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Transmission reliability cost allocation method based on market participants’ reliability contribution factors
Electric Power Systems Research 73 (2005) 31–36
Transmission reliability cost allocation method based on market participants’ reliability contribution factors Koo-Hyung Chunga , Balho H. Kima,1 , Don Hurb,∗ , Jong-Keun Parkb b
a School of Electronic and Electrical Engineering, Hong-Ik University, Sangsu-dong 72-1, Mapo-gu, Seoul 121-791, Republic of Korea School of Electrical Engineering, Seoul National University, 301 Dong 615 Ho, Shillim 9-dong, Gwanak-gu, Seoul 151-744, Republic of Korea
Received 19 December 2003; received in revised form 30 May 2004; accepted 31 May 2004 Available online 26 August 2004
Abstract Due to the complex and integrated nature of power systems, failures in any part of the system can cause interruptions which range from inconveniencing a small number of local residents to a widespread catastrophic disruption of supply. For this reason, the transmission reliability margin must be provided for the system to be operated at all times in such a way that the system will not be left in a dangerous condition even though unpredictable events occur. In this paper, Kirschen’s tracing method is employed to find the usage contributions of individual generators to the line flows under normal conditions. Apparently, it seems plausible to compute the reliability contributions of all market participants based on the probabilistic approach which takes notice of the forced outage rate for each transmission line as well as the line outage impact factor and then to allocate the transmission reliability cost among all the system users in proportion to their “extent of use” of reliability reserves in transmission facilities. © 2004 Elsevier B.V. All rights reserved. Keywords: Forced outage rate; Reliability contribution factor; Transmission reliability cost allocation
1. Introduction The electricity transmission system is an extensive, interconnected network of high-voltage power lines that pass electricity from generators to customers. Such a transmission system must be flexible enough, every second of every day, to accommodate the growing demand for reliable and affordable electricity. Nevertheless, rapid growth in electricity demand and new generation, lack of investment in new transmission facilities, and the incomplete transition to fully efficient and comAbbreviations: EUE, expected unserved energy; LOIF, line outage impact factor; LODF, line outage distribution factor; FOR, forced outage rate; RREF, relative reliability evaluation factor; NRREF, normalized relative reliability evaluation factor ∗ Corresponding author. Tel.: +82 2 880 7258; fax: +82 2 878 1452. E-mail addresses: [email protected] (B.H. Kim), [email protected] (D. Hur). 1 Tel.: +82 2 320 1462; fax: +82 2 320 1110. 0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.05.003
petitive wholesale markets have allowed transmission bottlenecks to emerge. These bottlenecks increase electricity costs to consumers and increase the risks of blackouts. Today, power failures, close calls, and near misses are much more common than in the past. The transmission systems of tomorrow must be operated in ways that maintain adequate safety margins for reliability and allow customers to follow strict tariffs for reliability with appropriate penalties for noncompliance. Despite the fact that transmission charges account for a small percent of operating expenses in utilities, we cannot afford to allow the relatively small transmission costs to prevent customers from enjoying the reliable and affordable electricity service that the properly managed competitive forces will deliver to our nation. Therefore, transmission pricing should be a reasonable economic indicator used by the market to make decisions on resource allocation, system expansion, and reinforcement [1]. The first step toward increasing the role of market forces in managing transmission system operations
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K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
efficiently and fairly is increasing the role of price signals to direct the actions of market participants toward outcomes that improve operations. Improving operations by relying on accurate price signals may, by itself, alleviate the need for some construction of new transmission facilities. Moreover, when new construction is needed, price signals will help market participants identify opportunities and assess options to address bottlenecks. Several aspects of transmission operations, including congestion and losses, could be effectively addressed by pricing based on the principle that if market participants see the true costs of transmission services reflected in prices, they will use or procure these services efficiently. Thus, reliance on uplift charges, in which costs are recovered from all transmission users on an equivalent basis, should be minimized. In the past few decades, many researchers have devoted themselves to achieving an efficient transmission pricing scheme that could fit all market structures in different locations so that participants in markets can see and respond to the true costs of using the transmission system. Generally, the transmission charge is grouped into the following parts: transmission line usage charge, system reliability charge, access charge, and so on [2]. Any transmission tariffs should be able to reflect these respective cost components without any distortion. Particularly, this paper suggests a probabilistic approach to allocating the reliability cost of the transmission system to each market participant. Based on the transmission line utilization of all market participants under normal conditions, this paper provides a helpful comparative framework for allocating the reliability cost in the context of a competitive electric market by taking care of the forced outage rate as well as the line sensitivity factors after a loss of one single circuit or (n − 1) criteria and then calculating the reliability contributions of all generators to the transmission lines. Finally, the case study exhibits the applications of the proposed methodology on a simple 6-bus test system.
