Pricing of Transmission Services: An Efficient Analysis Based on Fixed and Variable Imposed Costs

Amirsaman Arabali Seyed Hamid Hosseini Moein Moeini-Aghtaie

Department of Electrical Engineering Sharif University of Technology

Tehran, Iran

Saman_Arabali@yahoo.com hosseini@sharif.edu M.Moeini@ieee.org

Abstract—Open access to transmission networks as well as designing an efficient cost allocation method are the key points that provide free competition for participants in power market. Restructuring in power systems has created new challenges which emphasize the development and fairness of economical criteria such as pricing of different services in market environment. Besides, the charge of network usage is a controversial subject, itself. To address this problem, many methods for transmission line cost allocation have been proposed. Amongst them, MW-Mile methods are based on the "extent of use" concept. Inability to take various fixed together with variable imposed costs into account can be announced as the major disadvantage of this approach. In response, this paper presents a new combinatorial pricing method which is preferable over the other methods in considering two basic features of a proper pricing approach, i.e., fairness and producing effective economical incentives. In order to verify the effectiveness of the proposed method, it is applied to the IEEE 24-bus test system.

Keywords- Transmission line; pricing method; MW-Mile; fixed cost; variable cost

I. INTRODUCTION Transmission lines as a physical interface between the

generators and consumers undertake an extremely crucial role in providing the free access for all power market participants [1]. Also, transmission network provide an environment for generation companies (Gencos) to interchange their products, i.e., electricity energy, with distribution companies (Discos). as demand for electricity is increasing, the electrical energy price will experience a remarkable growth. This can create effective signals and motivation for GenCos and provide them with an opportunity to invest in new generation projects and as a consequence they harvest more benefit. These profitable conditions continue up to the point that more investing in new projects decrease the power price and quench the generation projects attractiveness. But, transmitting electrical energy through a weak network results congested lines and consequently escalates the energy price. Therefore, the power systems should have such a powerful transmission network that no bottle neck can be found in the network.

In restructured environments, it is desirable to absorb private investments in each section of power systems. To attain this goal, new transmission lines projects should be

attractive enough for investing. Generally, electric power markets cannot create sufficient appealing incentives for private investors to invest in transmission section. To understand why transmission lines are unable to be alluring for investors in contrast with other components of power systems, the efficient and challenging factors in transmission line investments should be recognized. Many factors can affect the attractiveness of a commodity for trading. The expected rate of return on investment in that commodity is one of the main factors. The rate of return for each transmission line is relying on the transmission pricing method [2].

The pricing is the process of transmission cost allocation between the consumers or transmission line users [3]. Being fair and comprehensive are of the main attributes of an efficient pricing method. A comprehensive pricing approach can address about those transmission services costs which need to be retrieved in a certain period. Besides, a fair transmission pricing method can make the transmission users pay the price which, in fact, shows their extent of use of transmission lines. Such pricing mechanism, can lead the transmission users and investors to the effective use and development of transmission network, [4]. In general, an appropriate pricing mechanism should cover the following challenges:

• It should recover the transmission service costs by properly allocation of these costs among users [5]. These costs include the running cost, the initial investment and the investment which is needed to maintain, strengthen and develop the network in step with the load growth, generation expansion and transactions enhancement [5].

• The pricing scheme should be fair and non-discriminatory. In other words, the transmission costs are assigned reasonably among the line users [4]-[6].

• It should be clear and practical. These attributes can lead to increased economic productivity and will keep market participants away from confusion. It must provide the suitable economical incentives for transmission network expansion and effective use [4], [6].

It is worth noting that the total cost of the transmission lines are divided into two parts, namely the fixed and variable costs. The cost of construction, designing, measurement, and tax are so called fixed costs of transmission lines. The

978-1-4577-1829-8/12/$26.00 ©2012 IEEE

operation as well as maintenance costs of transmission lines are named the variable costs. The transmission services pricing problem has been an attractive ongoing area of research which has eventuated in some remarkable number of papers revealed and still some others going to be published [4]-[8]. The Postage Stamp method, Peak Coincident load method, and Contract Path method are some pricing methods which have been reported as unfair and unable to reflect the true economical signals. The MW-Mile approach was introduced to compute the transmission costs based on the distance between the delivery and receiving points of the exchanged power and its quantity [9]. This method similar to the Contract Path method is unable to address the real path of the flows in transmission lines. Therefore, employing this approach results insufficient economical signals and improper incentives.

