代写ELEC4611 POWER SYSTEM EQUIPMENT LABORATORY EXPERIMENT 5代写数据结构语言程序

ELEC4611 POWER SYSTEM EQUIPMENT LABORATORY

EXPERIMENT 5

COMPUTER-BASED ANALYSIS OF ELECTRIC STRESS

1.      INTRODUCTION

Insulating materials used in power system equipment are subjected to severe electric stress. Breakdown will occur if the stress exceeds the material breakdown strength. Knowledge of the  electric  field  distribution  in  a  given  insulating   structure  is  important  as  it  enables determination of the permissible operating voltage and methods of controlling electric stress. This knowledge can be achieved using computer-based numerical methods such as the Finite Element  Method  (FEM)  to  solve  the  Laplace’s  or  Poisson’s  field  equations.  Note  that practical insulating systems usually involve a combination of different insulating materials with different permittivity and also require solving three-dimensional fields with complex boundary conditions.

2.      EXPERIMENT

This  experiment  involves  the  use  of  computer  programs.   There  are  many  commercial software programs for field analysis. One such product is the Ansys Maxwell 2D for two- dimensional field analysis (www.ansys.com). The workflow process to solve a field problem involves six steps: create a structure → assign materials → add boundaries → add excitations → setup the solution → solve → post processing.

(a)     Draw, set up, and solve for the electrostatic field in between two parallel copper plates (1 mm thickness, 15 mm length) at 5 mm apart with an applied voltage of 1 kV. Verify that the electric field is uniform.

   Starting Maxwell: do one of the following:

-    Double-click the ANASYS Electronics Desktop icon on Windows Desktop.

-    Use Start menu to select Programs>ANASYS Electronics Desktop

   Create a 2D Project:

-    From the toolbar Maxwell>Maxwell 2D

The Project Manager window will appear on the left. To create solution type, do one of the followings:

-    Choose Maxwell 2D>Solution Type>Electrostatic

-    Right click on Maxwell2Ddesign1 in Project Manager window, then choose Solution Type and Electrostatic.

Note: You need to set the Solution Type to Electrostatic when you insert a new project.

   Create modeling objects:

In order to draw the above structure (parallel plates), you can follow these steps: (a) Design the first plate:

-    Draw>Line

-    In status bar, enter 0 in X box and 0 in Y box.

-    Change the coordinate from Absolute to Relative.

-    Enter 0 in dX box and 1 in dY box (after this step, you can see a vertical line with length of 1mm will be drawn).

-    Enter 15 in dX box and 0 in dY box.

-    Enter 0 in dX box and -1 in dY box.

-    Enter -15 in dX box and 0 in dY box.

-    Right click on design window>Done. After this step, the object will be automatically named Polyline1.

(b) Design the second plate:

-    Repeat part (a) above with appropriate coordination start with 0 in X box and 6 in Y box.

-    The plate will be automatically named Polyline2.

(c) Design boundary:

-    Draw>Rectangle

-    In status bar, enter -20 in X box and 27 in Y box.

-    Enter 55 in dX box and -47 in dY box

-    It will be named Rectangle1

  Defining Materials:

In this step, the materials as well as their characteristics will be assigned to above created objects.

Choose Polyline1 and Polyline2 objects > Modeler > Assign Material. In materials tab, choose copper > OK.

   Setup Boundaries and Excitation:

(a)  Choose Polyline1>Maxwell 2D>Excitation>Assign>Voltage>enter 1000 V>OK

(b)  Choose Polyline2>Maxwell 2D>Excitation>Assign>Voltage>enter 0 V>OK

(c)  Edit>Selection Mode>Edges.

Hold Ctrl + left click on 4 edges of Rectangle1

>Maxwell 2D>Boundaries>Assign>Balloon>OK.

   Generating a Solution

(a)  Setup a Matrix Calculation: Maxwell 2D>Parameters>Assign>Matrix>Check Voltage 1 as Signal Line and Voltage 2 as Ground.

(b)  Setup a Solution: Maxwell 2D>Analysis Setup>Add Solution Setup>Leave these criteria as default.

   Checking Validity and Run Simulation:

(a)  Maxwell 2D> Validation Check Make sure all steps are checked. (b)  Run simulation: Maxwell 2D>Analyze All.

   Monitoring electric stress:

Choose Rectangle1 >Maxwell 2D>Fields>Fields>Mag_E>AllObjects

(b)    Consider a right-angled structure as shown in Figure 1:

    Create a new Maxwell 2D project and obtain the field plot for this structure.

    Comment of the results.

    Suggest a minor modification that can be done to the structure to reduce the stress. Redo the plot to verify.

Note that:

    Properly set the solution type.

    When designing boundary, create a rectangle that is relatively large in order to see the complete field distribution.

    When  drawing  the  object,  choose  an  origin  by  yourself  (or   following   the instructions of your lab demo) and work out the relative coordinates for the rest of points.

