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4 fragments were found in a text with the title: "Evaluation of transmission pricing methods for liberalized markets a literature survey ElektronischeDaten", located on:http://e-collection.ethbib.ethz.ch/eserv/eth:26847/eth-26847-01.pdf

2 fragments were found in a text with the title: "Evaluating bounds on voltage and thermal security margins under power transfer uncertainty",located on:http://www.pscc-central.org//uploads/tx_ethpublications/pscc2008_272.pdfhttp://www.pscc-central.org//uploads/tx_ethpublications/s27p05.pdf

2 fragments were found in a text with the title: "Bulk electric system reliability simulation and application", located on:http://library2.usask.ca/theses/available/etd-12152005-133551/unrestricted/WijarnWangdee_PhDthesis.pdf

1 fragment found in a text with the title: "A Tracing Method for Pricing Inter-Area Electricity Trades", located on:http://www.econ.cam.ac.uk/dae/repec/cam/pdf/wp0107.pdfhttp://www.dspace.cam.ac.uk/bitstream/1810/286/1/wp0107.pdf

1 fragment found in a text with the title: "Development of transmission use of system charges scheme for Malaysia transmission network", locatedon:http://eprints.utm.my/6409/1/NoorAzamSamsudinMFKE2007TTT.pdf

1 fragment found in a text with the title: "Two stages of uniform delivered pricing and a monopolistic network in competitive electricity markets",located on:http://www-sre.wu-wien.ac.at/ersa/ersaconfs/ersa01/papers/full/280.pdf

1 fragment found in a text with the title: "Challenges of electric power industry restructuring for fuel suppliers / Energy Information Administration,Office of Coal, Nuclear, Electric and Alternate Fuels, Office of Oil and Gas, Office of Integrated Analysis and Forecasting, U.S. Department ofEnergy.", located on:http://www.eia.doe.gov/pub/electricity/chg_str_fuel.pdf

1 fragment found in a text with the title: "Review Of The Electricity Act 2003", located on:http://www.eSocialSciences.com/data/articles/Document14582005220.2760279.pdf

1 fragment found in a text with the title: "Untersuchungen der Struktur von Preissystemen für Erdgastransportkapazitäten", located on:http://miami.uni-muenster.de/servlets/DerivateServlet/Derivate-3091/diss_pustisek.pdf

1 fragment found in a text with the title: "Assessing Policy Choices For Managing SO2 Emisions From Indian Power Sector", located on:http://www.eSocialSciences.com/data/articles/Document1185200940.3193781.pdf

1 fragment found in a text with the title: "Implementation of Artificial Intelligence Techniques for Steady State Security Assessment in Pool Market",located on:http://www.cscjournals.org/csc/manuscript/Journals/IJE/volume3/Issue1/IJE-27.pdf

1 fragment found in a text with the title: "congressional requesters Why GAO Did This Study The Help America Vote Act of 2002", located on:http://www.gao.gov/new.items/d05956.pdf

1 fragment found in a text with the title: "Electricity Bill Act'2003", located on:http://129.3.20.41/eps/le/papers/0505/0505005.pdf

1 fragment found in a text with the title: "Eleventh Five Year Plan (2007–2012) Volume III Agriculture, Rural Development, Industry,Services, andPhysical Infrastructure", located on:http://www.eSocialSciences.com/data/articles/Document11882008110.2548944.pdf

1 fragment found in a text with the title: "The VLDB Journal DOI 10.1007/s00778-006-0011-4 SPECIAL ISSUE PAPER Privacy leakage in multi-relational databases: a semi-supervised", located on:http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.80.5728&rep=rep1&type=pdf

1 fragment found in a text with the title: "18.69 % OF THE FULLY DILUTED POST ISSUE PAID-UP CAPITAL OF THE COMPANY. THE NET ISSUE WILLCONSTITUTE...", located on:http://www.moneycontrol.com/news_html_files/pdffiles/aug2007/bgrenergy.pdf

1 fragment found in a text with the title: "PUBLIC ISSUE OF 9,136,000 EQUITY SHARES OF Rs. 10 EACH OF BGR ENERGY SYSTEMS LIMITED (“BGRENERGY ” OR THE “COMPANY ” OR THE “ISSUER”)", located on:http://www.moneycontrol.com/news_html_files/pdffiles/nov2007/bgrfinal.pdf

1 fragment found in a text with the title: "International Journal of Computational Cognition", located on:http://www.yangsky.com/ijcc/pdf/ijcc441.pdf

1 fragment found in a text with the title: "The detection, prevention and mitigation of cascading outages in the power system", located on:http://repository.tamu.edu/bitstream/handle/1969.1/ETD-TAMU-1109/SONG-DISSERTATION.pdf?sequence=1

1 fragment found in a text with the title: "Risk Management in Electricity Markets Emphasizing Transmission Congestion", located on:http://ntnu.diva-portal.org/smash/get/diva2:123302/FULLTEXT01

1 fragment found in a text with the title: "Design of secondary voltage and stability controls with multiple control objectives", located on:http://smartech.gatech.edu/bitstream/handle/1853/29714/song_yang_ys_200908_phd.pdf?sequence=1

1 fragment found in a text with the title: "State estimation and transient stability analysis in power systems using artificial neural networks", located

on:

http://ir.lib.sfu.ca/bitstream/1892/9023/1/b39308534.pdf

1 fragment found in a text with the title: "Spreadsheet Implementations for Solving Power-Flow Problems", located on:http://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1051&context=ejsie

1 fragment found in a text with the title: "Optimal static capacitor allocation by discrete programming", located on:http://deepblue.lib.umich.edu/bitstream/2027.42/8461/4/bad5510.0001.001.txt

1 fragment found in a text with the title: "Infeasible primal-dual interior point algorithms for solving optimal power flow problems", located on:http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq21399.pdfhttp://uwspace.uwaterloo.ca/bitstream/10012/128/1/nq21399.pdf

1 fragment found in a text with the title: "Project Team", located on:http://www.pserc.wisc.edu/documents/publications/reports/2000_reports/Report.pdf

1 fragment found in a text with the title: "A Volterra filter for neuronal spike detection", located on:http://hal.inria.fr/docs/00/34/70/48/PDF/spike_HAL.pdfhttp://hal.archives-ouvertes.fr/docs/00/34/70/48/PDF/spike_HAL.pdf

1 fragment found in a text with the title: "Primary Detection Methods for Laugh Tracks", located on:http://cnx.org/content/m15642/1.2/?format=pdf

1 fragment found in a text with the title: "Detection and identification of topological errors in online power system analysis", located on:http://e-collection.ethbib.ethz.ch/eserv/eth:38000/eth-38000-01.pdf

1 fragment found in a text with the title: "A Real-Time Baseband Communications Processor For High Data Rate Wireless Systems", located on:http://www.ece.rice.edu/~sridhar/research/proposal.pdf

1 fragment found in a text with the title: "Table of Contents Table ofContents.............................................................................................................................. 2", located on:http://www.pserc.cornell.edu/matpower/manual.pdf

1 fragment found in a text with the title: "A methodological approach to BISDN signalling performance", located on:http://doc.utwente.nl/71051/1/Hou94methodological.pdf

1 fragment found in a text with the title: "Modifying a local measure of spatial association to account for non-stationary spatial processes.", locatedon:https://dspace.library.uvic.ca:8443/bitstream/1828/1240/1/Thesis_IanMackenzie_August2007.pdf

Subsequent the examined text extract:

CHAPTER-1 INTRODUCTION1.1 Preliminaries

[1]

In competitive Power Market, the former vertically integrated utility, which performed

all the functions involved in power industry, i.e. generation, transmission, distribution and

retail sales, is dis-aggregated into separate companies devoted to each function. The

electricity bill for the end consumer now involves at least two components: one from the

distribution and transmission network and the other from the company that generates the

electrical energy.

All this seems to be very straightforward at first glance, but there are several

complexities involved in restructuring and many issues have been raised. In the discussions to

follow, the issues involved in the restructuring process will be considered.

1.2 Basic Concepts of Regulation and Deregulation[2]

Regulation: ‘Regulation means that the Government has set down laws and rules that put

limits on and define how a particular industry or company can operate.’

Deregulation: ‘Deregulation in power industry is a restructuring of the rules and economic

incentives that government has set up to control and drive the electric power industry.’

1.3 Regulated Electric Power Industry[2]

1.3.1 Basic Structure of Regulated Electric Power Industry

The electric power industry has been dominated by the large utilities up to the last

decade. These large utilities were owned by the authority and all activities like generation,

transmission and distribution of power performed by them in the particular region. Such

utilities have been referred as vertically integrated utilities which carried out its operation in

regulated structure. There is no scope for separate calculation of costs of generation,transmission and distribution of power for this kind of structure. Therefore, the utilities often

charged their customers an average tariff rate depending on their aggregated cost during a

period.

1

Figure 1.1: Basic Structure of Regulated Electric Power Industry

1.3.2 Characteristics of Regulated Power Industry

• Monopoly franchise: Only the local electric utility can produce, move, or sell

commercial electric power within its service territory.

• Obligation to serve: The utility must provide service to all electric consumers in its

service territory, not just those that would be profitable.

• Regulatory oversight: The utility’s business and operating practices must confirm to

guidelines and rules set down by government regulators.

• Least-cost operation: The utility must operate in a manner that minimizes its overall

revenue requirements.

• Regulated rates: The utility’s rates are set in accordance with government regulatory

rules and guidelines.

• Assured rate of return: The utility is assured a fair return on its investment, if it

confirms to the regulatory guidelines and practices.

