usage based cost allocation technique for ehv networks using non-linear utility factors

7/28/2019 USAGE BASED COST ALLOCATION TECHNIQUE FOR EHV NETWORKS USING NON-LINEAR UTILITY FACTORS

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Electrical and Electronics Engineering: An International Journal (ELELIJ) Vol 2, No 2, May 2013

61

USAGE BASEDCOSTALLOCATIONTECHNIQUE FOR

EHVNETWORKSUSINGNON-LINEARUTILITY

FACTORS

Tarun Tailor1

,Ganga Agnihotri2

and Anuprita Sandeep Mishra3

Department of Electrical Engineering, MANIT , Bhopal, [email protected], [email protected], [email protected]

ABSTRACT

Amongst the available usage based cost allocation technique; this work is based on realization of Amp-

Mile method with some amendment as it is applicable only on distribution networks. By carrying the

advantages of Amp-Mile method and eradicating limitations this work promotes non-linear sensitivity

(utility factors) in conjunction with dispersed slack bus concept to allocate embedded cost of EHV (Extra

High Voltage) networks by introducing a correction in algorithm of base method. While available usagebased methods are assuming linear sensitivities, authors re-evaluated Amp-Mile methodology using

Newton Raphson based load flow algorithm and presented simple, realistic - revised Amp-Mile method

which shows promise for practical implementation. In this work, a 6 bus power system is simulated in

MATLAB/SIMULINK to carry out load flow analysis, results of which are used in determining current

sensitivities. Sensitivity patterns can assist ISO (Independent System Operator) to check congestion and

forecast day-ahead price with day-ahead scheduling of electricity market.

KEYWORDS

Non-linear sensitivity, dispersed slack bus, current utility factors, price forecasting

NOMENCLATURE

CUF Current utility factorCUPFldk

t Current utility active factor ofl

thline wrt k

thdemand bus at t

thinstant

CUPFlgkt

Current utility active factor oflth

line wrt kth

generator bus at tth

instantCUQFldk

t Current utility reactive factor ofl

thline wrt k

thdemand bus at t

thinstant

CUQFlgkt Current utility reactive factor ofl

thline wrt k

thgenerator bus at t

thinstant

EU Extent of UseACCl

tAdapted circuit cost t

thinstant

UCClt Used circuit capacity t

thinstant

CClt

Levelized cost for each hour tth

instantAEUDlk

t Active extent of use by k

thbus demand on l

thline at t

thinstant

AEUGlkt

Active extent of use by kth

bus generation on lth

line at tth

instantREUDlk

tReactive extent of use by kth bus demand on lth line at tth instant

REUGlkt

Reactive extent of use by kth

bus generation on lth

line at tth

instant

Ilt Absolute current in lthline at tthinstantPdk

tActive demand on k

thbus at t

thinstant

Pgkt Active generation on kth bus at tthinstant

Qdkt

Reactive demand on kth

bus at tth

instant

Qgkt

Reactive generation on kth

bus at tth

instant

ALkt Locational charges due to active demand on k

thbus at t

thinstant

AGkt Locational charges due to active demand on k

thbus at t

thinstant

RLkt

Locational charges due to active demand on kth

bus at tth

instant


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RGkt

Locational charges due to active demand on kth

bus at tth

instant

RCClt Remaining circuit cost

CCI Currency cost impact

EC Embedded costCA Cost allocated

1.INTRODUCTION

In open access electricity market allotment of embedded cost is one of the momentous facets.

Many usage based costs allocation methods are in hand but no offered method is proved to belevel headed to all operational conditions of diverse power systems and not endowed enough to

evaluate entire embedded cost but strive to allocate total embedded cost. Each country has had tofind its solution in agreement with the characteristics of its transmission system and degree of

deregulation adopted. Allocation of embedded costs, despite of the method, is utterly necessaryfor the owners of transmission or distribution infrastructure so they may recover the costs

associated with providing services. In essence intend of usage-based cost allocation method,

involve few foremost apprehension:

Accurate and efficient algorithms for transmission usage evaluationFair and equitable allocation rules

Full recovery of embedded cost

Based on the above issues, cost allocation signifies to identify cost causer who is responsiblefor incurring these costs. In many real world situations, unfortunately, to identify the causer

may be intricate because the non-linear nature of power flow equations causes difficulty

(theoretically) to decompose the network flow into components associated with individual

participant. But it is possible and satisfactory to apply approximate models or sensitivity indices(distribution factors) to estimate the contribution from individual participant to network flows.

