Characterization and Robustness of HVDC Insulation

2013 IEEE International Conference on Solid Dielectrics, Bologna, Italy, June 30 – July 4, 2013

Characterization and Robustness of HVDC Insulation Thomas Christen ABB Schweiz AG, Corporate Research, CH-5405 Baden-Dättwil Email: [email protected] Abstract—The physical complexity and the sensitive parameter dependence of electric conduction in polymer insulation materials make the development of high voltage direct current (HVDC) insulation devices a challenging task. Two prerequisites for a successful design process are discussed: 1) modeling and characterization of insulation materials, and 2) concepts for robust and fault tolerant insulation systems.

I.

I NTRODUCTION

Recent progress in power electronics and ongoing changes in power infrastructure induced a considerable demand for DC insulation systems. In contrast to alternating current (AC), for DC the electric field distribution is governed by the verylow frequency electric and dielectric properties [1]. Although polymer insulation materials are used in high voltage (HV) technology since many decades, the understanding of their DC conduction behavior and concepts for accurate material characterization are still poor. The complexity of the underlying physics [2] leads not only to a lack of understanding but also to a lack of robustness of the electric behavior, which provides a serious challenge for designing HVDC insulation devices. This paper presents some fundamentals of HVDC insulation designing with focus on solid polymer materials. It emphasizes the design development process (Sect. II), the special effort required for predicting the electric behavior (Sect. III), and ways to develop robust insulation systems (Sect. IV). II.

I NSULATION D ESIGN D EVELOPMENT

The development of a new geometry and/or new materials for insulation devices is an economic optimization task with constraints defined by mechanical, thermal, and electrical specification requirements. While in many cases the coarse dimensions and the mechanical material properties follow from the mechanical functionality, this article focuses on electrical or electro-thermal issues that eventually determine the details of the geometry and the electric material properties. The requirements are concretized in electrical tests [3] that must be successfully passed and which insure correct insulation behavior during a prescribed lifetime. Most relevant are the ”type tests” for new prototype devices. They may consist of enhanced AC or DC voltage stress conditions, polarity reversal, load cycling, and different types of voltage pulses on micro(lightning pulse) to millisecond (switching surge) time scales, sometimes superimposed to DC pre-stress. The development of a new design requires a prediction of the electro-thermal behavior with the help of numerical simulations. The calculated field values must be smaller than design values that are associated with the possible failure modes. Design values consist of critical values associated with detrimental effects like electric breakdown, and of safety margins.

Simulations providing the electric field E = −∇ϕ (or the potential ϕ) are based on Ampere’s law in the form of total current conservation, ∇ · j(tot) = 0 with j(tot) = j + ∂t D being the sum of conduction and displacement current densities. The temperature T is governed by the heat balance equation. The Poisson equation provides the space charge density ρ = ∇ · D, where D = ϵ0 E + P is the dielectric displacement. This must be complemented with material models for the polarization P, the current density j, and the heat power density p. A. AC Insulation It is helpful to recall first the AC insulation design process. Because at harmonic voltages with ω/2π = 50 or 60 Hz, the displacement current ωD ≫ j is much larger than the conduction current, and since polymer insulation materials can at these frequencies be considered as linear dielectrics, D = ϵ0 ϵr E, the potential is governed by the Laplace equation ∇·(ϵ0 ϵr ∇ϕ) = 0. For the field calculation, the small imaginary part of the dielectric constant is negligible. Space charge effects for AC as well as for pulses are usually irrelevant, and charge is only located on metallic parts like electrodes. The field distribution is thus called capacitive. Possible exceptions are, e.g., small regions of large field enhancements where the insulation material can become conductive due to its field dependence, or in the presence of resistive field grading [4], [5], [6], [7], [8], [9]. The Joule heat power contains two contributions, one from ˙ reflected by the small (negative) polarization relaxation, P, imaginary part ϵi of the complex dielectric constant ϵc (ω) = ϵr − iϵi , and another from the small conduction current, j = σE. For simplicity, we assume constant σ for the moment. 2 The power density can be written as p = ω tan(δ)ϵ0 ϵr Erms , with tan(δ) = 1/ωτM + ϵi /ϵr , where δ is the loss-angle and τM = ϵ0 ϵr /σ the dielectric relaxation time. A capacitive field distribution and low losses require small tan(δ). For typical values σ = 10−16 to 10−14 S/m τM is of the order of hours to days. Hence ωτM ≫ 1 and free carriers hardly contribute. Reasonable tan(δ)-values are not much larger than 10−3 , which leads to p ≈ 103 W/m3 at fields E ≈ 107 V/m for ϵ0 ϵr ≈ 10−11 F/m. In practice, the dominating heat source usually is, however, not dielectric loss in the insulation material but due to current flowing through the adjacent metal conductors, like the conductor of a cable. The critical issue is thus often not the absolute T -value produced by the insulation loss, but the temperature dependence of tan(δ): d tan(δ)/dT should be small enough to prevent a thermal runaway instability. Although it is straightforward to perform thermal runaway simulations with electro-thermal multi-physics simulation tools, a remaining difficulty that qualifies exact quantitative predictions refers to the modeling of realistic thermal boundary conditions, particularly in case