1.4 Deregulated Electric Power Industry[2]

1.4.1 Motivation for Deregulation

There are many reasons that led to deregulation of power system. One force that led to

the deregulation of electric power was the change in generation economies of scale that

occurred throughout the 1980s. Traditionally, electric utility systems evolved with the central

station concept because of significant economy of scale in power generation. Very large

generators produced power at less than half the cost per kilowatt of small generator units, and

the bigger the generator size, the more economical the power it produced.

Following are the main motivations:

• Technological innovation improved the efficiency of small units.

2

• Improvements in materials like metals with high melting point, special lubricants,

ceramics, and carbon fibre, permit vastly stronger and less expensive small machinery

to be built.

• Computerized control systems have been developed that often reduce the number of

on-sight personnel.

• Data communications and off-site monitoring systems.

1.4.2 Basic Structure of a Deregulated Electric Power Industry

The first step in the restructuring process was to separate out the generation activities

from that of the distribution and transmission, following was to introduce competition in

generation activities, either through the creation of power pools, provision of direct bilateral

contracts or bidding the spot markets. So in competitive electricity market there may be

several generation companies, Independent Power Producers (IPP) or/and Non-Utility

Generators (NUG).

Figure 1.2: Structure of a Deregulated Electric power industry

On the other hand it felt necessary to introduce regulation in transmission so as to prevent it

from overcharging for its services. Hence the trend has been to establish new legal and

regulatory framework offering third parties open access to transmission network.

1.4.3 Different Entities in Deregulated Electric Power Industry

3

Generating Companies (GENCOs): GENCOs are owner-operators of one or more

generators that run them and bid the power into the competitive market place. GENCO sells

energy at their sites in the same manner that a coal mining company might sell coal in bulk at

its mine.

Transmission Companies (TRANSCOs): TRANSCO moves power in bulk quantities from

where it is produced to where it is delivered. The TRANSCO owns and maintains the

transmission facilities, and may perform many of the management and engineering functions

required to ensure the system can continue to do its job. In most deregulated industry

structures, the TRANSCO owns and maintains the transmission lines under monopoly

franchise, but does not operate them. That is done by Independent System Operator (ISO).

The TRANSCO is paid for the use of its lines.

Distribution Companies (DISCOs): It is the monopoly franchise owner-operator of the

local power delivery system, which delivers power to individual businesses and homeowners.

In some places, the local distribution function is combined with retail function, i.e. to buy

wholesale electricity either through the spot market or through direct contracts with GENCOs

and supply electricity to the end use customers. In many other cases, however, the DISCO

does not sell the power. It only owns and operates the local distribution system, and obtains

its revenues by renting space on it, or by billing for delivery of electric power.

Retail Energy Service Companies (RESCOs): It is the retailer of electric power. Many of

these will be the retail departments of the former vertically integrated utilities. Others will be

companies new to the electric industry that believes they are good at selling services.

RESCOs buy power from GENCOs and sell it directly to the consumers

4

Independent System Operator (ISO): The ISO is an entity entrusted with the responsibility

of ensuring the reliability and security of the entire system. It is an independent authority anddoes not participate in the electricity market trades. It usually does not own generating

resources, except for some reserve capacity in certain cases. In order to maintain the system

security and reliability, the ISO procures various services such as supply of emergency

reserves, or reactive power from other entities in the system.

Customers: A customer is entity, consuming electricity. In deregulated markets, the customer

has several options for buying electricity. It may choose to buy electricity from the spot

market by bidding for purchase, or may buy directly from GENCOs or even from the local

distribution company.

1.5 Market Models in Deregulated electric Power Industry[2]

The market mechanisms that have arisen out of deregulation can be classified into Pool

and Bilateral. In most of the restructured electric power systems both the pool and bilateral

market models coexist with variation from one system to another. In this thesis we call this

combined market the hybrid market. In the next section, different market structures will be

discussed.

At present the deregulated electricity market comprises of generating companies

(GENCOs), Transmission companies (TRANSCs) and Distribution Companies (DISCOs)

and these entities are independent. Due to the economies of scale inherent in the transmission

system the TRANSCOs are natural monopolies and operate under the authority of a regulator.

In the deregulated environment, therefore planning for generation capacity investment and

location of the same is therefore market driven. There may not be any coordination between

transmission and generation investment. This has resulted in a marked increase in the level of

risk and uncertainty associated with transmission operation and investment

1.5.1 Pool based market

There is only one buyer in this system. The Pool model is a governmental or quasi-

governmental agency that buys for everyone, taking bids from all sellers and buying enough

power to meet the total need, taking the lowest cost bidders. The Pool operator also has

responsibility for running the power system, and is thus a combined buyer-system operator.

In the pool model shown in Fig. 1.3, competition is initiated in the generation business by

5

creating more than one Genco and is gradually brought to the distribution side where retailers

could be separated from Discos and where consumers could be allowed to phase in a choice

of retail supply.

Figure 1.3: Power Pool Trade Model

The transmission system is centrally controlled by independent system operator which is

disassociated from all market participants and ensures open access to transmission network.

The ISO operates the electricity pool to perform a price-based dispatched and provides a

forum for setting the system prices and handling electricity trades.

1.5.2 Bilateral Trade Model

Bilateral contracts are direct agreement between buyers (Distribution Company or large

customer or energy brokers) and sellers (generation companies or energy brokers) and can

take place in numerous forms. In this type of multi-seller/ multi-buyer system, individual

buyers and sellers make a deal to exchange a power at prices and under the conditions they

agree to, privately. Bilateral market structure is shown in Fig. 1.4. There is no role of ISO in

the formation of these contracts and the two transacting parties are free to negotiate their

price. However, once the transactions are negotiated, the ISO needs to be informed about the

trades. Modelling of bilateral transaction is usually through the use of the bilateral transaction

matrices (BTM).

6

Figure 1.4: Bilateral Trade Model

From the perspective of the ISO in bilateral markets, its objective is to ensure that thesystem is secure and reliable. Therefore, under certain circumstances, it might be necessary

for the ISO to curtail some of the transactions for system security reasons. The choice of

curtailment of transaction is important to the parties involved in them, since curtailment

would affect the financial deals. Therefore, in the case of bilateral market model, ISO should

act in an impartial and fair manner to all parties, while deciding on the curtailment of

transactions.

1.5.3 Multilateral Trades Model

Multilateral trades are a generalization of bilateral transactions where a power broker

puts together a group of energy producers and buyers to form a balanced transaction. In

practice, multilateral and bilateral transaction may coexist with a power pool. Conceptually

the extreme case is where the concepts of pool disappear in to this multi-market structure as

illustrated in Fig. 1.5.

7

Figure 1.5: Multilateral Trades Model

Here each market is managed by a broker under its individual rules. Different market may

have different rules and that could give rise to different strategies for participants. The

objective of the ISO is restricted to system operation and security. All the contracts in the

energy markets will be respected by the ISO without discrimination. Only when system

security is threatened will the ISO interfere in managing contracted dispatches. Many of new

entrants will enter in to market as intermediaries. Marketers, who buy and then resell

electricity supply contracts, and brokers who arrange transaction between buyers and seller,

will enter the markets. These intermediaries will have a constructive role in promoting

competition but there is also the danger of price volatility and market instability.

1.5.4 Combined Pool and Bilateral Trade Model (Hybrid Trade Model)

In this, pool model will exist simultaneously with bilateral and multilateral

transactions. The difference in this model and the pool model is that the transmission sector is

unbundled in to “market” sector and “security sector as shown in Fig. 1.6.

Figure 1.6: Combined Pool and Bilateral Model

In the market sector, there are multiple separate energy markets, containing a pool market

taken care of by PX and bilateral contracts established by energy brokers. The ISO is

8

responsible for system operation and guarantees system security and holds superior positions

over other in operational matters. Market participant may not only bid into the pool but also

make bilateral contracts with each other. Therefore this model provides more flexible options

for transmission access. Consumer has more choice in this type of model and hence market

becomes more competitive. In all the market mechanisms the ISO has to execute the

schedules and ensure the reliability and security as well as handling the emergencies like

congestion in the system.

1.7 The Electricity Act 2003[2] [10]

The conceptual framework underlying this new legislation is that the electricity sector

must be opened for competition. The Act moves towards creating a market based regime in

the power sector. The Act also seeks to consolidate, update and rationalize laws related to

generation, transmission, distribution, trading and use of power.

It focuses on:

• Creating competition in the industry

• Protecting consumer interest

• Ensuring supply of electricity to all areas

• Rationalizing tariff

• Elimination of licensing for setting up a generating station, subject to compliance with

technical standards. This excludes Hydro-Electric power station

• Provision for issuing more than one license for transmission and distribution in the

same geographical area.

• Provision of Open Access with respect to transmission

• Unbundling of the SEBs on the basis of functions (generation, Transmission and

Distribution)

State Governments will have the freedom to decide the sequence and phases of restructuring,and also retain the integrated structure of the SEB for a limited period.

CHAPTER 2 LITERATURE REVIEW

A.R.Abhyankar and Prof. S.A.Khaparde explained concepts of Regulation

and Deregulation in Power Industry. Structures of regulated and deregulated power industries

have been discussed with their characteristics. Market models for energy trading and role of

9

ISO in deregulated power industry have been also presented. Issues of transmission operation

and its management techniques in deregulated power system have been discussed. Current

scenario of deregulation around world and in India has been presented at last.

