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Paper accepted for presentation at 2003 IEEE Bologna Power Tech Conference, June 23th-26th, Bologna, Italy

Power system planning under uncertainty conditions. Criteria for transmission network flexibility evaluation P. Bresesti, A. Capasso, Senior Member IEEE M.C. Falvo, Student Member IEEE, S. Lauria Member IEEE

Abstract - In a free-market scenario, power system planning has to deal with a significant degree of uncertainty about time and location of generating assets expansion. A methodology for the evaluation of the attitude of the transmission system to keep up a desired standard of reliability under such uncertainty (that is, flexibility) is presented. The method, relying on the Monte Carlo simulation approach, is applied to check the effectiveness of a flexibility index, based on structural as well as operational network parameters. The results of tests carried out on simple networks and on IEEE RTS are reported showing the encouraging agreement between the probabilistic simulations and the proposed index. Keywords – Power transmission planning, reliability, Monte Carlo methods, open-access, uncertainty, flexibility I. INTRODUCTION Bulk electric power systems are currently experiencing significant changes, in both the operational and economic spheres, due to the liberalization of the electric energy market. In an open-access scenario, in fact, vertically integrated utilities are superseded, after 'unbundling', by independent new entities, managing generation and transmission separately. As a consequence, the constraints imposed on the planner in order to ensure the required levels of quality and continuity of supply are also changing. Planners are most notably affected by the much-increased uncertainty about siting, sizing and commissioning of new power plants, i.e. about growth of generation as a whole. Today's generation scenarios, in the planner's view, change quite rapidly due the short commissioning times of com___________________________________ This work was supported by the Italian Ministry of Industry, Commerce and Handicraft within the activity Ricerca di Sistema DM 17/04/2001, 28/02/2003. P. Bresesti, is with CESI - Centro Elettrotecnico Sperimentale Italiano, Milan, Italy (e-mail: [email protected]) A. Capasso, S. Lauria, M. C. Falvo are with University of Rome "La Sapienza", Electrical Engineering Dept., Rome, Italy. (e-mail: [email protected]).

0-7803-7967-5/03/$17.00 ©2003 IEEE

bined-cycle gas turbine plants and to the attitudes of independent power producers, who are autonomous by definition, and thus decide freely (within the technical regulatory framework) where, when and how much capacity they will build. Network planners are no longer in control of the expansion of generating capacity: they can make forecasts, with an attendant degree of uncertainty, about it, so that total installed capacity, composition and siting of the future power plants can be regarded, to a certain extent, as random variables. Even in this new framework, however, generation expansion must cope with the physical realities of power transmission: the location of new plants depends of the ability of the network of delivering the power they produce. On the other hand, the future development of the transmission infrastructures must satisfy two concurring requirements: of accommodating the new plants and keeping at least unchanged the current levels of supply quality and continuity. Given the uncertainties about generation expansion and operation, it becomes apparent that indexes and criteria are needed in order to evaluate the attitude of the transmission system to keep up a desired standard of reliability, at reasonable operation costs, when the generation scenarios change. The above "attitude" can be defined as "system flexibility" (with regard to the changes in generation). It is an important feature of system planning. Reliability is, of course, an essential and long-standing planning requirement; in today's open-access scenario, however, flexibility is also crucial to the system. The two planning requirements must be therefore combined together. Based on the above considerations, there has been in recent years much interest about criteria for the quantitative evaluation of network flexibility. The prevalent planning methodology is today probabilistic, usually based on the Monte Carlo simulation approach, which takes into account the uncertainties of operation: this approach is implicitly able to evaluate the flexibility of networks. Starting from probabilistic simulations, several criteria for the evaluation of flexibility have been proposed. Some are based on an indirect evaluation of flexibility through the use of traditional system reliability indexes (risk indexes), e.g. TRS (Transmission line Reliability Sensitivity) [2], or

