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An automatic procedure, based on a genetic algorithm capable of optimizing a diagnostic system for the recognition and identification of partial-discharge (PD) pulse patterns in the terminations and joints of solid dielectric extruded power distribution cables, is described. The core of the diagnostic system is a fuzzy neural network, namely a Min-Max classifier. The genetic optimization is capable for reducing the system complexity, while enhancing its diagnostic performance. The developed procedure is sufficiently general to be applied to PD source identification in the cables themselves as well as other electric power apparatus. Index Terms--Automatic feature selection, cable accessories, fuzzy neural networks, genetic algorithms (GAs), partial-discharge (PD) patterns classification, XLPE.

The nature and causes of corrosive sulfur induced failures are examined in oil-filled transformers and shunt reactors. Copper sulfide, which is formed when the corrosive sulfur in a mineral oil reacts with the copper conductors, is likely to diffuse into the paper tapes insulating the conductors. Since copper sulfide is partially conducting, the dielectric losses of the contaminated oil-impregnated-paper tapes are markedly increased; paper tapes in close proximity to the copper conductors are found to attain tan [delta] values > 1.0 even at room temperature. It is highly likely that thermal instabilities develop at those sites at operating temperatures, leading to increased loss currents and, ultimately, short circuits between the turns. This sequence of events is substantiated by evidence from the field, which indicates large areas of thermally degraded insulations and charred breakdown regions along the coils, the extent of which becomes more pronounced at higher operating temperatures (toward the top of the windings). Index Terms--Corrosive sulfur, dibenzyl disulfide (DBDS), failures, oil insulation, standardization, transformers/shunt reactors.

The Rogowski coil method for the measurements and detection of PD signals represents a cost effective and practical way to measure PD signals in electrical power apparatus; however it is subject to excessive noise pick-up because of its inductive nature. This paper discusses the implementation of a de-noising algorithm using Eigen-decomposition approach, which can be utilized in order to minimize the extraneous noise encountered with on-line tests in the field. The proposed algorithm possesses the inherent advantage of decomposing the signal space and separates it from the noise subspaces. Results discussed in the paper demonstrate the performance of the proposed technique for both simulated and experimental PD signals. Index Terms--Partial discharge, detection, noise, Eigen value decomposition.

Acoustic measurements of partial discharge (PD) are employed to classify particles in transformer mineral oil according to material and size. Wavelet multi-resolution analysis data of the acoustic signals together with higher order statistics of the particle intercollision times and magnitudes comprise the input features to a Support Vector Machine (SVM) classifier. The training and validation measurement data, which are contaminated by time varying noise, are first filtered using wavelet decomposition. Results indicate that the SVM algorithm with the selected features provides a remarkably high success rate when classifying particles by size and material type. A potentially significant conclusion is that acoustic measurements alone are by themselves effective in classifying discharged particles in terms of the foregoing selected features. The proposed algorithm can be employed to enhance quality control procedures based on acoustic measurements of partial discharge. Index Terms--Wavelet, multi-resolution analysis, particle contamination, wavelet denoising, Support Vector Machines (SVM), higher order moments, PD acoustic measurements.

The partial discharge (PD) pulse burst characteristics of a transformer type synthetic organic ester fluid were compared with those of an equivalent transformer type mineral oil. Wide and narrow bandwidth measurements were carried out to determine simultaneously the apparent charge transfers associated with the overall PD pulse burst as well as that of the individual discrete pulses within the PD pulse burst. The PD pulse burst behavior was found to be similar in both insulating liquids. The discharge cavity formation times ranged from 0.5 to 1.5 [micro]s, while the charge transfers associated with the PD pulse bursts in the liquids were found to extend from approximately 5 to 30 pC. Index Terms-Partial discharges, mineral oil, synthetic ester.

The mechanisms of discharge channel expansion and constriction are briefly examined, with particular reference to discharge behavior between dielectric surfaces and their effect upon the magnitude and rise time of PD pulses. Index Terms-Discharge channel development, dielectric surfaces, partial discharges.