D.Shirmohammadi, C.Rajagoapalan, E.R.Alward and C.L.Thomas, explains several

categories of transmission transaction, major cost components of transmission transaction &

evaluation of the cost of transmission transaction.

D. Shirmohammadi, Xisto Vieira, Boris Gorenstin, Mario V.P.Pereira, discusses the basic

technical concept involved in developing cost based transmission pricing. It introduces the

concept of transmission pricing paradigms and methodologies to better illustrate how

transmission costs are transformed into transmission prices. The role of these paradigms &

methodologies in promoting “economic efficiency”.

Mohammad Shadehpour, Hatim Yamin, Zuyi Li, discusses some of the existing

approaches for transmission pricing and present an overview of recent techniques used for

designing equitable access fees to recover fixed transmission charge. They have shown some

recent methods that determine a generator’s (load’s) contribution to a line power flow and a

consumer load. The problems associated with transmission congestion and pricing can be

resolved with help of Firm transmission rights (FTR) and Locational marginal prices (LMP).

The major transmission cost allocation methods like Postage stamp rate method, Contract

path method, MW-MILE method, Unused transmission capacity method, MVA-mile method,

Counter-flow method, Distribution factor method, Bialek’s Tracing method & Kirschen’s

Tracing method are shown with example. Finally comparisons of cost allocation method

according to the application are shown.

M. Murli, M. Sailaja Kumari and M. Sdyulu describes appropriate pricing scheme that can

provide the useful economic information to market participants, such as generation,

transmission companies and customers. The proper pricing method is needed for transmission

network to ensure reliability and secure operation of power system. This paper shows an

overview of different costs incurred in transmission transaction, types of transmission

transactions and the transmission pricing methodologies. Transmission pricing methods

includes Incremental transmission pricing and Embedded transmission pricing. Incremental

transmission pricing includes Short-run Incremental pricing (SRIC), Long-run Incremental

pricing (LRIC), Short-run Marginal cost (SRMC), Long-run Marginal cost (LRMC).

Embedded transmission pricing includes network based method and flow based method.

Network based consist of Postage stamp method, Contract path method, MW-MILE method,

MVA-MILE method. On the other hand, Flow based method consists of Bialek tracing

10

method & Distribution factors method. This paper mainly focuses on determining the

Embedded transmission cost by various methods and compares the results for 6 BUS, IEEE

14 bus and RTS 24 BUS systems.

J.Bialek introduces the method of tracing the flow of electricity in meshed electrical

networks that may be applied to both real and reactive power flows. This method allows

assessment of how much of the real and reactive power output from a particular station goes

to a particular load. The lossless real power flow required for the method can be obtained in

one of the three ways. In the first approach, it average the line flows over sending and

receiving end and adjust correspondingly the nodal injections. The second approach is to

consider the gross flow which would exist if no power was lost in the network. The third

approach is to consider the net flows when all loses are removed from the network. In the

upstream-looking algorithm, the transmission usage/supplement charge is allocated to

individual generators and losses are apportioned to loads. In the downstream-looking

algorithm, the transmission usage/supplement charge is allocated to individual loads and

losses are apportioned to generators.

Satyavir Singh discuss the issue related to tracing the flow of electricity that had gain

importance as its solution helps in evaluating a fair and transparent tariff. An electricity

tracing method would make it possible to charge the generators and/or consumers on the

basis of actual transmission facility used. This paper focuses on tracing of electricity using

Bialek’s tracing algorithm. This paper shows case study on IEEE 14-bus system with three

simultaneous bilateral transactions.

Stefan Kilyeni, Oana Pop, Titus Slavici, Cristian Craciun, Petru Andea, Dumitru

Mnerie, in this paper an analysis of the allocation method using distribution factors is

proposed. The distribution factors are the relative change of power flow on a network

element, causing by the change of power generated and / or those consumed. They have been

used to approximately determine the impact of generation and load on transmission flows.

This factors are suggested as a mechanism to allocate transmission payments in restructured

power systems, as these factors can efficiently evaluate transmission usage.. The distribution

factors are used in the regime, safety operation and contingencies analysis, reflecting the

impact of the power generated and consumed in the transport of electricity. In this paper

distribution factors method is applied to 12 nodes test system and a notable difference of

generators and consumers transmission costs allocation, between the cases without and with

active power losses observed.

11

CHAPTER-3 TRANSMISSION PRICING METHOD INDEREGULATED POWER SYSTEM

The transmission network plays a vital role in competitive electricity markets. In a

restructured power system, the transmission network is the key mechanism for generators to

compete in supplying large users and distribution companies. A proper transmission pricing

scheme could motivate investors to build new transmission and/or generating capacity for

improving the efficiency. In a competitive environment, proper transmission pricing could

meet revenue expectations, promote an efficient operation of electricity markets, encourage

investment in optimal locations of generation and transmission lines, and adequately

reimburse owners of transmission assets. Thus, transmission pricing should be a

reasonable economic indicator used by the market to make decisions on resource

allocation, system expansion, and reinforcement[1]

.

In general, strategic pricing of any service, without regard to political considerations,

seeks to:

• Increase customer value by providing a wider variety of service and price operations.

• Promote economic efficiency by ensuring that the value of service and the cost of

service are balanced.

• Change customer consumption patterns, where appropriate to improve the utilization

of existing resources.

12

• Encourage service use of applications where it is the least-cost option and discourage

the use where it is not.

However, it is difficult to achieve an efficient transmission pricing scheme that could

fit all market structures in different locations. The ongoing research on transmission pricing

indicates that there is no generalized agreement on pricing methodology. In practice, each

country or each restructuring model has chosen a method that is based on the particular

characteristics of its network. Measuring whether or not a certain transmission pricingscheme is technically and economically adequate would require additional standards.

3.1 Main Functions of Electricity Transmission[1]

• To link generators and consumers: both located at different geographic locations of

the network

• To provides economies of scope: The interconnection of generating power plants of

different characteristics (fuel type and marginal cost, capacity, technical limits) allows

minimisation of overall production costs, coordination of maintenance schedules and

sharing operational reserves capacity. Market for ancillary services can be developed

because of transmission network.

• To provide security of supply: The interconnection of generating units through

transmission network minimises the impact of forced outages of generators or

transmission line on customers.

• To make possible trading of electricity: Interconnecting electricity producers and

loads through which offer and demand match to discover appropriate price in

competitive energy market. Electricity cannot be stored in bulk and has to be supplied

on real time basis. Hence generators and consumers have to pay for the use of

transmission network.

3.2 Important Characteristics of Electricity Transmission[2]

• It is capital intensive: To install new transmission lines, substations and power

transformers requires huge capital and long time.

• It has long life assets: Transmission lines and substations have economic life of 30

years or more.

13

• Investments require long time of construction: Environmental and other

permissions and difficulty in erection of transmission towers and lines require long

time.

• Economies of scale: Transmission cost per MW reduces as MW transported through

line increases. It implies that more network capacity means less marginal price.

• Natural monopoly characteristic: the presence of dedicated assets, irreversible

investments and economies of scale leads to natural monopoly. Hence small

companies find it unprofitable or impossible to enter the market. Hence transmission

business must be regulated to mitigate any kind of market power coming from

transmission asset owners. Hence regulators must prevent network companies from

overcharging users of the network and must monitor quality of service provided.

3.3 Components of the Transmission Cost[8]

The major components of the transmission cost of transmission transactions are:

1) Operating Cost: This is the cost due to generation rescheduling and redispatches to

minimize the system losses, relieve congested transmission lines and enhance the system

voltage profile.

2) Opportunity Cost: Benefits of all the transactions that the utility forgoes due to operating

constraints. It is defined as costs that may be encountered in the transmission constrained

case where the wheeling may prevent the transmission capacity. In other words it is the profit

obtained to ISO during congestion in the system.

3) Reinforcement Cost: Capital cost of new transmission facilities needed to accommodate

the transaction. It also includes the installation of additional reactive power resources to

support the transaction.

4) Embedded Cost: The allocated cost of existing transmission facilities used by the

transmission transaction. It includes:

• Investment costs (including returns and depreciation of capital equipment) which is

the highest proportion of the overall cost.

• Administrative and general costs including scheduling and coordination services,

billing and accounting staff, and salaries.

• Cost of voltage control and reactive power support.

Operating cost, opportunity cost and reinforcement cost constitute the incremental cost of the

transmission transaction. Incremental costs are two types. They are short run and long run

14

incremental costs "Short-Run Incremental Cost" refer to operating cost and opportunity cost,

"Long-Run Incremental Cost" refers to operating cost, opportunity cost and reinforcement

cost. "Congestion Cost"(Out of merit production cost due to transmission constraints) is also

called opportunity cost and "Embedded Cost" is also called existing system cost.

Fixed cost are cost related to network facilities such as return and depreciation of the capital

equipment, expense for the operation and maintenance of the transmission network hardware.

Variable costs include transmission losses, congestion costs and costs returned from ancillary

services such as generating reserves, reactive power and so on.

3.4 Categories of Transmission Transactions[4] [8]

The following are the categories of transmission transactions:

1) Firm Transmission Transactions: These transactions are not subject to discretionary

interruptions and are specified in terms of MW of transmission capacity that must be reserved

for the transaction. The transco makes arrangements for enough capacity on the network to

meet these transaction needs. These could either be on a long-term basis, in the order of years

or on short-term contracts (up to one year).

2) Non-firm Transmission Transactions: These transactions may be curtailable or as-

available. Curtailable transactions are ongoing transactions that may be curtailed at the

utility's discretion.

