37201858 Transmission Network Cost Allocation Using Bus Impedance Mat

1

A DISSERTATION

SUBMITTED TO THE FACULTY OF ENGINEERING

OF

NATIONAL INSTITUTE OF TECHNOLOGY, WARANGAL (A.P)

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE AWARD OF THE DEGREE OF

MASTER OF TECHNOLOGY

IN

POWER SYSTEMS ENGINEERING

BY

D. Veera Nageswara Rao(061725)Under the esteemed guidance of

Prof.M.Sydulu

DEPARTMENT OF ELECTRICAL ENGINEERING

NATIONAL INSTITUTE OF TECHNOLOGY

WARANGAL-506 004(A.P)MAY-2008

TRANSMISSION NETWORK

COST ALLOCATION USING BUS IMPEDANCE

MATRIX (ZBUS)

2

DEPARTMENT OF ELECTRICAL ENGINEERINGNATIONAL INSTITUTE OF TECHNOLOGY

WARANGAL-506004

CERTIFICATE

This is to certify that the dissertation work entitled

“Transmission Network Cost Allocation using Bus Impedance

Matrix(Zbus is bonafide record of the work doneby D.Veera nageswara rao

(Roll No. 061725) and submitted in partial fulfillment of the

requirements for the award of degree of Master of Technology in

Electrical Engineering with specialization in Power Systems

Engineering, from National Institute of Technology, Warangal.

Dr. M. Sydulu Dr.D.M.Vinod Kumar

Professor (Thesis Advisor) Professor and Head of the Department

Head Power System Section Dept. of Electrical Engineering

Dept. of Electrical Engineering National Institute of Technology

National Institute of Technology Warangal.

Warangal.

3

ACKNOWLEDGEMENT

I write this acknowledgement with great honor, pride and pleasure to pay my respects to

all who enabled me either directly or indirectly in reaching this stage.

I am indebted forever to my guide Dr. M. Sydulu, Professor, Department of Electrical

Engineering, for his suggestions, guidance and inspiration in carrying out this project

work.

I express my profound thanks to Dr.D.M.Vinod Kumar, Professor and Head of Electrical

Engineering Department, for providing me with all the facilities to carry out this project

work.

I take this opportunity to convey my sincere thanks to all my class mates who have

directly and indirectly contributed for the successful completion of this work.

D.VEERA NAGESWARA RAO

4

SYNOPSIS

With the introduction of restructuring into the electric power industry, the price of

electricity has became the focus of all activities in the power market. In general, the price

of a commodity is determined by supply and demand.

In the present open access restructured power system market, it is necessary to

develop an appropriate pricing scheme that can provide the useful economic information

to market participants, such as generation, transmission companies and customers.

However, accurately estimating and allocating the transmission cost in the transmission

pricing scheme is a challenging task although many methods have been proposed.

The purpose of the methodology is to allocate the cost pertaining to the

transmission lines of the network to all the generators and demands. Once a load flow

solution is available, the proposed method determines how line flows depend on nodal

currents. This result is then used to allocate network costs to generators and demands.

This work addresses the problem of allocating the cost of the transmission

network to generators and demands. This work proposes three methods using bus

impedance matrix Zbus. The three techniques are Zbus method , Zbusavg method and a

newly proposed technique. The new method is very effective in transmission cost

allocation A physically-based network usage procedure is proposed..

The techniques presented in this work is related to the allocation of the cost of

transmission losses based on the Zbus. It should be emphasized that all transmission lines

must be modeled including actual shunt admittances. Doing so, the impedance matrix

presents an appropriate numerical behavior.A salient feature of the proposed techniques

are its embedded proximity effect, which implies that a generator/demand uses mostly the

lines electrically close to it. This is not artificially imposed but a result of relying on

circuit theory.

5

The proposed method provides a methodology to apportion the cost of the

transmission network to generators and demands that use it. How to allocate the cost of

the transmission network is an open research issue as available techniques embody

important simplifying assumptions, which may render controversial results. This work

contributes to seek an appropriate solution to this allocation problem using an usage-

based procedure that relies on circuit theory.

This new procedure exhibits desirable apportioning properties and is easy to

implement and understand. Case studies on 4-bus system and IEEE 24-bus system are

used to illustrate the working of the proposed techniques. Relevant and important

conclusions are finally drawn

6

CONTENTSNOMENCLATURE

LIST OF TABLES

LIST OF FIGURES

Page NoCHAPTER 1: INTRODUCTION 1

1.1 Deregulation 11.2 Independent System Operator (ISO) 21.3 Open Access Same time Information System (OASIS) 31.4 Transmission Use of System Tariffs (TUSTs) 41.5 power wheeling costs 61.6 Literature Review 71.7 Contributions 81.8 Outlines of the Thesis 9

CHAPTER 2: TRANSMISSION NETWORK COST ALLOCATION

USING ZBUS TECHNIQUE 10

2.1 Problem Statement 102.2 Background 102.3 Transmission Cost Allocation 132.4 Algorithm For Transmission Network Cost Allocation Using Zbus Technique 152.5 Case study – 4 bus system 18 2.5.1 step by step results 192.6 Conclusions 22

CHAPTER 3: TRANSMISSION NETWORK COST ALLOCATION

USING avgbusZ TECHNIQUE 23

3.1 Problem Statement 233.2 Background 233.3 Transmission Cost Allocation 263.4 Effect of Flow Directions 283.5 Algorithm For Transmission Network Cost Allocation Using

avgbusZ Technique 29

7

3.6 Case study – 4 bus system 343.6. 5.1 step by step results 35

3.7 Conclusions 42

CHAPTER 4: A NEW APPROACH FOR TRANSMISSION

NETWORK COST ALLOCATION USING

MODIFIED avgbusZ TECHNIQUE

4.1 Problem Statement 434.2 Background 434.3 Transmission Cost Allocation 464.4 Algorithm for Transmission network cost allocation Using modified avg

busZ technique (newly proposing technique) 484.5 Case Study - 4 - Bus System 53

4.5.1 Step By Step Results – 4 bus system 544.6 Conclusions 60

CHAPTER 5: RESULTS-IEEE RTS 24 BUS SYSTEM AND

CONCLUSIONS 61

5.1 Zbus technique Results 615.2 avg

busZ technique results 685.3 Modified avg

busZ technique results 755.4 comparison of Zbus based techniques 825.5 conclusions 84

APPENDIX 85

A.1 4-Bus System Data 85A.2 IEEE 24- Bus Reliability Test System 86

REFERENCES 89

8

NOMENCLATURE

jkC -Cost of line jk ($/h)

Ii -Nodal current (A)

Ijk - Current through the line jk (A)

n -Number of buses

PGi - Active power consumed by the generator located at bus i (W)

PDi - Active power consumed by the load located at bus i (W)

Pjk - Active power flow through line jk (W)

Sjk - Complex power flow through line jk calculated at bus j (VA)

Vj - Nodal voltage at bus j (V)

yjk - Series admittance of the -equivalent circuit of line jk (S)shjky - Shunt admittance of the - equivalent circuit of line jk (S)

Zbus - Impedance matrix (ohm)

Zij - Element ij of the impedance matrix (ohm)ijka - Electrical distance between bus i and line jk (adimensional)

DiC - Total transmission cost allocated to the load located at bus i ($/h)GiC - Total transmission cost allocated to the generator located at bus i ($/h)DijkC - Transmission cost allocated to the generator located at bus i ($/h)

GijkC - Transmission cost allocated to the generator located at bus i ($/h)

ijkP - Active power flow through the line jk associated with the nodal current i(W)

rjk - Cost rate for line jk ($/W & h)GijkU - Usage of line jk allocated to the generator located at bus (W).

DijkU - Usage of line jk allocated to the generator located at bus (W).

ijkU - Usage of line associated with nodal current (W).

Ujk - Usage of line jk (W).

9

LIST OF TABLESPage No

Table 2.1 Converged Voltages of Zbus technique 19

Table 2.2 Bus Currents of Zbus technique 19

Table 2.3 Powerflow Contributions P(i,k)in Pjk>0 direction of Zbus technique 19

Table 2.4 Powerflow Usage Contributions U(k,i)in Pjk>0 direction of Zbus technique 20

Table 2.5 Powerflow Usage of Line usage(k)in Pjk>0 direction of Zbus technique 20

Table 2.6 Powerflow Contributions Ug(i,k)in Pjk>0 direction of Zbus technique 20

Table 2.7 Powerflow Contributions Ud(i,k)in Pjk>0 direction of Zbus technique 20

Table 2.8 Generator Cost Contributions cg(k,i)in Pjk>0 direction of Zbus technique 21

Table 2.9 Load Cost Contributions cd(k,i) in Pjk>0 direction of Zbus technique 21

Table 2.10 total generation and load costs and Total cost for all the buses in Pjk>0

direction of Zbus technique 21

Table 3.1 Converged Voltages of avgbusZ technique 35

Table 3.2 Bus Currents of avgbusZ technique 35

Table 3.3 Powerflow Contributions P(i,k)in Pjk>0 direction of avgbusZ technique 35

Table 3.4 Powerflow Usage Contributions U(k,i)in Pjk>0 direction of avgbusZ technique 36

Table 3.5 Powerflow Usage of Line usage(k)in Pjk>0 direction of avgbusZ technique 36

Table 3.6 Powerflow Contributions Ug(i,k)in Pjk>0 direction of avgbusZ technique 36

Table 3.7 Powerflow Contributions Ud(i,k)in Pjk>0 direction of avgbusZ technique 36

Table 3.8 Generator Cost Contributions cg(k,i)in Pjk>0 direction of avgbusZ technique 37

Table 3.9 Load Cost Contributions cd(k,i) in Pjk>0 direction of avgbusZ technique 37

Table3.10 Total generation and load costs and Total cost for all the buses in Pjk>0

direction of avgbusZ technique 37

Table3.11 Powerflow Contributions P1(k,i)in Pjk<0 direction of avgbusZ technique 38

Table3.12 Powerflow Usage Contributions U1(k,i)in Pjk<0direction of avgbusZ technique 38

Table3.13 Powerflow Usage Of Line usage1(k)in Pjk<0 direction of avgbusZ technique 38

10

Table3.14 Powerflow Contributions Ug1(i,k)in Pjk<0 direction of avgbusZ technique 38

Table3.15 Powerflow Contributions Ud1(i,k) in Pjk<0 direction of avgbusZ technique 39

Table3.16 Generator Cost Contributions cg1(k,i) in Pjk<0 direction of avgbusZ technique 39

Table3.17 Load Cost Contributions cd1(k,i) in Pjk<0 direction of avgbusZ technique 39

Table3.18 Total generation and load costs and Total cost1 for all the buses in Pjk<0

direction of avgbusZ technique 39

Table3.19 Average Generator Cost Contributions cgavg(k,i) of avgbusZ technique 40

Table3.20 Average Load Cost Contributions cdavg(k,i) of avgbusZ technique 40

Table3.21 Total average generation and load costs and Total avgcost for all the buses

of avgbusZ technique 40

Table 4.1 Converged voltages of modified avgbusZ technique 54

Table 4.2 Bus Currents of modified avgbusZ technique 54

Table 4.3 Powerflow Contributions S1(i,k) in Pjk>0 direction of modified avgbusZ

technique 54


technique 54


technique 55

Table 4.6 Powerflow Contributions S4(i,k) In Pjk>0 Direction of modified avgbusZ

technique 55

Table 4.7 Powerflow Contributions Ug(i,k) in Pjk>0 direction of modified avgbusZ

technique 55

Table 4.8 Powerflow Contributions Ud(i,k) in Pjk>0 direction of modified avgbusZ

technique 55

Table 4.9 Generator Cost Contributions cg(k,i) in Pjk>0 direction of modified avgbusZ

technique 56

Table 4.10 Load Cost Contributions cd(k,i) in Pjk>0 direction of modified avgbusZ

11

technique 56

Table 4.11 Total generation and load costs and Total cost for all the buses of modifiedavgbusZ technique 56

Table 4.12 Powerflow Contributions S11(i,k) in Pjk<0 direction of modified avgbusZ

technique 57


technique 57


technique 57


technique 58

Table 4.16 Powerflow Contributions Ug1(i,k)IN Pjk<0 direction of modified avgbusZ

technique 58

Table 4.17 Powerflow Contributions Ud1(i,k)IN Pjk<0 direction of modified avgbusZ

technique 58

Table 4.18 Generator Cost Contributions cg1(k,i) in Pjk<0 direction of modified avgbusZ

technique 58

Table 4.19 Load Cost Contributions cd1(k,i) in Pjk<0 direction of modified avgbusZ

technique 58

Table 4.20 Total generation and load costs and Total cost for all the buses

in Pjk <0 direction of modified avgbusZ technique 59

Table 4.21 Average Generator Cost Contributions cgavg(k,i) of modified avgbusZ

technique 59

Table 4.22 Average Load Cost Contributions cdavg(k,i) of modifiedavgbusZ technique 59

Table 4.23 Total average generation and load costs and Total avgcost for all the buses

of modified avgbusZ technique 59

Table 5.1 Generator Cost Contributions Cg(k,i) in Pjk>0 Direction of Zbus technique 61

Table 5.2 Generator Cost Contributions Cg(k,i) in Pjk>0 Direction of Zbus technique 62

12

Table 5.3 Load Cost Contributions Cd(k,i) in Pjk>0 Direction of Zbus technique 63




Table 5.7 Cost For Individual Generators/Loads And Total Cost in Pjk>0 Direction of

Zbus technique 67

Table 5.8 Average Generator Cost Contributions Cgavg(k,i) of avgbusZ technique 68

Table 5.9 Average Generator Cost Contributions Cgavg(k,i ) of avgbusZ technique 69

Table 5.10 Average Load Cost Contributions Cdavg(k,i) of avgbusZ technique 70




Table 5.14 Average Cost For Individual Generators/Loads and Total Avg Cost of avgbusZ

technique 74


technique 75


technique 76

Table 5.17 Average Load Cost Contributions cdavg(k,i) of modified avgbusZ technique 77

Table 5.18 Average Load Cost Contributions cdavg(k,i) of modifiedavgbusZ technique 78

Table 5.19 Average Load Cost Contributions Cdavg(k,i) of modified avgbusZ technique 79

Table 5.20 Average Load Cost Contributions Cdavg(k,i) of modified avgbusZ technique 80

Table 5.21 Average Cost For Individual Generators/Loads and total average cost of

modified avgbusZ technique 81

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LIST OF FIGURES Page No

Fig 1.1 Expansion in Centralized Systems 5

Fig 1.2 Expansion in Competitive Environment 5

Fig. 2.1.Equivalent circuit of line jk of Zbus technique 10

Fig. 2. 2 Four Bus System of Zbus technique 18

Fig. 3.1 Equivalent circuit of line jk of avgbusZ technique 23

Fig. 3. 2Four Bus System of avgbusZ technique 34

Fig. 4.1.Equivalent circuit of line jk of modified avgbusZ technique 43

Fig. 4. Four Bus System of modified avgbusZ technique 53

Fig A.1 IEEE 24-bus Reliability Test System 85

14

CHAPTER 1INTRODUCTION

1.1 DeregulationIn Eighties, almost all electric power utilities throughout the world were operated

with an organizational model in which one controlling authority—the utility—operated

the generation, transmission, and distribution systems located in a fixed geographic area

and it refers to as vertically integrated electric utilities(VIEU). Economists for some time

had questioned whether this monopoly organization was efficient. With the example of

the economic benefits to society resulting from the deregulation of other industries such

as telecommunications and airlines, electric utilities are also introducing privatization in

their sectors to improve efficiency. During the nineties many electrical utilities and power

network companies world wide have been forced to change their ways of doing business

from vertically integrated mechanism to open market system. This kind of process is

called as deregulation or restructuring or unbundling.

Deregulation word refers to un-bundling of electrical utility or restructuring of

electrical utility and allowing private companies to participate. The aim of deregulation is

to introduce an element of competition into electrical energy delivery and thereby allow

market forces to price energy at low rates for the customer and higher efficiency for the

suppliers and the necessity for deregulation is

(i) To provide cheaper electricity.

