Modelling of Transformer for Surges by Udaya Kumar (IISc)

Modelling of Transformer for Surges

Dr. Udaya KumarProfessor

HVE Lab, Dept. of EE, Indian Institute of ScienceBangalore, INDIA 560 012

• Electrical stress on transformer• Surge propagation on lines• Closer look into the surge distribution in transformer windings• Classical approach & Field based approaches• Distributed circuit based modelling approach• Salient aspects of parameter extraction• Summary

Modeling of Transformer for Surges

Prof. Udaya Kumar, Department of Electrical Engineering, Indian Institute of Science

Contents



Electrical stress due to power frequency voltages• Linear voltage distribution• Stress pattern is fixed• Major insulation

- Between inner coil and core, phase to phase, Primary and Secondary • Minor insulation - Inter turn Insulation The J & P Transformer Handbook, Martin J. Heathcote, 12th Edition , Newnes Publication , 1998

• Switching impulse voltage• Lightning impulse voltage• Very fast transient overvoltages



Transient electrical stresses

• Surges are of much higher magnitudes (LI 1050, 1425, 2400 kV)• Typical VT characteristics

- Higher strength for surges- Breakdown is instantaneous



VT characteristics of the insulation

Design Insulation Level for ANSI dielectric testsNelson Jk & Shaw C, “The impulse design of Transformer Oil-Cellulose Structures”, IEEE Trans. On DEI, Vol. 13, No. 3, June 2006

• Voltage is a function of spatial position along the winding, as well as, time• Non uniform voltage distribution Series stress can be very detrimental to turn-turn or coil-coil insulation failure• Amplification of the voltage

(global and local)



Salient aspects of the surge distribution

Modelling of the transformer for the dielectric stress under:• Switching surges• Lightning surges



Scope of the present discussion



Lightning surge on transmission line

Ground

LineLightning channel



Switching surge on transmission lineGroundSource

0.01 µs 0.1 µs



Switching surge on transmission line - Efield0.01 µs

0.1 µs



Surge on transmission line

• ZnO arrester is employed for protection• In further discussion no ZnO is considered• Voltage doubles at the transformer end

XXX

The surge response of the transformer winding was correctly picturised in 1920 itself !!!• For a step input, the initial true electromagnetic wave response settles down within 0.1 – 0.2 µs• Thereafter a distributed circuit-like response prevails Pseudo or Slow wave response• In principle two possible solution approaches



Surge response of transformer

• Governing equations for single-layer uniformly wound air cores coil



Classical approach Surge response of transformer

022

224

44

tVLCtx

VLCxV

gs

022

224

22

tVLCtx

VLCxV

gs

Wagner- Rudenberg’s Equation localized inductance

Blume-Boyajian’s Equation Total inductive coupling

• Winding non-uniformity, Presence of other windings and shields complicate the analytical approach• Investigation with model coils …• Numerical simulation using ladder network approach became the most feasible one

Accuracy of modelling critically depends on spatial and temporal resolution employed



Classical approach Surge response of transformer

• Most of the numerical packages provide complete solution of Maxwell’s equation• It would provide electrical stress as solution

appears to be an ideal choice !!!• Recall that we are at Pseudo-wave domain more precisely we are with quasi-static fields • Within the bulk of the conductor (winding c/s) no wave propagation can exist



Why not fully field based approach ?

• Outside (in the insulation) wave effects have already disappeared • Any Brute-force approach to arrive at quasi-static fields from wave solution would be a dumb exercise

- As such even for static fields, modelling of the individual turns is not practical - The existing discretisation does not permit global modelling and late time instability can arise

• Can we adopt a quasi-static approach ????



Fully field based approach for surge response ?



Suitable field based approach for surge response ?02 For Electric Field (Quasi-static):

For Magnetic Field:• Inside Conductor:(Conductors are relatively thin)

• Outside Conductor sJA 2

sJtAA

2

Coupled through conditions along the winding

Transient response solely due to boundary conditions Not generally dealt in the literature



Suitable field based approach for surge response ?

