Electrostatic (Capacitive) Coupling

2.2.1 Case Study

3.1.1 Electrostatic (Capacitive) Coupling

With electrostatic coupling, energy is transferred through the electrical capacitance that exists between the powerline and the pipeline. Any two conductors that are separated by a dielectric material can be considered a capacitor. Capacitance is a measure of the ability to store electrical charge Q between two conductors, relative to the voltage V between the conductors; that is:

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C= Q coulombs/volt [3-1]

The unit of coulombs/volt is more commonly referred to as a farad (f).

Capacitance is proportional to the area A of the conductors but is inversely proportional to the separation d between the conductors (Figure 3-3).

Furthermore, capacitance is directly dependent upon a physical property of the dielectric material known as permittivity (ε), having the units of f/m. Therefore,

C =ε A [3-2]

Dielectric Conducting Plate (having area A)

Conducting Plate

C ∝ A d

Figure 3-3: Elements of a Capacitor

When a direct current (DC) voltage source is applied to a capacitor, current will flow and charges will accumulate on the plates of the capacitor. As time passes and charges continue to accumulate, the current flow decreases and eventually becomes zero when the voltage on the capacitor is equal to the applied voltage.

This time period is very short; for all practical purposes, a capacitor appears as an open circuit to DC.

When an AC voltage source is applied to a capacitor, current begins to flow and the conducting plates again begin to accumulate charges. As the polarity of the voltage source reverses during the second half of the AC cycle and current flows in the opposite direction, however, the plates of the capacitor discharge and begin charging with the opposite polarity. This process of charging, discharging, charging in the opposite direction, and discharging again repeats itself every cycle, and an AC continually flows through the capacitor. As the frequency of the voltage source increases, fewer charges can accumulate on the capacitor’s plates.

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As a result, there is less opposition to the flow of current. At very high frequencies, a capacitor therefore appears as a short circuit to AC.

The opposition that a capacitor offers to the flow of AC is called capacitative reactance, Xc. Reactance has the units of ohms (Ω) and is similar to resistance—

except that it not only controls the magnitude of the current flowing in the circuit, but also affects the phase relationship between the voltage and the current (Section 3.2.1 discusses this). Reactance is dependent upon both frequency f and capacitance and is determined by the following equation:

fC X_C

= π 2

1 [3-3]

Consider the case in Figure 3-4 where a pipeline is under construction. Lengths of pipe have been strung out along the pipeline route and have been placed on wooden skids in preparation for welding. Although this may not look like a capacitor as previously discussed, the elements necessary for the construction of a capacitor are present; these elements include two conductive plates separated by a dielectric material. In this case, the powerline is one conductive plate and the pipe is another. They are separated by air, which serves as a dielectric. Similarly, a second capacitor is formed between the pipe and the earth because the earth (although nonmetallic) is also a conductive plate. A section of pipe sitting on skids beneath an AC powerline can therefore be represented as an electrical circuit consisting of two capacitors in series with an AC source, which forms a capacitive voltage divider.

Conducting

Plates Air

Dielectric

Figure 3-4: Electrostatic Coupling during Pipeline Construction

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Recalling Kirchhoff’s Laws, the sum of the voltage drops across the resistors in a series circuit (Figure 3-5) will be equal to the sum of the voltage sources.

Furthermore, these voltage drops are in direct proportion to the resistances that create them. Similarly, the voltage drops across the capacitors in an AC series circuit will be in direct proportion to the respective capacitive reactances; their sum will be equal to the sum of the voltage sources.

I R1

R2 V

R1 R2 V1 V2 =

I C1

C2 V

X_C1 X_C2 V₁

V₂ = = C₂

C₁

Figure 3-5: Voltage Divider Circuits – Resistive (left) and Capacitive (right)

Therefore, in the pipeline construction case of Figure 3-4, the line-to-ground voltage of the powerline is divided between the two capacitors in inverse proportion to their capacitances.

Depending upon the relative capacitance values and the powerline voltage, very large voltages can be electrostatically generated on a single pipe joint—assuming it is well insulated from earth. To provide a very rough estimate of the magnitude of the induced voltages, consider the case of a single pipe section raised upon on skids (Figure 3-6).

Example Calculation:

The pipe has a diameter of 0.3m and is 5m in length. It therefore has a surface area of approximately 5m². The powerline conductor has a much smaller diameter than that of the pipe. Hence, it has a smaller surface area while the underlaying earth has a greater surface area than the pipe. Assume that these areas are 0.2m² and 20m², respectively.

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Figure 3-6: Calculation of Typical Capacitance Values for a Pipe on Skids

The powerline conductor and the pipe, which form the two places of C1, have different areas. So, in order to use Equation 3-2, the geometric mean of the two areas is used. Similarly, the pipe and the earth lying beneath it have different areas. So, the geometric mean is calculated to determine the area of the plates for C2.

The separation distance between the powerline conductor and the pipe is typically much greater than between the pipe and the earth. These distances are given as being 10m and 1m, respectively. The values of C1 and C2 can now be calculated, given the permittivity of air (εair) has a value of 9×10^-12 f/m.