"robustness", defined as the ability of the system to adapt to market-driven changes and quantified by many “attributes” which are a function of “plan” and “future” [3]. Other criteria are based on operation-related parameters deemed to give a straightforward flexibility evaluation, like ATC (Available Transfer Capability)[4-5] or GRU (Grid Utilization), a functional parameter indicating the degree of exploitation of available transmission resources [6]. In this context the Authors opt for a methodology based on conventional planning tools and results, yielding quantitative parameters useful for the flexibility evaluation of transmission networks with regard to changes in generation. The proposed methodology and indexes are meant to give, in the "open-access" context, a tool for the selection of planning alternatives: the flexibility indexes for uncertain scenarios. Tests have been performed first on simple networks and then on the IEEE Reliability Test System (IEEE-RTS).

of the generating units; all patterns have the same probability of implementation. Operational Hypotheses • Reliability level of the same order for the different planning scenarios, when considering the initial, 'base' generation pattern, with only the EENS quota due to transmission network overloads taken into account. The requisite for similar transmission-originated EENS values in the starting configurations is needed in order to separate the assessed "flexibility" of the test networks by their initial reliability. Networks with the same calculated reliability index (i.e. EENS) in the starting generation configuration can have different behaviours once the pattern of generation changes, namely different transmission deficits and thus different flexibility. C. Proposed index Based on the above hypotheses, the proposed index has the following form: Nb

II. PROPOSED METHODOLOGY A. Evaluation of the transmission deficit In order to check the performance of the proposed flexibility indexes, network flexibility has been indirectly assessed by means of the evaluation of reliability, in terms of EENS- Electric Energy Not Supplied [see II.D]. The probabilistic simulation program used to this purpose, MO.RE (MOntecarlo REliability), is based on the Monte Carlo approach described in detail in [7]. MO.RE can account separately for the shares of EENS due to lack of generation and to transmission deficit, respectively. The transmission-originated EENS is in turn subdivided among: • EENS caused by overloads in the transmission system; • EENS due to load shedding in an islanded portion of the network, following system separation. To evaluate flexibility, only the "overload" component of transmission-related EENS has been considered. Lack of capacity does not depend on system structure, being related only to mismatch between generation and load. Moreover, EENS due to islanded operation, though originated by shortcomings of the transmission system, is generally not related to network flexibility with respect to changes of generation (as can be easily seen by considering a load supplied by a single radial line, when load is shed due to local lack of generating capacity). B. Simulation hypotheses In order to reduce problem complexity, the simulations aimed at checking the effectiveness of the proposed index were based on the following simplifying assumptions: Structural Hypotheses • Comparison between test networks made of the same components, but topologically different (m transmission lines, out of n, differing for each network). • For each test network, the same "base" generation scenario. • For each test network, k different generation 'patterns' representing uncertainty, with the same overall generating capacity but with different spatial locations

C ij (I m arg ) =


ij m arg

i =1, j =1 Nb


ij Ctot

i≠ j ij m arg

i =1, j =1

where: Nb: number of nodes; ij: branch between nodes "i" and "j"; Iijmarg, current margin (difference between the limit carrying capability and the average current) on branch ij, calculated in the starting generation configuration; Cijtot, defined as "total distribution factor" (see below). The index is the average of the total distribution factors of the branches, weighted with the current margins of the branches. The total distribution factor of a branch is given by:


ij tot

N gb

= ∑ | Ckij | k =1

It is the sum of the absolute values of the distribution factors of the branch ij with respect to all generation nodes (see Appendix). Ngb: number of generation nodes; Ckij,: distribution factor of branch ij with respect to node k. The network with the smallest value of the index can be regarded as most flexible: this can be explained resorting to the definitions of distribution factor and current margin. Under the simplifying assumption of DC load flow, the distribution factor of a branch, with respect to a node, gives the change in power flow through the branch due to a unit injection in the node itself. The current margin is the difference between maximum allowable loading and actual loading of the branch as yielded by the Monte Carlo simulation (averaged on a 1-year simulation span, see Fig. 1). Lines with higher margins have greater capability to cope with changes in nodal injections and thus in power flows. With equal margins, the network having the smaller distribution factors is more flexible, being less affected by changes in generation patterns.