0 0

tlI

tJ

tA

RlV

RItAJ

tAE

11

• Due to the quasi-static nature of the field electric and magnetic fields are in separable form Distributed circuit model can be built

• Circuit based approach would be easier• However, it does not provide any knowledge on the field (& hence electrical stress)• A two-step procedure:

- Solve for the currents and voltages using suitable distributed network model- Use these voltages as input boundary condition in the field solution at every time instants



Suitable approach for surge response ?

• Only ladder network approach is possible with general circuit simulators• Accuracy v/s computational burden

• Each T or PI network assumes step-like changes in currents and voltages• Higher spatial resolution requires large number of steps low time steps• Note that while the turn-turn modelling of the winding is legal, modelling does not and cannotcross the quasi-static boundary !!!



Circuit based modelling

• Role of resistance (series and shunt) is very minimal• Only coupled L & C are to be fixed• Transformer has so many types of L & C’s• Quite often the salient features of power frequency model valid for specified sinusoidal voltage levels are considered to be universal• Some insight can be obtained from classical standing wave solution



Circuit based modelling – arriving at parameters

• Current and voltages vary both in space and time • Schematic current pattern for a standing wave component Current flowsin opposite directions !No or little axial flux &significant radial flux



Some insight from standing wave theory

• Spatial resolution decided by significant standing waves (or rate of rise)• Individual discs (of HV) can form PI or T elements• When modelling of LV is required, higher number of sections than HV is essential• Coupling across adjacent phases may not be essential • To make a “colourful” presentation FEMM simulation are carried out



Evaluation of network elements

FEMM - free 2d FEM software by David Meeker. http://www.femm.info/wiki/HomePage

• Most common practice is to consider individual elements for Cg and adjacent elements for Cs in the evaluation• Note that capacitance of the system is not same as that of the constituent elements taken in isolation Field solver codes would be very handy With good insight burden can be reduced

• Some exception are possible for the series capacitances (due to the geometry)• For both Cg and Cs genesis is field due to charges and it is orthogonal to conductorsAll the results hereafter are only for illustrative purposes



Evaluation of capacitances



Role of neighbouring conductors in C evaluation

By definition other conductors are to be grounded

• Multiple-load-cases option could be very handy basic element matrix does not change and only the applied voltage changes Neighbours cannot be ignored



Role of neighbouring conductors in C evaluation

• Is more complicated than evaluation of C’s• At surge frequencies, core does not carry flux• LV connected to distribution line is equivalent to shorted winding• Even otherwise, its mere presence can restrict the flux The L of HV winding would be lower than its air cored inductance



Evaluation of inductances


Prof. Udaya Kumar, Department of Electrical Engineering, Indian Institute of ScienceL at 50 kHz = 0.32 – 0.00059j HL at 50 Hz = 26.6 – 25.6j H

Flux expelledfrom the core

Evaluation of inductances – Role of core

• Even the leakage flux is pushed out core is more like a magnetic insulation• Grounded conductor for capacitance calculations



L at 50 kHz = 0.179 – 0.0005j H L at 50 Hz = 0.31 -0.012j H

Evaluation of inductances – Role of core



Evaluation of inductances – Role of LV

50 Hz 50 kHz

Flux expelledfrom LV region

Numericalpackages would bevery useful

• Stress under switching & lightning surges is an important input to the design• Surge distribution is governed by quasi-static fields, which permits distributed circuit modelling approach• Circuit results then can be used for field and dielectric stress calculation• Evaluation of elements of the ladder network needs careful modelling and insight Numerical packages would be very useful• Distinction needs to made between numerical resolution and modelling resolution

Adequate knowledge and tools exist for accurate evaluation of the stress under LI and SI



Summary

Acknowledgement: Special thanks to research scholars

Santosh J ****; Sethupathy K ***; Ashiq M **

Thank you … Questions ?



Modelling of Transformer for Surges by Udaya Kumar (IISc)

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