Author: Maik Koch and Michael Krueger – Omicron Electronics Austria
Analysis of Dielectric Measurements
Interpretation in Frequency Domain
Dielectric diagnostic methods deduce moisture in paper or pressboard from dielectric properties like polarisation and depolarisation currents, complex capacitance and dissipation factor. Moisture strongly influences these quantities.
The dissipation factor plotted via frequency shows a typical s-shaped curve. With increasing moisture content, temperature or aging the curve shifts towards higher frequencies. Moisture influences the low and the high frequency parts. The middle part of the curve with the steep gradient reflects oil conductivity. Insulation geometry conditions determine the “hump” left of the steep gradient. In order to determine the moisture content of the insulation, the measurement should also provide data left of the “hump”, where the properties of the solid insulation dominate.
Moisture determination bases on a comparison of the transformers dielectric response to a modelled dielectric response. A fitting algorithm rearranges the modelled dielectric response and delivers moisture content and oil conductivity.
A reliable moisture analysis of onsite measurements bases on an exact data pool for the modeled dielectric response. The data pool constitutes of measurements on new pressboard at various temperatures, moisture contents and oils used for impregnation . The dielectric properties of aged pressboard were investigated as well in order to compensate for the influence of aging. To ensure the reliability of the achieved data base the results were compared to previous investigations, e.g. .
In the moisture analysis algorithm at first the insulation temperature T from the measured dielectric response C(f) is taken and the corresponding permittivity record ‹PB(f) from the extra- and interpolated data base. The so called XY-model combines this permittivity record ‹PB(f) with the complex oil permittivity ‹Oil(f). The XY-model allows for the computation of the dielectric response of a linear multi-layer-dielectric , where X represents the ratio of barriers to oil and Y the ratio of spacers to oil.
The obtained modelled permittivity sm(f) = stot(f) is converted into a modelled capacitance Cm(f) and then compared to the measured dielectric response C(f). The modelled capacitance Cm(f) with the best fitting to the measured capacitance C(f) gives the moisture content in cellulose and the oil conductivity of the real transformer. Figure 5 (left) depicts the programming flowchart of the new analysis algorithm.
Consideration of Conductive Aging Byproducts
Aging of cellulose and oil causes conductive by-products as carboxylic acids. These acids are deposited in the solid insulation and dissolved in oil. Their DC-conductivity increases the losses and thus “imitates” water.
Figure 6 compares the dissipation factor of aged material to that of new material. At similar moisture content the losses in aged materials are much higher than in the new material. Accordingly, a moisture analysis algorithm that does not compensate for conductive aging products will overestimate moisture content. This may mislead to unnecessary drying of transformers. The newly developed software compensates for the influence of conductive aging byproducts, resulting in a more reliable moisture analysis at aged transformers. Still more practical measurements will be used to improve the functionality of the compensation algorithm.
Moisture Measurement through Moisture Equilibrium
Moisture equilibrium bases on three conditions: thermal equilibrium (temperature), mechanical equilibrium (e.g. pressure) and chemical equilibrium. Thermodynamic equilibrium is reached, if the macroscopic observables do not change with time and place. An equilibrium regarding the time aspect is possible during a constant load period of a transformer. Still the observables will change with place. Equilibrium for time and place can be reached only in locally limited areas, e.g. between cellulose and the surrounding oil at high temperatures and slow oil flows.
Moisture equilibrium means, that the no migration of water molecules inside materials and between oil and cellulose occurs. Moisture migrates until the water vapour pressure p gains the same value, thus differences in the moisture vapour pressure are the driving force for moisture migration, (2).
p (Cellulose) =p (Oil) =p (Air) (2)
Supposed the same temperature and pressure rules, moisture exchange can be described in terms of relative saturation. The moisture content relative to saturation level in adjacent materials becomes equal (3). The material might be cellulose, oil, air or even a plastic.
RS (Cellulose) =RS (Oil) =RH (Air) (3)
Conventional Equilibrium Diagrams
It is a standard procedure for operators of power transformers to derive the moisture by weight (%) in cellulose from the moisture by weight in oil (ppm). This approach consists of three steps: (1) Sampling of oil under service conditions, (2) Measurement of water content by Karl Fischer Titration and (3) Deriving moisture content in paper via equilibrium diagrams (e.g. ) from moisture in oil.