The proposed index can be defined as "Uncertain Scenarios Flexibility Index" (USFI), since it allows to know which one of several alternative configurations of a transmission network is more flexible with respect to "transfer" of generation among selected nodes. It can thus suggest planning choices for the transmission system, given an array of future generation scenarios.

Fig.2. Test network #1

Fig.1. Current - duration curve output for a sample branch

D. Assessment of the index effectiveness The flexibility of the power system, with respect to the changes in generation, consists in the attitude of the system to keep up its desired level of reliability with different generation patterns. The evaluation of the traditional risk indexes, notably of EENS, actually yields information about the flexibility of the network under examination, without resorting to other indexes: this could be defined an "indirect" or deductive approach to the assessment of flexibility. According to the above definition of flexibility, in fact, the most flexible network is the one whose risk indexes are less affected by changes in the pattern of generation (within a reasonable range). The comparison of EENS values calculated, for each network, in all the different generation scenarios, gives thus an assessment of the networks' flexibility: the more flexible will be the one whose EENS varies less moving from one case to another. This criterion has been used to check the results yielded, in a more direct way, by the proposed index. The indirect flexibility evaluation, as outlined above, requires the probabilistic simulation of every expected generation scenario for each candidate network, in order to find the relevant risk indexes. The proposed flexibility index allows to obtain the desired information, for each given system, independently from the expected patterns of generation: this index-based approach could thus be defined "semidirect" or "predictive". III. APPLICATION A. Simple test networks At first, the flexibility indexes have been evaluated for several small test networks; three of them are shown in Figs. 2 to 4 below. For each network, the branches depicted with a thicker line is the one "characterizing" the topology

Fig.3. Test network #2

Fig.4. Test network #3

of the network. The three test networks all have 10 generating units, of two different sizes, grouped in 3 power plants in the three generation nodes. All the networks consist of the same number and length of branches, so they have the same transmission assets costs. Actually the test networks were obtained from each other by "moving" one line at a time (n=9, m=1).This allows to eliminate large differences of reliability due to different numbers of network components. For the sake of simplicity, loads have been considered spatially and temporally uniform. Moreover, the networks have been chosen with the same values of EENS (due to branch overloads), in the "base" generation scenario. The test networks yield the following results:

Table I - Test networks' index values N coll

Test network


i m arg

avg( C ijtot )


0,456 0,430 0,481

0,467 0,428 0,504

i =1

Net #1 Net #2 Net #3

8,793 7,929 8,946

According to the proposed index, their ranking in decreasing order of flexibility is: network #2, network #1, network #3. For each test network, two additional generation scenarios, obtained by shifting 18% of the total installed generation capacity, are examined (see Table II): Table II - Generation scenarios for flexibility evaluation Generation Node 1 Node 3 Node 5 configuration Base 3x70+ 3x70 MW 3x70 MW (gen. conf.1) 1x140 MW 1° transfer 3x70+ 3x70 MW 3x70 MW (gen. conf. 2) 1x140 MW 2° transfer 3x70+ 3x70 MW 3x70 MW (gen. conf. 3) 1x140 MW

The probabilistic simulation of the above scenarios gives the following values of overload-originated EENS: Table III - Overload component of transmission-related E.E.N.S. [MWh] Base 1° transfer 2° transfer Test network (gen.conf.1) (gen.conf.2) (gen.conf.3) Net #1 0 71,4 3,9 Net #2 0 0 0 Net #3 0 104,6 2,9

Fig. 5. IEEE RTS

From the above reported EENS values, the indirect flexibility evaluation yields the same ranking of the direct method. In this simple case, the proposed index gives results in full agreement with the indirect method for the assessment of flexibility. Larger changes in the spatial pattern of generation have been tested, up to 30% of total installed capacity, with the same result.

