transmission pricing scheme based on transaction pair

THE HONG KONG POLYTECHNIC UNIVERSITY

DEPARTMENT OF ELECTRICAL ENGINEERING

Project ID: FYP_39

Transmission Pricing Scheme Based on Transaction Pair

Matching for Pool Market

by

HUANG jiahui

14073637D

Final Report

Bachelor of Engineering (Honours)

in

Electrical Engineering

Of

The Hong Kong Polytechnic University

Supervisor: Dr. C.W. YU Date:26/3/2018



Abstract

Nowadays, many things around us related to electricity. It is an indispensable part of our

life. The price of electricity would affect our behavior and life quality. Therefore,

electricity transmission pricing scheme is always a problem in power market. Meanwhile,

one scheme should not apply in different systems like educational and political systems,

different regions or countries have their unique scheme. A good pricing scheme should

reflect the actual usage such as providing economic signals to promote the maximum use

of the current electricity network, ensuring open and fair, thus improve the efficiency.

This project performs a novel transmission pricing scheme which not only fulfills the

advantages of existing pricing scheme, it also encourages appropriate bidding behaviors

in pool market and helps to reduce the appearing price spikes. The scheme is based on

paid-as-bid (PAB), combined with point-to-point (PTP) tariff and transaction pair

matching (TPM) scheme that applies to a pool market. The models and progress are

presented in detail. The performance of the proposed scheme was analysis by comparing

the results of point of connect (POC) method.

The test result of modified IEEE 30-bus system and 57-bus system under the new scheme

operation demonstrates the advantages of the proposed scheme. It is shown that most

generators have lower average transmission prices and increased profit comparing to

POC method. Meanwhile, the scheme helps to reduce price spike and generate correct

signals for market regulation. In summary, this project shows the performance

advantages over the conventional scheme to a great extent.



Acknowledgments

I would like to express my great appreciation to Professor C.W. Yu for his valuable

advice and support in the whole project.



Content

1. Introduction ..................................................................................................................... 1

2. Objective ......................................................................................................................... 4

3. background ...................................................................................................................... 5

3.1 Background information on electricity market: ..................................................... 5

3.2 Principle of transmission pricing scheme............................................................... 6

3.3 Point of connect and point-to-point tariff ............................................................... 6

3.4 Marginal pricing and pay-as-bid scheme ............................................................... 8

3.5 Scheme of used in this project ............................................................................. 10

4. Methodology ................................................................................................................. 11

4.1 Theories: ............................................................................................................... 11

4.2 Brief Description of the scheme: .......................................................................... 12

4.3 Method 1 (Point of connect scheme).................................................................... 13

4.4 Method 2 (Proposed method) ............................................................................... 14

4.5 Case study ............................................................................................................ 25

5. Results and finding: ...................................................................................................... 33

5.1 Adjustment on trading profit: ............................................................................... 33

5.1.1 IEEE 30-bus system.................................................................................... 33

5.1.2 IEEE 57-bus system.................................................................................... 37

5.2 Adjustment on the marginal generator ................................................................. 46

5.3 Adjustment in the congestion scenario: ............................................................... 47

6. Conclusions ................................................................................................................... 48

7. Reference ...................................................................................................................... 49

8. Appendix ....................................................................................................................... 51



1

1. Introduction

Transmission pricing scheme is always a considerable issue in power market. It affects

the market efficiency significantly and is a key component in the infrastructure of power

market.

In electricity market, it is an oligopolistic-based situation, the inelastic demand would

make the spikes and uplift the in purchasing cost. However, the economist stated that the

price of electricity would be lower and the efficiency would be better in the market

operation rather than monopoly regulation or government policy [1]. It is a challenging

task to make a fair and open pricing scheme such that the network cost can be allocated

to all users equally and give them the correct market signals at the same time [1].

Since the electricity tariff consists of a large proportion of transmission cost, reducing in

transmission cost may decrease the price of electricity. In general, transmission pricing

scheme can be classified into two methods: point-to-point scheme (PTP) and point-of-

connect scheme (POC) [2]. POC is widely used as it is simple. However, the scheme

cannot figure out the actual usage of the network and cause great transmission loss. Some

buyers may pay an excessive price and some may pay a lower price such that over-the-

counter (OTC) trading may occur but the market cannot regulate.

In Hong Kong, the two investor-owned electricity companies (CLP power and HEC)

provide electricity to their own region independently. Unlike other countries, they are



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vertically integrated firms that have absolute control over the entire spectrum of

electricity provision, from generation, transmission, to distribution [3]. Therefore, the two

utilities have no direct or indirect competition between them, this situation can be viewed

as regional monopolies. Since there is no competition in Hong Kong such that the

regional electricity come from the certain electricity industry in Hong Kong and most of

them are local transmission, the new scheme which combined by PAD and PTP tariff

cannot be applied. However, excess capacity is 40% in Hong Kong which is very high

compared to average 15% in Asian countries [3]. So, the electricity efficiency in Hong

Kong is quite low.

Figure 1 cross-countries comparison of excess capacity

In China, marginal pricing (MP) is not a suitable pricing scheme. The reason is that a

power plant may supply electricity to more than one province. It means that the power

does not deliver locally. Also, the distinctions in society, culture and economic

development levels between different provinces are huge. Unfair may occur by using MP



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as the uniform price which seems reasonable to rich provinces may always be far beyond

the affordable level of poor provinces [4]. Actually, this situation may be found in the

regional electricity market. Therefore, PAB with TPM is more suitable for China and a

trial operation of Northeast China and South China regional power markets since 2005

and 2006 [4]. The advantage is that the pricing would be fair for each buyer. In this

project, one MatLab script and was written for TPM and two scripts found online to find

the power flow and help to generate the PTP matrix. The full scripts can be found in

Appendix. The result will show the transaction pair, profit, transmission price, PTP

matrix, comparison, and evaluation between POC and proposed scheme.

The report will begin with the objectives of this project in Section 2. Then, the

background information is organized in Section 3. In Section 4, the actual design and

operation of the two schemes will be introduced. Next, the proposed scheme will be

evaluated by analyzing and comparing the results of the case study in Section 5. Finally,

a conclusion will be made in the last section.



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2. Objective

a) Analysis of pros and cons of current transmission pricing scheme

b) Apply the proposed scheme in IEEE test system by software simulation.

c) Evaluate the proposed scheme by comparing the results.



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3. background

3.1 Background information on electricity market:

Rapid economic growth in the world in the stage of has led to an uncommon rise in the

demand for electricity. Therefore, the expansion of capacity (investment) is extremely

important for satisfy the large demand for electricity. The investment of capacity

expansion involved a huge amount of money. However, the revenue under most of the

current pricing scheme cannot cover the investment but operation cost. This is because

the current schemes are not fair and wrong market-based economic signals, thus the

revenue is not enough to cover the investment. Therefore, transmission pricing has a

great impact on the development of power market such as the power seller may know the

location of new capacity of expansion through the scheme. Also, transmission of

electricity pricing scheme is a key factor in the infrastructure of power market, assuring

fair, open and non-discriminatory access [5].

In mainland China, transmission pricing has been one of the hard issues in electric reform.

There are two national grips in Mainland China, the State Grid and the China Southern

Power Grid. China government plan to make a grid that is interconnected within all the

provinces. Therefore, the National Development and Reform Commission release

electricity reform in 2017 to change the style of profit gain of producers. They would like

to make a reliable, high-quality service and the transmission cost can be reflected by the

prices [6].



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3.2 Principle of transmission pricing scheme

In economic theories, there are two main functions of price. Firstly, it is the signal of

relative cost. The second function is to determine the distribution for any transaction [7].

Six principles for transmission pricing were stated by Energy Modeling forum of

Stanford University. A great pricing should follow the principles during designation:

1. promote the efficient day-to-day operation of the bulk power market;

2. signal locational advantages for investment in generation and demand;

3. signal the need for investment in the transmission system;

4. compensate the owners of existing transmission assets;

5. be simple and transparent; and

6. be politically implementable.

It is a challenge for designing an efficiency, equally and transparency scheme in pricing.

In order to offer a lower price, higher quality and more secure service, the proposed

pricing scheme is introduced.

3.3 Point of connect and point-to-point tariff

As the paper mentioned before, the transmission scheme could be classified into POC and

PTP scheme. The characteristic of point of connect (POC) is that the buyers should pay

the specific transmission fee due to the point they connected. Just like postage-stamp,

different point has its fix transmission price no matter what is the distance between the

two points [8]. This method is widely used as it is simple and can be applied to both

bilateral and pool market. However, POC does not consider the actual operation of the



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system and the distance, thus ineffective transaction occurs. Ineffective transaction causes

large transmission loss and the POC tariff could cover the transmission cost. An example

is shown below. All buyers will buy electricity from generator A since it has lower POC

tariff no matter what the distance is. Then the transmission loss is large in the case. As a

result, the pricing scheme cannot show the economic signals [8] [9].

Figure 2 Explanation of POC

In this paper, point to point tariff (PTP) is used. It also called transaction based tariff. The

characteristic of point to point tariff is that the transmission fee is determined by the

augments of power flow in transmission facilities. Mostly, large power flow would result

in a high tariff such that the tariff would change due to the power flow and buyer may

change the seller due to the variable price. In order to calculate the tariff of PTP, MW-

Mile, contract path, monetary methods and so on can be used [10] [11] [2] [12]. In

contract path method, the path is selected by both utility company and wheeling

customers, but it does not consider the performance of power flow. Therefore, incorrect



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signals may be generated, thus lead to economic inefficient [10]. In monetary method,

active and reactive power flows are converted into monetary flows by using nodal prices

[12]. MW-Mile is an embedded cost method that widely used in transmission pricing. It

calculated based on the distance of transmission and the active power flow in each

transmission branch. But it ignores the quality of the load in allocating the transmission

cost [11].

The advantage of PTP tariff is that can reflect the real operation of the market and

maximum use of the system could be promoted [2] [5]. However, it does not apply to

pool market as generation schedules are always determined unilaterally such that no

transaction pairs is generated. According to [7], most generators do not send its prices

since the transmission are not separated. In this project, the proposed scheme overcome

the problem.

3.4 Marginal pricing and pay-as-bid scheme

Market price is also important in transmission scheme. In general, pay-as-bid (PAB) and

marginal pricing (MP) are the two common pricing schemes. The choice between the two

schemes for electricity market become a subject of market study [13]. The papers stated

different arguments for supporting MP or PAB, no absolute conclusion can be made that

which one is better for all situation.

The basic principle of PAB is that the prices are different from different generators.

Under the PAB mechanism, the generators are paid their own bids they have offered;



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whereas under the MP scheme, accepted suppliers are paid the market marginal price

(either the last accepted price-offer, LAO, or the first rejected price-offer, FRO). The

PAB scheme may force generators to bid higher than their true marginal costs in order to

make a profit. However, under the proposed scheme, the generators have to reduce the

bidding price to gain more profit. while under MP, non-price setting generators gain

profits even if they bid their marginal costs [13]. The basic principle of uniform marginal

pricing (MP) is the main option for determining transaction price in pool market. The

main advantage is that it is a relatively simple pricing method that quick to calculate and

easy to implement. However, marginal pricing cannot provide a correct economic signal

to improve the efficiency. An additional issue is that the income cannot recover the

investment in required new facilities under economies of scale. [14].

In some research [15], it states that MP is fair to all consumers as all of them pay the

same prices, thus no winner in this scheme. No generator offers the price lower or equal

to the market clearing price. However, MP is not suitable for mainland China. Due to the

policy of reform and opening at 1987, some of the provinces being rich first such as the

Guang Dong, Shan Dong that the provinces near to the sea. Meanwhile, interprovincial

transmission is used in mainland China. If the cost were equally distributed, it was unfair

to the poor provinces. Moreover, the supplier in MP can exercise market power by

enhancing the bidding price that higher than marginal cost to affect the prices [15]. PAB

is a scheme to prevent the exercise of market power.



