Power line insulation is of external type (i.e., exposed to atmospheric conditions) and self-restoring (i.e., it recovers its insulating properties after a disruptive discharge), and it must be selected to meet the stresses produced by power-frequency voltage and any type of overvoltage.
Insulation strength is expressed in terms of withstand voltage, a quantity determined by tests conducted under specifi ed conditions with specifi ed waveshapes. The same insula-tion may have different withstand voltages for different voltage waveshapes; that is, insu-lation withstand strength depends greatly on the waveshape of the applied voltage. If the value of withstand strength measured during tests is to be a fair measure of the insulation behavior, the waveshape of the test voltage should well represent the waveshape of the actual stress on the insulation. However, overvoltages may have a wide range of wave-shapes, so rather than attempting to determine the withstand strength for each stress by test, it is common practice to assign a specifi c testing waveshape and duration of its appli-cation to each category of overvoltage.
A plot of withstand strength versus waveshape is known as a volt–time curve. The parameter of waveshape generally used is the so-called front time of the testing impulse.
Such a curve shows only the withstand strength of the insulation when exposed to stan-dard laboratory-generated test voltages.
Power line insulation must be chosen after a careful study of both transient and power-frequency voltage stresses and the corresponding strengths of each insulation element. Transient stresses may be divided into lightning and switching surges. As a rule of thumb, one can consider that lightning overvoltages dictate the insulation level at distribution and subtransmission levels, and switching overvoltages control the design at transmission levels. Nevertheless, it is advisable to consider both types of transients.
Power line insulation must be suffi cient to ensure a reliable operation; however, a design that assumes no insulation failures is extremely conservative and expensive. In addition, insulation design for transient voltages is complicated by the great variety of transient and meteorological conditions that an overhead line experiences, and by statistical fl uctua-tions in the insulation strength itself. Transients appear in all shapes and with different amplitudes. Each type of transient may occur with any meteorological condition, which affects the fl ashover strength differently. The larger transients occur more rarely than the
smaller ones, and the greatest possible transients may have an extremely low probability of occurring in actual service. Therefore, a proper balance must be reached between the reliability and the cost of insulation. Sophisticated design methods may assess the relative frequencies of occurrence of all the combinations of electrical and meteorological events, evaluate how overall performance would change as the choice of insulation is changed, and determine how additional insulation investment would affect the outage rate. These methods explore the problem in detail, but they require a systematic evaluation of meteo-rological and transient voltage conditions.
This section covers the aspects needed to understand how power line insulation behaves under any type of stress, waveshape, and meteorological condition. It presents a short description of the phenomena that occur during breakdown caused by either switching or lightning stresses, a summary of mathematical models aimed at representing the behav-ior of power line insulation, and procedures to obtain the dielectric strength for frequency voltage, switching and lightning impulses, at any atmospheric condition. A summary of standard concepts needed to describe external and self-restoring insulation is also presented.
The section is mostly based on Refs. [3,113,114]. For more details and further information, readers are encouraged to consult these references. Other basic references related to the main topics of this chapter are [1,2,74,115].
2.6.2 Definitions
2.6.2.1 Standard Waveshapes
The standard lightning and switching impulse waveshapes are described by their time-to-crest and their time-to-half value measured on the tail, see Figure 2.51.
Lightning impulse waveshape: The (virtual) time-to-crest or front time,
• tf, can be
defi ned by the equation
( )
= −
f 1.67 90 30
t t t
(2.128) where
t90 is the actual time to 90% of the crest voltage t30 is the actual time to 30% of crest voltage
Voltage
Time th
t90 t30
tf V30 V50 V90 V100
Voltage
Time tf
th V50
V100
(a) (b)
FIGURE 2.51
Standard impulse waveshapes. (a) Lightning impulse waveshape, (b) switching impulse waveshape.
The time-to-half value or tail time, th, is the time between the virtual origin (the point at which the line between t30 and t90 intersects the zero voltage) and the point at which the voltage decreases to 50% of the crest value. In general, the wave-shape is denoted as a tf/th impulse. The standard lightning impulse waveshape is 1.2/50 μs.
Switching impulse waveshape: The time-to-crest or front time is measured from
•
the actual time zero to the actual crest of the impulse, while the tail is defi ned as the time-to-half value, and is also measured from the actual time zero. The wave-shape is denoted in the same manner as for the lightning impulse. The standard switching impulse waveshape is 250/2500 μs.
2.6.2.2 Basic Impulse Insulation Levels
Basic lightning impulse insulation level (BIL) [116]: It is the electrical strength
•
expressed in terms of the crest value of the standard lightning impulse, at stan-dard dry atmospheric conditions. The BIL may be either statistical or conventional.
The “statistical BIL” is the crest value of standard lightning impulse for which the insulation exhibits a 90% probability of withstand; that is, a 10% probability of failure. The “conventional BIL” is the crest value of a standard lightning impulse for which the insulation does not exhibit disruptive discharge when subjected to a specifi c number of applications of this impulse. The statistical BIL is appli-cable only to self-restoring insulations, whereas the conventional BIL is appliappli-cable to non-self-restoring insulations. In IEC Std 60071 [117], the BIL is defi ned in the same way but known as the lightning impulse withstand voltage.
