supply factor of each phase, which measures the percentage value of the maximum admissible current and the power supply in each phase in relation to what the transformer would have operating with linear loads, without harmonics, -^^^ is the overheating factor of each phase ^, expressed as a percentage;l) the value of the supply factor of the transformer (^^^%) is obtained by means of the expression

[0038] : where: -^^^% is the transformer supply factor, which determines the maximum percentage availability of power supply in relation to that which the transformer would have operating with linear loads, -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^ is the supply factor of each phase ^, expressed as a percentage; m) the value of the loss factor of each harmonic (^^^%) is obtained by means of the expression

[0039] : 100

[0039] , in which: -^^^% is the loss factor of each harmonic, which defines the percentage importance of each current harmonic in the load losses of the transformer at the fundamental frequency, -^^^,^ are the load losses of the harmonic of order ℎ, - ^^^,^ are the load losses of the fundamental harmonic, that is, the harmonic of order ℎ=1. According to a third aspect, the present invention also provides a device for monitoring the operating status of a three-phase transformer in service, based on the use of short-circuit resistors of the first aspect of the invention. The device makes it possible to carry out the method of the second aspect of the invention. The device comprises: - a physical system for measuring and acquiring electrical signals; - a processor system; and - a measurement program, responsible for obtaining the value of one or more electrical magnitudes of the transformer to be monitored when it supplies loads.In this document, the word "comprises" and its variants are to be interpreted as open-ended expressions that are not intended to exclude the possibility of other technical features or components in addition to those explicitly recited. In addition, the word "comprises" includes the case "consists of", being interpreted as a closed-ended expression that is limited only to the technical features or components explicitly recited. For those skilled in the art, other objects, advantages and characteristics of the invention will be apparent in part from the description and in part from the practice of the invention. In addition, the present invention covers all possible combinations of embodiments indicated herein.BRIEF DESCRIPTION OF THE DRAWINGS The present invention will be better understood with reference to the following figures, where the following has been represented for illustrative and non-limiting purposes: Figure 1 schematically represents the equivalent single-phase circuit, referred to the primary, for the operation of three-phase transformers, on which the technology proposed by L. Sima et. al. and IEEE Standard C57.110 is based. Figure 2 schematically represents the equivalent circuit, referred to the secondary, for the operation of three-phase transformers on which the technology of the present invention is based.Figure 3 is a diagram showing the operational sequence of a method for calculating the different effective short-circuit resistances, load losses and monitoring factors of three-phase transformers in service, according to a preferred embodiment of the present invention, applicable to measuring and monitoring instruments for three-phase transformers. Figure 4 is a diagram representing a device for measuring the short-circuit resistances and load losses of three-phase transformers with several sensors installed in the electrical network, according to a preferred embodiment of the present invention.Figure 5 is a diagram showing the programming modules for measuring, in each phase, the effective short-circuit resistances, the load losses, the superheating coefficients, and the supply factors of three-phase transformers, according to a preferred embodiment of the present invention. Figure 6 is a diagram showing the programming modules for measuring the short-circuit resistances, the load losses, and the loss factor of each current harmonic of three-phase transformers, according to a preferred embodiment of the present invention. Figure 7 shows a possible configuration of the short-circuit resistance and load losses screen of distribution transformers shown on a display means of the monitoring device, according to a preferred embodiment of the present invention.Figure 8 represents a possible configuration of the display of the monitoring factors for the operation of distribution transformers shown on a display means of the monitoring device, according to a preferred embodiment of the present invention. MODES OF EMBODIMENT OF THE INVENTION The limitations of the short-circuit resistance developed by L. Sima et. al. have been overcome by the inventors of the present invention by developing expressions for the effective short-circuit resistances referred to the secondary of the transformer, based on an adequate use of IEEE Standard C57.110-2018. To this end: Firstly, expressions for the load losses of three-phase transformers with non-linear loads, which are of general application, have been established. These expressions have been obtained by adapting equation [3], included in IEEE Standard C57.110, to the usual case where the currents are different in the three phases of the transformer. As a result, the expression [6] for the total load losses of the transformer as a function of the secondary currents has been developed, as follows: where ^^^ is the effective value of the current harmonic of order ℎ^ = ^^^ / ^^ present in phase ^ =^, ^, ^ of the transformer secondary, ^^^ is the nominal value of the secondary current, and ^^^^ = ^^^^^, ^^^^ = ^^^^^ and ^^^^^ = ^^^^^^ are the nominal load losses defined in IEEE Standard C57.110. The use of secondary currents instead of primary currents, included in equation [3] and used by L. Sima et. al., is justified by the fact that the installation work of measuring instruments is simpler in the secondary than in the primary. Another advantage of equation [6], compared to [3], is the possibility of knowing the load losses dissipated in each phase (^ = ^, ^, ^) of the transformer: The effective resistances referred to each phase of the transformer secondary are then defined (^ ^^,^ ) as those that give rise to load losses ^ ^^,^when the currents of these phases circulate through them, that is: The comparison of equations [7] and [8] determines the expression of the effective short-circuit resistances referred to each phase of the transformer secondary, which constitutes a novelty of the present invention: where, are the nominal short-circuit resistances referred to the secondary of the transformer in the direct current test (^ ^^^ ), as well as by Skin effect (^ ^^^ ) and by electromagnetic induction in the metallic parts of the transformer (^ ^^^^ ), operating at industrial frequency (50–60 Hz). The values ​​for the nominal losses ^^^^, ^^^^ and ^^^^^ in the equations above can be provided by the transformer manufacturers. However, if these values ​​are not available, ^ ^^^can be obtained by measuring the losses in the transformer windings in direct current. On the other hand, the nominal load losses of the transformer (^^^^ = ^^^^ + ^^^^ + ^^^^^) can be determined by performing a short circuit test at industrial frequency (50 − 60 ^^), from which the sum of the other two losses verifies that: ^^^^ = ^^^^ + ^^^^^ = ^^^^ − ^^^^ . Finally, the values ​​of ^^^^ and ^^^^^can be obtained separately by applying IEEE Standard C57.12.90, which states that in oil-immersed transformers ^^^^ = 2 / 3 ∙ ^^^^ and in dry-type transformers ^^^^ = 1 / 3 ∙ ^^^^. If it is desired to avoid carrying out the direct current test, the approximation ^^^^ ≈ 0.08 ÷ 0.1 ∙ ^^^^ usually provides values ​​of the three nominal losses (^^^^ , ^^^^ , ^^^^^) quite close to the real ones. In order to simplify the programming of calculation software, another expression of the effective short-circuit resistances referred to each phase of the secondary of three-phase transformers, developed by the inventors, is the following: ^^^,^ = ^^^^ + ^^^^ ∙ ^ ^^^^ + ^^^^^ ∙ ^ ^^^^ = ^^^^ + ^^^,^ + ^^^^,^