derived from it show different values of EENS due to branch overloads, in the base case (it has not been possible to obtain the desired 'leveling' of the starting risk indexes). Namely, the 'base' EENS value of the original RTS (IEEEnet #1) is lower than those of the derived networks. (IEEEnets #2 and #3). The results of the flexibility assessment by way of the proposed index for the 3 networks are shown below. 0,93


0,92 0,92 0,91 USFI

B. IEEE RTS In order to test the index performance, the methodology described in par. II-B has been applied to the IEEE-RTS [7], [8], shown in Fig. 5 and named IEEE-net #1; two test networks, namely IEEE-net #2 and IEEE-net #3, have been obtained by making small changes to the RTS. IEEE-net #2 differs from IEEE-Net #1in the following aspects: • Line 2-4 has been transferred between nodes 8 and 9 (in parallel to the existing 8-9 line); • Line 11-13 has been transferred between nodes 15 and 21 (in parallel with the existing 15-21 line). IEEE-net #3 differs from IEEE-net #1 in the following aspects: • Line 2-4 has been transferred between nodes 8 and 10 (in parallel to the existing 8-10 line); • Line 11-13 has been moved between nodes 15 and 24 (in parallel with the existing 15-24 line). In both cases, 2 branches out of 38 (m=2, n=38) have been moved, obtaining 3 networks with the same item list and thus same cost. Anyway, the RTS and the test networks


0,91 0,90


0,90 0,89 0,89 IEEE-net 1

IEEE-net 2

IEEE-net 3

Fig.6. USFI values for the three networks

Calculation of USFI yields the following ranking, in decreasing order of flexibility: IEEE-net #1, IEEE-net #3, IEEE-net #2. The indirect assessment of flexibility has been carried out via probabilistic simulation, by considering different generation scenarios, with a 15% shift of the total installed

generating capacity between nodes: namely, in one case 700 MW were moved between nodes 18 and 23 (gen. conf. 2); in another 400 MW were moved between nodes 18 and 13 (gen. conf. 3). The subsequent evaluation of the overload-originated EENS figures, gives the same results of the proposed index, i.e. the networks ranked the same (net #1, net #3, net #2). gen.conf.1 1000


gen.conf. 3


The validation of the proposed method, as well as the assessment of an appropriate flexibility index, requires further investigation. This includes the application of the proposed index to actual planning scenarios involving complex networks, with random changes in generation represented by probability density functions. Moreover, the analysis will have to consider the uncertainty affecting load evolution in the planning time horizon.


E.E.N.S. [MWh]

V. APPENDIX 100 35,37 19,95


31,68 25,08

8,28 7,63 4,38

1 IEEE-net 1

IEEE-net 2

IEEE-net 3

Fig. 7. Overload component of transmission-related E.E.N.S.

Other experimental indexes tested by the authors, either based on purely structural parameters (e.g. the sum of total distribution factors) or relying on purely operational parameters (e.g. the average value of the branches' current margins) did not generally give results in agreement with the probabilistic simulations. IV. CONCLUSIONS A Monte Carlo simulation approach has been adopted in order to check the performance of indexes aimed at estimating the transmission system's flexibility, defined as: "the attitude of the transmission system to keep up a desired standard of reliability, at reasonable operation costs, when the generation scenarios change". When comparing networks with different initial reliability, such an index does not have to take into account their reliability in absolute terms, according to the definition of flexibility given above; instead, the index must point out which one is most flexible, i.e. the network whose reliability is less affected by the changes in the location of generators. In particular, a flexibility index, USFI, based on structural (distribution factors) as well as operational (current margins of network branches) parameters, has been considered. Flexibility evaluations carried out with the proposed index have then been checked by means of Monte Carlo simulations of the investigated network configurations, with encouraging results. At the planning stage, when dealing with uncertainty about location of generation expansions (rather than about total increase of generating capacity), the main benefit of a 'direct' method for the assessment of flexibility lies in the sharp reduction of the computational burden, in comparison with the classical, indirect approach. To evaluate the proposed index, probabilistic simulation is required for base case only, instead of exploring all the envelope of generation scenarios.

