INVESTMENT PERSPECTIVES ON THE INTERCONNECTION OF ISOLATED SYSTEMS WITH THE MAINLAND GRID: CRETE CASE STUDY

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1 INVESTMENT PERSPECTIVES ON THE INTERCONNECTION OF ISOLATED SYSTEMS WITH THE MAINLAND GRID: CRETE CASE STUDY Emmanouil Loukarakis, Konstantinos Kalaitzakis, Eftichios Koutroulis, Georgios Stavrakakis Electronic an Computer Engineering Department Technical University of Crete, Chania, Greece ABSTRACT A Monte-Carlo base, probabilistic poer flo metho is use to evaluate ifferent poer system interconnection options. Suitable inices are propose to assess the potential profit of each interconnection scenario an the require interconnection rating. Separate investment perspectives are ientifie an the respective optimal solutions are compare. Inicative results are presente regaring a possible submarine interconnection of the Greek islan of Crete ith the mainlan gri. KEY WORDS Monte-Carlo simulation, optimal poer flo, poer system interconnection, submarine interconnection NOMENCLATURE nc nc fc Pc Generator cost function - a quaratic function is use for each generator P Win park active poer n 1 vector k Win park cost n 1 vector P Active poer eman n 1 vector δ Voltage angles nb 1 vector T Line active poer nl 1 vector Yb Bus amittance nb nb matrix YT A nl nb matrix - if line k ith amittance y k connects buses i an j then ro k has Y ( k, i) Y ( k, j) 1 y an other elements T T k equal to Cc Generators connection nb nc matrix - element ( i, j ) is 1 if generator j is connecte to bus i, an otherise C Win park connection nb n C Poer eman connection nb n p Buses marginal costs 1 b P L matrix n vector Interconnection nominal poer Interconnection cable length matrix 1. Introuction In many aspects planning of possible interconnections beteen poer systems is similar to the typical transmission expansion problem. The time, location, type an capacity of the ne interconnection have to be etermine, base on economic or reliability criteria, or a combination of both. Different formulations an optimization criteria appear in relevant publications. A common approach is to minimize investment costs require to supply system loa [1], incluing poer generation costs [2,3]. In [4] reliability constraints are ae to the optimization problem. A multi-perio approach is consiere in [5], optimizing investments by splitting the overall time frame into smaller perios, ithin hich congestion an generation costs are minimize. Finally, [6] an [7] consier eregulate systems an market base criteria, giving solutions base on congestion costs an market competitiveness or social elfare. While such approaches may also be use for evaluating the connection of an isolate system to the mainlan gri, such a problem presents its on peculiarities. A ne interconnection typically involves costs much larger than those require for the construction of overhea ac transmission lines. It allos access (for one of the to systems) to energy at a loer cost, hich may very ell be seen as a goo traing opportunity. Aitionally it affects the usage of existing equipment or might create ne nees. For example, construction of ne conventional plants may be avoie in the smaller system hile alloing a higher reneable energy penetration. At the same time reserve requirements may be reuce, but aitional overlan transmission might be require to fully utilize the systems' interconnection. As can be expecte, interconnection equipment etermines to a large extent both initial (installation) an operation (losses) costs of the interconnection, an is not alays stanarize. Given the energy cost variations uring the ay, especially in systems ith high reneable energy penetration, etermination of the projecte interconnection usage (poer transfer), an in turn estimation of the require equipment rating, is also an important issue. Evaluation of a potential interconnection scenario