(ii) To offer greater choice to the customer in purchasing the economic Energy.

(iii) To give more choice of generation.

(iv) To offer better services with respect to power quality i.e. Constant voltage,

Constant frequency and uninterrupted power supply.

15

The benefits that the customers and government will get with the deregulated power

systems are

(i) Cheaper Electricity

(ii) Efficient capacity expansion planning at GENCO level, Transco level

and disco level.

(iii) Pricing is cost effective rather than a set tariff.

(iv) More choice of generation.

(v) Better service is possible.

1.2 Independent System Operator(ISO)In deregulated power systems TRANSCOs, GENCOs, DISCOs are under

different organizations. To maintain the coordination between them there will be one

system operator in all types of deregulated power system models, generally called

Independent System Operator (ISO).

In deregulated environment, all the GENCOs and DISCOs make the transactions

ahead of time, but by the time of implementations, there may be congestion in some of

the transmission lines. Hence, ISO has to relieve that congestion so that the system is

maintained in secure state.

Cost free means:

(i) Out-aging of congested lines.

(ii) Operation of transformer taps/phase shifters.

(iii) Operation of FACTS devices particularly series devices.

Non-cost-free means:

(i) Re-dispatch of generation in a manner different from the natural settling point

of the market. Some generators back down while others increase their output.

The effect of this is that generators no longer operate at equal incremental

costs.

(ii) Curtailment of loads and the exercise of (not-cost-free) load interruption

options.

16

In the deregulated power system the challenge of congestion management for the

transmission system operator (ISO) is to create a set of rules that ensure sufficient control

over producers and consumers (generators and loads) to maintain and acceptable level of

power system security and reliability in both the short term (real-time operation) and the

long term while maximizing market efficiency. The rules must be robust, because there

will be many aggressive entities seeking to exploit congestion to create market power and

increased profits for themselves at the expense of market efficiency. The rules should

also be fair in how they affect participant, and they should be transparent, that is, it

should be clear to all participants why a particular outcome has occurred.

As deregulation of the electric system becomes an important issue in many

countries, the transmission congestion management, which the ISO has to perform more

frequently, is challenging.

1.3 Open Access Same time Information System (OASIS):

Power transaction between a specific seller bus/area and a buyer bus/area can be

committed only when sufficient Available Transfer Capacity (ATC) is available for that

interface to ensure the system security. The information about the ATC is to be

continuously updated and made available to the market participants through the Internet-

based system such as Open Access Same time Information System (OASIS).

In a Deregulated Power Structure, Power producers and customers share a

common Transmission network for wheeling power from the point of generation to the

point of consumption.

17

1.4 Transmission Use of System Tariffs (TUSTs):In many countries worldwide important changes in the electric sector have

occurred, through a process whose main characteristic is the substitution of a centralized

environment, where a planning institute is responsible by the system expansion, for a

competitive environment in generation (G) and retailing. In turn, the transmission (T) and

distribution (D) sectors remain under regulation due to their characteristics as natural

monopolies. The implementation of a competitive environment in the generation area is

conceptually straightforward: agents freely decide to construct generating units and

compete for energy sales contracts with utilities and customers. The decision on plant

type and size will typically depend on investment and fuel costs, duty cycle, availability

rates etc. However, the plant sitting decision also depends on the transmission cost

associated to energy transport from generation to load centers. For obvious reasons, it is

neither feasible nor economical to build independent transmission systems for each

generation-load pair. The transmission network then becomes a service to which all

generators and customers have access and it becomes necessary to develop rules which

allow the shared use of the transmission system. This transmission service cost is

allocated among generators and consumers though transmission use of system tariffs

(TUSTs).

Therefore, TUSTs play an important role in this new environment, where they are

responsible for a fair allocation of the transmission costs among the agents as well as for

providing efficient economic signals, i.e. induce private agents to build generation

facilities at sites that will lead to the best overall use of the generation-transmission

system.

For example, Fig.1.1 depicts a centralized process of expansion, where the

planner aims at conciliating both expansion and operation planning decisions of the

system. In this figure, variable x represents the decisions on the generation projects to be

built while variable y is related to transmission investments decisions. Variables I(x) and

O(x) represent the investment and operation expenses associated with the decisions x and

y while D(x,y) represents the redispatch cost of the generating system x considering the

transmission projects y. The single node dispatch represents the optimal operation

18

without considering transmission constraints, which are strongly influenced by the

reinforcements in the grid.

GenerationExpansion

Single nodeDispatch

TransmissionExpansion

Redispatch Gen.and Transm.

+

X

MIN

Y

I(X)

D(X,Y)

O(X)

I(Y)

Fig 1.1 Expansion in Centralized Systems

GenerationExpansion

Single nodeDispatch

TransmissionExpansion

Redispatch Gen.and Transm.

+

X

MIN

Y

I(X)

D(X,Y)

O(X)

I(Y) +

MIN

T(X)

Fig 1.2 Expansion in Competitive Environment

19

In this process, all steps of the study are known and, through an analysis of investment

costs and their impacts in operation costs, the planner decides which is the optimal

planning in global terms, i.e., generation and transmission.

Figure 1.1 - Expansion in Centralized Systems Figure 1.2 – Expansion in

Competitive Environment In processes based on competitive schemes in generation,

TUSTs play a fundamental role in the expansion of system. As it can be seen in Fig. 2,

studies of transmission system expansion could be illustrated as a “black box” where

investors have access only to its results through the TUSTs. In this sense, TUSTs shall

signal the impacts of transmission costs in electric sector in a fair and efficient way and

these signals are important to induce the generation investors correctly, and to allow an

optimal expansion of the electric sector.

Given the acquired importance of TUSTs, many methods to allocate transmission

costs among network users have been discussed and developed in a worldwide context. In

general, it can be said that each method has its own advantages and disadvantages and

there is no consensus related to the most appropriate method to be adopted. However, as

a general guideline, the transmission tariff structure should be efficient – i.e. it should

induce generation investments that lead to the overall best use of the transmission system

and fair – i.e. it should not create cross-subsidies from one market agent to the other.

1.5 Power wheeling costs:In a Deregulated Power Structure, Power producers and customers share a common

Transmission network for wheeling power from the point of generation to the point of

consumption. They are given by

1. Rolled-In-Embedded Method or Postage Stamp Method:

The rolled-in method assumes that the entire transmission system is used in wheeling,

irrespective of the actual transmission facilities that carry the transaction. The cost of

wheeling as determined by this method is independent of the distance of the power

transfer.

20

2. Contract Path Method:

The second traditional method, called the contract path method, is based upon the

assumption that the power transfer is confined to flow along a specified electrically

continuous path through the wheeling company’s transmission system. Note that

changes in flows in facilities that are not within the identified path are ignored. The

embedded capital costs, correspondingly, are limited to those facilities that lie

along the assumed path.

1.6 Literature Review:A brief description of the most significant proposals reported in the technical

literature on the allocation of the cost of the transmission network among generators and

demands follows.

1.In the traditional pro rata method, both generators and loads are charged a flat

rate per megawatt-hour, disregarding their respective use of individual

transmission lines.

2.Other more elaborated methods are flow-based .

These methods estimate the usage of the lines by generators and demands and

charge them accordingly. Some flow-based methods use the proportional sharing

principle which implies that any active power flow leaving a bus is proportionally

made up of the flows entering that bus, such that Kirchhoff’s current law is

satisfied.

3.Other methods that use generation shift distribution factors , are dependent on the

selection of the slack bus and lead to controversial results.

4.The usage-based method uses the so-called equivalent bilateral exchanges (EBEs).

To build the EBEs, each demand is proportionally assigned a fraction of each

generation, and conversely, each generation is proportionally assigned a fraction

of each demand, in such a way as both Kirchhoff’s laws are satisfied.

The technique presented in this project is related to the allocation of the cost of

transmission losses based on Zbus matrix approach. It should be emphasized that all

transmission lines must be modeled to include actual shunt admittances and taps.

21

Doing so, the impedance matrix presents an appropriate behavior of all the elements of

the transmission network.

A salient feature of the proposed technique is its embedded proximity effect,

which implies that a generator/demand uses mostly the lines electrically close to it. This

is not artificially imposed but a result of relying on circuit theory.

This proximity effect does not take place if the equivalent bilateral exchanges

(EBE) principle is used, as this principle allocates the production of any

generator/demand proportionally to all loads/generators, which implies treating“close by”

and “far away” lines in same manner .the proximity effect is ignored.

Other techniques require stronger assumptions, which diminish their practical

interest. Applying the proportional sharing principle implies imposing that principle, and

using the pro-rata criterion implies disregarding altogether network locations.

Particularly, it should be noted that the proposed methodology simply relies on circuit

laws in identifying the contribution factors, while the proportional sharing technique

relies on the proportional sharing principle.

1.7 Contributions:The contributions of this project are stated below. The proposed techniques:

1) uses the contributions of the nodal currents to line power flows to apportion the

use of the lines;

2) shows a desirable proximity effect; that is, the buses electrically close to a line

retain a significant share of the cost of using that line;

3) is slack independent.

4) does not require an a priori definition of the proportion in which to split

transmission costs between generators and demands.

Specifically, the main contribution of this project is a physical-based technique to

identify how much an individual power injection “uses” the network.

22

1.8 Outlines of the Thesis:

Chapter 2 discusses the problem of transmission network cost allocation and

presents the solution methodology using Zbus. A detailed algorithm is presented and a

case study on 4 - bus system is considered and explained in detail by giving step by step

results and drawn some conclusions.

Chapter 3 covers the problem of transmission network cost allocation and

presents the solution methodology using avgbusZ technique . A detailed algorithm is

presented and a case study on 4 - bus system is considered and explained in detail by

giving step by step results and relevant conclusions are reported..

Chapter 4 presents a new technique which is based on bus impedance matrix,

discusses the problem of transmission network cost allocation and indicates the solution

methodology using modified avgbusZ technique . A detailed algorithm is presented and a

case study on 4 - bus system is considered and explained in detail by giving step by step

results. The effectiveness of the new technique is investigated and the salient features of

it are summarized.

Chapter 5 gives the results of the above three techniques performed on IEEE

RTS 24 - bus system

Finally, Appendix presents the Input data of 4- bus and IEEE RTS 24- bus systems

23

CHAPTER 2TRANSMISSION NETWORK COST ALLOCATION

USING ZBUS TECHNIQUE

2.1 Problem Statement:The methodology starts from a converged load flow solution which gives the

entire information pertaining to the network such as bus voltages, complex line flows,

slack bus power generation etc. The purpose of the methodology presented in this work is

to allocate the cost pertaining to the transmission lines of the network to all the generators

and demands. Once a load flow solution is available, the proposed method determines

how line flows depend on nodal currents. This result is then used to allocate network

costs to generators and demands.

2.2 Background:

The equivalent circuit of a line having a line with primitive admittance jky and half line

charging susceptanceshjky connected between the buses j and k is shown in Fig.2.1

[10]. jv and kv represent the nodal voltages of buses j and k respectively.

j k

+ Sjk jky +

jkI

jv shjky sh

jky kv

- -

Fig. 2.1 equivalent - circuit of line jk .

24

From the load flow solution we can write expression for the complex line flow jkS in

terms of the node voltage and the line current jkI through the line jk as

*jkS j jkV I= (2.1)

The voltage at node j in terms of the elements of bus impedance matrix Zbus and the nodal

current iI is given by ( from Vbus =Zbus Ibus )

1

n

j j i ii

V Z I=

= ∑ (2.2)

where jiZ is the element ji of Zbus and ‘n’ is the total number of buses.

Current through the line jk can be written as

( ) shjk j k jk j jkI V V y V y= − + (2.3)

Substituting (2.2) in (2.3) and rearranging

1( )

nsh

jk ji ki jk ji jk ii

I Z Z y Z y I=

= − + ∑ (2.4)

At this stage,we wish to make equ(2.4) as dependent on Pgen, Qgen, Pload and Qload of the

bus-i. This would help in building up the relevant mathematical support in identifying the

contribution of each generator and load on the line flow jk.this aspect is considered in

proposing new technique.

From the load flow analysis, the nodal current can be written as a function of active and

reactive power generations at bus i (i

genP andigenQ respectively) and the active and

reactive load demands at bus i ( iloadP and

iloadQ respectively ) as

*

( ) ( )i i i igen load gen load

ii

P P j Q QI

V− − −

= (2.5)

25

Note that the first term of the product in (2.4) is constant, as it depends only on network

parameters. Thus, (2.4) can be written as

iN

I

ijkJK IaI ∑ =

=1 (2.6)

Where

( ) shjkjijkkiji

ijk yzyzza +−= (2.7)

Observe that the magnitude of parameterijka provides a measure of the electrical

distance between bus i and line jk .

Substituting (2.6) in (2.1)

( ) ∑∑ ====

n

i iijkj

n

i iijkjjk IaVIaVS

1***

1 (2.8)

Then, the active power through line jk is

{ }∑ =ℜ=

n

i iijkjjk IaVP

1** (2.9)

or, equivalently

{ }∑ =ℜ=

n

i iijkjjk IaVP

1**

(2.10)

Note that the terms in the summation represent contribution due to each bus - Ii Thus, the

active power flow through any line can be identified as function of the nodal currents in

a direct way. Then, the active power flow through line jk due to the nodal current Ii is

( )**i

ijkj

ijk IaVP ℜ= (2.11)

26

2.3. Transmission Cost Allocation:Following (2.11), we define the usage of line jk due to nodal current as the absolute

value of the active power flow component ijkP , i.e.,

ijk

ijk PU = (2.12)

That is, we consider that both flows and counter-flows do use the line.

The total usage of line jk is theni

jk

N

ijk UU ∑ ==

1 (2.13)

Then, we proceed to allocate the use of transmission line jk to any generator and

demand. Without loss of generality, we consider at most a single generator and a single

demand at each node of the network.

Then, the usage of line jk apportioned to the generator or demand located at bus is stated

below.

If bus i contains only generation, the usage allocated to generation pertaining to line jk

isijk

Gijk UU = (2.14)

On the other hand, if bus contains only demand, the usage allocated to demand pertaining

to line jk isijk

Dijk UU = (2.15)

Else, if bus i contains both generation and demand, the usage allocated to the generation

at bus pertaining to line jk is

( )[ ] ijkDiGiGi

Gijk UPPPU += (2.16)

and the usage allocated to the demand at bus pertaining to line jk is

( )[ ] ijkDiGiDi

Dijk UPPPU += (2.17)

27

The complex power flow components through line jk due to individual power

generations and load demands have been found out. Having found the contributions of

individual generators and demands in each of the line flows and the usage of line by those

generations and demands, allocation of transmission cost among generators and demands

can be found out. Let jkC in $/h, represents the total annualized line cost including

operation, maintenance and building costs [8].

Then the per unit usage cost rate j kr can be written as

j kj k

j k

Cr

U= (2.19)

Using the per unit cost rate, we can write,GijkC , the allocated cost of line jk to the

generator ‘i' located at bus ‘i' isGi Gijk jk jkC r U= (2.20)

In the same way, we can write,DijkC , the allocated cost of line jk to the demand ‘i'

located at bus ‘i' isDi Dijk jk jkC r U= (2.21)

The total transmission network cost, GiC , allocated to generator ‘i' is the sum of the

individual cost components of each line due to that generator.

( , )

G i Gijk

j k nlineC C

∈

= ∑ (2.22)

where ‘nline’ represents the set of all transmission lines present in the system.

Similarly, the total transmission cost, DiC , allocated to the demand ‘i' is given as

( , )

D i D ijk

j k nlineC C

∈

= ∑ (2.23)

28

2.4 Algorithm For Transmission Network Cost Allocation Using

Zbus Technique

Algorithm1. (a) Read the system line data and bus data

Line data: From bus, To bus, line resistance, line reactance, half-line charging

Susceptance and off nominal tap ratio.

Bus data: Bus no, Bus itype, Pgen, Qgen, Pload, Qload, and Shunt capacitor data.

(b) Form Ybus using sparsity technique.

2. (a) k1=1 iteration count

(b) Set maxP∆ =0.0 , maxQ∆ =0.0

(c) Cal Pshed(i),Qshed(i), for i=1 to n.