With foundation of distribution factors, the Amp-Mile method [3] is good enough to attain aimfor distribution network at the same time posses two drawbacks. First not able to implement for

EHV (Extra High Voltage) network and second can not allocate entire embedded cost of

networks. As due to discrete nature of the elements and reliability constraints, power flows areusually smaller than the corresponding element limits. Therefore grid looks under usedaccordingly remaining costs are incurred through complementary charges [8-11]. Thus Extent-of-

Use (EU) is never 100% of the elements capacity eventually service cost based on the network

usage will be smaller than transmission embedded cost.

This work tries to remove the drawbacks of Amp-Mile method and promotes applicability of

Amp-Mile method on EHV networks if prominence is put on stability limits, (steady state andtransient limits) apart from thermal capability as in distribution network. Non-linear sensitivities

along with dispersed slack bus notion are utilized to allocate entire embedded cost of EHV

networks and re-evaluated Amp-Mile method using Newton Raphson based load flow algorithmto present simple and efficient Modified Amp-Mile methodology for full recovery under stressful

conditions. Currently sensitivities naming current utility factors (CUF) are used, capturing the

effects of unbalanced network parameters, loads and generator locations, assessing true portrayalof the network causing fair allocation based on usage to each participant.

The paper is organized as follows section 2 furnished literature review of existing techniques

whereas section 3 presented overview of Amp-Mile method and its limitations in the companyof corrections. Section 4 explores the concept of dispersed slack bus and its implication in cost

allocation. Section 5 makes available results on standard IEEE 6 bus system by implementing


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Amp-Mile method with amendments and also put forward the view of non linear nature of

sensitivity indices. Finally section 6 establishes conclusion.

2.LITERATURE REVIEW

The embedded/Usage based cost methods allocate the system total costs among the transmissionparticipants based on some Extent-of-Use (EU) rule. It is defined as the revenue requirementsneeded to pay for all existing facilities plus any new facilities added to the power system during

the life of the contract for transmission service. In these methods flows related to each transactionare computed in all transmission lines either by tracing methods [18] or using sensitivity factors

(Distribution factors) [19] or by means of marginal participation [1] or else through cooperativegame theory [8]. Many utilities pursue postage stamp rate method for transmission pricing, where

participants are not differentiated by the EU of network facilities. One more method is Contractpath method based on the assumption of power flows through certain, pre specified path [2]

where first the least cost electrical path between generation and load points is determined and

then transaction is charged by postage stamp rate. This method is far away from physical laws.Whereas Megawatt (MW) power flow tracing [4] and a next version of MW-mile method Vector

Absolute Mega-Watt Mile (VAMM) [20] can assess the extent of network usage by the

participants that can be effectively used for multiple objectives like transmission pricing, lossallocation, etc. These shares are sensitive to quantity and distance as against the postage stampmethod, which is immune to distance. Critique is, not able to incur full recovery of embedded

cost and handles only active power however considering some simplifying assumptions thismethod can be inferred as a solution to the optimal transmission planning problem from a static

point of view [23, 24]. Modulus method overcomes first shortcoming [5] and second by MVA-

KM method [21], applies to AC power flow and considers apparent power but not capable toforetell reactive power flow direction as required in case of wind DGs(Distributed Generation).

Another AC power flow based method [6] determines the individual participants impact on the

transmission line; the line utility factors (LUFs) between a source and sink are developed.Similarly a physical path based monetary flow method [12] for transmission pricing has

introduced in which usage characteristic of a transmission line is described by the corresponding

investment and operation costs instead of its length. Later a novel attitude Amp-Mile [3] was

introduced for the allocation of embedded costs at the medium voltage distribution level, anaugmentation of MW-Mile method and the motivation of present proposed methodologydiscussed in detail in the subsequent section. Further a method MW+MVAr-Mile [22],

acknowledging the full cost-benefit of network participants, especially embedded generators isintroduced, takes into care the power factor as well as the leading or lagging nature of power

factor by separating the MW and MVAr power flows but its applicability only on distributionnetworks. [7] Suggested a new paradigm that tries to capture the best of the two methodologies

Megawatt (MW) power flow tracing and postage stamp method by exploring multiplicity of the

solution space of the tracing problem, within the given constraints. [14] Attempted to test the

fairness of different usage-based transmission cost allocation methods along with methods used torecover the total transmission network cost. While [1] proposed a prototype, min-max fair tracing

algorithm for transmission system usage cost allocation problem specifically suitable for large

system applications.