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of convection cooling. One can summarize the AC-insulation design-process as follows. For AC and pulse stress conditions, the electric field values must be below design field values, and the temperature must remain below maximum design values, and sufficiently below a thermal runaway instability. The needed capacitive field simulations are straightforward and sufficiently accurate, because the permittivities and loss angles are usually wellknown, e.g., from dielectric spectroscopy. For design optimization, the electric fields can be controlled by appropriately shaping the electrodes (capacitive field grading) or by resistive field grading in small regions (local field enhancements) or for short times (during impulse) [6], [7]. Field grading materials are usually sufficiently conductive in order to model the bulk conductivity with an E and T dependent function σ(E, T ). B. DC Insulation HVDC insulation tests often involve DC voltage as well as impulse voltages, that may be superimposed to DC prestress. Current conservation implies that the steady state obeys ∇ · j = ∇ · (σE) = 0. After switching on a steady DC voltage, this resistive field distribution forms while the capacitive field distribution relaxes on the time scale τM to the steady-state with space charge ρ = ϵE · ∇ ln τM . This follows from the continuity equation, which can be written as τM ∂t ρ = ϵE · ∇ ln τM − ρ. Of course, no relaxation occurs if ρ ≡ 0. The heat power, p = σE 2 , due to DC leakage currents should not lead to a large temperature increase, which is satisfied for usual insulation material up to moderate temperatures but can be violated at high temperatures. Particularly the T dependence of the conductivity should be weak enough for absence of thermal runaway and large field enhancements by temperature gradients. A rough order of magnitude estimate with the assumption of σ ∝ exp(T /T0 ) recommends for absence of thermal runaway σ ≪ λT0 /U 2 , where U is the DC voltage and λ the heat conductivity. For example, if λT0 ≈ 1 W/m and the maximum U = 1 MV, one has σ ≪ 10−12 S/m. A problem may occur in systems with more than one insulation material. While permittivities of insulation materials in use are well-defined and vary only moderately, which makes capacitive field distributions relatively robust, this is completely different for conductivities. They may differ or be uncertain by orders of magnitudes, which makes DC field distributions in systems with more than a single uniform material rather unpredictable. This lack of robustness affects the final DC steady state as well as the transient behavior, and it is worth to have a closer look on reasons thereof and consequences for HVDC insulation design development. First, the crucial role of space charge must be emphasized. It is well-known that its presence can lead to harmful field enhancements, be it hetero-charge or homo-charge, either at given voltage or after polarity reversal. It is thus important to know the relevance of space charge and its origin. Besides ionic double layer forming, majority carrier injection from ohmic contacts can be a main reason. The associated spacecharge controlled field-distributions occur if the dielectric relaxation time τM , associated with the intrinsic carriers, is larger than the time of flight, τtof = L/µE, of the carriers with mobility µ through the insulation of thickness L. For µ ≈ 10−14 m2 /Vs, σ ≈ 10−16 S/m, and E ≈ 107 V/m,