In extracting partial discharge (PD) signals embedded in excessive noise, the need for an online and automated tool becomes a crucial necessity. One of the recent approaches that have gained some acceptance within the research arena is the Wavelet multi-resolution analysis (WMRA). However selecting an accurate mother wavelet, defining dynamic threshold values and identifying the resolution levels to be considered in the PD extraction from the noise are still challenging tasks. This paper proposes a novel wavelet-based technique for extracting PD signals embedded in high noise levels. The proposed technique enhances the WMRA by decomposing the noisy data into different resolution levels while sliding it into Kaiser's window. Only the maximum expansion coefficients at each resolution level are used in de-noising and measuring the extracted PD signal. A small set of coefficients is used in the monitoring process without assigning threshold values or performing signal reconstruction. The proposed monitoring technique has been applied to a laboratory data as well as to a simulated PD pulses embedded in a collected laboratory noise. Index Terms--Partial discharge, detection, noise, Wavelet analysis, Kaiser's window.

Comparative experimental and theoretical studies are carried with 0.5-mm gaps using metallic and dielectric electrodes to examine the influence of dielectric surfaces upon the behavior of atmospheric pressure glow discharges in helium at frequencies of up to 22 kHz. The charge transfers associated with the discrete discharge current pulses exhibit a direct proportionality to the difference between the breakdown [V.sub.b] and residual [V.sub.r] voltages. The introduction of dielectric surfaced electrodes markedly increases the magnitude of [V.sub.r], which leads to substantially lower discharge currents. The calculated ionic and electronic charge carrier components comprising the discharge current pulses were found to be approximately equal when both electrodes were either metallic or dielectric. With one electrode metallic and the counter electrode dielectric, the electronic charge carrier component magnitude exceeded that of the ionic one by a factor of 2 in the positive half cycle. Index Terms--Dielectric surfaces, discharge currents, electronic charge carrier components, glow discharges, helium, ionic, residual voltages.

Electrical and acoustic partial discharge (PD) measurement and pattern recognition procedures are described for detecting and identifying contaminating particles in transformer mineral oils. This work introduces the use of Support Vector Machines (SVM), a nonlinear non-parametric automatable machine learning algorithm, for the purpose of classifying the size and composition of such particles. The training and validation of acoustic and electrical PD measurement data, which are contaminated by time varying noise, are first filtered adaptively using wavelet decomposition. Statistics of a particle's impact upon collision with the walls of a tank, containing the electrode test assembly and the inter arrival time between collisions constitute the features for the SVM classifier. These statistics include higher order moments and the entropy of the estimated density function of the features. Results based on experimental training and testing data indicate that fusing of the acoustic and electric PD information at the features level provides a nearly perfect classification success rate. These observations demonstrate that, while electrical and acoustic PD data are correlated, they contain individually independent and complementary information regarding the state and condition of transformer type mineral oils. Index Terms--Entropy, higher order moments, learning algorithms, particle contamination, partial discharge, wavelet denoising, Support Vector Machines (SVM).

An identification technique is described, based on a developed adaptive fuzzy logic network, that enables the recognition of partial discharges (PD) generated by different defects in heat-shrinkable joints and terminations of XLPE insulated power distribution cables. It is shown that different sources of PD can be identified on the basis of fuzzy rules applied to a selection of parameters derived from PD-pulse phase and amplitude distributions. A comparison with other PD pattern recognition techniques based on traditional neural networks is presented and discussed. Index Terms--Joints, neural networks, terminations, XLPE.

The aging characteristics of stator bars, which have been subjected to accelerated aging tests in a three-phase model stator under simultaneously applied electrical, mechanical, and thermal stresses, have been evaluated using diagnostic test procedures. The ac breakdown test has been found to be the most effective means for assessing the extent of aging undergone by the stator bars. The results indicate that under multistress conditions relatively small increases in the magnitudes of the stress acceleration factors are sufficient to lead to significant increases in the aging rate of the insulating systems of stator bars. Index Terms--ac breakdown, accelerated aging, degradation, diagnostic tests, multistress, partial discharge, stator bars.

Discrete partial discharge (PD) pulse occurrence times within the PD pulse bursts in transformer oils were found to extend from approximately 0.42 to 2.9 [micro]s, with the discrete pulse separation times evincing a weak dependence on the inverse of the oil viscosity. Many PD pulse burst patterns exhibited substantial deviation from the classical behavior, which is normally characterized by successive discrete pulses of ascending amplitude with well defined increases in the pulse separation times. The average elapsed time from the incipient formation for the cavity to the onset of the first partial discharge event extended downwards from 0.62 to 0.42 [micro]s with increasing oil viscosity.