The distribution factor of branch i-j with respect to node k, Ckij , is given by:

Cijk = yij ⋅ (Z ik − Z jk )

where: yij series admittance of branch i-j; Zik i-k term of the network nodal impedance matrix; Zjk j-k term of the network nodal impedance matrix. Under the hypotheses of the DC load flow, the distribution factor Ckij gives the change of power flowing on branch i-j for a unit injection of power at node k. VI. REFERENCES [1] O. Bertoldi, “Flexibility and reliability of power transmission network - planning in a competitive market” [in Italian], L’Energia Elettrica, Vol.75, May-June 1998 [2] Satoru Niioka, Akira Kozu, Ryuichi Yokoyama, “Probabilistic supply reliability evaluation for liberalized elettctricity market”, 7th international conference PMAPS, Naples 22-26 September 2002 [3] T. De la Torre, J.M. Feltes, T.G. San Roman, H.M. Merrill, “Deregulation, Privatization and Competition: Transmission Planning Under Uncertainty”, IEEE Transactions on Power Systems, Vol.14, No.2, May 1999 [4] A.M. Leite De Silva, J.G.C. Costa, L.A.F. Manso, G.J. Anders, “Evaluation of Transfer Capability of Transmission System in Competitive Enviroment”, 7th international conference PMAPS, Naples 22-26 September 2002 [5] M.H. Gravener, C. Nwankpa, “Available Transfer Capability And First Order Sensitivity"; IEEE Transactions on Power Systems, Vol.14, No.2, May 1999 [6] M.T. Schilling, M.B. Do Coutto Filho, J.M. Marangon et al., “Network trasmissibility measures”, CIGRE Symposium, Tours (France) 1997 [7] O.Bertoldi, L.Salvaderi, S.Scalcino, “Montecarlo Approach in Planning Studies: an Application to IEEE RTS”, IEEE Transactions on Power Systems, Vol.3, No.3, August 1988

[8] IEEE Committee Report, “IEEE Reliability Test System”, IEEE Transactions on Power Apparatus and Systems, Vol.PAS-98, No.6, November-Dicember 1979 VII. BIOGRAPHIES Paola Bresesti received her Doctoral Degree in EE from University of Pavia, Italy in 1991. She joined CESI in 1991 where she currently is the Head of Network Study Unit in T&D Network Department. Her main research interests include power system planning and operation, power system modeling and power system economics. Alfonso Capasso has joined the University of Rome "La Sapienza" since 1968, where he has been Assistant Professor since 1970, Associate Professor since 1973 and Professor in Electric Power Systems since 1980. From 1997 to 2000 he was also President of the Italian University Research Group in Electrical Power Systems. His main interests are in computer applications to electric power systems, power quality and railway electrification. He has been involved, as a part-time consultant, in many Railway electrification studies; presently he is engaged in the design activities of the new Italian High-Speed Lines Bologna-Florence and Turin-Milan, under construction. He is a member of AEI (Italian Electrical Association), CEI Committee 110 (EMC), CIFI (Italian Railway Engineers Association) and Senior Member of IEEE. Maria Carmen Falvo was born in Locri (RC), Italy, in 1979. She received with honours the Doctor degree in electrical engineering from the University of Rome "La Sapienza" in 2002. Her main research interests include power system planning, environmental and energy items. She is a member of AEI (Italian Electrical Association), IEEE and ISES (International Solar Energy Society). Stefano Lauria (M'99) was born in Rome, Italy, in 1969. He received the Doctor degree and the Ph.D. in electrical engineering from the University of Rome "La Sapienza" in 1996 and in 2001, respectively. In 2000 he joined the department of Electrical Engineering of University of Rome "La Sapienza" as an Assistant Professor. His main research interests are in power systems analysis, power quality and electromagnetic transients. He is a member of AEI (Italian Electrical Association) and a registered professional engineer in Italy.

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