Harmonic mitigation in power transformers through third winding current injection

Abstract

A three-winding transformer includes core, a primary winding wrapped about the core, and a secondary winding wrapped about the core. The primary winding and the secondary winding being configured to generate a fundamental wave having a fundamental frequency. A third winding is also wrapped around the core. A harmonic mitigation system is operatively connected to the third winding. The harmonic mitigation system selectively introduces a harmonic mitigation current into the third winding to reduce harmonic frequencies of the fundamental frequency induced into the primary winding.

Description

Attorney Docket No. 2115-008441 -WO-POAHARMONIC MITIGATION IN POWER TRANSFORMERS THROUGH THIRD WINDING CURRENT INJECTIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application No. 63 / 755,872, filed on February 7, 2025. The entire disclosure of the above application is incorporated herein by reference.FIELD

[0002] The present disclosure relates to the art of power transformers and, more particular, to a system for mitigating harmonics in power transformers through third winding current injection.BACKGROUND

[0003] This section provides background information related to the present disclosure which is not necessarily prior art.

[0004] Modern power systems are complex, interconnected networks that include generators, transmission lines, distribution systems, and end-users. These systems increasingly rely on advanced technologies, such as renewable energy sources and power electronic switching devices, to deliver energy efficiently and reliably. Despite this, integrating nonlinear components, such as power converters and variable-speed drives, introduces harmonic distortions that can significantly degrade power quality. Harmonic distortions pose critical challenges in power distribution networks, leading to equipment overheating, increased transformer losses, overloaded neutral conductors, circuit breaker tripping, and reduced power factors. Consequently, harmonic mitigation techniques (HMTs) are essential for maintaining power quality, stabilizing voltage and current waveforms, and ensuring reliable grid operations. These techniques address harmonic distortions at multiple levels, enhancing power systems' efficiency and robustness.

[0005] Extensive research on the effects of harmonic distortion has led to various techniques aimed at eliminating it, as reviewed in numerous studies. HMTs can be classified into three main groups. The first group includes active harmonic filters (AHFs), which provide dynamic compensation by detecting and injectingAttorney Docket No. 2115-008441 -WO-POAcompensating currents in real-time. These filters are particularly useful in industrial and commercial applications, where harmonic levels fluctuate due to variable nonlinear loads. For instance, shunt harmonic active filters (SHAFs) have demonstrated effective voltage and current regulation in complex systems with distributed nonlinear loads. The second group encompasses hybrid filtering and transformer integration solutions, which combine passive and active elements to offer broader harmonic suppression and greater adaptability to varying harmonic levels. Hybrid filters address the limitations of each type, providing both cost-effective and flexible solutions.

[0006] Transformer integration solutions involve incorporating harmonic mitigation techniques directly within transformer designs, such as through current injections or specialized winding configurations. These approaches can effectively mitigate phase-shifted harmonics, reducing the need for external filtering components and offering efficient alternatives for systems where transformer harmonics are a significant concern. The third group, a more advanced approach to harmonic mitigation, includes modulation and control-based techniques, which manage harmonics directly at the source. Techniques like selective harmonic mitigation PWM and switching frequency minimize harmonics, allowing precise control over switching patterns, reducing power loss and enhancing system efficiency. These methods benefit high-power applications, where effective switching control directly impacts harmonic suppression. The most sophisticated techniques employ adaptive impedance and feedback control mechanisms. For instance, virtual impedance control introduces controlled impedance at selected harmonic frequencies, minimizing harmonic propagation by adjusting the apparent system impedance. This technique benefits microgrids and distributed systems, where grid conditions may fluctuate significantly. Adaptive feedback further enhances this approach by monitoring grid conditions in real-time and adjusting control parameters to counter harmonic effects proactively. Selecting an optimal harmonic mitigation strategy depends on the specific harmonic characteristics, operational requirements of the power system, and desired performance goals.

[0007] By utilizing advanced control methods like AHFs and PWM, high harmonic mitigation (HM) levels can be achieved, and electrical systems’ performance and reliability can be enhanced. The suggested strategies aim to boost the accuracy of high harmonic current sharing, lower implementation costs, and offerAttorney Docket No. 2115-008441 -WO-POAan optimal balance between cost, complexity, and performance. Using control methods for HM is vital to maintaining power quality and ensuring the efficient operation of electrical systems. In all previously explored methods, the harmonics mitigation techniques are applied at the load or generator site, where they are connected to the grid at relatively high voltage and current. The question is whether the same HM tasks and power quality improvements could be made with higher efficiency and reliability using lower voltage / current rating filtering equipment.

[0008] Most renewable generation sites or power electronic-based equipment such as industrial loads, electric vehicles, etc., are usually connected to the grid using power transformers. The proposed method in this document will investigate the potential benefits of using such transformers to mitigate harmonics and address power quality challenges using transformers’ core magnetic-flux. Addressing power quality issues at the transformer level gives the flexibility of using arbitrary values for the voltage and current of the harmonic mitigating equipment.

[0009] Nonlinear loads, such as diode rectifiers and thyristor rectifier converters, can cause distortions in the power grid’s normal sinusoidal current and voltage waveforms. With the increasing use of electronic equipment, waveform distortion has become a more serious issue. FIG. 1 A shows an ideal AC waveform 2 and associated harmonics 4. FIG. 1 B shows a distorted waveform 6, representing real-world harmonics and non-linearities. In order to analyze this problem, it is necessary to create a model of an oscillating harmonic waveform to calculate non-sinusoidal voltages and currents. We assume the following finite Fourier series to describe a steady-state waveform with N harmonics asx(t) = po+ ∑Nn=1pncos(nωt) + q0+ ∑Nn=1qnsin(nωt) (1)

[0010] Individual harmonics (p and q coefficients) can be computed using the Fourier transform (FT) technique if the shape of the waveform is repeated (steady state). The model can be modified to work with fluctuating waveforms in which the fundamental components and harmonics are independently smoothly modulated. The coefficients in (1) can be substituted by complete polynomial functions of normalized time (t) with restricted ordering under these circumstances, as described by EquationAttorney Docket No. 2115-008441 -WO-POAx(t) = ∑Kk=0[ao,k] + ∑Nn=1an,kcos(nωt) + bo,k+ ∑Nn=1[an,kcos(nωt)]tk(2)

[0011] Analyzing this signal requires acquiring the matrices that contain the coefficients of the a and b polynomials. When a sinusoidal voltage is applied to a nonlinear load, the current becomes non-proportional to the voltage, resulting in a non-sinusoidal waveform.

[0012] Harmonic distortion is a deviation from the ideal sinusoidal waveform in alternating current systems caused by various factors. Companies that supply electric power systems must analyze their data on harmonics to identify potential problems and compare them with power quality standards. The voltage magnitudes with specific harmonic orders determine the level of harmonic voltage distortion, which varies based on the level of harmonic current injected by nonlinear load components into the distribution grid. To evaluate the impact of harmonics on the distribution system, it is important to use total harmonic distortions (THD) measurements. THD is a metric that measures waveform distortion relative to the fundamental frequency. This calculation is based on data collected while powering a nonlinear load, and it assesses the level of harmonic distortion in both voltage and current. Equation (1), shown below [2], defines THD.y°°THD = - x 100 (3)uiv 7

[0013] THD is defined by equation (3). When calculating the sum for harmonic order, it usually begins from the second order (n = 2) up to the 50th order. The letter U can represent either voltage or current. A further approach is to compute the THD for current and voltage, as shown in (4) and (5). The following expression expresses the amplitude of the THD in current and voltage as:J h 'r2ms-Jii2rmsTHD! = * - x 100 (4)firms. / ivzr2ms- rv?i2rmsTHDV= - x 100 (5)Virmswhere subscript 1 represent the fundamental load current and voltage.

[0014] Upon analyzing the output voltage and current in the frequency domain using Discrete Fourier Transform (DFT), it is seen that the nonlinear loadsAttorney Docket No. 2115-008441 -WO-POAproduce harmonics at multiple frequencies, including 180 Hz, 300 Hz, 420 Hz, 540 Hz, 660 Hz, 780 Hz, and 900 Hz, respectively, in the third, fifth, seventh, ninth, eleventh, thirteenth, and fifteenth orders.SUMMARY

[0015] This section provides a general summary of the disclosure and is not a comprehensive disclosure of its full scope or all of its features.