This paper presents a novel approach in the area of time dependent partial discharge (PD) pulse pattern recognition, to applications based on the inductive learning (decision tree) approach. Different attributes based on pulse shape analysis are used as representative feature vectors that can accurately capture the unique and salient characteristics of the PD pulse shape. In the training phase, a decision tree is developed to relate the pulse shape with the cavity size by using inductive machine learning. The C4.5 machine learning algorithm is deployed to realize the tree using the training data, since it has the capability of inferring the rules and to produce the tree in terms of continuous features. During testing, the cavity size is recognized by means of the rules extracted from the decision tree. The dependency between the features and the classes are examined using the mutual information approach. The proposed algorithm possesses the inherent advantage of explaining the result via the self-created rule base as demonstrated by the results obtained. Those self-created rules can be employed as the basis for applying a fuzzy expert system for the classification of void sizes in an easily interpreted fashion. Index Terms--Cables, feature extraction, partial discharges, pattern classification.

Partial discharge (PD) detection, measurement and classification constitute an important tool for quality assessment of insulation systems utilized in HV power apparatus and cables. The patterns obtained with PD detectors contain characteristic features of the source/class of the respective partial discharge process involved. The recognition of the source from the data represents the classification stage. Usually, this stage consists of a two-step procedure, i.e., extraction of feature vector from the data followed by classification/recognition of the corresponding source. The various techniques available for achieving the foregoing task are examined and analyzed; while limited success has been achieved in the identification of simple PD sources, recognition and classification of complex PD patterns associated with practical insulating systems continue to pose appreciable difficulty. Index Terms--Partial discharge, PD pulse, PD detector, pattern classification.

The influence of the discharge mechanism upon the rise time of partial discharge pulses is examined. In contrast to the long rise times characterizing the discharge pulses generated by glow discharges, spark discharges exhibit typically short rise times and large magnitude pulses. The occurrence of the latter is favoured by cavities wherein there is a paucity of free electrons that are necessary for electron avalanche formation. As a consequence, breakdowns across these cavities occur under overvoltage conditions, thus leading to space charge formation and photoemission at the cathode; this results in a rapid development of constricted spark-type breakdown channels. The question of detectability of short and long rise time pulses, utilizing PD detectors having different bandwidths, is considered both in the proximity to, as well as far removed from, the discharge sites. Index Terms--Partial discharge, rise time, cavities, discharge pulses.

Accelerated aging tests have been carried on stator bars under simultaneous electrical, thermal and mechanical multi-stress conditions, using a simulated three-phase model stator. Over each thermal load cycle, the partial discharge activity has been found to be a strong function of temperature. Tests at twice rated electrical stress did not result in any bar specimen failures up to a total of 1500 load cycles. However, when the three phase load current was increased above its rated value, current-limited type failures were observed to occur below 1000 load cycles, thereby indicating a marked influence of thermal and mechanical stresses associated with the elevated three phase load current. Index Terms--Accelerated aging, degradation, multi-stress, partial discharge, stator bars, three-phase system.

An approach for the classification of cavity sizes based on their maximum charge transfer characteristics, applied voltage partial discharge pattern using Hidden Markov Models, is described. In these models, the partial discharge patterns for different cavity sizes are represented by a sequence of events rather than by the actual curves. In the training phase, each cavity size represents a unique class, which emits its own eigen sequence. Vector Quantization is deployed to assign labels for this particular sequence of events. A Hidden Markov Model is trained for each class, using a set of training patterns consisting of the labels produced by Vector Quantization. During testing, the sequence of events to be recognized is quantized and then matched against all the developed models. The best-matched model pinpoints the cavity size class. Experimental results demonstrate the remarkable capability of the proposed algorithm. Index Terms--Hidden Markov models (HMMs), partial discharge, pattern recognition, vector quantization.

Different partial discharge (PD) detection and measurement procedures suitable for use on cables, capacitors, transformers and rotating machines are examined and compared. Both narrow and wide bandwidth PD detectors are considered; particular attention is given in regard to their suitability to different types of electrical apparatus and cable specimens under test as well as their applicability to discharge site location and their capability to detect different forms of PD. A rather substantial portion of the discussion is devoted to the use of intelligent machines as applied to ED pattern recognition in terms of either ED pulse-height/discharge epoch (phase) distributions or discharge pulse shape attributes.

