Transformer Modeling for Lower-Frequency Phenomena. R. A. Walling

Transcription

1 Transformer Modeling for Lower-Frequency Phenomena R. A. Walling

2 Lower - Frequency Phenomena Phenomena well below first winding resonance frequency < several khz Includes: most line switching transients capacitor switching harmonic interactions ferroresonance control interactions

3 Transformer Characteristics Series characteristics resistance leakage inductance only series characteristics need to be modeled for most simulations Shunt characteristics saturation - needs to be modeled only in simulations having high flux core loss - particularly important for ferroresonance simulations winding capacitance - important for some ferroresonance and switching (TRV) cases

4 Winding Resistance Resistance = R dc + DR ac ac resistance component due to eddy currents in windings, stray eddies, skin effect X / R Frequency (Hz) Actual Transformer Series R- L Model

5 Frequency-Dependent Winding Resistance Model Determine R dc and DR ac from transformer test data Use series - parallel R-L network to model series winding impedance so that R = R dc + DR ac * (f/f 0 ) 1.2 to 1.8

6 Key Saturation Parameters Flux Intercept Air-Core Inductance 1.0 p.u. Flux Magnetizing Inductance Current

7 Air Core Inductances For concentric windings, inner winding has smaller X ac than outer winding most often, inner winding is lower-voltage winding H V L V C O R E L V H V For core - form construction in HV and EHV transformers, X ac of HV winding generally p.u. on OA base

8 Air Core Inductances Other winding configurations are sometimes used: H V L V H V C O R E H V L V H V HV LV HV LV C O R E Interleaved winding pancake winding (used in shell-form construction)

9 Modeling Saturation Use test data -- manufacturer s curves High current data rarely based on tests Complicating factors Exciting current includes core loss and magnetizing components RMS currents usually provided, not crest Winding capacitance can significantly affect lowcurrent data Hysteresis biases curve Or, estimate key parameters based on construction detail of curve usually not critical

10 Excitation Curve Reduction Step 1 - Extract loss component from current for each point I q = P Core_ V Loss 2 2 m exc q I = I I

11 Excitation Curve Reduction Step 2 - Convert RMS curve to instantaneous SATURATION auxiliary function in EMTP performs conversion using recursive approach Irms Ipk

12 Excitation Curve Reduction Step 3 - Compensate for effect of winding capacitance winding capacitance can dominate magnetizing reactance causing cobra flux-current curves smaller capacitance can cancel much of the magnetizing current

13 Excitation Curve Reduction Step 4 - Remove offset due to coercive current Flux Current Biased by Coercive Current Anhysteretic Curve

14 Core Loss Representation Very important for low-current phenomena such as ferroresonance Accuracy requires good hysteresis model do they exist? Linear resistance representation is usual approach actual core loss increases more rapidly than V 2 as core reaches saturation

15 Limitations of Nonlinear Resistor for Core Loss Model Hysteresis loss is dependent on maximum flux, not voltage loss match for 60 Hz excitation does not mean that correct Flux - Current trajectory is followed

16 Division of Leakage Inductance in Model Without saturation, leakage division is arbitrary for a two-winding transformer or autotransformer without tertiary Division between primary and secondary impedance determined by air-core impedances X H X H-L =X H + X L X L X ach =X H + X ac X acl =X L + X ac X ac

17 Default Assumptions for Leakage Split and Air Core Put most of leakage impedance on HV side 75% - 90% of total impedance as X H assumes concentric winding with HV as outer Adjust final slope of saturation curve (X ac ) so that X ac + X H = a reasonable estimate of X ach 0.5 p.u. on OA base for large, high BIL transformer as low as p.u. for distribution transformers More accuracy requires winding design info: build, height, mean diameter, turns, etc.

18 3 - Winding Transformers Star model used by most modelers X H X L X ac X T 6 parameters to match with 4 variables inadequate model where detailed data are available good enough where air core impedances are guessed; put saturation on tertiary winding terminals (not node) sometimes problems with negative inductance Good model can be devised with coupled inductances add fictitious winding for core representatio

19 3-Phase Core Topology Core topologies can be represented by duality models can be important for some phenomena

20 Summary Simple assumptions and available data are sufficient for most simulations remember frequency dependence of leakage Accurate, detailed models require test data and design data extreme detail rarely justified ferroresonance sensitive to model