[0016] A three-winding transformer, in accordance with the present disclosure, includes core, a primary winding wrapped about the core, and a secondary winding wrapped about the core. The primary winding and the secondary winding being configured to generate a fundamental wave having a fundamental frequency. A third winding is also wrapped around the core. A harmonic mitigation system is operatively connected to the third winding. The harmonic mitigation system selectively introduces a harmonic mitigation current into the third winding to reduce harmonic components associated with the fundamental frequency induced into the primary winding.

[0017] In other features, the harmonic mitigation system introduces the harmonic mitigation current having a selected magnitude and a selected frequency.

[0018] In other features, a high pass filter is operatively connected between the harmonic mitigation system and the third winding.

[0019] In other features, a load is operatively connected to the secondary winding.

[0020] In other features, the load includes a harmonic generating load connected to the secondary winding, the harmonic generating load being a nonlinear load configured to generate high-frequency multiples of the fundamental frequency that are introduced into the primary winding.

[0021] In other features, an alternating current (AC) power source is operatively connected to the primary winding.

[0022] In other features, a feedback control system is operatively connected to the primary winding and the harmonic mitigation system, the feedback control system operating to adjust the harmonic mitigation current based on changes in AC power source.

[0023] In other features, the harmonic mitigation current is based on a relative phase difference and a relative magnitude difference between currentAttorney Docket No. 2115-008441 -WO-POApassing through the primary winding and current flowing through the secondary winding.

[0024] In other features, the harmonic mitigation system is configured to control magnetic-flux within a transformer core such that harmonic flux components induced by nonlinear loads are substantially canceled in the primary winding.

[0025] In other features, harmonic mitigation is achieved by maintaining a selected ampere-turn product in the third winding independent of an absolute magnitude of current flowing in the third winding.

[0026] In other features, the harmonic mitigation system independently controls a magnitude and a phase of each selected harmonic order.

[0027] In other features, the harmonic mitigation system includes a voltage source converter operatively connected to the third winding and configured to generate a synthesized voltage waveform that produces the harmonic mitigation current.

[0028] In other features, the synthesized voltage waveform includes a fundamental-frequency component phase-aligned with the primary winding and one or more harmonic components having substantially equal magnitude and opposite phase relative to load-generated harmonic components.

[0029] In other features, a frequency-selective impedance network is operatively connected to the third winding and configured to substantially block fundamental-frequency components while allowing harmonic-frequency components to pass.

[0030] In other features, the frequency-selective impedance network includes at least one of a series-resonant circuit, a parallel-resonant circuit, or a tuned band-pass circuit.

[0031] In other features, the harmonic mitigation system is configured to mitigate multiple harmonic orders simultaneously or sequentially according to a control scheduling strategy.

[0032] In other features, the harmonic mitigation current is based on at least one of current flow through the third winding, voltage across the third winding, or a combination thereof.

[0033] In other features, the harmonic mitigation system adaptively updates a magnitude and phase of the harmonic mitigation current in response to time-varying harmonic conditions.Attorney Docket No. 2115-008441 -WO-POA

[0034] In other features, the voltage source converter is rated for a fraction of an apparent power rating of the transformer while achieving harmonic mitigation through magnetic-flux control.

[0035] A three-winding transformer, in accordance with the present disclosure, includes a core, a primary winding wrapped about the core, and a secondary winding wrapped about the core. The primary winding and the secondary winding are configured to generate a fundamental wave having a fundamental frequency. A third winding is also wrapped about the core. A harmonic mitigation system is operatively connected to the third winding. The harmonic mitigation system selectively introduces a harmonic mitigation current into the third winding to reduce harmonic components associated with the fundamental frequency induced in the primary winding. The harmonic mitigation current is configured to generate a compensating magnetic flux that reduces one or more harmonic components of the fundamental frequency induced by nonlinear loads on the three-winding transformer.

[0036] Further areas of applicability will become apparent from the description provided herein. The description and specific examples in this summary are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings described herein are for illustrative purposes only of selected embodiments and not all possible implementations and are not intended to limit the scope of the present disclosure.

[0038] FIG. 1 A depicts an electrical waveform with harmonic distortion with extracted harmonics, in accordance with the prior art;

[0039] FIG. 1 B depicts an electrical waveform with harmonic distortion with the waveform being distorted by harmonics, in accordance with the prior art;

[0040] FIG. 2 depicts a circuit diagram illustrating power transformer having a harmonic mitigation circuit, in accordance with an aspect of the present disclosure;

[0041] FIG. 3 illustrates a power transformer designed for current injection to mitigate harmonics, in accordance with the present disclosure;

[0042] FIG. 4 depicts a diagram depicting an equivalent magnetic circuit of the power transformer of FIG. 3, in accordance with the present disclosure;Attorney Docket No. 2115-008441 -WO-POA

[0043] FIG. 5 depicts a circuit diagram illustrating a simulation test setup of the harmonic mitigation system, in accordance with the present disclosure;

[0044] FIG. 6A illustrates a simulation result depicting harmonic voltage on a primary winding of a power transformer, in accordance with the present disclosure;

[0045] FIG. 6B illustrates a simulation result depicting harmonic currents on a primary winding of a power transformer, in accordance with the present disclosure;

[0046] FIG. 7A illustrates a simulation result depicting harmonic voltage on a secondary winding of a power transformer, in accordance with the present disclosure;

[0047] FIG. 7B illustrates a simulation result depicting harmonic currents on a secondary winding of a power transformer, in accordance with the present disclosure;

[0048] FIG. 8A illustrates voltage on the primary winding of FIG. 6A after current injection, in accordance with the present disclosure;

[0049] FIG. 8B illustrates current on the primary winding of FIG 6B after current injection, in accordance with the present disclosure;

[0050] FIG. 9A illustrates voltage on the secondary winding of FIG. 7A after current injection, in accordance with the present disclosure;

[0051] FIG. 9B illustrates current on the secondary winding of FIG 7B after current injection, in accordance with the present disclosure;

[0052] FIG. 10 depicts an exemplary test set up, in accordance with an aspect of the present disclosure;

[0053] FIG. 11 A depicts a voltage waveform on a primary winding of the power transformer, in accordance with the present disclosure;

[0054] FIG. 11 B depicts a current waveform on the primary winding of the power transformer, in accordance with the present disclosure;

[0055] FIG. 11 C depicts a voltage waveform on a secondary winding of the power transformer, in accordance with the present disclosure;

[0056] FIG. 11 D depicts a current waveform on the secondary winding of the power transformer, in accordance with the present disclosure;

[0057] FIG. 12A depicts a voltage response on the primary winding before harmonic mitigation by current injection, in accordance with the present disclosure;

[0058] FIG. 12B depicts a voltage response on the primary winding after harmonic mitigation by current injection, in accordance with the present disclosure;Attorney Docket No. 2115-008441 -WO-POA

[0059] FIG. 13A depicts a voltage response on the secondary winding before harmonic mitigation by current injection, in accordance with the present disclosure;

[0060] FIG. 13B depicts a voltage response on the secondary winding after harmonic mitigation by current injection, in accordance with the present disclosure;

[0061] FIG. 14 depicts a simulation test setup for harmonic mitigation, in accordance with another aspect of the present disclosure;

[0062] FIG. 15 depicts a feedback control system for the harmonic mitigation system of the present disclosure;

[0063] FIG. 16 depicts a circuit diagram illustrating as three-winding power transformer having a harmonic mitigation circuit including a harmonic mitigation system that employs voltage injection and flux control, in accordance with an aspect of the present disclosure;

[0064] FIG. 17 depicts a circuit diagram illustrating as three-winding power transformer having a harmonic mitigation circuit including a harmonic mitigation system that employs a voltage source converter having a pulse-width modulation (PWM) driver operatively connected to a third winding of the three winding transformer, in accordance with an aspect of the present disclosure;

[0065] FIG. 18 depicts a PWM waveform generated by the PWM driver of FIG. 17, in accordance with the present disclosure;

[0066] FIG. 19 illustrates the three-phase power transformer of FIG. 19 designed for current injection to mitigate harmonics, in accordance with another aspect of the present disclosure; and

[0067] FIG. 20 illustrates the three-phase power transformer having a second configuration designed for current injection to mitigate harmonics, in accordance with another aspect of the present disclosure.

[0068] Corresponding reference numerals indicate corresponding parts throughout the several views of the drawings.DETAILED DESCRIPTION

[0069] Example embodiments will now be described more fully with reference to the accompanying drawings.