As a whole, the work listed out quantity of usage based cost allocation methodologies for large

systems in the company of distribution systems. Out of listed techniques any philosophy can beadopted by utilities for allocation of embedded cost depending on the degree of deregulation andtype of network.


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3. OVERVIEW OF AMP-MILE METHOD, LIMITATIONS AND MODIFICATION

This section is providing the description of base Amp-Mile methodology with its limitations andmodifications

3.1. Characteristic of Amp-Mile method

The Amp-Mile method [3] is usage based embedded cost allocation method for medium voltage

distribution network. In this methodology EU for circuits is measured in terms of the contributionof each customer to the current flow i.e. current utility factors (CUPF lk

t& CUQFlk

t), not the

power flow at any instant of time. Since there is least governance of system stability (steady stateand transient) in distribution system, hence current capacity can be taken up to thermal limit. For

this reason current flows may attribute network customers, therefore method is acknowledged as

Amp-mile or I-mile methodology. Thus different EUs are found out using currentdistribution factors (CUPFlk

t& CUQFlk

t) and this rational is being used to accomplish allocation

of cost. This method unambiguously accounts for flow direction to provide better long-term price

signals and incentives for DG to locate optimally in the distribution network and to alleviatepotential constraints and reduce losses. Steps to allocate embedded cost as well as remaining cost

are as follows:

AEUDlkt

=CUPFlkt Pdk

t/Il

t= (Il/Pdk) Pdkt/ Ilt

AEUGlkt

=CUPFlkt -Pgk

t/Il

t= (Il/Pgk) -Pdkt/ Ilt

REUDlkt

=CUQFlkt Qdk

t/Il

t= (Il/Qdk) Qdkt/ Ilt

REUGlkt

=CUQFlkt-Qgk

t/Ilt = (Il/Qgk) -Qgkt/ Ilt (1)

Let CCltbe the levelized annual cost per hour of circuit l. Then

ACClt=UCCl

tCCl

t(2)

Where UCClt

is the used circuit capacity of l, for time t, and is defined by

UCClt=Il

t/ CAPl (3)

Where Iltis absolute current through circuit l for time t and CAPl is the capacity of circuit l. Two

types of charges are quoted for each participant (generator/demand) to recover embedded costs ofdistribution network - Locational and Non-locational.

3.1.1. Locational ChargesThese charges are based on the EU that should be paid to cover the portion of embedded cost fornetwork service considering both active power and reactive power injections or withdrawals.

Active and reactive locational charges for demand/generation at bus k are as given below.nline

ALkt= AEUDlkt ACClt

i=1


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nline

AGkt= AEUGlkt ACClt

i=1

nline

RLkt= REUDlkt ACClt

i=1

nlineRGk

t= REUGlktACClt (4)

i=1

3.1.2. Nonlocational charges

These are the Charged to recover the cost of the unused network capacity.

nlineRCCl

t= [CClt - ACClt] (5)i=1

Non locational charges are reflecting security feature of the power system and charged to only

loads.

3.2. Limitations of Amp-Mile method with Amendments

The present effort has extracted some limitations through numerical studies. Limitations are listed

as

(1)Amp-Mile method is not able to recover full embedded cost unless and until system is fullyloaded.

(2) Amp-Mile method is pertinent only on radial networks since currents are relative to thethermal capacity of distribution network (high R/X ratio). But if more emphasis is given on

stability limits (steady state and transient) of EHV networks then Amp-Mile method can be

applied on EHV networks as well.

(3) Amp-Mile method has endowed with an algorithm to realize sensitivity indices CUPFlkt

and

CUQF lkt . Present work turned basic Amp-Mile method algorithm and uses NR based load flow tofind sensitivity indices CUPF lk

tand CUQF lk

t.