one obtains L ≈ τM µE ≈ 10−2 m, i.e., space charges can appear in good insulators on centimeters. It is clear that the strong variability of parameters like carrier density, mobility, and injection properties, as well as their strong dependences on temperature, production process, or even age of the material, is a large source for lack of robustness. Another source for lack of robustness lies in interfaces themselves. Interfaces create no significant AC voltage drop, which is different for DC in case of a high interface resistance. The latter may depend sensitively on the interface pressure, roughness etc.. Furthermore Faradaic, i.e. electro-chemical, processes at contacts and interfaces may lead to chemical changes and material deposition. This might result in abrupt changes of the electric behavior even after long time. These effects may depend on substances present in the form of trace ions or auxiliary substances, like the grease, used for installation, in the interface of cables and their accessories. As interfaces are electrically weak regions, the consequences may affect not only the field distribution but also breakdown. One can summarize for the DC-insulation design process that robustness is the main issue. First, in contrast to AC, the prediction of the DC field distribution is highly sophisticated and requires a reliable physical model based on a deep understanding of the conduction processes, and reasonable characterization methods in order to determine the model parameters. Secondly, one has to design DC insulation systems in a creative way by controlling the global and local field distribution, and introduce fault tolerance mechanisms which minimize the damage in case of failures. Both issues will be discussed in the following. III.

M ODELING AND C HARACTERIZATION OF DC I NSULATION M ATERIALS

A. Simulation of DC conduction With the help of modern commercial multi-physics numerical simulation tools it is straightforward to simulate nonlinear transient and steady-state electric fields together with the heat conduction equation. The main problem is the lack of an appropriate model, or if a generic model is defined, of its parameter values. A generic model should cover the full complexity of the underlying physics, like majority carrier injection from electrode contacts, presence of different types of physical and chemical traps, various types of possible carriers (electrons, holes, ions), strong carrier-lattice interactions that may lead to polarons and self-trapping, local anisotropy, disorder, semicrystalline and spherulitic super-structures, to mention a few [2]. Although a reasonable conduction model for field simulations can only be a rough simplification, it should take into account the most important effects, like space charge or the importance of mobility edges [2], [4], [5]. As a consequence, a model should go beyond the oversimplifying description by an E and T dependent bulk conductivity σ(E, T ). A simple illustrative example considers the space charge density ρ as a dynamic variable governed by the continuity equation, and writes the current density as j = (σ0 + µρ)E − D∇ρ, where D is the diffusion constant, and σ0 is a bulk equilibrium conductivity. Crucial is a reliable electrode-contact model modeled in the boundary conditions for ρ [10], [11]. Such unipolar models can be generalized to bipolar models, in principle with arbitrary number of carriers and traps [12]. Although such models are at the moment the best one can

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do, they are at best pragmatic ”effective medium” models [13] for the complex morphological micro- and meso-structure of polymer materials.

ductivity the field distribution itself is not robust. In order to eventually obtain a sustainable DC insulation design, one may increase the robustness with resistive field grading materials (FGM) and fault tolerance.

B. Electric Characterization Even if a model is accepted, the extremely low currents, the long equilibration times, and the large sensitivities make it impossible to exactly determine the model parameter values. For instance, it is difficult to separate the isothermal conduction current from other contributions. For a plate sample with thickness L and area A after application of a step voltage U at t = 0, the measured (total) current is I = U/R + U C˙ + C U˙ , where R and C are resistance and capacitance, respectively. While in the ideal case the total current equals the conduction current, I = U/R, for large R small low-frequency fluctuations give rise to nonzero C˙ and U˙ which may mask the conduction current. The capacitance may change, e.g., because weak temperature variations may affect the geometry and/or the permittivity. Similarly, the applied DC voltage source might slightly vary due to a not completely stable steady-state voltage. The effects are relevant if τRC C˙ ≥ C or τRC U˙ ≥ U with RC-time τRC , which equals τM if one uses a simple conductivity model. The long measurement times needed for determining the DC steady state characteristics also make it difficult to obtain reasonable statistics for the determination of model parameter values, which is required because of their sensitive dependence on temperature, on secondary parameters like oxidation, trace molecules, processing, and even on the history (e.g., storage conditions). Furthermore the conduction current can be masked by polarization currents, e.g. in polar polymers, or in semicrystalline polymers due to re-crystallization or other structural changes leading to Maxwell-Wagner polarization at internal interfaces. It may even occur that a steady state is not observable at all, without sometimes being clear if this is due to intrinsic dynamics (like traveling space-charge clouds) or an due to an experimental artifact. Consequently, material characterization must be based on a toolbox of partially redundant analysis methods, involving different techniques like isothermal polarization-depolarization currents, low-frequency dielectric spectroscopy, thermally stimulated currents [14], [15], surface potential decay [16], electro-acoustic space charge measurements [17], electroluminescence [15], as well as breakdown field measurements. These experimental tools should be complemented by theoretical first-principle methods like density functional theory for the determination of the density of states [18] and molecular dynamics for ion mobility. Furthermore, it is unavoidable to characterize contacts and interfaces; at least they should be classified according to ohmic or blocking behavior [2]. In particular, the understanding of the injection barrier is a key to conduction of polymer insulation [19]. Similarly, the charge-build up at insulator-insulator interfaces and their resistance should be under control. Last but not least, the electric DC breakdown behavior at interfaces and triple points needs a systematic investigation, because failure modes at DC may strongly differ from AC. IV.