2. Background of the work Recent research has shown that the maximum transmission utilization over a period of time is, in theory, limited by the amount of spare transmission capacity or transmission reserves required for the reliability of the overall transmission network. These reserves must be secured to maintain the system reliability during circuit outages for contingencies such as the sudden loss of generation or transmission facilities. These reserves also allow sales to and purchases from other systems to change with times of the day and seasons of the year, and provide capacity for parallel-path or loop flows throughout the system. In this regard, the objective evaluation of reliability contributions in the transmission system and the reasonable allocation of transmission reliability costs are of growing importance. Accordingly, the transmission tariffs actually being enforced should apparently reveal fair and
transparent properties, representing a crucial element for the installation of the market structures. There was absolutely no consensus as to the transmission tariffs in terms of the reliability cost. In practice, each country or each restructuring model has chosen a method that is governed by the particular characteristics of its network.Yu and David [3] give convincing answers to the transmission pricing issue pertaining to the operating and embedded costs. Capacity use as well as reliability benefit is taken into account in the disbursement of charges for investment recovery, where the reliability benefit for a particular transaction is calculated as the increment of the total probability of system failure, with the line out of service, compared to when the line is in service. Some insights into the marginal pricing approach to the recovery of operating costs are also elaborated.Silva et al. pay special attention to the transmission cost allocation method associated with not only the probability impact of transaction on the electrical system but also the power flow values with and without wheeling transaction [4]. Their intention, then, is to carry implications that an important part of transmission assets is indispensable to system reliability as far as the power systems operations under both normal conditions and contingencies are specifically concerned. However, this suggestion has a drawback in the sense that it is heavily dependent on the base-case flow and the implementation of the cost allocation rule is not really easy. In [5], with probabilistic criteria and appropriate software available, the planner can assess system-wide bulk power transmission reliability, impact of varying reinforcement expenditure levels, and reliability outcomes for many alternatives. Once the reliability merits of each reinforcement have been analyzed, ranking the merits among all alternatives is drastically performed with the so-called expected unserved energy (EUE), which serves to convert the predicted reliability to a cost value for a specific location and time. This rule’s shortcoming is that it is not merely obscure but complex to assess the reliability criteria covering the residual uncertainties related to power system planning and operations. To put it plainly enough, Kirschen explores a method to allocate the usage of transmission system based on the traceable contributions of each generator and/or of each load to the maximum branch flows determined by security considerations [6,7], while Bialek presents a topological approach to determining the contributions of individual generators or loads to every line flow based on the calculation of topological distribution factors, thereby applying it to the transmission supplement charge allocation [8,9].
3. Description of the algorithm Contingency analysis techniques are commonly proposed to predict the effects of outages. And so, contingency analysis procedures model single failure events (i.e., one-line outage or one generator outage) or multiple equipment failure events (i.e., two transmission lines, one transmission line plus one
K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
generator, etc.), one after another in sequence until all credible outages have been studied [10]. For simplicity, this paper touches on a loss of one single line for making an approximate analysis of the effect of each outage. 3.1. Line outage impact factor (LOIF) The problem of treating thousands of possible outages becomes very difficult to work out if it is desired to get the corresponding results as quickly as possible. One of the easiest ways to overcome this limitation is to adopt the linear sensitivity factor such as the line outage impact factor under contingency situations. The line outage impact factor is designated Sl,k and has the following definition: k |fl o | − 1, |fl k | > |fl o |, Sl,k = |fl | (1) 0, |fl k | ≤ |fl o |, where l, k are the line index, flk is the flow on the line l after an outage on the line k and flo the original flow on the line l, implying that for the flow on the line l under failure state below that under normal state, flo , the line outage impact factor is zero because this case is unlikely to have any influence on the system reliability. On the contrary, it jumps to a positive value once the flow on the line l in the (n − 1) criteria applied to network reliability analysis is more than that transported under normal state. More specifically, this factor is very similar to the line outage distribution factor (LODF) as mentioned in [10], but there is the distinct difference between these two factors. The latter gives the fraction of flow picked up on the line l with respect to the pre-outage flow on a particular line k when that line k is lost, while the former measures the impact of the single line outage k available in a network on a specific line l. That is, this line outage impact factor represents changes in flow on the line l due to the outage of one of the remaining lines. One of the easiest ways to gain speed of solution in a line outage procedure is to use DC load flow models because the approximate DC load flow can provide sufficient accuracy with respect to the megawatt flows and the voltage magnitudes may not be of great concern for many systems. 3.2. Forced outage rate (FOR) As analyzed by Billinton and Allan [11], the forced outage rate may be simply defined as the mean number of outages per unit exposure time per component where a forced outage unpredictably results from emergency conditions linked with the improper operation of equipment or human error. This paper illustrates the application of the basic index, as it were, the expected number of hours when one single line is out of service over an operating life to make a quantitative reliability assessment of transmission facilities.
33
3.3. Relative reliability evaluation factor (RREF) With the line outage impact factor and forced outage rate obtained from the foregoing sections, the relative reliability evaluation factor for the network reliability is defined by Wl,k = Sl,k Fk ,
(2)
where Wl,k is the relative reliability evaluation factor of the line l with the line k out, Sl,k the line outage impact factor of the line l with the line k out, and Fk the forced outage rate of the line k. Here, a simple way to address the relative impact of the failure in the line k on the line l in the proposed method while retaining its advantage is to divide Wl,k in Eq. (2) by the sum of all relative reliability evaluation factors of that line l involved in all the other lines: Wl,k NWl,k = n , (3) j=1,j=l Wl,j where n is the total number of transmission lines, and NWl,k the normalized relative reliability evaluation factor of the line l with the line k out. 3.4. Reliability contribution Based on the normalized relative reliability evaluation factor calculated by Eq. (3), the reliability contributions of each generator to a particular line may be expressed mathematically as RCGi,l =
n k=1,k=l
(NWl,k UC0Gi,k ),
(4)
where Gi is the generator index, RCGi,l the reliability contribution of the generator Gi to the line l and UC0Gi,k the usage contribution of the generator Gi to the flow on the line k under normal state. It is straightforward from the above that the reliability contribution of the generator Gi to the line l is affected by the impacts of the failure in each line on the specific line l concerned with the forced outage rates of each transmission facility as well as each entity’s capacity use of those failed transmission lines under normal conditions. Consequently, the reliability cost of transmission lines can be allocated to the market participants in proportion to the reliability contributions of each generator to the lines as indicated by Eq. (4). Given the reliability cost of each line, the reliability cost charged to a generator is as follows: R CG = RCGi,l TCR l , i,l
(5)
R is the reliability cost of the line l charged to the where CG i,l
generator Gi and TCR l the total reliability cost of the line l. Note that the assessment of transmission reliability costs, as such, is merely beyond the scope of this paper. How-
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K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36 Table 2 Usage contributions of each generator to the lines under normal state (UC0Gi,l ) Line no.