An account is given of the time when the ISEI was inaugurated, the Group on Electrical insulation was elevated to Society status, Dr. van Roggen was appointed as Editor of the Transactions upon the retirement of E. J. McMahon, the Scientific Achievement award was established in honor of Dr. Dakin, and when, much to the consternation of many, discussions began on the transfer of the CEIDP from it aegis of the NAS/NRC to a more humble abode, namely that of the EIS.

A time-series approach has been employed to devise neural-network topologies for time dependent partial discharge pulse pattern recognition applications. The cascaded output neural-network structure was found to provide the highest success rate in differentiating between two different partial discharge patterns. This was accomplished by utilizing the indexed feature of the first stage output as one of the inputs into the second stage of the cascaded neural network. Index Terms--Cascaded output, cavity size classification, network topology, partial discharges, time series approach.

Partial discharge (PD) diagnostics are utilised to examine the aging process of mineral oil-impregnated-high density kraft paper capacitor bushing models, subjected to repetitive voltage switching surges. It is demonstrated that the PD measurements of cumulative apparent charge transfer and discharge inception stress constitute an effective means for assessing aging and its reversibility due to gas evolution and re-absorption or solubility of a mineral oil-impregnated-paper insulation system in the presence and absence of switching surges. While the experimental results indicate that electrically overstressed solid-liquid insulation can recover in part its initial electrical properties following an electrical stress-free period, long term stability is only effectively achieved by a reduction in the switching surge overstress through an increase in the overall insulation thickness. The electrical stress levels, employed in the experiments, are found to be not sufficiently elevated to lead to any detectable partial discharge formation within the oil phase itself; the observed discharge behavior is rather characteristic of the type that is normally associated with macroscopic cavities occluded within the oil-paper insulation systems.

A tentative mathematical model is described for estimating the time required for tracking to occur in rotating wheel water-spray or dip tests on polymeric insulating materials. The model is based on the energy balance criterion. In the derivation of the model, the required time for tracking to occur is treated as a function of the geometrical dimensions, the thermal characteristics and the volume and surface conductivities of the specimen. It is also considered to be dependent upon the applied voltage, wheel speed as well as the time required for arcing to occur, the discharge activity and the number of dry bands formed upon the surface of the specimen. The validity of the model is assessed, using experimental data obtained with epoxy fibre glass composite specimens; reasonable agreement is found between the experimental results and the calculated values.

The short and long-term dielectric behavior of a number of representative electrical insulating systems is compared in the presence of space charge. Dielectric materials, used both in the communications and power application areas, are considered. In this overview, particular attention is given to thin inorganic films, organic solid-liquid and solid polymer systems as regards to the manner in which space charge affects their dielectric loss, voltage breakdown, treeing and electrical aging characteristics.

Two accelerated aging test procedures are proposed for use on solid dielectric extruded distribution cables under wet conditions. One test method is a fixed time duration test in which the degree of cable specimen aging is assessed in terms of breakdown tests, while the other test method is a time to breakdown test in which the cable specimens are voltage stressed until failure ensues.

Stator bars subjected to operating stresses for 7 and 22 year periods were retrieved from a hydro-generator to undergo short term electrical diagnostic tests in order to determine whether any significant aging of the insulation had taken place. The ac breakdown voltage ([U.sub.bk]), partial discharge inception voltage (PDIV), the maximum charge ([Delta] [Q.sub.m]) and total apparent charge ([summation of] [Delta][Q.sub.j] where j to n) transfer of the partial discharges, tan[Delta] and tan[Delta] tip-up comprised the measured quantities statistically evaluated in the diagnostic test procedure. The ac breakdown voltage, PDIV and [Delta][Q.sub.m] were found to exhibit a systematic trend with in-service time, thereby suggesting the occurrence of aging effects. That is, both the ac breakdown voltage and the PDIV were characterized by a decrease with time in-service, whilst the [Delta] [Q.sub.m] value exhibited an increase. However, no definite behavior was evinced by the ([summation of] [Delta] [Q.sub.j] where j to n), tan[Delta] and tan[Delta] tip-up values. The significance of the diagnostic test results is discussed in terms of Weibull statistics and the partial discharge behavior with time.