ROBUST I NSULATION S YSTEMS

Not only are electrical test simulations unavoidably fraught with uncertainty, but because of the variability of the con-

A. Resistive field grading A robust DC field distribution, e.g. in case of composite insulation or if local field enhancements occur, can be forced with the help of resistive FGM [6], [7]. For instance, different insulation materials can be topologically separated by the FGM and are then electrically decoupled. For this, the FGM conductivity should be about 100 times larger than the maximum conductivity of the insulation materials; but on the other hand the FGM leakage current should be sufficiently small. Application examples are the flexible joint in Fig. 1 [20], and the prefabricated HVDC cable joint [21], [22]. Similar field grading works in cable terminations. However, the DC field simulation of a termination must include the poorly understood air insulation and air-solid interface and goes beyond the purpose of this paper; results based on σ(E, T ) models for air are highly questionable even for rough estimates. As mentioned above, also impulse-voltage tests must be

Fig. 1. Interface (3) in a flexible cable joint between cable insulation (1) and joint insulation (2) materials (dashed line: mirror plane / joint center). The angle α must be small to prevent failures along the material interfaces (cylindrical geometry with radial r and axial z coordinates). If the insulation conductivities differ (a) σ2 ≫ σ1 , b) σ2 ≪ σ1 ), field enhancements occur, while in the presence of a field grading material in the interface (σ2 ≫ σ1,2 ), a robust equalized field distribution establishes.

successfully passed by DC devices. For this the FGM is usually equipped with a nonlinear electric behavior. Its conductance as a function of the field strongly increases at a certain field value, which helps to suppress field enhancements beyond this field. FGMs are rubbers filled with semiconductor particles and/or carbon black (CB), which leads to a reversible current switching behavior with a nonlinearity α = d ln j/d ln E that should be high. Conventional SiC/CB-based FGMs have α values below 10, while modern ZnO micro-varistor based FGMs can reach values up to 20 [6], [7], [23].

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B. Fault tolerance

R EFERENCES

Two important mechanisms to make an insulation system fault tolerant are self-healing and bridging. Self-healing in solid insulation (liquids can exhibit naturally self-healing behavior) can be found in, e.g., high energy density capacitors [24], [25] for converters. They consist of polypropylene films with sufficiently thin metallization. When a breakdown occurs, electrode material is evaporated and a demetallization area forms (Fig. 2 a)). This reduces the field in this region and breakdown stops. The evaporating spot can be at the location of the puncture (”natural” self-healing), or can be determined by an appropriate segmentation of the metallization (”controlled” self-healing). Bridging can occur if an insulation distance is subdivided by

Fig. 2. a) Self-healing in capacitors. After an electric breakdown (left) the sufficiently thin electrode metallization evaporates (right), leading to breakdown interruption. b) Bridging in series connected insulation systems. During breakdown (left) the electrodes melt and form a conductive bridge which connects the two adjacent electrode layers (right) with slight field increase outside.

intermediate conductive layers, e.g., metal foils, floating electrodes etc. (Fig. 2 b)). When an electric breakdown occurs, the breakdown channel will connect the two adjacent conductive layers. If the system is appropriately designed, the channel becomes conductive, cools down, solidifies and leads to a permanent conductive connection between the two layers. The most prominent example of bridging is realized not in polymer dielectrics but in power semiconductor modules for HVDC applications, leading to their specific short circuit failure mode behavior [26]. V.

C ONCLUSION

The intrinsic lack of robustness is a main challenge for HVDC insulation technology. As compared to AC insulation, a successful design process for DC insulation needs thus additional effort in two directions. First, for the prediction of electric fields a reliable conduction model with the necessary experimental material characterization tools is required. Contact and interface physics must be appropriately included. Secondly, in order to mitigate the risk of electric breakdown, DC insulation has to be made electrically robust with special methods like resistive field grading and fault tolerance mechanisms.

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