Where Pshed(i) = Pgen(i)- Pload(i)

Qshed(i) = Qgen(i)- Qload(i)

(d) Calculate Pcal(i)= )cos(1

iqiqiqq

n

qi YVV θδ −∑

=

Qcal(i)= )sin(1

iqiqiqq

n

qi YVV θδ −∑

=

(e) Calculate ∆ P(i)=Pshed(i) – Pcal(i)

∆ Q(i)=Qshed(i) - Qcal(i) for i=1 to n

Set ∆ Pslack=0.0, ∆ Qslack=0.0,

(g) Calculate maxP∆ and maxQ∆ form [ ∆ p] and [ ∆ Q] vectors

(h) Is maxP∆ ≤∈ and maxQ∆ ≤∈

If yes, go to step no. 6

3. Form Jacobian elements:

(a) Initialize A[i][j]=0.0 for i=1 to 2n , j=1 to 2n

(b) Form diagonal elements Hpp, Npp, Mpp & Lpp

(c) Form off – diagonal elements: Hpq, Npq, Mpq & Lpp

29

(d) Form right hand side vector(mismatch vector)

B[i]= ∆ P[i] , B[i+n]= ∆ Q[i] for i=1 to n

(e) Modify the elements

For p=slack bus; Hpp=1e20=1020; Lpp=1e20=1020;

4. Use Gauss – Elimination method for following

[A] [ ∆ X] = [B]

Update the phase angle and voltage magnitudes i=1 to n

For itype=1 &2, calculate iii X∆+= δδ & Vi=Vi+{ ∆ X(i+n)}Vi

5. One iteration over

Advance iteration count k1=k1+1

If (k1< itermax) then goto step 2(b) else print problem is not converged in

“itermax” iterations, Stop.

6. Print problem is converged in ‘iter’no. of iterations.

a. Calculate line flows

b. Bus powers, Slack bus power.

c. Print the converged voltages, line flows and powers.

7. Form the bus impedance matrix Zbus. (Zbus is calculated using 1−busY )

8. Do for all the lines in the system, 1 to nline

A) If the active power flow direction is ‘from bus’ to ‘to bus’

a) Do for all the buses from 1 to n

i) Calculate ijka ,

GijkU Di

jkU and ijkU using the equations (2.12),(2.16),(2.17).

End of Do loop

b) Find usage allocated to the line jk

1

ni

jk jki

U U=

=∑

End of if

30

B) Do for each bus, 1 to n

a) Determine the contributions of generators and loads paying for

using the line jk , jkr , GijkC , Di

jkC using equations (2.19), (2.20) and (2.21)

b) Find the factor per unit usage cost rate rjk interchanging ‘from bus’

and ‘to bus’

jk

jkjk U

Cr =

c) Find the generation i cost contributions for using line jk

interchanging ‘from bus’ and ‘to bus’Gijkjk

Gijk UrC =

d) Find the load cost contributions for using line jk

interchanging ‘from bus’ and ‘to bus’Dijkjk

Dijk UrC =

End of bus Do loop

End of line Do loop

9. Find the cost of contribution of generator i using all the lines in the network

( , )

Gi Gijk

j k nline

C C∈

= ∑

10. Find the cost of contribution of load i using all the lines in the network

( , )

Di Dijk

j k nline

C C∈

= ∑

31

2.5 Case study – 4 bus system:

The proposed usage based technique has been illustrated with the help of a sample

four bus, 5 line system shown in Fig. 2.2 All the lines have equal per unit resistance,

reactance and half line charging susceptance of 0.01275, 0.097, 0.4611 respectively. For

the sake of simplicity either a single generator or a single load demand of 250 MW has

been taken at each bus. Finally, cost of each line, jkC is considered to be proportional

to its series reactance jkx i.e. 1000jk jkC x= × $/h[8].

250.0 MW 500 MW

Line 5

3 4

63.0 MW

Line 2 Line 3 Line 4

191.7 MW 190.0 MW

129.2 MW

Line 1

60.0 MW

1 2

261.3 MW 250.0 MW

Fig. 2.2 Four Bus System

32

2.5.1 Step By Step Results – 4 bus system:

Detailed line data and bus data are given in appendix.

The slack bus power is 261.311351 MW+j -96.154655 MVAR

The total loss =11.311357 MW

Table 2.1 Converged Voltages

E(1)=1.050000+j-0.000000

E(2)=1.048494+j0.056220

E(3)=1.038233+j-0.178619

E(4)=1.049926+j-0.121420

Table 2.2 Bus Currents

ibus(1)=2.48868+i0.915759

ibus(2)=2.34015+i0.824762

ibus(3)=-2.33872+i0.402353

ibus(4)=-2.34969+i0.27173

Table 2.3 Powerflow Contributions P(i,k)in Pjk>0 direction,equ(2.11)

Line\Bus 1 2 3 4

1 -0.3385 1.25 0 -0.3111

2 0.8486 0.5044 0.752 -0.1879

3 0.916 0.2492 -0.2488 0.3757

4 0.3385 1.25 0 0.3111

5 0.1907 0.484 0.7672 -0.8119

33

Table 2.4 Powerflow Usage Contributions U(k,i)in Pjk>0 direction,equ(2.12)

Line\Bus 1 2 3 4

1 0.3385 1.25 0 0.3111

2 0.8486 0.5044 0.752 0.1879

3 0.916 0.2492 0.2488 0.3757

4 0.3385 1.25 0 0.3111

5 0.1907 0.484 0.7672 0.8119

Table 2.5 Powerflow Usage of Line usage(k)in Pjk>0 direction,equ(2.13)

Line Usage

1 1.89966

2 2.29286

3 1.78977

4 1.89966

5 2.25381

Table 2.6 Powerflow Contributions Ug(i,k)in Pjk>0 direction,equ(2.14) to ,equ(2.17)

Bus\Line 1 2 3 4 5

1 0.339 0.849 0.916 0.339 0.191

2 1.25 0.504 0.249 1.25 0.484

3 0 0 0 0 0

4 0 0 0 0 0

Table 2.7 Powerflow Contributions Ud(i,k)in Pjk>0 direction,equ(2.14) to ,equ(2.17)

Bus\Line 1 2 3 4 5

1 0 0 0 0 0

2 0 0 0 0 0

3 0 0.752 0.249 0 0.767

4 0.311 0.188 0.376 0.311 0.812

34

Table 2.8 Generator Cost Contributions cg(k,i)in Pjk>0 direction,equ(2.20)

Line\Gen GEN-1 GEN-2

1 17.285 63.8273

2 35.8984 21.3386

3 49.6443 13.5066

4 17.285 63.8273

5 8.209 20.8313

Table 2.9 Load Cost Contributions cd(k,i) in Pjk>0 direction,equ(2.21)

Line\Load LOAD-3 LOAD-4

1 0 15.8877

2 31.8153 7.9477

3 13.4857 20.3634

4 0 15.8877

5 33.0189 34.9408

Table 2.10 total generation and load costs and Total cost for all the buses

in Pjk>0 direction,equ(2.22) and ,equ(2.23)

Bus CG CD TOTAL COST

1 128.3219 0 128.3219

2 183.331 0 183.331

3 0 78.31983 78.31983

4 0 95.02724 95.02724

Table 2.11. relationship between the line costs and reactance of the line

Line\Bus 1 2 3 4 Cjk=1000*Xjk=971 17.285 63.8273 0 15.8877 972 35.8984 21.3386 31.8153 7.9477 973 49.6443 13.5066 13.4857 20.3634 974 17.285 63.8273 0 15.8877 975 8.209 20.8313 33.0189 34.9408 97

35

From above tables it can be noted that, for all the lines, the Zbus method have the

property that they allocate a significant amount of the cost of each line to the buses

directly connected to it. For lines 1, 2, 3, and 5, the two buses with the highest line usage

are these at the ends of the corresponding line. Taking into account that the power

injected and extracted at each bus is very similar, the results reflect the location of each

bus in the network. For instance, the Zbus allocate most of the usage of line 5 (between

buses 3 and 4) to buses 3 and 4.

Note also that, for line 4 (between buses 2 and 4), the results provided by the zbus

method are somewhat different, since the allocation to bus 1, not directly connected to

line 4, is also relevant. This happens, mostly, because the power injected at bus 1 is

greater than the power extracted at bus 4: 261.3 and 250.0 MW, respectively. In addition,

the absolute values of the electrical distance terms 124a and 4

24a are identical, as well as

the values of z12 and z24 , which makes buses 1 and 4 being at the same electrical distance

to line 2–4. Nevertheless, the cost allocated to bus 4 is significant and similar to the cost

allocated to bus 1.

2.6 Conclusions:

The busZ technique to allocate the cost of the transmission network to generators

and demands are based on circuit theory. This technique generally behave in a similar

manner as other techniques previously reported in the literature. However, they exhibit a

desirable proximity effect according to the underlying electrical laws used to derive them.

This proximity effect is more apparent on peripheral rather isolated buses. For these

buses, other techniques may fail to recognize their particular locations.

The busZ technique allocates a higher line usage to generators versus demands.

Thus, we conclude that the proposed methods are appropriate for the allocation of the

cost of the transmission network to generators and demands, complement existing

methods, and enrich the available literature.

36


USING avgbusZ TECHNIQUE



slack bus power generation etc. The purpose of the methodology presented in this work is

to allocate the cost pertaining to the transmission lines of the network to all the generators

and demands. Once a load flow solution is available, the proposed method determines

how line flows depend on nodal currents. This result is then used to allocate network

costs to generators and demands.

3.2 Background:


charging susceptanceshjky connected between the buses j and k is shown in Fig.3.1


j k

+ Sjk jky +

jkI

jv shjky sh

jky kv

- -

Fig. 3.1 equivalent -circuit of line jk .

37



*jkS j jkV I= (3.1)


current iI is given by

1

n

j j i ii

V Z I=

= ∑ (3.2)





1( )

nsh


I Z Z y Z y I=

= − + ∑ (3.4)






*


ii

P P j Q QI

V− − −

= (3.5)

Note that the first term of the product in (3.4) is constant, as it depends only on network

parameters. Thus, (3.4) can be written as

iN

I

ijkjk IaI ∑ =

=1 (3.6)

At this stage, we wish to make equ(2.4) as dependent on Pgen, Qgen, Pload and Qload of the


38

contribution of each generator and load on the line flow jk.this aspect is considered in

proposing new technique.

Where

( ) shjkjijkkiji

ijk yzyzza +−= (3.7)

Observe that the magnitude of parameterijka provides a measure of the electrical

distance between bus i and line jk .

Substituting (3.6) in (3.1)

( ) ∑∑ ====

n

i iijkj

n

i iijkjjk IaVIaVS

1***

1 (3.8)

Then, the active power through line jk is

{ }∑ =ℜ=

n

i iijkjjk IaVP

1** (3.9)

or, equivalently

{ }∑ =ℜ=

n

i iijkjjk IaVP

1**

(3.10)

Note that the terms in the summation represent contribution due to each bus - Ii .Thus, the

active power flow through any line can be identified as function of the nodal currents in a

direct way. Then, the active power flow through line jk due to the with nodal current Ii is

( )**i

ijkj

ijk IaVP ℜ= (3.11)

39

3.3 Transmission Cost AllocationFollowing (3.11), we define the usage of line jk due to nodal current as the absolute

value of the active power flow component ijkP , i.e.,

ijk

ijk PU = (3.12)

That is, we consider that both flows and counter-flows do use the line.

The total usage of line jk is theni

jk

N

ijk UU ∑ ==

1 (3.13)

Then, we proceed to allocate the use of transmission line jk to any generator and

demand. Without loss of generality, we consider at most a single generator and a single

demand at each node of the network.

Then, the usage of line jk apportioned to the generator or demand located at bus is stated

below.

If bus-i contains only generation, the usage allocated to generation pertaining to line jk

isijk

Gijk UU = (3.14)

On the other hand, if bus contains only demand, the usage allocated to demand pertaining

to line jk isijk

Dijk UU = (3.15)

Else, if bus i contains both generation and demand, the usage allocated to the generation

at bus pertaining to line jk is

( )[ ] ijkDiGiGi

Gijk UPPPU += (3.16)

and the usage allocated to the demand at bus pertaining to line jk is

( )[ ] ijkDiGiDi

Dijk UPPPU += (3.17)

40


generations and load demands have been found out. Having found the contributions of

individual generators and demands in each of the line flows and the usage of line by those

generations and demands, allocation of transmission cost among generators and demands

can be found out. Let jkC in $/h, represents the total annualized line cost including

operation, maintenance and building costs [8].


j kj k

j k

Cr

U= (3.18)







( , )

G i Gijk

j k nlineC C

∈

= ∑ (3.21)



( , )

D i D ijk

j k nlineC C

∈

= ∑ (3.22)

41

3.4 Effect of Flow Directions:

It is to be noted that complex power flow equation (3.1) can be written either in

the direction of active power flow i.e. 0jkP ≥ or in the direction of active power counter

flows [3]. This way to write (3.1) leads to electrical distance parameters ijka and i

kja .

However, (3.7) shows that distance parameters are not generally symmetrical with

respect to line indexes, i.e., ikj

ijk aa ≠ , which results in different usage allocations

depending on whether (3.1) is written in the direction of the active power flows or

counter-flows [see (3.10)–( 3.11)]. The proposed usage based technique takes the average

value of allocated cost (usage) obtained

1) with (3.1) written in the direction of the active power flows and

2) with (3.1) written in the direction of the active power counter-flows.

42

3.6 Algorithm For Transmission Network Cost Allocation UsingavgbusZ Technique

Algorithm1 (a) Read the system line data and bus data






(b) Set maxP∆ =0.0 , maxQ∆ =0.0





iqiqiqq

n

qi YVV θδ −∑

=

Qcal(i)= )sin(1

iqiqiqq

n

qi YVV θδ −∑

=









(c) Form diagonal elements Hpp, Npp, Mpp & Lpp



43


(f) Modify the elements



[A] [ ∆ X] = [B]








d. Calculate line flows

e. Bus powers, Slack bus power.

f. Print the converged voltages, line flows and powers.

7. Form the bus impedance matrix Zbus. ( Zbus is calculated using 1−busY )




i) Calculate ijka ,

GijkU Di

jkU and ijkU using the equations given in equ(3.12) to equ(3.17)

ii) Obtain the values of ikja ,

1GijkU , 1Di

jkU and 1ijkU by interchanging the ‘from bus’

and ‘to bus’ and repeating step a)

End of Do loop

44


1

ni

jk jki

U U=

=∑

c) Find usage allocated to the line by interchanging the ‘from bus’

and ‘to bus’

11 1

ni

jk jki

U U=

=∑

Else

Assign ‘from bus’ as ‘to bus’ and ‘to bus’ as ‘from bus’ and

repeat steps 1), 2) & 3)

End of if




jkC using equations (3.19), (3.20) and (3,21)

b) Find the factor per unit usage cost rate r1jk interchanging ‘from bus’

and ‘to bus’

11

jkjk

jk

Cr

U=


interchanging ‘from bus’ and ‘to bus’

1 1 1Gi Gijk jk jkC r U=

e) Find the load cost contributions for using line jk


1 1 1Di Dijk jk jkC r U=

End of bus Do loop

End of line Do loop

45


( , )

Gi Gijk

j k nline

C C∈

= ∑



( , )

1 1Gi Gijk

j k nline

C C∈

= ∑


( , )

Di Dijk

j k nline

C C∈

= ∑



( , )

1 1Di Dijk

j k nline

C C∈

= ∑

13. Do for all lines

Do for all the buses

A) Find the average cost contribution of generator i using the line jk

12

Gi Gijk jkGi

jk

C CCavg

+=

B) Find the average cost contribution of load i using the line jk

12

Di Dijk jkDi

jk

C CCavg

+=

End of bus loop

End of line loop

46

14. Find the average cost contribution of generator i using all the lines in the

network

∑ ==

sforalllinejkGijk

Gi CavgCavg

15. Find the average cost contribution of load i using all the lines in the

network

∑ ==

sforalllinejkDijk

Di CavgCavg

47

3.6 Case study – 4 bus system:


four bus, 5 line system shown in Fig.3.2 All the lines have equal per unit resistance,





250.0 MW 500 MW

Line 5

3 4

63.0 MW


191.7 MW 190.0 MW

129.2 MW

Line 1

60.0 MW

1 2

261.3 MW 250.0 MW

Fig. 3. 2 Four Bus System

48

3.6.1 Step By Step Results - 4 bus system:

Detailed line data and bus data are given in appendix.