[0070] Most renewable generation sites or power electronic-based equipment such as industrial loads, electric vehicles, etc., are usually connected to the grid using power transformers. The present disclosure employs such transformersAttorney Docket No. 2115-008441 -WO-POAto mitigate harmonics and address power quality challenges using transformers’ core magnetic-flux. Addressing power quality issues at the transformer level gives the flexibility of using arbitrary values for the voltage and current of the harmonic mitigating equipment.

[0071] A three-winding transformer, in accordance with the present disclosure is illustrated at 20 in FIG. 2. Three-winding transformer 20 includes a primary winding 22 connected to a power source 24. Power source 24 takes the form of an alternating current (AC) input 26. Three-winding transformer 20 also includes a secondary winding 30 connected to a non-linear load 34. A diode 36 may be connected across secondary winding 30. When the power source 24 is connected to non-linear load 34, Three-winding transformer 20 generates an output having a fundamental frequency.

[0072] Three-winding transformer 20 is also shown to include a third winding 40. In accordance with the present disclosure, third winding 40 is connected to a harmonic mitigation system 50. As illustrated, harmonic mitigation system 50 includes a current injection source 52. Current injection source 52 delivers a harmonic mitigation current having a selected frequency into third winding 40 of Three-winding transformer 20 as part of a harmonic mitigation (HM) process. The harmonic mitigation system 50 can significantly reduce high-order harmonics. Additionally, harmonic levels can be manually adjusted by introducing a current source with a specific frequency.

[0073] By utilizing a current injection source 52 that matches the magnitude and frequency of existing harmonics, the amplitude of the harmonic content in the line currents can be significantly reduced. This is achieved by introducing a harmonic mitigating current having a specific harmonic frequency into the third winding 40 of the Three-winding transformer 20. The disclosed technique offers a solution to mitigate power quality issues in power systems. This approach involves adding third winding 40 or circuit to the Three-winding transformer 20, which effectively counters the negative effects of harmonics and enhances voltage regulation. By injecting current into the third winding 40, the impact of harmonics is significantly reduced, leading to enhanced power system performance and reliability, outweighing its potential complexity and cost compared to other mitigation techniques. With the harmonic injection approach, as depicted in FIG. 2, the need for a filter is eliminated.Attorney Docket No. 2115-008441 -WO-POA

[0074] As shown in FIG. 3, Three-winding transformer 20 includes a transformer core 60 that supports primary winding 22, secondary winding 30, and third winding 40. Transformer core 60 is shown to include a core window or central opening 62. The transformer core 60 substantially reduces one or more harmonic orders. The primary objective of harmonic mitigation system 50 is to minimize the impact of nonlinear components on the electric grid, which generate harmonic currents and cause voltage and current distortions. The harmonic suppression strategy incorporates simulation analysis and experimental validation to illustrate its function and practical application.

[0075] The Three-winding transformer 20, in accordance with the present disclosure, addresses multiple factors to ensure optimal performance and efficiency. It involves selecting suitable materials for transformer core 60, configuring primary winding 22, secondary winding 30, and third winding 40, and designing an insulation system tailored to specific voltage and power requirements. The transformer core 60, typically made of laminated steel, is chosen to minimize core losses and reduce magnetic-flux leakage. Transformer core 60, in accordance with the present disclosure, includes a depth of about 6.5 cm, a length of about 16.5 cm and a height of about 11 cm. Third winding 40 is selected with design considerations including conductor size needed to meet the a selected current. This approach ensures that the Three-winding transformer 20 is functional and optimized for harmonic mitigation.

[0076] Table 1 lists design parameters of an exemplary transformer and tests them before using them in the experiment. Moreover, the design process that ensures optimal performance and efficiency for the Three-winding transformer 20 is as follows: The flux density in a Three-winding transformer 20 can be calculated by considering various factors, such as the power input, frequency, number of turns in the primary winding 22, and the area of the transformer core 60, and can be obtained as shown in equation (6):4.44XP.(6)FxNpxWhere Bmis the flux density, F is the frequency and Npis the number of turns in primary winding 22. A is the area of the transformer core 60. The conductor's current density is a measure of the amount of electric current that a conductor can carry, and it is affected by its cross-sectional area. Consequentially, the current density isAttorney Docket No. 2115-008441 -WO-POAcalculated by dividing the electric current passing through the conductor by its cross- sectional area and can be derived aso = - A (v7)7Where I represents the electric current flowing through the material and A represents the cross-sectional area of the material. The voltage per turn in the primary winding 22 of Three-winding transformer 20 is a parameter that determines the voltage required to generate a single turn of the primary winding 22. This parameter is calculated using (8)V I'pn NTable 1 The parameters of the proposed transformerSpecifications Values Specifications Values rated voltage 120 / 60 / 40 flux density 0.758 T Vrated current 4.8 / 1.6 / 2.4 current density 11.11 power A volt / turn A / mm^2 frequency 2098 W core window space 1.165 primary winding 60 Hz factor V / turn turns 103 width of stamping 0.311 secondary winding 50 specific gravity of 0.148 m turns 65 copper 8.96 tertiary winding 14 AWG specific gravity of g / cm^3 turns 18 AWG iron 7.8g / cm^3 copper size primary 12 AWG volts per turn 1.165 primary V / turnAttorney Docket No. 2115-008441 -WO-POAcopper size W = 6.5 volts per turn 1.165 secondary cm, secondary V / turn copper size tertiary H = 11 cm, volts per turn third 1.165 dimensions L = 16.5 V / turn cm

[0077] The space for central opening 62 factor determines the percentage of window area occupied by the copper conductor calculated asV / SF = (9)AwindowWhere: Acopperrepresents the total area of the copper conductor and Awindowrepresents the window area.A width of transformer stamping that can determine the stamping size required to accommodate the transformer's window area is expressed as:a = (Window area)^(1 / 2) (10)To find the specific gravity of copper and iron, divide their densities by the density of water asCopper's specific gravity = 8.96 g — cm3— Iron'sspecific gravity (11)The volts per turn in a transformer's core determines the voltage required to generate a single turn of the core, which can be derived asWhere I is core mean length per turn Hence, the KVA rating of a transformer is given by the window area, which is the area of the window through which the coils are wound.Attorney Docket No. 2115-008441 -WO-POAAw×Bm×Kwσ×1000 (13)where Awis the window area, Bmis the flux density, Kwis the specific gravity of copper, a is the current density.

[0078] This section provides an overview of the model used for Three-winding transformer 20 having three windings, primary winding 22, secondary winding 30, and third winding 40. The primary winding 22, secondary winding 30, and tertiary or third winding 40 are rectangular coils wrapped around a common magnetic transformer core 60. A design factor for the harmonic mitigation system 50 is selecting the frequency and magnitude of current sources in the third winding 40 since we have variable harmonic order, and the shape of the voltage and current waveforms is sensitive to the primary and secondary winding.

[0079] Fig. 3 shows Three-winding transformer 20 as used for this analysis. Three-winding transformer 20 includes transformer core 60 that supports primary winding 22, secondary winding 30, and third winding 40. Third winding 40 delivers an input signal with specific frequencies to cancel the undesired harmonics.

[0080] To accurately model harmonic transformer, it is necessary to examine three coupled coils energized by three independent current sources, which are I1, I2and I3respectively. The L1, L2and L3components represent inductance associated with the primary, secondary, and third windings, respectively. The magnetizing flux, 0mis the component that is common to all three windings: primary, secondary, and third, as a result:Øm= Ø = Ø1= Ø2= Ø3(14)

[0081] From Fig. 4, the third winding 40 is used to inject currents that cancel out harmonic distortions in the main circuit formed by power source 24, primary winding 22, secondary winding 30, and non-linear load 34. The induced voltages in the primary winding 22, secondary winding 30, and the third winding 40 follow the relationships:V1= N1dØ1 / dt (15)V2= N2dØ2 / dt (16)3=N^5dt (17)Attorney Docket No. 2115-008441 -WO-POAwhere V1, V2, V3are the voltages induced in the primary winding 22, secondary winding 30, and third winding 40, respectively, and Φ is the magnetic-flux in the core. These relationships represent the induced voltages due to the flux variation. Such relationships are valid for harmonics as well, since harmonics also cause flux variations but with a different frequency.

