transmission pricing scheme based on transaction pair
Post on 25-Oct-2021
3 Views
Preview:
TRANSCRIPT
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
Acknowledgments
I would like to express my great appreciation to Professor C.W. Yu for his valuable
advice and support in the whole project.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
2
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
3
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
4
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
5
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].
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
6
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
7
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
8
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;
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
9
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
10
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
11
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
12
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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 ๐ถ๐ is assumed. Base on the theory of point of connect method, the
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
14
transmission price is calculated as shown:
๐ถ๐๐๐ = ๐ถ๐
๐๐๐ก๐๐ ๐ก๐๐๐๐ ๐๐๐ก๐๐๐ ๐ฃ๐๐๐ข๐๐ (C1)
Also, the profit for each generator is calculated as shown:
๐๐๐๐ = ๐๐ต โ ๐๐ โ ๐ถ๐๐๐ . โ ๐๐ฟ (๐ถ2)๐ฟโ๐๐ , ๐๐ โ๐๐๐๐๐
Where ๐๐ต is the bidding price, ๐๐ is the production cost of the generator, ๐๐ is the
transaction pair, ๐๐๐๐๐ represents all the transaction pair in the pool, ๐๐ฟ 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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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 ( ๐ถ๐,๐๐,๐ท
)
respectively. The value of cT ,B is a uniform payment for one unit power delivery, while
the values of ๐ถ๐,๐๐,๐ท
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 ๐ถ๐,๐๐,๐ท
is shown in the equation
below, while the unit is in $/MWh:
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
17
๐ถ๐,๐๐,๐ท = ๐ฝ๐๐๐ . โ |๐น๐ฟ| . ๐พ๐ฟ (1)
๐ฟโ๐๐ต๐๐๐
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 ๐ถ๐,๐๐,๐ท by inputting
the results in the previous
step to the program
(shortest length)
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
18
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 ๐ถ๐,๐๐,๐ท 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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
19
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:
๐๐ฟ,๐ = ๐๐ฟ โ ๐๐ โ ๐๐,๐๐,๐ท , ๐ฟ โ ๐, ๐ โ ๐, (2)
Where ๐๐ฟ,๐ denote the profit for a unit transaction from generator L to load bus M. ๐๐ฟ is
the bidding price, ๐๐ is the production cost and ๐๐,๐๐,๐ท
is the corresponding PTP tariff (the
basic part of tariff is ignored). ๐ฟ โ ๐ means that generator connects to point a and ๐ โ ๐
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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 ๐๐, the transaction
volume ๐๐๐ , and the corresponding price ๐๐ฟ are recorded.
๐๐๐ = (๐๐ฟ,๐, ๐๐,๐) (3)
Where ๐๐ฟ,๐ and ๐๐,๐ 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, ๐๐ฟ,๐and ๐๐,๐ must be revised
simultaneously. The transaction volume should be subtracted for both generator and LSE:
๐๐ฟ,๐ = ๐๐ฟ,๐ โ ๐๐๐ (4)
๐๐,๐ = ๐๐,๐ โ ๐๐๐ (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 ๐๐ฟ,๐ 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 ๐๐,๐ have become
zero, the data of dth column in generator matrix and PTP matrix should be removed as
well. w the value of ๐๐,๐ or ๐๐ฟ,๐ has become zero, it means that the process of
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
21
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 ๐๐๐,๐ต
and the
differential part ๐๐๐,๐ท
. Firstly, ๐๐๐,๐ท
is calculated based on the load flow, cost proportion
and corresponding transaction volume, so we have:
๐๐๐,๐ท = โ ๐๐,๐
๐ . ๐๐,๐๐,๐ท
๐ฟโ๐๐ , ๐๐ โ๐๐๐๐๐
(6)
๐ถ๐,๐ท = โ ๐๐๐,๐ท
๐ฟโ๐๐๐๐๐ก
(7)
Where ๐๐๐๐๐ represents all the transaction pair in the pool, ๐๐๐๐๐ก represents all the
participants in the pool, and ๐ถ๐,๐ท 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 ๐ถ๐,๐ท. As the value of ๐ฝ๐๐๐ is adjustable, there could be offset between CT and
๐ถ๐,๐ท. 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 ๐ถ๐,๐ตis:
๐ถ๐,๐ต =๐ถ๐ โ ๐ถ๐,๐ท
g (8)
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
22
๐ถ๐ฟ๐,๐ต = ๐ถ๐,๐ต. ๐๐ฟ (9)
Where g is the total transaction volume in the pool market, and ๐๐ฟ 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 ๐๐,๐ต to every element
(๐๐,๐๐,๐ท
) in the matrix to form the new element ๐๐,๐๐ :
๐๐,๐๐ = ๐๐,๐
๐,๐ท+ ๐๐,๐ต (10)
Hence, the total transmission payment for participant L is shown as:
๐๐ฟ๐ = ๐๐ฟ
๐,๐ท+ ๐๐ฟ๐,๐ต (11)
๐๐๐ = โ ๐๐,๐
๐ . ๐๐,๐๐
๐ฟโ๐๐,๐๐,โ๐๐๐๐๐
(12)
The expression in formula (11) and (12) are the same.
Apart from ๐ฝ๐๐๐, ๐ ๐๐๐๐ is another control parameter to show the proportion of differential
part in the total transmission cost which is defined as:
๐ ๐๐๐๐ =
๐ถ๐,๐ท
๐ถ๐ (13)
By comparing to the parameter ๐ฝ๐๐๐, ๐ ๐๐๐๐ 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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
23
Figure 4 Flowchart TPM scheme
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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;
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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)
Bidding price($/MWh)
Production cost($/MWh)
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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;
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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)
Bidding price($/MWh)
Production cost($/MWh)
400
76
63.2
45
58.2
45.2
40
54.4
41.9
25
45.7
33.5
70
46.8
33.9
190
49.1
36.4
150
69.2
53.5
100
57.7
43.4
30
62.5
52.1
Generator 22 25 27 29 30 32 36 38 47
Maxi capacity(MW)
Bidding price($/MWh)
Production cost($/MWh)
22
70.1
57.5
15
55.4
42.1
30
52.1
39.3
35
60.4
44.5
24
56.3
43.4
35
71.2
52.1
30
73.5
50.7
35
66.6.
