partial dischargeriskunderspacecharges generation ...€¦ · m. e. banda -comsol conference...

Partial discharge risk under space charges generation and transport effects

M. E. BANDA*, D. MALEC, J-P. [email protected]

LAPLACE, Toulouse University, CNRS, INPT, UPS, France.

Comsol Conference, LausanneOct. 22-24, 2018

PD risk under space charges generation and transport effects – 2M. E. BANDA - Comsol Conference – Lausanne, Oct. 22-24, 2018

STUDY CONTEXT AND PROBLEMATIC

COMSOL® IMPLEMENTATION & SIMULATION MODEL

MAIN SIMULATION RESULTS


Study context and problem - From power electronics systems to busbars

Electronics components




Power Converters




Busbars powered by a HVDC 2.5kV voltage bus

Power Converters




Busbars powered by a HVDC 2.5kV voltage bus

Power Converters

Ea = +2500 V

Insulator

Ek = 0 V

Air

Air

AirTriple point = Conductor(busbar)

+dielectrics(insulator)

+Air contact region


Study context and problem - Charge generation in dielectrics materials

Impurity

Dipolar polarization

IonisationDissociationRecombinaison

Cath

ode

Injection

Discharges

Ano

de

Insulator

+

__ _

_+

_+ _+

_ +

_

+__ +

+++

__

+++

__

__

Ea = +2500 V

Insulator

Ek = 0 V

Air

Air

Air

Main charge generationmechanisms



Impurity



Cath

ode

Injection

Discharges

Ano

de

Insulator

+

__ _

_+

_+ _+

_ +

_

+__ +

+++

__

+++

__

__

V V V V

t(time)

Vacuole

Increase of internal electric field

Partial dischargeInside vacuole Electrical tree

Defaults Pre-breakdown

Electrical breakdown

Dielectrics damage

Ea = +2500 V

Insulator

Ek = 0 V

Air

Air

Air




Impurity



Cath

ode

Injection

Discharges

Ano

de

Insulator

+

__ _

_+

_+ _+

_ +

_

+__ +

+++

__

+++

__

__

V V V V

t(time)

Vacuole

Increase of internal electric field

Partial dischargeInside vacuole Electrical tree

Defaults Pre-breakdown

Electrical breakdown

Dielectrics damage

Ea = +2500 V

Insulator

Ek = 0 V

Air

Air

Air


A better characterization of charge mechanisms in dielectrics material to preventpartial discharge risk in air surrounding HVDC power systems.


Implementation under Comsol (1/2) - Simulation conditions

☞ Geometry and meshing

2D-simulation model

162 k domain elements~4 MFinite elements

Interfaces refinement50 Boundary layers

☞ Initial conditions

ρ = 0.05 C ⋅m−3 Dielectrics( )p = 1 barT ° ~ 293,15 K 20 °C( )Dielectrics : PTFE, ε = 2,1 ;~ 4 ⋅105 Finite elements ;~ 94,93% meshing quality factor ;

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

Variable distribution

Initial charge and associatedElectric field distribution

Potential distribution

Cathode Anode


Implementation under Comsol (1/2) - Simulation conditions

☞ Geometry and meshing

2D-simulation model

162 k domain elements~4 MFinite elements

Interfaces refinement50 Boundary layers

☞ Initial conditions

ρ = 0.05 C ⋅m−3 Dielectrics( )p = 1 barT ° ~ 293,15 K 20 °C( )Dielectrics : PTFE, ε = 2,1 ;~ 4 ⋅105 Finite elements ;~ 94,93% meshing quality factor ;

⎧

⎨

⎪⎪⎪⎪

⎩

⎪⎪⎪⎪

Variable distribution

Initial charge and associatedElectric field distribution

Potential distribution

Triple points

Cathode Anode


Implementation under Comsol (2/2) - Model equations for bipolar conduction

☞Main model equations

§ Transport equation ),(),(),(),( txEtEtxntxj ⋅⋅= µ

),(),(),( txsxtxj

ttx =

∂∂+

∂∂ρ

∂E(x, y)∂x∂y

= ρ(x, y)ε rε0

§ Poisson equation :

§ Continuity equation :