[0082] Considering Fig. 4, the relationship among the transformer windings’ ampere turns is articulated through the following equation:N1I1+ N2I2+ N3I3+ RcØ = 0 (18)Equation (18) represents the relationship between the currents and number of turns in the transformer windings under normal operating conditions at the fundamental frequency of 60 Hz.N1I1corresponds to the ampere-turns in the primary winding, similar for secondary (N2I2) and tertiary (N3I3). Φ represents the flux in the transformer core 60 and Rcrepresents the core reluctance, core's magnetization. Considering a highly permeable material for the core 60, the reluctance of the transformer core 60 can be ignored from equation (18). At this stage, all components are free from harmonic content.This equation can also be extended to different frequencies since harmonic currents behave similarly but with different rates of change depending on the harmonic order. The intention is to prevent harmonic currents from appearing in the primary winding 22, thereby N1I1should be set to zero ensuring that the equation holds across frequencies, including the fundamental and harmonics (h), we will have:(N1I1)h = 0 and (N2I2)h + (N3I3)h = 0 (19)

[0083] Turning to equation (19), the principal objective is to cancel harmonics from the primary winding 22 (I1) to maintain power quality. Harmonics are canceled through the introduction of a harmonic mitigation current into the third winding. The term “harmonic mitigation current” should be understood to describe a current that is introduced into a third winding of a three-winding transformer. The harmonic mitigation current is configured to generate a compensating magnetic flux that reduces or cancels one or more harmonic components induced by nonlinearAttorney Docket No. 2115-008441 -WO-POAloads on the three-winding transformer independent of the specific means by which the current is generated or controlled.

[0084] The harmonic mitigation current is determined based on the relative phase and magnitude differences between the primary winding current and the secondary winding current. The calculation involves measuring the harmonic components present in both the primary and secondary windings and deriving a compensatory current that, when introduced into the tertiary winding, reduces the total harmonic distortion within the transformer. This compensatory harmonic mitigation current is configured to optimize power quality by minimizing harmonic frequencies, thereby enhancing transformer efficiency and stability.

[0085] For harmonics of any fundamental frequency, the harmonic component I1at any harmonic frequency h must be zero, (N1I1)h = 0. Achieving this necessitates that the aggregate of harmonic currents in the secondary and tertiary windings also equates to zero, (N2I2)h + (N3I3)h = 0. To enforce this condition, harmonic mitigation system 50 introduces a selected current I3into the third winding 40, such that it cancels the harmonic current produced in the secondary winding 30. This injected current is specifically calculated to counterbalance the harmonic current generated in the secondary winding 30. By determining I3based on the detected harmonic content in the secondary winding, the harmonic impact at primary level is neutralized, thus maintaining I1= 0 for all harmonics. In other words,where where N2I2represents the secondary winding ampere turns for harmonic (h) and (N3) represents the number of turns on the third winding. Harmonic generating or non-linear loads such as power electronics circuits used as inverters, variable frequency drives (VFDs), computers, light emitting diode (LED) lighting and the like that generate high frequency harmonics of the fundamental frequency passing through the transformer primary winding 22 and the secondary winding 20 of Three-winding transformer 20. Their generated harmonic is a function of their fundamental frequency component, and the coefficients (ChS) are usually represented as a table. Assuming harmonic h will be Ch times the fundamental load current ( 2), the required hh for third winding can be calculated as:Attorney Docket No. 2115-008441 -WO-POA- ^2 ^211 _N2hh — x Chx l23(21)N3NBesides, I2 is a function of h, which is the transformer’s primary winding current, therefore, hh can be calculated as:Nr1^2 = — X I 1 N2(22)In cases that the specific harmonic table for the inverter is not available, an offline test or feedback loop and control circuit will determine the value of Chand subsequently, the value of kh. Ultimately, by ensuring (N1I1)h = 0, the design effectively impedes harmonic currents from infiltrating the grid, enhancing power quality and preventing the dissemination of harmonics into the broader distribution system. This strategic approach not only preserves the integrity of the primary circuit but also minimizes the systemic impact of harmonics, optimizing the transformer's overall performance in distributing clean and stable power.

[0086] Harmonic mitigation system 50, in accordance with the present disclosure provides a proactive solution to enhance power quality by directly addressing harmonic distortions in real-time. In this method, current injection source 52 is introduced into the third winding 40 of the Three-winding transformer 20, effectively cancelling harmonics by generating compensating currents that oppose harmonic components produced by nonlinear loads. This strategic injection of harmonics at the beginning of the system prevents them from spreading throughout, providing targeted mitigation before they impact the entire system. The current injection source 52 selectively counteracts distortions by dynamically detecting and addressing specific harmonic frequencies, reducing issues such as equipment overheating, transformer losses, and poor power factors.

[0087] Unlike traditional filtering methods, which passively absorb or block harmonics, current injections actively neutralize harmonic components within the system, making it adaptable to variable load conditions and fluctuating harmonic levels. This technique is particularly advantageous in environments with complex,Attorney Docket No. 2115-008441 -WO-POAnonlinear loads, such as industrial systems with variable-speed drives or power electronic converters where harmonic levels vary significantly. With precise control over the amplitude and phase of the injected current, this approach can target specific harmonics, such as the third, fifth, or seventh, without disturbing the fundamental frequency.

[0088] A core strength of current injection methods lies in their adaptability. The current injection source 52can adjust to evolving harmonic profiles in real time, making it especially suitable for dynamic grid environments, including those with high levels of renewable energy integration. This adaptability allows it to respond effectively to the unpredictable nature of any distortions associated with renewable energy sources, EV charging stations, and complex industrial loads. Additionally, it can be implemented for other power quality concerns, such as inter-harmonics and flicker, and can provide a resilient and efficient solution for modern power distribution systems.

[0089] The proposed method is verified in this section using MATLAB Simulations. As shown in Fig. 5, the full-wave rectifier 70 supplying a resistive load is connected to the secondary winding 30 of a three-winding transformer 20. The primary winding 22 is connected to a power source 24 such as an AC supply, and the third winding 40 is connected to harmonic mitigation system 50 including the AC current injection source 52with the frequency of harmonics to be cancelled. In order to minimize the impact of fundamental frequency components of primary winding 22 and secondary winding 30 on the third winding 40, a capacitor 74 is added in series with the third winding 40. The capacitor 74 acts as a very high impedance for 60 Hz and very low impedance for harmonics, therefore limiting the impact of the primary winding 22 and secondary winding 30 and on the third winding 40 for harmonics only.

[0090] To verify the proposed method, the harmonic components in the voltage and current waveforms of the primary winding 22 and secondary winding 30 are compared with those before the injection of current into third winding 40. The harmonic voltages and currents created in the primary winding 22 from the simulated circuit are shown in Fig. 6A.

[0091] Fig. 6B presents the harmonics produced on the secondary winding 30. FIG. 6A illustrates the harmonics on the voltage primary winding 22 and FIG. 6B illustrates the harmonic current on the secondary winding 30. As shown in FIGS. 7A and 7B, the simulation model, illustrated in Fig. 5, has been examined, and theAttorney Docket No. 2115-008441 -WO-POAfindings show a significant reduction in the harmonic distortions of the primary winding 22 and secondary winding 30, respectively, when harmonic mitigation system 50 introduces a harmonic mitigating current into third winding 40. These findings were obtained after comparing and analysis of FIGS. 8A, 8B, 9A, and 9B. Harmonics distortion for the current waveforms of the primary winding 22 (FIGS. 8A and 8B) and secondary winding 30 (FIGS. 9A and 9B) before injecting the current into the third winding are 5.61% and 7.25%, respectively.

[0092] It is worth noting that the DC-side harmonics also change simultaneously since the AC side of the converter is coupled with the DC side of the converter. To reduce the harmonic amplitude in the power system, injecting sources can be added to the third winding of the transformer.

[0093] FIG. 10 depicts an experimental setup 80 used to validate the effects of harmonic mitigation system 50 in accordance with the present disclosure. In addition to mitigating harmonics, the harmonic mitigation system 50. The experimental setup 80, illustrated in Fig. 10, encompasses power source 24, a three-winding transformer 20, a function generator 84, a band-pass circuit such as a high-pass filter 86, non-linear load 34, and a compact Rio (cRIO) hardware 90. Notably, the high-pass filter 86 allows only high frequencies to traverse the third winding 40, eliminating low harmonic orders. Probes establish connections between the cRIO hardware 90 and the primary winding 22 and secondary winding 30 of the Three-winding transformer 20, facilitating the analysis of harmonic components using LabVIEW software running on a computer 96. The third winding 40 of the Three-winding transformer 20 functions as an input source, linked to a function generator 84 and a DC voltage source, primarily to produce the pulse signal required to neutralize the harmonic within the transformer core. The output frequency of the function generator 84 can be directly observed to gauge the magnitude of harmonic orders, and its magnitude is amplified using a transistor-based amplifier. The adopted high-pass filter 86 will only allow the high frequencies to pass through the third winding 40 to eliminate the high order of harmonics.

