Finite Element Model of HVDC Converter Harmonic ...

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Finite Element Model of HVDC Converter. Harmonic Effects on Partial Discharge. M. Azizian Fard, A. J. Reid and D.M. Hepburn. Institute for Sustainable ...
Finite Element Model of HVDC Converter Harmonic Effects on Partial Discharge M. Azizian Fard, A. J. Reid and D.M. Hepburn Institute for Sustainable Engineering and Technology Research Glasgow Caledonian Universality Glasgow, UK [email protected]

Abstract—Partial discharge (PD) measurement as a non-destructive diagnostic tool is a proven technique that has served in both design improvement and condition monitoring of insulation systems. An understanding and interpretation of the physical phenomena and influencing parameters of PD in AC systems have been established through experience over the past decades, however, flexible alternating current transmission system (FACTS) and high-voltage direct current (HVDC) systems present new challenges. These are due to the differences in physical space charge phenomena and the complexities introduced by power electronic switching. More meaningful information on the physical condition of the dielectric insulation could be gained given a better understanding of the physical discharge phenomena occurring in the region of a defect. Numerical modelling of these complex phenomena can go some way to achieving this. In this paper, PD behavior in HVDC systems has been investigated with the employment of Finite Element Methods (FEM). An insulation defect, consisting of a single void within a polymeric insulation layer, has been modeled to investigate the idealized behavior of such a defect in, for example, a sub-sea HVDC shielded cable. The multi-physics simulation package COMSOL interlinked with MATLAB were used to study the electric field distribution imposed by the HVDC waveform and the PD process. It was found that additional harmonic content results in an increased PD repetition rate to be proportional to the dominant harmonic amplitude. Keywords— Finite element analysis; Power conversion harmonics; HVDC transmission; Insulation; Partial Discharge

I.

INTRODUCTION

With the increasing trends towards offshore electricity generation and interconnecting power networks, polymeric HVDC cables are increasingly attractive for technical and economical reasons [1]. However, the operational nature of HVDC systems introduces some new challenges like harmonic injection and space charge accumulation [2, 3]. Converters are the main source of characteristic harmonics which are caused by the switching operation of power electronic valves and also they are transferor of non-characteristic harmonics that stem from nonlinear loads or unbalanced operation of the interconnected AC systems [4, 5]. Due to exposure to voltage ripples and abrupt

waveform changes, dielectrics undergo higher stresses which may lead to their hastened degradation and premature failure. Concerning partial discharges under AC fields, well established work has been conducted over the past few decades and harmonics have been reported to have undesirable effects both on insulation integrity and the diagnostics process [6]. Superimposed on the supply voltage, they cause higher PD repetition rate [7], shorten the tree initiation and growth time in XLPE insulation [8] and could change PD intensity and discharge magnitude. In addition, distorted power supply waveforms could result in misinterpretation of PD analysis, particularly, harmonic contents influence phase position of PD discharges [6]. Hence, derived PD statistical parameters and distribution patterns will change, as well. Although valuable research works have been conducted concerning insulation behavior and PD activity under DC regime [9-11], less has dealt with the effect of HVDC with superimposed harmonics on PD behavior. Therefore, the aim of this paper is to present the investigation, through modeling, on the influence of rippled HVDC waveforms on the characteristics of partial discharges. The model consists of a slab of polymeric insulation containing a single cavity and the influence of the first three dominant characteristic harmonics- 6th, 12th and 18th harmonics that appear in the output of six-pulse line commuted converters (LCC) [4]have been considered. II.

PD PHYSICS AND MECHANISM

Partial discharge in a gas filled cavity will start as the electric field across it exceeds the minimum breakdown strength of the medium providing a free electron is available in enough mean free path away from anodic wall of the cavity to initiate an avalanche [12]. These two requirements are dynamic in nature and depend on driving parameters and the condition of the site in which PD occurs, i.e. the geometry, location, encompassed gas pressure, material of the bulk insulation, mechanism of electron emission and magnitude of the electric field to name a few [13]. Generally, when the two conditions are fulfilled a PD occurs and the discharge will last until the field across it drops below the extinction level. Then, the resultant charge carriers

recombine via the conductive part of cavity wall, drift away through the bulk of the insulation, or trapped in potential walls being source of next avalanche starting electron [14]. Availability of a starting electron is a stochastic function of conditions governing the insulation and the cavity, and the time for its availability is known as statistical time lag. Therefore, PDs have a stochastic behavior [15]. III.

PD MODELING UNDER HARMONIC DC VOLTAGE

A. Governing Equations and PD Inception Field In order to simulate partial discharge due to the modeled gas-filled defect within the geometry of insulation, the discharge phenomenon has been considered as a macroscopic process [16, 17]. Distribution of the electric field within the insulation and across the void is governed by Gauss’s Law, Ohm’s Law and the equation of continuity as follows: D  

C m

3

(1)

where D is the electric flux density and ρ is the volume density of free charges.