A modified version of the MW-Mile method which calculates the transmission charges based on the power flow analysis and the line usage, can represent the real situation of the network [4], [10]. This method can recover the total costs of transmission lines to some extent. The more general form of the MW-Mile method is called the Unused Capacity method. In this scheme, the line user should pay the transmission charges for both used and unused capacity of each line, so, it can retrieve the embedded costs of lines. Although the costs in this method are recovered but it has been proved that it cannot give the economical signals to find the most appropriate places for new lines and therefore it cannot lead to the effective extension of the transmission network placement [3], [4], [8], and [10]. Some references claim that this method is totally unfair [4], [8]. Several works included the reliability costs in their transmission pricing methods [12, 15, 16 and 17]. These references consider reliability costs as a way to recover the transmission expenses. Although they have shown that considering the reliability costs in their pricing methods can appropriately retrieve the transmission costs, the fairness and ability of their methods to provide effective incentives for proper extension of transmission network are not evaluated.

Considering the need to have an effective transmission pricing method, this paper proposes a new transmission line pricing scheme. This new scheme is based on the combination of two various MW-mile methods which considers the line cost from two different perspectives. In compare to the other methods, this new pricing scheme associates the charges to the transmission line users fairly and creates appropriate economical signals for the transmission network investors.

In the following, the proposed method necessities together with its algorithm will be described in Section II. Section III is devoted to the case studies, where the proposed transmission services pricing method is verified by implementing it on the IEEE-RTS 24-bus test system. Finally, the conclusions are presented in Section IV.

II. METHODOLOGY

A. Merits and Demerits of Different Pricing Methods One of the most common methods for transmission pricing

is the Postage Stamp method which allocates the fixed cost for

transferring energy regardless of the distance and power trace. This method recovers the transmission cost, but, since there is no relation between the allocated cost and real usage of the line, this method is unfair and cannot provide the proper economical incentive for the effective use and transmission expansion [6], [8], and [10].

Another common pricing method is the Contract Path. In this method, transmission line users and transmission companies agree on a contract path. This contract path is an artificial electrical path which connects the power injection point to the power consumption point. Based on the distance of this path some portion of the transmission cost is allocated to the user. The same as Postage Stamp, this method is unfair because the true path of the flow and extent of use may be different from the contract path, so, this method cannot produce the true economical signal for efficient use and expansion [4] and [5].

The MW-Mile method is a pricing approach that can consider the real state of power system and power flow path by applying the DC power flow analysis. In this method, transmission cost is allocated based on the extent of use of the transmission network by each user. There are two improved MW-Mile methods which are known as Unused Transmission Capacity methods [4], [5], and [6]. Equation (1) shows the formulation of the first Unused Transmission Capacity (UTC1) method.

,

,

.Kk k t

t Tk 1

k tt 1

C fTC

f=

=

=∑∑

(1)

where TCt, Ck, fk,t, T, and K are representative for the total charge of transaction t, total cost of line k, the flow in line k due to use of transaction t, number of transactions, and number of lines, respectively.

This approach forces the user to pay the cost of used capacity as well as unused capacity and can recover all the transmission cost. Although all the cost is recovered, this method is not a proper pricing method and cannot produce appropriate economical signals for the effective use and expansion of transmission system since regardless of the extent of use, all the cost is recovered. Therefore, transmission lines may be installed at improper locations with no help to decrease the network congestion. Also, this method can be unfair because there may be some users which are forced to pay the large portion of the transmission costs while their usages are low. Another deficiency of this method is that the cost of capacity for maintaining the reliability is not considered in this method.

Equation (2) shows the formulation of the second Unused Transmission Capacity (UTC2) method. In (2), kf denotes the maximum thermal capacity of line k. This method had been proposed to solve some of the UTC1’s deficiencies. For example, this method allocates the cost to each user based on the extent of use of line capacity which can provide the true economical signal for efficient use of the transmission lines. But in this method, the cost of transmission lines is not recovered since the total flow of line is usually smaller than

the line capacity. The main drawback of this method is that the cost of the extra capacity which is related to satisfy the reliability criteria is not considered, therefore, the transmission cost is not recovered [4] and [11].

,.Kk k t

tk 1 k

C fTC

f==∑ (2)

B. Different Perspectives of Transmission Cost The total cost of a transmission line in the period of its

longevity can be divided into two parts: fixed and variable costs. The variable cost is related to the transmission services while the fixed cost is independent from these services. The fixed cost includes the equipment cost, equipment construction cost, design, measurement, dept and tax some of which are at the beginning of the project and the others are annually. The variable cost includes operation cost, maintenance, reactive power, loss compensation, and opportunity cost. The initial cost can be converted to an equivalent annual cost using (3) and can be added to the other annual costs.

