Real-Time Monitoring of Iron-Core and Copper Losses of Transformers Under (Non)Sinusoidal Operation

Lin, D.; Fuchs, E.F.

doi:10.1109/tpwrd.2006.874118

Cited by 33 publications

(20 citation statements)

References 12 publications

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“…2 Pseries-l~Tpseries(t)dt. (2)(3)(4)(5)(6)(7)(8)(9) The power dissipated in Zshun t is Pshunt=r~rpshunt(t)dt. ( …”

Section: Direct Loss Measurementmentioning

confidence: 99%

“…2-12) are proportional to the square of the current and frequency: PEC = gee/2h2, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13) where KEc is a proportionality constant. Under rated (sinusoidal) conditions, the load loss resulting in the hot spot temperature can be expressed as PLL-R =/2R2 + PEC-R, (2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) where PEC-R is the eddy-current loss resulting in the hot spot temperature under rated (sinusoidal) operating conditions. In per unit of the rated FR loss, Eq.…”

Section: Derating Of Transformers Determined From the K-factormentioning

confidence: 99%

“…This half-cycle saturation of transformers operating within a power system is the source of nearly all operating and equipment problems caused by GICs during magnetic storms (reactive power demand and its associated voltage drop). The direct consequences of the half-cycle transformer saturation are 9 The transformer becomes a rich source of even and odd harmonics; 9 A great increase in inductive power (VAr) drawn by the transformer occurs resulting in an excessive voltage drop; and 9 Large stray leakage flux effects occur with resulting excessive localized (e.g., tank) heating.…”

Section: Power System Effects Of Gicmentioning

confidence: 99%

“…R0 < X1, X0 < 3X1, where X1 is the leakage reactance, and X0 and R0 are the grounding reactance and resistance, respectively. 9 Reactance grounded: Xo < 10X~. 9 Resistance grounded: Ro > 2X0.…”

Section: Definitionsmentioning

confidence: 99%

“…9 Reactance grounded: Xo < 10X~. 9 Resistance grounded: Ro > 2X0. 9 High-resistance grounded: ground fault up to 10 A is permitted.…”

Section: Definitionsmentioning

confidence: 99%

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Harmonic Models of Transformers

2008

Power Quality in Power Systems and Electrical Machines

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Extensive application of power electronics and other nonlinear components and loads creates single-time (e.g., spikes) and periodic (e.g., harmonics) events that could lead to serious problems within power system networks and its components (e.g., transformers). Some possible impacts of poor power quality on power transformers are 9 saturating transformer core by changing its operating point on the nonlinear ~-i curve, 9 increasing core (hysteresis and eddy current) losses and possible transformer failure due to unexpected high losses associated with hot spots, 9 increasing (fundamental and harmonic) copper losses, 9 creating half-cycle saturation in the event of even harmonics and DC current, 9 malfunctioning of transformer protective relays, 9 aging and reduction of lifetime, 9 reduction of efficiency, 9 derating of transformers, 9 decrease of the power factor, 9 generation of parallel (harmonic) resonances and ferroresonance conditions, and 9 deterioration of transformers' insulation near the terminals due to high voltage stress caused by lightning and pulse-width-modulated (PWM) converters.Pfe = Phys + Peddy = ghys (Bmax)Sf + geddy(Bmax)2f 2, (2-1) where Phys, Peddy, Bmax, and f are hysteresis losses, eddy-current losses, maximum value of flux density, and fundamental frequency, respectively. Khys is a constant for the grade of iron employed and Keddy is the eddy-current constant for the conductive material. S is the Steinmetz exponent ranging from 1.5 to 2.5 depending on the operating point of transformer core.9 Elsevier Inc. All rights reserved. I ~,H I i r 9 FIGURE 2.4 Magnetic field strength inside and outside of a conductor. / / I i \ % o 9 "% ~Ho3 / %% u / / %

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“…2 Pseries-l~Tpseries(t)dt. (2)(3)(4)(5)(6)(7)(8)(9) The power dissipated in Zshun t is Pshunt=r~rpshunt(t)dt. ( …”

Section: Direct Loss Measurementmentioning

confidence: 99%

Section: Derating Of Transformers Determined From the K-factormentioning

confidence: 99%

Section: Power System Effects Of Gicmentioning

confidence: 99%

Section: Definitionsmentioning

confidence: 99%

“…9 Reactance grounded: Xo < 10X~. 9 Resistance grounded: Ro > 2X0. 9 High-resistance grounded: ground fault up to 10 A is permitted.…”

Section: Definitionsmentioning

confidence: 99%

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Harmonic Models of Transformers

2008

Power Quality in Power Systems and Electrical Machines

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Liquid‐Filled Transformers: Design, Optimization, and Monitoring

Fuchs

2017

Wiley Encyclopedia of Electrical and Electronics Engineering

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Liquid‐filled transformers have as cooling medium biodegradable, noncarcinogenic synthetic or natural esters. Three‐phase transformers of various configurations with and without grounding have several functions: increase/decrease of voltages and currents, filtering of harmonics, assist in protection of power systems, and permit a change of grounding reference. Oriented and amorphous electrical steels permit an efficient and economic design even for operating conditions above the knee of the nonlinear (B‐H) characteristic. Finite‐difference and finite‐element numerical methods can be successfully applied to model the influence of harmonics through phase‐factors to minimize skin effects. Real‐time monitoring of transformer losses is based on the calibration of voltage and current differences which limit the measuring errors to a few percent, for example, 6% at a measured power efficiency of larger than 98%, and permit the use of off‐the shelf transformers without any sensors installed within windings, iron cores, or coolant. Online measuring of total losses provides a mechanism for limiting the temperature increase. The performance of transformers underDCbias is important for renewable energy systems employing converters (e.g., rectifiers, inverters) and exposure to geomagnetically induced currents (GICs). Transformers are suitable for 6‐, 12‐ or 18‐pulse rectifiers used in high‐voltageDC(HVDC) transmission lines. Superconducting MW‐range transformers are available but costly, while superconducting magnets are widely used in the health (magnetic resonance imaging) and research fields: Large Hadron Collider in Switzerland/France and fusion reactor such as Wendelstein 7‐Xin Germany.

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