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3.5 Scheme of used in this project

The new transmission pricing scheme based on point to point tariff, and combined with

pay-as-bid and transaction pair matching in power pool market [1]. Basically, PTP is that

consumers pay transmission fee according to given transaction pairs from buyers to

sellers. Under this scheme, lower PTP rate will be preferred for almost all transaction.

Then, effective economic signals are generated and sent to all market participants.

Participants will compare the tariff for all transaction before making their decisions as a

smart consumer, thus the maximum use of the existing system could be promoted and the

market competition could be intense and free.

Besides, pay-as-bid (PAB) serves as the main choice to determine the price in pool

market. Participants will introduce a selling price for each certain short period, buyers

will choose the transaction under this real-time balancing mechanism. It will encourage

competition that bring lots of advantages to both buyers and seller, and which create an

efficiency transaction environment.



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4. Methodology

In this section, the details and the procedures of the whole scheme and the project will be

presented. In order to have a clear understanding, some basic concepts will be introduced

below:

4.1 Theories:

a) Pool market

Electricity pool market can be classified into a compulsory pool or voluntary pool [16].

In the compulsory pool or gross pool, all generators except the smallest one required to

sell all of the power output into the pool at the pool's price. In a voluntary pool or net

pool, the generators can sell the power that has not sold already by bilateral contract only.

Before the opening of the market, all generators are required to submit the volume that

they can generate at a given price.

b) Market regulation

A market can be regulated by two ways: regulated by government or regulated by market

power. Mostly, the government only regulate the market in natural monopoly market to

control the price and ensure the fairness. The second regulation method mostly occurs

naturally in a free market. The price will be regulated by demand, supply and finally

reach an equilibrium point.



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4.2 Brief Description of the scheme:

a) Software Adopted in the Project

MatLab is the main software to construct the project. MATPOWER is an open source

package for calculating load flow developed by Cornell University. It contains various

cases of bus systems from five buses to thousand buses.

b) Aims and Flow of the Project

In this project, two methods are applied for calculating the transmission price and profit

for comparison. The point-of-connect scheme is simple and widely used in calculating

the transmission price as the price for each unit is equal. The price and profit calculated

by POC scheme will be regarded as a reference for comparing the results of the proposed

method.

The proposed method aims to perform the same task by using the point-to-point scheme

that combined with transaction pair matching based on pay as bid. Evaluation of the

proposed scheme in terms of promoting maximum use, encouraging bidding behaviors in

the pool and reducing the price spikes can be achieved by comparing the transmission

price, profit and results obtained in both methods. Moreover, the two methods will be

studied under IEEE 30 bus system and IEEE 57 bus system to obtain the data for

examination and comparison.

c) Experimental Setting and Default Setting

In this project, there are experimental setting and default setting respectively. The setting



13

will be used to test and analyze the methods.

In the default setting, the parameters in the MATPOWER package remains almost

unchanged except the data of generators. The change will be discussed later. All the

changes of the test system help to understand the function and performance of the

proposed method.

In the experimental setting, all the parameters of the branch, bus, and generator remain

the same for both methods. The data obtained by different methods will be compared

against each other to verify the proposed method.

Besides, grip corporation is set as the single-buyer of the pool and generators bid a single

discrete price segment to reduce the complexity of the case, then, a clear performance of

the proposed method can be shown. Also, the generators are assumed to submit the

maximum capacities since they have no incentive to reduce available capacities. DC

power flow model is adopted in the pool for market clearing and calculation of point-to-

point tariff. Some technical consideration such as ramping rates and start-up and

downtime are neglected.

4.3 Method 1 (Point of connect scheme)

In this project, a basic point of connect method is used for calculating the transmission

fee and profit [17]. The basic principle is discussed above. For each test system, a total

transmission cost 𝐶𝑇 is assumed. Base on the theory of point of connect method, the



14

transmission price is calculated as shown:

𝐶𝑝𝑜𝑐 = 𝐶𝑇

𝑇𝑜𝑡𝑎𝑙 𝑡𝑟𝑎𝑛𝑠𝑎𝑐𝑡𝑖𝑜𝑛 𝑣𝑜𝑙𝑢𝑚𝑒 (C1)

Also, the profit for each generator is calculated as shown:

𝑃𝑝𝑜𝑐 = 𝜇𝐵 − 𝜇𝑃 − 𝐶𝑝𝑜𝑐 . ∑ 𝑔𝐿 (𝐶2)𝐿∈𝑇𝑛 , 𝑇𝑛 ∈𝑋𝑝𝑎𝑖𝑟

Where 𝜇𝐵 is the bidding price, 𝜇𝑃 is the production cost of the generator, 𝑇𝑛 is the

transaction pair, 𝑋𝑝𝑎𝑖𝑟 represents all the transaction pair in the pool, 𝑔𝐿 is the volume of

the power output of generator L or volume of purchased power for the load bus at that

transaction.

4.4 Method 2 (Proposed method)

1. General description

In the proposed scheme, there are three steps in progress: 1) forming primary PTP tariff

matrix, 2) transaction pair matching and 3) transmission fee settlement.

As the background stated, PTP tariff effectively reflects the actual usage of the network

and transmission cost between the buyers and sellers. By evaluating the load flow study

and all transaction pair in the pool, a PTP tariff matrix is formed. Each value in the

matrix represents the corresponding transmission price for delivering one unit of energy

between two specified points. The PTP tariff in the first step is the primary matrix that

only consists the differential part of transmission price. The detailed explanation of



15

transmission fee of the basic part and differential part will be discussed later. The primary

matrix is announced before the market opening.

After the closing of the pool, trading results for between buyers and sellers are obtained

such as the price, output of generators and load demand. Thus, the TPM scheme started.

The pairing results just to decide the PTP tariff for each pair by differential part of

transmission fee, the final trading result will not change. Transaction pairs are then

formed in sequence one by one due to the rule, such that the generators bid a lower price

has the priority to choose their dealing point by the lower transmission price. The trading

profit equal to buying price minus selling price and corresponding PTP rate. During the

process of TPM, the technical factors for determining the PTP tariff are neglected. Four

basic elements in a transaction pair are considered, they are transaction volume, named

buyer, named seller and PTP rate respectively.

In the last step, transmission fee is settled. The basic part of PTP tariff is determined

and the primary PTP tariff matrix is revised. Each buyer may be involved in several

transaction pairs with different generators, transaction volume, and PTP rate. Total

transmission fee for each participant is calculated by paying every involved pair such that

the transaction volume times PTP rate. The PTP rate should include basic and differential

part.

2. Forming primary PTP tariff matrix

PTP rate (caT

b) is the price for delivering one unit of power from point a to point b. As the



16

background introduced, several methods have been developed for finding the PTP

transmission rate. In this project, the determination of PTP rate is mainly based on the

ideas of MW-KW and Monetary flow [12] [18] [11]. Before calculating the PTP tariff,

load flow analysis for each branch is required. Generalized distribution factors based on

DC power flow model is adapted to determine the transaction-related power flows in this

project. The total transmission cost of each branch cover number of important factors

such as the maximum capacity, service cycle and the investment of capital. The power in

the system is recognized as bi-directional flow. Therefore, the power flows in the branch

are treated as an absolute value, thus rescinding the problem of counter-flow [5].

PTP rate caT

,b could be divided into basic part (cT, B) and differential part ( 𝐶𝑎,𝑏𝑇,𝐷

)

respectively. The value of cT ,B is a uniform payment for one unit power delivery, while

the values of 𝐶𝑎,𝑏𝑇,𝐷

are different for every transaction pair due to various location. When

the involved generator and the load are located at the same point such that they are on the

same bus, no differential part is required in the calculation. So the transmission fee for

local delivery just includes basic part (cT, B). However, the differential part should be a

positive value when the location of generator and load bus are different in a given

transaction pair. In this non-local delivery situation, the buyer should pay both basic part

and differential part in transmission payment.

In this section, the method for calculating the differential part of transmission part is

introduced to form the PTP matrix. The expression of 𝐶𝑎,𝑏𝑇,𝐷

is shown in the equation

below, while the unit is in $/MWh:



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𝐶𝑎,𝑏𝑇,𝐷 = 𝛽𝑃𝑇𝑃 . ∑ |𝐹𝐿| . 𝛾𝐿 (1)

𝐿∈𝑋𝐵𝑟𝑎𝑛

Where FL is the augment of load flow in line L that taken place by delivering one unit of

power production between the connected points a and b; FL is dimensionless. L is the

proportion of the total transmission cost for the branch L in the whole system, which is

dimensionless as well.L is calculated according to the proportion of the branch

impedance to the total impedance of the system. XBran represents the set of all the branch

in the system; and PTP is introduced as a control parameter with the same unit as caT

,b

which is the price for a unit of power production.

Input the modified case

and obtain the power

flow from MATPOWER

Start

Obtain transmission fee between two connected points by

substituting power flow in (1)

Calculate 𝐶𝑎,𝑏𝑇,𝐷 by inputting

the results in the previous

step to the program

(shortest length)



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Figure 3 Flow chart of forming primary PTP tariff

By adjusting the value of PTP, the value in the PTP tariff could be adjusted when some

other factors are changed. The primary matrix is announced to the public before the

opening of pool market. It should be noted that despite the matrix is primary, the TPM

can start by using the primary PTP matrix. The basic part of PTP rate just a uniform uplift

on the whole system. It will not affect the trading results but just some change in payment.

C. Transaction pair matching

1) Forming judging matrix

In pool market, generators submit bids to generate different amount of power supply at

specific prices. A supply curve is produced by arranged the prices in ascending order.

The result of 𝐶𝑎,𝑏𝑇,𝐷 to every

point are obtained in the

matrix

Remove the data that no

generator or load connected

to the bus

Primary PTP

tariff is

formed



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While the demand curve is produced by the load demand of buyers and ranked in

descending order. Then, the equilibrium point is the intersection between the two curve

and the marginal price is obtained at that point. In the case of non-congestion, generators

bid under the marginal price would be scheduled on by market operations, while power

supply can be obtained by bidding higher than the marginal price. In the case of

congestion, the plan would be revised due to the law of maximum use or minimum

generation costs. As PAB is adopted, the market rules and operation would determine the

settlement prices for participants.

After pool market clearing, the data of generators with maximum capacity, bidding price,

and production cost are shown in a matrix, while the load demand on each bus is shown

in another matrix. The generator with a lower bidding price has priority to choose the

load bus, which means the choosing order of generators is decided by the bidding price

on increasing order. Then, the generators would choose the load bus due to the lower PTP

rate. If the market is single-buyer based, load demands in different points could be taken

as many independent load service entities(LSE). The profit for a unit power transaction in

each pair is shown below:

𝑃𝐿,𝑀 = 𝜇𝐿 − 𝜇𝑀 − 𝑐𝑎,𝑏𝑇,𝐷 , 𝐿 ∈ 𝑎, 𝑀 ∈ 𝑏, (2)

Where 𝑃𝐿,𝑀 denote the profit for a unit transaction from generator L to load bus M. 𝜇𝐿 is

the bidding price, 𝜇𝑀 is the production cost and 𝑐𝑎,𝑏𝑇,𝐷

is the corresponding PTP tariff (the

basic part of tariff is ignored). 𝐿 ∈ 𝑎 means that generator connects to point a and 𝑀 ∈ 𝑏



20

means that load M connects to point b.

2) Matching in sequence

Transaction pairs are matched one by one in sequence. For each pair 𝑇𝑛, the transaction

volume 𝑔𝑛𝑝 , and the corresponding price 𝜇𝐿 are recorded.

𝑔𝑛𝑝 = (𝑔𝐿,𝑐, 𝑔𝑀,𝑑) (3)

Where 𝑔𝐿,𝑐 and 𝑔𝑀,𝑐 respectively represent the purchasing power volume of LSE c and

the power outputs of generator h in pool market.