2 involves first an foremost the estimation of expecte gains ith respect to the corresponing require rating of the interconnection (in other ors the require capital). Thus a potential investment in interconnection can be justifie or rejecte. Of importance is also the evaluation of system reliability an transmission congestion as these are inicative of the nee for ne generation or transmission capacity, hich may affect interconnection profit. Estimation of all the above amount to solving a short-term problem (evaluation of the system ith a stanar set of generating sources an loas) an a longterm one (evaluation of the system evelopment for the economic lifetime of the interconnection equipment an the overall erive benefits). 2. Short Term Analysis In orer to solve the short term problem a Monte-Carlo base probabilistic loa flo is use. This allos consieration of most possible system states an estimation of the expecte values of system costs an reliability inices. Certain simplifications are mae to reuce ata requirements an variability in the system, hich allos for a faster convergence. These, along ith the metho basics, are iscusse in the folloing sections. 2.1 State Generation A non-sequential Monte-Carlo (MC) metho [8] is use to generate system states. For each state the loa in each bus is etermine by sampling a loa uration curve. Availability of conventional generators is estimate base on their force outage rate (FOR). In a similar manner transmission system outages may be accounte for. Hoever, ue to transmission lines high availability, the costs incurre ue to line outages can be expecte to be small compare to the overall interconnection costs an benefits. Each in park is moele as a single equivalent generator, hose output is etermine base on a in park poer versus in spee characteristic. Shaoing an ake effects, or effects relate to ifferent in spees ithin the in park area, are assume to be incorporate into the aforementione characteristic. Win parks FOR is base on typical outage rate of the equipment connecting them to the high voltage netork. Iniviual in turbine outages may be easily taken into account using i.e. a multistate moel for the equivalent generator [9]. A key factor that has to be consiere is in spee correlation beteen in parks, hich are locate in ifferent areas. The same is true for the poer eman of ifferent buses an/or systems. In orer to generate correlate ranom numbers stanar copula theory is use. First a multivariate set of normally istribute numbers ith a knon rank correlation is generate, base on the Cholesky ecomposition of the set s covariance matrix. Then these are transforme to uniform istribution numbers an again inverte to the esire istribution. Through these transformations only rank correlation is preserve, hoever a relationship ith the commonly use Pearson correlation may be estimate. 2.2 Optimal Poer Flo Formulation The Monte-Carlo simulation efines for each case the available generation an loa. In orer to estimate the exact system state the folloing objective function has to be minimize: f f c P c k P k P (1) The above equation reflects the fact that eman is consiere inelastic. The vector k is a penalty factor associate ith loa sheing. Typically this penalty is set at a much higher value than generators cost. As a result loa curtailments are minimize first, an poer generation costs are minimize secon. The constraints involve ith the optimal poer flo problem are as follos: C P C P C P Y δ (2) c c b P P, P P, P P (3) max max max c c max YT δ T (4) Eq. 2 escribes the set of linear equations of the transmission system. Eq. 3 escribes the typical constraints associate ith generation an eman. Finally eq. 4 eals ith line active poer limits. The c formulation is preferre as it allos a significant ecrease in computation time an an aequate representation of transmission an interconnection poer flos. An aitional constraint is ae to cover in poer penetration limitations. In small systems in generation is typically limite to 25-3% of the total system loa, i.e.: n j n P.3 P ( k) (5) j1 k 1 It is assume that this constraint still stans after the interconnection. Whether or not reneable poer penetration levels may be increase, epens on the interconnection ynamic response characteristics, an is also a matter of unit commitment. For example an interconnection loae to capacity cannot provie frequency support. In case of a DC link beteen the to systems, each interconnection point is moele as an aitional poer injection since both its active an reactive poer are controllable, an also assuming that the cost of interconnection losses is not significant. Given the fact that interconnection rating has yet to be etermine, there is no point of using a more etaile moel. This is especially so in the case of submarine interconnections, here cables are typically tailor mae for the specific application [1]. In case of an AC interconnection the link is simply simulate as an aitional line. In this paper the former case is examine. The above optimization problem is solve by a primal-

