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A New Hysteretic Reactor Model for Transformer Energization Applications Title: By : Afshin Rezaei-Zare & Reza Iravani University of Toronto June 2011

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Outline 1. 1.Existing hysteresis models in EMT programs 2. 2.Drawbacks of the existing models 3. 3.New hysteretic reactor model 4. 4.Impact on Remnant Flux (Lab. Measurement) 5. 5.De-energization / Re-energization 6. 6.33kV-VT Ferroresonance Lab. test results 7. 7.Conclusions 8. 8.Applications

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EMTP Type-96 EMTP Type-92 (Current Hysteresis model of the EMTP-RV) PSCAD/EMTDC Jiles-Atherton model (Not a reactor but incorporated in the CT model) Proposed New Hysteretic Reactor Existing Hysteresis Models in EMT Programs

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Type 96 model Piecewise linear model Piecewise linear model Originally developed by Talukdar and Bailey in 1976 and modified in 1982 by Frame and Mohan Originally developed by Talukdar and Bailey in 1976 and modified in 1982 by Frame and Mohan Simple and computationally efficient Simple and computationally efficient Minor loops are obtained by linearly decreasing the distance between the reversal point and the penultimate reversal point Minor loops are obtained by linearly decreasing the distance between the reversal point and the penultimate reversal point

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Drawbacks of Type 96 Model No stack is used to store the extrema of excitation which leads to open cycles Similarity of minor loops to the major loop due to scaling approach used by the model (such a similarity is not valid in reality) The existence of a saturation point is not verified experimentally The model implemented in EMTP-V3 is pseudo nonlinear

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Drawbacks of Type 96 Model – Cont’d Noisy behavior and erroneous results (in some transients such as ferroresonance) due to switching the operating point between two adjacent branches of the piece-wise linear characteristic (Artificial switching & Numerical oscillations) Piece-wise linear modelSmooth nonlinear model

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Type 92 model Developed in 1996 by Ontario Hydro Developed in 1996 by Ontario Hydro Based on hyperbolic functions Based on hyperbolic functions Instantaneous flux is separated in two components: i) hysteresis (irreversible) ii) saturation (reversible) Instantaneous flux is separated in two components: i) hysteresis (irreversible) ii) saturation (reversible) Current EMTP-RV model is based on this approach Current EMTP-RV model is based on this approach

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Hyperbolic functions in Type 92: instantaneous flux is used to find unsaturated flux which is then used to find instantaneous current Model Type 92 slope Saturated flux vs. Unsaturated flux (to describe saturation) Unsaturated flux vs. Current (to describe hysteresis)

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Drawbacks of Type 92 Model Raw data Fitted data Inaccuracy (1) Limited flexibility to fit to the hysteresis major loop (only based on one hyperbolic term)

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Drawbacks of Type 92 Model Inaccuracy (2) Only upper part of the trajectory is used and the lower part is assumed to be symmetric to the upper part (while in reality the shapes of the two parts are independent) Current (A)

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Jiles-Atherton Model Physically correct model decomposes the magnetization into “reversible anhysteretic” and “irreversible” components based on a weighted average: Reversible part is based on Langevin function: Irreversible part is based on the differential equation:

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Drawbacks of the Jiles-Atherton Model Limited flexibility to fit to the measurements due to the utilized Langevin function, and the model very few parameters (5 parameters) In some cases, non-physical results as the input current changes the direction Formations of minor loops and the major loop are dependent (changing the parameters changes both minor and major loop shapes) In the PSCAD/EMTDC, it is not available as a reactor to build a desired general system for transient studies. (Only incorporated in a CT model)

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New Hysteretic Reactor Model A modified Preisach Model - a time-domain implementation with true-nonlinear solution within the EMTP-RV - Independent formation of minor loops from the major loop (consistent with the observed hysteresis loops of the magnetic materials) Physically correct hysteresis model Memory dependent model: past excitation extrema are stored in memory to form the magnetization trajectories. Representing wiping-out property, (a well-known physical property of the ferromagnetic materials)

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New Hysteretic Reactor Model Same major loops – Different minor loops Forms major loop Forms minor loop

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New Hysteretic Reactor Model

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Hysteresis Shapes

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Remnant Flux 40% 80% -50% 0%

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Harmonic Initialization

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Impact on Remnant Flux (Lab. Measurement) Close-up Window imim

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Impact on Remnant Flux (Lab. Measurement) – Cont’d

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De-energization / Re-energization Auto-reclosure operations on a 12kA Fault Current

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Remnant Flux subsequent to the second current interruption Different Minor loop shapes Different Remnant Flux (for the same switching scenario) Remnant flux

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Impacts on CT Saturation and protection (Following the final reclosure on the permanent fault)

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30.7 kV (1.14pu) 63.5 kV (2.36pu) 52.4 kV (1.94pu) 38.4 kV (1.43pu) 11.8 kV (0.44pu) 33kV-VT Ferroresonance Laboratory test results Source peak voltage Measured VT voltage

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33kV-VT Ferroresonance Lab Test 52.4 kV (1.94pu) 63.5 kV (2.36pu) 103 W 29 W Power Loss Voltage 218 W

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33kV-VT Ferroresonance Lab Test Model Type-92 Hysteresis Loop

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33kV-VT Ferroresonance Lab Test Major loop Hysteresis loop at rated voltage New Reactor Hysteresis Loops

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33kV-VT Ferroresonance Lab Test Bifurcation Points

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33kV-VT Ferroresonance Lab Test Core Power Loss Power Loss Comparison

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33kV-VT Ferroresonance Lab Test – Cont’d Hysteresis Loops Comparison Measurement EMTP-RV (Type 92) EMTP Type-96 New Reactor

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33kV-VT Ferroresonance Lab Test Dynamic Inductance ( Slope of magnetization trajectories ) Before Ferroresonance (Normal conditions) Under Ferroresonance conditions

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Capability of the models to represent the core dynamic behaviors Core Inductance change As the core is driven into ferroresonance with respect to normal operation Change directionModel Measurement New Reactor EMTP Type-96 EMTP-RV (Type-92) Single-valued saturation curve No change

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Another Example – Comparison between two hysteresis models with the same major loop but different minor loop formations Model 1Model 2 Bifurcation diagrams

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Ferroresonance demo

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Conclusions The model is based on widely-verified and accepted Preisach model of hysteresis Independent formation of major and minor loops True nonlinear solution within the EMTP-RV Can accurately represent the physical properties of the magnetic core materials Can accurately represent the dynamic core behavior under electromagnetic transients New Model Features

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Applications For accurate EMTP studies on : De-energizing/re-energizing of transformers Ferroresonance phenomena in power and instrument transformers Determination of the core remnant flux Precise modeling of VTs, CTs, and CVTs for protection studies Accurate modeling of electrical machines Efficient design of control systems for power-electronic based drives by taking into account the machine nonlinearity and actual power loss

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Important points It is evident that a more detailed model needs more parameters. although, a model with simple implementation and with less required parameters is generally preferable, the accuracy of such models are limited. For a sophisticated hysteresis model, “not needing minor loop data”, is a drawback not an advantage. Due to different behavior of minor loops (extensively verified by experiments), neglecting the minor loop parameters can result in completely different and unexpected results. For the new reactor, if the minor loop data are not available, a set of pre-specified default values can be considered.

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