After every step of the transaction pair has been matched, 𝑔𝐿,𝑎and 𝑔𝑀,𝑏 must be revised

simultaneously. The transaction volume should be subtracted for both generator and LSE:

𝑔𝐿,𝑐 = 𝑔𝐿,𝑐 − 𝑔𝑛𝑝 (4)

𝑔𝑀,𝑑 = 𝑔𝑀,𝑑 − 𝑔𝑛𝑝 (5)

3) Updating matrix

After each transaction pair is matched, the matrix of generators, load and PTP matrix

should be updated. The capacity of the generator and load of the bus will be checked, if

the values of 𝑔𝐿,𝑐 have become zero, the data of cth row in the load bus matrix and cth

column in PTP matrix should be removed. The same, if the values of 𝑔𝑀,𝑑 have become

zero, the data of dth column in generator matrix and PTP matrix should be removed as

well. w the value of 𝑔𝑀,𝑑 or 𝑔𝐿,𝑐 has become zero, it means that the process of



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transaction pair matching end. Otherwise, update the matrix and go back to match the

next pair.

D. Transmission fee settlement

Transmission fee for each participant is settled by paying every involved transaction pair.

As mentioned above, the fee divided into two parts: the basic part 𝑐𝑖𝑇,𝐵

and the

differential part 𝑐𝑖𝑇,𝐷

. Firstly, 𝑐𝑖𝑇,𝐷

is calculated based on the load flow, cost proportion

and corresponding transaction volume, so we have:

𝑐𝑖𝑇,𝐷 = ∑ 𝑔𝑐,𝑑

𝑝 . 𝑐𝑎,𝑏𝑇,𝐷

𝐿∈𝑇𝑛 , 𝑇𝑛 ∈𝑋𝑝𝑎𝑖𝑟

(6)

𝐶𝑇,𝐷 = ∑ 𝑐𝑖𝑇,𝐷

𝐿∈𝑋𝑝𝑎𝑟𝑡

(7)

Where 𝑋𝑝𝑎𝑖𝑟 represents all the transaction pair in the pool, 𝑋𝑝𝑎𝑟𝑡 represents all the

participants in the pool, and 𝐶𝑇,𝐷 is the sum of the differential part of transmission fee

paid by all participants.

By assuming that the total transmission cost of the whole system recovered in the time

interval is 𝐶𝑇,𝐷. As the value of 𝛽𝑃𝑇𝑃 is adjustable, there could be offset between CT and

𝐶𝑇,𝐷. However, as the recovery of investment is one of the important targets in the

transmission pricing scheme. The offset is averagely assigned to each transaction unit of

power transmission in the pool market. The basic part of transmission 𝐶𝑇,𝐵is:

𝐶𝑇,𝐵 =𝐶𝑇 − 𝐶𝑇,𝐷

g (8)



22

𝐶𝐿𝑇,𝐵 = 𝐶𝑇,𝐵. 𝑔𝐿 (9)

Where g is the total transaction volume in the pool market, and 𝑔𝐿 is the volume of the

power output of generator L or volume of purchased power for the load bus at that

transaction. Then, the primary PTP tariff is updated by adding 𝑐𝑇,𝐵 to every element

(𝑐𝑎,𝑏𝑇,𝐷

) in the matrix to form the new element 𝑐𝑎,𝑏𝑇 :

𝑐𝑎,𝑏𝑇 = 𝑐𝑎,𝑏

𝑇,𝐷+ 𝑐𝑇,𝐵 (10)

Hence, the total transmission payment for participant L is shown as:

𝑐𝐿𝑇 = 𝑐𝐿

𝑇,𝐷+ 𝑐𝐿𝑇,𝐵 (11)

𝑐𝑖𝑇 = ∑ 𝑔𝑐,𝑑

𝑝 . 𝑐𝑎,𝑏𝑇

𝐿∈𝑇𝑛,𝑇𝑛,∈𝑋𝑝𝑎𝑖𝑟

(12)

The expression in formula (11) and (12) are the same.

Apart from 𝛽𝑃𝑇𝑃, 𝑅𝑃𝑇𝑃𝑇 is another control parameter to show the proportion of differential

part in the total transmission cost which is defined as:

𝑅𝑃𝑇𝑃𝑇 =

𝐶𝑇,𝐷

𝐶𝑇 (13)

By comparing to the parameter 𝛽𝑃𝑇𝑃, 𝑅𝑃𝑇𝑃𝑇 is easy to realize the concept that related to

unit price. It can directly show the change in the differential part of PTP tariff.

E. Flowchart of TPM scheme



23

Figure 4 Flowchart TPM scheme



24

Figure 5 Flow chart the whole proposed method

*It is noted that the detailed script of forming PTP tariff and TPM tables will show in the

appendix.

The process of forming PTP

matrix in flow chart 1

Start

Input the PTP matrix, data of

load buses and generators

The process of forming TPM

result in flow chart 2

The detail of

each transaction

pair is shown in

the table



25

4.5 Case study

Actually, the proposed method has been added in the power market designation of some

provinces in China, but no data can be obtained since the market did not enter the

practical state. In order to test the performance and effectiveness of the scheme. An IEEE

30- bus system and an IEEE 57-bus system are used.

The scale of IEEE 30-bus system is a typical case of the provincial power market in the

early state. In IEEE 30-bus system, it includes 21 load buses and 13 power generators.

The basic data of the system is shown in the next section. The branch data is shown in fig.

6, bus data is shown in fig. 7 and generators data is shown in fig 8. The pool market is set

in the hourly base and the number of generators is increased since more generators can

show the change effectively and easily.

IEEE 57 bus system includes 41 load buses and 23 power generators. The basic data of

the system is shown in the next section. The branch data is shown in fig. 9, bus data is

shown in fig. 10 and generators data is shown in fig 11. The pool market is set on an

hourly base and the number of generators is increased since more generators can show

the change effectively and easily. The aim of this system is to test the proposed scheme in

a more complex situation, as the situation of current power market would become

complex after more participants enter the market.



26

IEEE 30 bus system with 13 generators and 21 load buses

Figure 6 IEEE 30 bus system with 13 generators and 21 load buses

In this case, the total transmission cost is set as 2000$/h. It includes the cost of line

related to the operation, investment and maintenance. The total load demand is 283.4

MWh and the maximum generation is 349.5 MWh. As Dc model is adopted, transmission

losses are neglected.



27

%% bus data % bus_i type d Qd Gs Bs area Vm Va baseKV zone Vmax Vmin mpc.bus = [ 1 3 0 0 0 0 1 1 0 135 1 1.05 0.95; 2 2 21.7 12.7 0 0 1 1 0 135 1 1.1 0.95; 3 2 2.4 1.2 0 0 1 1 0 135 1 1.1 0.95; 4 1 7.6 1.6 0 0 1 1 0 135 1 1.05 0.95; 5 2 94.2 10 0 0 1 1 0 135 1 1.1 0.95; 6 1 0 0 0 0 1 1 0 135 1 1.05 0.95; 7 1 22.8 10.9 0 0 1 1 0 135 1 1.05 0.95; 8 2 30 30 0 0 1 1 0 135 1 1.1 0.95; 9 2 0 0 0 0 1 1 0 135 1 1.1 0.95; 10 1 5.8 2 0 0 3 1 0 135 1 1.05 0.95; 11 2 0 0 0 0 1 1 0 135 1 1.1 0.95; 12 1 11.2 7.5 0 0 2 1 0 135 1 1.05 0.95; 13 2 0 0 0 0 2 1 0 135 1 1.1 0.95; 14 2 6.2 1.6 0 0 2 1 0 135 1 1.1 0.95; 15 1 8.2 2.5 0 0 2 1 0 135 1 1.05 0.95; 16 2 3.5 1.8 0 0 2 1 0 135 1 1.1 0.95; 17 1 9 5.8 0 0 2 1 0 135 1 1.05 0.95; 18 2 3.2 0.9 0 0 2 1 0 135 1 1.1 0.95; 19 1 9.5 3.4 0 0 2 1 0 135 1 1.05 0.95; 20 1 2.2 0.7 0 0 2 1 0 135 1 1.05 0.95; 21 1 17.5 11.2 0 0 3 1 0 135 1 1.05 0.95; 22 2 0 0 0 0 3 1 0 135 1 1.1 0.95; 23 2 3.2 1.6 0 0 2 1 0 135 1 1.1 0.95; 24 1 8.7 6.7 0 0 3 1 0 135 1 1.05 0.95; 25 1 0 0 0 0 3 1 0 135 1 1.05 0.95; 26 1 3.5 2.3 0 0 3 1 0 135 1 1.05 0.95; 27 1 0 0 0 0 3 1 0 135 1 1.05 0.95; 28 1 0 0 0 0 1 1 0 135 1 1.05 0.95; 29 1 2.4 0.9 0 0 3 1 0 135 1 1.05 0.95; 30 1 10.6 1.9 0 0 3 1 0 135 1 1.05 0.95; ];

Figure 7 Bus data of IEEE 30 bus system

%% branch data % fbus tbus r x b rateA rateB rateC ratio angle

status angmin angmax mpc.branch = [ 1 2 0.02 0.06 0.03 130 130 130 0 0 1 -360 360; 1 3 0.05 0.19 0.02 130 130 130 0 0 1 -360 360; 2 4 0.06 0.17 0.02 65 65 65 0 0 1 -360 360; 3 4 0.01 0.04 0 130 130 130 0 0 1 -360 360; 2 5 0.05 0.2 0.02 130 130 130 0 0 1 -360 360; 2 6 0.06 0.18 0.02 65 65 65 0 0 1 -360 360; 4 6 0.01 0.04 0 90 90 90 0 0 1 -360 360; 5 7 0.05 0.12 0.01 70 70 70 0 0 1 -360 360; 6 7 0.03 0.08 0.01 130 130 130 0 0 1 -360 360; 6 8 0.01 0.04 0 32 32 32 0 0 1 -360 360; 6 9 0 0.21 0 65 65 65 0 0 1 -360 360; 6 10 0 0.56 0 32 32 32 0 0 1 -360 360; 9 11 0 0.21 0 65 65 65 0 0 1 -360 360; 9 10 0 0.11 0 65 65 65 0 0 1 -360 360;



28

4 12 0 0.26 0 65 65 65 0 0 1 -360 360; 12 13 0 0.14 0 65 65 65 0 0 1 -360 360; 12 14 0.12 0.26 0 32 32 32 0 0 1 -360 360; 12 15 0.07 0.13 0 32 32 32 0 0 1 -360 360; 12 16 0.09 0.2 0 32 32 32 0 0 1 -360 360; 14 15 0.22 0.2 0 16 16 16 0 0 1 -360 360; 16 17 0.08 0.19 0 16 16 16 0 0 1 -360 360; 15 18 0.11 0.22 0 16 16 16 0 0 1 -360 360; 18 19 0.06 0.13 0 16 16 16 0 0 1 -360 360; 19 20 0.03 0.07 0 32 32 32 0 0 1 -360 360; 10 20 0.09 0.21 0 32 32 32 0 0 1 -360 360; 10 17 0.03 0.08 0 32 32 32 0 0 1 -360 360; 10 21 0.03 0.07 0 32 32 32 0 0 1 -360 360; 10 22 0.07 0.15 0 32 32 32 0 0 1 -360 360; 21 22 0.01 0.02 0 32 32 32 0 0 1 -360 360; 15 23 0.1 0.2 0 16 16 16 0 0 1 -360 360; 22 24 0.12 0.18 0 16 16 16 0 0 1 -360 360; 23 24 0.13 0.27 0 16 16 16 0 0 1 -360 360; 24 25 0.19 0.33 0 16 16 16 0 0 1 -360 360; 25 26 0.25 0.38 0 16 16 16 0 0 1 -360 360; 25 27 0.11 0.21 0 16 16 16 0 0 1 -360 360; 28 27 0 0.4 0 65 65 65 0 0 1 -360 360; 27 29 0.22 0.42 0 16 16 16 0 0 1 -360 360; 27 30 0.32 0.6 0 16 16 16 0 0 1 -360 360; 29 30 0.24 0.45 0 16 16 16 0 0 1 -360 360; 8 28 0.06 0.2 0.02 32 32 32 0 0 1 -360 360; 6 28 0.02 0.06 0.01 32 32 32 0 0 1 -360 360; ];

Figure 8 Branch data of IEEE 30 bus system

Generator data:

Generator 1 2 3 5 8 9 11 13 14

Maxi capacity(MW)

Bidding price($/MWh)

Production cost($/MWh)

30

58.2

46.6

100

73.5

50.7

40

64.9

51.9

25

47.6

33.0

15

45.9

32.0

15

66.9

53.5

20

67.9

54.4

17.5

69.1

50.3

22

63.7

50.9

Generator 16 18 22 23

Maxi capacity(MW)



30

71.5

52.2

12

59.4

47.5

15

55.6

41.5

8

51.8

41.4

Figure 9 Generator data of IEEE 30 bus system



29

IEEE 57 bus system with 23 generators and 41 load buses

Figure 10 IEEE 57 bus system with 23 generators and 41 load buses

In this case, the total transmission cost is set as 8000$/h. It includes the cost of line

related to the operation, investment and maintenance. The total load demand is 1250.8

MWh and the maximum generation is 1499 MWh. As Dc model is adopted, transmission

losses are neglected.