Generator A
Generator B
Generator C
Total
1 2 3 4 5 6 7 8 9
0.5276 0.5276 0.0000 0.0000 0.5276 0.0000 0.0000 0.0000 0.0000
0.1886 0.1886 0.7164 1.0000 0.1886 0.0000 1.0000 0.0000 0.0000
0.2838 0.2838 0.2836 0.0000 0.2838 1.0000 0.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Table 3 Forced outage rate of the line k (Fk ) Fig. 1. A 6-bus test system for the case study.
ever, many engineers and researchers independently continue to investigate alternative pricing schemes in order to better determine the reliability cost of transmission system [12,13]. Likewise, our methodology is applicable to the reliability cost of transmission line charged to loads by revisiting Eqs. (4) and (5).
4. Illustrative example Fig. 1 shows a 6-bus test system with its line parameters given in Table 1. This system is selected to promote the understanding and performance of the proposed method. Table 2 shows the usage contributions of three generators in this system to the nine lines under normal state by the method adapted from Kirschen et al. [7]. This topological trace method organizes the buses and branches of the network into homogeneous groups according to several concepts which consist of domains, commons, and links with directed flows between commons. Starting from the active branch flows, the method finds recursively how much each generator contributes to line flows on a proportionality assumption that the proportion of inflow traced to any generator is equal to the proportion of outflow traced to the same generator for a given common.
Table 1 Line data of a 6-bus test system Line From no. no. 1 2 3 4 5 6 7 8 9
1 1 1 2 2 2 3 4 5
bus To bus no. 2 4 5 3 4 6 5 6 6
Resistance (pu)
Reactance (pu)
Shunt capacitance (pu)
0.0012 0.0150 0.0230 0.0170 0.0230 0.0020 0.0010 0.0120 0.0150
0.0150 0.0920 0.1380 0.1660 0.1380 0.0240 0.0120 0.0150 0.0920
0.0000 0.1810 0.2710 0.3260 0.2710 0.0000 0.0000 0.0000 0.1810
Line no.
Average time of occurrence of a failure event (h/year)
1 2 3 4 5 6 7 8 9
12 24 15 48 20 18 36 18 30
In Table 3, the average time of occurrence of the outage, briefly referred to as the forced outage rate, is summarized, which can vary so radically by the selection of transmission structures. 4.1. Step 1: calculation of line outage impact factor In all simulations where voltage magnitudes are the critical factor in assessing contingencies, a full AC load flow for a given load under normal conditions is executed. Then, the load flow programs are repeated for the outage of each line in turn and used to test all lines in the network for reliability for the outage of a particular line. Ultimately, the line outage impact factors are calculated by Eq. (1) and displayed in Table 4. 4.2. Step 2: computation of normalized relative reliability evaluation factor As seen in Table 5, the normalized relative reliability evaluation factors for each line are found by Eqs. (2) and (3) together with the data in Table 3 and the results in Table 4. 4.3. Step 3: derivation of reliability contributions of each generator The reliability contributions of each generator to a branch required to apportion the transmission reliability cost to each generator are depicted in Table 6, by making use of the utilization indices of all generators under normal state in Table 2 and the normalized relative reliability evaluation factors in
K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
35
Table 4 Line outage impact factor (Sl,k ) Line no.
Failed line 1
1 2 3 4 5 6 7 8 9
3.3875 0.8859 0.3100 0.6030 0.4580 0.0000 0.2131 0.0000
2
3
4
5
6
7
8
9
0.1793
0.0000 0.0000
0.1377 0.0122 1.0777
0.0000 0.8661 0.0000 0.0000
0.0803 0.0000 0.5954 0.1698 0.0000
0.0000 0.0376 0.9280 2.6077 1.4227 0.0000
0.0851 0.3260 1.1381 0.3102 1.3497 0.6415 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.6447 0.1894 0.5484
0.0000 0.0005 0.6176 0.0000 0.0000 0.0450 0.0000
0.0922 0.0000 0.1273 0.0000 0.1102 0.0000
0.0000 0.4265 0.3815 0.3529 0.0000
0.0000 0.0367 0.2653 0.0000
0.0000 0.2914 0.3367
0.0000 1.6914
0.6307
Table 5 Normalized relative reliability evaluation factor (NWl,k ) Line no.
