Mathematical linkage of units commitment and optimal dispatch of large grid power system

MATHEMATICAL

OF UNITS COMMITMENT AND LARGE GRID POWER SYSTEM

LINKAGE OF

OPTIMAL

DISPATCH

Denno

K.

New Jersey Institute New Jersey Newark,

of Technology 07102 U.S.A.

'bstract. This paper introduces mathematical model for Power generating inits commitments and optimization of economic power dispatch The in a large Interconnected multi-area grid power system. model incorporates the developed method by this author in previously published work of the calculation for the transmission losses through its matrix in the 6th reference into the optimization mechanism using the first and the frame, 2nd gradient methods in addition to the base point and participation factors methods.

A.

THE

NEW

MODEL

PARTICIPATION

OF

BASE

POINT

where

FACTORS METHOD IN

aF -.L=F

FRAME NO. 6

+F

iipi

api

i

(7)

This is expressed by: C. aP DC ap. I

apL api

(1)

MODELLING OF THE SECOND ORDER GRADIENT METHOD IN THE 6th REFERENCE FRAME With

in

(2)

6th

the

( 9 ) and frame

same for

constraint Lagrange

replacing

the

model presented in ( 2) matrix model expressed

as

expressed

function total

in

the

C"st matrix

will take below:

the

new

L Pf

=

/l-

api

= penalty

pf and

that

Pf

aFi =api=x

apl factor

of

plant

i ap2 (4)

I t I

B.

r%XXLLING OF THE ?IRST ORDER ap

GRADIENT METHOD IN THE 6th

_

REFERENCE FRAME perturbaion Lagrange

AF, function

Will t,

be

replaced

by

where,

the

txox+ xpLx the dependent

is

the

Lagrange

function

of

Lagrange

function

of

plant

\_I

where @

is the

objective

.'.Perturbational method

could

function

mode now

be

- r Pi-P,_PL

according modeled

as

to

thfs

L,-

@n + iPL"

the

nth

similarly

below:

is

the

plant. as

- Participation

in modeling and

the

method, the matrix model reference frame indicated

(6)

is 476

explicitly

secured

of First

the

Base

in the 6th in reference

since

Point

gradient

closed

(2) form of

477

MATHEMATICAL LINKAGE

solutions

are

already

power

established

grid

economic

in

terms

Pi, P

of

aPi j'api

aB,j aP.

a"d

1

the the

large

6th reference basic stand

will proceed and commiting power using methodology. conclusions being 1.

2.

frame point

grid would

that

system ensure

and

from

successfully for eco”omizi”g the dispatch of electric any working mathematical In this paper, the followi”R could be drawn from the work

The new model of base-point and part icipat ion factors method would accompl ish optimal economic dispatch a”d commitme”t in the 6th reference frame “ith the knowledge of the trhnhmiSsi0”

in

terms

transmission ivative with

4.

of

solutions

loss respect

power

a”,j

dispatch

carrying using the is establ

commitment

der cap

US i”R

the

gradient method is newly on reliable and secure of functional dependency

among the transmission loss matrix in the 6th reference frame, the first and second order partial derivatives of the [B] matrix with respect to the state of change wdll asdependency s .turces within

5.

Establishing

of any power source as between eny two power the entire grid system. the

basic

economic

power

dispatch and commit q ent model in the 6th reference frame, is the central phase for the characterization. and modelling of the entire grid system in the fir’st or the actual network design System that can be secured by reverse SYStem erence

representation is the actual

in the first design of the

power

E.,

ref

System”,

Communications 1974.

and

systems,

Identif lcat Frame”, and Engineer 1977.

Pergamon

Text

ational

Paterson,

W.,

vol.

““e

Press,

N.Y.

and

ion

Publishers,

on Electr

two.

11977.

z"d Sze, T. Engineering,

Mickle, Marlin, H. ation in Systems

W., opt Intext

imiz Educ

1972.

Podgnrski, A. S., "Three Dimensional Systems Modeling of HV Systems", IEEE Transact ions on Power Apparatus andsystems, ~.2899-2903, 1984. Rharat.

proceedings Application vol. II, Patel,

Denno,

aTI,+

Techniques

acity of any power source as wellas the secured functional dependency between any two power sources, and the model of fuel cost data of any sourcewithin the entire grid system. Mathematical linkage model for optimal second order set-up based information

Canadian

Conference,

A.

ical

Pntel ,

of

matrix, to the

Guile,

-

for

the its first variele

Power

‘“Power System Synthesis Denno, Khalil. from Solution of Opt imum Transmission Loss Coeff icie”ts”, IEEE Transactions Power Apparatus and Systems, 1973.

presented:

Mathematical linkage model dispatch and unit commitment first order gradient method

of

Power

and DY”=~=

“Steady-State an Integrated

of

System Denno, Khalil . “Power in the Power Flow Reference Journal of Applied Science i”g A, vol. 2, p. 141-153,

optimization

Solutions in closed mathematical form have been establishedfor the funftio “al dependency between any two power sources in the 6th reference frame in terms of their source capacitywithin the maximum and minimum limits, their fuel cost data and the no-load running This solution 1s unique and of costs. extreme significance for the complete” ess of this model.

ished

.

Khalil,

proceedings

i”

loss c”efficent matrix. the first order of change of the [B] matrix with respect to any power source. and with the established information for the functional dependence of every power source with respect to any other with in the entire grid system.

3.

,

Modeling

power

optimum

REFERENCES

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