30

%% bus data

% bus_i type Pd Qd Gs Bs area Vm Va baseKV zone Vmax

Vmin

mpc.bus = [

1 3 55 17 0 0 1 1.04 0 0 1 1.06 0.94;

2 2 3 88 0 0 1 1.01 -1.18 0 1 1.06 0.94;

3 2 41 21 0 0 1 0.985 -5.97 0 1 1.06 0.94;

4 1 0 0 0 0 1 0.981 -7.32 0 1 1.06 0.94;

5 1 13 4 0 0 1 0.976 -8.52 0 1 1.06 0.94;

6 2 75 2 0 0 1 0.98 -8.65 0 1 1.06 0.94;

7 1 0 0 0 0 1 0.984 -7.58 0 1 1.06 0.94;

8 2 150 22 0 0 1 1.005 -4.45 0 1 1.06 0.94;

9 2 121 26 0 0 1 0.98 -9.56 0 1 1.06 0.94;

10 1 5 2 0 0 1 0.986 -11.43 0 1 1.06 0.94;

11 1 0 0 0 0 1 0.974 -10.17 0 1 1.06 0.94;

12 2 377 24 0 0 1 1.015 -10.46 0 1 1.06 0.94;

13 1 18 2.3 0 0 1 0.979 -9.79 0 1 1.06 0.94;

14 1 10.5 5.3 0 0 1 0.97 -9.33 0 1 1.06 0.94;

15 1 22 5 0 0 1 0.988 -7.18 0 1 1.06 0.94;

16 1 43 3 0 0 1 1.013 -8.85 0 1 1.06 0.94;

17 2 42 8 0 0 1 1.017 -5.39 0 1 1.06 0.94;

18 2 27.2 9.8 0 10 1 1.001 -11.71 0 1 1.06 0.94;

19 1 3.3 0.6 0 0 1 0.97 -13.2 0 1 1.06 0.94;

20 1 2.3 1 0 0 1 0.964 -13.41 0 1 1.06 0.94;

21 1 0 0 0 0 1 1.008 -12.89 0 1 1.06 0.94;

22 2 0 0 0 0 1 1.01 -12.84 0 1 1.06 0.94;

23 1 6.3 2.1 0 0 1 1.008 -12.91 0 1 1.06 0.94;

24 1 0 0 0 0 1 0.999 -13.25 0 1 1.06 0.94;

25 2 6.3 3.2 0 5.9 1 0.982 -18.13 0 1 1.06 0.94;

26 1 0 0 0 0 1 0.959 -12.95 0 1 1.06 0.94;

27 2 9.3 0.5 0 0 1 0.982 -11.48 0 1 1.06 0.94;

28 1 4.6 2.3 0 0 1 0.997 -10.45 0 1 1.06 0.94;

29 2 17 2.6 0 0 1 1.01 -9.75 0 1 1.06 0.94;

30 2 3.6 1.8 0 0 1 0.962 -18.68 0 1 1.06 0.94;

31 1 5.8 2.9 0 0 1 0.936 -19.34 0 1 1.06 0.94;

32 2 1.6 0.8 0 0 1 0.949 -18.46 0 1 1.06 0.94;

33 1 3.8 1.9 0 0 1 0.947 -18.5 0 1 1.06 0.94;

34 1 0 0 0 0 1 0.959 -14.1 0 1 1.06 0.94;

35 1 6 3 0 0 1 0.966 -13.86 0 1 1.06 0.94;

36 2 0 0 0 0 1 0.976 -13.59 0 1 1.06 0.94;

37 1 0 0 0 0 1 0.985 -13.41 0 1 1.06 0.94;

38 2 14 7 0 0 1 1.013 -12.71 0 1 1.06 0.94;

39 1 0 0 0 0 1 0.983 -13.46 0 1 1.06 0.94;

40 1 0 0 0 0 1 0.973 -13.62 0 1 1.06 0.94;

41 1 6.3 3 0 0 1 0.996 -14.05 0 1 1.06 0.94;

42 1 7.1 4.4 0 0 1 0.966 -15.5 0 1 1.06 0.94;

43 1 2 1 0 0 1 1.01 -11.33 0 1 1.06 0.94;

44 1 12 1.8 0 0 1 1.017 -11.86 0 1 1.06 0.94;

45 1 0 0 0 0 1 1.036 -9.25 0 1 1.06 0.94;

46 1 0 0 0 0 1 1.05 -11.89 0 1 1.06 0.94;

47 2 29.7 11.6 0 0 1 1.033 -12.49 0 1 1.06 0.94;

48 1 0 0 0 0 1 1.027 -12.59 0 1 1.06 0.94;

49 2 18 8.5 0 0 1 1.036 -12.92 0 1 1.06 0.94;

50 2 21 10.5 0 0 1 1.023 -13.39 0 1 1.06 0.94;

51 1 18 5.3 0 0 1 1.052 -12.52 0 1 1.06 0.94;

52 1 4.9 2.2 0 0 1 0.98 -11.47 0 1 1.06 0.94;

53 2 20 10 0 6.3 1 0.971 -12.23 0 1 1.06 0.94;

54 2 4.1 1.4 0 0 1 0.996 -11.69 0 1 1.06 0.94;

55 1 6.8 3.4 0 0 1 1.031 -10.78 0 1 1.06 0.94;

56 2 7.6 2.2 0 0 1 0.968 -16.04 0 1 1.06 0.94;

57 1 6.7 2 0 0 1 0.965 -16.56 0 1 1.06 0.94;];

Figure 11 Bus data of IEEE 57 bus system



31

%% branch data % fbus tbus r x b rateA rateB rateC ratio angle status angmin angmax mpc.branch = [ 1 2 0.0083 0.028 0.129 0 0 0 0 0 1 -360 360; 2 3 0.0298 0.085 0.0818 0 0 0 0 0 1 -360 360; 3 4 0.0112 0.0366 0.038 0 0 0 0 0 1 -360 360; 4 5 0.0625 0.132 0.0258 0 0 0 0 0 1 -360 360; 4 6 0.043 0.148 0.0348 0 0 0 0 0 1 -360 360; 6 7 0.02 0.102 0.0276 0 0 0 0 0 1 -360 360; 6 8 0.0339 0.173 0.047 0 0 0 0 0 1 -360 360; 8 9 0.0099 0.0505 0.0548 0 0 0 0 0 1 -360 360; 9 10 0.0369 0.1679 0.044 0 0 0 0 0 1 -360 360; 9 11 0.0258 0.0848 0.0218 0 0 0 0 0 1 -360 360; 9 12 0.0648 0.295 0.0772 0 0 0 0 0 1 -360 360; 9 13 0.0481 0.158 0.0406 0 0 0 0 0 1 -360 360; 13 14 0.0132 0.0434 0.011 0 0 0 0 0 1 -360 360; 13 15 0.0269 0.0869 0.023 0 0 0 0 0 1 -360 360; 1 15 0.0178 0.091 0.0988 0 0 0 0 0 1 -360 360; 1 16 0.0454 0.206 0.0546 0 0 0 0 0 1 -360 360; 1 17 0.0238 0.108 0.0286 0 0 0 0 0 1 -360 360; 3 15 0.0162 0.053 0.0544 0 0 0 0 0 1 -360 360; 4 18 0 0.555 0 0 0 0 0.97 0 1 -360 360; 4 18 0 0.43 0 0 0 0 0.978 0 1 -360 360; 5 6 0.0302 0.0641 0.0124 0 0 0 0 0 1 -360 360; 7 8 0.0139 0.0712 0.0194 0 0 0 0 0 1 -360 360; 10 12 0.0277 0.1262 0.0328 0 0 0 0 0 1 -360 360; 11 13 0.0223 0.0732 0.0188 0 0 0 0 0 1 -360 360; 12 13 0.0178 0.058 0.0604 0 0 0 0 0 1 -360 360; 12 16 0.018 0.0813 0.0216 0 0 0 0 0 1 -360 360; 12 17 0.0397 0.179 0.0476 0 0 0 0 0 1 -360 360; 14 15 0.0171 0.0547 0.0148 0 0 0 0 0 1 -360 360; 18 19 0.461 0.685 0 0 0 0 0 0 1 -360 360; 19 20 0.283 0.434 0 0 0 0 0 0 1 -360 360; 21 20 0 0.7767 0 0 0 0 1.043 0 1 -360 360; 21 22 0.0736 0.117 0 0 0 0 0 0 1 -360 360; 22 23 0.0099 0.0152 0 0 0 0 0 0 1 -360 360; 23 24 0.166 0.256 0.0084 0 0 0 0 0 1 -360 360; 24 25 0 1.182 0 0 0 0 1 0 1 -360 360; 24 25 0 1.23 0 0 0 0 1 0 1 -360 360; 24 26 0 0.0473 0 0 0 0 1.043 0 1 -360 360; 26 27 0.165 0.254 0 0 0 0 0 0 1 -360 360; 27 28 0.0618 0.0954 0 0 0 0 0 0 1 -360 360; 28 29 0.0418 0.0587 0 0 0 0 0 0 1 -360 360; 7 29 0 0.0648 0 0 0 0 0.967 0 1 -360 360; 25 30 0.135 0.202 0 0 0 0 0 0 1 -360 360; 30 31 0.326 0.497 0 0 0 0 0 0 1 -360 360; 31 32 0.507 0.755 0 0 0 0 0 0 1 -360 360; 32 33 0.0392 0.036 0 0 0 0 0 0 1 -360 360; 34 32 0 0.953 0 0 0 0 0.975 0 1 -360 360; 34 35 0.052 0.078 0.0032 0 0 0 0 0 1 -360 360; 35 36 0.043 0.0537 0.0016 0 0 0 0 0 1 -360 360; 36 37 0.029 0.0366 0 0 0 0 0 0 1 -360 360; 37 38 0.0651 0.1009 0.002 0 0 0 0 0 1 -360 360; 37 39 0.0239 0.0379 0 0 0 0 0 0 1 -360 360; 36 40 0.03 0.0466 0 0 0 0 0 0 1 -360 360; 22 38 0.0192 0.0295 0 0 0 0 0 0 1 -360 360;