The slack bus power is 261.311351 MW+j -96.154655 MVAR

The total loss =11.311357 MW

Table 3.1 Converged Voltages

E(1)=1.050000+j-0.000000

E(2)=1.048494+j0.056220

E(3)=1.038233+j-0.178619

E(4)=1.049926+j-0.121420

Table 3.2 Bus Currents

ibus(1)=2.48868+i0.915759

ibus(2)=2.34015+i0.824762

ibus(3)=-2.33872+i0.402353

ibus(4)=-2.34969+i0.27173

Table 3.3 Powerflow Contributions P(i,k)in Pjk>0 direction,equ(3.11)

Line\Bus 1 2 3 4

1 -0.3385 1.25 0 -0.3111

2 0.8486 0.5044 0.752 -0.1879

3 0.916 0.2492 -0.2488 0.3757

4 0.3385 1.25 0 0.3111

5 0.1907 0.484 0.7672 -0.8119

49

Table 3.4 Powerflow Usage Contributions U(k,i)in Pjk>0 direction,equ(3.12)

Line\Bus 1 2 3 4

1 0.3385 1.25 0 0.3111

2 0.8486 0.5044 0.752 0.1879

3 0.916 0.2492 0.2488 0.3757

4 0.3385 1.25 0 0.3111

5 0.1907 0.484 0.7672 0.8119

Table 3.5 Powerflow Usage of Line usage(k)in Pjk>0 direction,equ(3.13)

Line Usage

1 1.89966

2 2.29286

3 1.78977

4 1.89966

5 2.25381

Table 3.6 Powerflow Contributions Ug(i,k)in Pjk>0 direction,equ(3.14)to ,equ(3.16)

Bus\Line 1 2 3 4 5

1 0.339 0.849 0.916 0.339 0.191

2 1.25 0.504 0.249 1.25 0.484

3 0 0 0 0 0

4 0 0 0 0 0

Table 3.7 Powerflow Contributions Ud(i,k)in Pjk>0 direction,equ(3.15)to ,equ(3.17)

Bus\Line 1 2 3 4 5

1 0 0 0 0 0

2 0 0 0 0 0

3 0 0.752 0.249 0 0.767

4 0.311 0.188 0.376 0.311 0.812

50

Table 3.8 Generator Cost Contributions cg(k,i)in Pjk>0 direction,equ(3.19)


1 17.285 63.8273

2 35.8984 21.3386

3 49.6443 13.5066

4 17.285 63.8273

5 8.209 20.8313



1 0 15.8877

2 31.8153 7.9477

3 13.4857 20.3634

4 0 15.8877

5 33.0189 34.9408

Table3.10 Total generation and load costs and Total cost for all the buses

in Pjk>0 direction,equ(3.21) and equ(3.11)

Bus CG CD TOTAL COST

1 128.3219 0 128.3219

2 183.331 0 183.331

3 0 78.31983 78.31983

4 0 95.02724 95.02724

51

Table3.11 Powerflow Contributions P1(k,i)in Pjk<0 direction

Line\Bus 1 2 3 4

1 0.8486 -0.7536 -0.5032 -0.1879

2 -0.3081 0 -1.25 -0.3164

3 -0.3815 0.2391 -0.2538 -0.8763

4 0.1907 -0.7231 -0.5134 -0.8119

5 0.3081 0 -1.25 0.3164

Table3.12 Powerflow Usage Contributions U1(k,i)in Pjk<0 direction

Line\Bus 1 2 3 4

1 0.8486 0.7536 0.5032 0.1879

2 0.3081 0 1.25 0.3164

3 0.3815 0.2391 0.2538 0.8763

4 0.1907 0.7231 0.5134 0.8119

5 0.3081 0 1.25 0.3164

Table3.13 Powerflow Usage Of Line usage1(k)in Pjk<0 direction

Line USAGE1

1 2.293242

2 1.874441

3 1.750674

4 2.239097

5 1.874441

Table3.14 Powerflow Contributions Ug1(i,k)in Pjk<0 direction

Bus\Line 1 2 3 4 5

1 0.849 0.308 0.381 0.191 0.308

2 0.754 0 0.239 0.723 0

3 0 0 0 0 0

4 0 0 0 0 0

52

Table3.15 Powerflow Contributions Ud1(i,k) in Pjk<0 direction

Bus\Line 1 2 3 4 5

1 0 0 0 0 0

2 0 0 0 0 0

3 0.503 1.25 0.254 0.513 1.25

4 0.188 0.316 0.876 0.812 0.316

Table3.16 Generator Cost Contributions cg1(k,i) in Pjk<0 direction


1 35.8924 31.8763

2 15.9432 0

3 21.1366 13.2477

4 8.263 31.3261

5 15.9432 0

Table3.17 Load Cost Contributions cd1(k,i) in Pjk<0 direction

Table3.18 Total generation and load costs and Total cost1 for all the buses

in Pjk<0 direction

Bus No CG1 CD1 COST1

1 97.17843 0 97.17843

2 76.45012 0 76.45012

3 0 186.9605 186.9605

4 0 124.411 124.411


1 21.285 7.9464

2 64.686 16.3708

3 14.0631 48.5526

4 22.2404 35.1705

5 64.686 16.3708

53

Table3.19 Average Generator Cost Contributions cgavg(k,i)


1 26.5887 47.8518

2 25.9208 10.6693

3 35.3905 13.3772

4 12.774 47.5767

5 12.0761 10.4156

Table3.20 Average Load Cost Contributions cdavg(k,i)


1 10.6425 11.917

2 48.2506 12.1592

3 13.7744 34.458

4 11.1202 25.5291

5 48.8524 25.6558

Table3.21 Total average generation and load costs and Total avgcost1 for all the buses

Bus No CGAVG(I) CDAVG(I) TOTAL COSTAVG(i)

1 112.7502 0 112.7502

2 129.8906 0 129.8906

3 0 132.6402 132.6402

4 0 109.7191 109.7191

From above tables it can be noted that, for all the lines, the Zbus and Zbus average

methods have the property that they allocate a significant amount of the cost of each line

to the buses directly connected to it. For lines 1, 2, 3, and 5, the two buses with the

highest line usage are these at the ends of the corresponding line. Taking into account that

the power injected and extracted at each bus is very similar, the results reflect the location

of each bus in the network. For instance, the Zbus and Zbus average allocate most of the

usage of line 5 (between buses 3 and 4) to buses 3 and 4.

54

Also note that , for line 4 (between buses 2 and 4), the results provided by the Zbus

method are somewhat different, since the allocation to bus 1.bus that is not directly

connected to line 4, is also relevant. This happens, mostly, because the power injected at

bus 1 is greater than the power extracted at bus-4, 261.3 and 250.0 MW, respectively. In

addition, the absolute values of the electrical distance terms 124a and 4

24a are identical, as

well as the values of z12 and z24 , which makes buses 1 and 4 being at the same electrical

distance to line 2–4. Nevertheless, the cost allocated to bus 4 is significant compared to

the cost allocated to bus 1. It should also be noted that for line 4.The Zbus average

approach allocated the highest portion of line usage to buses 2 and 4, which are the

terminal buses of line 4.

It may be noted that the Zbus based approach usually allocates higher transmission cost to

generator buses compared to load buses. Comparing the methods Zbus and Zbus average

methods, it can be concluded that the Zbus average method smoothes the trend of the zbus

one (as well as of other methods)and avoids allocation of higher portion of usage to

generating buses compared to demand buses. In view of the results are significantly

different.

55

3.7 Conclusions:

The avgbusZ technique to allocate the cost of the transmission network to generators

and demands are based on circuit theory. This technique generally behave in a similar

manner as other techniques previously reported in the literature. However, they exhibit a

desirable proximity effect according to the underlying electrical laws used to derive them.

This proximity effect is more apparent on peripheral rather isolated buses. For these

buses, other techniques may fail to recognize their particular locations.

The avgbusZ approach smoothes the trend of the method (as well as of other

techniques) and avoids to allocate a higher line usage to generators compared to

demands. We have performed extensive numerical simulations on IEEE-RTS-24 bus

system and encountered neither numerical induced ill-conditioning nor unreasonable

results. Thus, we conclude that the proposed methods are appropriate for the allocation of

the cost of the transmission network to generators and demands, complement existing

methods, and enrich the available literature.

56


USING MODIFIED avgbusZ TECHNIQUE (newly proposing technique)



slack bus power generation etc. This paper presents a comprehensive methodology that

finds the coefficients of the power generations and load demands in the complex line

flow. Once the coefficients are determined, next step is to find the allocation of

transmission cost pertaining to individual generators and loads.

4.2 Background:


charging susceptanceshjky connected between the buses j and k is shown in Fig. 4.1


j k

+ Sjk jky +

jkI

jv shjky sh

jky kv

- -

Fig. 4.1. equivalent -circuit of line jk .

57



*jkS j jkV I= (4.1)


current iI is given by ( from Vbus=Zbus Ibus )

1

n

j j i ii

V Z I=

= ∑ (4.2)





1( )

nsh


I Z Z y Z y I=

= − + ∑ (4.4)

At this stage, we wish to make equ(2.4) as dependent on Pgen, Qgen, Pload and Qload of the


contribution of each generator and load on the line flow jk.






*


ii

P P j Q QI

V− − −

= (4.5)

Substituting the values jkI and iI from (4.4) and (4.5) in (4.1) and rearranging

58

1

[( ) ( )]n

i i i i ijk jk gen load gen load

iS Factor P P j Q Q

=

= − + −∑ (4.6)

where

*( ) shj ji ki jk ji jki

jki

V Z Z y Z yFactor

V

− + = (4.7)

Thus , the active and reactive power flow jkS through any line jk is represented as a

function of the power generation and load at all buses

i.e , ,i i igen load genP P Q and

iloadQ ; i = 1,2,3…..n

Eq. (6) can be rewritten as

1( 1 2 3 4 )

ni i i i

jk jk jk jk jki

S S S S S=

= + + +∑ (4.8)

Where

1 * ; 2 *

3 * ; 4 *

i i i i i ijk jk gen jk jk load

i i i i i ijk jk gen jk jk load

S Factor P S Factor P

S jFactor Q S jFactor Q

= = −

= = −

Note that, for a converged load flow solution, the magnitude of parameter ijkF a c tor

provides a measure of the electrical distance between bus i and line jk .

Eq. (4.6) clearly illustrates the fact that complex power flow through any line depends on

the power generations (active and reactive) and demands (active and reactive). The

components 1 , 2 , 3 & 4i i i ijk jk jk jkS S S S represent the contribution/share of each of the

power generation and demand to the complex power flow through the line jk . Hence

the complex power flow through a line j k can be split up into individual components

associated to power generations and demands at a particular bus as shown below. Thus,

the component of complex power flow due to bus i through a line j k associated with

the bus power generation and demand at bus i can be written as

1 2 3 4i i i i ijk jk jk jk jkS S S S S= + + + (4.9)

59

This approach can be considered as new contribution in the area of transmission cost

aloocation among generators and load buses. Following the information reported in

reference [8], we consider that both flows and counter-flows do use the line. The usage of

line jk by any generator ‘i' , GijkU , is defined as the sum of the absolute value of the

active power flow components due to active and reactive power generation of the

generator ‘i' , i.e.,i

genP and igenQ .

4.3 Transmission Cost Allocation:

Thus, usage of line jk by generator ‘i' can be written as

| ( 1 )| | ( 3 ) |Gi i ijk jk jkU S S= ℜ + ℜ (4.10)

Similarly, the usage of line jk by any demand ‘i’,DijkU is defined as the sum of the

absolute value of the active power flow components due to active and reactive parts of

demand ‘i' i.e.,i

loadP andiloadQ .

Hence, the usage of line jk by demand ‘i’ can be written as

| ( 2 )| | ( 4 ) |Di i ijk jk jkU S S= ℜ + ℜ (4.11)

The usage of line by bus ‘i' , ijkU , is then given by

i Gi Dijk jk jkU U U= + (4.12)

The total usage of line jk , jkU , by all buses is then

1

ni

jk j ki

U U=

= ∑ (4.13)


generations and load demands have been found out directly without much additional

complexity and computation Having found the contributions of individual generators and

demands in each of the line flows and the usage of line by those generations and

demands, allocation of transmission cost among generators and demands can be found

60

out. Let jkC in $/h, represents the total annualized line cost including operation,

maintenance and building costs [8]. cost of each line, jkC is considered to be

proportional to its series reactance jkx i.e. 1000jk jkC x= × $/h[8].


j kj k

j k

Cr

U= (4.14)







( , )

G i Gijk

j k nlineC C

∈

= ∑ (4.17)



( , )

D i D ijk

j k nlineC C

∈

= ∑ (4.18)

It is to be noted that complex power flow equation (4.8) can be written either in the

direction of active power flow i.e. 0jkP ≥ or in the direction of active power counter

flows [3]. This way to write (4.8) leads to electrical distance parameters ijkFactor and

ikjFactor . However, (4.7) shows that distance parameters are not generally symmetrical

61

with respect to line indexes, i.e., i ijk kjFactor Factor≠ , which results in different usage

allocations depending on whether (4.8) is written in the direction of the active power

flows or counter-flows [see (4.10)–( 4.11)]. The proposed usage based technique takes

the average value of allocated cost (usage) obtained 1) with (4.8) written in the direction

of the active power flows and 2) with (4.8) written in the direction of the active power

counter-flows.

4.4 Algorithm for Transmission network cost allocation

Using modified avgbusZ technique (newly proposing technique)

Algorithm1 (a) Read the system line data and bus data






(b) Set maxP∆ =0.0 , maxQ∆ =0.0





iqiqiqq

n

qi YVV θδ −∑

=

Qcal(i)= )sin(1

iqiqiqq

n

qi YVV θδ −∑

=




62






(d) Form diagonal elements Hpp, Npp, Mpp & Lpp




(g) Modify the elements



[A] [ ∆ X] = [B]








g. Calculate line flows

h. Bus powers, Slack bus power.

i. Print the converged voltages, line flows and powers.