[0011] , where, are the loss factors of each phase of the transformer, also established by the inventors and which constitute another novelty of the present invention. These loss factors usually have different values ​​in each phase and are not the same as those included in IEEE Standard C57.110, whose values ​​are referred to the entire transformer. Likewise, the expressions of the components of the effective short-circuit resistances of each phase referred to the secondary ^^^,^ = ^^^^ ∙ ^ ^^^^ ^^^^,^ = ^^^^^ ∙ ^^ ^ ^ ^

[0013] , included in the expression

[0011] , constitute another novelty developed in the present invention. Based on the expressions [9] and

[0011] it is possible to deduce that the effective short-circuit resistances can have different values ​​in each phase, because their components ^ ^^,^ and ^ ^^^,^ depend on the effective values ​​(^ ^^ ) and frequencies (ℎ ^) of the harmonics of the currents of each phase, as shown in expression

[0013] . Additionally, the inventors of the present invention have developed expressions for the short-circuit resistances of each harmonic reduced to the secondary (^ ^^,^ ). These resistances determine the value of the load losses of each phase of the transformer according to the following expression: Comparing this last expression with [7], the expression of the short circuit resistances of each harmonic of order ℎ^, of phase ^ = ^, ^, ^, reduced to the secondary of the transformer is obtained as follows: ^^^,^ = ^^^^ + ^^^^ ∙ ℎ^^ + ^^^^^ ∙ ℎ^ ^.^

[0015] . The short-circuit resistances expressed by

[0015] are another novelty of the present invention. It is observed in

[0015] that the values ​​of ^^^,^, unlike what happens with ^^^,^, only depend on the frequency of the harmonic (ℎ ^), but not of the effective value of the currents of each phase. Furthermore, since the currents of distribution networks usually have the same harmonics in the three phases, it is concluded that the short-circuit resistances of each harmonic of order ℎ ^ have the same values ​​in the three phases and, therefore, the short-circuit resistances of each harmonic (^ ^^,^ ) are characteristic parameters of each transformer. Among all the short-circuit resistances of each harmonic, the one corresponding to the fundamental frequency (50 − 60 ^^, ℎ = 1) stands out,^^^,^ = ^^^^ + ^^^^ + ^^^^^ = ^^^^

[0016] . This resistance is independent of the frequency and its value coincides with that of the nominal short-circuit resistance ^ ^^^, obtained with equation [2], after performing the nominal short-circuit test of the transformer, at industrial frequency. Equating equations [8] and

[0014] , the value of the effective short-circuit resistances of each phase is obtained (^ = ^, ^, ^) as a function of the short-circuit resistances of the current harmonics (^ ^^ ) of that phase: All the short-circuit resistances expressed previously are referred to the secondary of distribution transformers, since the values ​​of the quantities necessary for their calculation are more easily obtained by measuring in the secondary than in the primary. However, it is possible to determine the values ​​of these short-circuit resistances referred to the primary simply by multiplying the previous expressions by the square of the transformer transformation ratio (^^ = ^^ / ^^^), calculated by the quotient between the effective values ​​of the primary voltage (^ ^) and the secondary voltage in no-load condition (^ ^^ ). In order to know the state of the three-phase distribution transformers in service, the following operating factors are proposed in the present invention, which are defined using their short-circuit resistances: ^Overheating factor (^^^): defines the increase in losses in each phase (^ = ^, ^, ^) in relation to the losses that would occur in the transformer operating without non-linear loads, [ 18 ] . ^Supply factor of each phase (^^^%): measures the percentage value of the maximum admissible current and the power supply in each phase in relation to what the transformer would have operating with linear loads, without harmonics, ^ ^ % = ^^,^^^ ∙ 1001 ^ ^100 = ∙ 100 ^ ^^^ ^ ^ Transformer Supply Factor (^^^%): Determines the maximum percentage availability of power supply (^ ^^^) in relation to what the transformer would have operating with linear loads (^ ^ ), 100

[0020] . ^Loss factor of each harmonic (^^^%): defines the percentage importance of each current harmonic in the load losses of the transformer at the fundamental frequency, 100

[0021] . where ^ = the effective value of the current harmonics of order ℎ = ^^ of the three phases of the transformer and the effective value of the three of fundamental frequency (^^ = 50 − 60 ^^). Figure 2 represents the equivalent circuit of a three-phase transformer operating with non-linear loads. It differs from the transformer model proposed by L. Sima et. al., shown in Figure 1, which is based on the direct application of IEEE Standard C57.110, in that the short-circuit resistances have different values ​​in each phase. This fact is important for monitoring the operating status of the transformer, since it indicates that the losses and, therefore, also the temperature and heating in each of its phases may be different, not only because the circulating currents are different, but also because the resistances of its windings are different, due to the Skin or film phenomena and electromagnetic induction.The meaning of the symbols shown in Figure 1 is given below:- ^^^ are the short-circuit resistances of each phase of the direct current windings referred to the primary of the transformer.- ^^^ are the short-circuit resistances referred to the primary of L. Sima et. al. due to the Skin effect of each phase.- ^^^ are the short-circuit resistances referred to the primary of L. Sima et. al.corresponding to the electromagnetic induction phenomenon of each phase.- ^^^,^ are the short-circuit reactances of each phase referred to the primary of the transformer.- ^^ are the core loss resistances.- ^^^ are the magnetizing reactances, which characterize the common magnetic flux of the transformer.- r^ is the transformer transformation ratio.- I^ is the no-load current referred to the primary.- The subscripts “p” and “s” denote magnitudes (voltages and currents) of the primary and secondary, respectively: V. ^is the voltage of each phase of the primary; V ^ is the voltage of each phase of the secondary; I ^ is the current of each phase of the primary; I ^is the current of each phase of the secondary. The meaning of the symbols that appear in figure 2 is included below: - ^^^,^, ^^^,^, ^^^,^, denote the short-circuit resistances of phases R, S and T referred to the secondary of the transformer. - ^^^ are the short-circuit reactances referred to the secondary. - ^^ are the core loss resistances referred to the secondary. - ^^ are the magnetizing reactances referred to the secondary. - r^ is the transformation ratio of the transformer. - The subscripts “1” and “2” refer to magnitudes of phases R, S and T of the primary and the secondary, respectively: V^^, V^^ and V^^ are the voltages of phases R, S and T of the primary, respectively; I^^, I^^ and I^^ are the currents of phases R, S and T of the primary, respectively; V^^, V^^ and V^^ are the voltages of the R, S and T phases of the secondary, respectively; I^^, I^^ and I^^ are the currents of the R, S and T phases of the secondary, respectively.- I^^, I^^, I^^ denote the open-circuit currents of phases R, S and T of the transformer referred to the secondary. According to a preferred embodiment of the invention, the effective short-circuit resistances of each phase (^ = ^, ^, ^) of the transformer,. They are those that originate the load losses caused by the circulation of currents through each phase of the windings, namely This last expression is not included in the text of IEEE Standard C57.110, which only proposes expressions for the total load losses, nor is it known in the technical literature. Substituting equation

