Frankfurt (Germany), 6-9 June 2011 Pyeongik Hwang School of Electrical Engineering Seoul National...

Frankfurt (Germany), 6-9 June 2011

Pyeongik Hwang

School of Electrical Engineering

Seoul National University

Korea

Hwang – Korea – RIF Session 4a – 0324

A control method of distributed generators in smart distribution system

considering system loss and voltage


Increased installation of distributed generations(DGs) The characteristics of the distribution system is changed

Voltage profile, system loss, power flow, etc.

Introduction of the smart distribution system The status of the distribution system can be measured and

calculated more accurately The power output of DGs can be controlled using the

communication infrastructures.

Chance to more effective operation using DGsChance to more effective operation using DGs


Introduction


The objectives of the proposed method Minimize the system loss Maintain the system voltage within its limit

- Minimize

- Subject to


DG control problem formulation

) ,(

maxnDG,

min

maxmDG,

min

maxl

min

nn

mm

lDGsDGsl

QQQ

PPP

VQPVV

) ,( DGsDGsloss QPP


Relationship among loss, voltage, and output of DGs is highly non-linear Formulated DG control problem is a non-linear optimization

problem

Sequential Linear Programming(SLP) method is adopted Optimal solution is calculated by solving series of linear

programming (LP) problem linearized at the operation point Operation point is determined at the previous iteration


Sequential Linear Programming


Sub-functions of SLP LP formulation Step size adjustment Convergence test

Decision variable for LP


SLP application to DG control

DGs

DGs

Q

PX


Linearized Optimization problem

-Minimize

-Subject to


LP formulation

X

X

QX

P

Q

V

P

VQP

V

PP

bus

bus

busbus

busbuslossloss

||||||

1max

1max

1min

1min

min1

1max

||||

||||

nDGsDGs

nDGsDGs

nDGsDGs

nDGsDGs

lnl

nll

bus

bus

busbus

busbus

QQ

PPX

QQ

PP

VV

VVX

X

QX

P

Q

V

P

VQ

V

P

V

Loss sensitivity matrixVoltage sensitivity matrixInjection power sensitivity matrix


Differences between distribution system and transmission system Existence of mutual impedance in line parameter Unbalanced connection of DGs

Bus admittance matrix with mutual line impedance Used for calculation of loss and voltage sensitivity matrices

A : bus incidence matrix, [y] : primitive admittance matrix.


LP formulation

AyAY Tbus ][


Injection power sensitivity matrix calculation method


LP formulation

A=zeros(N, M)

for i=1:1:M

switch connection topology of P(Q) controllable DG i

case : single phase

A(bus #, i)=1

case : two phase

A(bus # 1, i)=1/2; A(bus # 2, i)=1/2

case : three phase

A(bus # 1, i)=1/3; A(bus # 2, i)=1/3; A(bus # 3, i)=1/3


Step size adjustment Prevent oscillation in SLP

Convergence test


SLP application to DG control

XSQ

P

Q

P T

nDGs

nDGs

nDGs

nDGs

1

1

ni

nii

i XXSS

signsign If 5.0

1nfor 11

|| XST


Flow chart of the proposed method


Proposed method


DG 1A-B-C phase

DG 2A-B phase

DG 3B-C phase

IEEE 37 node test feeder system with three DGs


Case Study


Under voltage violation is occurred in case 2 and case 3


Initial voltage vs. voltage limit

0 5 10 15 20 25 30 35 400.96

0.97

0.98

0.99

1.00

1.01

1.02

1.03

1.04

Case 3

Case 3

Case 2

Case 2

Case 2

Case 1

Case 1

Node V

oltage (

p.u

.)

Node Number

Phase A Phase B Phase C

Under Voltage


The proposed method is implemented as a Matlab code Matlab provided function “linprog” is utilized as the LP solver

Comparing with results of the function “fmincon” Maximum error is less than 0.1% Proposed method is at least 90 times faster than fmincon


Performance of the proposed method

MethodSystem loss(kW) Time(sec)

Case 1 Case 2 Case 3 Case 1 Case 2 Case 3

SLP 78.99 85.51 89.85 1.28 3.15 1.29

Fmincon 78.96 85.51 89.77 142 285 290


The system loss is reduced about 19 %(97kW 78 kW)

Operation cost can be reduced by minimizing the loss


Case 1 ( Vmin = 0.97 p.u., Vmax = 1.03 p.u. )

0 5 10 15 20 25 30 35 40

0.98

0.99

1.00

1.01

1.02

Node V

olta

ge (p.u

.)

Node Number



Without proposed method, tap position of OLTC must be changed to eliminate the voltage violation Increasing operation cost

With proposed method, Under violation is eliminated without tap changing

System operation cost can be reduced by preventing the tap changing of OLTC

System stability can be improved by maintaining system voltage within its limit


Case 2 ( Vmin=0.98 p.u., Vmax=1.02 p.u.)


System voltage



0 5 10 15 20 25 30 35 40

0.98

0.99

1.00

1.01

1.02

Nod

e V

olta

ge (p.

u.)

Node Number



Tap changing to eliminate the under voltage violation

New over voltage violation is occurred



0 5 10 15 20 25 30 35 400.98

0.99

1.00

1.01

1.02

Node V

olta

ge (p.u

.)

Node Number


Over voltage


System voltage can be maintained within its limit

Power quality can be enhanced by controlling the voltage more tightly



0 5 10 15 20 25 30 35 400.98

0.99

1.00

1.01

1.02

Node V

olta

ge (p.u

.)

Node Number




Conclusions



Thank You !([email protected])

Frankfurt (Germany), 6-9 June 2011 Pyeongik Hwang School of Electrical Engineering Seoul National...

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