quasielectrostatic induction on stationary vehicles under high … · 2012. 11. 9. · voltage...
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Quasielectrostatic Induction on Stationary Vehicles under High
Voltage Power Lines
Jon Leman, P.E. Rob Schaerer, P.E.
Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston
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INTRODUCTION
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The National Electrical Safety Code ® states:
“For voltages exceeding 98 kV ac to ground, either the clearances shall be increased or the electric field, or the effects thereof, shall be reduced by other means as required to limit the steady-state current due to electrostatic effects to 5 mA if the largest anticipated truck, vehicle, or equipment under the line were short-circuited to ground.”
Current (60 Hz) Physiological Effect
0.5-1 mA Threshold of perception
10-20 mA Sustained muscular contraction
>100 mA Ventricular fibrillation
INTRODUCTION
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INTRODUCTION
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INTRODUCTION
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INTRODUCTION
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=
I < 5 mA
I
INTRODUCTION
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Electric Field Magnitude Profile at Ground Level
(kV/m)
Include Extra Length for End Effects
Cen
terl
ine
Integrate over Vehicle Length to Obtain Average, Undisturbed Electric Field
Estimate the Effective Charge Collecting
Surface Area of the Vehicle or Object
SEMI-EMPIRICAL APPROACH
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Cost vs. Electrical Clearances
Need to understand
assumptions in order to optimize the design!
THE PROBLEM
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Key Characteristics: 1. Transmission line allows 2D analysis, but vehicle requires 3D
2. ELF AC voltages and currents => Electric Currents Interface
3. Steady state 60 Hz => Frequency domain
4. Ground and vehicle body are assumed to be very good conductors with charge relaxation times much smaller than a 60 Hz period (hence classification as quasistatic).
PHYSICS of the STUDY
Equation Summary
𝑬 = −𝛻𝑽 Relationship between electric potential and electric fields
∇ ∙ 𝑬 =𝜌
𝜀0
Gauss’ Law: Electric flux through a surface is proportional to the enclosed charge
𝐧 ∙ (𝜀0𝑬𝒂 − 𝜀0𝑬
𝒃) = 𝜎𝑠 Relationship between surface charge density and electric
field at the surface boundaries
∇ ∙ 𝑱 = −𝜕𝜌
𝜕𝑡
Law of conservation of charge: Current in or out of a volume is equal to the rate of change of charge
𝑱 = 𝜎𝑬 + 𝑗𝜔𝑫 + 𝑱𝒆 Equation for current density given a steady-state
frequency domain problem
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COMSOL MODEL
CAD Model of Vehicle Imported into COMSOL
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Electric insulation for top and side boundary surfaces
Zero Potential Ground Plane
COMSOL MODEL
Electric Potential Assigned to Conductor Surface (345 kV)
Vehicle is a conducting body at a height above ground
Air volume
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COMSOL MODEL
Largest dimension in space = 200 ft Conductor diameter = 1 inch => 2400:1
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COMSOL MODEL
Perform parametric sweep of V2
133:1
Perform parametric sweep of R
400:1
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COMSOL MODEL
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Results of Comparison
COMSOL MODEL
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Approach 1:
• Electric Currents Interface with iterative solver => easily handled about 1.2M DoF
• Truck volume meshed and included in solution space
• Conducting cylinder connects vehicle to ground
COMSOL MODEL
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COMSOL MODEL
Approach 1
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Approach 2:
• Electric Currents Interface and Electrical Circuits Interface with direct solver => could only handle about 200K DoF
• Truck volume not meshed and not included in solution space
• Electric Shielding element with conducting properties used on vehicle surfaces
COMSOL MODEL
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COMSOL MODEL
Approach 2
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Results of Parametric Sweeps
RESULTS
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Approach Short Circuit Current
Truck 1 Truck 2 Truck 3
Semi-empirical n/a n/a 4.2 mA
COMSOL approach 1
3.8 mA 4.1 mA 4.2 mA
COMSOL approach 2
4.0 mA 4.0 mA 4.1 mA
CDEGS n/a 4.1 mA 4.2 mA
RESULTS Short Circuit Current
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RESULTS Parametric Sweep of Vehicle Length
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RESULTS Parametric Sweep of Body Resistance
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For The Case Studied:
1. The semi-empirical approach with geometric simplifications provides reasonably accurate results and is biased appropriately on the side of safety
2. The “largest anticipated vehicle” is not necessarily the controlling case for electrical clearances
3. Resistances in the range of that of the human body have negligible effect on the flow of current to/from the vehicle
CONCLUSIONS
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QUESTIONS?