[0023] into

[0022] determines the expressions for the short-circuit resistances of each phase developed in the present invention: or also, in a simplified form for implementation in calculation and monitoring software, ^^^,^ = ^^^^ + ^^^^ ∙ ^ ^^^^ + ^^^^^ ∙ ^^ ^ ^ ^

[0025] , where ^ ^^^ ^ ^ ^ ^^^^ = ^ ^^ ^^^^ 3^ ^ ^^^ = ^ ^ ^^^^ = ^ 26 , ^^ 3^ ^^ 3^ ^^ [ ] are the nominal short-circuit resistances reduced to the secondary in direct current (^ ^^^ ), as well as by Skin effect (^ ^^^ ) and by electromagnetic induction in the metallic parts of the transformer (^^^^^), defined at the industrial frequency (50 – 60 Hz), and are the loss factors for each phase (^ = ^, ^, ^) due to the Skin effect and electromagnetic induction in the metallic parts of the transformer, respectively. These factors differ from those included in IEEE Standard C57.110 in that they are defined for each phase and not for the entire transformer. The values ​​for the nominal losses ^ ^^^ , ^ ^^^ and ^ ^^^^, necessary to calculate the three components of the short-circuit resistances at industrial frequency (^^^^ , ^^^^ , ^^^^^) in equations

[0026] , are usually provided by the transformer manufacturers. However, if these values ​​are not available, the present invention proposes a method for calculating these resistances which is a combination of the inventors' own experience, the performance of tests and the use of existing regulations. This method comprises: I) Obtaining the values ​​of the losses of the windings in direct current (^ ^^^) by carrying out a DC transformer test. II) Measurement of the total nominal load losses (^^^^) by carrying out a short-circuit test at industrial frequency (50 − 60 ^^). III) Application of IEEE Standard C57.90 to calculate the individual values ​​of ^^^^ and ^^^^^, which establishes: ^^^^ = 2 / 3 ∙ ^^^^ and ^^^^^ = 1 / 3 ∙ ^^^^, in oil-immersed transformers, and ^^^^ = 1 / 3 ∙ ^^^^ and ^^^^^ = 2 / 3 ∙ ^^^^, in dry-type transformers. In this aspect of the invention, additionally, the calculation of the components of the effective short-circuit resistances referred to each phase of the secondary for the Skin phenomena (^ ^^,^ ) and electromagnetic induction (^ ^^^,^ ), as follows: ^^^,^ = ^^^^ ∙ ^ ^^^^ [28.1] ^^^^,^ = ^^^^^ ∙ ^^ ^ ^ ^ [28.2]. Alternatively, the short-circuit resistances of each phase (^ ^^,^) can be determined based on the short-circuit resistances of the harmonics of that phase (^ ^^,^ ) according to the following expression: It is also proposed to use the following expressions for the calculation of the load losses in each phase (^ = ^, ^, ^) of the transformer, and for calculating the total load losses of the transformer. According to a second preferred embodiment of the invention, the short-circuit resistances for each harmonic (ℎ) are obtained. ^ ) of the secondary currents (^ ^^,^ ) as follows: These resistances depend only on the harmonic frequency and, in practice, are the same in all three phases of the transformer. The present invention uses the short-circuit resistances of each harmonic to calculate the load losses caused by each current harmonic as follows: ^^^,^ = ^^^,^ ∙ ^ ^^ ^ ^ [ 33 ], ^^^,^,^ as well as the load losses of each phase: and the total load losses of the transformer, according to the following expression: According to a third preferred embodiment of the invention, the following factors are proposed for the evaluation and monitoring of the operating status of distribution transformers: ^The superheating factor of each phase (^^^), for monitoring the increase in losses (i.e. heating) in each phase (^ = ^, ^, ^) in relation to the losses that would occur in the transformer operating without harmonics, where ^^^,^ = ^^^^ is the value obtained in

[0032] with ℎ^ = 1 (fundamental frequency, 50 − 60 ^^).^ The supply factor of each phase (^^^%), ^^ ^ ^^^ 1 ^ % = ^ [ ^∙ 100 = ∙ 100 37], ^^,^ ^^^ ^to monitor the reduction in the maximum allowable current and power supply in each phase relative to what the transformer would have operating without harmonics. ^The transformer supply factor (^^^%), It allows monitoring the decrease in the maximum power available for supply by the transformer operating with current harmonics. ^The loss factor of each harmonic (^^^%), ^^^% ∙ 100

[0039] , to determine the harmonics that cause the greatest load losses in relation to the transformer losses at the fundamental frequency and which are therefore most dangerous for the proper functioning of the transformer. Simply to illustrate the advantages of the present invention over other known technologies (L. Sima et. al. and industrial practice), a comparative table is included below showing, in summary, the values ​​of the effective short-circuit resistances of each phase (^^^,^ , ^^^,^, ^^^,^) according to the present invention and the short-circuit resistance of L. Sima et. al. reduced to the secondary (^ ^ ^ = ^^ / ^^ ^) recorded every hour, throughout a day, as well as some of the operating factors of the 630 kVA, Dyn11, three-phase transformer, immersed in oil, with transformation ratio ^^ = 57.143 and short-circuit resistance at industrial frequency ^^^^ = ^^^,^ = 2.889 ^Ω, which supplies a real distribution network with non-sinusoidal currents. Also included in that table are the supply factors per phase (^^^%) and of the transformer (^^^%) calculated according to expressions