( )( )

N

N

i 1 iA P1 i 1

⎡ ⎤+= ⎢ ⎥+ −⎣ ⎦ (3)

where A, P, I, and N are the annual cost, the initial investment cost (present value), interest rate, and the period of study, respectively. Finally, we will have two costs for transmission line: annual fixed cost (Cfix) which is related to the capacity of line and annual variable cost (Cvar) which is related to the extent of use of transmission services.

C. Incentive Example It was shown that the MW-Mile methods somehow

consider the extent of use of the transmission line and therefore are preferred to the other methods. Some of the deficiencies of these methods are discussed in this section. We concentrate on the deficiency of these methods from the viewpoint of the cost type. For all transmission cost assigning approaches including MW-Mile methods, the term "cost" is referred to all the transmission costs and dealt with as a whole. (i.e., it is not divided into fixed and variable costs), therefore, these approaches are totally unfair. The reason of unfairness can easily be interpreted with an example. Suppose that there is a power system with one Genco, one transmission company (Transco), and one Disco. In this system, the Disco uses the Transco's transmission services through a 100 MW transmission line. The Disco only occupies 50 percent of this line. According to the UTC2, all the transmission cost (including fixed and variable costs) is allocated to the Disco, while the Disco only uses the half of the line capacity (half of the investment capacity or the fixed cost). So, it is unfair to allocate all the cost to Disco. On the other hand, according to the UTC1, half of the transmission cost (including fixed and variable costs) is allocated to the Disco, while Disco is the only user of the transmission line and must pay all the variable cost regardless of the extent of use. Bearing in mind that regardless of the extent of use of the line, the Transco has to pay all the variable cost including the costs of operation,

maintenance, and other services. So, it is necessary to reach an algorithm which can properly and fairly assign these two cost types.

D. Transmission Extra Capacity Cost Recovery Generally in power systems, the installed capacities of

transmission lines are much more than the extent of use of these lines. These extra capacities can be intentional or unintentional. If these capacities are unintentional, it can be inferred that these transmission lines were not installed in proper places. So, the effective use of these lines is impossible. Therefore, it is necessary for a complete pricing mechanism to provide the appropriate economical signals to Transcos and owners of transmission lines to extend the transmission network in a good manner. If these extra capacities are intentional, with the current methods, the costs of those are not recovered. These capacities might be installed in order to satisfy the reliability criteria in critical conditions, so in normal condition, the extents of use of these capacities are low and the usage-based approach cannot recover their costs. Thus, to recover the cost of these capacities, the transmission cost allocation mechanisms must have the ability to calculate the reliability capacity usage and cost (cost of capacity for improving the reliability criteria). The n-1 security criterion is a common approach for evaluating and determining the extent of network use in single contingency condition [8] and [12].

E. The Proposed Method Here, the proposed method that combines UTC1 and UTC2

is presented which has all the positive proprieties of the MW-Mile method and has priority over the conventional MW-Mile methods in the more fairly allocating the costs (fixed and variable costs) and producing the proper economical signals for effective use of transmission lines, transmission operation, maintenance, reinforcement, and expansion. In this method, first the total transmission cost is split into two annual fixed and variable costs. The extent of consumption of each transmission line for every transmission user is defined as the that user's share of the transmission line power. Since the fixed cost is proportional to the transmission capacity and the variable cost is proportional to the transmission usage, the ratio of the extent of use to the transmission flow (similar to UTC2) is used to allocate the transmission variable cost and the ratio of the extent of use to the transmission capacity (similar to UTC1) is used to allocate the transmission fixed cost. Under this circumstance, it is guaranteed that all the variable cost is recovered which means that all the users must pay all the variable cost regardless of the extent of use and the fixed cost recovery is due to the extent of use of the capacity which can produce the effective economical signals. Meanwhile, for reasonable allocation, transactions which contribute flow components in the opposite direction of the net flow, have to pay only the variable cost, because, they do not occupy any line capacity, however, they use the transmission lines.

Distribution factors concept based on DC model of power system is an effective tool for evaluating the usage of transmission line which represents the contribution of each

element including generators and loads in the power flow of each transmission line [5], [6], and [13]. The extent of use and consequently the cost of use of each transmission line can be allocated to each market participator in three ways: first, with respect to the generalized generation distribution factor (GGDF) concept [5], the extent of use can be allocated to the generators according to (4), second, with respect to the generalized load distribution factor (GLDF) concept [5], the extent of use can be allocated to the loads according to (5), and finally, with respect to the generalized distribution factor (GDF) concept [5], the extent of use can be allocated to the net power of buses according to (6). In this paper, the cost is allocated to the generators.

