Tranmission loss allocation by conductor renting method.ppt

7/29/2019 Tranmission loss allocation by conductor renting method.ppt

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TRANSMISSIONLOSSES ALLOCATION

BY CONDUCTORRENTING METHODunder the guidance of

Sri P.Venkata Narayana (M.Tech)Assistant ProfessorJNTUH by

J. DHARMA REDDYM.tech(PTPG) EPE


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I. INTRODUCTION

In the context of competitiveelectricity marketplaces, the costof the transmission losses, whichpresents an importantcomponent of transmission costs,

should be compensated throughcertain way.


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The compensation method may

have unneglectable impact on1. Profit and decision-making of

market participants

2.Economic efficiency of the

electricity markets.


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Transmission losses must be

carefully designed to providecorrect economic signals.

Basically, there are two types of

losses compensation methods.

1. Marginal cost based method.

2. post-stamp method.


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1. Marginal cost based method:

which can lead to the optimalsocial benefit and nodal price.

The drawbacks of methods of this

category include the dependencyof reference bus selection, the

complexity of the calculation andover charge in losses costs.


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2. post-stamp method :-

which allocates losses to transactionsin proportion to quantities of thepower transmitting.

It is the simplest allocation method butcannot provide correct economic

signals.


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The concept and arithmetic ofconductor renting is proposed forthe first time and is used to analyzetransmission losses allocation

problem. It properly solves the problem of

interaction impact of different

trnasactions on the transmissionlosses.


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In this section, a single conductor is taken asan example to illustrate the basic concept andarithmetic of conductor renting. DC conductor,

which refers to pure resistance conductor, isfirstly analyzed, then ACconductor, whichrefers to conductor with both resistance and

reactance, is analyzed.

2.MATHEMATICAL MODALOF LOSS ALLOCATION OF A

SINGLE CONDUCTOR


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A.LossonaDC conductor

Suppose that there is a DC conductor and the

current on it is composed of two components,say, 1A and 3A. The total current on theconductor is 4A. In steady state, since currentdensities are equal in the different section of

the conductor, it can be regarded that the 1Acurrent uses 1/4 section acreage of theconductor and the 3A current uses 3/4 section

acreage of the conductor. The correspondingconductance is 1 unit and 3 units respectively.The losses on the two sections can be writtenas


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We can get from the above formulas that the lossescaused by the two current components are inproportion to magnitudes of the currents.

Generally, if the current, conductance and sectionacreage of a conductor are I, Gand Srespectively,the loss on the conductor can be expressed as PL=I2/ G.

Suppose that current Iis composed ofNcurrentcomponents, that is, I1,I2,IN..

Denoting Kithat Iiconstitute proportion of the totalcurrent I, SiSection acreage used by Iiand Gi

the corresponding conductance, we would get.


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where PL,i is the losscaused by current

component Ii. Equation (1) indicates thatlosses caused by current components in a

single DC conductor are in proportion totheir current magnitudes, section acreage

they used and the corresponding

conductances. They have linear


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B. The losson anAC conductorDenoting gl, bl,Il,Vl, Sl,g and

Sl,bthe conductance, susceptance current,voltage, apparent conductor sectionacreage of anAC conductor. We could

get:

Fig. 1 AC conductor


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where V*lis the voltage drop on theconductor, PLl+ jQLI is the power loss on the

conductor and lis the angle of the current phasorlagging the voltage phasor.

For convenience, we make a coordinates

take the direction of voltage drop Vlas the active

power axis (P axis) and take the direction leadingV*l90

o as the reactive power axis (Q axis).Denoting symbols with subscript p variables ofPaxis and symbols with subscript q variables of Qaxis, we could get from (2) that:


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Formula (3)indicates that active power loss is in direct ratio to thecurrent active component (component that has the same phase

angle with voltage drop V*land in inverse ratio to the conductance.There are similar rules for reactive power loss.

Supposing that the current on the conductor is composed ofNcomponents (caused by Ntransactions), we could get


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where Il(t)is the magnitude of thetth currentcomponent,

l

(t)

is the angle of the t*current componentlagging the conductor voltage drop, Il,p(t) and

Il,q(t) are the active and reactive component of

the tthcurrent component respectively.

Based on the concept of conductor renting, we

could get


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Kl,p(t): usage ratio ofIl,p

(t)to the conductor conductance;Kl,q

(t)usage ratio ofIl,q(t) to the conductor susceptance;

Sl,p(t), Sl,q

(t): apparent conductor conductance and

susceptance

section acreage used by current component t;gl

(t), bl(t):: conductor conductance and susceptance

used bycurrent component t.PLl

(t), QLl(t) : active and reactive loss caused by current

component t.


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We could get from (6)-(9) that active lossescaused by the transactions (equ. (7)) are inproportion to their P-axis current components,

apparent conductor conductance sectionacreages and the corresponding conductance;reactive losses caused by the transactions (equ.

(9)) are in proportion to their Q-axis currentcomponents, the apparent conductorsusceptance section acreages and the

corresponding susceptance. They all havelinear relationship.


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From the above sections we canconclude that the active and reactivelosses on a single conductor caused bythe current components corresponding to

multiple transactions are in proportion tothe conductance and susceptance theyused, which is the theory foundation of"conductor renting".

3.TRANSMISSION LOSSESALLOCATION BASED ON

CONDUCTOR RENTINGCONCEPT


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The conductor-renting basedlosses allocation method regards

that each transaction rents aportion of the conductoradmittance, or a portion of the

section acreage, and the totallosses are allocated among thetransactions in proportion to the

corresponding admittance and thelosses on the sections.


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In this method, the shared termsdo not appear in the analysis and

calculation, which makes theallocation simple. The losses can

be allocated to transactionsaccurately and the transmissionowner could be break-even. Bothactive and reactive losses can beallocated.


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In actual transmission network, thereis always a great deal of branches. If

contribution of each transaction tocurrent on each branch is gotten, losson each branch can be allocated to

the transactions according to theconcept of conductor renting.

Summing the losses allocated to atransaction on all branches will getthe total losses allocated to thetransaction.

T d t i th t ib ti f


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To determine the contribution oftransactions to branch currentsaccording to superposition principle

The bus voltage function ofN-busnetwork can be written as

ZI=V

I= (I1, I2 ,. In,..., IN)T v= (VI,V2, vn;..,VN)T

where Iis the complex bus current vector, V

is the complex bus voltage vector and Zis thebus resistance matrix. The node currentinjection of transaction k (k= 1,2, - - K )canbe expressed as


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where V(K) is the vector of the node voltage caused by

transaction k; Vb(k)and Ib

(k) are the vectors ofvoltage drops and currents on the branches caused

by transaction k; MNXBis the bus-branch incidence

matrix; Bis the number of branches;

di (Yb) i th di l t i f b h


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diag(Yb)is the diagonal matrix of branchacceptance. Getting the currents on eachbranch caused by the transactions, losses

of branches can be allocated to thetransactions based on conductor rentingconcept and formula developed in the

former section.

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Tranmission loss allocation by conductor renting method.ppt