[0037] and

[0038] of the present invention, respectively. In view of the table, the following can be deduced: -The effective short-circuit resistances referred to each phase of the secondary (^^^,^ , ^^^,^, ^^^,^) obtained according to the technology of the present invention have different values ​​in each phase and, in general, these values ​​are different from those of the short-circuit resistances referred to the secondary of L. Sima et. al. (^ ^ ^ = ^^ / ^^ ^) and the nominal short-circuit resistance (^ ^^^ ), calculated at the fundamental frequency, whose values ​​are equal in all three phases of the transformer. -The greater the differences between the above short-circuit resistances,the greater the differences in the losses calculated with them. This fact is noted from the values ​​of the supply factors in the table above. The supply factors are lower (and therefore the load losses are greater) the greater the difference between the effective short-circuit resistances of each phase (^^^,^ , ^^^,^, ^^^,^) of the present invention and the short-circuit resistance at the fundamental frequency (^ ^^^). A value of 80% for the supply factor of a phase means that the current supply capacity (and therefore also the power supply capacity) in that phase has been reduced to 80% of what it would be without harmonics. Based on the inventors' own experience, a supply factor below 75% poses significant risks to the proper functioning and useful life of the transformer, due to overheating caused by the excessive increase in losses. The operational sequence of an application example according to a preferred embodiment of the present invention is explained below, based on Figure 3.This implementation focuses on measuring one or more of the following quantities of the three-phase distribution transformer being monitored: the effective short-circuit resistances of each phase, the short-circuit resistances of each current harmonic, the load losses of each harmonic, of each phase and total of the transformer, as well as the transformer monitoring factors. The procedure shown in Figure 3 comprises the following actions: I) Acquisition of electrical signals (1 in Figure 3): Samples of the secondary currents of the distribution transformer being monitored are acquired, and said signals are stored.II) Signal analysis (2 in figure 3):After acquiring the current signals (in 1 of figure 3), the corresponding effective value matrices of these electrical quantities (^^ , ^^, ^^) and their harmonic components (^^^ , ^^^, ^^^) are obtained (in 2 of figure 3), preferably by Fourier Series.III) Calculation of the loss factors of each phase of the transformer (3 in figure 3):From the matrices obtained in the previous action (2 in figure 3), the values ​​of the loss factors of each phase (^ = ^, ^, ^) of the transformer are obtained (in 3 of figure 3) according to equations

[0027] . IV) Calculation of the components of the nominal short-circuit resistances referred to the secondary of the transformer (^^^^ , ^^^^ , ^^^^^): From the nominal losses and currents of the transformer (^^^^ , ^^^^ , ^^^^^ , ^^^) provided (in 4 according to figure 3), the nominal short-circuit resistances are obtained (in 5 according to figure 3), using the expressions

[0026] ^ ^ ^^^ ^ ^^^ ^ ^^ ^^^ = ^ = ^ = ^^ 3^ ^ ^^^ 3 ^ ^^^^ ^ [ 26 ] . ^^ ^ ^^ 3^ ^^V) Calculation of the short-circuit resistances of each harmonic (6 in figure 3): From the values ​​of the components of the nominal short-circuit resistances of the transformer (obtained at 5 according to figure 3, using expressions

[0026] ), the values ​​of the short-circuit resistances of each harmonic of the secondary current are obtained (at 6 according to figure 3), of order ℎ = ^^ / ^^, using the expression

[0032] ^^^,^ = ^ ^^^^ + ^^^^ ∙ ℎ^ + ^^^^^ ∙ ℎ^ ^.^ [ 32 ] .VI) Calculation of the effective short-circuit resistances of each phase (7 in figure 3): From the values ​​of the components of the nominal short-circuit resistances (obtained at 5 according to figure 3) and the supply factors of each phase (determined at 3 according to figure 3, using expressions

[0027] ), the values ​​of the effective short-circuit resistances referred to the secondary phases (^^^,^, ^ = ^, ^, ^) are obtained (at 7 according to figure 3) using expressions

[0025] ^^^,^ = ^^^^ + ^^^^ ∙ ^ ^^^^ + ^^^^^ ∙ ^^ ^ ^ ^

[0025] , as well as the value of its components due to the Skin effect (^ ^^,^ ) and the phenomenon of electromagnetic induction (^ ^^^,^ ), according to expressions [28.1] and [28.2], respectively: ^^^,^ = ^^^^ ∙ ^ ^^^^ [28.1] ^^^^,^ = ^^^^^ ∙ ^^ ^ ^ ^ [ 28.2 ]. Alternatively, the effective short-circuit resistances of each phase can be calculated (at 7 according to Figure 3) from the short-circuit resistances of the harmonics of that phase (obtained at 6 according to Figure 3) by means of the expression

[0029] : VII) Calculation of the load losses of each phase (8 in figure 3): From the values ​​of the effective short-circuit resistances referred to each phase of the transformer secondary (obtained at 7 according to figure 3) and the effective values ​​of the harmonics of the currents of each phase (obtained at 2 in figure 3), the load losses of each phase are obtained (at 8 according to figure 3) (^ ^^,^ ), using the expression

[0030] Alternatively, these losses can also be calculated from the values ​​of the short-circuit resistances of each secondary current harmonic, ^ ^^,^, (obtained in 6 according to figure 3) and the effective values ​​of the harmonics of the currents of each phase, ^ ^^ (obtained in 2 in figure 3), using the expression

[0034] VIII) Calculation of the load losses of each harmonic (9 in figure 3):From the values ​​of the short-circuit resistances of each harmonic of the currents of each phase of the secondary, ^ ^^,^ , (obtained in 6 according to figure 3 using the expression

[0032] ) and the effective values ​​of the harmonics of the currents of each phase, ^ ^^ (obtained at 2 in figure 3), the load losses of each harmonic are obtained (at 9 according to figure 3) (^ ^^,^ ), by means of the expression

[0033] ^^^,^ = ^^^,^ ∙ ^ ^^ ^ ^

[0033] . ^^^,^,^IX) Calculation of the total load losses of the transformer (10 in figure 3):From the values ​​of the load losses of each phase ^ ^^,^(obtained at 8 according to figure 3, using expressions

