High voltage Riddle No.5 - Temperature vs Voltage
How does the temperature of the surroundings affect the voltage of something?

#1
Mon, January 16th, 2012 - 12:12
Normally, all dielectrics are good insulators at lower magnitudes of field intensities.
But as the electric field increases, the electrons bound to the molecules of the dielectric will be subjected to higher forces, and some of them are freed from their molecular bonding. The electrons move in the opposite direction to the electric field and thus create conduction current. This dissociation is temporary in gases in which a combination occurs when the field is removed, whereas it is a partial or permanent feature in liquids and solids. Also, this phenomenon depends on a number of factors like impurities present in the substance, temperature, humidity, length of time for which an electric field is present, etc. The phenomenon is called dielectric breakdown, and the magnitude of an electric field that gives rise to the dielectric breakdown and destroys the property of insulation in dielectric materials is called the dielectric breakdown strength.
In order to account for the effect of temperature, the PasChen's law is generally stated as V =f(Nd) where N is the density of the gas molecules. This is necessary, because the pressure of the gas changes with temperature according to the gas law pv = NRT, where v is the volume of the gas, T is the temperature, and R is a constant.
Based on the experimental results, the breakdown potential of air is expressed as a power function in pd as:

It may be noted from the above formula that the breakdown voltage at constant pressure and temperature is not constant (At 760 torr and 293 °K).
This equation yields a limiting value for E of 24 kV/cm for long gaps and a value of

which means a pressure of 760 torr at 2O °C with 1 cm gap.
This is the usually quoted breakdown strength of air at room temperature and at atmospheric pressure.

Also electrotechnical products rely on electrical or electronic insulating materials to provide the protection  required for the safety of people and the insulation of conductors from one another. Solid electrical insulations are often based on plastic materials, either thermoplastic, thermoset, or crosslinked, and they represent a major use of such materials. Electrical insulating liquids and gases are, however, also essential when used singularly or as combinations as electrical insulation or as an environment for electrical insulation. Standards have been issued, both in the United States and internationally, dealing with specifications for such materials, and with test methods for assessing a variety of properties for those materials. For example a primary objective in the design of a reliable transformer is to limit internal temperatures.
In an effective design, a balance is reached between the heat generated by electrical loading (and overloading) the core and coils in the transformer and the capacity of the internal oil circulation system to remove this heat to cooler external surfaces. The standardization of limits on kinematic viscosity at several temperatures allows transformer manufacturers to develop standard design practices for the sizing and placement of oil ducts, reservoirs, baffles, pumps, radiators, etc. The ASTM and IEC test methods for viscosity are quite similar. Specified measurement temperatures are only the same at 40 °C Again the IEC has three classes of oils with different physical properties. The Class III oils are for use in certain types of circuit breakers.
During the service life of electrical equipment, organic electrical insulating materials used at elevated service temperatures can degrade as a result of progressive chemical reactivity. It is therefore essential that normal operating temperature limits be established for such materials. The traditional approach is to accelerate the degradation process with simultaneous testing at moderately elevated temperatures above the intended service temperatures of both the candidate material and a control reference material. With proper application of a chemical kinetic model, a service limit is established for the candidate material based on the comparative test performance, with the control having known long-term thermal service capabilities. There are practical limits on the maximum test temperatures and corresponding minimum test times to ensure an accurate representation of the service degradation mechanism during the test program. This results in an onerous, unavoidably protracted test time for these thermal aging sfudies.
Tom Dakin of Westinghouse introduced concepts of thermal aging based on reaction rate theory (the Arrhenious equation) In 1948. A tremendous amount of activity followed in AIEE (now IEEE) and ASTM D09. It became apparent that temperature limits based on the broad description of insulating materials (first defined by Steinmetz of GE and Lamme of Westinghouse in 1913) were no longer technically adequate or appropriate.
First in IEEE generally and then in ASTM D09, heat aging tests based on reaction rate theory were developed. These tests provided thermal indices based on change of electrical properties, mechanical properties or weight loss for many insulating materials including magnet wire, varnishes, tubing and sheet. Higher thermal limits for electrical insulation based on these tests permitted the design of smaller and otherwise improved electrical equipment.
The aliphatic carbon-carbon bond energy of hydrocarbon oils is about 90 kcal/mol (about 4 eV). Thermal excitation of molecules becomes sufficient to break these bonds at temperatures of 350 to 550  °C Thermal cracking of petroleum products is carried out in this temperature range. Below 100 °C the normal maximum operating temperature of high-voltage transformers, there is insufficient thermal energy to excite valence electrons.