Failed line 1
1 2 3 4 5 6 7 8 9
0.6180 0.0837 0.0346 0.0742 0.0935 0.0000 0.0519 0.0000
2
3
4
5
6
7
8
9
0.3098
0.0000 0.0000
0.4758 0.0089 0.4074
0.0000 0.2633 0.0000 0.0000
0.1041 0.0000 0.0844 0.0284 0.0000
0.0000 0.0206 0.2631 0.8722 0.5249 0.0000
0.1103 0.0892 0.1614 0.0519 0.2490 0.1965 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.3291 0.2298 0.3342
0.0000 0.0001 0.1519 0.0000 0.0000 0.0219 0.0000
0.0128 0.0000 0.0325 0.0000 0.0336 0.0000
0.0000 0.3484 0.7405 0.3441 0.0000
Table 5. Plus, it can be acknowledged that the sum of usage and reliability contributions of all generators to each line is equivalent to unity, as observed in Tables 2 and 6. These properties are derived in Appendix A. As expected, we can see that the results of our reliability cost allocation are different from those of other conventional methods depending on only the usage contributions, which can be easily verified by a sharp contrast between Tables 2 and 6. For instance, generators A and C do not need to pay the transmission reliability cost of line 4 provided that the cost allocation rule is subject to the capacity use only. On the contrary, generators A and C are believed to take the responsibility for the reliability cost of line 4 to some extent that the reliability contributions are estiTable 6 Reliability contributions of each generator to the lines under failure state (RCGi,l ) Line no.
Generator A
Generator B
Generator C
Total
1 2 3 4 5 6 7 8 9
0.1635 0.4650 0.0442 0.0183 0.1193 0.0493 0.0157 0.0958 0.0000
0.5343 0.1957 0.6863 0.8879 0.5676 0.3893 0.7461 0.4024 0.7776
0.3022 0.3393 0.2695 0.0938 0.3131 0.5614 0.2382 0.5018 0.2224
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.0000 0.0297 0.1078 0.0000
0.0000 0.1065 0.0774
0.0000 0.7776
0.1450
mated from the proposed framework, allowing for the line outages and their probability at the same time. Furthermore, the proposed technique will be extended to the sufficiently large networks to demonstrate a wide variety of challenges which can be encountered without additional postulates or procedures.
5. Conclusion This paper has examined an alternative mechanism to allocate the transmission reliability cost to market participants in a more equitable manner. In fact, we have attempted to fully quantify the relative influences of each outage in network on a particular transmission line by taking advantage of changes in flow on that line for all the outages analyzed and the forced outage rates of the failed lines as well. Finally, the reliability cost allocation is achieved by the reliability contributions of individual entities to the corresponding transmission line which consist of the normalized relative reliability evaluation factors and their “extent of use” of the line under normal conditions.
Acknowledgements Research for this article was supported by a grant from the Electrical Engineering and Science Research Institute
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K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
(EESRI-02-Jeon-01), with funds provided by the Ministry of Commerce, Industry and Energy (MOCIE), Korea.
all generators Gi
The following property that usage contributions satisfy may be stated from Table 2: ∀l ∈ L, UC0Gi,l = 1, (A.1) all generators Gi
where UC0Gi,l is the usage contribution of the generator Gi to the branch l under steady state and L the set of transmission lines. It can be intuitively construed that the sum of the utilization of an arbitrary branch by all the generators is equivalent to unity. In a similar manner, the general relationship of a reliability contribution may be listed and derived from its definition of Eq. (4) and the properties of Eqs. (3) and (A.1): ∀l ∈ L, RCGi,l = 1, (A.2) all generators Gi
Let us assume that n stands for the total number of transmission lines. Upon substitution of Eq. (4) into Eq. (A.2), we have RCGi,l all generators Gi
all generators Gi
= NWl,1 ×
n
k=1,k=l
(NWl,k UC0Gi,k )
all generators Gi
NWl,l−1 ×
UC0Gi,1 + · · · +
all generators Gi
NWl,l+1 ×
all generators Gi
NWl,n ×
k=1,k=l
(NWl,k UC0Gi,k )
= NWl,1 + · · · + NWl,l−1 + NWl,l+1 + · · · + NWl,n
Appendix A
=
n
all generators Gi
UC0Gi,l−1 + UC0Gi,l+1 + · · · +
UC0Gi,n .
(A.3)
With Eqs. (3) and (A.1), it is readily shown that Eq. (A.3) becomes
=
n
NWl,j = 1,
l = 1, 2, . . . , n.
(A.4)
j=1,j=l
Indeed, we are evidently able to check out this characteristic in Table 6.
References [1] M. Shahidehpour, H. Yamin, Z. Li, Market Operations in Electric Power Systems, 1st ed., Wiley, New York, 2002. [2] M. Einhorn, R. Siddiqi, Electricity Transmission Pricing and Technology, 1st ed., Kluwer Academic Publishers, Massachusetts, 1996. [3] C.W. Yu, A.K. David, Pricing transmission services in the context of industry deregulation, IEEE Trans. Power Syst. 12 (1) (1997) 503–510. [4] E.L. Silva, S.E.C. Mesa, M. Morozowski, Transmission access pricing to wheeling transactions: a reliability based approach, IEEE Trans. Power Syst. 13 (4) (1998) 1481–1486. [5] R. Billinton, L. Salvaderi, J.D. McCalley, H. Chao, Th. Seitz, R.N. Allan, J. Odom, C. Fallon, Reliability issues in today’s electric power utility environment, IEEE Trans. Power Syst. 12 (4) (1997) 1708–1714. [6] G. Strbac, D. Kirschen, S. Ahmed, Allocating transmission system usage on the basis of traceable contributions of generators and loads to flows, IEEE Trans. Power Syst. 13 (2) (1998) 527–534. [7] D. Kirschen, R.N. Allan, G. Strbac, Contributions of individual generators to loads and flows, IEEE Trans. Power Syst. 12 (1) (1997) 52–60. [8] J. Bialek, Topological generation and load distribution factors for supplement charge allocation in transmission open access, IEEE Trans. Power Syst. 12 (3) (1997) 1185–1193. [9] J. Bialek, Allocation of transmission supplementary charge to real and reactive loads, IEEE Trans. Power Syst. 13 (3) (1998) 749– 754. [10] A.J. Wood, B.F. Wollenberg, Power Generation, Operation Control, 2nd ed., Wiley, New York, 1996. [11] R. Billinton, R.N. Allan, Reliability Evaluation of Power Systems, 2nd ed., Plenum Press, New York, 1996. [12] D. Hur, J.K. Park, W.G. Lee, B.H. Kim, Y.H. Chun, An alternative method for the reliability differentiated transmission pricing, Electr. Power Syst. Res. 68 (1) (2004) 11–17. [13] D. Hur, C.I. Yoo, B.H. Kim, J.K. Park, Transmission embedded cost allocation methodology with consideration of system reliability, IEE Proc.-Gener. Transm. Distrib., in press.