Unfortunately crucial errors effect this procedure:
- Sampling, transportation to the laboratory and moisture measurement by Karl Fischer titration,
- Equilibrium conditions are rarely achieved (depending on temperature after hours/days/months),
- A steep gradient and high uncertainty in the low moisture region compounds the accuracy,
- Diagrams from various literature sources lead to different results,
- The temperature gradient in windings (up to 30 K) causes a uneven moisture distribution,
- Equilibrium depends on moisture solubility in oil and moisture adsorption capacity of cellulose.
The validity of equilibrium diagrams is restricted to the original materials that were used to establish the diagrams. Especially aging changes the moisture adsorption capacity substantially. The following Figure 7 (left) displays the graphs for equilibrium of new Kraft paper with new oil at 20, 40, 60 and 80°C. Additionally for 60°C it shows moisture equilibrium for new pressboard in new oil and for aged Kraft paper and aged pressboard in aged oil. Assumed the moisture content in oil is 20 ppm these curves lead to a moisture content in new paper of 2,9 %, in new pressboard of 2,6 %, in aged paper and aged oil it is 2,1 % and for aged pressboard and aged oil 1,5 %. Thus equilibrium diagrams not adapted to the specific materials are inapplicable to calculate moisture in paper from moisture in oil.
Diagrams Adapted to the Moisture Adsorption Capacity
The first step to improve equilibrium diagrams is to adapt them to the water adsorption capacity of the materials involved . Diagrams as Figure 7 (right) might be used to determine the “true” water content in cellulose, since they are adapted to the moisture adsorption capacity of the materials. They still have the essential drawback, that their validity is restricted to the involved materials. For other materials and ageing conditions they have to be redrawn, that is, a correction is necessary for every transformer with its special materials and aging conditions. Because of this disadvantage the following subsection describes the next step to more universal equilibrium diagrams
Measurement via Moisture Saturation of Oil
In this approach instead of moisture in oil relative to weight (ppm) the relative saturation in oil (%) is used. Additionally the diagrams are adapted to the moisture adsorption capacity of the cellulose. Based on equation (3) via moisture adsorption isotherms the moisture content in cellulose is derived from moisture relative to saturation of the surrounding oil. The advantages are:
- Oil aging and its influence on moisture saturation level becomes negligible, since it is already included into the measurement of moisture
- With relative moisture on the X-axis the graphs become less temperature dependent compared to moisture by weight on this axis (Figure 8, right)
- Errors due to sampling, transportation to the lab and titration are excluded.
- Continual, accurate measurement and easy implementation into a monitoring systems
Figure 8 (right) shows moisture by weight in thermally degraded Kraft paper as a function of moisture saturation. With thermal aging the ability of cellulose to adsorb moisture decreases. In this example a moisture saturation of 4,1 % at 47°C oil temperature gives in Kraft paper 2,2 % moisture content relative to weight. The approach to use moisture saturation of oil substantially improves moisture determination in transformers; still the diagrams have to be adapted to the moisture adsorption capacity of the specific cellulose material. The next section shows a way to overcome this drawback.
Moisture saturation is a critical factor that determines the amount of water available for interactions with materials. The destructive effects of water in power transformers are a decreased breakdown strength of oil, accelerated aging of cellulose and bubble formation. Water molecules that are available for interactions with materials cause all these destructive effects. This is not the case for molecules that are strongly bound, e.g. by hydrogen bonds to OH-groups of cellulose molecules forming a monolayer. Just water relative to weight, measured by Karl Fischer titration, reflects the bound and less active water as well. Moisture relative to saturation – not relative to weight – determines the available water for destructive effects. This approach gives the following advantages:
- Neither oil nor paper aging effects the validity
- Conversion via equilibrium charts unnecessary
- Direct relation to the destructive impacts of water
- Continual, accurate measurement and easy implementation into a monitoring systems
Figure 8 (left) illustrates the application of a relative saturation measurement using a capacitive probe in a power transformer equipped with an online monitoring system. The load factor influences the top oil temperature, which follows in diffusion processes changing the relative saturation in oil. A long term average equilibrates the relative saturation in oil with the relative saturation of the surrounding cellulose and comes to 4,1 %. Using a moisture isotherm as Figure 8 (right) one can derive the moisture by weight in cellulose as well, that would be 2,2 % in this case.
( To be continued….)