(4) Base algorithm provides only two types of sensitivities in the form of distribution factors

CUPF lkt

(Il/Pdk) with CUQF lkt (Il/Qdk) and agreed upon common distribution factor fordemand variation as well as generation variation at the same bus with a difference of sign i.e

(Il/Pdk) = - (Il/Pgk)Or

Il/Pdk = Il/Pgk (6)

Many literatures like [8] agree on the same but this does not reflect true operating conditions of a

network. Reason being, by load flow any bus has to work as slack bus which gives compensation

of demand and losses. As a result magnitude of generation/load variation at any bus directly

influences loss compensation and demand fulfilled by slack bus. Same feature was narrated inRudnicks method [19] accordingly lines connected to slack bus would have different currentvariations with respect to change in active (reactive) generation than change in active (reactive)

demand at any bus. Hence current sensitivities Il/Pgk and Il/Pdk would not be same. Therefore


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(Il/Pdk) - (Il/Pgk)Or

Il/PdkIl/Pgk (7)

(5) If a system is large chances of load and generation on same bus increases, in such cases

comparisons can be pulled out between Il/Pdk and Il/Pgk (or Il/Qgk and Il/Qdk).Thereforesensitivity indices must be of form

CUPFldkt

= Il/PdkCUPFlgk

t= Il/Pdk

CUQFldkt= Il/Qdk

CUQFlgkt= Il/Qgk (8)

(6) In small systems where demand is positioned differently from generator bus, we can club

CUPFldktand CUPFlgk

t(or CUQFldk

tand CUQFlgk

t) i.e.

CUPFlkt

= CUPFldkt+ CUPFlgk

t

CUQFlkt= CUQFldk

t+ CUQFlgk

t(9)

In this work it has been followed because each bus is having either generation or load.(7) Expression

nbusIl

t= [ CUPFlkt (Pdkt - Pgkt)] + [ CUQFlkt (Qdkt - Qgkt)] (10)

k=2

The current Ilt

does not turn out to be close approximation of a circuit current, because noconsideration was taken regarding active and reactive powers of slack bus. Therefore a

reconciliation factor is needed to get actual value of line current, signifying part of line current

due to contribution of power from slack bus.

(8) This is also stated in [3] that circuit currents are approximately linear function of active andreactive power at bus, but current sensitivity indices CUPFlk

tand CUQFlk

tare possessing non-

linear nature with respect to active and reactive powers at a bus, which is discussed in section V.

(9) In Amp-Mile method it is narrated that a reconciliation factor is needed so that the EU factorsfor a given line sum to unity. Contradictory to this the present work furnished EU factors for agiven line sum to always unity without needing reconciliation factor because of Il

t.

(10) Base method does not suggest how to find sensitivity indices relating to slack bus. In

modified Amp-Mile method dispersed slack bus perception resolves this problem.

4.DISPERSED SLACK BUS

The concept of dispersed slack bus is established in many literatures [13, 26] consideringdifferent criteria. Moreover, as the electricity market is more and more deregulated, the idea that

some specified groups of generators play the role in slack bus and all losses are assigned to slack

bus looks unfit. Hence this notion removes the rigorous burden on a single slack bus for balancingdemand and supplying losses.

Applying dispersed slack bus conception means to reschedule the generation, since distinguishing

load and loss contributions of each source is very important to correctly account for revenue and


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cost. Thus dispersed slack bus provides advantages over the single slack bus model for cost

analysis. Distinguishing load and loss contribution of each source is achieved by sensitivityindices. In addition with a dispersed slack bus model, cost analysis can be fine tuned to identify

different costs/revenue for load contribution and loss contribution. Thus this model allows more

detailed profit and cost evaluations of individual sources. Simulation may illustrate that thedispersed slack bus models have significant impacts on cost analysis and adequate cost allocation

can be achieved. By implementing it the currency cost impact (CCI) of different slack busmodels can be quantified and fair allocation of embedded cost can be accomplished. Authors of

this paper are still researching in this direction hence future scope exist in fair and adequate

allocation of embedded cost with dispersed slack bus. Authors are proposing an idea at eachloading conditions a new slack bus can be considered and then perform Load Flow consequently

CUFs directly gets affected by the selection of slack bus and eventually affects cost allocation.In addition the network based approach to assign slack bus and associated cost analysis can better

capture and identify optimal locations to install DG. The single slack bus model may significantlydistort computed power flows hence to provide more realistic power flows; power flow analysis

with a dispersed slack bus model has to be investigated.