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Again, note that these capacitance values are very rough estimates only;

although accurate capacitance values could be calculated, such a task would involve much more complicated equations. It is only important to understand that the earth capacitance should always be larger than the pipe-to-powerline capacitance and that these capacitance values are typically very small. For instance, a capacitor used on an electronic circuit board (having a physical size similar to that of a pencil eraser) might have a capacitance of 10

× 10^-6farads (10 μf)—yet this capacitance would be roughly a million times larger than the pipe capacitances calculated above.

In order to calculate the voltage that is electrostatically induced on the pipe in Figure 3-6, the values of C1 and C2 are substituted into the capacitive voltage divider circuit of Figure 3-5. In Figure 3-5, the voltage applied across the capacitors is the line-to-ground voltage of the powerline; it is given as 100 kV in this example.

powerline

Figure 3-7: Calculation of Typical Electrostatically Induced Voltage for a Pipe on Skids

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The pipe voltage in the example seems unrealistically high. However, this is indeed the magnitude of voltage that might be typically induced electrostatically on a single pipe joint—provided that the pipe is well-insulated from earth and that the voltage is measured with a high-impedance voltmeter. In order to determine if this voltage may present an electrical safety hazard, it is necessary to calculate the current that could possibly be generated by this circuit.

The current that can be produced is limited by the reactance of the powerline-to-pipe capacitance (C1). The reactance is calculated using Equation 3-3.

The current that can flow through a human body, assuming the worst-case of a zero-ohm body resistance, is then determined using a calculation that is essentially Ohm’s Law.

Figure 3-8: Calculation of Typical Shock Current Resulting from Electrostatic Coupling

Such a low current is considered non-hazardous. It is in fact well below the 1-mA threshold at which the human body can sense electric current (this is discussed in Section 3.4.1). Therefore, even though electrostatic coupling can induce large voltages on sections of pipe that are well-insulated from ground, the circuit impedance is generally too high to produce a significant shock current.

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Consider the case where an automobile is parked beneath a high-voltage power transmission line (Figure 3-9). Because the car is well-insulated from earth by the rubber tires, the situation is very similar to the one illustrated in Figure 3-8. If the high voltages generated by electrostatic coupling were capable of presenting an electrical shock hazard, then consider the problems this scenario might cause to the public.

C₂

C₁ = 0.01C2

V = 100 kV

V = 1 kV

Figure 3-9: Calculation of Typical Electrostatically Induced Voltage for an Automobile

The sample calculations for a pipe raised up on skids were for the case of a single pipe joint. As the pipe joints become welded together, the surface area of the pipe increases and the pipe-to-powerline capacitance increases accordingly. This results in a lower capacitive reactance between the pipeline and powerline, which will permit more current to flow through the body (Figure 3-8). However, as the pipeline increase in length, two other factors become important. Firstly, the amount of energy being electromagnetically induced in the pipeline becomes significant—more significant, in fact, than the electrostatically induced energy (see Section 3.1.2). Secondly, as the pipe increases in length, the total resistance between the pipe and earth through the increasing number of skids decreases.

Therefore, the voltage generated across C2 decreases (a bar pipe on skids would have an even lower electrostatically induced voltage). Most importantly, however, is that as the pipe joints are welded together the construction crews begin to lower the pipe into the trench. This not only results in an even lower pipe-to-earth resistance, but also results in a much higher pipe-to-earth capacitance (Figure 3-10).

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Figure 3-10: Calculation of Typical Electrostatically Induced Voltage for a Buried Pipe

Considering only the effect of the increased pipe-to-earth capacitance, a decrease of the pipe-to-earth separation from 1m to 1mm (the thickness of the coating) would result in a 1000 times increase in the capacitance C2, a 1000 times reduction in the capacitive reactance XC2, and a 1000 times reduction in the pipe voltage Vpipe. Electrostatically induced voltages thus essentially disappear once the pipeline is laid into the trench.

Note that in the example of Figure 3-10, a pipe-to-ground capacitive reactance of 30 kΩ is sufficient to reduce the pipeline voltage from 1000 V to 1 V. This suggests that when the pipe is raised up on skids, it should be very easy to ground the pipe to mitigate electrostatically induced voltages. In practice, it is found that nearly any type of ground connection—even one as insignificant as a test lead connected to the pipe and contacting the earth—is often sufficient to completely mitigate the induced voltages.

In the capacitance calculations in the examples above, note two things: the capacitance calculations are very approximate and the effects of only one phase of the three-phase circuit have been considered. It should also be apparent from the sample calculations that powerline voltage—not powerline current—determines the magnitude of the electrostatically induced pipe voltages.

Although electrostatic coupling generally cannot produce enough current to create an electrical safety hazard, it may result in nuisance voltages that produce a sensation similar to a shock from static electricity. This, in turn, could

3 x 10⁹

3 x 10⁴

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conceivably create a secondary safety hazard if, for instance, someone on a pipeline construction project was to overreact to the sensation of an electrostatic voltage on a section of pipe.

Because electrostatically induced voltages are typically not hazardous and are easily mitigated, the remainder of Chapter 3 will focus on the much more serious concerns of electromagnetic and conductive coupling effects.

In document NACE CP Interference January 2008 (Page 115-124)