[0030] or

[0034] ), the values ​​of the total load losses of the transformer are obtained (at 10 according to figure 3), using expression

[0031] Alternatively, the values ​​of the total load losses of the transformer (^ ^^ ) can be obtained (in 10 according to figure 3), from the values ​​of the load losses of each harmonic ^ ^^,^ (obtained in 9 according to figure 3), using the expression

[0035] ^^,^^^ ^^^ = ^ ^^^,^

[0035] . ^ ^ ^^X) Calculation of the superheating factor of each phase (11 in figure 3): From the effective short-circuit resistances of each phase (obtained at 7 according to figure 3 using expression

[0025] or

[0029] ) and the short-circuit resistance at the fundamental frequency (obtained at 6 according to figure 3 using expression

[0032] ), the superheating factors of each phase are obtained (at 11 according to figure 3) using expressions

[0036] XI) Calculation of the supply factor of each phase (12 in figure 3): From the superheating coefficients of each phase (obtained at 11 according to figure 3 using expressions

[0036] ), the supply factors of each phase are obtained (at 12 according to figure 3) using expressions

[0037] 100

[0037] . XII) Calculation of the transformer supply factor (13 in Figure 3):From the supply factors of each phase (obtained at 12 according to Figure 3 using expressions

[0037] ), the supply factors of each phase are obtained (at 13 according to Figure 3) using expression

[0038] ∙ 100

[0038] .XIII) Calculation of the loss factors of each harmonic (14 in Figure 3):From the load losses of the harmonic of order ℎ and the fundamental harmonic, ℎ =1, (obtained at 9 according to Figure 3 using expression

[0033] ), the loss factors of each harmonic are obtained (at 14 according to Figure 3) using expression

[0039] 100

[0039] . XIV) Display (15 in Figure 3): The values ​​of the magnitude or magnitudes obtained according to the method (effective short-circuit resistances and losses in each phase, short-circuit resistances and losses of each harmonic, total load losses, superheating factor and supply factor of each phase, transformer supply factor and loss factor of each harmonic) are shown on a display means. According to another aspect, the present invention also provides a device (A) for monitoring the operating status of a three-phase distribution transformer based on the use of the effective short-circuit resistances of each phase and the short-circuit resistances of each harmonic, described above.Likewise, the device (A) allows the procedure described above to be carried out; specifically, by means of the device (A) of the present invention it is possible to obtain several of the magnitudes and parameters for monitoring the distribution transformer, such as, for example, effective values ​​of the phase currents and their harmonic components, the loss factors of each phase, the short-circuit resistances and the load losses corresponding to each phase and each harmonic, the total load losses of the transformer, as well as the monitoring factors. As shown in Figure 4, the device (A) of the present invention is a measuring device that comprises: a physical system for measuring and acquiring electrical signals (C); a processor system (D); and a measuring program (E), responsible for obtaining the value of one or more electrical magnitudes of the transformer (G) to be monitored when it supplies loads (H).The device (A) of the present invention also comprises a display means (F), preferably a screen, where the value of the electrical magnitudes and the monitoring parameters obtained are displayed, which allow monitoring the operation of the distribution transformer. According to a preferred embodiment, the physical system for measuring and acquiring electrical signals (C) comprises: current measurement sensors (B); signal conditioners; and a data acquisition card. The signal conditioners are responsible for adapting instantaneous values ​​of the currents obtained by means of the current measurement sensors (B), such that the voltages at the outputs of the signal conditioners are applicable to the analog inputs of the data acquisition card.The data acquisition card converts the analog voltage and current signals into a series of discrete samples, which are used as inputs to the measurement program (E). Preferably, the physical system for measuring and acquiring electrical signals (C) is arranged on the secondary lines of the transformer as shown in Figure 4, so that it can acquire signals from the secondary line currents. of the distribution transformer. According to one option, the nominal values ​​of the load losses and the secondary currents of the transformer are entered into the physical system for measuring and acquiring electrical signals (C) and stored, for later use depending on the magnitudes and parameters to be obtained. According to a preferred embodiment, the processing system (D) is connected to a motherboard, to which the data acquisition card is also connected, which allows the discrete samples of the voltage and current signals to be exchanged with the measurement program (E).According to a preferred embodiment, the measurement program (E) comprises the following modules (shown in Figures 5 and 6): a data input and acquisition module (E12); a Fourier analysis module (E13); a loss factor module for each phase (E14); a nominal short-circuit resistance module (E15); a short-circuit resistance module for each harmonic (E16); a short-circuit effective resistance module for each phase (E17); a load loss module (E18); a transformer supply factor module (E19); a harmonic loss factor module (E20); and a display module (E21). The data input and acquisition module (E12) is responsible for receiving current samples and storing them in a vector for each of them.The Fourier analysis module (E13) is responsible for obtaining, from the samples received in the data input and acquisition module (E12), the effective values ​​of the harmonic components of said current samples, obtained by Fourier Series. The loss factors module for each phase (E14) is responsible for obtaining the loss factors due to the Skin effect and the electromagnetic induction phenomena in each of the transformer phases (^. ^ ^^^ , ^^ ^ ^ ^), from the information obtained in the Fourier analysis module (E13), according to expressions

[0027] . The nominal short-circuit resistance module (E15) is responsible for obtaining the values ​​of the components of the nominal short-circuit resistances (^^^^ , ^^^^ , ^^^^^) based on the entered values ​​of the nominal losses and currents of the transformer (^^^^ , ^^^^ , ^^^^^ , ^^^) according to expressions

[0026] . The short-circuit resistance module for each harmonic (E16) is responsible for obtaining the values ​​of the short-circuit resistances for each of the frequencies of the current harmonics of each phase (^ ^^,^ ), according to the expressions

[0032] . The module of effective short-circuit resistances of each phase (E17) is responsible for obtaining the values ​​of the effective short-circuit resistances of each phase of the transformer (^ ^^,^), according to expression

[0025] , and its components (^^^,^ , ^^^^,^), according to expressions [28.1] and [28.2]. Alternatively, the effective short-circuit resistances of each phase of the transformer (^ ^^,^ ) can be calculated based on the short-circuit resistances of the harmonics (^ ^^,^ ), according to the expression