7. Form the bus impedance matrix Zbus. ( Zbus is calculated using 1−busY )

63




i) Calculate ijkFactor , 1 , 2 ,i i

jk jkS S 3 , 4i ijk jkS S ,

GijkU Di

jkU and ijkU using the equations given equ(4.7) to equ(4.12)

ii) Obtain the values of 1ijkFactor , 11 ,i

jkS 21ijkS , 31 , 41i i

jk jkS S

1GijkU , 1Di

jkU and 1ijkU by interchanging the ‘from bus’

and ‘to bus’ and repeating step a)

End of Do loop


1

ni

jk jki

U U=

=∑

c) Find usage allocated to the line by interchanging the ‘from bus’

and ‘to bus’

11 1

ni

jk jki

U U=

=∑

Else

Assign ‘from bus’ as ‘to bus’ and ‘to bus’ as ‘from bus’ and

repeat steps 1), 2) & 3)

End of if




jkC using equations (4.14), (4.15) and (4.16)

b) Find the factor per unit usage cost rate r1jk interchanging ‘from bus’

and ‘to bus’

11

jkjk

jk

Cr

U=

64



1 1 1Gi Gijk jk jkC r U=

f) Find the load cost contributions for using line jk


1 1 1Di Dijk jk jkC r U=

End of bus Do loop

End of line Do loop


( , )

Gi Gijk

j k nline

C C∈

= ∑



( , )

1 1Gi Gijk

j k nline

C C∈

= ∑


( , )

Di Dijk

j k nline

C C∈

= ∑



( , )

1 1Di Dijk

j k nline

C C∈

= ∑

65

13. Do for all lines

Do for all the buses

A) Find the average cost contribution of generator i using the line jk

12

Gi Gijk jkGi

jk

C CCavg

+=

B) Find the average cost contribution of load i using the line jk

12

Di Dijk jkDi

jk

C CCavg

+=

End of bus loop

End of line loop

14. Find the average cost contribution of generator i using all the lines in the

network

∑ ==

sforalllinejkGijk

Gi CavgCavg

15. Find the average cost contribution of load i using all the lines in the

network

∑ ==

sforalllinejkDijk

Di CavgCavg

66

4.5 Case Study - 4 - Bus System:


four bus, 5 line system shown in Fig. 4.2 All the lines have equal per unit resistance,





250.0 MW 500 MW

Line 5

3 4

63.0 MW


191.7 MW 190.0 MW

129.2 MW

Line 1

60.0 MW

1 2

261.3 MW 250.0 MW

Fig. 4. 2 Four Bus System

67

4.5.1 Step By Step Results – 4 bus system:

Detailed line data and bus data are given in appendix.The slack bus power is 261.311351 MW+j -96.154655 MVARThe total loss =11.311357 MW

Table 4.1 Converged voltages

Table 4.2 Bus Currentsibus(1)=2.48868+i0.915759ibus(2)=2.34015+i0.824762ibus(3)=-2.33872+i0.402353ibus(4)=-2.34969+i0.27173

Table 4.3 Powerflow Contributions S1(i,k) in Pjk>0 direction,equ(4.8)

Bus/Line

1 2 3 4 5

1 -0.332+j-0.019 0.849+j-0.000 0.916+j 0.000 0.332+j 0.019 0.199+j-0.023

2 1.250+j-0.000 0.512+j-0.026 0.253+j-0.013 1.250+j-0.000 0.509+j-0.085

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

Table 4.4 Powerflow Contributions S2(i,k) in Pjk>0 direction,equ(4.8)Bus/Line

1 2 3 4 5

1 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

2 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

3 0.000+j 0.000 0.752+j 0.132 -0.249+j-0.043

0.000+j 0.000 0.767+j 0.045

4 -0.311+j-0.054 -0.188+j-0.022 0.376+j 0.044 0.311+j 0.054 -0.812+j 0.000

E(1)=1.050000+j-0.000000E(2)=1.048494+j0.056220E(3)=1.038233+j-0.178619E(4)=1.049926+j-0.121420

68

Table 4.5 Powerflow Contributions S3(i,k) in Pjk>0 direction,equ(4.8)Bus/Line

1 2 3 4 5

1 -0.007+j 0.122 -0.000+j-0.312 0.000+j-0.337 0.007+j-0.122 -0.008+j-0.073

2 -0.000+j-0.367 -0.008+j-0.150 -0.004+j-0.074 -0.000+j-0.367 -0.025+j-0.149

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

Table 4.6 Powerflow Contributions S4(i,k) In Pjk>0 Direction,equ(4.8)

Bus/Line

1 2 3 4 5

1 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

2 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

Table 4.7 Powerflow Contributions Ug(i,k) in Pjk>0 direction,equ(4.10)

Bus\Line 1 2 3 4 51 0.339 0.849 0.916 0.339 0.2072 1.25 0.519 0.257 1.25 0.5343 0 0 0 0 04 0 0 0 0 0

Table 4.8 Powerflow Contributions Ud(i,k) in Pjk>0 direction,equ(4.11)

Bus\Line 1 2 3 4 51 0 0 0 0 02 0 0 0 0 03 0 0.752 0.249 0 0.7674 0.311 0.188 0.376 0.311 0.812

69

Table 4.9 Generator Cost Contributions cg(k,i) in Pjk>0 direction,equ(4.15)

Line\Gen GEN-1 GEN-21 17.285 63.82732 35.6653 21.83313 49.4319 13.86394 17.285 63.82735 8.6695 22.3176


Line\Load LOAD3 LOAD41 0 15.88772 31.6061 7.89553 13.4279 20.27634 0 15.88775 32.073 33.9399

Table 4.11 Total generation and load costs and Total cost for all thebuses,equ(4.17)andequ(4.18)

Bus no CG CD cost1 128.3367 0 128.33672 185.6693 0 185.66933 0 77.10707 77.107074 0 93.88696 93.88696

70

Table 4.12 Powerflow Contributions S11(i,k) in Pjk<0 direction

Bus/Line

1 2 3 4 5

1 0.849+j-0.000 -0.329+j0.056 -0.398+j0.045 0.199+j-0.023 0.329+j-0.056

2 -0.765+j0.039 0.000+j-0.000 0.252+j-0.042 -0.760+j0.127 0.000+j-0.000

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000


Bus/Line

1 2 3 4 5

1 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

2 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

3 -0.503+j-0.088 -1.250+j 0.000 -0.254+j-0.014 -0.513+j-0.030

-1.250+j 0.000

4 -0.188+j-0.022 -0.316+j 0.017 -0.876+j-0.000 -0.812+j 0.000 0.316+j-0.017


Bus/Line

1 2 3 4 5

1 -0.000+j-0.312 0.021+j 0.121 0.017+j 0.146 -0.008+j-0.073 -0.021+j-0.121

2 0.011+j 0.224 0.000+j 0.000 -0.012+j-0.074 0.037+j 0.223 0.000+j 0.000

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

71


BUS/LINE

1 2 3 4 5

1 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

2 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

3 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

4 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000 0.000+j 0.000

Table 4.16 Powerflow Contributions Ug1(i,k)IN Pjk<0 direction

Bus\Line 1 2 3 4 51 0.849 0.349 0.415 0.207 0.3492 0.776 0 0.264 0.798 03 0 0 0 0 04 0 0 0 0 0

Table 4.17 Powerflow Contributions Ud1(i,k)IN Pjk<0 direction

Bus\Line 1 2 3 4 51 0 0 0 0 02 0 0 0 0 03 0.503 1.25 0.254 0.513 1.254 0.188 0.316 0.876 0.812 0.316

Table 4.18 Generator Cost Contributions cg1(k,i) in Pjk<0 direction

Line\Gen GEN-1 GEN-21 35.5409 32.51642 17.6803 03 22.2418 14.15494 8.6317 33.20725 17.6803 0

Table 4.19 Load Cost Contributions cd1(k,i) in Pjk<0 direction

Line\Load LOAD-3 LOAD-41 21.0748 7.86792 63.2998 16.023 13.6111 46.99224 21.3689 33.7922

72

5 63.2998 16.02

Table 4.20 Total generation and load costs and Total cost for all the busesin Pjk <0 direction

Bus No CG1 CD1 COST11 101.7749 0 101.77492 79.87851 0 79.878513 0 182.6543 182.65434 0 120.6923 120.6923

Table 4.21 Average Generator Cost Contributions Cgavg(k,i)

Line\Gen GEN-1 GEN-21 26.413 48.17182 26.6728 10.91663 35.8368 14.00944 12.9584 48.51725 13.1749 11.1588

Table 4.22 Average Load Cost Contributions Cdavg(k,i)

Line\Load LOAD-3 LOAD-41 10.5374 11.87782 47.453 11.95773 13.5195 33.63424 10.6844 24.83995 47.6864 24.9799

Table 4.23 Total average generation and load costs and Total avgcost for all the buses

Bus No CG CD TOTALAVGCOST

1 115.0558 0 115.05582 132.7739 0 132.77393 0 129.8807 129.88074 0 107.2896 107.2896

73

4.6 Conclusions:

The “modified avgbusZ “ technique to allocate the cost of the transmission network to

generators and demands are based on circuit theory. This technique generally behave in a

similar manner as other techniques previously reported in the literature. However, they

exhibit a desirable proximity effect according to the underlying electrical laws used to

derive them. This proximity effect is more apparent on peripheral rather isolated buses.

For these buses, other techniques may fail to recognize their particular locations.

From the above cost allocation tables, it is clear that, the proposed new method

allocates a significant part of the usage of any line to the buses which are directly

connected to it. This is evident from the results of line 5 ,line 1 and line 4. the proposed

method allocate most of the usage of line 5 (between buses 3 and 4) to buses 3 and 4. In

the proposed new approach, the factors S1,S2,S3,S4 for forward flows and

S11,S21,S31,S41 for reverse direction flows have offered very useful information about

the contribution of generator buses and load buses towards the line flow of line jk.

Rigorous calculations without any approximations are possible and cost allocation results

would be more reliable and accurate compared to other methods.It is also noted that

proposed usage based method allocate the transmission cost of line 1(between buses 1 &

2) and line 4 (between buses 2 & 4) to all the buses where as Zbus method allocates zero

cost for bus 3.

Better cost allocation has been observed with modified Zbus average approach

compared to Zbus and Zbus average methods.

74

CHAPTER 5

RESULTS-IEEERTS 24BUS SYSTEM AND CONCLUSIONSIn this project work a software package has been developed for three algorithms:

1. Zbus based

2. Zbus average based

3. Modified Zbus average based transmission cost allocation.

The third method is a new approach proposed in this project which is accurate and

offered very promising results compared to other two methods. The basic calculation of

all three methods is illustrated, step-by-step, for a 4-buses test system. The software

package has been tested on IEEE RTS-24 bus system. The results are reported in this

chapter. The input data of the 24 -bus system is reported in appendix of this thesis.

5.1 Zbus technique Results:

The Contributions of Generators in Forward Power flow Direction are reported inTable 5.1

Table 5.1 Generator Cost Contributions Cg(k,i) in Pjk>0 Direction of Zbus technique

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN

15

GEN

16

GEN

18

GEN

21

GEN

22

GEN

23

1 0.7487 0.8363 0.1668 0.0328 0.2025 0.1133 0.1905 1.6169 0.9663 1.815

2 5.0854 5.6053 1.4917 0.4735 4.185 2.1864 3.8471 32.6249 19.2029 30.4166

3 6.78 7.3634 1.6495 0.1434 0.3169 0.0226 0.2194 1.392 0.2927 4.3349

4 3.7852 5.3342 2.685 0.4072 1.5066 0.8639 1.4996 11.9357 6.8788 18.0482

5 7.2876 9.8898 2.0525 0.4321 2.6979 1.4042 2.5466 20.8026 11.9398 22.9481

6 1.0155 0.8952 3.3997 0.1858 2.3564 1.0147 1.9529 17.5389 10.2822 2.7046

7 1.0514 1.327 0.913 0.0514 1.9537 1.1252 1.6831 16.4305 10.6746 9.6374

8 2.5175 3.5746 2.2181 0.3397 1.2862 0.7374 1.276 10.2029 5.8986 15.1844

9 5.7097 6.0786 1.8782 0.1989 0.0129 0.189 0.0921 1.1361 1.1429 7.0168

10 0.4164 0.446 1.4864 0.2361 0.9839 0.5737 0.9622 7.9148 4.6796 11.045

11 0 0 40.1096 0 0 0 0 0 0 0

12 0.4867 0.6213 20.2469 0.3032 1.5718 0.7979 1.5128 11.896 6.6119 14.5572

75

The Contributions of Generators in Forward Power flow Direction are reported inTable 5.2

Table 5.2 Generator Cost Contributions Cg(k,i) in Pjk>0 Direction of Zbus technique

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN1

5

GEN

16

GEN1

8

GEN

21

GEN

22

GEN

23

13 0.0262 0.0593 25.195 0.1887 1.0895 0.4821 1.0456 7.7682 4.001 8.825

14 1.3784 1.834 3.6991 0.2802 0.5364 0.4817 0.6474 5.0429 3.1767 6.6427

15 1.5383 2.0519 4.0091 0.3785 0.0445 0.0593 0.0899 0.212 0.3339 17.396

16 0.1283 0.1445 0.1174 0.3523 1.5703 1.0828 1.5323 13.7365 8.8505 16.5803

17 0.1297 0.1423 0.069 0.3988 1.4092 0.9748 1.3702 12.3649 8 21.7699

18 0.2463 0.3189 0.5066 0.953 0.1948 0.1518 0.2011 1.7827 1.171 21.2532

19 0.1749 0.2355 0.4794 0.0531 0.9034 0.6679 0.8962 8.1401 5.3566 4.1353

20 0.2505 0.3317 0.6126 0.8201 0.8242 0.6018 0.8227 7.364 4.797 10.2632

21 0.3026 0.4254 0.7815 0.0175 1.4519 1.22 1.4167 14.0643 9.8966 34.406

22 0.1939 0.2755 0.555 0.3796 1.2563 1.0494 1.2242 12.1369 8.5256 34.1715

23 0.2018 0.2916 0.5663 0.0533 1.2825 1.1262 1.2408 12.7593 9.1876 6.8785

24 0.0326 0.0352 0.0747 0.0306 0.8117 0.2554 0.2449 4.2469 2.0801 2.8473

25 0.2251 0.3086 0.2702 0.0141 0.6747 0.0553 1.6593 23.7125 14.4716 0.2534

26 0.2251 0.3086 0.2702 0.0141 0.6747 0.0553 1.6593 23.7125 14.4716 0.2534

27 0.5473 0.7078 0.3772 0.0475 1.2023 0.7856 1.0301 10.8055 7.4297 6.9974

28 0.1102 0.1564 0.2221 0.0313 0.1975 0.1721 1.0044 8.0954 7.5969 2.3767

29 0.0045 0.0013 0.0656 0.0356 0.45 0.38 0.4349 4.3855 3.1094 6.1403

30 0.0123 0.0201 0.0561 0.0119 0.2137 0.0923 0.9725 7.0825 1.3768 1.0804

31 0.2037 0.2879 0.2391 0.0117 0.5372 0.0393 0.212 15.2865 82.5741 0.3507

32 0.0678 0.0893 0.0358 0.0078 0.4805 0.1236 1.7238 14.4758 3.1589 1.1103

33 0.0678 0.0893 0.0358 0.0078 0.4805 0.1236 1.7238 14.4758 3.1589 1.1103

34 0.0841 0.1209 0.2685 0.0818 0.713 0.587 0.6951 6.8341 4.7698 11.5888

35 0.0841 0.1209 0.2685 0.0818 0.713 0.587 0.6951 6.8341 4.7698 11.5888

36 0.067 0.0945 0.1801 0.0477 0.3643 0.3053 0.3552 3.5245 2.4781 6.4798

37 0.067 0.0945 0.1801 0.0477 0.3643 0.3053 0.3552 3.5245 2.4781 6.4798

38 0.0985 0.1391 0.1156 0.0057 0.2596 0.019 0.1025 7.3881 57.1613 0.1695

76

The Contributions of loads in Forward Power flow Direction are reported inTable 5.3

