# Feature Focus

October 9 , 2012

Wind turbine farms are becoming an acceptable and common form of energy. Part of their construction includes buried cables to deliver the generated power from the wind turbines back to a station and ultimately into the power grid. One potential design consideration is evaluating the heat generated when an electric current passes through the cable.The rate of heat generation may cause the insulation power cables to fail when the cable temperature exceeds the design limit.

Buried electrical cables in wind collection systems may be under rated and even fail if the thermal properties and heat transfer calculations are inferred and/or improperly determined. Typically, buried power cables are conservatively rated and over designed because of the complex nature of coupled heat and moisture flow around a buried cable. A coupled heat and moisture flow program is warranted to model this transient behavior caused by climatic conditions and heat generated by the cable. The SVHeat/SVFlux model can be used to predict the long-term thermal behavior of cable backfill. Results of the model can be used to design electrical collector systems more cost effectively and with more confidence.

The example in this article illustrates the analysis of a typical scenario and was developed based on a research collaboration between the University of Wisconsin and SoilVision Systems Ltd.

In this modeled scenario, the cable temperature is influenced by heat transfer between the cable and the surrounding soil. Heat transfer depends on the soil type, moisture retention properties, and the climate conditions. The SVHeat™/ SVFlux™/ SVAirFlow™software couples together water flow, conductive and convective heat flow, and pore-air flow to simulate the temperature distribution around a power cable buried underground with the different backfill soils. The most efficient design for reducing the risk of power cable failure may then be determined.

#### Geometry and Boundary Conditions

Figure 1 illustrates a simple cable model. A coupled model of heat flow and water flow is used in this example to simulate the precipitation and evaporation effects on the cable temperature. The power cable is buried under the ground at the depth of 1 m. The cable has a diameter = 0.065 mand a heat load = 110 w/m.

The general process may be described as follows:

1. As the cable temperature increases, the moisture in the soil backfill around the cable begins to change phase to vapor.
2. The soil begins to dry as the moist vapor migrates away.
3. The thermal conductivity of air is much lower than the thermal conductivity of water. Therefore, as the soil dries out, the thermal conductivity of the entire soil matrix is reduced.
4. A lower thermal conductivity means there is less opportunity for the heat surrounding the cable to dissipate.
5. Countering this drying process is the fact that as the soil dries it creates an increased suction which then has the tendency to draw water from the surrounding soil and therefore increase thermal conductivity around the cable.

The atmospheric evaporation and precipitation is another significant factor influencing the soil moisture around the cables. The balance of these drying and re-wetting unsaturated processes is critical for the design of the system such that cable overheating does not occur.

Figure 1 Geometry and boundary settings for cable model

A coupled model of heat flow, water flow, and air flow is used in this example to simulate soil refill types, ground water table, and climate precipitation and evaporation effects on the cable temperature. The heat generation of power cables is simulated as a heat source in SVHeat. The heat source is calculated according to the heat load and the cross area of the power cable, i.e.

Heat source = heat load per length / cross area = 2.86411E+09 J/day-m³)

It is assumed that the geomembrane is used to prevent water in refill from flowing out. The initial moisture of refill can be specified by an initial condition in SVFlux.

#### Boundary and Initial Conditions

The initial water content is specified by each regions:
Ground water table = - 2.5 m.
Refill is close to saturation with the water head = -0.2 m.
Cable water head = -10 m.

The initial temperature = 20 in the whole domain.

Material Properties

The thermal conductivity for ground soil is calculated with Johansen approach, and the thermal conductivity for soil refill is specified according to the laboratory data of soil thermal dry-out curves that is a relationship between the thermal resistivity and water content for a soil.

#### Discussion of Results

The results of the analysis demonstrate the changing water content of the soil refill as the cable temperature increases. The rebound effect of water content and therefore temperature of soil material around the cable can be observed by plotting the temperature and water contents at key locations close to the buried cable.

The simulation results are presented in Figure 2, Figure 3, and Figure 4 for the soil refill water content, thermal conductivity, and temperature predicted by the coupling SVHeat/SVFlux (TH) and SVHeat/SVFlux/SVAirFlow (THA) models.

The decrease in the water content of soil refill with the time is caused by the dry evaporation under the combined effect of cable heat release and the atmospheric evaporation. At the same time, the soil suction is created with the soil drying, and the liquid water will migrate from the high water pressure (wetting area) to the low water pressure (drying area). The infiltration of precipitation will also affect the refill water content. It appears the final balance of water content in soil refill depends on the combined effect of dry evaporation, precipitation, ground water table, and soil properties.

The thermal conductivity of entire soil matrix depends on the thermal conductivity of components and their fraction in the soil. The air has much lower value of thermal conductivity (0.026 w/m-Â¡Ã£C) than water which has the thermal conductivity = 0.605 w/m-°C. As a soil is drying, the air content in the soil increases. Consequently, the thermal conductivity of soil will dramatically decrease, as shown in Figure 3.

In this example the heat convection and radiation are not considered. Therefore the heat transfer is dominated by the heat conduction. The heat transfer performance of soil around the power cable will decrease with the decrease in the thermal conductivity of soil refill. As a result, the cable temperature increases dramatically, as shown in Figure 4.

#### Conclusion

This example presents the results of a typical analysis of a buried cable use to carry power from a group of wind turbines. The example demonstrates the successful coupling of the SVHeat/SVFlux/SVAirFlow software packages such that the temperature of the soil surrounding the cable can be simulated in a detailed and rigorous manner. The software would then allow analysis of differing design scenarios with varying refill material such that the chance of cable overheating can be reduced.

Figure 2 Refill water content changing with time at different locations
simulated by the coupling models of SVHeat /SVFlux (TH) and SVHeat/SVFlux/ SVAirFlow (THA)

Figure 3 Refill thermal conductivity changing with time at different locations
simulated by the coupling models of SVHeat /SVFlux (TH) and SVHeat/SVFlux/ SVAirFlow (THA)

Figure 4 Refill temperature changing with time at different locations
simulated by the coupling models of SVHeat /SVFlux (TH) and SVHeat/SVFlux/ SVAirFlow (THA)

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