[0029] . The load loss module (E18) is responsible for obtaining the load loss values ​​of each phase (^ ^^,^ ), according to the expression

[0030] , the total load losses of each harmonic (^ ^^,^ ), according to expression

[0033] , and the total load losses of the transformer (^ ^^ ), according to expression

[0031] . Alternatively, the losses in each phase can be calculated, based on the short-circuit resistances of the harmonics (^ ^^,^), according to expression

[0034] and the total load losses of the transformer can be obtained according to expression

[0035] . The transformer supply factor module (E19) is responsible for obtaining the values ​​of the superheating factor of each phase (^^ ^ ), according to the expression

[0036] , of the supply factor of each phase (^^ ^ %), according to expression

[0037] , and the transformer supply factor (^^^%), according to expression

[0038] . The harmonic loss factor module (E20) is responsible for obtaining the values ​​of the loss factors for each harmonic of the currents (^^ ^%), according to expression

[0039] . The display module (E21) is responsible for displaying on the display means (F) the information of one or more magnitudes of the distribution transformer obtained by the device (A). In a first preferred embodiment, one or more electrical magnitudes are displayed selected from the group comprising: the effective short-circuit resistances of each phase, the short-circuit resistance of the selected harmonic of order ℎ, the load losses of each phase, the total load losses of the transformer and the load losses of the selected harmonic, as shown on a first screen of the display means (F), in Figure 7.Likewise, in another preferred embodiment, the display means (F) shows on a second screen, represented in Figure 8, the following parameters for monitoring the transformer: the superheating factor of each phase, the supply factor of each phase, the supply factor of the transformer and the loss factor of the harmonic of order ℎ selected. According to a preferred embodiment shown in Figures 5 and 6, the measurement program (E) comprises the modules E12 - E21 mentioned above.More specifically, Figure 5 shows the modules of the measurement program (E) configured to intervene in the measurement and display of the effective short-circuit resistances of each phase and the load losses and the monitoring factors of the transformer obtained with these resistances (specifically, modules E12 - E19 and E21); and Figure 6 shows the modules of the measurement program (E) configured to intervene in the measurement and display of the short-circuit resistances of the harmonics, the load losses of each harmonic and the loss factor of each harmonic (specifically, modules E12, E13, E15, E16, E18, E20 and E21). Although the present invention has been described with reference to particular options and embodiments thereof, those skilled in the art may make modifications and variations to the previous teachings without departing from the scope and spirit of the present invention.