3) Long-term Transmission Transactions: Long term transaction is long enough to allow

building new transmission facilities.

4) Short-term Transmission Transactions: These transactions not associated with

transmission reinforcements. Short term transaction may be a bilateral contract or pool

trading.

3.5 Transmission Pricing Methods [4] [6]

3.5.1 Incremental Transmission Pricing:

15

These pricing methods allocate the incremental cost (i.e., variable cost) of the transmission

transaction. Fig. shows different types of incremental pricing methods.

1) Short-run Incremental Cost Pricing (SRIC): This pricing methodology entails

evaluating and assigning the operating costs associated with a new transmission transaction to

that transaction.

2) Long-run Incremental Cost Pricing (LRIC): This pricing methodology entails

evaluating all long-run costs (operating and reinforcement costs) necessary to accommodate a

transmission transaction and assigning such costs to that transaction. The reinforcement cost

component of a transmission transaction can be evaluated based on the changes caused in

long-tem transmission plans due to the transmission transaction.

3) Short-run Marginal Cost Pricing (SRMC): The short run marginal cost of a Transco is

the cost of supplying an additional 1 MW of power in a transaction .SRMC is the difference

in marginal costs of supply bus and delivery bus. The marginal costs of two buses can be

determined from the optimal power flow solution as the dual variables associated with the

demand balance equation.

4) Long-run Marginal Cost Pricing (LRMC):

LRMC determines the present value of future investments required to support a marginal

increase in demand at different locations in the system, based on peak scenarios of future

demands and supply growth. In this pricing methodology the marginal operating and

reinforcement costs of the power system are used to determine the prices for a transmissiontransaction.

3.5.2 Embedded/Rolled in Transmission Pricing [6]

In this paradigm, all the costs incurred during building the infrastructure and the future

investment, operating, maintenance costs are summed up (rolled-in) together and then are

allocated to various wheeling customers on various biases. The basic philosophy behind this

paradigm of transmission pricing paradigm is shown in Figure 3.2.

16

This pricing method allocates the embedded system costs i.e. fixed cost among transmission

system users. Embedded cost may be categorised as in below figure.

3.6 Network-Based Methods[1] [4] [6]

: These methods depend on the structure of the

transmission system but do not recognize the physical laws governing its operation.

3.6.1 Postage Stamp Method

A postage stamp rate is a fixed charge per unit of power transmitted within a particular zone.

The rate does not take into account the distance involved in the wheeling. There are various

versions of postage stamp methodology. In some versions, both, generators and loads are

charged for transmission usage, while in others, only loads pay for the same. Some variants

17

charge loads for their peak value while in others, they are charged on the basis of average

loads.

Some of the advantages of Postage Stamp Method are as follows:

• The method is simple and easy to implement.

• It is transparent and is easily understood by all.

• There is no mathematical rigor involved.

• Recovers embedded cost of transmission system.

• Politically implementable

Disadvantages of the Postage Stamp Method can be quoted as follows:

• Pancaking: In case a transaction takes place such that the power is transmitted

through multiple intermittent utilities or zones, pancaking of access charges takes

place.

• No economic signal: Postage stamp allocation does not create an economic signal

associated with the effect of a particular transaction.

• No extent of use of network: Postage stamp allocation does not take into

consideration the extent of use of the network by a particular transaction. The

transmission charges paid by two loads, out of which, one is very near to a generator,

while the other is miles apart, is the same. So that proper economic signal is not

produced.

3.6.2 Incremental Postage Stamp Method

This method is developed to reduce effect of pancaking. An incremental postage stamp rate

could be applied to a zone which is much smaller than a region. This avoids pan-caking in the

case of inter-regional transactions. In this method big control areas are divided in several sub

areas and transmission cost is decided for each sub area.

3.6.3 Contract Path Methodology

This method is based on charging the transacting entities between two points, based on a pre-

defined path. To define formally, contract path is the shortest route formed by a series of

transmission lines which can carry the contract power between the take-off point and

18

injection point. In the earlier days, when the wheeling contracts were rare, the contracts were

used to be written between the utility and the contracting parties. Hence, the word contract in

the name. Even though contracting parties know that the power will split into multiple

parallel paths, they compute the prices for a single path.

Some of the advantages of this methodology are as follows:

• Simple to implement

• Avoid problem of pancaking to a large extent

• Directly or indirectly, the method takes into account the distance involved in

wheeling.

Disadvantages of contract path method are as follows:

• The contract path between the points of takeoff and injection is decided a priory

without doing any simulation. Hence contract path is not necessarily a physical power

flow path.

• This method fails to provide correct economic signals.

• In meshed electrical network power flow cannot be restricted to particular path if

other parallel paths are available.

• If different transmission and distribution companies are involved in parallel paths then

it may create financial disputes.

3.6.4 MW-Mile Methodology

Power flow based MW-Mile method takes into account both the quantity of transacted power

and the electrical distance between source and sink and allocates the total costs in proportion

to the MW-Mile of transactions. There are various versions of power flow based MW-Mile

methods.

Given a transaction with the actual points and the variation of generation and load specified,

MW-Mile methodology calculates the maximum transaction related power flow on every

transmission line using a DC power flow.

For transaction t, according to MW-Mile methodology, real power flows on all network lines

are calculated using the DC power flow algorithm. The magnitude of MW flow on every line

is then multiplied by its length L 1and a predetermined weighting factor reflecting the cost per

unit capacity of the line, W 1and summed over all network lines.

19

1 ,1 1

1

t tMWMile W MW L=∑

This process is repeated for every transaction by considering only the generations and loads

associated with that transaction. The share of the total transmission network capacity cost is

shared among all the transaction.

*t

t

t

MWMileTCt TC

MWMile=

∑

Advantages of Power flow based MW-Mile Methodology are:

• It is insensitive to the order of wheeling transaction.

• It produces correct economic signals to both short distance and long distance entities.

• This method is logical and straightforward.

3.6.5 MVA-Mile Method

The MVA-mile method is an extended version of the MW mile method. It takes into

consideration both real power and reactive power where as MW-mile method considers only

real power. This method also allocates the transmission charges based on the magnitude of

power and the geographical distance between the delivery point and the receipt point. This

method is AC power flow based method.

3.7 Flow Based Methods[1] [4] [6]

: This approach allocates the charges of each

transmission facility to a wheeling transaction based on the extent of use of that facility by

the transaction. This is determined as a function of magnitude, the path, and the distance

travelled by the transacted power. The flow based methods are Bialek tracing method and

Distribution factors method.

3.7.1 Power Flow Tracing Based Network Fixed Cost Allocation Method[1]

Power tracing is a tool applied post facto on power flow snap shot that can provide complete

power audit information. The power flow tracing methods notionally quantify the usage of

the network elements by various generators and loads. By making use of this information, the

network fixed costs can be allocated to various entities.

Proportional Sharing Principle[1] [6]

The main principle used to trace the power flow is proportional sharing, The network node is

a perfect ‘mixer’ of incoming flows so that it is impossible to tell which particular incoming

20

electron goes in to which outgoing line, The figure shows four lines connected to a node. The

outflows (f1 and f2) can be represented in terms of the inflows (fa and fb); in other words, we

can determine how much of f1 comes from fa and how much of f1 comes from fb. The same

applies to f2.

1 1 1

2 2 2

fa fbf f f

fa fb fa fb

fa fbf f f

fa fb fa fb

= ++ +

= ++ +

(4.7)

Fig. 3.1. Proportional Sharing Principle

In general, by notional decomposition of transmission line flows and losses, the power

tracing algorithms provide following information:

• Contribution of kth

generator in meeting jth

load.

• Loss incurred while transferring kth

generator’s power to jth

load.

• Decomposition of power flows on a line into its constituent generators and loads.

• Losses supplied by various generators.

• Losses due to various loads.

For power flow tracing three things required: state estimation solution or power flows over

lines, injections at generator and load buses and network topology (single line diagram).

3.7.2 Distribution Factors Method[10]

: Distribution factors are calculated based on DC load

flows. These factors are used to determine the impact of generation and load on transmission

flows. The various distribution factors are Generation shift distribution factors (GSDF’s) and

Generalized Generation/ load distribution factors (GGDF’s/GLDF’s) have been used

extensively in power system security analysis to approximate the transmission line flows and

generation /load values. GSDF’s or A factors provide line flow changes due to a change in

generation. These factors can be used in determining maximum transaction flows for

21

bounded generation and load injections. GGDF’s are applied to estimate the contribution by

each generator to the line flow on the transmission grid and GLDF’s determine the

contribution of each load to line flows.

CHAPTER-4 METHODOLOGY FOR TRANSMISSION COST

ALLOCATION

4.1 Bialek’s tracing Method[7] [8]

Tracing methods determine the contribution of transmission users to transmission usage.

Tracing methods may be used for transmission pricing and recovering fixed transmission

costs. An electricity tracing method would make it possible to charge generators and/or

consumers on the basis of actual transmission facility used. Bialek’s tracing method is one of

the important tracing methods. Tracing methods are generally based on the so-called

proportional sharing principle.

In Bialek’s tracing method, it is assumed that nodal inflows are shared proportionally among

nodal outflows. This method uses a topological approach to determine the contribution of

individual generators or loads to every line flow based on the calculation of topological

distribution factors. This method can deal with both dc power flow and ac power flows; that

is, it can be used to find contributions of both active and reactive power flows. Bialek’s

tracing method considers:

• Two flows in each line, one entering the line and the other exiting the line (to consider

losses in line).

• Generation and load at each bus.