Transmission reliability cost allocation method based on market participants’ reliability contribution factors Koo-Hyung Chunga , Balho H. Kima,1 , Don Hurb,∗ , Jong-Keun Parkb b
a School of Electronic and Electrical Engineering, Hong-Ik University, Sangsu-dong 72-1, Mapo-gu, Seoul 121-791, Republic of Korea School of Electrical Engineering, Seoul National University, 301 Dong 615 Ho, Shillim 9-dong, Gwanak-gu, Seoul 151-744, Republic of Korea
Received 19 December 2003; received in revised form 30 May 2004; accepted 31 May 2004 Available online 26 August 2004
Abstract Due to the complex and integrated nature of power systems, failures in any part of the system can cause interruptions which range from inconveniencing a small number of local residents to a widespread catastrophic disruption of supply. For this reason, the transmission reliability margin must be provided for the system to be operated at all times in such a way that the system will not be left in a dangerous condition even though unpredictable events occur. In this paper, Kirschen’s tracing method is employed to find the usage contributions of individual generators to the line flows under normal conditions. Apparently, it seems plausible to compute the reliability contributions of all market participants based on the probabilistic approach which takes notice of the forced outage rate for each transmission line as well as the line outage impact factor and then to allocate the transmission reliability cost among all the system users in proportion to their “extent of use” of reliability reserves in transmission facilities. © 2004 Elsevier B.V. All rights reserved. Keywords: Forced outage rate; Reliability contribution factor; Transmission reliability cost allocation
1. Introduction The electricity transmission system is an extensive, interconnected network of high-voltage power lines that pass electricity from generators to customers. Such a transmission system must be flexible enough, every second of every day, to accommodate the growing demand for reliable and affordable electricity. Nevertheless, rapid growth in electricity demand and new generation, lack of investment in new transmission facilities, and the incomplete transition to fully efficient and comAbbreviations: EUE, expected unserved energy; LOIF, line outage impact factor; LODF, line outage distribution factor; FOR, forced outage rate; RREF, relative reliability evaluation factor; NRREF, normalized relative reliability evaluation factor ∗ Corresponding author. Tel.: +82 2 880 7258; fax: +82 2 878 1452. E-mail addresses: [email protected] (B.H. Kim), [email protected] (D. Hur). 1 Tel.: +82 2 320 1462; fax: +82 2 320 1110. 0378-7796/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2004.05.003
petitive wholesale markets have allowed transmission bottlenecks to emerge. These bottlenecks increase electricity costs to consumers and increase the risks of blackouts. Today, power failures, close calls, and near misses are much more common than in the past. The transmission systems of tomorrow must be operated in ways that maintain adequate safety margins for reliability and allow customers to follow strict tariffs for reliability with appropriate penalties for noncompliance. Despite the fact that transmission charges account for a small percent of operating expenses in utilities, we cannot afford to allow the relatively small transmission costs to prevent customers from enjoying the reliable and affordable electricity service that the properly managed competitive forces will deliver to our nation. Therefore, transmission pricing should be a reasonable economic indicator used by the market to make decisions on resource allocation, system expansion, and reinforcement [1]. The first step toward increasing the role of market forces in managing transmission system operations
32
K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
efficiently and fairly is increasing the role of price signals to direct the actions of market participants toward outcomes that improve operations. Improving operations by relying on accurate price signals may, by itself, alleviate the need for some construction of new transmission facilities. Moreover, when new construction is needed, price signals will help market participants identify opportunities and assess options to address bottlenecks. Several aspects of transmission operations, including congestion and losses, could be effectively addressed by pricing based on the principle that if market participants see the true costs of transmission services reflected in prices, they will use or procure these services efficiently. Thus, reliance on uplift charges, in which costs are recovered from all transmission users on an equivalent basis, should be minimized. In the past few decades, many researchers have devoted themselves to achieving an efficient transmission pricing scheme that could fit all market structures in different locations so that participants in markets can see and respond to the true costs of using the transmission system. Generally, the transmission charge is grouped into the following parts: transmission line usage charge, system reliability charge, access charge, and so on [2]. Any transmission tariffs should be able to reflect these respective cost components without any distortion. Particularly, this paper suggests a probabilistic approach to allocating the reliability cost of the transmission system to each market participant. Based on the transmission line utilization of all market participants under normal conditions, this paper provides a helpful comparative framework for allocating the reliability cost in the context of a competitive electric market by taking care of the forced outage rate as well as the line sensitivity factors after a loss of one single circuit or (n − 1) criteria and then calculating the reliability contributions of all generators to the transmission lines. Finally, the case study exhibits the applications of the proposed methodology on a simple 6-bus test system.