32

11 41 0 0.749 0 0 0 0 0.955 0 1 -360 360; 41 42 0.207 0.352 0 0 0 0 0 0 1 -360 360; 41 43 0 0.412 0 0 0 0 0 0 1 -360 360; 38 44 0.0289 0.0585 0.002 0 0 0 0 0 1 -360 360; 15 45 0 0.1042 0 0 0 0 0.955 0 1 -360 360; 14 46 0 0.0735 0 0 0 0 0.9 0 1 -360 360; 46 47 0.023 0.068 0.0032 0 0 0 0 0 1 -360 360; 47 48 0.0182 0.0233 0 0 0 0 0 0 1 -360 360; 48 49 0.0834 0.129 0.0048 0 0 0 0 0 1 -360 360; 49 50 0.0801 0.128 0 0 0 0 0 0 1 -360 360; 50 51 0.1386 0.22 0 0 0 0 0 0 1 -360 360; 10 51 0 0.0712 0 0 0 0 0.93 0 1 -360 360; 13 49 0 0.191 0 0 0 0 0.895 0 1 -360 360; 29 52 0.1442 0.187 0 0 0 0 0 0 1 -360 360; 52 53 0.0762 0.0984 0 0 0 0 0 0 1 -360 360; 53 54 0.1878 0.232 0 0 0 0 0 0 1 -360 360; 54 55 0.1732 0.2265 0 0 0 0 0 0 1 -360 360; 11 43 0 0.153 0 0 0 0 0.958 0 1 -360 360; 44 45 0.0624 0.1242 0.004 0 0 0 0 0 1 -360 360; 40 56 0 1.195 0 0 0 0 0.958 0 1 -360 360; 56 41 0.553 0.549 0 0 0 0 0 0 1 -360 360; 56 42 0.2125 0.354 0 0 0 0 0 0 1 -360 360; 39 57 0 1.355 0 0 0 0 0.98 0 1 -360 360; 57 56 0.174 0.26 0 0 0 0 0 0 1 -360 360; 38 49 0.115 0.177 0.003 0 0 0 0 0 1 -360 360; 38 48 0.0312 0.0482 0 0 0 0 0 0 1 -360 360; 9 55 0 0.1205 0 0 0 0 0.94 0 1 -360 360; ];

Figure 12 Branch data of IEEE 57 bus system

Generator data

Generator 1 2 3 6 8 9 12 17 18

Maxi capacity(MW)



400

76

63.2

45

58.2

45.2

40

54.4

41.9

25

45.7

33.5

70

46.8

33.9

190

49.1

36.4

150

69.2

53.5

100

57.7

43.4

30

62.5

52.1

Generator 22 25 27 29 30 32 36 38 47

Maxi capacity(MW)



22

70.1

57.5

15

55.4

42.1

30

52.1

39.3

35

60.4

44.5

24

56.3

43.4

35

71.2

52.1

30

73.5

50.7

35

66.6.

53.4

28

61.5

49.1

Generator 49 50 53 54 56

Maxi capacity(MW)



25

57.9

46.4

75

63.9

49.8

45

74

56.5

15

59.5

47.1

35

68.9

56.5

Figure 13 Generator data of IEEE 57 bus system



33

5. Results and finding:

5.1 Adjustment on trading profit:

5.1.1 IEEE 30-bus system

In case of IEEE 30-bus system, the total transmission cost is set as 2000$/h. Then the

POC rate for a unit power delivery is 7.06$/MWh. The profit of each generator is

calculated by (C2) is shown in fig. 14. The profit of generator in POC scheme is

proportional to the transaction volume.

Figure 14 Profit of IEEE 30 bus system under POC scheme

For the proposed method, TPM scheme is applied. Firstly, power flow in fig.15 is studied

to find the PTP matrix in fig. 16. The PTP matrix has been updated. The smallest value is

5.33$/MWh which is the basic part of the transmission. The control parameter 𝛽𝑃𝑇𝑃 is

0

100

200

300

400

500

600

G1 G2 G3 G5 G8 G9 G11 G13 G14 G16 G18 G22 G23

Profit under POC scheme



34

assumed to be 0.25. In the local delivery, the rate is 5.33$/MWh, while the rates between

5.54$/MWh to 11.31$/MWh are in non-local delivery. Higher PTP rate means a longer

transmission distance and larger power flow in the branch.

Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)

# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ----- ----- -------- -------- -------- ------

1 1 2 -20.77 5.58 20.86 -8.29 0.096 0.29

2 1 3 -10.84 1.98 10.90 -3.74 0.063 0.24

3 2 4 1.68 -1.09 -1.68 -0.91 0.002 0.00

4 3 4 26.70 -4.37 -26.62 4.66 0.073 0.29

5 2 5 46.37 -10.22 -45.25 12.69 1.118 4.47

6 2 6 9.38 -3.36 -9.33 1.53 0.056 0.17

7 4 6 36.47 -7.93 -36.33 8.49 0.140 0.56

8 5 7 -23.95 18.41 24.41 -18.28 0.466 1.12

9 6 7 47.91 -6.50 -47.21 7.38 0.701 1.87

10 6 8 14.72 -6.66 -14.69 6.77 0.026 0.10

11 6 9 -20.55 -0.13 20.55 1.02 0.000 0.89

12 6 10 -4.84 0.64 4.84 -0.50 0.000 0.13

13 9 11 -20.00 0.42 20.00 0.42 0.000 0.84

14 9 10 14.45 4.13 -14.45 -3.88 0.000 0.25

15 4 12 -15.77 2.58 15.77 -1.91 0.000 0.66

16 12 13 -17.50 -4.55 17.50 5.01 0.000 0.46

17 12 14 -7.13 0.80 7.19 -0.66 0.063 0.14

18 12 15 5.98 -2.33 -5.95 2.38 0.029 0.05

19 12 16 -8.32 0.48 8.38 -0.34 0.063 0.14

20 14 15 8.61 -5.33 -8.38 5.54 0.226 0.21

21 16 17 18.12 -2.53 -17.85 3.16 0.268 0.64

22 15 18 1.62 -4.33 -1.60 4.38 0.024 0.05

23 18 19 10.40 2.61 -10.33 -2.46 0.069 0.15

24 19 20 0.83 -0.94 -0.83 0.94 0.000 0.00

25 10 20 1.37 1.65 -1.37 -1.64 0.004 0.01

26 10 17 -8.80 9.09 8.85 -8.96 0.048 0.13

27 10 21 8.52 -4.19 -8.50 4.25 0.027 0.06

28 10 22 2.72 -4.18 -2.70 4.22 0.018 0.04

29 21 22 -9.00 -15.45 9.04 15.52 0.032 0.06

30 15 23 4.51 -6.09 -4.45 6.20 0.058 0.12

31 22 24 8.66 4.32 -8.55 -4.15 0.112 0.17

32 23 24 9.25 2.34 -9.13 -2.10 0.118 0.25

33 24 25 8.98 -0.46 -8.82 0.73 0.159 0.28

34 25 26 3.55 2.37 -3.50 -2.30 0.049 0.07

35 25 27 5.28 -3.11 -5.23 3.19 0.044 0.08

36 28 27 8.09 7.06 -8.09 -6.59 -0.000 0.47

37 27 29 6.18 1.70 -6.09 -1.52 0.097 0.18

38 27 30 7.13 1.70 -6.95 -1.35 0.184 0.34

39 29 30 3.69 0.62 -3.65 -0.55 0.037 0.07

40 8 28 -0.31 1.48 0.31 -3.46 0.004 0.01

41 6 28 8.41 2.65 -8.40 -3.59 0.016 0.05

Figure 15 Load flow study of IEEE 30-bus system



35

Load bus: 2 3 4 5 7 8 10 12 14 15 16 17 18 19 20 21 23 24 26 29 30

G1 5.71 5.95 5.79 8.25 7.38 6.39 7.04 7.04 7.60 7.27 7.54

7.25 7.38 7.15 7.13 7.22 7.55 7.64 8.94 9.66 10.16

G2 5.33 5.74 5.41 7.87 7.00 6.01 6.66 6.66 7.22 6.89 7.16

6.88 7.00 6.77 6.75 6.84 7.17 7.26 8.57 9.28 9.79

G3 5.74 5.33 5.65 8.13 7.26 6.27 6.92 6.90 7.46 7.13 7.40

7.13 7.24 7.02 7.00 7.09 7.41 7.51 8.82 9.54 10.04

G5 7.87 8.13 7.80 5.33 6.20 7.53 8.18 9.04 9.33 8.81 9.44

8.40 8.70 8.29 8.27 8.36 9.08 8.78 10.09 10.80 11.31

G8 6.01 6.27 5.94 7.53 6.66 5.33 6.32 7.18 7.47 6.95 7.58

6.54 6.84 6.43 6.41 6.50 7.22 6.92 8.23 8.94 9.44

G9 7.14 7.40 7.07 8.67 7.79 6.80 5.81 6.67 6.96 6.43 7.07

6.02 6.32 5.91 5.90 5.99 6.71 6.41 7.71 8.43 8.93

G11 8.42 8.67 8.35 9.94 9.07 8.08 7.08 7.94 8.23 7.71 8.34

7.30 7.60 7.19 7.17 7.26 7.98 7.68 8.99 9.70 10.21

G13 7.40 7.64 7.31 9.79 8.92 7.92 6.93 6.07 6.63 6.31 6.58

7.14 6.41 6.83 6.84 7.11 6.58 7.34 8.65 9.36 9.86

G14 7.22 7.46 7.13 9.33 8.46 7.47 6.47 5.89 5.33 5.85 6.39

6.69 5.96 6.37 6.39 6.65 6.12 6.88 8.19 8.90 9.41

G16 7.16 7.40 7.08 9.44 8.57 7.58 6.59 5.83 6.39 6.07 5.33

6.37 6.18 6.59 6.60 6.76 6.34 7.10 8.41 9.12 9.63

G18 7.00 7.24 6.92 8.70 7.83 6.84 5.84 5.67 5.96 5.44 6.18

6.06 5.33 5.74 5.76 6.02 5.71 6.44 7.75 8.46 8.97

G22 6.79 7.04 6.72 8.31 7.44 6.45 5.45 6.31 6.60 6.07 6.71

5.66 5.97 5.56 5.54 5.38 6.35 5.80 7.11 7.82 8.33

G23 7.17 7.41 7.08 9.08 8.21 7.22 6.22 5.84 6.12 5.60 6.34

6.44 5.71 6.12 6.14 6.40 5.33 6.09 7.39 8.11 8.61

Figure 16 PTP tariff of IEEE 30-bus system

pair_order load_bus generator volume Price Cost PTP_rate Profit

1 8 8 15 45.9 32 5.3276 128.59

2 5 5 25 47.6 33 5.3276 231.81

3 23 23 3.2 51.8 41.4 5.3276 16.23

4 15 23 4.8 51.8 41.4 5.6013 23.034

5 21 22 15 55.6 41.5 5.3822 130.77

6 2 1 21.7 58.2 46.6 5.7057 127.91

7 4 1 7.6 58.2 46.6 5.7923 44.139

8 3 1 7 58.2 46.6 5.9525 39.533



36

9 18 18 3.2 59.4 47.5 5.3276 21.032

10 15 18 3.4 59.4 47.5 5.4357 21.979

11 12 18 5.4 59.4 47.5 5.6716 33.633

12 14 14 6.2 63.7 50.9 5.3276 46.329

13 12 14 5.8 63.7 50.9 5.89 40.078

14 19 14 9.5 63.7 50.9 6.3684 61.1

15 20 14 5 63.7 50.9 6.386 3.207

16 3 3 1.7 64.9 51.9 5.3276 13.043

17 8 3 15 64.9 51.9 6.2661 101.01

18 10 3 5.8 64.9 51.9 6.9166 35.284

19 20 3 1.7 64.9 51.9 7.0038 10.194

20 21 3 2.5 64.9 51.9 7.0945 14.764

21 17 3 9.0 64.9 51.9 7.1301 52.829

22 7 3 4.3 64.9 51.9 7.2571 24.695

23 24 9 8.7 66.9 53.5 6.4061 60.847

24 16 9 3.5 66.9 53.5 7.068 22.162

25 26 9 2.8 66.9 53.5 7.7145 15.919

26 26 11 7 67.9 54.4 8.9888 3.1578

27 7 11 18.5 67.9 54.4 9.0693 81.968

28 29 11 8 67.9 54.4 9.7034 3.0373

29 29 13 1.6 69.1 50.3 9.3612 15.102

30 5 13 15.9 69.1 50.3 9.7872 143.3

31 5 16 30 71.5 52.2 9.4429 295.71

32 5 2 23.3 73.5 50.7 7.8747 347.76

33 30 2 10.6 73.5 50.7 9.7852 137.96

Figure 17 TPM result of IEEE 30-bus system

As discussed in section 4.5, the maximum generation is 349.5 MWh, which is higher than

the load demand 283.4 MWh. Generator except G2 will generate their maximum capacity,

and G2 only generate 33.9MWh out of 100 MWh. On the above table, there are total 33

transaction pairs in this case. Due to the TPM scheme, the generator with lower bidding

price has priority to match. Therefore, G8 with the lowest bidding price will choose first

and G2 with the highest bidding price will choose at last. According to the PTP tariff, the

best option of G8 is load bus 8 with 5.33$/MWh which is a local transmission. However,

G2 choose at last, it can just match the remaining load bus 5 and 30 with PTP rate

7.87$/MWh and 9.79$/MWh.