),(),(),( txsxtxj

ttx =

∂∂+

∂∂ρ

∂E(x, y)∂x∂y

= ρ(x, y)ε rε0


☞With§ j(x,t) the injection/extraction at interfaces : J (x,t) = AT 2 exp −

qWe,h

kBT

⎛

⎝⎜⎞

⎠⎟exp

qkBT

⎛

⎝⎜⎞

⎠⎟qE(x,t)4πε

−1⎡

⎣⎢⎢

⎤

⎦⎥⎥






),(),(),( txsxtxj

ttx =

∂∂+

∂∂ρ

∂E(x, y)∂x∂y

= ρ(x, y)ε rε0


☞WithJ (x,t) = AT 2 exp −

qWe,h

kBT

⎛

⎝⎜⎞

⎠⎟exp

qkBT

⎛

⎝⎜⎞

⎠⎟qE(x,t)4πε

−1⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TktxEq

TktxEtEµ

BB

a

2),(sinhexp

),(2),( λφλν

§ µ(E,t) Charge mobility as function of E(x,t) :


§ j(x,t) the injection/extraction at interfaces :





),(),(),( txsxtxj

ttx =

∂∂+

∂∂ρ

∂E(x, y)∂x∂y

= ρ(x, y)ε rε0



qWe,h

kBT

⎛

⎝⎜⎞

⎠⎟exp

qkBT

⎛

⎝⎜⎞

⎠⎟qE(x,t)4πε

−1⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TktxEq

TktxEtEµ

BB

a

2),(sinhexp

),(2),( λφλν


§ s(x,t), Source terms (case of mobile electrons)

seµ(x,t) = −Be ⋅neµ 1−netN0, et

⎛

⎝⎜

⎞

⎠⎟

trapping! "### $###

+ net ⋅υ exp −φtrekBT

⎛

⎝⎜⎞

⎠⎟

detrapping! "### $###

− S1 ⋅neµ ⋅nht − S3 ⋅neµ ⋅nhµ

recombination% &#### '####







),(),(),( txsxtxj

ttx =

∂∂+

∂∂ρ

∂E(x, y)∂x∂y

= ρ(x, y)ε rε0



qWe,h

kBT

⎛

⎝⎜⎞

⎠⎟exp

qkBT

⎛

⎝⎜⎞

⎠⎟qE(x,t)4πε

−1⎡

⎣⎢⎢

⎤

⎦⎥⎥

⎟⎟⎠

⎞⎜⎜⎝

⎛⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−=

TktxEq

TktxEtEµ

BB

a

2),(sinhexp

),(2),( λφλν


§ s(x,t), Source terms (case of mobile electrons)

seµ(x,t) = −Be ⋅neµ 1−netN0, et

⎛

⎝⎜

⎞

⎠⎟

trapping! "### $###

+ net ⋅υ exp −φtrekBT

⎛

⎝⎜⎞

⎠⎟

detrapping! "### $###

− S1 ⋅neµ ⋅nht − S3 ⋅neµ ⋅nhµ

recombination% &#### '####


11 variables to compute for model solving - Implementation under General-PDE modules



Results validation - Paschen limit applied to partial discharges

(P, T°) = (1,013 bar, 20°C) ;Uniforme electric field /air gap ;Plane electrodes ;

☞

[1] F. Paschen Über die zum Funkenübergang in Luft, Wasserstoffand Kohlensäure beiverschi edenen Drücken erforderliche Potentialdifferenz, Wied. Annalen der Physikund Chemie. Wiede-manns Annalen, Ser. 3, 37(1), 69 (1889)

Up =B ⋅( pd)

ln( pd)+ A

ln 1+ 1γ

⎛⎝⎜

⎞⎠⎟

γ i =nsecondarynion

Bair ! 365 (V.Torr−1.cm−1)

Aair ! 15 (Torr−1.cm)Einception, air ≥ 3 kV/mm


Main simulation results - Cartographies of simulated Electric field

§ Emax(x, t) decreases by 72% at anodetriple point and increases by 4% atcathode triple point ;

Electric field at triple points

§ Implanted charges disturb the electricfield distribution in dielectrics ;

§ |Emax(x, t)| in air ≥ 3 kV/mm ;

Partial discharge risk at triple points.


Main simulation results - Injected charges distributions at triple points (y=1)

§ More holes injection from anode thanelectrons from cathode ;

Charge injection mechanism at triple points

§ Each charge type increases with time atboth interfaces ;

§ Low trapping and transport mechanismsin the bulk with time ;

The nature and distribution of injected chargeshas a significant impact on partial dischargerisk at triple points.


Conclusion

Simulated Model giving well agreement with experimental measurements for LDPE material

Simulation Measurement

Confrontation with PTFE experimental measurements

Use of Powerful Comsol® solver to compute themodel more quickly than Fortran® source code


THANK YOU FOR YOUR ATTENTION

partial dischargeriskunderspacecharges generation ...€¦ · m. e. banda -comsol conference...

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