Table 5.3 Load Cost Contributions Cd(k,i) in Pjk>0 Direction of Zbus technique

LINE\LOAD LD-1 LD-2 LD-3 LD-4 LD-5 LD-6 LD-7 LD-8 LD-9

1 0.4701 0.4716 1.2265 0.5368 0.7893 0.2462 0.0869 0.3784 0.2296

2 3.1931 3.1611 33.0204 1.8625 4.7767 4.3675 0.7769 3.3941 8.3068

3 4.2572 4.1526 9.2438 5.861 16.135 0.9425 0.8591 3.7246 2.666

4 2.3767 3.0083 3.3178 16.969 3.453 3.664 1.3985 6.1629 12.7388

5 4.5759 5.5774 16.799 9.6788 6.3284 18.8057 1.069 4.7252 11.2395

6 0.6376 0.5048 35.3106 2.463 0.4308 0.8557 1.7707 7.7714 13.3119

7 0.6602 0.7484 11.0976 1.4091 1.0901 1.4528 0.4755 2.0278 2.8423

8 1.5808 2.0159 3.1262 15.6109 2.1483 2.0191 1.1553 5.091 9.7108

9 3.5851 3.428 7.1124 4.808 20.8505 1.5319 0.9782 4.2794 1.3335

10 0.2615 0.2515 3.2471 1.0872 1.1004 1.9558 0.7742 3.4052 3.2762

11 0 0 0 0 0 0 20.8904 0 0

12 0.3056 0.3504 7.9938 3.3321 0.4182 2.164 10.5453 46.1185 12.2192

13 0.0164 0.0334 6.4433 2.7572 1.3694 4.1143 13.1226 57.8444 11.4203

14 0.8655 1.0343 8.3953 5.129 1.2242 1.2272 1.9266 8.2638 16.9764

15 0.9659 1.1572 10.1767 5.6673 1.2722 1.1234 2.0881 8.9347 18.7899

16 0.0806 0.0815 3.6815 0.7653 0.9526 2.5037 0.0612 0.2798 3.7787

17 0.0814 0.0803 3.617 0.8426 0.9742 2.5587 0.0359 0.1754 4.1099

18 0.1546 0.1798 0.4812 0.4519 0.4544 0.8949 0.2638 1.1308 1.0699

77



LINE\LOAD LD-10 LD-13 LD-14 LD-15 LD-16 LD-18 LD-19 LD-20

1 0.5774 0.0304 0.6417 0.2986 0.0731 0.1586 0.6619 0.4338

2 1.4353 0.4398 10.6353 6.1704 1.4106 3.2027 12.1888 7.5391

3 10.9098 0.1332 1.6291 0.4673 0.0146 0.1827 0.5282 0.7781

4 0.1612 0.3782 6.5075 2.2214 0.5573 1.2485 5.7803 4.112

5 1.6897 0.4014 8.1421 3.9778 0.9059 2.1201 8.4599 5.503

6 2.7396 0.1726 0.587 3.4744 0.6546 1.6258 3.9605 1.3833

7 1.4269 0.0478 3.1761 2.8806 0.7259 1.4012 5.013 2.6775

8 0.7249 0.3155 5.47 1.8965 0.4758 1.0623 4.894 3.4673

9 10.6898 0.1848 2.584 0.019 0.122 0.0767 1.5361 1.4253

10 3.8974 0.2193 3.9601 1.4507 0.3701 0.8011 3.6526 2.5457

11 0 0 0 0 0 0 0 0

12 4.8144 0.2816 5.2117 2.3175 0.5148 1.2594 5.1193 3.4282

13 7.7313 0.1752 3.1697 1.6064 0.311 0.8705 3.2268 2.1065

14 0.1413 0.2603 8.8925 0.7909 0.3107 0.5389 2.659 1.6446

15 0.2802 0.3515 0.8081 0.0656 0.0383 0.0748 2.8091 3.2838

16 4.5466 0.3272 8.6103 2.3153 0.6986 1.2757 5.9934 3.9527

17 4.6608 0.3704 4.8536 2.0778 0.6289 1.1407 6.349 4.8146

18 1.33 0.8852 5.821 0.2872 0.0979 0.1674 3.515 4.0356

78




19 0.1098 0.1328 0.6244 0.362 0.3984 0.855 0.2497 1.0634 0.9124

20 0.1573 0.1871 0.301 0.493 0.5238 1.0896 0.3191 1.3629 1.2127

21 0.19 0.2399 0.9969 0.5771 0.6369 1.3475 0.407 1.6891 1.4615

22 0.1218 0.1554 1.0481 0.3903 0.4436 0.9629 0.2891 1.2004 1.0076

23 0.1267 0.1644 1.0745 0.3937 0.4488 0.9689 0.295 1.2114 1.019

24 0.0205 0.0198 1.1152 0.0056 0.0329 0.1395 0.0389 0.1568 0.0438

25 0.1414 0.1741 1.4422 0.2986 0.2617 0.4244 0.1407 0.5714 0.6622

26 0.1414 0.1741 1.4422 0.2986 0.2617 0.4244 0.1407 0.5714 0.6622

27 0.3437 0.3992 6.0695 0.6626 0.4814 0.5615 0.1965 0.8259 1.3085

28 0.0692 0.0882 0.0407 0.1795 0.1863 0.3672 0.1157 0.4697 0.4386

29 0.0028 0.0007 0.5802 0.0191 0.04 0.1191 0.0342 0.1404 0.0767

30 0.0078 0.0114 0.239 0.0305 0.0403 0.0952 0.0292 0.1172 0.0869

31 0.1279 0.1623 1.1915 0.2548 0.2245 0.3631 0.1245 0.4935 0.5727

32 0.0426 0.0504 0.7867 0.0746 0.0504 0.049 0.0187 0.0779 0.1441

33 0.0426 0.0504 0.7867 0.0746 0.0504 0.049 0.0187 0.0779 0.1441

34 0.0528 0.0682 0.6655 0.1798 0.2106 0.4691 0.1398 0.5816 0.4737

35 0.0528 0.0682 0.6655 0.1798 0.2106 0.4691 0.1398 0.5816 0.4737

36 0.042 0.0533 0.2746 0.1304 0.1456 0.3113 0.0938 0.3894 0.3328

37 0.042 0.0533 0.2746 0.1304 0.1456 0.3113 0.0938 0.3894 0.3328

38 0.0618 0.0785 0.5759 0.1232 0.1085 0.1755 0.0602 0.2385 0.2768

79




19 1.3531 0.0494 8.229 1.332 0.4309 0.7461 2.7998 1.3093

20 1.6864 0.7618 5.0714 1.2152 0.3882 0.6849 3.4695 2.3885

21 2.1629 0.0162 3.2444 2.1407 0.7871 1.1794 8.6588 7.2818

22 1.5689 0.3526 0.9345 1.8523 0.677 1.0191 8.1002 7.1081

23 1.5892 0.0495 7.9214 1.8909 0.7266 1.0329 4.386 2.113

24 0.299 0.0284 0.9669 1.1968 0.1648 0.2039 1.1885 0.7194

25 0.5656 0.0131 0.1155 0.9947 0.0357 1.3814 0.1255 0.007

26 0.5656 0.0131 0.1155 0.9947 0.0357 1.3814 0.1255 0.007

27 0.4338 0.0441 2.3143 1.7726 0.5069 0.8576 3.4041 1.8874

28 0.5744 0.0291 0.8216 0.2911 0.111 0.8362 0.8522 0.5663

29 0.2271 0.0331 0.9119 0.6635 0.2451 0.3621 2.9018 1.6352

30 0.1675 0.011 0.3678 0.3151 0.0596 0.8096 0.4262 0.2671

31 0.496 0.0109 0.1444 0.7921 0.0254 0.1765 0.0597 0.0379

32 0.0201 0.0073 0.3669 0.7084 0.0797 1.4351 0.5199 0.2947

33 0.0201 0.0073 0.3669 0.7084 0.0797 1.4351 0.5199 0.2947

34 0.7747 0.076 1.2115 1.0513 0.3787 0.5787 4.301 3.044

35 0.7747 0.076 1.2115 1.0513 0.3787 0.5787 4.301 3.044

36 0.5028 0.0443 0.567 0.5371 0.197 0.2957 2.2527 1.9336

37 0.5028 0.0443 0.567 0.5371 0.197 0.2957 2.2527 1.9336

38 0.2397 0.0053 0.0698 0.3828 0.0123 0.0853 0.0288 0.0183

80

The individual generator/load costs for using all the lines in the network and total cost inforward power flows are reported in Table 5.7

Table 5.7 Cost For Individual Generators/Loads And Total Cost in Pjk>0 Direction of Zbus

technique

Bus No CG CD TOTAL

COST

1 41.3522 25.9653 67.3176

2 50.6569 28.5682 79.2251

3 0 184.485 184.485

4 0 84.0901 84.0901

5 0 68.6698 68.6698

6 0 59.9801 59.9801

7 117.549 61.2232 178.772

8 0 175.917 175.917

9 0 145.662 145.662

10 0 72.2811 72.2811

11 0 0 0

12 0 0 0

13 7.15621 6.64702 13.8032

14 0 116.219 116.219

15 35.7738 52.7455 88.5193

16 20.812 13.4271 34.2391

17 0 0 0

18 39.1378 32.5822 71.7199

19 0 127.021 127.021

20 0 89.022 89.022

21 383.247 0 383.247

22 352.952 0 352.952

23 378.857 0 378.857

24 0 0 0

81

5.2 avgbusZ technique results :

The average Contributions of Generators are reported in Table 5.8

Table 5.8 Average Generator Cost Contributions Cgavg(k,i) of Zbus average method

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN

15

GEN

16

GEN

18

GEN

21

GEN

22

GEN

23

1 1.0584 1.4225 0.1836 0.0251 0.1274 0.0641 0.1139 0.9855 0.5826 1.0933

2 5.3927 5.9318 1.2554 0.4511 4.1783 2.1341 3.8358 32.2454 18.7824 29.3645

3 6.5615 7.0593 1.7605 0.1657 0.218 0.077 0.1241 0.7898 0.4634 5.2913

4 3.5983 5.0471 2.7274 0.4194 1.5511 0.8723 1.5453 12.1758 6.9383 18.363

5 7.5152 10.0346 1.8561 0.4191 2.6807 1.3122 2.535 20.0821 11.1289 21.7555

6 0.9692 0.8291 3.5701 0.2084 2.3423 0.9786 1.9346 17.2185 9.977 1.9537

7 1.0347 1.269 0.9236 0.055 2.0301 1.0698 1.7673 16.2605 10.0645 9.6072

8 2.6043 3.6646 2.2015 0.34 1.2724 0.7161 1.2655 9.9983 5.7092 14.9588

9 5.8857 6.2671 1.8333 0.1893 0.0633 0.1573 0.0598 0.6577 0.8745 6.4938

10 1.1231 1.4259 0.9379 0.1658 0.8058 0.4305 0.7784 6.2384 3.555 7.9423

11 0.0305 0.0365 38.5351 0.0095 0.0407 0.0225 0.0397 0.319 0.1835 0.4361

12 0.3948 0.5045 21.059 0.2863 1.4958 0.7281 1.442 11.1015 6.0159 13.4793

13 0.1226 0.1729 24.4106 0.2131 1.1821 0.5321 1.1377 8.4817 4.3991 9.881

14 1.3604 1.786 3.7184 0.2871 0.5403 0.4672 0.6554 4.9819 3.0636 6.5694

15 1.5065 1.977 4.0144 0.3889 0.053 0.0518 0.083 0.2656 0.3679 17.1791

16 0.1252 0.1379 0.1156 0.3688 1.6077 1.0478 1.5786 13.6456 8.5166 16.5465

17 0.126 0.1346 0.0654 0.421 1.4473 0.9377 1.4174 12.2616 7.6465 21.7209

18 0.3349 0.4274 0.6718 0.967 0.1017 0.0898 0.1126 0.9794 0.654 20.3868

The Contributions of Generators are reported in

82


Table 5.9 Average Generator Cost Contributions Cgavg(k,i ) of Zbus average method