This method uses load flow program to estimate how much of the real and reactive power

output from a particular station goes to a particular load. It is possible to access contribution

of individual generator to individual line flow.

22

The proposed algorithm works only on lossless flows, i.e. when the flows at the beginning

and end of each line are same. The lossless real power required by this method can be

obtained as follows:

• Averaging the line flows over the sending and receiving end.

• Consider .gross flows, i.e. the flows which would exist if no power was lost in the

network.

• Consider the network with net flows

This method uses either the upstream-looking algorithm or the downstream-looking

algorithm. In the upstream-looking algorithm, the transmission usage/supplement charge is

allocated to individual generators and losses are apportioned to loads. In the downstream-

looking algorithm, the transmission usage/supplement charge is allocated to individual loads

and losses are apportioned to generators. Bialek’s tracing method is used to determine how

much of a particular generator’s output supplies a particular load or how much of a particular

load is supplied by a particular generator.

Topological distribution factors calculated in this method are always positive; therefore this

method would eliminate the counter-flow problem. To show how this algorithm works, we

define the gross demand as the sum of a particular load and its allocated part of the total

transmission loss. The total gross demand in a system is equal to the total actual generation.

Topological distribution factors are given by the following equation in which Dg

ij,krefers to

the kth

generator’s contribution to line i–j flow

23

[ ]

[ ]

[ ]

1

,

1 1

1

1

1

,

1 1

;

; 1, 2,...,

1;

;

0;

u

i

gn n

ijg g d

ij Gk i j k Gk ig

k kiki

g g

i ij Gi

j

i j

ji u

ii j

j

i j

ng

i Gk

k ik

g n nijg g

ij Gk i j k Gkg

k kiki

g

i j

pP Au P D P j

P

P p P i n

Au i j

PAu j

P

Au otherwise

P Au P

pP Au P D P

P

Where

D

α

α

α

−

= =

∈

−

=

−

= =

= = ∈

= + =

= =

= − ∈

=

=

= =

∑ ∑

∑

∑

∑ ∑

1 1

,

ij

g u ij uik ik

k g

i i

P A P A

p P

− −

= =

Where,

g

ijP

=an unknown gross line flow in line i-j

g

iP

=an unknown gross nodal power flow through node i

Au=upstream distribution matrix

GkP

=generation in node kd

iα

=set of node supplied directly supplied from node i

u

iα

=set of buses supplying directly bus i

,

g

ij kD

=Topological distribution factors

24

The gross power at any node is equal to the generated power at the node plus the imported

power flows from neighbouring nodes. The total usage of the network by the kth generator

UGk is calculated by summing up the individual contributions (multiplied by line weights) of

that generator to line flows. This is given by:

1

,

1 1d d

i i

n nu

g g ik

Gk ij ij k Gk Gk ijg

i ij ji

AU w D P P C

Pα α

−

= =∈ ∈

= =∑ ∑ ∑ ∑

Where,

C ij = Total suppliment charge for the use of line i-j

wg

ij = Charge per MW of each line i-j

The method can be summarized as follows:

1. Solve power flow (either ac or dc) and define line flows (inflows and outflows).

2. If losses exist, allocate each line’s loss as additional loads to both ends of the line.

3. Find matrix Au .

4. Define generation vector P G

5. Invert matrix Au (i.e., Au-1

)

6. Find gross power P gusing P g=Au-1

PG . The gross power at node i is given as

1

1

n

g

i Gk

k ikP Au P

−

==∑

7. The gross outflow of line i–j, using the proportional sharing principle, is given as

1

,

1 1

g n nijg g

ij Gk i j k Gkg

k kiki

pP Au P D P

P

Where

−

= =

= =∑ ∑

1 1

,

ij

g u ij ug ik ik

i j k g

i i

P A P AD

p P

− −

= =

and j is the set of nodes supplied directly from node i .

The downstream-looking method that allocates usage charges to individual loads would use

the same methodology.

25

Flow chart of Bialek Tracing method:

Fig.4.1 Flowchart For Proposed Transmission Pricing Methodology

4.2 Distribution factor[11]

The distribution factors method was extended to calculate the AC power flow, having the

object the calculus of the system cost allocation forth regime with active power losses. The

distribution factors are the relative change of power flow on a network element, causing by

the change of power generated and / or those consumed. Generally speaking, they depend on

the power system topology, the operating system and the direction of power flow. The

distribution factors are used the regime, safety operation and contingencies analysis,

reflecting the impact of the power generated and consumed in the transport of electricity.

4.2.1There are three categories of factors:

4.2.1.1 Generation Shift factors (A factors), which provide line flow changes due to a

change in generation (without changing of overall of system power balance). They depend on

the selection of reference bus, but are independent of the system.

.................................................... (1)

26

Input Line and Bus DataStart

Solve Load flow Problem

Average the line flows at the

sending and receiving end.

Are there losses

Compute Upstream distribution Matrix Au

Input Generation vector

Compute Inverse of Au and Pgen

Compute cost for transmission line t (Tct)

Compute security constraint charge

Compute cost allocated to each generator

End

Where, ΔP l,jk = Change in active power through network element jk.

A jk,i= Generation Shift Factors through network element jk corresponding to

generation at bus i.

ΔP gi = Change in generation at bus i,

ΔP ge = Change in generation at slack bus.

The A factors are determined by DC power flow (which means the neglecting of longitudinal

resistance, transversal susceptances and conductances of network elements, neglecting

reactive power flow and considering all voltages equal to unity).

............................................................ (2)

Where, P – vector of injected power in system buses;

δ – vector of nodal voltage angles,

B – nodal susceptance matrix.

The voltage angle result:

........................................................... (3)

This means

........................................................ (4)

With the same condition, the relation (2) becomes:

... ...................................................... (5)

Where,

P l= vector of active power through network elements,

δ l= vector of difference of voltage angles from ends of network element jk,

B l= diagonal matrix of longitudinal susceptances of network element jk.

Writing in Extended variant the relation (5) lead to:

............................................. (6)

Using the relation (4), relation (6) becomes:

27

.................... (7)

Relation (7) is linear and modification of power through network element, ΔP lj ,k due to

injected power in bus i, ΔP ican be expressed:

.................................. (8)

Comparing the relations (8) and (1), the expression of A factors for network element jk,

corresponding to the change of generated power in bus i:

................................. (9)

4.2.1.2 Generalized Generation Distribution Factors (D factors) determine the impact of

each generator on active power flow through network elements.

....................................... (10)

Where,

Pl,jk

= active power flow through network element jk,

P gi= generated power in bus i,

D jk,i = D factor of the network element jk, corresponding to the generated

power

.................................. (11)

Where,

P jkO

= power flow through network element jk from the previous iteration,

e = the Slack bus.

D factors reflect the utilization rate of electricity transmission capacity depending on

generated power (unlike the A factors, which indicated the incremental rate of use). They

depend on network elements and operating regime and not on the choice of reference bus.

28

CHAPTER-5TEST CASES AND RESULT FOR TRANSMISSION COST

ALLOCATION METHODS

5.1 System 1:12-Bus test System The test system with 12 Buses is shown in figure 5.1. Bus 1 is the slack bus. The

network element parameters are represented in table 5.2. Table 5.3 contains the initial data of buses. The ac power flows solution is done using NR method in matlab as shown in table 5.4 and 5.5. In this section show the result using different cost allocation methods.

Figure 5.1: 12-Bus System

29

Table 5.1: Line Data for 12 – Bus System

Line No. Bus i Bus j R (p.u) X (p.u) B (p.u) L (K.M)

1 1 2 0.00415 0.025 0.04 30

2 1 6 0.00969 0.05838 0.0949 70

3 1 7 0.0166 0.1 0.1613 120

4 2 8 0.00415 0.025 0.04 30

5 3 7 0.00526 0.03169 0.0511 386 8 3 0.00623 0.03752 0.06 45

7 5 4 0.0083 0.05 0.08 60

8 7 4 0.00387 0.02335 0.0376 28

9 11 4 0.0083 0.005 0.08 60

10 6 5 0.00554 0.03335 0.5379 40

11 6 9 0.00415 0.025 0.04 30

12 6 11 0.00692 0.0417 0.06725 50

13 10 7 0.00554 0.03335 0.05379 40

14 9 10 0.00277 0.01667 0.0269 20

15 10 11 0.00692 0.0417 0.06725 50

16 10 12 0.00484 0.02912 0.047 34

30

17 11 12 0.00346 0.0208 0.0336 25

Table 5.2: Bus Data for 12-System

Bus

BusType

Voltage(P.U)

Angle(Deg.)