[0094] Experiments were conducted on a single-phase circuit to suppress harmonics by employing the harmonic injection mitigation method using a current source with a suitable frequency. The circuit design utilizes a diode bridge rectifier to generate the harmonic voltage and current, as shown in Figs. 10. Although the harmonic waveforms of the primary and secondary windings differ significantly inAttorney Docket No. 2115-008441 -WO-POAterms of magnitude and phase, these differences do not affect the effectiveness of the harmonic cancellation technique. Once the cancellation method is applied, the harmonic distortions in both windings are effectively minimized. An injected source produces a current waveform with harmonics of the same frequency as those caused by the diode rectifier. A comparison between the waveforms generated by Fig. 11 A, 11 B, 11 C, and 11 D and the one in FIG. 12A and FIG. 12B reveals the difference in the harmonics. It has been demonstrated that the 3rd harmonic voltage has decreased from 0.13% to 0.102%, the 5th harmonic has been reduced from 1.64% to 1.02%, while the 7th harmonic has decreased from 1.35% to 1.12%. The 9th and 11th harmonics have increased slightly, while the 13th and 15th harmonics have been slightly reduced. Fig. 11 B displays the primary winding current waveforms, indicating a significant improvement in the total current drawn from the primary winding, as shown in FIG. 12B. Additionally, the harmonic contents of the waveforms in Fig. 13B indicate a significant reduction in the 3rd, 5th, 7th, 9th, 11 th, and 13th harmonics, from 0.1566% to 0.135%, 1.679% to 1.296%, 1.24% to 1.13% and 0.295% to 0.221%, respectively. On the other hand, the 15th harmonic has been slightly reduced from 0.081% to 0.034%. The results depicted in FIG. 14 demonstrate that the 3rd, 5th, 7th, 11th, 13th, and 15th harmonics in the voltage across the secondary winding have decreased from 3.14%, 1.7%, 1.45%, 0.261%, 0.912%, 0.346%, and 0.077% to 0.115%, 0.876%, 1.18%, 0.114%, 0.391%, 0.022%, and 0.042%, respectively. Moreover, the THDi decreased from 15.842% to 3.69%.

[0095] The current's harmonic contents on the primary winding in practical results have differences of 0.1566%, 1.679%, 1.24%, 0.295%, 0.814%, 0.342%, and 0.081 % in the 3rd, 5th, 7th, 9th, 11th, 13th, and 15th harmonics. The practical results show a slight difference in the harmonic contents of the primary winding voltage and current compared to the simulation results. However, the proposed HM method has been validated by both simulation and practical results. The method has successfully improved the THDi of the primary and secondary current, reducing them from 4.607% to 2.5067% and from 15.842% to 3.69%, respectively (FIGS 12A and 12B and FIGS 13A and 13B).

[0096] For instance, the harmonic contents of the total current after using the mitigation technique have a difference of harmonic orders in the 3rd, 5th, 7th, 9th, 11 th, 13th and 15 harmonics, and the THDi is less in the simulation results thanAttorney Docket No. 2115-008441 -WO-POAthe practical. The mitigation technique affects the total current's harmonic contents, resulting in a difference in harmonic orders of 3rd, 5th, 7th, 9th, 11 th, 13th, and 15th.

[0097] The practical results show a higher THDi than the simulation results due to factors such as lossy elements, stray parameters, dynamic performance of the current measuring system, and noises. The proposed method for mitigating harmonics has been successfully validated through simulations and experiments. This method has improved the THD on the transformer's primary and secondary sides. The consistency of the hardware experiment and the simulation in MATLAB Simulink is a testament to the effectiveness of this method.

[0098] Eliminating harmonics in power distribution systems can be explored through sensitivity studies that focus on different parameters. First, testing the system with a half-wave rectifier introduces significant harmonic distortion, primarily oddorder harmonics like the third, fifth, and seventh. This provides a baseline to evaluate harmonic levels and the effectiveness of mitigation techniques.

[0099] Next, changing the number of turns in the third winding transformer affects the voltage transformation and magnetic-flux within the core, influencing the generation and suppression of harmonics. Increasing or decreasing the number of turns can either exacerbate core saturation, leading to more harmonics, or help reduce them by adjusting the core's operating point. Similarly, changing the current magnitude on the third winding impacts the level of harmonic currents flowing through the system, with higher currents typically causing more distortion due to nonlinearity in the system components, particularly transformers.

[0100] Finally, altering the load magnitude modifies the system's impedance, which can amplify or attenuate harmonic components depending on the load's nature. By conducting these sensitivity studies, one can identify optimal conditions for harmonic mitigation and fine-tune the system for better power quality. A circuit 110 designed for a half-wave rectifier is shown in FIG. 14. The study employs MATLAB Simulink to model harmonic components generated by nonlinear loads for various scenarios and test them with implemented mitigation techniques.

[0101] As shown in Tables 2 and 3, the influence of these harmonic loads, such as shown in Tables 2 and 3, on the primary winding 22 of Three-winding transformer 20 is comprehensively investigated within the scope of half-wave rectifiers. The THDv and THDi are assessed on each primary winding 22 and subsequently compared. Table 4 presents the THDi measured on the primary windingAttorney Docket No. 2115-008441 -WO-POA22 of the circuit 100 employing a half-wave rectifier 120. After implementing the mitigation method, the THDv on the primary winding 22 decreased significantly from 1.21% to 0.35%, indicating the effectiveness of harmonic mitigation system 50. Subsequently, Table 4 demonstrates that employing the same HM for the load resulted in a 6.79% decrease in THDi to 2.9%, which resulted in the primary winding 22.Table 2 Harmonic voltage contents on primary windingH Before HM (%) After HM (%)3 0.43 0.155 0.22 0.077 0.17 0.079 0.12 0.0211 0.10 0.0013 0.09 0.0215 0.08 0.02THD 1.21 0.35Table 3 Harmonic current contents on primary windingH Before HM (%) After HM (%)3 1.45 0.795 1.05 0.567 0.93 0.439 0.87 0.3811 0.85 0.3113 0.83 0.2615 0.81 0.19THD 6.79 2.9

[0102] Changing the turn ratio represented by N3significantly impacts harmonic in power distribution systems. Adjusting N3modifies the voltage and current relationship, directly influencing the effectiveness of harmonic suppression. AAttorney Docket No. 2115-008441 -WO-POAproperly tuned N3enhances the system's ability to cancel harmonics, often generated due to core nonlinearity. However, an incorrect choice of N3can diminish harmonic mitigation effectiveness and potentially introduce additional distortions, making precise control of N3critical for optimal harmonic suppression. The system was tested with variable values of N3both before and after harmonic injections, and results indicate that an optimal value of N3=1.75 provides the most effective harmonic mitigation. This configuration yielded lower THDv and THDi values, as shown in Tables 4 and 5, compared with other N3values applied to the primary windings. Specifically, following the harmonic injection using the optimal / V3=1.75, the THDv in the primary winding was reduced to a reasonable magnitude. These results confirm that careful tuning of N3is essential for achieving effective harmonic suppression and improving overall power quality in the system.Table 4 Harmonic voltage contents on primary windingH Before HM N=4 N=3.2 N=2.67 N=2.29 N=2 N=1.78 N=1.6 (%) (%) (%) (%) (%) (%) (%) (%) 3 0.43 0.15 0.15 0.15 0.09 0.05 0.12 0.11 5 0.22 0.10 0.07 0.07 0.04 0.03 0.02 0.06 7 0.17 0.04 0.06 0.07 0.03 0.03 0.01 0.03 9 0.12 0.06 0.04 0.02 0.03 0.03 0.01 0.02 11 0.10 0.05 0.04 0.02 0.03 0.04 0.01 013 0.09 0.04 0.01 0.02 0.02 0.02 0.02 0.0215 0.08 0.03 0.02 0.02 0.02 0.02 0.01 0.01Table 5 Harmonic current contents on primary windingH Before HM N=4 N=3.2 N=2.67 N=2.29 N=2 N=1.78 N=1.6 (%) (%) (%) (%) (%) (%) (%) (%) 3 1.45 0.97 0.70 0.68 0.89 0.85 0.84 0.70 5 1.05 0.55 0.62 0.49 0.49 0.49 0.53 0.46 7 0.93 0.51 0.43 0.48 0.39 0.43 0.39 0.37 9 0.87 0.4 0.41 0.38 0.37 0.43 0.36 0.29 11 0.85 0.38 0.34 0.32 0.32 0.30 0.29 0.25 13 0.83 0.34 0.31 0.26 0.24 0.26 0.26 0.2215 0.81 0.3 0.27 0.26 0.21 0.24 0.20 0.19

