Introduction of Damping Resistances in

Simulations of Electromagnetic

Transients Using Alternate Structures

Code: 19.009

Melissa de Oliveira Santos, Luis Henrique Jús, Thainá

Guimarães Pereira, Aghatta Cioquetta Moreira, Afonso José

do Prado

UNESP, São João da Boa Vista, Brazil

13/11/2017 1

• Apply a different structure of π circuit in

cascade;

• Generate three-dimensional graphics that

show the behavior of the highest voltage

peak in the wave reflection;

• Compare with the model wich includes

damping resistance in all units of π circuits

in cascade;

• Check the results accuracy.

Objectives

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• Simulates long-range circuits (power) or circuits

that work in high frequency;

• Model transmission lines: π circuits in cascade;

• Digital simulations cause numerical errors;

• Numerical erros cause Gibbs oscillations;

• 𝑅𝐷 softens the oscillations;

• Initially, 𝑅𝐷 was introduced in all units of π circuits;

• Studies try to reduce computational time without

losing the accuracy.

Introduction

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• Classic structure of π circuit:

Methodology

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G

2

C

2

R L

G

2

C

2 v x t, v x x t ,

i x t, i x x t ,

Methodology

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• Cascade structure:

• System solved by

Methodology

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Input Output

ሶ𝑥 = 𝐴𝑥 + 𝐵𝑢

• Matrix A structure:

Methodology

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CGG

CCG

LLR

L

CCG

C

LLR

L

CG

CCGG

CCG

LLR

L

CG

CCGG

C

LLR

A

DD

DDD

DD

22200

11

0

0110

11

121

11

0

121

001

Π circuit with RD

• Matrix A structure:

Methodology

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CGG

CCG

LLR

L

CCG

C

LLR

L

CG

CCGG

CCG

LLR

L

CG

CCGG

C

LLR

A

DD

DDD

DD

22200

11

0

0110

11

121

11

0

121

001

Π circuit without RD

Methodology

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Input Output

DDDD

RG

t

LkR

12

Includes 𝑅𝐷 in all circuits, with 𝑘𝐷 = 5 .

Experimental results

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3D Graph for the original model:

Experimental results

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Includes 𝑅𝐷 in alternating structure, with 𝑘𝐷 = 15 .

Experimental results

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301 π

circuits

101 π circuits

201 π circuits

3D Graph for all time of simulation:

Experimental results

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3D Graph of highest voltage peak 𝟎<∆𝒕<𝟏𝟖𝒎𝒔:

Experimental results

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• It is not possible to keep the accurate;

• 5% error in original model;

• 25% error in alternating structure

model;

• 20% error difference between the

models;

• 𝑅𝐷 aplication in all π circuits of cascade

still is a simple model better.

Conclusions

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Acknowledgments

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Process 2015/ 20684-7