Basic switching impulse insulation level (BSL) [116]: It is the electrical strength
•
expressed in terms of the crest value of a standard switching impulse, at standard wet atmospheric conditions. The BSL may be either statistical or conventional.
As with the BIL, the statistical BSL is applicable only to self-restoring insula-tions, while the conventional BSL is applicable to non-self-restoring insulations.
The statistical BSL is the crest value of a standard switching impulse for which the insulation exhibits a 90% probability of withstand, a 10% probability of fail-ure. The conventional BSL is the crest value of a standard switching impulse for which the insulation does not exhibit disruptive discharge when subjected to a specifi c number of applications of this impulse. In IEC Std 60071 [117], the BSL is called the switching impulse withstand voltage and the defi nition is the same.
IEEE and IEC standards recommend values for both BILs and BSLs that equipment manu-facturers are encouraged to use [116,117].
2.6.2.3 Statistical/Conventional Insulation Levels
In general, the strength characteristic of self-restoring insulation may be represented by a cumulative normal of Gaussian distribution [1,3]. Under this assumption, the probability of fl ashover for a specifi ed voltage V is given by the following expression:
−μ
where
μ is the mean value
σf is the standard deviation
In a normalized form, this expression can be written as follows:
−
The mean of this distribution is known as the critical fl ashover voltage or CFO (in IEC it is known as the U50 or 50% fl ashover voltage). The insulation exhibits a 50% probability of fl ashover when the CFO is applied; that is, half the impulses fl ashover. From the defi nition of BIL and BSL (at the 10% point) the following equations result:
⎛ σ ⎞
where σ in per unit of the CFO is called the coeffi cient of variation.
Assuming a normal distribution, insulation strength is fully specifi ed by providing the values of CFO and σf. An alternate method is to provide the values CFO and σf/CFO.
The assumption of a normal or Gaussian distribution is adequate for most practical appli-cations, but some researches have shown that the probability distributions can sometimes be far from normal (Gaussian) [118]. In addition, the Gaussian distribution is unbounded to the right and the left; that is, it is defi ned between +∞ and −∞. A limit of −∞ indicates that there exists a probability of fl ashover for a voltage equal to zero, which is physically impossible. Since the Gaussian distribution is valid to at least four standard deviations below the CFO, it is reasonable to believe that there exists a nonzero voltage for which the probability of fl ashover is zero. A distribution with this property is the Weibull whose cumulative distribution function is
In IEC 60071, the value of β is rounded to 5, and the distribution is approximated by the following expression [2]:
2.6.3 Fundamentals of Discharge Mechanisms 2.6.3.1 Description of the Phenomena
The behavior of air insulation depends on various factors, such as the type and polarity of the applied voltage, electric fi eld distribution, gap length, and atmospheric conditions. The dielectric breakdown of a gas is characterized by the formation of free charges of opposite sign due to ionization of molecules by collision with free electrons accelerated by the elec-tric fi eld. This phenomenon develops in successive phases.
1. The fi rst phase is the fi rst corona, which develops in the region of high electric fi eld in the proximity of the electrodes, in the form of thin fi laments, called streamers, propagating only for one part of the gap.
2. The second phase is the leader phase, characterized by the formation and the elon-gation of a channel, more ionized than a streamer, which propagates with leader corona development from its tip. Depending on the value and shape of the applied voltage and to the gap length, the leader can either stop or reach the opposite electrode.
3. Once either fi rst corona streamers or leader corona streamers have reached the opposite electrode, the third phase develops. The leader channel elongates at increasing velocity bridging the whole gap. At this point the channel becomes highly ionized and the electrodes are short circuited.
In the case of rod–rod geometry, the phenomenon develops from both electrodes, and the last phase occurs when fi laments of opposite polarity meet inside the gap.
The fi rst corona phase and the leader phase strongly depend on the polarity of the applied voltage. In almost all practical geometries, the breakdown voltage with positive polarity is lower than that with negative polarity, and the minimum breakdown voltage, with the same gap length and impulse shape, belongs to the case of rod–plane gap (i.e., a geometry in which only one region of the gap is stressed).
The different phases detailed above are clearly defi ned and detectable in the case of impulse voltages of long-duration front. By reducing the time-to-crest, some overlapping of the various phases can occur, and some phases can be absent. In the case of lightning impulses, because of the fast decrease of the applied voltage during the tail, the leader cannot develop as in the case of switching impulses. To reach breakdown, the voltage has to be increased very much. Due to the very high rate of rise of the voltage during the front, fi rst corona is almost immediately followed by a succession of pulses which launch streamers into the gap. Before a leader has time to develop signifi cantly, the streamers reach the opposite electrode, causing a condition in the gap similar to that occurring at the fi nal jump; that is, there is a leader-propagation phase. Breakdown voltage cor-responds to the average fi eld along the streamer zone multiplied by the gap length. In the case of short-front impulse voltage, the infl uence of the tail duration may be very important.
2.6.3.2 Physical–Mathematical Models
They do not describe physical phenomena, although they are based on the characteristics of the various phases of the discharge mechanism. Since the infl uence of these phases depends on the electrode geometry and voltage-impulse shape, a good modeling of the
dominant phase is of primary importance. Some approaches developed to represent the behavior of air insulation under lightning and switching impulses are summarized in the following.