Avaliação da Capacidade de Máxima Transferência de Potência em

Sistemas Elétricos Interligados via Programação Linear Sequencial

Code: 02.024

T.G. Moreira, K.R. Barbosa, J.A. Passos Filho, J.L.R. Pereira

Federal University of Juiz de Fora (UFJF)

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Use of a Linear Programming (LP) based Optimal Power

Flow (OPF), to solve the problem of the maximum active

power transfer capacity

The proposed approach is implement using MatLab

environment and the results are validated through the

comparison with FLUPOT program, developed by CEPEL

Objectives

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Countries with a vast territorial extension, such as Brazil, have a Electric

Power Systems (EPS) normally divided into regions - exporting and

importing

The interconnections of these regions are made by a complex

transmission system that allows the import and export of electric energy

In addition, permit a better use of the strongly hydroelectric matrix

The determination of the maximum transfer of power is a factor of

significant importance to define the limits of interchange, respecting the

physical and operational security of the EPS

Introduction

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Introduction

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Belo Monte

Teles Pires

São Luiz do Tapajós Sto Antônio / Jirau Brazilian Interconnected Power System - BIPS

Hydrological Complementarity

Renewable Energy Sources

Wind

Bagasse

...

Distributed Generation

Natural Gas

...

Increasing Load

Multiple Generation Scenarios

Introduction

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Introduction

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“When detailed analyses are to be performed for online DSA, high-quality models of the interconnected system are needed. In fact, as all analyses are

dependent on the quality of the system model, it may be the most important component in the DSA system. “

Morison, K; Wang, L. and Kundur, P.: "Power System Security Assessment", IEEE Power & Energy Magazine, vol. 2, no. 5, pp. 30-39, Sept.-Oct. 2004.

Introduction

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G1

REGIÃO

EXPORTADORA

REGIÃO

IMPORTADORA

Conjunto de linhas

de interligação

G2

G3

Transferência de Potência

REXP RIMP

tie lines

Import Area Export Area

Generation Transfer

Generation Groups

Introduction

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G2 (MW)

G3

(M

W)

Viável

Inviável

Ponto de Operação1ºQ

3ºQ 4ºQ

2ºQ

Curva Limite de

Segurança ou de Geração

{

Passo de Transferência de Geração

θ 0º

Generation Transfer Step

Infeasible

Feasible

Generation Limit Curve

Security or

Security Region

G2 (MW)

G3

(M

W)

Ponto de

Operação

0º (referência)

1ºQ

3ºQ 4ºQ

2ºQ

θ

G2 G3

G2 G3G2 G3

G2 G3

G1 ® Grupo de “referência” faz o balanço entre a carga e geraçãoG1 – Slack generation group is responsible for load and generation balance

(reference)

Operating

Point

Limit Search Strategy 1

Introduction

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Feasible

Operating

Point

1

2

3 4 5 Infeasible

Operating

Point

6 7

Violation! Violation!

Last

Feasible

Operating

Point Generation

Transfer

Step

Infeasible

Operating

Point

Limit

Generation Transfer Step

Stopping Criteria – Violation OR Power Flow Divergence OR Power Flow Non Convergence

Active Generation

Transfer Direction

Limit Search Strategy 2

Introduction

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Feasible

Operating

Point

1

2

3

4

5 Infeasible

Operating

Point

6

Violation! Violation!

Infeasible

Operating

Point

< Minimum Generation Transfer Step

Last

Feasible

Operating

Point

Limit

Generation

Transfer

Step

Generation Transfer Step Generation Transfer Step Generation Transfer Step

Stopping Criteria –

Violation OR Power Flow Divergence OR Power Flow Non Convergence

OR

Maximum Number of Consecutive Reductions of the Generation Transfer Step

OR

Current Generation Transfer Step < Minimum Generation Transfer Step

Active Generation

Transfer Direction

To achieve the objectives proposed in this paper, it was first necessary to

implement a conventional AC power flow and then an OPF

This paper proposes the use of Sequential Linear Programming (SLP)

to mitigate this problem and solve a nonlinear OPF

The results achieved by the implementation in MatLab using SLP are

compared with those obtained by the Interior Point Method (IPM) used by

the FLUPOT program

Methodology

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To obtain maximum power transfer, the system must be divided into

exporting and importing regions

EXPORTING REGIONS: there are successive increases in generation

IMPORTING REGIONS: there are successive decreases in generation

Methodology

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variables

Methodology

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BEGINNING To run the Power Flow for the base case

Convergence limits was reached?

Linearization around the previously obtained operating point

Solving the linear programming problem

Obtaining the new control variables

Active power generation limits or maximum

number of iterations was reached?