5.SIMULATIONS AND PERFORMANCE INVESTIGATION

In this work Amp-Mile method is implemented with proposed corrections to verify the feasibilityand effectiveness of new algorithm on EHV networks. Application of proposed algorithm has

been illustrated using IEEE 6-bus network. For that 6-bus network has simulated to carry out loadflow, results of which used in determining current utility factors. Simulation model has been

developed in MATLAB and its tool SIMULINK and SIM POWER SYSTEM block set. Figure1

shows IEEE 6-bus power network and the simulated power circuit is shown in figure2. The

performance characteristics obtained from the simulation have been presented in this section.

Figure1. 6- Bus Network


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powergui

Continuous

Load at bus 6

A B C

Load at bus 4

A B C

Line 6-5

A

B

C

A

B

C

Line 5-4

A

B

C

A

B

C

Line 3-6

A B C

A B C

Line 3-5

A B C

A B C

Line 2-6

A

B

C

A

B

C

Line 2-5

A

B

C

A

B

CLine 2-4

A B C

A B C

Line 2-3

A

B

C

A

B

C

Line 2-1

A B C

A B C

Line 1-5

A

B

C

A

B

C

Line 1-4

A B C

A B C

Generator at bus 3

Pm

E

m

A

B

C

SSM

Generator at bus 2

Pm

E

m

A

B

C

SSM

Generator at bus 1

Pm

E

m

A

B

C

SSM

Constant5

-C-

Constant4

-C-

Constant3

-C-

Constant2

-C-

Constant1

-C-

Constant

-C-

Bus1

c

cA

B

C

a

b

c

Bus 6

c

cA

B

C

a

b

c

Bus 5

c

cA

B

C

a

b

c

Bus 4

c

cA

B

C

a

b

c

Bus 3

c

cA

B

C

a

b

c

Bus 2

c

cA

B

C

a

b

c

Load at bus 5

A B C

Figure 2. Block Diagram of Simulated System

5.1. Data of Standard IEEE 6-Bus System

Authors presented results on IEEE 6-Bus system where embedded cost to be allocated is assumed

equal to the length of individual transmission lines in currency/hour (Cu/hr). Thus the benchmark

of total embedded cost to be allocated among the participants is equal to the amount of the entirecircuit length 5435 Cu/hr. Data regarding IEEE 6-Bus system has given in table 2 and 3 whereas

table 1 places bench mark for the cost to be allocated.

6-Bus system Embedded cost (Cu/hr) to be allocated

Bench Mark 5435

Table 1. Bench Mark: Cost to be recovered

Bus

no.

Type of

bus

V(p.u.

)

Angle(deg

.)Pd (p.u.)

Qd

(p.u.)

Pg

(p.u.)

Qg

(p.u.)

1 Slack 1.05 0 0 0 0 0

2 Generator 1.05 - 0 0 0.5 03 Generator 1.07 - 0 0 0.6 0

4 Load - - 0.7 0.7 0 0

5 Load - - 0.7 0.7 0 0

6 Load - - 0.7 0.7 0 0

Table 2. Busdata: IEEE 6 Bus System


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Line

Number

Start and end

busR(p.u.) X(p.u.) Length(Km)

Circuit Cost(CCl

Cu./hr) (Bench

Mark)

1 1-2 0.1 0.2 578 578

2 1-4 0.05 0.2 289 289

3 1-5 0.08 0.3 463 4634 2-3 0.05 0.25 289 289

5 2-4 0.05 0.1 289 289

6 2-5 0.1 0.3 578 578

7 2-6 0.07 0.2 405 405

8 3-5 0.12 0.26 694 694

9 3-6 0.02 0.1 116 116

10 4-5 0.2 0.4 1156 1156

11 5-6 0.1 0.3 578 578

Table 3. Line data: IEEE 6 Bus System

5.2. Cost Allocation

For the given data in tables II and III, costs were evaluated by implementing Amp-Mile method

with proposed corrections. Results are revealed in Table 4 with locational charges and remainingcharges (non-locational charges) whereas figure 3 gives bar graph of cost allocated at different

lines. Result depicts embedded cost recovered through locational charges are approximately 19%while the remaining 81% is recovered by the non locational charges. In order to find cost

allocation different EUs are evaluated using current utility factors like CUPF and CUQF. Table 5presents the CUPF at base case condition whereas Table 6 presents EU of different transmission

lines.