[0103] Injecting I3with an appropriate magnitude through the third winding 40 of Three-winding transformer 20 plays a crucial role in mitigating harmonic distortions, particularly those arising from nonlinear load in the transformer core 60.Attorney Docket No. 2115-008441 -WO-POABy fine-tuning I3low-order harmonics, such as the 3rd, 5th, and 7th, can be significantly suppressed. The system was tested by varying current magnitudes before and after adjustment. Results indicated that an optimal current of 0.3 A yielded the lowest THDv for the case study, as shown in Table 6. Additionally, a current of 0.5 A provided optimal harmonic reduction in the primary winding 22, as presented in Table 7, showing improved performance compared to other current magnitudes tested. These findings demonstrate the substantial benefits of adjusting I3to minimize harmonic distortion and enhance overall system efficiency.Table 6 Harmonic voltage contents on primary winding 22H Before 1=0.3 1=0.5 1=0.75 1=1.5 1=2.25 l=3 A 1=3.75 l=4.5 HM A A (%) A (%) A (%) A (%) (%) A (%) A (%) (%) (%)3 0.43 0.03 0.13 0.15 0.12 0.04 0.11 0.14 0.19 5 0.22 0.04 0.04 0.07 0.09 0.05 0.03 0.08 0.07 7 0.17 0.06 0.01 0.07 0.07 0.02 0.03 0.02 0.05 9 0.12 0.02 0.01 0.04 0.03 0.02 0.04 0.02 0.01 11 0.10 0.02 0.01 0.02 0.01 0.04 0.01 0.01 0.02 13 0.09 0.02 0.01 0.02 0.02 0.02 0.01 0.01 0.015 0.08 0.02 0.01 0.02 0.01 0.01 0.01 0.01 0.0Table 7 Harmonic current contents on primary winding 22H Before 1=0.3 1=0.5 1=0.75 1=1.5 1=2.25 l=3 A 1=3.75 l=4.5 HM A A (%) A (%) A (%) A (%) (%) A (%) A (%) (%) (%)3 1.45 0.79 0.7 0.68 0.87 0.85 0.92 1.01 1.08 5 1.05 0.56 0.51 0.49 0.62 0.58 0.56 0.44 0.45 7 0.93 0.43 0.43 0.48 0.56 0.39 0.33 0.32 0.39 9 0.87 0.38 0.34 0.38 0.34 0.35 0.33 0.24 0.26 11 0.85 0.31 0.26 0.33 0.34 0.3 0.3 0.2 0.22 13 0.83 0.26 0.22 0.28 0.22 0.21 0.21 0.18 0.2215 0.81 0.19 0.19 0.26 0.18 0.17 0.17 0.17 0.21

[0104] A comparative analysis of various resistance magnitudes revealed significant differences in THD values on the primary winding 22, as illustrated in Tables 8 and 9. Table 8 shows the harmonic voltage contents on the primary winding 22 across different resistance values, while Table 9 details the harmonic current contents. The analysis indicates that increasing load resistance generally leads to elevated THD in both voltage and current on the primary winding 22. Specifically, a 20-ohm load resistor achieved the lowest harmonic distortion for primary voltage,Attorney Docket No. 2115-008441 -WO-POAwhile a 15-ohm resistor provided the best performance for minimizing primary current harmonics. Simulation results further illustrated the impact of each resistance value on individual harmonic orders (3rd, 5th, 7th, etc.). For instance, Table 8 demonstrates that the 3rd harmonic voltage content is lowest at 20 ohms, while Table 9 reveals that the 3rd harmonic current is minimized with a 15-ohm resistor. Furthermore, the harmonic content for both voltage and current decreased consistently compared to the values before HM, demonstrating the effectiveness of tuning R for harmonic reduction. These findings highlight the benefits of optimizing resistance values for harmonic suppression and emphasize accurate load control to enhance overall power quality.Table 8 Harmonic voltage contents on primary winding 22H Before HM R=10 Q R=15 Q R=20 Q R=25 Q R=30 Q R=35 Q R=40 Q (%) (%) (%) (%) (%) (%) (%) (%) 3 0.43 0.15 0.11 0.06 0.18 0.19 0.19 0.20 5 0.22 0.07 0.11 0.04 0.04 0.13 0.03 0.10 7 0.17 0.07 0.07 0.03 0.08 0.07 0.02 0.05 9 0.12 0.02 0.04 0.04 0.06 0.05 0.02 0.05 11 0.10 0.02 0.01 0.01 0.04 0.02 0.02 0.05 13 0.09 0.02 0.01 0.01 0.02 0.03 0.03 0.0315 0.08 0.02 0.01 0.0 0.02 0.01 0.03 0.03Table 9 Harmonic current contents on primary winding 22H Before HM R=10 Q R=15 Q R=20 Q R=25 Q R=30 Q R=35 Q R=40 Q (%) (%) (%) (%) (%) (%) (%) (%) 3 1.45 0.68 0.45 0.92 0.67 0.63 0.64 0.84 5 1.05 1.05 0.49 0.58 0.65 0.65 0.69 0.66 7 0.93 0.38 0.47 0.54 0.62 0.62 0.67 0.63 9 0.87 0.41 0.43 0.49 0.58 0.58 0.60 0.50 11 0.85 0.41 0.33 0.36 0.45 0.45 0.54 0.50 13 0.83 0.26 0.32 0.32 0.42 0.42 0.46 0.4915 0.81 0.08 0.28 0.26 0.41 0.41 0.46 0.49

[0105] In accordance with the present disclosure, harmonic mitigation system 50 has been verified with simulations and experiments. The method involves injecting current via the third winding 40 on Three-winding transformer 20 and controlling it to produce a signal that targets and eliminates specific harmonic frequencies. This technique effectively controls the harmonics generated by nonlinear loads, significantly reducing total harmonic distortions for both voltage and current at the primary and secondary windings.Attorney Docket No. 2115-008441 -WO-POA

[0106] The MATLAB / Simulink model and practical experiment were utilized to confirm the efficacy of the proposed technique. The system was tested in two scenarios: the first employed a full-wave bridge rectifier, and the second used a halfwave rectifier. It was discovered that various factors, including the size of impedances, transformer characteristics, converter type, and the presence of nonlinear loads, influence the harmonic performance of the system. Additionally, after being tested on hardware, the method demonstrated significant percentage differences in each harmonic order, including THD, following the application of the injection source. These findings indicate that integrating the mitigation approach into the power grid can significantly enhance harmonic distortions.

[0107] Further embodiments focus on an in-depth analysis of the proposed mitigation technique, including a feedback loop for time-varying harmonics, within a three-phase system. This will thoroughly compare high-fidelity simulations and experimental results benchmarked against IEEE harmonic standards. Advanced harmonic distortion and power quality metrics will be employed to assess the method’s efficacy under varying load conditions and nonlinearities. Additionally, further optimization techniques and adaptive control algorithms may be explored to enhance real-time harmonic suppression, paving the way for more robust implementation in practical power distribution networks.

[0108] The harmonic mitigation system, in accordance with the present disclosure further includes a feedback-control system 150 for updating a magnitude and phase of the harmonic mitigation current in response to time-varying harmonic conditions as shown in paragraph FIG. 15. To adapt to dynamic power systems where harmonic profiles change over time, feedback-control system 150 can be employed. Feedback-control system 150 continuously monitors harmonic levels and adjusts the operation of Three-winding transformer 20 in real time by injecting appropriate harmonics in the third winding 40.