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN

15

GEN

16

GEN

18

GEN

21

GEN

22

GEN

23

19 0.1999 0.2651 0.5312 0.0608 0.8994 0.6511 0.8957 8.0083 5.2044 3.889

20 0.3436 0.4478 0.7886 0.8433 0.7643 0.555 0.7685 6.7962 4.394 9.5734

21 0.48 0.6381 1.1382 0.0378 1.3875 1.0836 1.3761 12.8656 8.6841 33.7182

22 0.3591 0.4813 0.87 0.4586 1.1775 0.9306 1.1638 10.998 7.4789 33.5097

23 0.232 0.3224 0.6425 0.0665 1.3185 1.0638 1.2922 12.4819 8.6094 6.5393

24 0.0274 0.0281 0.0828 0.0316 0.8071 0.2558 0.2414 4.184 2.0328 2.8867

25 0.2893 0.3922 0.3864 0.0286 0.7137 0.0521 1.5705 21.865 12.9979 1.1077

26 0.2893 0.3922 0.3864 0.0286 0.7137 0.0521 1.5705 21.865 12.9979 1.1077

27 0.5991 0.7646 0.4712 0.0397 1.2058 0.7411 1.036 10.4884 7.0189 6.4817

28 0.12 0.1678 0.2413 0.0346 0.1899 0.1739 1.0101 7.8887 7.2881 2.4801

29 0.006 0.008 0.0758 0.0373 0.4477 0.3716 0.4339 4.3186 3.0352 6.1873

30 0.0184 0.0284 0.0656 0.0129 0.2079 0.0945 0.9644 6.9476 1.3219 1.1352

31 0.488 0.6815 0.7662 0.0797 0.3793 0.325 0.3081 10.5486 69.9922 5.1344

32 0.0455 0.0635 0.0704 0.015 0.4401 0.1481 1.7214 13.8608 2.8669 1.5654

33 0.0455 0.0635 0.0704 0.015 0.4401 0.1481 1.7214 13.8608 2.8669 1.5654

34 0.0486 0.0734 0.2101 0.0754 0.7492 0.6138 0.7293 7.1663 4.9958 11.2918

35 0.0486 0.0734 0.2101 0.0754 0.7492 0.6138 0.7293 7.1663 4.9958 11.2918

36 0.0562 0.08 0.1628 0.046 0.3752 0.3116 0.3659 3.6129 2.5307 6.3782

37 0.0562 0.08 0.1628 0.046 0.3752 0.3116 0.3659 3.6129 2.5307 6.3782

38 0.2355 0.3295 0.3376 0.0294 0.3461 0.0956 0.1882 7.614 49.8338 1.7586

83

The average Contributions of loads are reported in Table 5.8

Table 5.10 Average Load Cost Contributions Cdavg(k,i) of Zbus average method


1 0.6646 0.8022 1.2497 1.0773 1.0016 0.8395 0.0956 0.4185 0.5102

2 3.3861 3.3452 33.7739 2.2226 5.2429 5.072 0.6539 2.8649 7.9768

3 4.12 3.9811 8.7652 5.6637 16.0448 1.1503 0.9169 3.9943 2.2917

4 2.2594 2.8463 3.5079 16.6219 3.2589 3.3607 1.4205 6.2792 12.6535

5 4.7189 5.659 17.179 10.1288 6.5551 20.8938 0.9667 4.3113 11.2526

6 0.6086 0.4676 35.7829 2.6166 0.3345 1.079 1.8594 8.1849 13.8081

7 0.6497 0.7157 11.4744 1.4543 1.127 1.5068 0.4811 2.084 2.9057

8 1.6352 2.0667 3.0216 16.135 2.2829 2.2154 1.1466 5.0679 9.8123

9 3.6957 3.5343 7.5158 5.016 21.4331 1.4148 0.9549 4.1771 1.5829

10 0.7052 0.8041 3.696 1.793 1.3508 11.5488 0.4885 2.1599 2.9665

11 0.0191 0.0206 0.1476 0.058 0.0554 0.1044 20.0703 0.0751 0.1313

12 0.2479 0.2845 7.7597 3.2555 0.6142 2.5862 10.9682 48.2077 12.1924

13 0.077 0.0975 6.6819 2.8456 1.1436 3.6384 12.7138 56.1448 11.4339

14 0.8542 1.0072 8.438 5.1879 1.2318 1.2302 1.9367 8.3643 17.1536

15 0.9459 1.1149 10.2023 5.7194 1.2746 1.1155 2.0908 9.0225 18.9383

16 0.0786 0.0778 3.7516 0.7848 0.9693 2.5648 0.0602 0.2781 3.8571

17 0.0791 0.0759 3.6947 0.8678 0.994 2.631 0.0341 0.1688 4.2104

18 0.2103 0.241 0.8724 0.6161 0.6121 1.1931 0.3499 1.5085 1.4446

84




1 0.3662 0.0234 0.3949 0.1879 0.0413 0.0948 0.3313 0.2446

2 2.2407 0.419 10.2613 6.1605 1.3768 3.1933 11.9228 7.3157

3 11.093 0.1539 1.9723 0.3214 0.0497 0.1033 0.8648 1.0032

4 0.3245 0.3895 6.6277 2.287 0.5628 1.2864 5.8905 4.1853

5 2.6349 0.3893 7.7379 3.9524 0.8465 2.1104 8.108 5.2362

6 3.0901 0.1936 0.3146 3.4536 0.6314 1.6106 3.7605 1.2222

7 1.4585 0.051 3.1911 2.9931 0.6902 1.4713 4.9971 2.6673

8 0.5548 0.3158 5.3964 1.8761 0.462 1.0535 4.8137 3.4132

9 10.733 0.1758 2.3984 0.0934 0.1015 0.0498 1.3421 1.2996

10 2.3759 0.154 2.843 1.1881 0.2778 0.648 2.7395 1.8577

11 0.1458 0.0088 0.1566 0.0599 0.0145 0.0331 0.1457 0.1008

12 5.4568 0.266 4.8353 2.2055 0.4697 1.2005 4.7638 3.179

13 6.9915 0.198 3.5513 1.7429 0.3433 0.9472 3.5685 2.3479

14 0.1217 0.2667 8.872 0.7966 0.3014 0.5456 2.6352 1.6273

15 0.3153 0.3612 0.8353 0.0781 0.0335 0.0691 2.7589 3.2371

16 4.6341 0.3426 8.6276 2.3704 0.676 1.3142 5.9804 3.9424

17 4.7641 0.391 4.8618 2.134 0.605 1.18 6.3305 4.7994

18 1.7506 0.8982 6.2681 0.15 0.058 0.0937 3.1846 3.8234

85




19 0.1255 0.1495 0.5384 0.4122 0.4475 0.9519 0.2766 1.1847 1.0285

20 0.2158 0.2526 0.3587 0.6635 0.6891 1.4049 0.4107 1.7624 1.6053

21 0.3014 0.3599 0.648 0.9246 0.9757 2.0093 0.5928 2.5199 2.2636

22 0.2255 0.2714 0.6046 0.6944 0.7392 1.5321 0.4531 1.9202 1.7108

23 0.1457 0.1818 1.0054 0.4682 0.523 1.1254 0.3347 1.4029 1.1935

24 0.0172 0.0158 1.0952 0.0078 0.0404 0.1533 0.0431 0.1746 0.062

25 0.1816 0.2212 1.676 0.4084 0.3684 0.6241 0.2012 0.8269 0.9159

26 0.1816 0.2212 1.676 0.4084 0.3684 0.6241 0.2012 0.8269 0.9159

27 0.3762 0.4312 6.4697 0.7675 0.5781 0.7304 0.2454 1.0406 1.534

28 0.0753 0.0946 0.082 0.1988 0.205 0.4035 0.1257 0.5152 0.4828

29 0.0038 0.0045 0.5604 0.0287 0.0494 0.1369 0.0395 0.1631 0.0993

30 0.0115 0.016 0.2154 0.0395 0.0489 0.1109 0.0342 0.1376 0.1079

31 0.3064 0.3843 1.756 0.7113 0.6824 1.2381 0.3991 1.6179 1.6611

32 0.0285 0.0358 0.6169 0.0658 0.0629 0.1135 0.0367 0.1486 0.1534

33 0.0285 0.0358 0.6169 0.0658 0.0629 0.1135 0.0367 0.1486 0.1534

34 0.0305 0.0414 0.8094 0.1238 0.1571 0.371 0.1094 0.4547 0.3444

35 0.0305 0.0414 0.8094 0.1238 0.1571 0.371 0.1094 0.4547 0.3444

36 0.0353 0.0451 0.3175 0.1139 0.1299 0.2827 0.0848 0.3522 0.2947

37 0.0353 0.0451 0.3175 0.1139 0.1299 0.2827 0.0848 0.3522 0.2947

38 0.1479 0.1858 1.0469 0.3276 0.306 0.5363 0.1758 0.7084 0.7548

86




19 1.4909 0.0565 8.2476 1.3262 0.4201 0.7457 2.7365 1.2568

20 2.1369 0.7833 4.8595 1.127 0.3581 0.6398 3.2313 2.2265

21 3.1026 0.0351 2.6067 2.0457 0.6991 1.1456 8.2822 7.0786

22 2.3826 0.4259 0.6603 1.7361 0.6004 0.9689 7.7343 6.9128

23 1.8089 0.0618 8.1441 1.944 0.6863 1.0758 4.2919 2.038

24 0.3187 0.0294 0.9818 1.19 0.165 0.201 1.199 0.7278

25 0.8559 0.0266 0.4158 1.0522 0.0336 1.3074 0.2778 0.2033

26 0.8559 0.0266 0.4158 1.0522 0.0336 1.3074 0.2778 0.2033

27 0.6585 0.0369 2.1403 1.7779 0.4781 0.8625 3.2537 1.7724

28 0.6251 0.0322 0.8607 0.28 0.1122 0.8409 0.8826 0.589

29 0.2529 0.0347 0.8868 0.66 0.2397 0.3612 2.9128 1.6447

30 0.1903 0.012 0.3875 0.3065 0.061 0.8028 0.4422 0.2792

31 1.8245 0.074 1.8072 0.5592 0.2097 0.2565 1.6484 1.1611

32 0.1667 0.0139 0.5273 0.6488 0.0956 1.433 0.6585 0.3971

33 0.1667 0.0139 0.5273 0.6488 0.0956 1.433 0.6585 0.3971

34 0.6331 0.07 1.3656 1.1046 0.396 0.6071 4.4476 2.9807

35 0.6331 0.07 1.3656 1.1046 0.396 0.6071 4.4476 2.9807

36 0.4612 0.0427 0.6116 0.5532 0.201 0.3046 2.2911 1.9591

37 0.4612 0.0427 0.6116 0.5532 0.201 0.3046 2.2911 1.9591

38 0.7734 0.0273 0.6261 0.5103 0.0617 0.1567 0.5054 0.3812

87

The individual average generator/load costs for using all the lines in the network andtotal average cost reported in Table 5.7

Table 5.14 Average Cost For Individual Generators/Loads and Total Avg Cost of Zbus average

method

BUS

NO:

CGAVG(I) CDAVG(I) TOTAL

COSTAVG

1 43.7322 27.4597 71.1919

2 53.5085 30.1763 83.6848

3 0 188.735 188.735

4 0 88.7323 88.7323

5 0 72.2478 72.2478

6 0 77.2602 77.2602

7 117.51 61.2032 178.713

8 0 180.024 180.024

9 0 151.042 151.042

10 0 78.8505 78.8505

11 0 0 0

12 0 0 0

13 7.44293 6.91334 14.3563

14 0 117.195 117.195

15 35.4253 52.2317 87.657

16 20.2819 13.0851 33.367

17 0 0 0

18 38.8784 32.3663 71.2447

19 0 126.608 126.608

20 0 88.6508 88.6508

21 364.838 0 364.838

22 320.599 0 320.599

23 377.002 0 377.002

24 0 0 0

88

5.3 Modified avgbusZ technique results :


Table 5.15 Average Generator Cost Contributions Cgavg(k,i)of Modified Zbus average method

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN

15

GEN

16

GEN

18

GEN

21

GEN

22

GEN

23

1 2.092 2.2894 0.2677 0.2874 0.258 0.1564 0.4713 0.4701 0.3118 0.522

2 12.6363 11.2804 2.1561 5.7334 9.404 5.9291 17.6071 17.4092 11.4801 15.8537

3 14.5713 12.9648 2.8358 2.2263 0.2661 0.1488 0.5712 0.5449 0.2986 2.6812

4 8.5644 9.9267 4.7126 5.2465 3.3567 2.4947 6.8889 6.6101 4.3524 9.969

5 17.5622 19.7619 3.1142 4.8653 5.5603 3.6705 10.8311 10.5594 6.8069 11.4396

6 2.5106 1.7661 6.6436 2.9489 5.8467 2.9054 9.8227 10.0785 6.5408 1.1434

7 2.3777 2.316 1.6461 0.7487 5.0274 2.895 8.8188 8.9247 6.0439 5.2734

8 6.3267 7.3654 3.8785 4.3417 2.8151 2.0855 5.7634 5.5346 3.6474 8.2804

9 13.7611 12.2483 3.0636 2.5619 0.1484 0.3643 0.6828 0.5723 0.4603 3.4177

10 2.9972 3.2709 1.7308 2.2129 1.8915 1.3172 3.7526 3.6393 2.3858 4.6222

11 0.0443 0.0447 39.2035 0.0711 0.0536 0.0383 0.1074 0.1039 0.0685 0.142

12 1.0304 1.1572 38.4848 3.5782 3.3016 2.2583 6.596 6.3754 4.0721 7.7403

13 0.3507 0.4823 45.256 2.5691 2.5504 1.7167 5.1235 4.9387 3.0845 5.7527

14 3.4791 3.7008 7.1417 4.028 1.2894 1.425 3.2519 2.9464 2.0669 3.8854

15 3.98 4.2252 7.9959 5.8057 0.3911 0.241 0.3601 0.4844 0.2256 10.5224

16 0.32 0.3034 0.2113 5.2675 4.0128 2.9699 7.9636 7.7406 5.3415 9.3864

17 0.3264 0.3023 0.1237 6.1541 3.6617 2.6943 7.2466 7.0497 4.8607 12.4888

18 0.6578 0.6754 1.0042 11.7117 0.2119 0.199 0.4695 0.4422 0.321 9.3162

19 0.4758 0.5068 0.973 0.8825 2.2927 1.7719 4.5891 4.4543 3.1491 2.1635

89


Table 5.16 Average Generator Cost Contributions Cgavg(k,i) Modified Zbus average method

LINE\

GEN

GEN

1

GEN

2

GEN

7

GEN

13

GEN

15

GEN

16

GEN

18

GEN

21

GEN

22

GEN

23

20 0.5912 0.6184 1.0441 9.1055 1.4011 1.1002 2.8346 2.7418 1.9348 3.8621

21 1.302 1.378 2.4354 0.6737 4.2628 3.3204 8.4482 8.2361 5.9456 21.6369

22 0.8434 0.8978 1.6276 7.4154 3.1951 2.4814 6.3023 6.155 4.4619 18.7514

23 0.5209 0.57 1.1794 1.0389 3.5077 2.7024 6.8452 6.7097 4.8982 3.558

24 0.0516 0.039 0.148 0.509 2.0959 0.5916 1.262 2.0793 1.0481 1.4415

25 0.6035 0.6278 0.7185 0.5354 2.0345 0.1264 8.9535 11.5243 7.0479 0.6042

26 0.6035 0.6278 0.7185 0.5354 2.0345 0.1264 8.9535 11.5243 7.0479 0.6042

27 1.2968 1.2842 0.8491 0.6278 3.2168 1.8732 5.5057 5.6297 3.9809 3.4877

28 0.2407 0.2595 0.4275 0.5913 0.5169 0.4039 5.3266 3.9535 3.7783 1.2686

29 0.014 0.0171 0.1521 0.6756 1.308 0.9961 2.5196 2.4821 1.8302 3.5717

30 0.0287 0.034 0.0924 0.1816 0.4515 0.1682 4.0666 2.7001 0.5241 0.4604

31 1.425 1.5176 2.0419 2.1589 1.8217 1.0861 2.7637 8.9663 56.4575 3.8959

32 0.0697 0.0742 0.0997 0.2158 0.9806 0.2659 7.5031 5.4568 1.1479 0.6474

33 0.0697 0.0742 0.0997 0.2158 0.9806 0.2659 7.5031 5.4568 1.1479 0.6474

34 0.1178 0.1396 0.4176 1.3372 2.1614 1.6525 4.1859 4.1155 3.0216 6.4852

35 0.1178 0.1396 0.4176 1.3372 2.1614 1.6525 4.1859 4.1155 3.0216 6.4852

36 0.134 0.149 0.3254 0.829 1.0957 0.8422 2.1242 2.0881 1.5376 3.6861

37 0.134 0.149 0.3254 0.829 1.0957 0.8422 2.1242 2.0881 1.5376 3.6861

38 0.704 0.7479 0.9399 0.8751 1.6072 0.3295 1.7812 6.3656 41.4254 1.4084

90


Table 5.17 Average Load Cost Contributions Cdavg(k,i) Modified Zbus average method