37

Figure 18 Adjusting rate on profit and average transmission price of case 30

The bars depict the adjusting rate of profit comparing to POC scheme and the curve

represents the average transmission prices of each generator is shown in the above figure.

The positions of generators are ranked by the pair order. As the figure shown, the

generators with lower bidding price can match the load bus with lower PTP (comparing

to 7.06$/MWh) and thus get extra profit comparing to the POC scheme. Therefore, the

generators can obtain higher profit by reducing the bidding price.

5.1.2 IEEE 57-bus system

In case of IEEE 57-bus system, the total transmission cost is set as 8000$/h. Then the

POC rate for a unit power delivery is 6.40$/MWh. The profit of each generator is

calculated by (C2) is shown in fig.19. The profit of generator in POC scheme is

5

5.5

6

6.5

7

7.5

8

8.5

9

9.5

10

-40

-30

-20

-10

0

10

20

30

40

50

60

G8 G5 G23 G22 G1 G18 G14 G3 G9 G11 G13 G16 G2

Ave

rage

tra

nsm

issi

on

pri

ce (

$/M

Wh

)

Ad

just

ing

rate

(%)

Generators

Trading profits Average transmission price ($/MWh)



38

proportional to the transaction volume.

Figure 19 Profit of IEEE 57-bus system under POC scheme

For the proposed method, TPM scheme is applied. Firstly, power flow in fig.20 is studied

to find the PTP matrix in fig. 21. The PTP matrix has been updated. The smallest value is

5.62$/MWh which is the basic part of the transmission. The control parameter 𝛽𝑃𝑇𝑃 is

assumed to be 0.25. In the local delivery, the rate is 5.62$/MWh, while the rates between

5.54$/MWh to 11.34$/MWh are in non-local delivery. Higher PTP rate means a longer

transmission distance and larger power flow in the branch.

0

200

400

600

800

1000

1200

1400

1600

G6 G8 G9 G27 G3 G25 G30 G17 G49 G2 G54 G29 G47 G18 G50 G38 G56 G12 G22 G32 G36 G53 G1

Profit under POC scheme



39

Brnch From To From Bus Injection To Bus Injection Loss (I^2 * Z)

# Bus Bus P (MW) Q (MVAr) P (MW) Q (MVAr) P (MW) Q (MVAr) ----- ----- ----- -------- -------- -------- ------ 1 1 2 8.14 -9.38 -8.14 -4.55 0.006 0.02

2 2 3 50.14 45.73 -48.75 -50.17 1.386 3.95

3 3 4 40.98 -2.67 -40.79 -0.36 0.194 0.63

4 4 5 20.28 -7.21 -19.99 5.36 0.290 0.61

5 4 6 23.81 -7.58 -23.54 5.16 0.269 0.93

6 6 7 -20.82 -5.47 20.92 3.28 0.094 0.48

7 6 8 1.31 -14.40 -1.26 10.06 0.053 0.27

8 8 9 -45.15 48.52 45.61 -51.54 0.461 2.35

9 9 10 15.14 -3.71 -15.05 -0.09 0.089 0.41

10 9 11 -4.07 6.28 4.09 -8.30 0.019 0.06

11 9 12 20.95 -19.06 -20.50 13.45 0.455 2.07

12 9 13 0.58 -4.11 -0.58 0.21 0.003 0.01

13 13 14 -37.04 28.76 37.35 -28.81 0.305 1.00

14 13 15 -32.18 1.34 32.47 -2.65 0.290 0.94

15 1 15 48.93 42.61 -48.16 -48.85 0.772 3.95

16 1 16 62.01 -0.29 -60.39 1.86 1.617 7.34

17 1 17 12.49 17.88 -12.37 -20.38 0.117 0.53

18 3 15 6.77 -14.47 -6.74 9.27 0.031 0.10

19 4 18 -1.45 7.49 1.45 -7.18 0.000 0.32

20 4 18 -1.85 7.66 1.85 -7.40 -0.000 0.27

21 5 6 6.99 -9.36 -6.95 8.26 0.040 0.08

22 7 8 33.83 -23.99 -33.59 23.29 0.238 1.22

23 10 12 27.84 -36.00 -27.27 35.33 0.568 2.59

24 11 13 6.00 -13.95 -5.95 12.31 0.048 0.16

25 12 13 -93.47 85.45 96.33 -82.15 2.865 9.33

26 12 16 -17.34 2.89 17.39 -4.86 0.055 0.25

27 12 17 -68.43 16.17 70.37 -12.35 1.938 8.74

28 14 15 -21.36 -20.37 21.51 19.42 0.151 0.48

29 18 19 -0.50 1.93 0.52 -1.90 0.020 0.03

30 19 20 -3.82 1.30 3.87 -1.23 0.050 0.08

31 21 20 6.17 0.09 -6.17 0.23 0.000 0.32

32 21 22 -6.17 -0.09 6.20 0.14 0.028 0.04

33 22 23 -9.04 5.88 9.05 -5.86 0.011 0.02

34 23 24 -15.35 3.76 15.77 -4.00 0.412 0.64

35 24 25 -14.13 4.97 14.13 -2.45 0.000 2.52

36 24 25 -13.58 4.77 13.58 -2.35 0.000 2.42

37 24 26 11.94 -5.74 -11.94 5.83 0.000 0.09

38 26 27 11.94 -5.83 -11.64 6.29 0.299 0.46

39 27 28 32.34 -35.09 -30.88 37.34 1.459 2.25

40 28 29 26.28 -39.64 -25.33 40.98 0.951 1.34

41 7 29 -54.75 20.71 54.75 -18.59 0.000 2.12

42 25 30 -19.01 23.73 20.30 -21.79 1.294 1.94

43 30 31 0.10 5.35 -0.00 -5.19 0.101 0.15

44 31 32 -5.80 2.29 6.03 -1.96 0.226 0.34

45 32 33 3.81 1.91 -3.80 -1.90 0.008 0.01

46 34 32 -23.57 8.96 23.57 -2.99 0.000 5.97

47 34 35 23.57 -8.96 -23.22 9.16 0.341 0.51

48 35 36 17.22 -12.16 -17.03 12.26 0.200 0.25

49 36 37 42.70 -48.32 -41.43 49.92 1.266 1.60

50 37 38 38.93 -52.78 -36.04 57.07 2.898 4.49

51 37 39 2.50 2.86 -2.49 -2.86 0.004 0.01

52 36 40 4.33 4.15 -4.32 -4.13 0.011 0.02

53 22 38 24.84 -26.19 -24.60 26.56 0.245 0.38



40

54 11 41 -4.99 9.52 4.99 -8.69 0.000 0.83

55 41 42 -7.96 7.64 8.23 -7.17 0.278 0.47

56 41 43 7.10 -10.71 -7.10 11.46 0.000 0.75

57 38 44 33.91 -14.23 -33.53 14.80 0.380 0.77

58 15 45 -21.09 17.81 21.09 -17.07 0.000 0.74

59 14 46 -26.49 43.88 26.49 -42.24 0.000 1.64

60 46 47 -26.49 42.24 27.01 -41.05 0.517 1.53

61 47 48 -28.71 45.66 29.20 -45.03 0.496 0.64

62 48 49 4.45 -9.55 -4.37 9.17 0.084 0.13

63 49 50 -15.04 20.40 15.52 -19.63 0.479 0.77

64 50 51 38.48 -23.56 -35.79 27.84 2.696 4.28

65 10 51 -17.79 34.09 17.79 -33.14 0.000 0.95

66 13 49 -38.58 37.23 38.58 -32.68 0.000 4.55

67 29 52 -11.42 26.26 12.57 -24.76 1.159 1.50

68 52 53 -17.47 22.56 18.12 -21.72 0.647 0.84

69 53 54 6.88 -15.58 -6.30 16.29 0.577 0.71

70 54 55 17.20 -19.60 -16.01 21.15 1.187 1.55

71 11 43 -5.10 12.74 5.10 -12.46 0.000 0.28

72 44 45 21.53 -16.60 -21.09 17.07 0.446 0.89

73 40 56 4.32 4.13 -4.32 -3.72 0.000 0.41

74 56 41 11.56 -7.63 -10.43 8.76 1.132 1.12

75 56 42 15.92 -1.80 -15.33 2.77 0.582 0.97

76 39 57 2.49 2.86 -2.49 -2.66 0.000 0.19

77 57 56 -4.21 0.66 4.24 -0.61 0.034 0.05

78 38 49 12.85 -21.08 -12.17 21.80 0.676 1.04

79 38 48 34.87 -52.70 -33.66 54.58 1.214 1.88

80 9 55 -9.21 25.36 9.21 -24.55 0.000 0.81

Figure 20 Load flow study of IEEE 57-bus system

Load bus: 2 3 4 5 7 8 10 12 14 15 16 17 18 19 20 21 23 24 26 29 30

G1 5.62 5.65 6.20 6.74 6.79 6.82 6.56 6.89 7.25 6.55 6.34

6.19 7.26 5.80 6.49 6.54 6.75 7.19 9.85 8.12 7.72 7.52

10.34 10.35 10.91 10.93 7.90 7.08 7.08 7.44 6.71 6.82 6.83

6.99 7.23 7.05 7.63 7.41 7.21 6.71 8.47 8.03 ;

G2 5.65 5.62 6.17 6.71 6.76 6.79 6.58 6.91 7.27 6.57 6.37

6.22 7.29 5.82 6.46 6.51 6.72 7.21 9.87 8.09 7.69 7.49

10.36 10.37 10.93 10.95 7.92 7.10 7.11 7.47 6.73 6.84 6.85

7.01 7.26 7.07 7.65 7.43 7.23 6.73 8.49 8.05 ;

G3 6.20 6.17 5.62 6.16 6.22 6.25 6.04 6.36 6.72 6.02 5.82

5.67 6.90 6.37 5.92 5.96 6.17 6.66 9.32 7.54 7.14 6.95

9.81 9.82 10.38 10.40 7.37 6.55 6.56 6.92 6.18 6.29 6.30

6.46 6.71 6.53 7.11 6.89 6.68 6.18 7.95 7.50 ;

G6 6.79 6.76 6.22 5.68 5.62 5.65 5.94 6.27 6.65 5.96 6.16

6.26 6.83 6.97 6.13 6.17 6.38 7.06 9.56 6.95 6.55 6.35

10.05 10.06 10.62 10.64 7.77 6.95 6.47 6.83 6.09 6.89 6.64

6.80 7.05 6.43 6.63 6.79 6.59 6.09 8.34 7.90 ;

G8 6.82 6.79 6.25 5.71 5.65 5.62 5.92 6.24 6.62 5.93 6.13

6.28 6.81 7.00 6.15 6.20 6.41 7.03 9.59 6.98 6.58 6.38

10.08 10.09 10.65 10.67 7.74 6.92 6.44 6.80 6.06 6.91 6.62

6.78 7.02 6.41 6.65 6.76 6.56 6.06 8.31 7.87 ;

G9 6.56 6.58 6.04 6.00 5.94 5.92 5.62 5.95 6.33 5.63 5.84

5.99 6.51 6.74 6.33 6.38 6.59 6.74 9.39 7.27 6.87 6.67



41

9.89 9.89 10.46 10.47 7.45 6.62 6.14 6.50 5.77 6.62 6.32

6.48 6.73 6.11 6.69 6.47 6.27 5.76 8.02 7.58 ;

