1.Electrical Engineering Theoretical FoundationsAdditional Chapters
Simon DUBITSKY
Higher school of High Voltage Energy
QuickFieldFEA Software
Week 1. Introduction
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Spring 2023
2.Week 1: Introduction
How to solve the EM field equation using numerical simulation (practical aspects).
What math concept do we rely on in this course?
The equations we solve: Maxwell equations again.
What must be added to Maxwell equation to solve it?
Why we prefer to use potential instead of field vectors?
Concept of Field Formulation: Do we have to solve all equations at once?
How to jump from Maxwell equations to the first practical problem?
Summary: the Numerical Field Simulation workflow.
Let’s solve our first problem
Week 1. Introduction
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3.Basic concepts of vector calculus
Flux of a vector Circulation of a vector
What math will we use
Week 1. Introduction
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Divergence Rotor (Curl)
5.It is not a full story. What should be added?
1. Various material models describing the macroscopic field inside the material. Any material law is always an (simplified) approximation
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6.It is still not a full story. What more should be added?
2. For numerical solution field equation are often written with respect to potential, not field vectors
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You already know a lot about potentials.
Examples are:
Scalar potential of electric field: the potential U(x, y, z) is such scalar quantity thatQuestion: Why we are sure that such potential really exists?
Scalar potential of magnetic field: the potential UM (x, y, z) is such scalar quantity thatAgain: please think when the UM exists and when it does not exist?
Vector magnetic potential: the potential A(x, y, z) is such vector quantity thatQuestion: Does the vector potential A always exists?
Why the potential is numerically better than field vectors E, D, H, B ?
7.Simplified subset of Maxwell equations
Solving the full set of Maxwell equations is almost impossible (and always impractical)
Week 1. Introduction
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Simplified set of Maxwell equations (examples):
Electrostatics:
Nothing is changed in time;
No magnetic field exists (B=0; H=0)
Magnetostatics:
Nothing is changed in time;
No electric field exists (E=0; D=0)
AC Magnetics:
Every field quantity changed in time sinusoidal with the same frequency: H = H0cos (ωt + φ0)
No displacement current: JD = dD / dt = 0
8.What’s more?Geometry + Mesh + Boundary Conditions + Materials = Result
Every numerical problem is solved:
In the given geometry (bounded or unbounded) – the geometry is always a simplification
In discrete space (by the mesh)
With given boundary conditions and properties of materials
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1. Geometry
2. Mesh
9.What’s more?Boundary Conditions & Field Sources
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3. Boundary conditions
Each field problem is solved with boundary conditions (BC).
BC reflects the influence of the world outside our model
Sometimes BC serve as a field source (e.g. given potential)
BC may reflect the symmetry condition when our model is ½ or ¼ of the real geometry
10.The purpose of computing is insight, not numbers Richard Hamming, 1962
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4. Calculation Result
What we use to understand the calculated field:
Field pictures: color plot, vector plot, field lines
Local field values
Integral field quantities: flux, energy, force
XY-plot over various cross-section
Animated pictures
11.Resume: What you need to solve a field problem numerically?
Week 1. Introduction
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1. Choose formulation
2. Draw your geometry
3. Define your materials
4. Set boundary conditions
5. Build the mesh
6. Enjoy your results
12.Example:
Week 1. Introduction
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Finding the best place for an optical cable in overhead power transmission line
The communication fiber-optical cable if often mounted along with high voltage overhead power line.
The cable itself is self-supported and fully dielectric, i.e., it contains no metal parts.An optical cable should be properly located relative to phase conductors. What is a proper location?
According the Russian electrical code this is a place where the average potential U reaches its minimal value, U <=12 kV (25 kV with using special polyethylene). Also, the electric filed E should be checked.
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Model of Overhead Line: the cross-section
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Model of Overhead Line: the geometry model
The whole model
The tower
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Model of Overhead Line: boundary condition
Outer boundary: no field here (U=0)
Earth surface:U=0
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Model of Overhead Line: boundary condition
Left Circuit:
Momentary phase voltagesUA1, UB1, UC1
Right Circuit:
Momentary phase voltagesUA2, UB2, UC2
The Tower:
Is grounded: U=0
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Model of Overhead Line:the solution
Good place for an optical cable(the potential U<6 kV)
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Model of Overhead Line: XY-plot of Potential U(y)
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Model of Overhead Line: XY-plot of electric field E(y)
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Model of Overhead Line: Conclusion
By numerical simulation we have found a good place for the self-supported dielectric optical cable on the tower:
Optimal coordinates are: x=0; y=22 m
The potential is this point is: U=2.7 kV
The electric field stress there is: E=6.0 kV/m
Good place for an optical cable
21.Week 1. Introduction
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Your first homework
Next week we will focus on Electrostatic analysis – the simplest case of EM fields.
We will learn how to:
Create a QuickField problem,
Draw the geometry
Set up boundary conditions
Manage the mesh density
Obtain the problem solution, and
Understand and analyze the results
Be prepared:
order, download, and install your copy of ELCUT 6.6 Professional Edition
Learn with introductory videos on https://quickfield.com/seminar/arhive.htm