PG

(MW)QG

(MVAR)PL

(MW)Q L

(MVAR)

1 1 1.05 0 490.52 285.79 - -

2 2 1 0 340.49 -122.86 300 35

3 2 1 0 350 13.32 - -

4 2 1 0 293.72 41.82 - -

5 2 1 0 600 -15.85 350 25

6 2 1 0 200 126.55 230 60

7 3 0.989 0 - - 350 38

8 3 0.988 0 - - 300 25

9 3 0.979 0 - - 208 30

10 3 0.977 0 - - 170 20

11 3 0.979 0 - - 210 23

12 3 0.974 0 - - 130 15

Here,

1 – Slack Bus, 2-PV Bus, 3-PQ Bus

Table 5.3: Newton Raphson Network Analysis

INJECTION GENERATION LOAD

BusVoltage

(P.U)Angle MW MVAR MW MVAR MW MVAR

1 1.05 0 489.694 162.467 489.694 162.467 0 0

2 1.03 -1.9237 40.49 -14.636 340.49 20.364 300 35

3 1.01 -2.1594 350 6.709 350 6.709 0 0

4 0.99 -4.1455 293.72 -56.459 293.72 -56.459 0 0

5 1.01 -2.6951 250 52.366 600 77.366 350 25

6 0.99 -6.2981 -30 -49.82 200 10.18 230 60

7 0.9884 -6.4595 -350 -38 0 0 350 38

8 1.0115 -4.492 -300 -25 0 0 300 25

9 0.9732 -9.9763 -208 -30 0 0 208 30

10 0.9732 -9.9086 -170 -20 0 0 107 20

11 0.974 -9.5396 -210 -23 0 0 210 23

12 0.966 -10.641 -130 -15 0 0 130 15

Total 25.904 -50.3722273.90

4220.628 2248 271

Table 5.4: Line Flows and Losses

Line Loss

31

From

Bus

To

Bus

P

(MW)

Q

(MVAR)

From

Bus

To

Bus

P

(MW)

Q

(MVAR)MW MVAR

1 2 155.291 60.66 2 1 -154.245 -54.357 1.046 6.303

1 6 209.263 83.927 6 1 -204.795 -57.008 4.468 26.918

1 7 125.14 50.538 7 1 -122.397 -34.018 2.742 16.521

2 8 194.735 48.209 8 2 -193.16 -38.725 1.574 9.484

3 7 242.43 37.602 7 3 239.327 -18.904 3.103 18.679

8 3 -106.84 23.956 3 8 107.57 -19.559 0.73 4.397

5 4 55.891 31.763 4 5 -55.555 -29.737 0.336 2.026

7 4 -165.241 23.856 4 7 166.345 -17.194 1.104 6.663

11 4 -180.087 7.277 4 11 182.93 9.844 2.842 17.121

6 5 -191.999 -21.55 5 6 194.109 34.251 2.11 12.702

6 9 232.814 34.384 9 6 -230.469 -20.256 2.345 14.127

6 11 133.98 19.439 11 6 -132.685 -11.641 1.294 7.798

10 7 -175.165 -9.91 7 10 179.966 20.748 1.8 10.839

9 10 22.469 -3.407 10 9 -22.454 3.498 0.015 0.091

10 11 -14.542 0.584 11 10 14.557 -0.49 0.015 0.093

10 12 42.161 4.291 12 10 -42.069 -3.739 0.092 0.552

11 12 88.216 5.391 12 11 -87.931 -3.679 0.285 1.713

Total loss 25.904 156.043

Table 5.5: Line flows for the dc Load Flow Solution.

Line No. From Bus To Bus P ij

1 1 2 148.2

2 1 6 197.5

3 1 7 118.1

4 2 8 188.7

5 3 7 238.7

6 8 3 111.3

7 5 4 56.4

8 7 4 167.8

9 11 4 182.3

10 6 5 193.6

11 6 9 229.8

12 6 11 131.3

13 10 7 174.7

14 9 10 21.8

15 10 11 15.1

16 10 12 41.5

17 11 12 88.5

32

5.2 Cost Allocation using GGDFs Method:

Table 5.6: A Factors (GSDFs) of the 12-Bus

Line i-jA Factors

A ij ,1 A ij ,2 A ij ,3 A ij ,4 A ij ,5 A ij ,6 A ij ,7 A ij ,8 A ij ,9 A ij ,10 A ij ,11

1-2 0 -0.85055 -0.47680 -0.25322 -0.21004 -0.18124 -0.28736 -0.70110 -0.21205 -0.23259 -0.22328 -0.22716

1-6 0 -0.07761 -0.27170 -0.44492 -0.53958 -0.60271 -0.37008 -0.15522 -0.53517 -0.49013 -0.51054 -0.50204

1-7 0 -0.07184 -0.25150 -0.30186 -0.25039 -0.21605 -0.34256 -0.14368 -0.25278 -0.27727 -0.26618 -0.27080

2-8 0 0.14945 -0.47680 -0.25322 -0.21004 -0.18124 -0.28736 -0.70110 -0.21205 -0.23259 -0.22328 -0.22716

3-7 0 0.14945 0.52320 -0.25322 -0.21004 -0.18124 -0.28736 0.29890 -0.21205 -0.23259 -0.22328 -0.22716

8-3 0 -0.14945 0.47680 0.25322 0.21004 0.18124 0.28736 -0.29890 0.21205 0.23259 0.22328

5-4 0 -0.02159 -0.07558 -0.20825 0.38309 0.11052 -0.10295 -0.04318 0.03480 -0.01569 -0.02506

7-4 0 -0.03656 -0.12798 0.56300 0.33752 0.18713 -0.17431 -0.07311 0.13124 0.09398 0.22597

11-4 0 0.01497 0.05239 0.22876 0.04557 -0.07661 0.07136 0.02993 -0.09644 -0.10967 -0.25103 -0.19213

6-5 0 0.02159 0.07558 0.20825 0.61691 -0.11052 0.10295 0.04318 -0.03480 0.01569 0.02506

6-9 0 -0.03081 -0.10787 -0.09472 0.05672 0.15773 -0.14692 -0.06162 -0.52388 -0.31158 -0.13439 -0.20822

6-11 0 -0.02521 -0.08825 -0.14195 0.02061 0.12904 -0.12021 -0.05042 -0.04609 -0.16286 -0.35109 -0.27266

10-7 0 0.04105 0.14372 0.00792 -0.12290 -0.21016 0.19576 0.08211 -0.33359 -0.41589 -0.26349 -0.32699

9-10 0 -0.03081 -0.10787 -0.09472 0.05672 0.15773 -0.14692 -0.06162 0.47612 -0.31158 -0.13439 -0.20822

10-11 0 -0.00558 -0.01954 0.04730 0.03606 0.02857 -0.02661 -0.01116 -0.07766 -0.14849 0.21679

10-12 0 0.00466 0.01632 -0.03951 -0.03012 -0.02386 0.02223 0.00932 0.06487 0.12404 -0.18109 -0.47062

11-12 0 -0.00466 -0.01632 0.03951 0.03012 0.02386 -0.02223 -0.00932 -0.06487 -0.12404 0.18109

Table 5.7: D Factors (GGDFs) of the 12-Bus

Line i -j D Factors

33

D ij ,1 D ij ,2 D ij ,3 D ij ,4 D ij ,5 D

1-2 0.37000 -0.48055 -0.10681 0.11678 0.15996 0.18876

1-6 0.39314 0.31553 0.12144 -0.05178 -0.14644 -0.20957

1-7 0.22547 0.15363 -0.02603 -0.07639 -0.02492 0.00942

2-8 0.23806 0.38751 -0.23874 -0.01515 0.02803 0.05683

3-7 0.10613 0.25558 0.62933 -0.14708 -0.10390 -0.07510

8-3 -0.10613 -0.25558 0.37067 0.14708 0.10390 0.07510

5-4 -0.04424 -0.06583 -0.11982 -0.25249 0.33885 0.06628

7-4 -0.07925 -0.11581 -0.20723 0.48374 0.25827 0.10788

11-4 0.03501 0.04998 0.08741 0.26377 0.08059 -0.04160

6-5 -0.10968 -0.08809 -0.03410 0.09857 0.50722 -0.22020

6-9 0.10566 0.07484 -0.00221 0.01093 0.16237 0.26338

6-11 0.07666 0.05145 -0.01159 -0.06530 0.09727 0.20570

10-7 0.09843 0.13948 0.24215 0.10635 -0.02447 -0.11173

9-10 0.01418 -0.01663 -0.09368 -0.08054 0.07090 0.17191

10-11 -0.00764 -0.01322 -0.02718 0.03965 0.02842 0.02092

10-12 0.03021 0.03487 0.04653 -0.00930 0.00008 0.00634

11-12 0.02696 0.02230 0.01064 0.06647 0.05709 0.05083

Table 5.8: Transmission Usage Allocation using GGDFs

Line i-j P ijG1

P ijG2

P ijG3

P ijG4

P ijG5

P

1-2 181.1849 -163.6236 -37.3826 34.3004 95.9754 37.7520

1-6 192.5195 107.4355 42.5052 -15.2091 -87.8612 -41.9140

34

1-7 110.4111 52.3093 -9.1098 -22.4373 -14.9493 1.8836

2-8 116.5787 131.9450 -83.5587 -4.4505 16.8164 11.3657

3-7 51.9725 87.0235 220.2652 -43.2015 -62.3426 -15.0207

8-3 -51.9725 -87.0235 129.7348 43.2015 62.3426 15.0207

5-4 -21.6638 -22.4142 -41.9374 -74.1600 203.3129 13.2558

7-4 -38.8103 -39.4322 -72.5303 142.0849 154.9605 21.5751

11-4 17.1465 17.0180 30.5929 77.4751 48.3524 -8.3194

6-5 -53.7100 -29.9941 -11.9347 28.9505 304.3349 -44.0398

6-9 51.7394 25.4839 -0.7733 3.2109 97.4230 52.6764

6-11 37.5387 17.5177 -4.0578 -19.1786 58.3621 41.1403

10-7 48.1995 47.4923 84.7530 31.2366 -14.6836 -22.3460

9-10 6.9458 -5.6616 -32.7887 -23.6565 42.5394 34.3819

10-11 -3.7432 -4.5029 -9.5135 11.6466 17.0506 4.1848

10-12 14.7919 11.8723 16.2843 -2.7322 0.0496 1.2685

11-12 13.2041 7.5937 3.7253 19.5242 34.2526 10.1656

Table 5.9: Allocation of Transmission Charges using GGDFs Method for 12-Bus System