[0109] A feedback loop 156 and a controlled harmonic source 160 for injecting to the third winding 40 is shown in Figure 15. Feedback-control system 150 has the ability to maintain optimal harmonic levels in fluctuating environments, such as during variable renewable energy generation and diverse load conditions. A single winding can be used to address various harmonics through a time-based approach, where each harmonic frequency is sequentially targeted for cancellation. In fluctuating environments where different harmonics can be dominant at differentAttorney Docket No. 2115-008441 -WO-POAtimes, or multiple harmonics are dominant, each harmonic can be targeted by current injection in a fraction of time period. The time period could range from cycles of fundamental frequency to few seconds. Using timing mechanisms will adjust the winding’s operation to specifically cancel individual harmonics at designated intervals.

[0110] In accordance with another aspect of the present disclosure illustrated in FIG. 16, harmonic mitigation system 50 relies on a single-harmonic cancellation using a controlled voltage source applied to the third winding 40. Rather than relying on the absolute magnitude of injected current, harmonic suppression is governed by a harmonic flux produced in the transformer core, which is proportional to the product of injected current and the number of turns of the third winding 40.

[0111] For a selected harmonic order h, the injected harmonic flux d>h(3) generated by the third winding is expressed as shown in equation (23).4>h(3) oc N3-I3h (23)

[0112] Where Ns is the number of turns of the third winding 40, and Ish is the harmonic current component at harmonic order h.

[0113] To cancel a targeted harmonic flux component h(L) generated by nonlinear loads, the injected flux satisfies equation (24).N3-I3h=-N2-l2h (24)

[0114] where l2h represents the harmonic current component in the secondary winding 30. The negative sign indicates a phase opposition between the injected harmonic flux and the load-generated harmonic flux.

[0115] In this embodiment, a single harmonic voltage source operating at frequency hfi (where fi is the fundamental frequency) is applied to the third winding 40. The voltage source is configured to produce a harmonic voltage with magnitude corresponding to the measured harmonic content and with an opposite phase, thereby generating a compensating harmonic flux within the transformer core.

[0116] Importantly, the injected current magnitude is not a limiting factor. When lower current capability is available, harmonic cancellation can be equivalently achieved by increasing the number of turns Ns of the third winding 40, preserving the required ampere-turn product depicts in the expression (25).N3I311 = constant (25)

[0117] This provides significant flexibility in third-winding design, allowing harmonic mitigation using low-current, low-power electronics while maintainingAttorney Docket No. 2115-008441 -WO-POAeffective flux-based cancellation or higher-power electronic equipment with reduced winding material.

[0118] To prevent a fundamental frequency component from influencing the third winding circuit, a frequency-selective impedance network is employed. In one implementation, a series-resonant circuit 250 tuned to the fundamental frequency presents a high impedance at fi and very low impedance at hfi, thereby blocking fundamental current flow into the third winding. In an alternative implementation, a parallel-resonant circuit is used to create a notch characteristic at the fundamental frequency while allowing harmonic-frequency components to pass.

[0119] The resonant condition is defined by equation (26).mi = 1 / sqrt (LC) (26)

[0120] where wi=2irfi, and L and C are the inductance and capacitance of the resonance network. This configuration ensures that the third winding primarily interacts with the targeted harmonic frequency while remaining decoupled from the fundamental component.

[0121] This embodiment enables selective harmonic cancellation with minimal power processing requirements, enhances implementation flexibility, and allows scalable adaptation across different transformer ratings and harmonic profiles.

[0122] In another embodiment of the present disclosure illustrated in FIG.17, the harmonic mitigation system 50 includes a voltage source converter 290 blocking fundamental(VSC) operatively connected to the third winding of the transformer. The voltage source converter is configured to synthesize a controlled voltage waveform that simultaneously generates a fundamental-frequency component having substantially the same phase angle as the primary winding voltage and harmonic components having a substantially equal magnitude and opposite phase angle relative to the harmonic components produced by nonlinear loads.

[0123] The synthesized voltage applied to the third winding 40 may be expressed as equation (27).v3(t) = V±sin^t + + Xh=2 Vn sinC / i^it + (ph+ 7i) (27)

[0124] Where Vi and 1 represent the magnitude and phase of the fundamental frequency component phase-aligned with the primary winding 22, and Vh and 4>h represent the magnitude and phase of the h-th harmonic component measured in the system, and the phase shift of IT enforces harmonic cancellation through phase opposition.Attorney Docket No. 2115-008441 -WO-POA

[0125] The voltage source converter operates using pulse-width modulation (PWM) techniques to generate the composite waveform. The PWM switching strategy allows independent regulation of the fundamental and harmonic components, enabling precise shaping of the injected waveform while maintaining controllability over amplitude and phase. The reference voltage waveform used for PWM generation is defined as a superposition of a fundamental component and selected harmonic components as shown in equation (28).vre / (t) = V±sin^t + + Xh=2 Vn sinC / i^it + (ph+ 7i) (28) Where Vi and 4>i correspond to the magnitude and phase of the fundamental frequency component phase- aligned with the transformer primary voltage, and Vh and h correspond to the magnitude and phase of the h-th harmonic component measured within the system, and the added phase shift of IT ensures phase opposition for harmonic cancellation.

[0126] This reference waveform is compared against a high-frequency carrier signal vc(t), a triangular or sawtooth waveform as shown in FIG. 18 with frequency fs » f1. The switching function s(t) of the converter is determined by equation (29).s(t)={l, lfVref(t)> Vc(t) Of 0, If Vref(t) < Vc(t)} (29)

[0127] The resulting PWM switching signal controls the semiconductor devices of the voltage source converter, producing the synthesized output voltage V3(t) whose fundamental and harmonic components track the reference waveform.

[0128] When applied to the third winding 40, the injected voltage produces a controlled current that generates a compensating magnetic-flux within the transformer core. The resulting harmonic flux

[0129] 4>h(3) satisfies expression (30).< (3) oc N3I3h (30)

[0130] where Ns is the number of turns of the third winding 40 and Ish is the harmonic current generated by the voltage source converter. Harmonic cancellation is achieved when the injected flux counteracts the load-generated harmonic flux within the core, thereby minimizing the propagation of harmonic components into the primary winding.

[0131] This embodiment provides design flexibility by allowing the harmonic mitigation function to be realized using either low-power electronic equipment with higher third-winding turns, or higher-power electronic equipment with reduced windingAttorney Docket No. 2115-008441 -WO-POAmaterial, while maintaining the required flux-compensation capability through appropriate selection of voltage magnitude, PWM control scheduling strategy, and winding configuration.

[0132] In contrast to approaches that act directly on line currents, this embodiment operates by controlling the magnetic-flux within the transformer core itself, enabling harmonic mitigation at the transformer level. By synthesizing both fundamental and harmonic components through the voltage source converter, the system maintains proper magnetic coupling while selectively neutralizing undesirable harmonic flux components.

[0133] This approach supports scalable implementation across different transformer ratings, operating conditions, and harmonic profiles, and is particularly suitable for systems with dynamic and time-varying nonlinear loads.

[0134] PWM enables independent control of each harmonic component by constructing the modulation reference as a sum of orthogonal sinusoidal components, each corresponding to a desired harmonic order. The composite reference waveform is described by equation (31).vre / (t) =vh sinO^t + (pfj (31)

[0135] where each harmonic h has its own controllable magnitude Vh and phase h.

[0136] Because sinusoidal components at different harmonic orders are linearly independent, adjusting Vh affects only that harmonic and does not alter the others, provided the PWM carrier frequency satisfies expression (32).fs» hfi (32)This allows one harmonic to be strengthened, weakened, or phase-shifted; another harmonic to remain unchanged and fundamental and harmonics to be controlled simultaneously but independently.

[0137] At this point it should be understood that while shown and described in connection with a single-phase system, the harmonic mitigation system described in accordance with the present disclosure may also be employed in three-phase transformers such as shown at 300 in FIG. 19, including but not limited to wye-connected, delta-connected, and hybrid winding configurations. In such embodiments, the transformer 300 includes a plurality of phase windings, 304, 306, and 308 corresponding to phases A, B, and C. Each phase winding 304, 306, and 308 includes a primary winding 310, a secondary winding 312 and one or more thirdAttorney Docket No. 2115-008441 -WO-POAor tertiary windings 314 configured to generate compensating magnetic flux for harmonic mitigation. The third winding may be implemented as a separate winding associated with each phase or as a shared tertiary winding, including a delta-connected tertiary winding.