G12 7.25 7.27 6.72 6.71 6.65 6.62 6.33 6.07 5.62 6.32 6.53

6.68 5.80 7.20 7.02 7.06 7.27 7.42 10.08 7.98 7.58 7.38

10.57 10.58 11.14 11.16 8.13 7.31 6.85 7.21 6.48 7.30 7.01

7.17 7.32 6.24 7.40 7.18 6.97 6.47 8.71 8.26 ;

G17 5.80 5.82 6.37 6.91 6.97 7.00 6.74 7.06 7.20 6.72 6.52

6.37 7.38 5.62 6.67 6.71 6.92 7.36 10.02 8.29 7.89 7.70

10.51 10.52 11.08 11.10 8.07 7.25 7.26 7.62 6.88 6.99 7.00

7.16 7.41 7.23 7.81 7.59 7.38 6.88 8.64 8.20 ;

G18 6.49 6.46 5.92 6.07 6.13 6.15 6.33 6.66 7.02 6.32 6.11

5.96 7.20 6.67 5.62 5.67 5.88 6.96 9.61 7.45 7.05 6.86

10.11 10.11 10.68 10.69 7.67 6.84 6.85 7.21 6.48 6.59 6.60

6.76 7.00 6.82 7.13 7.18 6.98 6.47 8.24 7.80 ;

G22 7.17 7.19 6.64 7.10 7.04 7.01 6.72 7.05 7.40 6.71 6.50

6.60 7.59 7.34 6.94 6.98 7.20 5.64 8.30 6.61 7.01 7.20

8.79 8.80 9.36 9.38 6.54 5.72 7.24 7.60 6.86 5.97 6.02

6.01 6.25 7.21 7.48 7.57 7.36 6.86 7.11 6.67 ;

G25 9.85 9.87 9.32 9.62 9.56 9.59 9.39 9.72 10.08 9.38 9.18

9.27 10.26 10.02 9.61 9.66 9.87 8.28 5.62 8.24 8.63 8.83

6.12 6.12 6.68 6.70 9.22 8.39 9.91 10.27 9.54 8.65 8.69

8.68 8.93 9.88 9.10 9.33 9.53 9.54 9.79 9.34 ;

G27 8.12 8.09 7.54 7.00 6.95 6.98 7.27 7.60 7.98 7.28 7.49

7.58 8.16 8.29 7.45 7.49 7.71 6.59 8.24 5.62 6.02 6.22

8.73 8.74 9.30 9.32 7.53 6.70 7.79 8.15 7.41 6.96 7.01

6.99 7.24 7.76 6.49 6.71 6.92 7.41 8.10 7.65 ;

G29 7.52 7.49 6.95 6.41 6.35 6.38 6.67 7.00 7.38 6.69 6.89

6.99 7.56 7.70 6.86 6.90 7.11 7.19 8.83 6.22 5.82 5.62

9.32 9.33 9.89 9.91 8.12 7.30 7.19 7.55 6.82 7.55 7.37

7.53 7.78 7.16 5.90 6.12 6.32 6.82 8.69 8.25 ;

G30 10.34 10.36 9.81 10.11 10.05 10.08 9.89 10.21 10.57 9.88 9.67

9.77 10.75 10.51 10.11 10.15 10.36 8.77 6.12 8.73 9.13 9.32

5.62 5.63 6.19 6.21 9.71 8.88 10.41 10.77 10.03 9.14 9.19

9.17 9.42 10.38 9.60 9.82 10.02 10.03 10.28 9.84 ;

G32 10.91 10.93 10.38 10.68 10.62 10.65 10.46 10.78 11.14 10.44 10.24

10.34 11.32 11.08 10.68 10.72 10.93 9.34 6.68 9.30 9.69 9.89

6.19 6.18 5.62 5.64 10.28 9.45 10.98 11.34 10.60 9.71 9.76

9.74 9.99 10.95 10.17 10.39 10.59 10.60 10.85 10.41 ;

G36 7.78 7.80 7.26 7.71 7.65 7.62 7.33 7.66 8.02 7.32 7.11

7.21 8.20 7.96 7.55 7.59 7.81 6.44 9.10 7.41 7.81 8.00

9.59 9.60 10.16 10.18 5.74 6.33 7.85 8.21 7.47 6.58 6.63

6.62 6.86 7.82 8.28 8.18 7.97 7.47 6.31 6.27 ;

G38 7.08 7.10 6.55 7.00 6.95 6.92 6.62 6.95 7.31 6.61 6.41

6.50 7.49 7.25 6.84 6.89 7.10 5.73 8.39 6.70 7.10 7.30

8.88 8.89 9.45 9.47 6.45 5.62 7.15 7.51 6.77 5.88 5.92

5.91 6.16 7.11 7.57 7.47 7.27 6.77 7.02 6.57 ;

G47 6.83 6.85 6.30 6.70 6.64 6.62 6.32 6.65 7.01 6.31 6.10

6.25 7.19 7.00 6.60 6.64 6.85 6.04 8.69 7.01 7.40 7.37

9.19 9.19 9.76 9.77 6.75 5.92 6.84 7.20 6.47 6.18 5.62

5.78 6.03 6.81 7.39 7.17 6.97 6.46 7.32 6.87 ;

G49 6.99 7.01 6.46 6.86 6.80 6.78 6.48 6.81 7.17 6.47 6.26

6.41 7.35 7.16 6.76 6.80 7.01 6.02 8.68 6.99 7.39 7.53

9.17 9.18 9.74 9.76 6.74 5.91 7.00 7.36 6.63 6.17 5.78

5.62 5.87 6.96 7.55 7.33 7.13 6.62 7.31 6.86 ;

G50 7.23 7.26 6.71 7.11 7.05 7.02 6.73 6.87 7.32 6.72 6.51



42

6.66 7.51 7.41 7.00 7.05 7.26 6.27 8.93 7.24 7.64 7.78

9.42 9.43 9.99 10.01 6.98 6.16 7.25 7.61 6.87 6.41 6.03

5.87 5.62 6.71 7.80 7.58 7.37 6.87 7.55 7.11 ;

G53 7.41 7.43 6.89 6.85 6.79 6.76 6.47 6.80 7.18 6.48 6.69

6.84 7.36 7.59 7.18 7.22 7.44 7.58 9.33 6.71 6.32 6.12

9.82 9.83 10.39 10.41 8.30 7.47 6.99 7.35 6.62 7.47 7.17

7.33 7.58 6.96 5.84 5.62 5.83 6.33 8.87 8.42 ;

G54 7.21 7.23 6.68 6.65 6.59 6.56 6.27 6.59 6.97 6.28 6.48

6.63 7.16 7.38 6.98 7.02 7.23 7.38 9.53 6.92 6.52 6.32

10.02 10.03 10.59 10.61 8.09 7.27 6.79 7.15 6.41 7.26 6.97

7.13 7.37 6.76 6.05 5.83 5.62 6.12 8.66 8.22 ;

G56 8.47 8.49 7.95 8.40 8.34 8.31 8.02 8.35 8.71 8.01 7.80

7.90 8.89 8.64 8.24 8.28 8.50 7.13 9.79 8.10 8.50 8.69

10.28 10.29 10.85 10.87 6.43 7.02 8.54 8.90 8.16 7.27 7.32

7.31 7.55 8.51 8.97 8.87 8.66 8.16 5.62 6.96 ;];

Figure 21 PTP tariff of IEEE 57-bus system

pair

order

load gen volume price cost PTP rate profit

1 6 6 25 45.7 33.5 5.6217 164.5

2 8 8 70 46.8 33.9 5.6217 509.5

3 9 9 121 49.1 36.4 5.6217 856.5

4 13 9 18 49.1 36.4 5.6335 127.2

5 55 9 6.8 49.1 36.4 5.7644 47.16

6 43 9 2 49.1 36.4 5.7664 13.87

7 14 9 10.5 49.1 36.4 5.84 72.03

8 8 9 31.7 49.1 36.4 5.9152 215.1

9 27 27 9.3 52.1 39.3 5.6217 66.76

10 28 27 4.6 52.1 39.3 6.0184 31.2

11 29 27 16.1 52.1 39.3 6.2167 106

12 3 3 40 54.4 41.9 5.6217 275.1

13 25 25 6.3 55.4 42.1 5.6217 48.37

14 30 25 3.6 55.4 42.1 6.1152 25.87

15 31 25 5.1 55.4 42.1 6.1216 36.61

16 31 30 0.7 56.3 43.4 5.6281 5.09

17 32 30 1.6 56.3 43.4 6.1911 10.73

18 33 30 3.8 56.3 43.4 6.2088 25.43

19 23 30 6.3 56.3 43.4 8.7729 26

20 38 30 11.6 56.3 43.4 8.8848 46.58

21 17 17 42 57.7 43.4 5.6217 364.5

22 1 17 55 57.7 43.4 5.7951 467.8

23 2 17 3 57.7 43.4 5.8244 25.43

24 49 49 18 57.9 46.4 5.6217 105.8

25 47 49 7 57.9 46.4 5.7815 40.03



43

26 3 2 1 58.2 45.2 6.1697 6.83

27 15 2 22 58.2 45.2 6.2158 149.3

28 18 2 22 58.2 45.2 6.4648 143.8

29 54 54 4.1 59.5 47.1 5.6217 27.79

30 53 54 10.9 59.5 47.1 5.8269 71.65

31 29 29 0.9 60.4 44.5 5.6217 9.251

32 52 29 4.9 60.4 44.5 5.8958 49.02

33 53 29 9.1 60.4 44.5 6.1172 89.02

34 6 29 20.1 60.4 44.5 6.3511 191.9

35 47 47 22.7 61.5 49.1 5.6217 153.9

36 38 47 2.4 61.5 49.1 5.9238 15.54

37 50 47 2.9 61.5 49.1 6.0284 18.48

38 18 18 5.2 62.5 52.1 5.6217 24.85

39 19 18 3.3 62.5 52.1 5.6657 15.62

40 20 18 2.3 62.5 52.1 5.8789 10.4

41 5 18 13 62.5 52.1 6.0682 56.31

42 6 18 6.2 62.5 52.1 6.1258 26.5

43 50 50 18.1 63.9 49.8 5.6217 153.5

44 44 50 12 63.9 49.8 6.4135 92.24

45 51 50 18 63.9 49.8 6.7102 133

46 10 50 5 63.9 49.8 6.8731 36.14

47 35 50 6 63.9 49.8 6.9834 42.7

48 8 50 15.9 63.9 49.8 7.0222 112.5

49 57 38 6.7 66.6 53.4 6.5728 44.4

50 8 38 28.3 66.6 53.4 6.9177 177.8

51 56 56 7.6 68.9 56.5 5.6217 51.52

52 8 56 4.1 68.9 56.5 8.3134 16.76

53 6 56 23.3 68.9 56.5 8.3425 94.54

54 12 12 150 69.2 53.5 5.6217 1512

55 6 22 0.4 70.1 57.5 7.041 2.224

56 41 22 6.3 70.1 57.5 7.2392 33.77

57 12 22 15.3 70.1 57.5 7.4039 79.5

58 12 32 35 71.2 52.1 11.142 278.5

59 12 36 30 73.5 50.7 8.0157 443.5

60 12 53 45 74 56.5 7.1796 464.4

61 12 1 101.7 76 63.2 7.2485 564.6

62 16 1 43 76 63.2 7.2642 238

63 42 1 7.1 76 63.2 7.444 38.03

Figure 22 TPM result of IEEE 57-bus system



44

As discussed on section 4.5, the maximum generation is 1499 MWh, which is higher than

the load demand 1250.8 MWh. Generator except G1 will generate their maximum

capacity, and G1 only generate 151.8MWh out of 400 MWh. On the above table, there

are total 63 transaction pair in this case. Due to the TPM scheme, the generator with

lower bidding price has priority to match. Therefore, G6 with the lowest bidding price

will choose first and G1 with the highest bidding price will choose at last.

Figure 23 Adjusting rate on profit and average transmission price of case 57

The bars depict the adjusting rate of profit comparing to POC scheme and the curve

represents the average transmission rates of each generator is shown in the above figure.