2. Background of the work Recent research has shown that the maximum transmission utilization over a period of time is, in theory, limited by the amount of spare transmission capacity or transmission reserves required for the reliability of the overall transmission network. These reserves must be secured to maintain the system reliability during circuit outages for contingencies such as the sudden loss of generation or transmission facilities. These reserves also allow sales to and purchases from other systems to change with times of the day and seasons of the year, and provide capacity for parallel-path or loop flows throughout the system. In this regard, the objective evaluation of reliability contributions in the transmission system and the reasonable allocation of transmission reliability costs are of growing importance. Accordingly, the transmission tariffs actually being enforced should apparently reveal fair and
transparent properties, representing a crucial element for the installation of the market structures. There was absolutely no consensus as to the transmission tariffs in terms of the reliability cost. In practice, each country or each restructuring model has chosen a method that is governed by the particular characteristics of its network.Yu and David [3] give convincing answers to the transmission pricing issue pertaining to the operating and embedded costs. Capacity use as well as reliability benefit is taken into account in the disbursement of charges for investment recovery, where the reliability benefit for a particular transaction is calculated as the increment of the total probability of system failure, with the line out of service, compared to when the line is in service. Some insights into the marginal pricing approach to the recovery of operating costs are also elaborated.Silva et al. pay special attention to the transmission cost allocation method associated with not only the probability impact of transaction on the electrical system but also the power flow values with and without wheeling transaction [4]. Their intention, then, is to carry implications that an important part of transmission assets is indispensable to system reliability as far as the power systems operations under both normal conditions and contingencies are specifically concerned. However, this suggestion has a drawback in the sense that it is heavily dependent on the base-case flow and the implementation of the cost allocation rule is not really easy. In [5], with probabilistic criteria and appropriate software available, the planner can assess system-wide bulk power transmission reliability, impact of varying reinforcement expenditure levels, and reliability outcomes for many alternatives. Once the reliability merits of each reinforcement have been analyzed, ranking the merits among all alternatives is drastically performed with the so-called expected unserved energy (EUE), which serves to convert the predicted reliability to a cost value for a specific location and time. This rule’s shortcoming is that it is not merely obscure but complex to assess the reliability criteria covering the residual uncertainties related to power system planning and operations. To put it plainly enough, Kirschen explores a method to allocate the usage of transmission system based on the traceable contributions of each generator and/or of each load to the maximum branch flows determined by security considerations [6,7], while Bialek presents a topological approach to determining the contributions of individual generators or loads to every line flow based on the calculation of topological distribution factors, thereby applying it to the transmission supplement charge allocation [8,9].
3. Description of the algorithm Contingency analysis techniques are commonly proposed to predict the effects of outages. And so, contingency analysis procedures model single failure events (i.e., one-line outage or one generator outage) or multiple equipment failure events (i.e., two transmission lines, one transmission line plus one
K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
generator, etc.), one after another in sequence until all credible outages have been studied [10]. For simplicity, this paper touches on a loss of one single line for making an approximate analysis of the effect of each outage. 3.1. Line outage impact factor (LOIF) The problem of treating thousands of possible outages becomes very difficult to work out if it is desired to get the corresponding results as quickly as possible. One of the easiest ways to overcome this limitation is to adopt the linear sensitivity factor such as the line outage impact factor under contingency situations. The line outage impact factor is designated Sl,k and has the following definition: k |fl o | − 1, |fl k | > |fl o |, Sl,k = |fl | (1) 0, |fl k | ≤ |fl o |, where l, k are the line index, flk is the flow on the line l after an outage on the line k and flo the original flow on the line l, implying that for the flow on the line l under failure state below that under normal state, flo , the line outage impact factor is zero because this case is unlikely to have any influence on the system reliability. On the contrary, it jumps to a positive value once the flow on the line l in the (n − 1) criteria applied to network reliability analysis is more than that transported under normal state. More specifically, this factor is very similar to the line outage distribution factor (LODF) as mentioned in [10], but there is the distinct difference between these two factors. The latter gives the fraction of flow picked up on the line l with respect to the pre-outage flow on a particular line k when that line k is lost, while the former measures the impact of the single line outage k available in a network on a specific line l. That is, this line outage impact factor represents changes in flow on the line l due to the outage of one of the remaining lines. One of the easiest ways to gain speed of solution in a line outage procedure is to use DC load flow models because the approximate DC load flow can provide sufficient accuracy with respect to the megawatt flows and the voltage magnitudes may not be of great concern for many systems. 3.2. Forced outage rate (FOR) As analyzed by Billinton and Allan [11], the forced outage rate may be simply defined as the mean number of outages per unit exposure time per component where a forced outage unpredictably results from emergency conditions linked with the improper operation of equipment or human error. This paper illustrates the application of the basic index, as it were, the expected number of hours when one single line is out of service over an operating life to make a quantitative reliability assessment of transmission facilities.