Claims

CLAIMS 1- Use of short-circuit resistors for monitoring the operating status of a three-phase transformer in service, characterized in that said resistors are effective short-circuit resistances referred to the secondary of the three-phase transformer, with the particularity that the effective short-circuit resistance referred to a phase ^ of the secondary (^ ^^,^ ) is that which gives rise to load losses dissipated in phase ^ (^ ^^,^ ) when a current flows through phase ^, as reflected in the following expression: where: -^ generally denotes any phase of the transformer secondary, - ^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer, - ^^^,^ are the load losses dissipated in phase ^, - ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in phase ^used in the calculation, -^^^ is the effective value of the current harmonic of order ℎ^.2- Use of short-circuit resistors according to claim 1, with the particularity that the load losses dissipated in phase ^ (^^^,^) encompass several types of losses according to the following expression: in which: -^^^^ are nominal load losses in direct current, - ^^^^ are nominal load losses due to the Skin effect, - ^^^^^ are nominal load losses caused by the electromagnetic induction phenomenon, -^^^ is the nominal value of the current of the secondary of the transformer. 3- Use of short-circuit resistances according to any of the preceding claims, with the particularity that the effective short-circuit resistances are expressed with reference to the primary of the transformer by multiplying the effective short-circuit resistances referred to the secondary (^^^,^) by the square of a transformation ratio of the transformer ^^ = ^ ^ / ^ ^^, in which: -^^ is the effective value of the primary voltage, and- ^^^ is the effective value of the secondary voltage in no-load.4- Use of short-circuit resistances according to any of the preceding claims, with the particularity that the effective short-circuit resistances referred to the secondary of the transformer (^ ^^,^ ) are related to the short-circuit resistances of the current harmonics referred to the secondary of the transformer (^ ^^,^ ), according to the following expression: [29]. 5- Use of short-circuit resistors according to claim 4, with the particularity that the short-circuit resistors of current harmonics referred to the secondary of the transformer (^ ^^,^ ) are related to the nominal short-circuit resistances of the transformer according to the following expression: in which: -^^^^ is a nominal short-circuit resistance referred to the secondary in direct current, -^^^^ is a nominal short-circuit resistance referred to the secondary by Skin effect, - ^^^^^ is a nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer. 6- Use of short-circuit resistances according to any of claims 4 or 5, with the particularity that the short-circuit resistances of current harmonics are expressed with reference to the primary by multiplying the short-circuit resistances of current harmonics referred to the secondary of the transformer (^^^,^) by the square of a transformation ratio of the transformer ^^ = ^^ / ^^^, in which: - ^^ is the effective value of the primary voltage, and - ^^^ is the effective value of the secondary voltage in no-load.7- Procedure for monitoring the operating status of a three-phase transformer in service, based on the use of short-circuit resistors described in any of claims 1 to 6, characterized in that it comprises obtaining, by means of a monitoring device, the value of at least one magnitude of the transformer selected from. group comprising: harmonic short-circuit resistances referred to the secondary of the transformer (^^^,^), harmonic short-circuit resistances referred to the primary of the transformer, effective short-circuit resistances referred to the secondary of the transformer (^^^,^), component of said effective short-circuit resistances due to the Skin effect (^ ^^,^ ), component of said effective short-circuit resistances due to the phenomenon of electromagnetic induction (^ ^^^,^), effective short-circuit resistances referred to the transformer primary, load losses of each phase of the transformer secondary (^ ^^,^ ), load losses of each harmonic (^ ^^,^ ), total pressure losses (^ ^^ ), superheating factor of each phase (^^^), supply factor of each phase (^^^%), transformer supply factor (^^^%), loss factor of each harmonic (^^ ^ %), according to the particularities of the following sections: a) the value of the short-circuit resistances of harmonics referred to the secondary of the transformer (^ ^^,^ ) is obtained by the expression [32]: where: -^^^,^ is the short-circuit resistance of a current harmonic referred to phase ^of the transformer secondary, -^ generally denotes any phase of the transformer secondary,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -^^^^, ^^^^ , ^^^^^ are a nominal short-circuit resistance referred to the secondary in direct current (^ ^^^ ), a nominal short-circuit resistance referred to the secondary by Skin effect (^ ^^^ ) and a nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer (^ ^^^^ ), respectively, which are obtained by the expressions [26] where: ^^^^^ are nominal DC load losses,^ ^^^^ are nominal Skin effect load losses,^ ^^^^^ are nominal load losses caused by the electromagnetic induction phenomenon, ^^^^ is the nominal value of the transformer secondary current; b) the value of the harmonic short-circuit resistances referred to the transformer primary is obtained by multiplying the current harmonics short-circuit resistances referred to the transformer secondary (^^^,^) by the square of a transformer transformation ratio ^^ = ^^ / ^^^, where:- ^^ is the effective value of the primary voltage, and- ^^^ is the effective value of the open-loop secondary voltage; c) the value of the effective short-circuit resistances referred to the transformer secondary (^ ^^,^ ) is obtained by one of the following options: c1) by the expression [25]:^^^,^ = ^^^^ + ^^^^ ∙ ^ ^^^^ + ^^^^^ ∙ ^^ ^ ^^ [25], where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ^^^^, ^^^^ , ^^^^^ are a nominal short-circuit resistance referred to the secondary in direct current (^ ^^^ ), a nominal short-circuit resistance referred to the secondary by Skin effect (^ ^^^ ) and a nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer (^ ^^^^ ), respectively, which are obtained by the expressions [26] ^ ^ ^ ^ ^ ^^^ = ^^ ^ ^^^ ^^^^ ^^^ = ^ = [26], 3^ ^ 3^ ^ ^^^^ 3^ ^ ^ ^ ^^ ^^ where: ^^^^^ are nominal load losses in direct current,^ ^^^^ are nominal load losses due to the Skin effect,^ ^^^^^ are nominal load losses caused by the electromagnetic induction phenomenon, ^^^^ is the nominal value of the secondary current of the transformer;- ^ ^ ^^^ , ^ ^ ^^^ are a factor of phase losses ^ due to the skin effect (^^ ^ ^ ^ ), and a phase loss factor ^ due to electromagnetic induction in the metallic parts of the transformer respectively, which are obtained by means of the [27] in which: ^ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), ^ℎ^,^^^ is the order of the current harmonic of highest frequency present in the phase ^ used in the calculation,^ ^^^ is the effective value of the current harmonic of order ℎ^;c2) by means of the expression [29] where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ^^^,^ is the short-circuit resistance of a current harmonic referred to phase^ of the secondary of the transformer,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in phase ^ used in the calculation, - ^^^ is the effective value of the current harmonic of order ℎ^; d) the value of the component due to the Skin effect (^^^,^) of the effective short-circuit resistances of each phase referred to the secondary (^ ^^,^ ), is obtained by the expression [28.1] ^^^,^ = ^^^^ ∙ ^^ ^ ^ ^ [ 28.1 ] , where: -^^^^ are the nominal load losses due to the Skin effect, - ^^ ^ ^ ^is the loss factor of phase z due to the Skin effect; e) the value of the component due to the electromagnetic induction phenomenon (^^^^,^) of the effective short-circuit resistances of each phase referred to the secondary (^ ^^,^ ), is obtained by the expression [28.2] ^^^^,^ = ^^^^^ ∙ ^^ ^ ^ ^ [28.2], where: -^^^^^ is the nominal short-circuit resistance referred to the secondary by electromagnetic induction in the metallic parts of the transformer, - ^ ^^^^ is the loss factor of phase ^ due to electromagnetic induction in the metallic parts of the transformer; f) the value of the effective short-circuit resistances referred to the primary of the transformer is obtained by multiplying the effective short-circuit resistances referred to the secondary of the transformer (^^^,^) by the square of a transformation ratio of the transformer ^^ = ^^ / ^^^, in which: - ^^ is the effective value of the voltage of the primary, and - ^^^ is the effective value of the voltage of the secondary in no-load condition; g) the value of the load losses of each phase of the secondary of the transformer (^^^,^) is obtained by one of the following options: g1) by the expression [30] where: -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer,- ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in phase ^ used in the calculation, - ^^^ is the effective value of the current harmonic of order ℎ^;g2) by means of the expression [34] where: -ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in the phase ^ used in the calculation,- ^^^,^ is the short-circuit resistance of a current harmonic referred to the phase^ of the secondary of the transformer,- ^^^ is the effective value of the current harmonic of order ℎ^;h) the value of the load losses of each harmonic (^^^,^) is obtained by means of the expression[33]: ^^^,^ = ^^^,^ ∙ ^ ^^ ^ ^ [ 33 ] ,^^^,^,^ where: -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^ is the effective value of the current harmonic of order ℎ^, - ^^^,^ is the short-circuit resistance of a current harmonic referred to phase ^ of the transformer secondary;i) the value of the total load losses (^^^) is obtained by one of the following options: i1) by the expression [31]: in which: -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^,^ are the load losses of each phase of the transformer secondary; i2) by means of the expression [35]:^^,^^^ ^^^ = ^ ^^^,^[35], ^ ^ ^^where: -ℎ^ is the order of a current harmonic present in phase ^, said order being defined as the relationship between the frequency of the harmonic (^ ^ ), and the fundamental frequency (^ ^ ), -ℎ^,^^^ is the order of the current harmonic of highest frequency present in the phase ^ used in the calculation, - ^^^,^ are the load losses of each harmonic; j) the value of the superheating factor of each phase (^^^) is obtained by the expression [36]: where: -^^^ is the overheating factor, which defines the increase in losses in each phase ^ in relation to the losses that would occur in the transformer operating without non-linear loads, -^^^,^ is the effective short-circuit resistance referred to phase ^ of the transformer, - ^^^,^ is the short-circuit resistance of a harmonic (^^^,^) at the fundamental frequency, that is, of the harmonic of order ℎ=1;k) the value of the supply factor of each phase (^^^%) is obtained by means of the expression [37]: ^^^% = 1 ∙ 100 [37], ^ ^^ ^where:- ^^^% is the supply factor of each phase, which measures the percentage value of the maximum admissible current and the power supply in each phase in relation to those that the transformer would have operating with linear loads, without harmonics, -^^^ is the overheating factor of each phase ^, expressed as a percentage;l) the value of the supply factor of the transformer (^^^%) is obtained by means of the expression[38]: where -^^^% is the transformer supply factor, which determines the maximum percentage availability of power supply in relation to what the transformer would have operating with linear loads, -^ generally denotes any phase of the transformer secondary, - ^, ^, ^ specifically denote each of the three phases of the transformer secondary, respectively, -^^^ is the supply factor of each phase ^, expressed as a percentage; m) the value of the loss factor of each harmonic (^^^%) is obtained by means of the expression[39]: 1 00 [39], in which: -^^^% is the loss factor of each harmonic, which defines the percentage importance of each current harmonic in the load losses of the transformer at the fundamental frequency, -^^^,^ are the load losses of the harmonic of order ℎ, - ^^^,^ are the load losses of the fundamental harmonic, that is, the harmonic of order ℎ=1.8- Method according to claim 7, in which the value of the nominal losses ^^^^,^ ^^^ , ^ ^^^^is obtained by one of the following options: i) according to one option, the value of the nominal losses ^^^^, ^^^^, ^^^^^ is provided by the transformer manufacturer; ii) according to another option, the value of the nominal losses ^^^^, ^^^^, ^^^^^ is obtained by the following actions: - the value of ^^^^ is obtained by measuring the losses in the transformer windings by means of a direct current test; - the value of a total nominal load loss of the transformer (^^^^) is obtained by carrying out a short-circuit test; -the values of ^^^^ and ^^^^^ are obtained by means of the following expressions:^^^^ = 2 / 3 ∙ ^^^^ and ^^^^^ = 1 / 3 ∙ ^^^^, in the case of an oil-immersed transformer,and ^^^^ = 1 / 3 ∙ ^^^^ and ^^^^^ = 2 / 3 ∙ ^^^^, in the case of a dry-type transformer, in which ^^^^ = ^^^^ + ^^^^^ = ^^^^ − ^^^^;iii) according to another option, the value of the nominal losses ^^^^, ^^^^, ^^^^^ is obtained by the following actions: -the value of the total nominal load losses of the transformer (^^^^) is obtained by carrying out a short-circuit test; -the values of ^^^^ and ^^^^^ are obtained by the following expressions:^^^^ = 2 / 3 ∙ ^^^^ and ^^^^^ = 1 / 3 ∙ ^^^^, in the case of an oil-immersed transformer, and ^^^^ = 1 / 3 ∙ ^^^^ and ^^^^^ = 2 / 3 ∙ ^^^^, in the case of a dry-type transformer;- the value of ^^^^ is obtained from the following expression:^^^^ = ^^^^ + ^^^^^ = ^^^^ − ^^^^;with the particularity that the value of ^; ^^^ is assigned according to the following expression: ^ ^^^ ≈ 0.08 ÷ 0.1 ∙ ^^^^.9- Method according to any of claims 7 or 8, in which the effective value of the harmonics of the currents of each phase (^ ^^) are obtained from received transformer current samples by analyzing said samples by Fourier series.