The positions of generators are ranked by the pair order. As the figure shown, the

generators with lower bidding price except G30 and G12 can match the load bus with

lower PTP (comparing to 6.40$/MWh) and thus get extra profit comparing to the POC

5

6

7

8

9

10

11

12

-40

-30

-20

-10

0

10

20

G6

G8

G9

G2

7

G3

G2

5

G3

0

G1

7

G4

9

G2

G5

4

G2

9

G4

7

G1

8

G5

0

G3

8

G5

6

G1

2

G2

2

G3

2

G3

6

G5

3

G1

Ave

rage

tra

nsm

issi

on

pri

ce (

$/M

Wh

)

Ad

just

ing

rate

(%)

Generators

Trading profits Average transmission price ($/MWh)



45

scheme. Therefore, the generators can obtain higher profit by reducing the bidding price.

However, the connection of the network should also be considered during the

determination of PTP tariff. If the load bus is far away from the generator, the generator

is difficult to get extra profit or even getting losses. For example, G30 ranked 7th in the

TPM scheme. Only 25.4% of total output delivery is lower than the POC rate

(6.40$/MWh), while the remaining are matched to bus 23 and bus 38 for the best option

with PTP rates 8.77$/MWh and 8.88$/MWh respectively. So, the generator suffers a loss

in the scheme. In order to improve the profit gain, the generator can reduce the bidding

price or the maximum capacity. Besides, G12 obtains extra profit even it ranked in a late

order. This is because the nearest generator is far away from G12, which delivers to the

other load buses first due to lower PTP tariff, or due to the large power flow on the

branch connected to G12, the PTP is much higher.

In the above cases, the difference in the PTP tariff may not reflect the actual usage of the

network, but it can help to find the appropriate location for capacity expansion or

reduction. As shown above, G12 only deliver locally with low PTP rate but high PTP rate

to other buses. However, G3 delivers non-locally to over 15 buses with PTP rates lower

than POC rate. Therefore, assume the other factor is the same and remain unchanged, the

expansion of capacity is preferred on G3.



46

5.2 Adjustment on the marginal generator

Figure 24 Profit change for G2 in IEEE 30 bus system

As discussed above, the generator profit varies with bidding price. In order to have a

deeper understanding of the effect of bidding price, G2 is analyzed by changing the

bidding price on both TPM scheme and POC scheme. In fig.24, when the bidding price is

higher than 63.9$/MWh, G2 will suffer a loss in TPM scheme that means a negative

adjustment in profit compared to POC scheme. Otherwise, extra profit is obtained. Also,

in the above figure, the profit of generator decreases if the bidding price increases. Since

profit is proportional to the bidding price, the marginal price in section 1 is 67.8$/MWh,

69.0$/MWh for section 2 and 71.4$/MWh in section 3.

400

500

600

700

800

900

1000

1100

63 64 65 66 67 68 69 70 71 72 73

G2 profit

TPM POC

Section 1

Section 2

Section 3

Section 4



47

5.3 Adjustment in the congestion scenario:

Figure 25 Profit change for G5 in IEEE 30 bus system

On the above figure, the transmission capacity to bus 5 is decreased by half and the load

demand of bus 5 is increased to 1500MWh. The profit varies with the bidding price of G5

is shown. The green line represents the profit of POC scheme, while the red line

represents the profit of G5 under TPM scheme with 𝑅𝑃𝑇𝑃𝑇 = 40 %. In this situation, if

POC is used, G5 will bid a high price such as $83/MWh to get a higher profit. However,

G5 will be punished by increasing the bidding price. Therefore, the proposed scheme can

prevent the price spikes.

350

400

450

500

550

600

650

700

750

70 72 74 76 78 80 82

Generator 5 profit

TPM 40% POC



48

6. Conclusions

In this project, a new novel transmission pricing scheme combined with TPM scheme,

PTP tariff into the pool market which based on PAB scheme is introduced. The analysis

of advantages and disadvantages of related methods are discussed. Besides, two cases of

IEEE 30-bus and 57-bus system is studied by comparing the profit and transmission tariff

between the POC scheme and the proposed scheme.

The proposed scheme contains the benefits of the above three schemes such as such as

ensuring open, fair and non-discriminatory access, proper recovery for investment as well

as transparency. It also provides economic signals to participants to promote the

maximum use of the available transmission network and investment, encourages

appropriate bidding behaviors in the pool, and helps to reduce the appearing price spikes.

Then, the operation efficiency of the whole power system can be enhanced.

However, the real situation of power market is more complicated such as transmission

congestions and government policy. More effort should be put in this scheme to improve

the designation of the TPM scheme and more factors should be considered. Then, the

scheme will be better in the future.



49

7. Reference

[1] D. S. S. G. Kirschen, Fundamental of power system economics, Wiley, 2004.

[2] A. Roy, “Electricity Transmission Pricing: Tracing Based Point-of-Connection

Tariff for Indian Power,” in IEEE PES General Meeting, Montreal, 2006.

[3] StephenLuk, "Electricity tariffs in Hong Kong: what went wrong and what can we

do about it?," in Energy Policy, Hong Kong, Elsevier Ltd, 2005, pp. 1085-1093.

[4] Qixin Chen, Qing Xia, Chongqing Kang, “Novel Transmission Pricing Scheme

Based on Point-to-Point Tariff and Transaction Pair Matching for Pool Market,” in

Electric Power System Research, 2010, p. 8.

[5] J. Bialek, "Topological generation and load distribution factors for supplement

charge allocation in transmission open access," in IEEE Trans. on Power Systems,

Vol. 12,No. 3, , 1994, pp. 1185-1193.

[6] “Transmission and Distribution Pricing Methods,” National Development and

Reform Commission, 2017.

[7] Richard Green, "Electricity transmission pricing: an international comparison," in

Utilities Policy,Volume 6, Issue 3, 1997, pp. 177-184.

[8] A.R. Abhyankar, S.A. Khaparde, “Electricity transmission pricing: Tracing based

point-of-connection tariff,” in International Journal of Electrical Power & Energy

Systems,Volume 31, Issue 1, 2009, pp. 59-66.

[9] F. Rahimi, “Effective market monitoring in deregulated electricity markets,” in IEEE

Trans. Power Systems, no. 2, 2003, p. 486–493.

[10] I. Kranthi Kiran, A. Jaya Laxmi, “Power Flow Based Contract Path Method for,”

International Journal of Soft Computing and Engineering, pp. 61-65, Jan 2014.

[11] S. Nojeng, M. Y. Hassan, D. M. Said, Md. P. Abdullah, F. Hussin, “Improving the

MW-Mile Method Using the Power Factor-Based Approach for Pricing the

Transmission Services,” IEEE Transactions on Power Systems , pp. 2042 - 2048, 10

February 2014.

[12] Gang Duan, Zhao Yang Dong, Wei Bai, Xin Feng Wang,, “Power flow based

monetary flow method for electricity transmission and wheeling pricing,,” Electric

Power Systems Research,Volume 74, Issue 2, pp. 293-305, 2005.



50

[13] Hossein Haghighat, Hossein Seifi, Ashkan Rahimi Kian,, “Pay-as-bid versus

marginal pricing: The role of suppliers strategic behavior,,” International Journal of

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[14] Hugh Rudnick, Rodrigo Palma, Jose E. Fernandez, “MARGINAL PRICING AND

SUPPLEMENT COST ALLOCATION IN TRANSCATION OPEN ACCESS,"

IEEE transaction on Power System,” IEEE transaction on Power System, vol. 2,no.

10, 1995.

[15] C. P, “Alternative pricing rules. In: Proceeding of power system conference and

exposition,” New York, 2004.

[16] E. ONAIWU, “HOW DOES BILATERAL TRADING DIFFER FROM

ELECTRICITY POOLING?,” 2016.

[17] A. R. A. P. P. S. A. K. Anjan Roy, "Electricity Transmission Pricing: Tracing Based

Point-of-Connection Tariff for Indian Power System," IEEE, 2006.

[18] M. Oloomi-Buygi, M. Reza Salehizadeh,, “Considering system non-linearity in

transmission pricing,,” International Journal of Electrical Power & Energy

Systems,, pp. 455-461, 2008.

[19] Y. K. Wu, “Comparison of Pricing Schemes of Several Deregulated Electricity

Markets in the World,” in IEEE PES Transmission and Distribution Conf: Asia and

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[20] F. Rahimi, "Effective market monitoring in deregulated electricity markets," in IEEE

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[21] Haiying Wang,Baozeng Chu, MATLAB and Simulink Based Books(图论算法及其

matlab实现), Beihang University Press, 2010.



51

8. Appendix

Appendix 1: code of TPM clear;

clc;

x=input('please input the data of generator (in form of matrix

[Generator;Max capacity(MW);Bidding price($/MWh);production

cost($/MWh);]) = ');

y=input('please input the data of load buses (in form of matrix

[Bus;Load(MWh);]) = ');

z=input('please input the data of PTP tariff (in form of matrix [PTP

rate of G1;PTP rate of G2;PTP rate of G3]...;) = ');

N=100; for i=1:N if isempty(x) i=i-1; break elseif isempty(y) i=i-1; break elseif isempty(z) i=i-1; break else [Price(i), index1] = min(x(3,1:end));%index1 is the location of

generator [PTP_rate(i), index2] = min(z(index1,1:end));%index2 is the location of

bus F = x(2,index1)-y(2,index2); %D is the price, E is the PTP rate load_bus(i)= y(1,index2); generator(i)= x(1,index1); Cost(i)=x(4,index1); if F > 0 volume(i)= y(2,index2); value=sub2ind(size(x),2,index1); x(value)= x(2,index1)-y(2,index2); y(:,index2)=[]; z(:,index2)=[]; elseif F < 0 volume(i)=x(2,index1); value2=sub2ind(size(y),2,index2); y(value2)= y(2,index2)-x(2,index1); x(:,index1)=[]; z(index1,:)=[]; elseif F==0

volume(i)=x(2,index1); value2=sub2ind(size(y),2,index2);



52

y(value2)= y(2,index2)-x(2,index1); x(:,index1)=[]; z(index1,:)=[]; y(:,index2)=[]; z(:,index2)=[]; end end end Profit = volume.*(Price -Cost- PTP_rate); load_bus=load_bus'; generator=generator'; volume=volume'; Price=Price'; Cost=Cost'; PTP_rate=PTP_rate'; pair_order=1:i; pair_order=pair_order'; Profit =Profit'; T=

table(pair_order,load_bus,generator,volume,Price,Cost,PTP_rate ,Profit)

Appendix 2: code of the shortest length function a=Dijk(a)

n=length(a); for i=2:n for j=1:(i-1) a(i,j)=a(j,i); end end

%The main program

%¨B?2.1 for k=1:(n-1) b=[1:(k-1),(k+1):n]; kk=length(b); a_id=k; b1=(k+1):n; kk1=length(b1); %¨B?2.2.1 while kk>0 for j=1:kk1 te=a(k,a_id)+a(a_id,b1(j)); if te<a(k,b1(j)) a(k,b1(j))=te; end end

miid=1;

for j=2:kk



53

if a(k,b(j))<a(k,b(miid)) miid=j; end end

a_id=b(miid); b=[b(1:(miid-1)),b((miid+1):kk)]; kk=length(b); if a_id>k miid1=find(b1==a_id); b1=[b1(1:(miid1-1)),b1((miid1+1):kk1)]; kk1=length(b1); end end

for j=(k+1):n a(j,k)=a(k,j); end end

Appendix3: enter code of the shortest length n=12;

a=ones(n)+inf;

for i=1:n

a(i,i)=0;

end

a(1,2)=;

a(2,3)=;

a(2,6)=;

a(3,4)=;

a(3,9)=;

a(4,5)=;

a(4,7)=;

a(5,6)=;

a(7,8)=;

a(8,9)=;

a(8,11)=;

a(9,10)=;

a(10,11)=;

a(10,12)=;

Dijk(a)

transmission pricing scheme based on transaction pair

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