53.4
28
61.5
49.1
Generator 49 50 53 54 56
Maxi capacity(MW)
Bidding price($/MWh)
Production cost($/MWh)
25
57.9
46.4
75
63.9
49.8
45
74
56.5
15
59.5
47.1
35
68.9
56.5
Figure 13 Generator data of IEEE 57 bus system
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
33
5. Results and finding:
5.1 Adjustment on trading profit:
5.1.1 IEEE 30-bus system
In case of IEEE 30-bus system, the total transmission cost is set as 2000$/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 ๐ฝ๐๐๐ 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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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)
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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$/MWh which is the basic part of the transmission. The control parameter ๐ฝ๐๐๐ is
assumed to be 0.25. In the local delivery, the rate is 5.62$/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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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)
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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$/MWh respectively. So, the generator suffers a loss
in the scheme. In order to improve the profit gain, the generator can reduce the bidding
price or the maximum capacity. Besides, G12 obtains extra profit even it ranked in a late
order. This is because the nearest generator is far away from G12, which delivers to the
other load buses first due to lower PTP tariff, or due to the large power flow on the
branch connected to G12, the PTP is much higher.
In the above cases, the difference in the PTP tariff may not reflect the actual usage of the
network, but it can help to find the appropriate location for capacity expansion or
reduction. As shown above, G12 only deliver locally with low PTP rate but high PTP rate
to other buses. However, G3 delivers non-locally to over 15 buses with PTP rates lower
than POC rate. Therefore, assume the other factor is the same and remain unchanged, the
expansion of capacity is preferred on G3.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
46
5.2 Adjustment on the marginal generator
Figure 24 Profit change for G2 in IEEE 30 bus system
As discussed above, the generator profit varies with bidding price. In order to have a
deeper understanding of the effect of bidding price, G2 is analyzed by changing the
bidding price on both TPM scheme and POC scheme. In fig.24, when the bidding price is
higher than 63.9$/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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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 ๐ ๐๐๐๐ = 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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
49
7. Reference
[1] D. S. S. G. Kirschen, Fundamental of power system economics, Wiley, 2004.
[2] A. Roy, โElectricity Transmission Pricing: Tracing Based Point-of-Connection
Tariff for Indian Power,โ 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, โNovel Transmission Pricing Scheme
Based on Point-to-Point Tariff and Transaction Pair Matching for Pool Market,โ 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] โTransmission and Distribution Pricing Methods,โ 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, โElectricity transmission pricing: Tracing based
point-of-connection tariff,โ in International Journal of Electrical Power & Energy
Systems,Volume 31, Issue 1, 2009, pp. 59-66.
[9] F. Rahimi, โEffective market monitoring in deregulated electricity markets,โ in IEEE
Trans. Power Systems, no. 2, 2003, p. 486โ493.
[10] I. Kranthi Kiran, A. Jaya Laxmi, โPower Flow Based Contract Path Method for,โ
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, โImproving the
MW-Mile Method Using the Power Factor-Based Approach for Pricing the
Transmission Services,โ IEEE Transactions on Power Systems , pp. 2042 - 2048, 10
February 2014.
[12] Gang Duan, Zhao Yang Dong, Wei Bai, Xin Feng Wang,, โPower flow based
monetary flow method for electricity transmission and wheeling pricing,,โ Electric
Power Systems Research,Volume 74, Issue 2, pp. 293-305, 2005.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
50
[13] Hossein Haghighat, Hossein Seifi, Ashkan Rahimi Kian,, โPay-as-bid versus
marginal pricing: The role of suppliers strategic behavior,,โ International Journal of
Electrical Power & Energy Systems,Volume 42, Issue 1,, pp. 350-358, 2012,.
[14] Hugh Rudnick, Rodrigo Palma, Jose E. Fernandez, โMARGINAL PRICING AND
SUPPLEMENT COST ALLOCATION IN TRANSCATION OPEN ACCESS,"
IEEE transaction on Power System,โ IEEE transaction on Power System, vol. 2,no.
10, 1995.
[15] C. P, โAlternative pricing rules. In: Proceeding of power system conference and
exposition,โ New York, 2004.
[16] E. ONAIWU, โHOW DOES BILATERAL TRADING DIFFER FROM
ELECTRICITY POOLING?,โ 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,, โConsidering system non-linearity in
transmission pricing,,โ International Journal of Electrical Power & Energy
Systems,, pp. 455-461, 2008.
[19] Y. K. Wu, โComparison of Pricing Schemes of Several Deregulated Electricity
Markets in the World,โ in IEEE PES Transmission and Distribution Conf: Asia and
Pacific, Dalian, 2005.
[20] F. Rahimi, "Effective market monitoring in deregulated electricity markets," in IEEE
Trans. Power Systems, no. 2, 2003, pp. 486-493.
[21] Haiying Wang,Baozeng Chu, MATLAB and Simulink Based Books(ๅพ่ฎบ็ฎๆณๅๅ ถ
matlabๅฎ็ฐ), Beihang University Press, 2010.
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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);
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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
%ยจB?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); %ยจB?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
THE HONG KONG POLYTECHNIC UNIVERSITY
DEPARTMENT OF ELECTRICAL ENGINEERING
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)
top related