E = J

C m

2

Fig. 1. Geometry of the model containing an air-filled cavity. Table I MODEL PROPERTIES Quantity

Value

Units

Insulation dimensions Void radius Electrode dimensions Relative permittivity of insulation Relative permittivity of air Conductivity of insulation Conductivity of cavity during PD Conductivity of cavity without PD

50×5 0.6 30×5 2.25 1 1e-14 1e-2 8e-13

mm2 mm mm2 S/cm S/m S/m

(2)

where σ is the conductivity, E is the electric field intensity, and J is the current density.  3 J  (3) A m t Combining (1), (2) and (3) the field governing equation will be: dv  ( V   ( ))  0 (4) dt Equation (4) was solved for electric potential and field distribution for the model using finite element analysis in COMSOL Multiphysics software for the applied voltage waveforms. Considering Panchen’s Law, the minimum breakdown level for a gas filled cavity can be obtained by [18]:

E inc  (

E P

where

E P

) P (1  crit

B n

(2 pa)

)

(5)

, B and n characterize the ionization crit

processes in the gas. For air

 E P

 24.2VPa 1m 1 and crit

n=0.5, B=8.6 Pa0.5m0.5 and a is the radius of the cavity. B. Geometry of the Model A two dimensional model of a slab of polymeric insulation, polyethylene, containing a single void has been developed in COMSOL Multiphysics. The cavity is located in the center of the insulation which is placed between two copper electrodes. Fig. 1 shows the model and the properties of the model are given in Table I.

Fig. 2. Potential distribution within the model.

C. Discharge Process The test DC voltages superimposed with harmonics were generated in MATLAB, and applied iteratively to the model in COMSOL. For every value of the waveform the relevant field across the cavity is computed using FEM method in COMSOL and rendered to MATLAB through a live interlink, where the requirements of PD occurrence, discharge inception field and the availability of initiatory electron, are checked within a running codes. PD occurrence is simulated by changing the conductivity of the cavity as below [17]:

  max (1exp(  ( U  I ))) U inc I crit     0 

With PD

Without PD

 

QPD  

t

  E.dsdt

PD magnitude (pC)

Normalized applied DC voltage

where σmax is the maximum conductivity of the void during PD, U and I are the voltage across and the current through the cavity, Uinc is the inception voltage, Icrit is the critical current to start an electron avalanche, and σ0 is the normal conductivity of the cavity. In case the conditions of discharging are fulfilled, the conductivity of the void is increased to make a passage for current flow: simulating PD occurrence. During the partial discharge, likewise, the instantaneous field is computed and when its value falls below the extinction voltage Uext then the PD process is terminated, and the conductivity returns to its initial value. The charge magnitude of each PD pulse is calculated by integration of the resulting current density during PD occurrence time interval using Ohm’s law (7): (7)

s

where, s and Δt are the cross section of discharge region and duration of PD pulse, respectively.

Fig. 4. Simulated PD pulses for DC superimposed with 6th harmonic of (a) 5% (b) 10% (c) 15% and (d) 20% relative magnitude.

RESULTS

DC voltage superimposed with 6th, 12th, and 18th harmonics with relative magnitude of 5%, 10%, 15% and 20% were applied to the model separately and the simulated PD pulses due to relevant stressing fields are illustrated in Figures 3, 4 and 5 respectively. Generally, PD pulses occur in the peak region of the applied voltages but as the level of added harmonic increases PD tends to occur in other values of the applied voltage, as well.

PD magnitude (pC)

IV.

Normalized applied DC voltage

Whole the process is governed in a program coded in MATLAB which is in a live interlink with COMSOL as in the flow chart given in Fig. 2 [16,19].

Start

Initialize Model Parameter in COMSOL Generate Test Waveform in MATLAB

Fig. 5. Simulated PD pulses for DC superimposed with 12th harmonic of (a) 5% (b) 10% (c) 15% and (d) 20% relative magnitude

Solve Model in COMSOL

PD Conditions Fulfilled?

False

False

PD Extinction Condition Fulfilled?

True Decrease Conductivity in Void

Increase Timestep

False

PD magnitude (pC)

Increase Timestep

Normalized applied DC voltage

True Increase Conductivity in Void & Solve Model in COMSOL

Waveform End? True

Process in MATLAB

Terminate

Process in COMSOL

Fig. 3. Flow chart of PD simulation in the model (COMSOL interlinked with MATLAB).

Fig. 6. Simulated PD pulses for DC superimposed with 18th harmonic of (a) 5% (b) 10% (c) 15% and (d) 20% relative magnitude

Fig. 7 shows the trends of the simulated PD pulses under the application of rippled DC voltages. As the relative magnitude of the harmonic increases, the number of PD increases and there is a direct correlation between the total number of PDs occurring and the harmonic order for a given relative harmonic amplitude. V.

CONCLUSION AND FUTURE WORK

An insulation defect, a single void, within a polymeric insulation has been modeled to investigate the idealized behavior of PDs accruing under HVDC voltage superimposed with characteristic harmonics using the multiphysics simulation package COMSOL interlinked with MATLAB. It was found that additional harmonic content results in an increased PD repetition rate. Under such voltage impression PD pulses are majorly happened in peak regions and as the relative magnitude of added harmonic increases they occur at other voltage values, as well. According to the results, operating condition of HVDC converters have influence on PD characteristic playing a role in insulation diagnosis. Although an undesirable artifact of the converter operation, voltage harmonic, as shown in the results, may yield useful information on the nature of the defect. Increased PD repetition rate with harmonic voltage level indicates a potential for accelerated aging of the insulation system. This may inform quality assessment procedure and diagnostic routines in order to identify with a greater degree of confidence, potential defect and extend the life span of the equipment. Future work will concentrate on investigating PD behavior and characteristics in laboratory and field test under distorted HVDC voltage to compare the result with ones achieved in the model.

[2]

[3]

[4] [5] [6]

[7]

[8]

[9] [10]

[11]

[12] [13]

[14]

[15]

[16]

[17]

[18]

[19]

Fig. 7. PD repetition rate vs. relative harmonic magnitude for 6th, 12th and 18th harmonics.

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