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The Statistical Enlargement Law for HVDC Cable Lines. Part 2: Application to the Enlargement over Cable Radius
No full textThis paper is the second part of an investigation on the new enlargement law for HVDC cables developed by the authors. The previous Part 1 has illustrated the theoretical derivation of this law and its application to enlargements over cable length. The present Part 2 is dedicated to the enlargement over cable radius and to its noteworthy aspects, that are essentially associated with the complicated function HDC. These aspects are mainly relevant to the role played by cable conductor losses, or equivalently by conductor temperature. They are deeply investigated here via a series of three radial enlargements for HVDC extruded cables, that involve conductor cross-section and insulation thickness only: this enables focusing the attention on the HDC function, that includes the dependence of the enlargement law on the radial cable geometry
The practical effect of the enlargement law on the electrothermal life model for power-cable lines
No full textInsulation coordination is essential for designing and testing HV cable systems properly. In transient conditions, i.e., in the presence of transient voltage surges, insulation coordination is based on the individuation of a certain maximum acceptable risk of failure under the switching and lightning overvoltages that the insulation may encounter in service, and translates into a maximum number of expected failures per year per length of line that the cable line has to match. Given the design of the cable in steady-state conditions, the number of expected failures per year and per length of cable line can be reduced by a proper design of the shield wires of overhead lines, of the grounding systems of line towers and so on [1], and by selecting and installing properly voltage-surge arresters when needed.
However, insulation coordination in transient conditions implies that the design of the cable for its service in steady-state conditions, i.e., in the presence of constant levels of applied rated stresses, has already been accomplished properly, and this in turn implies that proper insulation coordination in steady-state conditions has been performed as well. Differently from transient conditions, insulation coordination in steady-state conditions can be defined as the selection of the stress levels that cable insulation is capable to withstand throughout a certain design life (time to failure) t0L with an acceptable design failure probability P0L.
This article recalls some popular modelistic tools for HV cables, namely, the life models, Weibull distribution, and the enlargement law, and describes how they can be integrated into a multipurpose probabilistic model for cable-insulation coordination in steady-state conditions. First, the probabilistic framework of insulation-life modeling is outlined and the traditional phenomenologic approach to insulation-life modeling is recalled, by presenting some fundamental life models available in the literature and that can be used for time-to-failure estimation of HV cable insulation. Then the so-called enlargement law is introduced, which enables evaluation of how much the electric stress has to be reduced in order to keep the same failure probability as the volume of insulation increases (e.g., from specimens or cable loops tested in the lab to full-size cables installed in the field).Finally, all these tools are merged into a multipurpose model for cable-insulation coordination in steady-state conditions
The application of the enlargement law to HVDC cable lines
No full textIn this paper the traditional enlargement law for AC
cables − based on the so-called “volume effect” − is extended to
DC cables via an innovative theoretical approach, that takes into
account some aspects peculiar of HVDC cables, i.e. the dependence
of the electric field profile on volume electrical resistivity of
the insulation, the associated dependence of volume resistivity on
electric field and temperature, the role played by the heat dissipated through the cable layers and by the thermal resistivity of
the insulation. An application of the novel enlargement law developed is given in the paper considering real HVDC cables and
examining the influence of some of the many parameters appearing
in the model
A procedure for space charge measurements in full-size HVDC extruded cables in order to access the electric field in the insulation wall
No full textThis paper proposes a procedure for the measurement of space charges in full-size HVDC extruded cables, that accounts for the experimental practices of such kind of measurements in terms of poling time, depolarization time, heating and cooling of specimens. The aim is to access the electric field in the insulation wall under different test conditions. Such procedure to be used in prequalification tests can give the fingerprint of the tested cables and the results could be useful in order to skip the prequalification tests on new cables manufactured with the same insulation and semiconductive compounds, but with different cross section geometry. It must be pointed out that there is no universal agreement about limits for space charge measured. However the change in the relevant electric field with respect to the Laplacian field seems a clear indication of the attitude of an insulation to give rise to field enhancement, and thus to behave unsatisfactorily in service. In any case, the aim of the procedure is not giving maximum acceptable space charge limits, but rather evaluating the electric field profile during the prequalification tests in full-size HVDC extruded cables
Parametric sensitivity analysis of the innovative enlargement law for extruded HVDC cables
No full textThe paper studies the effect of the Weibull shape parameter β and of conductor temperature on the reduction of breakdown voltage with cable length in the enlargement from test (small size) HVDC cables to power (full-size) HVDC cables for some typical extruded dielectrics, each characterized by the relevant temperature and field coefficients of electrical resistivity. A “reference enlargement” is considered – by selecting a typical set of values of conductor cross-section and insulation wall thickness for the test cable and the power cable – and various insulation compounds are compared.