    Choose Modeler >Units>cm

Figure 1

Note: The thickness of the above electrodes is 1cm, and the distance between two electrodes is 5cm.

(c)     A cable, shown in Figure 2, has an eccentric core and axial uniformity. There are  100 kilo-volts across the cable and the insulation has a relative permittivity εr  = 2.0 and resistivity  P = 1013    Ωm  (conductivity  can  be  worked  out  by  taking  the  inverse  of resistivity). The geometrical parameters can be determined using the scale provided in Fig. 2.

    Obtain the field plot for this cable using Maxwell 2D.

    Determine the stress and voltage at points P1  and P2. Compare simulation results with those obtained using manual field mapping (see Appendix).

    Identify the region of highest stress and determine its value.

    Calculate the cable capacitance and insulation resistance (per unit length).

    Explain why the lower half plot (in Fig.2) is incorrect.

    If this cable is concentric, redo the field plot and determine the highest stress. This case can also be solved analytically and the electric field at a radius r is given by:

where b is the outer radius, a is the inner radius, and Vis the total voltage across the

insulation. Compare the results. Also, compare against that of the eccentric core.   Note: inner circle (cable core) should be subtracted in order to achieve accurate result.

Fig.2: (a) curvilinear squares plot for an eccentric cable of constant cross- section, (b) general curvilinear square and its subdivisions, (c) expanded view of curvilinear square 2 that forms the ends of a curvilinear cell of depth d (m).

(d)    In  many  high  voltage  insulation  systems  multi-dielectric  structures  are  used  with dielectric materials with different relative permittivity in order to provide better use of insulation  by  reducing  the  overall  insulation  thickness  and  making  the  field  more uniform within the overall layer structure. In other cases, the use of multi-dielectric structures is unavoidable such as in a HV bushing where the small gap between the porcelain insulator and the inner HV conductor is normally filled with insulating oil. Consider the  11  kV  model  bushing  as  specified  in  Experiment  3  with  the  applied voltage of 20 kV.

    Obtain the field plot for the case when the gap is air, and determine the highest stress by modelling cross section of bushing

    Obtain the field plot when the gap is filled with oil, and determine the highest stress by modelling cross section of bushing

    Comment on the results.

3.      REFERENCES

1.   E. Kuffel, W.S. Zaengl, and J. Kuffel, High  Voltage Engineering: Fundamentals, 2nd ed., Butterworth-Heinemann, 2000.

2.   Ansoft  Corporation,  Getting  Started:  A  2D  Electrostatic  Problem,  Maxwell  2D Student Version, 2002.

4.      APPENDIX - FIELD ANALYSIS BY MANUAL FIELD MAPPING

To solve a field problem, we need to obtain the flux or potential distribution. From this, we can obtain the required macroscopic and microscopic properties 

e.g.  R, C, L ,  J , D , B , E , etc

There are three methods of obtaining flux and potential distribution:

1.      Solve Laplace’s equation  ( ▽2φ= 0) or Poisson’s equation  ( ▽2φ= −Pε) analytically or numerically

2.      Manual field mapping

3.     Numerical iteration

Field mapping

This technique uses known field properties to draw up a map of the field for a particular configuration. It can give surprisingly accurate results.

Field properties:

(i)        Flux lines and equi-potentials are orthogonal

(ii)       Surfaces of flux sources are equi-potentials

(iii)      Flux lines intersect sources and sinks orthogonally. 

The aim is to divide the field structure into curvilinear squares (assuming there is symmetry in the third dimension)

If the element is part of current flow and the current density is J , and electric field E

ΔI = J  × area = J × ( Δx ) = JΔx    ( =1 m)

ΔV = EΔy

Hence, resistance of the elemental section is:

 = P  if  = 1m  and  Δy = Δx

Thus,  each curvilinear  square of unit  depth has resistance P. The total resistance can be obtained by counting squares in the full map.

This holds for any field, the only difference being the property relative to the field type, e.g.

    For an electric field, capacitance of the unit square  = ε

    For a magnetic field, the unit square inductance  = μ

    For a thermal field, the unit square conductance  = k

e.g. for a current flow field above, if there are n equipotential drops and m flux tubes of current and the resistivity is P, then the total R is:

  ohms

In the above: n = 4, m = 8    →   R =   ohms   

If a capacitance:

ΔΨ = ΔQ  and  total Q = mΔQ = 8ΔQ Δφ = ΔV  and  total V = nΔV = 4ΔV

Hence:

For flux density and potential gradient, use the appropriate single square and the applicable scale factor of the map:

Flux density =

ΔΨ    Ψm

=       =

Δx       Δx

Thus if we know total Ψ and φ and get m and n, and Δx  (=Δy ) from the map, we can find ΔΨΔx  and  Δφ Δy .