3 ual interior point metho presente in [11] an also use in [12]. Marginal costs of each bus are equal to the Lagrange multipliers corresponing to the active poer balance loa flo equations [13]. Due to the fact that system losses are not consiere (as result of the c loa flo) marginal prices are slightly unerestimate. On the contrary ignoring the generators technical minimums (a simplification often use in transmission expansion) leas to a slight overestimation. Hoever it can be expecte that all evaluate scenarios are affecte in a similar manner, an consequently the results are sufficient for comparison purposes. 2.3 Short Term Analysis Inices As iscusse in [14] epening on the case uner stuy, ifferent evaluation criteria may have to be consiere, an not all may be irectly translate into economic costs. As mentione earlier first an foremost evaluation inices shoul justify the investment. Secon, they have to evaluate the nee for aitional generation or transmission. In a free market social, consumer or proucer surplus are a ominant factors in evaluating any project. In this ork hoever, eman is consiere inelastic. Maximizing social elfare is equivalent to minimizing prouction cost [15]. Thus, the folloing inices are eeme to most comprehensively escribe a possible interconnection: Expecte Consumer Benefit (ECB - M /year): Uner the assumption that a noal pricing system is use, if n cases are generate by the MC process, then the expecte average consumer cost on an annual basis is equal to: n 1 T CC p P 876 (6) n i 1 an the consumer benefit is equal to: ( l) ( l ) () ECB CC CC (7) ( l) here CC refers to the l th interconnection scenario () an CC to the system as is. Expecte Interconnection Commercial Benefit (EB - M /year): The interconnection congestion cost or commercial benefit is erive from the price ifference beteen the connecte buses. If T is the poer transferre through the interconnection beteen buses k an j its average value on an annual basis is equal to: n 1 EB j k T ( i ) p p 876 (8) n i 1 Expecte Transmission Commercial Cost (ETCC - M /year): Sum of transmission system congestion costs, efine similarly to EB. It is the aitional cost consumers pay ue to the limite transmission capacity an up to an extent inicative of transmission system usage. Loss of Loa Expectation (LOLE - h / year ): this is a measure of system reliability. While other inices are available mostly expresse in MWh / year e.g. EENS, it is not easy to evaluate the cost of a curtaile MWh. As a result LOLE is consiere more representative. The typical value of 1 ay in 1 years is set as the target that has to be achieve after the interconnection construction. Aitional inices may be efine [6,7,16] to account for market properties such as prices istribution, market poer of generation companies, generators benefits etc. Hoever ue to the nature of the examine problem (small system size, controllable interconnection, inelastic eman) such inices are not consiere as important an ill not be iscusse further in this paper. 3. Long Term Analysis & Investment Perspectives The solution of the long term problem is base on breaking the perio uner evaluation to several shorter perios (i.e. years), uring hich it may be assume that installe generation an the loa uration curve remain practically unchange. As a result the overall economic benefits associate ith the interconnection, uring its expecte lifetime, may be estimate. Optimality of the solution epens on ho an hy he invests on an interconnection. Initial investment cost for a DC submarine interconnection is roughly approximate by the folloing relation: /MW / km P L (9) These costs are base on [17], an have been increase to cover inflation an possible cost overruns. It is assume that maintenance an operation costs are equal to 3% of the installation cost. In orer to evaluate the economic value of the interconnection to basic inices ill be use. The first is the net present value of the investment efine as: t NB NPV i (1) i1 1 r here t is the equipment economic life time in years (ranging typically from 2 to 4 years [18]), NB the net benefit uring each year, an r the rate of return. The secon inex of interest is the internal rate of return, or the rate of return that yiels a zero NPV. Thus it is calculate base on the folloing equation: t NB i (11) i1 1 IRR In the interconnection of isolate systems three investment perspectives are ientifie. The first is the system operator (SO) point of vie. The system operator's objective oul be to maximize social benefit. Given that eman is consiere inelastic, this is equivalent to maximizing the NPV that may be erive base on ECB (in eq. 1 NB ECB ). The secon perspective is that of a private investor or regulate transmission company, that agrees ith the SO on a moerate but safe rate of