Epoxy resin coated electrode specimens were subjected to partial discharges (PD) in air at twice the discharge inception voltage for durations ranging to 5000 h. The PD behavior was characterized by a transition from initially large pulse type discharges ([approximately] 200 to 300 pC) to either small pulse ([approximately] 1 pC), pseudoglow, glow discharge, or a combination thereof. Although these different forms of discharges were capable of occurring simultaneously, each type tended to prevail over certain periods of the exposure time. The physical and chemical nature of the degradation products formed on the surfaces of the epoxy resin also varied accordingly, indicating that each discrete form of discharge exerts its particular effect on the overall degradation process. Droplet formation on the central portion of the epoxy surfaces typified the large pulse discharge regime, whilst crystals formed within the transition region over which small discharge pulses ([approximately] 1 pC) were usually superimposed upon a continuous glow (pseudoglow and true glow regime). The droplets were identified as being partially comprised of a mixture of acids, mainly formic, glycolic, glyoxalic and nitric acids, whilst the crystals consisted of hydrated oxalic acid. Since similar results were obtained with discharges in both air and nitrogen, the effects of gas phase reactions on the PD activity would appear to be only of secondary importance compared to the reactions taking place on the surface of the epoxy resin. Since the test cell design did not allow any pressure variation within the discharge gap, the observed discharge transition cannot be attributed to pressure changes such as may take place within occluded cavities. Nevertheless, the transition observed here is similar to what is found with actual stator bar type insulation, suggesting that pronounced chemical and physical modifications on the surface of the physical cavity inclusions in the bar insulation may account for the characteristic PD behavior observed as a function of time.

The excitation and ionization behavior of a 5 [[micro]meter] cavity, subjected to an electric field of 270 kV/cm, has been examined. Data on the production of electrons, ions, dissociated molecules and excited species is presented and the associated charge transfer characteristics are considered. The implications of the ionization and excitation processes, as concerns their effect upon the degradation rate of solid insulation, are discussed.

A neural network system, utilizing the multi-layer perceptron approach has been applied to distinguish between partial discharge pulse shapes that are characteristic of cavities and electrical trees. The neural network was found to be capable of recognizing the differences in PD pulses produced by single cavity and electrical tree discharge sources. It also could differentiate between the discharge pulse forms emanating from electrical trees of different lengths; likewise, it was able to recognize changes in the shape of the discharge pulses with time due to aging effects. However, as these recognition capabilities relate only to comparisons of single discharge sources on a one-to-one basis, the application of neural networks to PD pulse shape recognition on actual cables, where a number of different discharge sources may be discharging simultaneously, is quite premature at this time without more detailed exploratory work on complex discharge patterns.

A comparison has been carried out on the partial discharge (PD) pulse shape recognition capabilities of neural networks, using the nearest neighbor classifier, learning vector quantization and multilayer perceptron paradigms. The PD pattern recognition capabilities were assessed on artificial cylindrical cavities of different sizes. The performance of the three neural network paradigms was found to be equivalent in all respects, with the exception of the case where a distinction was required between small cavity sizes; under those circumstances, the learning vector quantization paradigm was distinctly superior to the two other paradigms. The experimental results also demonstrated that, even with simple metallic electrode cavities, the discrimination capabilities of the three types of neural networks are not always perfect.

A low speed rotating wheel spray test procedure is described and typical results are presented on a number of low tracking resistance polymers. It is found that the time to tracking is a monotonically increasing function of the wheel speed at low speeds of up to 2.0 rpm. This reverse behavior of what normally occurs at high wheel speeds is explained in terms of residence times of the specimen in the water spray and in the air as a function of the speed.

A detailed examination of the aging processes, that may take place in solid-dielectric extruded-type high voltage transmission cables under dry conditions, is presented. Particular emphasis is placed on the aging process as affected by the separate and simultaneous action of four main aging factors, namely the electrical, mechanical and thermal stresses, and the physical and chemical environment. A number of pertinent aging models are considered and their validity and applicability to accelerated aging tests on solid-type transmission cables are discussed.

The partial discharge (PD) pattern recognition capability of a neural network, employing the multilayer perceptron technique with data input based on five discharge pulse form parameters, was examined. Simple discharge sources, consisting of artificially created cylindrical cavities with metallic and dielectric electrodes, were employed. The PD pattern discrimination capability was tested using cavities of equal depth but with different electrodes, and cavities of varying depths but with similar electrodes.