, .m

n

ij ij m Gm 1

f D P=

= ∑ (4)

, .m

n

ij ij m Dm 1

f C P=

= ∑ (5)

, .n

netij ij m m

m 1f a P

=

= ∑ (6)

where fij, Dij,m, Cij,m, PGm, PDm, aij,m, Pmnet , and n denote the

flow of line between buses i and j, generation distribution factor, load distribution factor, generation of bus m, demand of bus m, distribution factor, the net power of bus m, and number of network buses, respectively.

The algorithm of the proposed method is as follows:

• Allocating the cost in the normal condition: 1) Calculate fixed and variable costs for each

transmission line. 2) Convert the initial fixed and variable costs to

equivalent annual fixed and variable costs according to the equation (3) and add them to other annual fixed and variable costs, respectively. After adding, there are two annual costs for each line k (Ck

fix and Ckvar).

3) Calculate the flows of transmission lines using a DC power flow in normal condition of the network.

4) Compute generalized generation distribution factors for each transmission line (Dij,m).

5) Calculate the contribution of each transaction to the flow of line i-j using (4).

6) Assign the fixed cost and variable cost to each transmission line according to (7). For any transaction whose flow is in the opposite direction of the net line flow, only the variable cost is considered.

var

, ,

,

. .fixk k t k k tk

t Tk

k tt 1

C f C fTC

f f=

= +∑

(7)

7) the TCt and TCk for each transaction and line by summing the TCt

k over all lines k and transactions t, respectively.

• Extra capacity cost recovery in the contingency condition:

8) Implement the n-1 security analysis, as the reliability criterion, by opening line k, then, repeat steps 4 to 6 and calculate TCk for the other lines by summing the TCt

k over all transactions. The biggest TCk is known as TCk

total (cost of capacity of line k for normal and contingency state).

9) Calculate the difference between TCktotal and TCk as the

cost of extra capacity for maintaining the reliability. Flowcharts of the proposed algorithm in the normal state of the power system and in the contingency state are respectively shown in Fig. 1 and Fig. 2.

III. CASE STUDY In this section, the proposed algorithm is applied to the

IEEE-RTS 24-bus test system. This network includes 38 transmission lines and 11 generators. Other network data of this system can be found in [14]. The total cost of lines has been assumed 500 $/MW-Mile. Also, the fixed and variable costs are 80 and 20 percent of the total cost, respectively. The annual rate of return has been assumed to be 20%.

Table I shows the results of applying the proposed algorithm to the test network. The results have been calculated before allocating the reliability cost. The costs in this table have been converted to annual amount.

Figure 1. Flowchart of allocating the transmission cost in normal state.

The Outage of Line k

End

Yes

No

Performing a DC OPF

Calculate & Save TCkout by

Summing TCkt for All

Transactions

TCktotal =Max(TCk

out) of Line Outages (k=1,2,…,K)

k=K

k=k+1

Yes

Set k=1

k=K

Set k=1

TCkreli=TCk

total-TCk

k=k+1

No

Figure 2. Flowchart of allocating the credit in the contingency state.

The total and reliability costs of transmission lines are presented in Table II by using the MW-Mile methods and the proposed method. As it can be seen in this table, total costs of lines are retrieved completely after five years by applying the UTC1. Therefore, the table emphasis the conclusion that this

TABLE I. ANNUAL TRANSACTION CHARGES ALLOCATION

Gen No.

Generation (MW)

UTC1

(M$/year) UTC2

(M$/year)

Proposed Algorithm (M$/year)

Proposed Algorithm

(10³$/MW-year)

G1 191.8 3.03 1.93 2.15 11.21 G2 192.3 3.09 1.93 2.16 11.23 G3 168.9 2.65 1.85 2.01 11.87 G4 167 2.8 0.47 0.94 5.62 G5 0 0 0 0 0 G6 215 2.84 0.78 1.19 5.54 G7 155 1.78 0.39 0.67 4.31 G8 400 6.4 1.28 2.3 5.75 G9 400 7.18 1.12 2.33 5.84 G10 300 9.13 0.73 2.41 8.02 G11 660 9.94 0.4 2.3 3.49

method is unable to reflect the effective use of lines and also to create the economical incentives for appropriate expansion of transmission network.

