Evaluation of Electric Field and Space Charge Dynamics in Dielectric Under DC Voltage with Superimposed Switching Impulse
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energies Article Evaluation of Electric Field and Space Charge Dynamics in Dielectric under DC Voltage with Superimposed Switching Impulse Ik-Soo Kwon , Sun-Jin Kim , Mansoor Asif and Bang-Wook Lee * Department of Electrical and Electronic Engineering, Hanyang University, Ansan 15588, Korea; [email protected] (I.-S.K.); [email protected] (S.-J.K.); [email protected] (M.A.) * Correspondence: [email protected] Received: 19 April 2019; Accepted: 12 May 2019; Published: 15 May 2019 Abstract: The influx of a switching impulse during DC steady-state operations causes severe electrical stress on the insulation of HVDC cables. Thus, the insulation should be designed to withstand a superimposed switching impulse. All major manufacturers of DC cables perform superimposed switching impulse breakdown tests for prequalification. However, an experimental approach to study space charge dynamics in dielectrics under a switching impulse superposed on DC voltage has not been reported yet. This is because, unlike the DC stress, it is not possible to study the charge dynamics experimentally under complex stresses, such as switching impulse superposition. Hence, in order to predict and investigate the breakdown characteristics, it is necessary to obtain accurate electric field distribution considering space charge dynamics using a numerical approach. Therefore, in this paper, a numerical study on the switching impulse superposition was carried out. The space charge dynamics and its distribution within the dielectric under DC stress were compared with those under a superimposed switching impulse using a bipolar charge transport (BCT) model. In addition, we estimated the effect of a superimposed switching impulse on a DC electric field distribution. It was concluded that the temperature conditions of dielectrics have a significant influence on electric field and space charge dynamics. Keywords: bipolar charge transport model; DC electric field; space charge dynamics; switching impulse superposition 1. Introduction A switching impulse superimposed on a DC voltage causes severe overvoltage stress that can cause dielectric breakdown in an HVDC cable system. It causes a significant potential difference, instantaneously resulting in increased electrical stress for a period of several microseconds [1]. Therefore, consideration of this superposition situation is vital for the design of insulation in HVDC cables. In recognition of the danger of breakdown, an electrical breakdown test considering superimposed switching impulse voltage has been strongly recommended for HVDC cables in recent literature [2,3]. However, it is quite difficult to experimentally study the microscopic phenomenon that results from switching impulse superposition [4]. Therefore, a numerical approach needs to be devised for studying the space charge dynamics and electric field distribution under superimposed switching impulse. This kind of information is paramount for optimal and compact insulation design. In this paper, low-density polyethylene (LDPE) was selected as the dielectric for numerical study. The application of high DC voltage causes the generation and transport of charge inside the polyethylene-based insulation materials. This results in an inevitable accumulation of space charge inside the insulation material [5,6]. This space charge accumulation not only distorts the electric field Energies 2019, 12, 1836; doi:10.3390/en12101836 www.mdpi.com/journal/energies Energies 2019, 12, x FOR PEER REVIEW 2 of 15 term. Consequently, by understanding the impact of space charge on insulating materials, we can answer the problematic issues such as increase of the working stresses, lifetime prediction, and Energies 2019, 12, 1836 2 of 15 development of improved materials [7]. A bipolar charge transport (BCT) model was applied to numerically evaluate the space charge behaviordistribution and underelectric DC field stress, distribution but also causes under the DC deterioration voltage and ofsuperimposed insulating materials switching in the impulse. long term. In thisConsequently, simulation, bythe understanding switching impulse the impact was applied of space to chargethe system on insulating under prestress materials, DC we voltage can answer after reachingthe problematic DC steady issues state. such When as increase considering of the working the complex stresses, stresses lifetime resulting prediction, from and two development different sources,of improved a suitable materials coupling [7]. should be adopted. Coupling of the switching impulse with the prestressA bipolar DC voltage charge is transportquite intricate (BCT) considering model was the applied various to numerically