This work strongly suggested implementation of Amp-Mile method on EHV networks by

following some corrections mentioned earlier.

Table 4. Cost Allocation for Base Case Condition

Transmission LinesLocational

Charges

Remaining

Charges

Circuit Cost(CCl Cu./hr)

(Bench Mark)

Line 1-4 142.5155 435.5 578

Line 1-5 160.0482 128.9 289

Line 2-1 70.2911 392.7 463

Line 2-3 51.2493 237.8 289

Line 2-4 147.9102 141.1 289

Line 2-5 110.003 468 578

Line 2-6 77.8005 327.2 405

Line 3-5 187.6923 5063 694

Line 3-6 69.8823 46.1 116

Line 5-4 6.9939 1149 1156Line 6-5 16.6271 561.4 578

% Cost Allocation 19 81 100


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Figure 3. Cost Allocated According to Locational Charges

Transmission

line

Gen. at

Bus 1

Gen. at

Bus 2

Gen. at

Bus 3

Load at

Bus 4

Load at

Bus 5

Load at

Bus 6

Line 1-4 0.6995 0.1124 0.163 -0.4495 0.304 0.2136

Line 1-5 0.2533 0.0851 -0.0066 0.1688 -0.1544 0.6562

Line 2-1 0.8964 0.1096 -0.0031 -0.1434 -0.1242 0.2529

Line 2-3 0.0428 0.5849 0.4148 -0.1003 0.0359 0.0342

Line 2-4 0.0201 0.5032 0.399 -0.2824 0.1206 0.2328

Line 2-5 0.1512 0.6491 0.1499 0.2499 0.1904 -0.7926

Line 2-6 0.3954 0.7799 -0.2493 0.6648 0.1904 -0.7926

Line 3-5 -0.0239 0.1342 0.8497 0.0093 -0.2105 0.2312

Line 3-6 0.0877 0.1401 0.7299 0.1065 0.1084 -0.1761

Line 5-4 1.889 1.9562 -3.1164 19.974 -20.050 -3.9603

Line 6-5 -0.6554 0.1948 1.3452 0.2455 1.331 -0.9719

Table 5. CUPF at base case condition

Table 6. Extent of Use EU, at base case

Transmission

line

Gen. at

Bus 1

Gen. at

Bus 2

Gen. at

Bus 3

Load at

Bus 4

Load at

Bus 5

Load at

Bus 6

Line 1-4 0.2957 0.0475 0.0689 0.1900 -0.1285 -0.0903

Line 1-5 0.2405 0.0808 -0.0063 -0.1603 0.1466 -0.623

Line 2-1 -0.2332 -0.0285 0.0008 -0.0373 -0.0323 0.0658

Line 2-3 -0.013 -0.1778 -0.1261 -0.0305 0.0109 0.0104

Line 2-4 0.0176 0.4415 0.3501 0.2478 -0.1058 -0.2043

Line 2-5 0.0493 0.2117 0.0489 -0.0815 0.114 -0.0453

Line 2-6 0.1302 0.2568 -0.0821 -0.2189 -0.0627 0.261

Line 3-5 -0.0111 0.0622 0.3939 -0.0043 0.0976 -0.1072

Line 3-6 0.0906 0.1447 0.7539 -0.11 -0.112 0.1819

Line 5-4 0.0197 0.0204 -0.0325 -0.2083 0.2091 0.0413Line 6-5 -0.0323 0.0096 0.0663 -0.0121 -0.0656 0.0479


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5.3. Sensitivity Patterns

Simulation results on test system after carrying load flow are used to determine the current utilityfactors. These current utility factors show the change in current over a particular line with respect

to change of active and reactive power of each player. Thus, these can be used as the basis for a

new determination of the stand-alone usage of individual player. Such current utility factors havebeen calculated by increasing a load in a marginal way and observing the change in current of a

particular line shown in figure 4-8 Thus obtained sensitivity patterns can assist ISO to check

congestion to provide ATC to supply the load and forecast day-ahead price with day-ahead

scheduling of electricity market. The physical significance of decrease in current can beinterpreted as even if increasing the active/reactive power at any bus its effect is decrease in

current, thereby serving in order to remove the congestion. In different figures 4-8, current isincreasing in nature which can be interpreted as increase in active bus loading, consequently line

loading is increasing. The physical significance is such that as even on increase in active power

its effect is increase in current. There by increasing the congestion in the system.