The result of applying the UTC2 proves that this method is rarely successful, even in variable costs retrieval. Therefore, this method cannot be called as a method based on the economical basis. But the results of applying the proposed method are supportive for this conclusion that not only the variable costs are retrieved for the used transmission lines but also the fixed costs are recovered with considering the extent of use of the line capacities. This algorithm can help the transmission line owners to recover the cost of capacities of all lines which have been constructed for reliability purposes.

TABLE II. PAYMENT TO TRANSMISSION LINES BY DIFFERENT METHODS

Line From To IC a CA b RCA c TCA d UTC1 UTC2 1 1 2 0.26 0.038 0.0143 0.0523 0.034 0.053 2 1 3 4.81 0.593 0.1161 0.7091 0.501 0.963 3 1 5 1.93 0.266 0.0594 0.3254 0.236 0.385 4 2 4 2.89 0.351 0.0774 0.4284 0.294 0.578 5 2 6 4.38 0.471 0.2232 0.6942 0.37 0.875 6 3 9 2.71 0.311 0.1782 0.4892 0.253 0.543 7 3 24 10 0.674 0.1629 0.8369 0.342 2 8 4 9 2.36 0.266 0.0639 0.3299 0.214 0.473 9 5 10 2.01 0.26 0.0612 0.3212 0.224 0.403

10 6 10 1.4 0.126 0.0504 0.1764 0.088 0.28 11 7 8 1.4 0.263 0.0225 0.2855 0.258 0.28 12 8 9 1.4 0.412 0.1062 0.5182 0.327 0.753 13 8 10 3.76 0.41 0.2358 0.6458 0.324 0.753 14 9 11 3.76 0.597 0.1044 0.7014 0.246 2 15 9 12 10 0.549 0.1557 0.7047 0.186 2 16 10 11 10 0.703 0.135 0.838 0.379 2 17 10 12 10 0.604 0.1269 0.7309 0.255 2 18 11 13 10 0.52 0.5283 1.0483 0.237 1.65 19 11 14 8.25 0.582 0.4554 1.0374 0.365 1.45 20 12 13 7.25 0.463 0.2115 0.6745 0.167 1.65 21 12 23 8.25 0.98 0.2295 1.2095 0.388 3.35 22 13 23 16.75 0.914 0.3087 1.2227 0.393 3 23 14 16 15 0.436 0.3366 0.7726 0.207 1.35 24 15 16 6.75 0.432 0.378 0.81 0.39 0.6 25 15 21 3 0.453 0.1485 0.6015 0.141 1.7 26 15 21 8.5 0.453 0.1485 0.6015 0.141 1.7 27 15 24 8.5 1.195 0.3681 1.5631 1.044 1.8 28 16 17 9 0.375 0.2169 0.5919 0.244 0.9 29 16 19 4.5 0.707 0.324 1.031 0.683 0.8 30 17 18 4 0.203 0.1044 0.3074 0.129 0.5 31 17 22 2.5 0.77 0.1881 0.9581 0.05 3.65 32 18 21 18.25 0.304 0.1476 0.4516 0.154 0.9 33 18 21 4.5 0.304 0.1476 0.4516 0.154 0.9 34 19 20 4.5 0.642 0.2781 0.9201 0.459 1.375 35 19 20 6.88 0.642 0.2781 0.9201 0.459 1.375 36 20 23 6.88 0.311 0.1521 0.4631 0.201 0.75 37 20 23 3.75 0.311 0.1521 0.4631 0.201 0.75 38 21 22 3.75 0.572 0.2871 0.8591 0.128 2.35

a. Investment Cost (M$)

b. Line Payment Using the Proposed Algorithm without Considering Reliability Capacity (M$/year)

c. Reliability Capacity Payment Using the Proposed Algorithm (M$/year)

d. Total Payment Using the Proposed Algorithm(M$/year)

IV. CONCLUSION This paper has presented a new combinatorial transmission

pricing algorithm. Being fair and incorporating various transmission services costs in the pricing process are of its major features. Besides, by dividing the transmission service costs into two basic parts, named fixed and variable costs, the proposed pricing scheme can reasonably create the essential incentives to fulfill the main deregulated environments goals. For each part of the cost, appropriate formulation based on the MW-Mile method is applied for recovering that cost. The formulation can ensure the fairness of the method, cover the usage cost, and provide correct economical incentive for efficient use, maintenance and future development of transmission network. Also, this method recovers the extra capacity cost for maintaining the reliability level in the power system.

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