[0138] In another aspect, a three-phase transformer 320 is shown in FIG.20. Three-phase transformer 320 includes a plurality of phase windings, 324, 326, and 328 corresponding to phases A, B, and C. Each phase winding 324, 326, and 328 includes a primary winding 330, a secondary winding 332 and one or more third or tertiary windings 334 configured to generate compensating magnetic flux for harmonic mitigation. In a manner similar to that described herein, the third winding may be implemented as a separate winding associated with each phase or as a shared tertiary winding, including a delta-connected tertiary winding.

[0139] Harmonic mitigation may be performed independently for each phase, such that harmonic components present in a given phase are mitigated through flux compensation associated with that phase, or coordinately across multiple phases, such that injected waveforms are jointly controlled to mitigate system-level harmonic effects. In three-phase embodiments, the harmonic mitigation system may target triplen harmonics, non-triplen harmonics, or combinations thereof, and may operate using current-based, voltage-based, or converter-based injection techniques as described herein. The principles of flux-domain harmonic mitigation, ampere-turn equivalence, and independent control of harmonic magnitude and phase remain applicable regardless of the specific three-phase winding configuration.

[0140] At this point, it should be understood that by employing multi-winding designs and adaptive control systems, the harmonic mitigation system, in accordance with the present disclosure enhances power quality, supports greater integration of renewable energy sources, and ensures stable operation for modern power systems.

[0141] Example embodiments are provided so that this disclosure will be thorough and will fully convey the scope to those who are skilled in the art. Numerous specific details are set forth such as examples of specific components, devices, and methods, to provide a thorough understanding of embodiments of the present disclosure. It will be apparent to those skilled in the art that specific details need not be employed, that example embodiments may be embodied in many different forms and that neither should be construed to limit the scope of the disclosure. In someAttorney Docket No. 2115-008441 -WO-POAexample embodiments, well-known processes, well-known device structures, and well-known technologies are not described in detail.

[0142] The terminology used herein is for the purpose of describing particular exemplary embodiments only and is not intended to be limiting. As used herein, the singular forms "a,” "an," and "the" may be intended to include the plural forms as well, unless the context clearly indicates otherwise. The terms "comprises," "comprising," “including,” and “having,” are inclusive and therefore specify the presence of stated features, integers, steps, operations, elements, and / or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof. The method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed.

[0143] When an element or layer is referred to as being "on," “engaged to,” "connected to," or "coupled to" another element or layer, it may be directly on, engaged, connected or coupled to the other element or layer, or intervening elements or layers may be present. In contrast, when an element is referred to as being "directly on," “directly engaged to,” "directly connected to," or "directly coupled to" another element or layer, there may be no intervening elements or layers present. Other words used to describe the relationship between elements should be interpreted in a like fashion (e.g., “between” versus “directly between,” “adjacent” versus “directly adjacent,” etc.). As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed items.

[0144] Although the terms first, second, third, etc. may be used herein to describe various elements, components, regions, layers and / or sections, these elements, components, regions, layers and / or sections should not be limited by these terms. These terms may be only used to distinguish one element, component, region, layer or section from another region, layer or section. Terms such as “first,” “second,” and other numerical terms when used herein do not imply a sequence or order unless clearly indicated by the context. Thus, a first element, component, region, layer or section discussed below could be termed a second element, component, region, layer or section without departing from the teachings of the example embodiments.Attorney Docket No. 2115-008441 -WO-POA

[0145] Spatially relative terms, such as “inner,” “outer,” "beneath," "below," "lower," "above," "upper," and the like, may be used herein for ease of description to describe one element or feature's relationship to another element(s) or feature(s) as illustrated in the figures. Spatially relative terms may be intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if the device in the figures is turned over, elements described as "below”, or "beneath" other elements or features would then be oriented "above" the other elements or features. Thus, the example term "below" can encompass both an orientation of above and below. The device may be otherwise oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.

[0146] The foregoing description of the embodiments has been provided for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure. Individual elements or features of a particular embodiment are generally not limited to that particular embodiment, but, where applicable, are interchangeable and can be used in a selected embodiment, even if not specifically shown or described. The same may also be varied in many ways. Such variations are not to be regarded as a departure from the disclosure, and all such modifications are intended to be included within the scope of the disclosure.

Claims

Attorney Docket No. 2115-008441 -WO-POACLAIMSWhat is claimed is:

1. A transformer comprising:a core;a primary winding wrapped about the core;a secondary winding wrapped about the core, the primary winding and the secondary winding being configured to generate a fundamental wave having a fundamental frequency;a third winding wrapped about the core; anda harmonic mitigation system operatively connected to the third winding, the harmonic mitigation system selectively introducing a harmonic mitigation current into the third winding to reduce harmonic components associated with the fundamental frequency induced in the primary winding.

2. The transformer according to claim 1, wherein the harmonic mitigation system introduces the harmonic mitigation current having a selected magnitude and a selected frequency.

3. The transformer according to claim 1, further comprising: a high pass filter operatively connected between the harmonic mitigation system and the third winding.

4. The transformer according to claim 1, further comprising: a load operatively connected to the secondary winding.

5. The transformer according to claim 4, wherein the load includes a harmonic generating load connected to the secondary winding, the harmonic generating load being a non-linear load configured to generate high-frequency multiples of the fundamental frequency that are introduced into the primary winding.

6. The transformer according to claim 1, further comprising: an alternating current (AC) power source operatively connected to the primary winding.Attorney Docket No. 2115-008441 -WO-POA7. The transformer according to claim 6, further comprising: a feedback control system operatively connected to the primary winding and the harmonic mitigation system, the feedback control system operating to adjust the harmonic mitigation current based on changes in AC power source.

8. The transformer according to claim 1, wherein the harmonic mitigation current is based on a relative phase difference and a relative magnitude difference between current passing through the primary winding and current flowing through the secondary winding.

9. The transformer according to claim 1, wherein the harmonic mitigation system is configured to control magnetic-flux within a transformer core such that harmonic flux components induced by nonlinear loads are substantially canceled in the primary winding.

10. The transformer according to claim 1, wherein harmonic mitigation is achieved by maintaining a selected ampere-turn product in the third winding independent of an absolute magnitude of current flowing in the third winding.

11. The transformer according to claim 1, wherein the harmonic mitigation system independently controls a magnitude and a phase of each selected harmonic order.

12. The transformer according to claim 1, wherein the harmonic mitigation system includes a voltage source converter operatively connected to the third winding and configured to generate a synthesized voltage waveform that produces the harmonic mitigation current.

13. The transformer according to claim 12, wherein the synthesized voltage waveform includes a fundamental-frequency component phase-aligned with the primary winding and one or more harmonic components having substantially equal magnitude and opposite phase relative to load-generated harmonic components.Attorney Docket No. 2115-008441 -WO-POA14. The transformer according to claim 1, further comprising a frequency-selective impedance network operatively connected to the third winding and configured to substantially block fundamental-frequency components while allowing harmonic-frequency components to pass.

15. The transformer according to claim 14, wherein the frequency-selective impedance network includes at least one of a series-resonant circuit, a parallel-resonant circuit, or a tuned band-pass circuit.

16. The transformer according to claim 1, wherein the harmonic mitigation system is configured to mitigate multiple harmonic orders simultaneously or sequentially according to a control scheduling strategy.

17. The transformer according to claim 1, wherein the harmonic mitigation current is based on at least one of current flow through the third winding, voltage across the third winding, or a combination thereof.

18. The transformer according to claim 1, wherein the harmonic mitigation system adaptively updates a magnitude and phase of the harmonic mitigation current in response to time-varying harmonic conditions.

19. The transformer according to claim 12, wherein the voltage source converter is rated for a fraction of an apparent power rating of the transformer while achieving harmonic mitigation through magnetic-flux control.

20. A three-winding transformer comprising:a core;a primary winding wrapped about the core;a secondary winding wrapped about the core, the primary winding and the secondary winding being configured to generate a fundamental wave having a fundamental frequency;a third winding wrapped about the core; anda harmonic mitigation system operatively connected to the third winding, the harmonic mitigation system selectively introducing a harmonic mitigation currentAttorney Docket No. 2115-008441 -WO-POAinto the third winding to reduce harmonic components associated with of the fundamental frequency induced in the primary winding, the harmonic mitigation current being configured to generate a compensating magnetic flux that reduces one or more harmonic components associated with the fundamental frequency induced by nonlinear loads on the three-winding transformer.

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