1 1.3148 1.2914 0.5741 0.488 0.4638 0.3865 0.1396 0.1967 0.2303

2 7.9786 6.3732 18.2347 1.2953 2.8921 2.7986 1.1239 1.5834 4.3066

3 9.195 7.3197 4.4114 2.8507 8.1468 0.5796 1.4786 2.0907 1.1527

4 5.3974 5.6035 1.9045 9.0713 1.7815 1.8303 2.4607 3.4226 6.869

5 11.1308 11.1729 9.0322 5.3398 3.491 11.1489 1.6297 2.2674 5.9164

6 1.5871 0.997 20.9452 1.5317 0.1957 0.6977 3.4654 4.8455 8.0825

7 1.5392 1.3162 6.7941 0.8555 0.6673 0.9026 0.8605 1.2063 1.6534

8 3.9864 4.1575 1.6726 9.0478 1.2701 1.2262 2.0251 2.8171 5.4315

9 8.7189 6.9215 3.9551 2.6397 11.3112 0.7446 1.5957 2.2601 0.8329

10 1.9117 1.8524 2.1727 1.0628 0.7953 6.9183 0.9039 1.2655 1.7362

11 0.0281 0.0253 0.048 0.0189 0.018 0.0346 20.4439 0.0244 0.0427

12 0.6618 0.6566 4.4577 1.8703 0.3538 1.488 20.0693 28.1343 7.0057

13 0.235 0.2761 3.8918 1.6574 0.667 2.1211 23.6252 32.8418 6.6608

14 2.2023 2.092 5.0271 3.2433 0.7385 0.7276 3.7314 5.2585 10.6215

15 2.5236 2.3894 6.347 3.7159 0.7919 0.6833 4.1785 5.8868 12.1862

16 0.2044 0.1719 2.2335 0.4849 0.573 1.5758 0.1116 0.1577 2.3195

17 0.2085 0.1713 2.2292 0.5459 0.5968 1.6422 0.0665 0.097 2.5792

18 0.4195 0.3825 0.4017 0.2985 0.2969 0.5974 0.5249 0.7392 0.6891

91




1 0.1791 0.2647 0.1898 0.3975 0.1057 0.3715 0.1612 0.1175

2 1.2099 5.2636 5.5996 14.559 4.0336 13.8121 6.4371 3.9497

3 5.5849 2.0621 1.0181 0.4819 0.1151 0.3992 0.4823 0.5171

4 0.2372 4.8073 3.6502 5.2533 1.7156 5.3515 3.1979 2.2721

5 1.3847 4.4403 4.1392 8.7242 2.5354 8.3886 4.2633 2.7533

6 1.8885 2.7136 0.2077 9.0035 1.9631 7.7476 2.2011 0.7154

7 0.8297 0.6904 1.7808 7.6436 1.9295 7.0401 2.7429 1.4641

8 0.4061 3.9786 3.0299 4.4028 1.4333 4.4798 2.6646 1.8894

9 5.6484 2.3697 1.2663 0.2816 0.2449 0.5263 0.7168 0.684

10 1.3759 2.0269 1.6782 2.9541 0.9045 2.9199 1.5961 1.0816

11 0.0475 0.0651 0.0517 0.0835 0.0263 0.0837 0.0474 0.0328

12 3.1384 3.261 2.8308 5.2143 1.5705 5.0782 2.7357 1.8255

13 4.0753 2.3298 2.1175 4.0656 1.207 3.9095 2.0777 1.367

14 0.0719 3.7003 5.2868 2.012 0.9705 2.5415 1.5586 0.9624

15 0.3552 5.3461 0.6256 0.6317 0.1888 0.2221 1.6898 1.9827

16 2.7622 4.8638 4.9203 6.1352 1.9923 6.3223 3.3925 2.2364

17 2.885 5.687 2.8102 5.5985 1.8076 5.7528 3.6398 2.7595

18 0.85 10.8579 2.8868 0.3204 0.1321 0.3763 1.4539 1.7469

92




19 0.3033 0.2871 0.3645 0.2444 0.2654 0.586 0.5094 0.7156 0.6051

20 0.3777 0.3504 0.1649 0.2849 0.296 0.6249 0.5464 0.7681 0.6813

21 0.8375 0.7822 0.5028 0.6447 0.6806 1.4564 1.277 1.7892 1.5631

22 0.5438 0.51 0.412 0.4238 0.4513 0.9736 0.8541 1.1952 1.0351

23 0.3381 0.3244 0.6703 0.2824 0.3149 0.7078 0.6203 0.8649 0.716

24 0.0359 0.0226 0.6558 0.0045 0.0232 0.0952 0.0784 0.1081 0.0406

25 0.4071 0.3605 1.0476 0.2581 0.233 0.4093 0.3794 0.5256 0.5645

26 0.4071 0.3605 1.0476 0.2581 0.233 0.4093 0.3794 0.5256 0.5645

27 0.8628 0.7348 4.0103 0.4707 0.3566 0.455 0.4455 0.6236 0.9032

28 0.1609 0.1487 0.0412 0.1185 0.1219 0.2511 0.2258 0.3126 0.2841

29 0.0098 0.0098 0.384 0.0187 0.032 0.0946 0.0803 0.1114 0.0668

30 0.0192 0.0195 0.1081 0.0188 0.0231 0.0555 0.049 0.0674 0.0515

31 0.97 0.8734 1.6086 0.6517 0.6224 1.1751 1.081 1.4913 1.4884

32 0.0474 0.0427 0.3063 0.0318 0.0304 0.0574 0.0528 0.0728 0.0727

33 0.0474 0.0427 0.3063 0.0318 0.0304 0.0574 0.0528 0.0728 0.0727

34 0.0768 0.0794 0.5571 0.0809 0.1022 0.2539 0.22 0.3059 0.2262

35 0.0768 0.0794 0.5571 0.0809 0.1022 0.2539 0.22 0.3059 0.2262

36 0.0877 0.085 0.2272 0.0754 0.0856 0.1952 0.1715 0.2384 0.1942

37 0.0877 0.085 0.2272 0.0754 0.0856 0.1952 0.1715 0.2384 0.1942

38 0.4824 0.4311 1.0015 0.3152 0.2936 0.5362 0.4981 0.6859 0.7087

93




19 0.8915 0.8173 4.5966 3.4733 1.1761 3.6761 1.5221 0.6991

20 0.9223 8.447 1.968 2.1267 0.7318 2.2665 1.3036 0.8982

21 2.1825 0.6179 1.7276 6.3941 2.1794 6.8333 5.3267 4.5525

22 1.4696 6.8548 0.4011 4.7817 1.6244 5.1091 4.3416 3.8785

23 1.103 0.9596 4.5137 5.2362 1.7684 5.5717 2.3387 1.1107

24 0.1912 0.4677 0.5181 3.0941 0.3825 1.0422 0.6021 0.3653

25 0.5386 0.4896 0.2363 3.0206 0.0824 7.4071 0.1505 0.1107

26 0.5386 0.4896 0.2363 3.0206 0.0824 7.4071 0.1505 0.1107

27 0.382 0.5796 1.2014 4.79 1.219 4.4863 1.7587 0.9571

28 0.3752 0.5418 0.4625 0.7673 0.2622 4.3988 0.452 0.302

29 0.1697 0.6217 0.5426 1.9385 0.6448 2.0626 1.6871 0.9521

30 0.0917 0.1659 0.1643 0.6733 0.1096 3.3797 0.1794 0.1133

31 1.6574 1.9695 1.4313 2.7443 0.7072 2.2521 1.2402 0.876

32 0.0813 0.197 0.2279 1.4651 0.1738 6.2385 0.2725 0.1642

33 0.0813 0.197 0.2279 1.4651 0.1738 6.2385 0.2725 0.1642

34 0.42 1.232 0.8308 3.2111 1.0726 3.4184 2.5568 1.7119

35 0.42 1.232 0.8308 3.2111 1.0726 3.4184 2.5568 1.7119

36 0.3084 0.7633 0.3763 1.6259 0.5459 1.7367 1.3301 1.137

37 0.3084 0.7633 0.3763 1.6259 0.5459 1.7367 1.3301 1.137

38 0.7388 0.796 0.5203 2.4115 0.2158 1.4684 0.3995 0.3023

94

The individual average generator/load costs for using all the lines in the network andtotal average cost reported in Table 5.7

Table 5.21 Average Cost For Individual Generators/Loads and total average cost Modified Zbus

average method

Bus

No:

CGAVG(I) CDAVG(I) TOTAL

COSTAVG

1 102.932 65.4225 168.355

2 103.933 58.7992 162.732

3 0 108.533 108.533

4 0 50.3883 50.3883

5 0 39.4342 39.4342

6 0 44.9461 44.9461

7 184.503 96.3466 280.849

8 0 106.113 106.113

9 0 88.5755 88.5755

10 0 45.8012 45.8012

11 0 0 0

12 0 0 0

13 100.928 92.9311 193.86

14 0.68239 65.4797 66.1621

15 88.2683 134.839 223.108

16 56.1084 37.6462 93.7545

17 0 0 0

18 194.107 155.471 349.578

19 0 70.8302 70.8302

20 0 49.6119 49.6119

21 201.267 0 201.267

22 217.313 0 217.313

23 210.789 0 210.789

24 0 0 0

95

5.4 comparison of Zbus based techniques:

The comparison of all the Zbus based techniques are reported in table 5.22

Table 5.22 comparison of all the Zbus based techniques

Zbus technique Zbus average technique Modified Zbus average techniqueBusNo

CG CD TOTALCOST

CGAVG(I) CDAVG(I) TOTALCOSTAVG

CGAVG(I) CDAVG(I) TOTALCOSTAVG

1 41.3522 25.9653 67.3176 43.7322 27.4597 71.1919 102.932 65.4225 168.3552 50.6569 28.5682 79.2251 53.5085 30.1763 83.6848 103.933 58.7992 162.7323 0 184.485 184.485 0 188.735 188.735 0 108.533 108.5334 0 84.0901 84.0901 0 88.7323 88.7323 0 50.3883 50.38835 0 68.6698 68.6698 0 72.2478 72.2478 0 39.4342 39.43426 0 59.9801 59.9801 0 77.2602 77.2602 0 44.9461 44.94617 117.549 61.2232 178.772 117.51 61.2032 178.713 184.503 96.3466 280.8498 0 175.917 175.917 0 180.024 180.024 0 106.113 106.1139 0 145.662 145.662 0 151.042 151.042 0 88.5755 88.575510 0 72.2811 72.2811 0 78.8505 78.8505 0 45.8012 45.801211 0 0 0 0 0 0 0 0 012 0 0 0 0 0 0 0 0 013 7.15621 6.64702 13.8032 7.44293 6.91334 14.3563 100.928 92.9311 193.8614 0 116.219 116.219 0 117.195 117.195 0.68239 65.4797 66.162115 35.7738 52.7455 88.5193 35.4253 52.2317 87.657 88.2683 134.839 223.10816 20.812 13.4271 34.2391 20.2819 13.0851 33.367 56.1084 37.6462 93.754517 0 0 0 0 0 0 0 0 018 39.1378 32.5822 71.7199 38.8784 32.3663 71.2447 194.107 155.471 349.57819 0 127.021 127.021 0 126.608 126.608 0 70.8302 70.830220 0 89.022 89.022 0 88.6508 88.6508 0 49.6119 49.611921 383.247 0 383.247 364.838 0 364.838 201.267 0 201.26722 352.952 0 352.952 320.599 0 320.599 217.313 0 217.31323 378.857 0 378.857 377.002 0 377.002 210.789 0 210.78924 0 0 0 0 0 0 0 0 0

The above table gives the information about the cost allocated to different

generators and loads for IEEE RTS 24 bus system for all the three Zbus based techniques.

From the above table it is concluded that the Zbus technique allocates more usage to

generators rather than demands and similarly allocates most of the cost to generators

compared to demands. The Zbus average technique avoids the allocating most of the cost

to generators than demands. Modified Zbus average technique allocates a fair allocation

96

between generators and loads when compared to both Zbus and Zbus average techniques.

other two methods not able to allocate the cost for the generators and loads which are

not directly connected to it. but this modified Zbus average method allocates the cost for

that buses which are not directly connected to it.

Better cost allocation has been observed with modified Zbus average approach

compared to Zbus and Zbus average methods.

97

5.5 Conclusions:

In the present open access restructured power system market, it is necessary to

develop an appropriate pricing scheme that can provide the useful economic information

to market participants, such as generation, transmission companies and customers.

However, accurately estimating and allocating the transmission cost in the transmission

pricing scheme is a challenging task although many methods have been proposed.

The purpose of the methodology is to allocate the cost pertaining to the

transmission lines of the network to all the generators and demands.

This work addresses the problem of allocating the cost of the transmission

network to generators and demands. This work proposes three methods using bus

impedance matrix Zbus. The three techniques are Zbus method , Zbusavg method and a

newly proposed technique Modified Zbus average method. The above methods are

compared and the new method is very effective in transmission cost allocation .

The proposed Zbusavg method method provides a methodology to apportion the

cost of the transmission network to generators and demands that use it.. This work

contributes to seek an appropriate solution to this allocation problem using an usage-

based procedure that relies on circuit theory. . In the proposed new approach, the factors

S1,S2,S3,S4 for forward flows and S11,S21,S31,S41 for reverse direction flows have

offered very useful information about the contribution of generator buses and load buses

towards the line flow of line jk. Rigorous calculations without any approximations are

possible and cost allocation results would be more reliable and accurate compared to

other methods.

For the above three techniques software is developed and implemented in

MATLAB and applied to 4-bus system and IEEE RTS-24 bus systems. This new

procedure exhibits desirable apportioning properties and is easy to implement and

understand. Case studies on 4-bus system and IEEE 24-bus system are used to illustrate

the working of the proposed techniques.

98

APPENDIX

A.1 4-BUS SYSTEM:

The number of buses : 4The number of lines : 5No.of generators :2

Bus data:

Bus Type Pgen Qgen Pload Qload Vspecified

1 P-V 0 0 0 0 1.05

2 P-V 2.5 0 0 0 1.05

3 P-Q 0 0 2.5 0 1

4 P-Q 0 0 2.5 0 1

Line data :

Line Frombus

To bus R X Halflinechargingsuceptance(ycp)

Halflinechargingsuceptance(ycq)

Tap ratio

1 1 2 0.01275 0.097 0.23055 0.23055 12 1 3 0.01275 0.097 0.23055 0.23055 13 1 4 0.01275 0.097 0.23055 0.23055 14 2 4 0.01275 0.097 0.23055 0.23055 15 3 4 0.01275 0.097 0.23055 0.23055 1

Table A.1 Bus data of 4- bus system

Table A.2 Line data of 4- bus system

99

A.2 IEEE 24- BUS RELIABILITY TEST SYSTEM:

No. of buses: 24

No. of lines: 38

No. of generators: 11

Bus Data:

Bus Type Pgen Qgen Pload Qload Vspecified

1 P-V 1.72 0.282 1.08 0.22 1.035

2 P-V 1.72 0.14 0.97 0.2 1.035

3 P-Q 0 0 1.8 0.37 1

4 P-Q 0 0 0.74 0.15 1

5 P-Q 0 0 0.71 0.14 1

6 P-Q 0 0 1.36 0.28 1

7 P-V 2.4 0.516 1.25 0.25 1.025

8 P-Q 0 0 1.71 0.35 1

9 P-Q 0 0 1.75 0.36 1

10 P-Q 0 0 1.95 0.4 1

11 P-Q 0 0 0 0 1

12 P-Q 0 0 0 0 1

13 Slack 2.853 1.221 2.65 0 1.02

14 P-V 0 0.137 1.94 0.39 0.98

15 P-V 2.15 0.0005 3.17 0.64 1.014

16 P-V 1.55 0.2522 1 0.2 1.017

17 P-Q 0 0 0 0 1

18 P-V 4 1.374 3.33 0.68 1.05

19 P-Q 0 0 1.81 0.37 1

20 P-Q 0 0 1.28 0.26 1

21 P-V 4 1.082 0 0 1.05

22 P-V 3 0.297-0.2976 0 0 1.05

23 P-V 0 0 0 0 1.05

24 P-Q 0 0 0 0 1

Table A.3 Bus data of IEEE RTS 24- bus system

100

Line data:

Line Frombus

To bus R X Halflinechargingsuceptance(ycp)

Halflinechargingsuceptance(ycq)

Tapratio

1 1 2 0.003 0.014 0.2305 0.2305 12 1 3 0.055 0.211 0.0285 0.0285 13 1 5 0.022 0.085 0.0165 0.0165 14 2 4 0.033 0.127 0.017 0.017 15 2 6 0.05 0.192 0.026 0.026 16 3 9 0.031 0.119 0.016 0.016 17 3 24 0.002 0.084 0 0 1.0158 4 9 0.027 0.104 0.014 0.014 19 5 10 0.023 0.088 0.012 0.012 110 6 10 0.014 0.061 1.2495 1.2495 111 7 8 0.016 0.061 0.0085 0.0085 112 8 9 0.043 0.165 0.0225 0.0225 113 8 10 0.043 0.165 0.0225 0.0225 114 9 11 0.002 0.084 0 0 1.0315 9 12 0.002 0.084 0 0 1.0316 10 11 0.002 0.084 0 0 1.01517 10 12 0.002 0.084 0 0 1.01518 11 13 0.006 0.048 0.05 0.05 119 11 14 0.005 0.042 0.044 0.044 120 12 13 0.006 0.048 0.05 0.05 121 12 23 0.012 0.097 0.1015 0.1015 122 13 23 0.011 0.087 0.091 0.091 123 14 16 0.005 0.059 0.041 0.041 124 15 16 0.002 0.017 0.018 0.018 125 15 21 0.006 0.049 0.0515 0.0515 126 15 21 0.006 0.049 0.0515 0.0515 127 15 24 0.007 0.052 0.0545 0.0545 128 16 17 0.003 0.026 0.0275 0.0275 129 16 19 0.003 0.023 0.0245 0.0245 130 17 18 0.002 0.014 0.015 0.015 131 17 22 0.014 0.105 0.1105 0.1105 132 18 21 0.003 0.026 0.0275 0.0275 133 18 21 0.003 0.026 0.0275 0.0275 134 19 20 0.005 0.04 0.0415 0.0415 135 19 20 0.005 0.04 0.0415 0.0415 136 20 23 0.003 0.022 0.023 0.023 137 20 23 0.003 0.022 0.023 0.023 138 21 22 0.009 0.068 0.071 0.071 1

Table A.4 Line data of IEEE RTS 24- bus system

101

1

4

2 7

58

6

39 10

2411

12

131415

16 19 20

23

222117

18

Fig A.1 IEEE 24-bus Reliability Test System

102

REFERENCES:

[1] “Power System Restructuring and Deregulation Trading, Performance andInformation Technology” Edited by Loi Lei Lai, John Wiley & Sons Ltd,Chichester.

[2]Mohammed Shahidehpour, Hatim Yamin, Zuyi Li, “Market Operations in ElectricPower System Forecasting,Scheduling and Risk managements”, John Wiley & SonsLtd, Newyork

[3] Jiuping Pan, Yonael Teklu, Saifur Rahman,, Review of Usage-Based TransmissionCost Allocation Methods under Open Access , IEEE Transactions On Power Systems,Vol. 15, No. 4, November 2000

[4] J. Bialek, “Topological generation and load distribution factors for supplementcharge allocation in transmission open access,” IEEE Trans Power Syst., vol. 12, no. 3,pp. 1185–1193, Aug. 1997.

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[7] F. D. Galiana, A. J. Conejo, and H. A. Gil, “Transmission network cost allocationbased on equivalent bilateral exchanges,” IEEE Trans. Power Syst., vol. 18, no. 4, pp.1425–1431, Nov. 2003.

[8] A. J. Conejo, J.Contreras,D.A.Lima,A.P.Feltrin “Zbus Transmission network costallocation,” IEEE Transactions On Power Systems, Vol. 22, No. 1, February 2007

[9] A. J. Conejo, F. D. Galiana, and I. Kockar, “Z-bus loss allocation,” IEEE Trans.Power Syst., vol. 16, no. 1, pp. 105–110, Feb. 2001.

[10] A. R. Berger and V. Vittal, Power Systems Analysis, 2nd ed. Englewood Cliffs, NJ:Prentice-Hall, 2000.

[11] Reliability Test System Task Force, “The IEEE reliability test system 1996,” IEEETrans. Power Syst., vol. 14, no. 3, pp. 1010–1020, Aug. 1999.

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