5.4. Non-Linear Natures of Sensitivity Indices

Existing literature [3, 8] considers linear nature of sensitivities assuming line flows areapproximately linear function of active and reactive power injection or withdrawal at a bus baralthough virtually they may not be always a linear function. But in [15] authors evaluated

different sensitivities at different loadings of the system and gave the indication of presence ofnonlinear sensitivity. Proposed amended Amp-Mile method proved it by evaluating and

identifying patterns for CUF under different generations or loads at a bus and identified nonlinear

or linear nature of sensitivities of a line depending on location and topological conditions. With

the help of NR based load flow algorithm using MATLAB, sensitivity patterns predicted forindividual line currents with respect to active power or reactive power injections or withdrawals

at a bus, are near to true picture by performing variation of P/Q at a bus from no P/Q to above

100% of base case (BC) P/Q. These sensitivity patterns are benefit to ISO for open access inderegulated market, and sensitivity patterns also give price signals with locational signals for

future expansion.

As current research established nonlinear nature of sensitivity depicted in figure 4-8, allocatedcharges would not necessarily be stable over differing load levels and obviously over time. In [3]

due to assumptions of linear nature of sensitivity, allocated locational charges remain constantover both time and differing loads as CCl

tand CAPl are constants which can not reflect true

conditions.

Figure 4. Current sensitivity Variation of line 4 with changes in reactive power at load

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.1

0.12

0.14

0.16

0.18

0.2

QL4

d

id

p

4

data 1

cubic


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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.136

-0.134

-0.132

-0.13

-0.128

-0.126

-0.124

-0.122

QL5

didp5

data 1

cubic

Figure 5. Current sensitivity Variation of line 5 with changes in reactive power at load 5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1.15

-1.1

-1.05

-1

-0.95

-0.9

-0.85x 10

-3

QL6

didp2

data 1

cubic

Figure 6. Current sensitivity Variation of line 2 with changes in reactive power at load 6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10.047

0.046

0.045

0.044

0.043

0.042

0.041

PL6

didp6

data 1

cubic

Figure 7. Current sensitivity Variation of line 6 with changes in active power at load 6

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-0.11

-0.105

-0.1

-0.095

-0.09

-0.085

-0.08

PL5

didp5

data 1

cubic

Figure 8. Current sensitivity Variation of line 5 with changes in active power at load 5


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6.CONCLUSION

In this work, new algorithm is implemented which is derived from the philosophy behind thewidely used Amp-mile Methodology, up gradation of MW-mile method, for usage based costallocations by evaluating extent of use using current utility factors, derived from load flows. In

this work, IEEE 6 bus power system is simulated in MATLAB/SIMULINK to carry out load flowanalysis, results of which are used to determine non-linear current sensitivities and cost hasallocated to different agents. In comparison to existing methods the new method has the

advantages in a way that it gives real time estimation thereby; exact situation is taken intoconsideration and not an approximation. The interest of improving methods of charging

transmission charges wills always remain. Authors have presented concept of dispersed slack busto evaluate sensitivities of different generator buses and suggested to establish CCI.

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Authors

Tarun Tailor was born In Neemuch, India, in 1986. He received BE degree (2008)

From the UEC, Ujjain, and received the MTech. degree (2010) in Power System

from MANIT, Bhopal, India. At the moment he is research scholar ( Part Time)and Assistant Professor (contract) at MANIT, Bhopal, India


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Dr. Ganga Agnihotri received BE degree in Electrical engineering from MACT,

Bhopal (1972), the ME degree (1974) and PhD degree (1989) from University

of Roorkee, India. Since 1976 she is with Maulana Azad National institute of

Technology, Bhopal , in various positions. Currently she is professor. Her

research interest includes Power System Analysis, Power System Optimization

and Distribution Operation.

Anuprita Sandeep Mishra was born in Indore, India, in 1972. She received

BE degree (1995) from the SGSITS, Indore, M.Tech. Degree (2005) in Heavy

Electrical Equipments and PhD degree (2012) from MANIT, Bhopal, India.

She had been working with Technocrats Institute of Technology, Bhopal,

since 2002.

usage based cost allocation technique for ehv networks using non-linear utility factors

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