4 4. Inicative Results The test system use approximates the system of the Greek islan of Crete. A 16 bus system ith presumable peak loa 89 MW, 946 MW conventional generation capacity, 184 MW installe nominal in poer an 138 /MWh average marginal generation cost. To possible interconnection scenarios are consiere, as seen on Fig. 1. The mainlan gri is moele as a single bus an it is assume its energy price - ith an average marginal cost 9 /MWh - is not affecte by the eman in Crete. In the example that follos the interconnection is to cover the islans nees an no aitional investments in generation or transmission are to be mae. Finally it shoul be note that ue to the typically lo values of reliability inices, these are the last to converge. In orer to spee up the simulations first the economically optimal solution is foun, an a check follos to see if it satisfies reliability criteria (in this case LOLE). 4.1 Short Term Results The short-run solution for the first simulation perio (year) is illustrate in Fig. 2 an Fig. 3. As can be seen in these figures, given that losses are not estimate, the to interconnection options in general coincie, up to aroun a capacity of 3-35 MW. After that in case A, congestion costs in the islan increase as inicate by ETCC. This is ue to congestion on the lines transferring poer from the est to the east. This in turn limits the maximum economic benefit for the consumers. Interconnection ith capacity greater than 35MW at point A ill have to be couple ith a potential overlan transmission expansion. An interconnection ith a capacity of 6-7MW at point B seems to offer the greatest social (consumer) benefit. Energy traing beteen the to systems ill reuce prices on the islan, hoever it is in the interests of the inepenent investor to limit these transactions so that profit may still be mae by the remaining price ifference. A capacity of 2-25MW maximizes the short-term commercial benefit inepenently of the point of connection. Of course these short term results o not take into account the relevant investment costs. 4.2 Long Term Results The final simulation results are illustrate in Fig. 3 an Fig. 4. The NPV is estimate ith a minimal rate of return equal to 5%. Despite the higher require investment cost the interconnection of case B, ith a capacity approximately 65MW maximizes social benefit. Hoever, hile this solution maximizes potential profit, it oes not maximize profit per capital investe. In both the inepenent an regulate investor cases, a smaller interconnection capacity oul be preferable for the investor ith respect to IRR. Case A oul be preferre. In the regulate investor case a capacity up to 35MW seems best, as ue to the loer investment cost, allos greater return rates. Specifically in the inepenent investor case a 2MW solution is optimal. Still, it shoul be kept in min that preicting ho the system ill evolve in the next ecaes is a ifficult task. Possible eman ecline, construction of aitional interconnections or installation of reneable sources on the islan, or an increase on mainlan system marginal price oul significantly loer the projecte profits of the interconnection. Thus the risk can be significant, an the estimate values of IRR (up to 15%) 25 ECBB 2 (M /year) return. In this case public benefit is also of interest, as the higher it is, the higher the profits that the investor may negotiate ith the SO. Hoever NPV oes not give a complete picture. Typically the investor oul ant to maximize the value of his money an opt for the highest possible IRR (in eq. 11 NB ( i ) ECB ( i ) ). Finally, the thir case is that of an inepenent investor that aims to take avantage of the price ifference of the to systems. The erive benefits in this case are calculate base on EB ( NB ( i ) EB ( i ) ), hile IRR is also the efining inex. ECB A 15 EB A 1 ETCCA EB B 5 Fig Short-term social an commercial benefit. 25 NPV (M ) 2 B 15 A Fig. 1 Evaluate interconnection scenarios. Fig Net present value from SO perspective. 8 9