To run the Power Flow

END

Adjustment of control variables

To run the Power Flow with the current control variables

END

YES

YES

NO

NO

Formulation of Nonlinear Optimal Power Flow

Subject to:

Methodology

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impnger

j jgPnger

i igPFOB_

1)1(

exp_

1)1(min

PV

PV

ji

ref

V

k

kkk

ggg

ggg

jidgq

jidgp

VV

VVV

QQQ

PPP

VQQQpuxg

VPPPpuxg

jijiji

jijiji

jijiji

jijiji

,

22

maxmin

maxmin

maxmin

,

,

,,,

,,,

,,,

,,,

0),(),,(

0),(),,(

bus

ger

ger

nk

nj

ni

,...,1

,...,1

,...,1

exp_

exp_

Linearization about a given Operating Point

Methodology

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o

o

q

p

x

u

x

g

u

g

x

u

x

g

u

g

x

u

x

g

u

g

pp

gx

x

gu

u

g

pxug

pxug

ji

ji

..

0

0.

0...

0

0

),,(

),,(

,

,

0

Sensibility Matrix

Toolbox Linprog

For example:

Subject to:

Methodology

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bopfb

eqopfeq

opf

uxl

bxA

bxA

xf

.

.

)(min

Vector of Variables: Inequality constraints:

Objective Function:

Inequality constraints: Lower bound and Upper Bound:

Methodology

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Small-scalle Tutorial System with 9-Bus

Experimental results

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Bus Type Region

1 - 142,50

2 PV Imp 90,00

3 PV Exp 85,00

)(MWPg

V

Bus Type

1 0,00 210,40

2 PV 0,00 163,20

3 PV 0,00 108,80

)(min MWPg )(max MWPg

V

Bus FLUPOT (MW)

OPF by SLP (MW)

1 210,10 209,78

2 0,10 0,00

3 108,50 108,80

Table I – Active Power Generation in the Base Case Tutorial System with 9-Bus

Table II – Active Power Limits - Tutorial System with 9-Bus

Table III – Active Power Generation by FLUPOT and OPF by SLP - Tutorial System with 9-Bus

Methodology Cost ($)

FLUPOT 318,60

OPF by SLP 318,58

Table IV – Minimum Cost of Active Power Generation – Tutorial System with 9-Bus

Table V - Number of Interation – Tutorial System

with 9-Bus

Methodology Interations

FLUPOT 14

OPF by SLP 5

IEEE 14-Bus System

Experimental results

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Bus Type Region

1 - 234,10

2 PV Imp 40,00

6 PV Exp 0,00

8 PV Exp 0,00

)(MWPg

V

Bus Type

1 0,00 234,10

2 PV 0,00 40,00

6 PV 0,00 0,00

8 PV 0,00 0,00

)(min MWPg )(max MWPg

V

Bus FLUPOT (MW) OPF by SLP (MW)

1 56,50 56,75

2 37,00 37,00

6 122,30 122,30

8 49,30 49,30

Table VI – Active Power Generation in the Base Case – IEEE 14-Bus

Table VII – Active Power Limits – IEEE-14 Bus

Table VIII – Active Power Generation by FLUPOT and OPF by SLP – IEEE 14-Bus

Methodology Cost ($)

FLUPOT 265,10

OPF by SLP 265,35

Table IX – Minimum Cost of Active Power Generation –

IEEE 14-Bus

Table X – Minimum Cost of Active Power Generation –

IEEE 14-Bus

Methodology Interations

FLUPOT 20

OPF by SLP 10

In future works, more improved tests should be performed aiming to

evaluate computational time and large-scale electrical power systems

Treatment of the operational limits

The computational behavior must be compared

On-line applications

Discussion

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In this work an algorithm was implemented to solve the problem of the

maximum active power transfer capacity through the use of OPF by LSP

• The approach is proving its validity.

The results obtained through the study of two systems

a small tutorial with 9-bus

IEEE 14-bus

In this results obtained through OPF by LSP in comparison with

FLUPOT program can be seen results highly satisfactory

Conclusions

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• This work was performed at Federal University of Juiz de Fora, Brazil.

Special thanks are given to CNPq, CAPES, FAPEMIG and INERGE by

financial support

• The authors also acknowledge at CEPEL for the use of the academic

version of the programs ANAREDE and FLUPOT

Acknowledgments

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Thank You !!

E-mail: jopass@ieee.org

ALMEIDA, FELIPE C. B. ; Passos Filho, João A. ; PEREIRA, JOSÉ L. R. ; HENRIQUES, RICARDO M. ; MARCATO, ANDRÉ L. M. . Assessment of Load Modeling in Power System Security Analysis Based on Static Security Regions. Journal of Control, Automation and Electrical Systems, v. 24, p. 148-161, 2013.

Acknowledgments

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