The behaviors are quite different for the treated compounds, thereby showing that beside the Weibull shape parameter, also the electrical resistivity of the insulation has a major effect in the “reference
enlargement”. Secondly, the behavior of the function H appearing in the enlargement formula is analyzed; for HVAC cables such a function is mainly close to 1 in practice, whereas for HVDC cables it has a much more cumbersome expression, whose behavior is not so easy to be assessed a priori. For this reason, the Monte Carlo method is used by generating a huge number of random values of the above-mentioned
parameters falling within the typical range of variation for HVDC cables commercially available. By plotting the relevant sampling distribution of the function H against each parameter, the sensitivity of the enlargement process to the various parameters is evaluated comparatively and the parameters that have a major effect on the function H are singled out.
Finally, on the basis of the Monte Carlo analysis, simplified – although approximate – expressions are proposed for the function H. These simplified expressions help in a fast preliminary screening of the enlargement effects, becoming a fundamental tool for insulation design and coordination
The Statistical Enlargement Law for HVDC Cable Lines. Part 1: Theory and Application to the Enlargement in Length
No full textIn this investigation the innovative enlargement law for HVDC cables, developed by the authors, is illustrated and applied extensively. In the present Part 1 of the investigation, the theoretical approach to the derivation of the enlargement law for HVDC cables is reported, with a broader and more rigorous formulation and a deeper insight compared to the first proposals by the same authors. Later on, the theoretical approach is applied to different volume enlargements relevant to mass impregnated and extruded cables, focusing mainly on cable line length. These are typical examples of the enlargements that designers may be asked to consider in practice when dealing with R&D activities that have a particular HVDC cable line project as their ultimate goal. Such examples also lead to single out some important aspects relevant to the complex function HDC, associated with the enlargement over cable radius. This latter enlargement is deeply analyzed via several case-studies in paper Part 2 of this study
A procedure for space charge measurements in full-size HVDC extruded cables
No full textThis paper proposes a procedure for space charge
measurements in full-size HVDC extruded cables, that consists in
a detailed protocol indicating voltage polarity, time intervals
between measurements, volt-on and volt-off conditions, and so
on. The proposed protocol accounts for the experimental practices
of such kind of measurements in terms of poling time, depolarization
time, heating and cooling of specimens. Such procedure
seems particularly useful for assessing the space charge behaviour
in terms of electric field of a cable that has undergone a prequalification
test. The measurement can also give indication
about the possibility of avoiding the repetition of prequalification
tests and/or type tests in the case of HVDC cables, for which the
Laplacian field profile cannot be taken – strictly speaking – as a
reference for comparing the electrothermal stress level of new
realizations with that of previously manufactured cables
A deeper insight into the application of the enlargement law to HVDC cables
No full textIn this paper the innovative theoretical approach to
the enlargement law for HVDC cables previously developed by
the authors is investigated in more detail, by evaluating the role
played by the main quantities that appear in the enlargement
law. Firstly, the paper studies the effect of the Weibull shape
parameter and of conductor temperature on the reduction of
breakdown voltage with cable length in the enlargement from
test to power HVDC cables by considering quantities related to
typical extruded compounds for DC applications, thereby demonstrating
a major role played not only by Weibull shape parameter,
but also by volume electrical resistivity of the insulation,
hence by the different compounds. Secondly, the behaviour of the
cumbersome function HDC appearing in the enlargement formula
for HVDC cables is analyzed via the Monte Carlo method and
approximate expressions for HDC are proposed that are useful for
insulation coordination and design
More insight into the extension of pre-qualification test for HV and EHV AC extruded cable systems
No full textIn a previous paper by the same authors, a new
method was proposed for the estimation of time to failure
percentiles and life fraction lost in the so-called “Extension of
Prequalification (EQ) test” according to CIGRE TBs 303. On
these grounds, an alternative to the EQ test was proposed,
referred to as “Improved Extension of Qualification (IEQ) test”, thereby taking into account the electrothermal endurance features of a given extruded cable design. Here the new method is investigated in more depth by broadening the previous sensitivity analysis. First of all, temperature transients calculated resorting to a thermal transient model of the cable layers and its surrounding environment are added to the parametric temperature transients previously considered. Moreover, a moderate synergism between the electrical and thermal stress is added to the maximum synergism that was solely treated before: in this way, more sound and accurate indications are derived about the test voltage levels to be chosen in the IEQ test for the various cable designs. Finally, two different designs of HV cables
are considered in addition to the two designs of EHV cables
previously treated
Effects of load cycles on AC extruded cable reliability: is a reduced pre-qualification test always the right choice?
No full textIn this paper, a new method is proposed for the
estimation of time to failure percentiles and life fraction lost in
the so-called “Extension of pre-Qualification (EQ) test”
according to CIGRE TBs 303. The method accounts for the timevarying
temperature during the EQ load cycles via an approach
that relies on: 1) Miner’s law of cumulated aging; 2) an improved
voltage-time characteristic that includes the electro-thermal
stress; 3) a probabilistic framework based on the Weibull
hypothesis. On these grounds, an alternative to the EQ test is
proposed, referred to as “Improved Extension of Qualification
(IEQ) test”, based on a more strict correlation between cable
insulation reliability in design stress conditions and that during
the test itself, thereby taking into account the electro-thermal
endurance features of a given extruded cable design
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