5 IRR (%) probably o not justify the investment. At any rate, commercial benefits oriente solutions might lea to unerinvestment in interconnection capacity. All iscusse solutions satisfy the target set for LOLE. This is of course only a measure of aequacy of supply. It shoul be note that system security consierations may impose limits on the interconnection capacity or ay of operation. Such limitations can be etermine by stuying the system's ynamic behaviour (e.g. [19]). 5. Conclusions A metho for interconnection scenarios evaluation has been presente along ith inicative results for the islan system of Crete. Possible investment perspectives have been iscusse, an as it has been illustrate the optimal interconnection solution largely epens also on ho is making the investment an consequently ho the profits from the interconnection are etermine. The current results may further be improve ith a more etaile representation of the mainlan gri, evaluation of a larger number of scenarios, an incorporation of ancillary services costs. The presente metho may further be extene to account for combine investments in transmission an generation, especially from reneable sources. References A c B c Fig. 4 Internal rate of return. The curves corresponing to the inepenent investor case are esignate by the inex c. [1] S. Binato, M. V. F. Pereira, an S. Granville, "A Ne Beners Decomposition Approach to Solve Poer Transmission Netork Design Problems," IEEE Trans. Poer Systems, 16(2), May 21, [2] N. Alguacil, A. L. Motto, an A. J. Conejo, "Transmission Expansion Planning: A Mixe-Integer LP Approach," IEEE Trans. Poer Systems, 18(3), Aug. 23, [3] A. Sharifnia an H. Z. Aashtiani, "Transmission Netork Planning: A Metho for Synthesis of Minimum Cost Secure Netorks," IEEE Trans. Poer Systems, 14(8), Aug. 1985, B A [4] J. Choi, et al., "A Metho for Transmission System Expansion Planning Consiering Probabilistic Reliability Criteria," IEEE Trans. Poer Systems, 2(3), Aug. 25, [5] A. S. D. Braga an S. J. T., "A Multiyear Dynamic Approach for Transmission Expansion Planning an Long-Term Marginal Costs Computation," IEEE Trans. Poer Systems, 2(3), Aug. 25, [6] M. O. Buygi, G. Balzer, H. M. Shanechi, an M. Shahiehpour, "Market-Base Transmission Expansion Planning," IEEE Trans. Poer Systems, 19(4), Nov. 24, [7] S.. l. Torre, A. J. Conejo, an J. Contreras, "Transmission Expansion Planning in Electricity Markets," IEEE Trans. Poer Systems, 23(1), Feb. 28, [8] R. Billinton an W. Li, Reliability Assessment of Electric Poer Systems Using Monte Carlo Methos (Ne York: Plenum Press, 1994). [9] R. Billinton an Y. Gao, "Multistate Win Energy Conversion System Moels for Aequacy Assessment of Generating Systems Incorporating Win Energy," IEEE Trans. Energy Conversion, 23(1), Mar. 28, [1] T. Worzyk, Submarine Poer Cables (Springer, 29). [11] H. Wang, C. E. Murillo-Sanchez, R. D. Zimmerman, an R. J. Thomas, "On Computational Issues of Market- Base Optimal Poer Flo," IEEE Trans. Poer Systems, 22(3), Aug. 27, [12] R. D. Zimmerman, C. E. Murillo-Sanchez, an R. J. Thomas, "MATPOWER: Steay-State Operations, Planning, an Analysis Tools for Poer Systems Research an Eucation," IEEE Trans. Poer Systems, 25(4), Jun. 21. [13] G. D. Luenberger an Y. Ye, Linear an Nonlinear Programming. (Springer, 28). [14] D. Camac, R. Bastias, R. Naira, C. Dortolina, an H. M. Merrill, "Transmission Planning Criteria an Their Application Uner Uncertainty," IEEE Trans. Poer Systems, 25(4), Nov. 21, [15] D. S. Kirschen an G. Strbak, Funamentals of Poer Systems Economics. (Wiley, 24). [16] H. Saboori an S. Jai, "Economic Assessment Methos for Transmission Netork Expansion Planning in Competitive Environments," in 18th Iranian Conference on Electrical Engineering, Isfahan, 21. [17] D. N. Nebery, N. H. Von er Fehr, an E. Van Damme, "UK-Netherlans DC Interconnector," report of Market Surveillance Committee of DTe, 23. [18] Public Poer Corporation, Distribution Gris Planning Guie. (Greece, 1995). [19] I. D. Margaris, J. C. Mantzaris, M. E. Karystianos, A. I. Tsouchnikas, C. D. Vournas, N. D. Hatziargyriou, I. C. Vitellas, "Methos for Evaluating Penetration Levels of Win Generation in Autonomous Systems," in IEEE PoerTech Bucharest, Romania, 29