Experimentally obtained partial discharge pulse forms have been compared with those derived theoretically, using a mathematical model of a short gap. The calculations indicate that with overvolted short gaps, the apparent absence of the protracted ion current tail in the overall pulse form is due to the large excess of the electron current component generated by strongly enhanced cathode emission by the photoeffect and other phenomena. Under conditions of high overvoltage the ion impact induced emission, the ion fluxes and, consequently, the ion current component are greatly reduced as compared to the electron current and the long ion current tail, representing not more than a few percent of the total current, passes undetected. Pulseless and pseudoglow discharges are also considered and preferred terms to designate the different forms of partial discharges are suggested.

The effects of long exposure of epoxy resin surfaces to partial discharges under ac field stress were examined. The use of electrical pulse measuring techniques in conjunction with light emission measurements using a photomultiplier tube, which allowed simultaneous detection of both spark and glow discharges, permitted the establishment of a definite transition from spark to glow discharges. Spark discharges were found to be responsible for the initial surface modification leading to increased surface conductivity, which favored the transition to a pulseless glow type discharge within the cavity. The latter form of discharge was found to prevail over the major portion of the remainder of the exposure period.

The aging of epoxy electrical insulation by unipolar, repetitive voltage surges has been investigated to determine whether such surges can precipitate premature failure of high voltage motor windings and gas insulated switchgear spacers. A full factorial statistical test was devised and performed on 180 pure epoxy insulation specimens to examine the effect of voltage magnitude, polarity and surge repetition rate on the life of unfilled epoxy specimens containing a needle-plane electrode geometry. All factors and interactions were determined to have a significant effect on the life, and life prediction equations were estimated. Increasing the voltage magnitude or repetition rate, decreased or increased the life, respectively. Aging was found to occur at as low a stress as 2 MV/cm. An important conclusion is that gradual aging of the epoxy does occur under repetitive voltage surges. Based on a realistic number of surges with typical voltage amplitudes which can normally occur from vacuum switchgear during service, gradual deterioration of the epoxy turn insulation in motor stator windings is possible in some situations. Situations where surge aging may occur are identified.

The influence of dry air admixtures upon the breakdown mechanism of helium in small gap separations was investigated, using plane parallel stainless-steel electrodes enclosed within a Pyrex chamber. The test chamber was evacuated to a limit pressure of [10.sup.-5] torr and the electrodes degassed under a glow discharge. All experiments were carried out under atmospheric pressure, with the additions of air being made at relative partial pressures of [p.sub.r] = 0, [10.sup.-4], 3 x [10.sup.-4], [10.sup.-3], and 3 x [10.sup.-3]. The initial breakdown current was measured by means of a digital oscilloscope and the semilogarithmic plots of the discharge current as a function of time (up to ca. 100[mu]A) were found to exhibit an exponential dependence. The reciprocal value of the time constant of the breakdown current rise, [tau.sup.-1], was demonstrated to vary in accordance with the linear relation [tau.sup.-1] = [tau.sub.o.sup.-1] [p.sub.r.sup.m] [DELTA] V for an overvoltage [DELTA] V = V - [V.sub.b] (for V > [V.sub.b], [V.sub.b] being the breakdown voltage) in the range between zero to ca. 35 V; a log-log plot of [tau.sup.-1] versus the applied voltage, [DELTA] V, with relative partial pressure [p.sub.r] as a parameter was shown to lead the empirical relationship [tau.sub.o.sup.-1] = [3.11p.sub.r.sup.0.6] ([s.sup.-1] [V.sup.-1]) valid within the range from ca. [10.sup.-4] to 3 x [10.sup.-3]. The values of the breakdown voltage were determined from the extrapolated intercepts of the [tau.sup.-1] versus the applied voltage, V, characteristics. The experimental rate of rise of the breakdown current was compared with the theoretical current growth, calculated using a two-dimensional model of the breakdown process. The calculations were performed at [p.sub.r] = [10.sup.-4] with [DELTA] V = 33. V. It has been found that the rate of rise of the calculated current exceeds the experimental one by a factor of about 2.6, but agrees quite satisfactorily with the value that is obtained when the experiment is conducted at [p.sub.r] = 3 x [10.sup.-4].