For practical purposes the power factor and dissipation factor are equal numeric values for new oils. Both the power factor and dissipation factor indicate the dielectric loss of an oil and, thus, the dielectric heating. Dielectric losses in the insulation system of transformers are very small and normally ignored as a source of heat, except in the case of some specialty transformers. A high dissipation factor is an indication of inadequate refining or contamination of new oils. For in-service oils, increases in power factor or dissipation factor may be caused by the presence of byproducts of oxidation, contamination or deterioration products such as moisture, carbon or other conducting matter, and metal soaps. The power factor and dissipation factor increase exponentially with temperature. ASTM and IEC requirements are at different temperatures and are different limit values with ASTM being stricter by its 100 °C requirement.

An understanding of the theoretical basis for expecting the classical thermal endurance line, for log times to reach an end-point state as a linear function of reciprocal absolute temperatures, is important since this relationship is applicable for both the traditional and oxidative stability methods. These thermal endurance lines are fundamental to several preeminent protocols, including standards IEC 216 Guide for the determination of thermal endurance properties of electrical insulating materials, UL 1446 Systems of Insulating Materials and UL 746B Polymeric Materials - Long Term Property Evaluations. The UL 746B protocol has been selected for the following discussion since it illustrates some important characteristics of test developed thermal endurance lines, when used to determine the long term thermal capability of materials in electotechnical applications. During UL 746B material evaluations, simultaneous destructive testing of a candidate material and a control reference material, is used to study the degradation of selected diagnostic properties of standard specimens during exposure to moderately elevated aging temperatures, above the maximum intended use temperature. For the property, an end-point at each elevated aging temperature is defined as that time required to produce a reduction in the property to some fraction ( e.g. 50% ) of the unaged value. These test properties serve as diagnostic indicators of the point where cumulative thermal degradation has progressed to the same ( though arbitrary and in fact unknown ) extent at each aging temperature. With proper application of chemical kinetic theory and subject to the limitations imposed by necessary underlying assumptions, then the log of these endpoint times should be a linear function of the reciprocal of the absolute aging temperatures.
This linear relationship is the thermal endurance line for the material, and is commonly and incorrectly known as the Arrhenius equation.
Following is a brief and simplified derivation of the linear thermal endurance equation. The true Arrhenius equation relates only specific reaction rate and absolute temperature :

The thermal endurance equation relating test times and temperatures, in either the exponential form ( 4 ) or the more common transformed linear form ( 5 ) has two parameters. The slope and intercept terms, m and b of ( 5 ), are commonly referenced as the activation energy and pre-exponential terms respectively. ( m ) is clearly directly proportional to the degradation reaction activation energy E through the Arrhenius equation. Most importantly, the defined relationship between test end-point times and exposure temperatures is not directly related to material service life and use temperature.
Please recall in the analysis, that the definition of the test end-point performance level is arbitrary (as is to some extent the choice of the diagnostic property) and only for determining the exposure times at each temperature to produce an equal, though unknown, extent of cumulative thermal degradation.
A primary function of the control reference material is to establish a link between test performances and maximum service use temperatures. The control must have an accepted maximum service temperature limit in general electrotechnical products with respect to long term thermal chemical degradation of a class of critical property. Parallel testing of this material, with a candidate material, is conducted using a suitable diagnostic property having a similar character as the class of critical service property, to define thermal endurance lines. A test correlation time is defined as that time corresponding to the control maximum service temperature, and the analysis is completed by assigning a relative temperature index to the candidate at that temperature corresponding to the correlation time. Another important function of the control is to reduce systematic errors. Due to a variety of uncontrollable and often undetectable factors, the resulting thermal endurance lines can vary considerably between valid programs, in spite of every effort to maintain consistency. This translates into differing test program correlation times, but the effect on the determined candidate maximum service temperature is minimal if the control is tested under identical conditions.