Line i-j Line Cost $GGDFs Method

C kL kMW 1’k C kL kMW 2’k C kL kMW 3’k C kL kMW 4’k C kL kMW 5’k C k L

1-2 60 10871 -9817 -2243 2058 5759

1-6 140 26953 15041 5951 -2129 -12301

1-7 240 26499 12554 -2186 -5385 -3588

2-8 60 6995 7917 -5014 -267 1009

3-7 76 3950 6614 16740 -3283 -4738

8-3 90 -4678 -7832 11676 3888 5611

35

5-4 120 -2600 -2690 -5032 -8899 24398

7-4 56 -2173 -2208 -4062 7957 8678

11-4 120 2058 2042 3671 9297 5802

6-5 80 -4297 -2400 -955 2316 24347

6-9 60 3104 1529 -46 193 5845

6-11 100 3754 1752 -406 -1918 583610-7 80 3856 3799 6780 2499 -1175

9-10 40 278 -226 -1312 -946 1702

10-11 100 -374 -450 -951 1165 1705

10-12 68 1006 807 1107 -186 3

11-12 50 660 380 186 976 1713

Total 1540 104106 78058 68318 53362 114210 30531

Σ C k L k MW t’k 448585

T c,t 357.3977 267.9744 234.5368 183.1927 392.0849 104.8134

Cost($/MW) 0.7298 0.7870 0.6701 0.6237 0.6535 0.5241

5.3 Cost Allocation Using Bialek’s Tracing Method:

Table 5.10: Upstream Distribution matrix (Au)

1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

-0.3171 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 -0.5497 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 1.0000 -0.0706 0.0000 -0.3045 0.0000 0.0000 0.0000 -1.2125

0.0000 0.0000 0.0000 0.0000 1.0000 -0.4691 0.0000 0.0000 0.0000 0.0000 0.0000

36

-0.4273 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 0.0000

-0.2555 0.0000 -0.5307 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 -7.7959 0.0000

0.0000 -0.3921 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 -0.5689 0.0000 0.0000 1.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.0965 1.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 -0.3274 0.0000 0.0000 0.0000 -0.6472 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.8764 -0.5940

Table 5.11: Inverse of (Au)

1 0 0 0 0 0 0 0 0 0 0

0.317118 1 0 0 0 0 0 0 0 0 0

0.068339 0.215498 1 0 0 0 0 0.549659 0 0 0

0.346717 0.034817 0.161567 1 0.07057 0.603443 0.30446 0.088807 0.304807 3.158275 1.212527

0.200477 0 0 0 1 0.469134 0 0 0 0 0

0.427334 0 0 0 0 1 0 0 0 0 0

0.474712 0.114358 0.530667 0 0 0.428001 1 0.291686 0.752382 7.795852 0

0.124329 0.392058 0 0 0 0 0 1 0 0 0

0.243094 0 0 0 0 0.568862 0 0 1 0 0

0.023461 0 0 0 0 0.054901 0 0 0.096511 1 0

0.15508 0 0 0 0 0.362901 0 0 0.062462 0.647203 1

37

0.136134 0 0 0 0 0.318565 0 0 0.218193 2.26082 0.593959

Nodal generation vector (P G) is as follows:

Bus1 489.694

2 40.49

3 350

4 293.725 250

6 30

7 350

8 300

9 208

10 17011 210

12 130

Bus1 489.694

2 340.49

3 350

4 293.72

38

5 6006 200

7 0

8 0

9 010 0

11 0

12 0

And unknown gross power vector (Pg) is as follows:

Table 5.12: Transmission Usage Allocation of Bialek’s Upstream Algorithm.

Line No. From Bus To Bus P ijG1

P ijG2

P ijG3

P ijG4

P ijG5

1 1 2 155.2910 0.0000 0.0000 0.0000 0.0000

2 1 6 209.2630 0.0000 0.0000 0.0000 0.0000

3 1 7 125.1400 0.0000 0.0000 0.0000 0.0000

4 2 8 60.8831 133.4919 0.0000 0.0000 0.0000

5 3 7 17.7588 38.9377 185.7335 0.0000 0.0000

6 8 3 33.4650 73.3750 0.0000 0.0000 0.0000

7 5 4 6.9280 0.0000 0.0000 0.0000 42.3417

8 7 4 70.7758 11.8550 56.5484 0.0000 0.0000 26.0618

39

9 11 4 92.0815 0.0000 0.0000 0.0000 0.0000 88.0055

10 6 5 98.1723 0.0000 0.0000 0.0000 0.0000 93.8267

11 6 9 119.0417 0.0000 0.0000 0.0000 0.0000 113.7723

12 6 11 68.5062 0.0000 0.0000 0.0000 0.0000 65.4738

13 10 7 89.5648 0.0000 0.0000 0.0000 0.0000 85.6002

14 9 10 11.4888 0.0000 0.0000 0.0000 0.0000 10.9802

15 10 11 7.4356 0.0000 0.0000 0.0000 0.0000

16 10 12 21.5576 0.0000 0.0000 0.0000 0.0000 20.6034

17 11 12 45.1063 0.0000 0.0000 0.0000 0.0000 43.1097

Table 5.13: Allocation of Transmission Charges using Bialek’s Methods.

Line i-j Line Cost $ C k L kMW 1’k C k L kMW 2’k C k L kMW 3’k C kL kMW 4’k C kL kMW 5’k C kL

1-2 60 9317.46 0 0 0 0

1-6 140 29296.82 0 0 0 0

1-7 240 30033.6 0 0 0 0

2-8 60 3652.986 8009.514 0 0 0

3-7 76 1349.665 2959.267 14115.75 0 0

8-3 90 3011.846 6603.754 0 0 0

5-4 120 831.3567 0 0 0 5081.006

7-4 56 3963.445 663.8785 3166.71 0 0 1459.462

11-4 120 11049.78 0 0 0 0 10560.66

6-5 80 7853.783 0 0 0 0 7506.137

6-9 60 7142.501 0 0 0 0 6826.339

40

6-11 100 6850.621 0 0 0 0 6547.379

10-7 80 7165.183 0 0 0 0 6848.017

9-10 40 459.551 0 0 0 0 439.209

10-11 100 743.5567 0 0 0 0 710.643310-12 68 1465.918 0 0 0 0 1401.03

11-12 50 2255.316 0 0 0 0 2155.484

Total 1540 126443.4 18236.41 17282.46 0 5081.006 44454.36

Σ C kL kMW t’k 211497.6272

T c,t 920.6856 132.7867 125.8406 0 36.9968 323.6902

Cost ($/MW) 1.88 0.39 0.36 0 0.06166 1.6184

5.4: Comparison of Bialek & GGDFs Method for 12-Bus system.

G1 G2 G3 G4 G5

Bialek Tracing method: Total cost = 211497.6272

Each Transaction Cost ($) T c,t 920.6856 132.7867 125.8406 0 36.9968 323.6902

Cost($/MW) Cost ($/MW) 1.88 0.39 0.36 0 0.06166

GGDF method : Total cost = 448585

Each Transaction Cost ($) T c,t 357.3977 267.9744 234.5368 183.1927 392.0849 104.8134Cost($/MW) Cost($/MW) 0.7298 0.7870 0.6701 0.6237 0.6535

41

42

5.5 ConclusionIn a restructured power environment, the transmission network is the key mechanism

for generators to compete, supplying large users and distribution companies. One of the main

objectives in electric industry’s restructuring is to bring fairness and open access to the

transmission network. For 12-Bus test system, the cost comparison table 5.14 shows that

overall transmission cost of the system is less in Bialek’s method compared to GGDFs

method but per unit MW cost is less in GGDFs method.

Bialek’s method can produce zero charges for some users. Where the Distribution

Factors tracing method charges all users of the system, since all users utilize all transmission

lines no matter how far they are located. However, it is very sensitive to system operating

conditions and can produce relative different results for different operating points.

Bialek tracing method is the best way of transmission pricing among all Pricing

methods. Different results were derived because each tracing method is based on different

principle. Moreover, it is not always clear which pricing method suits better a transmission

network; it depends mostly on the generation and load location as well as the network

topology itself. However, these pricing methods are able to full fill transmission pricing

objectives: economic efficiency, non-discrimination, transparency and cost coverage and can

be also applied to large power systems.

Future work• To determine the embedded transmission cost allocation using Bialek & Distribution

factor method on Gujarat Bus power system.

• Compare the result for Gujarat Bus power system

43

REFERENCES

BOOKS

i. Mohammad Shadehpour, Hatim Yamin, Zuyi Li, “Market Operations in Electric

Power Systems Forecasting, Scheduling And Risk Managements” Published by A John

Wiley & Sons Publication, pp. 372-393.

ii. Daniel kirschen, Goran Strabac “Fundamentals of Power System Economics”

Published by John Willey & Sons Ltd.

iii. Kankar bhattacharya, Math H.J.Bollen,Jaap E. Daalder “Operation of Restructured

Power System” Kluwer Acasemic Publishers

PAPERS

1. S, A. Khapade ,Transmission Pricing in a Restructured Electricity Market”, IIT

Mumbai ,pp-1-11

2. A.R. Abhyankar and S.A. Khaparde,” Introduction to Deregulation in Power

Industry”, IIT, Mumbai, pp.1-28

3. C. W. Yu, A. K. David , “Pricing Transmission Services in the Context of Industry

Deregulation” IEEE Transaction on Power Systems, Vol 12,No.1, February 1997

4. M. Murli, M. Sailaja Kumari and M. Sdyulu “A Comparison of Embedded Cost based

Transmission Pricing Methods” IEEE 2011

5. D. Shirmohammadi, Xisto Vieira, Boris Gorenstin, Mario V.P.Pereira, “Some

fundamental technical concepts about cost based transmission pricing”, IEEE

Transactions on Power Systems, Vol. 11, No. 2,May 1996

6. J. W. Bialek , “Tracing Flow of Electricity” IEE Proceedings-generation,

Transmission and Distribution, Vol. 143, No 4, July 1996,pp 313-320

7. D.Shirmohammadi, C.Rajagoapalan, E.R.Alward and C.L.Thomas, “cost of

transmission transactions: An introduction”, IEEE Transactions on Power systems,

Nov.’91, pp.1546-1556.