33
3.3. Relative reliability evaluation factor (RREF) With the line outage impact factor and forced outage rate obtained from the foregoing sections, the relative reliability evaluation factor for the network reliability is defined by Wl,k = Sl,k Fk ,
(2)
where Wl,k is the relative reliability evaluation factor of the line l with the line k out, Sl,k the line outage impact factor of the line l with the line k out, and Fk the forced outage rate of the line k. Here, a simple way to address the relative impact of the failure in the line k on the line l in the proposed method while retaining its advantage is to divide Wl,k in Eq. (2) by the sum of all relative reliability evaluation factors of that line l involved in all the other lines: Wl,k NWl,k = n , (3) j=1,j=l Wl,j where n is the total number of transmission lines, and NWl,k the normalized relative reliability evaluation factor of the line l with the line k out. 3.4. Reliability contribution Based on the normalized relative reliability evaluation factor calculated by Eq. (3), the reliability contributions of each generator to a particular line may be expressed mathematically as RCGi,l =
n k=1,k=l
(NWl,k UC0Gi,k ),
(4)
where Gi is the generator index, RCGi,l the reliability contribution of the generator Gi to the line l and UC0Gi,k the usage contribution of the generator Gi to the flow on the line k under normal state. It is straightforward from the above that the reliability contribution of the generator Gi to the line l is affected by the impacts of the failure in each line on the specific line l concerned with the forced outage rates of each transmission facility as well as each entity’s capacity use of those failed transmission lines under normal conditions. Consequently, the reliability cost of transmission lines can be allocated to the market participants in proportion to the reliability contributions of each generator to the lines as indicated by Eq. (4). Given the reliability cost of each line, the reliability cost charged to a generator is as follows: R CG = RCGi,l TCR l , i,l
(5)
R is the reliability cost of the line l charged to the where CG i,l
generator Gi and TCR l the total reliability cost of the line l. Note that the assessment of transmission reliability costs, as such, is merely beyond the scope of this paper. How-
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K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36 Table 2 Usage contributions of each generator to the lines under normal state (UC0Gi,l ) Line no.
Generator A
Generator B
Generator C
Total
1 2 3 4 5 6 7 8 9
0.5276 0.5276 0.0000 0.0000 0.5276 0.0000 0.0000 0.0000 0.0000
0.1886 0.1886 0.7164 1.0000 0.1886 0.0000 1.0000 0.0000 0.0000
0.2838 0.2838 0.2836 0.0000 0.2838 1.0000 0.0000 1.0000 1.0000
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
Table 3 Forced outage rate of the line k (Fk ) Fig. 1. A 6-bus test system for the case study.
ever, many engineers and researchers independently continue to investigate alternative pricing schemes in order to better determine the reliability cost of transmission system [12,13]. Likewise, our methodology is applicable to the reliability cost of transmission line charged to loads by revisiting Eqs. (4) and (5).
4. Illustrative example Fig. 1 shows a 6-bus test system with its line parameters given in Table 1. This system is selected to promote the understanding and performance of the proposed method. Table 2 shows the usage contributions of three generators in this system to the nine lines under normal state by the method adapted from Kirschen et al. [7]. This topological trace method organizes the buses and branches of the network into homogeneous groups according to several concepts which consist of domains, commons, and links with directed flows between commons. Starting from the active branch flows, the method finds recursively how much each generator contributes to line flows on a proportionality assumption that the proportion of inflow traced to any generator is equal to the proportion of outflow traced to the same generator for a given common.
Table 1 Line data of a 6-bus test system Line From no. no. 1 2 3 4 5 6 7 8 9
1 1 1 2 2 2 3 4 5
bus To bus no. 2 4 5 3 4 6 5 6 6
Resistance (pu)
Reactance (pu)
Shunt capacitance (pu)
0.0012 0.0150 0.0230 0.0170 0.0230 0.0020 0.0010 0.0120 0.0150
0.0150 0.0920 0.1380 0.1660 0.1380 0.0240 0.0120 0.0150 0.0920
0.0000 0.1810 0.2710 0.3260 0.2710 0.0000 0.0000 0.0000 0.1810
Line no.
Average time of occurrence of a failure event (h/year)
1 2 3 4 5 6 7 8 9
12 24 15 48 20 18 36 18 30
In Table 3, the average time of occurrence of the outage, briefly referred to as the forced outage rate, is summarized, which can vary so radically by the selection of transmission structures. 4.1. Step 1: calculation of line outage impact factor In all simulations where voltage magnitudes are the critical factor in assessing contingencies, a full AC load flow for a given load under normal conditions is executed. Then, the load flow programs are repeated for the outage of each line in turn and used to test all lines in the network for reliability for the outage of a particular line. Ultimately, the line outage impact factors are calculated by Eq. (1) and displayed in Table 4. 4.2. Step 2: computation of normalized relative reliability evaluation factor As seen in Table 5, the normalized relative reliability evaluation factors for each line are found by Eqs. (2) and (3) together with the data in Table 3 and the results in Table 4. 4.3. Step 3: derivation of reliability contributions of each generator The reliability contributions of each generator to a branch required to apportion the transmission reliability cost to each generator are depicted in Table 6, by making use of the utilization indices of all generators under normal state in Table 2 and the normalized relative reliability evaluation factors in
K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
35
Table 4 Line outage impact factor (Sl,k ) Line no.