continuities evaluateto be considered the space for charge the twobehavior systems. and For electric avoiding field distributionan unstable underintegration, DC voltage the continuity and superimposed of all equations switching at the impulse. moment In whenthis simulation, the switching the impulse switching was impulse superimposed was applied is maintained. to the system under prestress DC voltage after reachingIn this DC work, steady charge state. transport When considering properties the of complex LDPE under stresses the resulting application from of two DC di ffvoltageerent sources, were numericallya suitable coupling analyzed should in terms be adopted.of rates of Coupling generation ofthe and switching loss of charge impulse carriers. with the We prestress have also DC discussedvoltage is the quite space intricate charge considering dynamics the under various switching continuities impulse to be superimposed considered for on the the two prestress systems. DC For voltage.avoiding In anaddition, unstable we integration, have obtained the continuity the electric of field all equations distribution at the according moment to when temperature the switching and appliedimpulse voltage was superimposed types (i.e., DC is maintained.voltage or DC voltage with superimposed switching impulse). The maximumIn this electric work, field charge intensity transport caused properties by DC voltage of LDPE with under superimposed the application switching of DC impulse voltage werewas comparednumerically with analyzed that of inpure terms DC of to rates asse ofss generationthe effect of and the loss switching of charge impulse. carriers. We have also discussed the space charge dynamics under switching impulse superimposed on the prestress DC voltage. In 2.addition, Mechanism we have of Bipolar obtained Charge the electric Transport field distributionModel according to temperature and applied voltage typesThe (i.e., BCT DC voltagemodel oris DCdesigned voltage to with estimate superimposed space charge switching dynamics impulse). in The polyethylene-based maximum electric dielectricsfield intensity used caused in HVDC by DC cables voltage [4–10]. with It superimposed can overcome switching the following impulse limitations was compared of an with electrical that of conductivity-basedpure DC to assess themodel. effect of the switching impulse. • 2. MechanismUnder practical of Bipolar conditions, Charge dielectric Transport material Model is not homogenous, and local conditions can affect the transport processes and result in localized accumulations of space charge [8]. • ItThe cannot BCT account model for is the designed complicated to estimate charge transport space charge mechanisms, dynamics including in polyethylene-based charge injection dielectricsat the electrode, used in HVDC conduction, cables trapping, [4–10]. Itdetrapping can overcome, and therecombination following limitations in bulk of dielectrics of an electrical [9]. conductivity-basedThe BCT model model.used in this paper can not only overcome the aforementioned limitations, but realistically emulate the actual charge transport mechanism in the polyethylene-based insulation Under practical conditions, dielectric material is not homogenous, and local conditions can affect material• as well. The BCT model consists of five charge transport processes: injection, conduction, the transport processes and result in localized accumulations of space charge [8]. trapping, detrapping, and recombination. These five processes are based on four types of carriers in It cannot account for the complicated charge transport mechanisms, including charge injection at the• dielectric: mobile electrons, mobile holes, trapped electrons, and trapped holes. Figure 1 shows an overallthe electrode, schematic conduction, diagram. When trapping, the HVDC detrapping, voltag ande is applied, recombination the polyethylene-based in bulk of dielectrics dielectric [9]. is subjected to electrical stress, which results in charge injection at the interface between electrode The BCT model used in this paper can not only overcome the aforementioned limitations, but and dielectric. Thereafter, the injected charges become mobile carriers, and the BCT process begins. realistically emulate the actual charge transport mechanism in the polyethylene-based insulation Mobile carriers travel from injected electrode to the opposite electrode. This is the conduction material as well. The BCT model consists of five charge transport processes: injection, conduction, process which is based on hopping mechanism. The hopping mechanism means that mobile carriers trapping, detrapping, and recombination. These five processes are based on four types of carriers in hop over the shallow traps. However, not all mobile carriers can reach the counter electrode, because the dielectric: mobile electrons, mobile