10. Method according to any of claims 7 to 9, wherein the received transformer current samples are acquired by means of current measurement sensors.

11. Device (A) for monitoring the operating status of a three-phase transformer (G) in service, based on the use of short-circuit resistors described in any of claims 1 to 6, characterized in that it comprises: - a physical system for measuring and acquiring electrical signals (C); - a processor system (D); and - a measurement program (E), responsible for obtaining the value of one or more electrical magnitudes of the transformer (G) being monitored when it supplies loads (H).12- Device (A) according to claim 11, comprising a display means (F), preferably a screen, where the information of one or more of the electrical magnitudes of the transformer obtained is displayed.13- Device (A) according to any of claims 11 or 12, wherein the physical system for measuring and acquiring electrical signals (C) comprises: - current measuring sensors (B); - signal conditioners; and - a data acquisition card; with the particularity that the signal conditioners are responsible for adapting instantaneous values of the currents obtained by means of the current measuring sensors (B), such that the voltages at the outputs of the signal conditioners are applicable to the analog inputs of the data acquisition card; and the data acquisition card converts the analog voltage and current signals into a series of discrete samples, which are used as inputs of the measurement program (E).14- Device (A) according to claim 13, in which the processor system (D) is connected to a motherboard, to which the data acquisition card is also connected, which allows the discrete samples of the voltage and intensity signals to be exchanged with the measurement program (E).15- Device (A) according to any of claims 11 to 14, wherein the measurement program (E) comprises the following modules: - a data input and acquisition module (E12), which is responsible for receiving current samples and storing them in a vector for each of them; - a Fourier analysis module (E13), which is responsible for obtaining, from the samples received in the data input and acquisition module (E12), the effective values of the harmonic components of said current samples, obtained by Fourier Series; - a loss factor module for each phase (E14), which is responsible for obtaining the loss factors due to the Skin effect and the electromagnetic induction phenomena in each of the transformer phases (^. ^ ^^^ , ^^ ^ ^ ^), from the information obtained in the Fourier analysis module (E13); - a module of nominal short-circuit resistances (E15), which is responsible for obtaining the values of the components of the nominal short-circuit resistances (^^^^ , ^^^^ , ^^^^^) based on the values entered for the nominal losses and currents of the transformer (^^^^ , ^^^^ , ^^^^^ , ^^^ ); - a module of short-circuit resistances for each harmonic (E16), which is responsible for obtaining the values of the short-circuit resistances for each of the frequencies of the current harmonics of each phase (^ ^^,^ );- a module of effective short-circuit resistances of each phase (E17), which is responsible for obtaining the values of the effective short-circuit resistances of each phase of the transformer (^^^,^), and of its components (^^^,^ , ^^^^,^);- a load loss module (E18), which is responsible for obtaining the values of the load losses of each phase (^ ^^,^), the total load losses of each harmonic (^ ^^,^ ), and the total load losses of the transformer (^ ^^ );- a transformer supply factor module (E19), which is responsible for obtaining the superheating factor values for each phase (^^ ^ ), of the supply factor of each phase (^^ ^ %), and the transformer supply factor (^^^%); - a harmonic loss factor module (E20), which is responsible for obtaining the values of the loss factors for each harmonic of the currents (^^ ^ %); and - a display module (E21), which is responsible for displaying on the display medium (F) the information of one or more magnitudes of the distribution transformer obtained by the device (A).

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