Failed line 1
1 2 3 4 5 6 7 8 9
3.3875 0.8859 0.3100 0.6030 0.4580 0.0000 0.2131 0.0000
2
3
4
5
6
7
8
9
0.1793
0.0000 0.0000
0.1377 0.0122 1.0777
0.0000 0.8661 0.0000 0.0000
0.0803 0.0000 0.5954 0.1698 0.0000
0.0000 0.0376 0.9280 2.6077 1.4227 0.0000
0.0851 0.3260 1.1381 0.3102 1.3497 0.6415 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.6447 0.1894 0.5484
0.0000 0.0005 0.6176 0.0000 0.0000 0.0450 0.0000
0.0922 0.0000 0.1273 0.0000 0.1102 0.0000
0.0000 0.4265 0.3815 0.3529 0.0000
0.0000 0.0367 0.2653 0.0000
0.0000 0.2914 0.3367
0.0000 1.6914
0.6307
Table 5 Normalized relative reliability evaluation factor (NWl,k ) Line no.
Failed line 1
1 2 3 4 5 6 7 8 9
0.6180 0.0837 0.0346 0.0742 0.0935 0.0000 0.0519 0.0000
2
3
4
5
6
7
8
9
0.3098
0.0000 0.0000
0.4758 0.0089 0.4074
0.0000 0.2633 0.0000 0.0000
0.1041 0.0000 0.0844 0.0284 0.0000
0.0000 0.0206 0.2631 0.8722 0.5249 0.0000
0.1103 0.0892 0.1614 0.0519 0.2490 0.1965 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000 0.3291 0.2298 0.3342
0.0000 0.0001 0.1519 0.0000 0.0000 0.0219 0.0000
0.0128 0.0000 0.0325 0.0000 0.0336 0.0000
0.0000 0.3484 0.7405 0.3441 0.0000
Table 5. Plus, it can be acknowledged that the sum of usage and reliability contributions of all generators to each line is equivalent to unity, as observed in Tables 2 and 6. These properties are derived in Appendix A. As expected, we can see that the results of our reliability cost allocation are different from those of other conventional methods depending on only the usage contributions, which can be easily verified by a sharp contrast between Tables 2 and 6. For instance, generators A and C do not need to pay the transmission reliability cost of line 4 provided that the cost allocation rule is subject to the capacity use only. On the contrary, generators A and C are believed to take the responsibility for the reliability cost of line 4 to some extent that the reliability contributions are estiTable 6 Reliability contributions of each generator to the lines under failure state (RCGi,l ) Line no.
Generator A
Generator B
Generator C
Total
1 2 3 4 5 6 7 8 9
0.1635 0.4650 0.0442 0.0183 0.1193 0.0493 0.0157 0.0958 0.0000
0.5343 0.1957 0.6863 0.8879 0.5676 0.3893 0.7461 0.4024 0.7776
0.3022 0.3393 0.2695 0.0938 0.3131 0.5614 0.2382 0.5018 0.2224
1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
0.0000 0.0297 0.1078 0.0000
0.0000 0.1065 0.0774
0.0000 0.7776
0.1450
mated from the proposed framework, allowing for the line outages and their probability at the same time. Furthermore, the proposed technique will be extended to the sufficiently large networks to demonstrate a wide variety of challenges which can be encountered without additional postulates or procedures.
5. Conclusion This paper has examined an alternative mechanism to allocate the transmission reliability cost to market participants in a more equitable manner. In fact, we have attempted to fully quantify the relative influences of each outage in network on a particular transmission line by taking advantage of changes in flow on that line for all the outages analyzed and the forced outage rates of the failed lines as well. Finally, the reliability cost allocation is achieved by the reliability contributions of individual entities to the corresponding transmission line which consist of the normalized relative reliability evaluation factors and their “extent of use” of the line under normal conditions.
Acknowledgements Research for this article was supported by a grant from the Electrical Engineering and Science Research Institute
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K.-H. Chung et al. / Electric Power Systems Research 73 (2005) 31–36
(EESRI-02-Jeon-01), with funds provided by the Ministry of Commerce, Industry and Energy (MOCIE), Korea.
all generators Gi
The following property that usage contributions satisfy may be stated from Table 2: ∀l ∈ L, UC0Gi,l = 1, (A.1) all generators Gi
where UC0Gi,l is the usage contribution of the generator Gi to the branch l under steady state and L the set of transmission lines. It can be intuitively construed that the sum of the utilization of an arbitrary branch by all the generators is equivalent to unity. In a similar manner, the general relationship of a reliability contribution may be listed and derived from its definition of Eq. (4) and the properties of Eqs. (3) and (A.1): ∀l ∈ L, RCGi,l = 1, (A.2) all generators Gi
Let us assume that n stands for the total number of transmission lines. Upon substitution of Eq. (4) into Eq. (A.2), we have RCGi,l all generators Gi
all generators Gi
= NWl,1 ×
n
k=1,k=l
(NWl,k UC0Gi,k )
all generators Gi
NWl,l−1 ×
UC0Gi,1 + · · · +
all generators Gi
NWl,l+1 ×
all generators Gi
NWl,n ×
k=1,k=l
(NWl,k UC0Gi,k )
= NWl,1 + · · · + NWl,l−1 + NWl,l+1 + · · · + NWl,n
Appendix A
=
n
all generators Gi
UC0Gi,l−1 + UC0Gi,l+1 + · · · +
UC0Gi,n .
(A.3)
With Eqs. (3) and (A.1), it is readily shown that Eq. (A.3) becomes
=
n
NWl,j = 1,
l = 1, 2, . . . , n.
(A.4)
j=1,j=l
Indeed, we are evidently able to check out this characteristic in Table 6.
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