8. Satyavir Singh “ Power Tracing in Deregulated Power System IEEE 14 bus case”

IJCTA/May June 2012,Vol 3(3),pg. 887-894,ISSSN:2229-6093

9. The Indian electricity Act, 2003, (No.36 of 2003), “The Gazette of India”, pp.1-84.

10. Stefan Kilyeni, Oana Pop, Titus Slavici, Cristian Craciun, Petru Andea, Dumitru

Mnerie “Transmission Cost Allocation Using the Distribution Factors Method”

published in IEEE 2010, pp. 1093-109

APPENDIX : MATCODE PROGRAM LIST

44

------------------------------------------------------------------------------Bialek.m

------------------------------------------------------------------------------

% This is the main program for transmission embedded cost allocation using Bialek tracing method . As the cost is calculated from the generator side, upstream distribution algoritm is used.

clear all % clear the content in command window clc

Sb=[1 1 1 2 3 8 5 7 11 6 6 6 10 9 10 10 11]; % sending bus Eb=[2 6 7 8 7 3 4 4 4 5 9 11 7 10 11 12 12]; % receiving bus Pij=[155.291 209.263 125.140 194.375 242.430 106.840 55.891 165.241 180.087 191.999 232.814 133.980 175.165 22.469 14.542 42.161 88.216]; % actual power flow between i &

j,neglecting losses Pj=[489.694 340.490 350 293.72 600 200 0 0 0 0 0 0]; % real generation at the 12-bus PJ=Pj'; % coverting row matrix Pj to colume matrix PJ xlswrite('bialek12',PJ,'dm','O17'); % writes array PJ to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'O17'

m=12; % total number of buses n=17; % total number of lines ng=6; % total number of generator buses

% creating upstream distribution matrix Au

Au(1:m,1:m)=0; %defining dimension of Au

for i=1:n

z=0; for j=1:n if Eb(j)==Sb(i) % this loop checks for the same bus the incoming flow towards the bus z=z+Pij(j);

end end z=z+Pj(Sb(i)); %total power injected into the bus i.e line flow + generation at the bus Au(Eb(i),Sb(i))=-Pij(i)/z; % formation of upstream distribution matrix Au

for j=1:m if i==j % for i=j, Au = 1 otherwise 0 Au(i,j)=1 end end

end % Au is formed xlswrite('bialek12',Au,'dm','A1'); % writes array Au to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'A1' Ai(1:m,1:m)=inv(Au) % finding inverse of Au xlswrite('bialek12',Ai,'dm','A17'); % writes array Ai to the 'dm' worksheet in Excel file

filename 'bialek12', starting at cell 'A17'

45

Pgi=inv(Au)*Pj' % gross nodal power flow xlswrite('bialek12',Pgi,'dm','N1'); % writes array Pgi to the 'dm' worksheet in Excel

file filename 'bialek12', starting at cell 'O17'

% multiplying Au * real generation, so that contribution of the i generator to the j nodal

power is obtained S(m)=0; for i=1:m for j=i:m S(j,i)=Ai(j,i) * Pj(i); % calculation of individual generator contribution to

gross nodal power flow end end

% obtaining 6*6 matrix of line flow by repeating the colume L(m)=0; for i=1:m for k=1:n

L(k,i)=Pij(k); end end

C(m)=0; for i=1:m for k=1:n

C(k,i)=S(Sb(k),i)/Pgi(Sb(k)); % dividing Au*real generation with gross nodal power flow end end

% contribution of individual generators in transmission line flows is found out using below equation. Pijg=C.*L xlswrite('bialek12',Pijg,'dm','Q17'); % writes array Pijg to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'Q17'

L=[60 140 240 60 76 90 120 56 120 80 60 100 80 40 100 68 50]; %length of line in km

% adding the total length of the line sumL=0;

for i=1:n sumL=sumL+L(i); end % cost of each line for supplying power by the individual generator for i=1:n

for j=1:m R(i,j)=L(i)*abs(Pijg(i,j)); end end

46

xlswrite('bialek12',R,'dm','A34'); % writes array R to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'A34'

% adding the total cost for each generator & the total cost sumC=0; for i=1:n for j=1:m

if Pgi(j)>0 sumC=sumC+R(i,j); end end end

% adding the total cost for each generator & the total costfor i=1:m for i=1:m sumT=0; for j=1:n

sumT=sumT+R(j,i); end T(i)=sumT end

xlswrite('bialek12',T,'kkk','A51'); % writes array T to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'A51' % adding the total cost for each generator & the total cost y=0; for i=1:m

y=y+T(i); end xlswrite('bialek12',y,'kkk','A53'); % writes array y to the 'dm' worksheet in Excel file filename 'bialek12', starting at cell 'A53'

------------------------------------------------------------------------------Distribution factor.m

------------------------------------------------------------------------------% This is the main program for transmission embedded cost allocation using Distribution

Factor method % Transmission usage contributions of each generator based on GGDFs is done using matlab programming. clear all

clc sb=[1 1 1 2 3 3 5 4 4 5 6 6 7 9 11 10 11]; % sending bus

47

eb=[2 6 7 8 7 8 4 7 11 6 9 11 10 10 10 12 12]; % receiving bus r=[.00415 .00969 .01666 .00415 .00526 .00623 .0083 .00387 .0083 .00554 .00415 .00692 .

00554 .00277 .00692 .00484 .00346]; % resistance of lines x=[.025 .05838 .1 .025 .03169 .03752 .05 .02335 .05 .03335 .025 0.0417 .03335 .01667 . 0417 .02912 0.02080]; % reactance of line n=17; % number of lines

nb=12; % number of buses ng=6; % number of generator buses

% susceptance matrix formation from the system [b(1:nb,1:nb)]=0;

for i=1:n bse(i)=1/x(i); M=sb(i); N=eb(i); b(M,M)=b(M,M)+bse(i);

b(N,N)=b(N,N)+bse(i); b(M,N)=-bse(i); b(N,M)=b(M,N); end

B=[b(2:nb,2:nb)]; % deleting 1 row & 1 colume from the susceptance matrix ,corresponding to slack bus. Bi=inv(B); % inversing the susceptance matrix

% Create matrix from Bi,with addition of zero entries in 1 R & 1 C [X(1:nb,1:nb)]=0; for i=2:nb for j=2:nb X(i,j)=Bi(i-1,j-1)

end end

% forming 17*17 longitudinal susceptance matrix(Bl) with diagonal entries

[Bl(1:n,1:n)]=0;

for i=1:n Bl(i,i)=1/x(i); end

% the expression of A Factor for the network element jk, corresponding to % the change of generated power in bus i for i=1:nb for j=1:n

[A(j,i)]=(Bl(j,j))*(X(sb(j),i)-X(eb(j),i)); end end xlswrite('GGDF',A,'DDD','A1'); % writes array A to the 'DDD' worksheet in Excel file filename 'GGDF', starting at cell 'A1'

Pi=[489.694;40.490;350;293.720;250;-30;-350;-300;-208;-170;-210;-130]; Pgi=[489.694 340.490 350 293.720 600 200 0 0 0 0 0 0];

48

% Line flow Pl=A*Pi

sum=0; for i=1:nb sum=sum+Pgi(i); end

D(1:n,1:nb)=0; Pijg(1:n,1:nb)=0;

for i=1:n for j=1:nb if Pgi(j)>0 [D(i,j)]=((Pl(i)-((A(i,1)*Pgi(1))+(A(i,2)*Pgi(2))+(A(i,3)*Pgi(3))+(A(i,4)*Pgi(4))+ (A(i,5)*Pgi(5))+(A(i,6)*Pgi(6))))/sum)+A(i,j);

Pijg(i,j)=D(i,j)*Pgi(j); end end end xlswrite('GGDF',D,'DDD','A19'); % writes array D to the 'DDD' worksheet in Excel file

filename 'GGDF', starting at cell 'A19' xlswrite('GGDF',Pijg,'DDD','O1'); % writes array Pijg to the 'DDD' worksheet in Excel file filename 'GGDF', starting at cell 'O1' L=[60 140 240 60 76 90 120 56 120 80 60 100 80 40 100 68 50];

R=L*D;

for i=1:n y(i)=abs(Pl(i))*L(i); end

sumL=0; for i=1:n sumL=sumL+L(i);

end

for i=1:n for j=1:nb

R(i,j)=L(i)*(Pijg(i,j)); end end xlswrite('GGDF',R,'DDD','O19'); % writes array R to the 'DDD' worksheet in Excel file filename 'GGDF', starting at cell 'O19'

sumC=0; for i=1:n for j=1:nb if Pgi(j)>0

sumC=sumC+R(i,j);

end

49

end end

50

51