Developing concurrent investment plans for power generation and transmission

European Journal of Operational Research 166 (2005) 449–468 www.elsevier.com/locate/dsw

O.R. Applications

Developing concurrent investment plans for power generation and transmission € €kyazicı a, Linet Ozdamar Beste K€ ußcu b

b,*

, Shaligram Pokharel

b

a Yeditepe University, Systems Engineering Department, Kayisdagi, Istanbul, Turkey Nanyang Technological University, School of Mechanical and Production Engineering, Systems and Engineering Management Division, Singapore, Singapore

Received 7 October 2002; accepted 26 February 2004 Available online 19 May 2004

Abstract Decisions on electric power generation and transmission investments may have crucial effects on the development of industrial and residential areas. Decisions made on the infrastructure should have economically beneficial consequences for producers and consumers. The aim of this paper is to propose a model that considers transmission and generation investments simultaneously. The proposed model fills in the gap between models for developing long-term power generation policies and instantaneous power flow models. Unlike other investment models, it explicitly takes the high voltage transmission network into account and the selection of new generation plants located on the interconnected network is made in a more realistic manner considering transmission bottlenecks. The problem subsumes the capacitated network location problem and the network design problem, the former being related to decisions on generation expansion and the latter to decisions on transmission network expansion. The integrated model becomes NP in both feasibility and optimality, because of the sub-problems it contains. Here, a practical procedure is proposed to achieve overall feasibility and also to improve investment decisions when the solution is feasible. The model is tested on the dense interconnected network of an industrialized region in Turkey. The implementation shows how future infeasibilities in the transmission network are highlighted by the model and how generation investment decisions are affected by network expansion alternatives.
2004 Elsevier B.V. All rights reserved. Keywords: Energy; Power generation and transmission; Investment analysis

1. Introduction An adequate electric power generation and transmission capacity is essential for a sustained economic growth. As demand for power increases rapidly in developing countries, congestion becomes a key factor in the smooth functioning of the generation system and security of supply. *

Corresponding author. Address: Ak Teknik Makina San. Ve Tic. As, Perpa Ticaret Merkezi B Blok Kat: 8 No. 920, Okmeydani Istanbul, Turkey. Tel.: +90-212-222-0231; fax: +90-212-222-0232. € €kyazicı), [email protected], [email protected] (L. Ozdamar). E-mail addresses: [email protected] (B. K€ ußcu 0377-2217/$ - see front matter
2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2004.02.019

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Power generation and transmission should be planned in an integrated manner since they constitute two inseparable components of electrical power infrastructure. Transmission plans have immediate impacts on generation development schemes. Concurrent planning of generation and transmission is particularly important in developing countries, where substantial loss of natural resources exist due to congested lines and a standard grid system is not yet developed. In some developing countries, there exists a substantial potential of renewable resource based generation at locations that are remote to industrialized regions. The availability of adequate access to the transmission system has a strong impact on the locations, types and sizes of generation facilities that are added to the system. An important factor to be considered is that many developing countries are also in the process of liberalizing the electricity market. In competitive market conditions, where generation is privatized and electricity prices depend on marginal generation costs, congestion prevents the full exploitation of market opening, because it increases unit electricity prices (consumer costs) and leads to undeserved gains or losses for generating firms affecting their return on investment (producer’s loss). Consequently, a reliable transmission planning system that accounts for medium to long-term generation capacity planning is required to prevent any intentional or non-intentional blockage in the transmission system. Bottlenecks in the transmission system also affect international electricity trade. Expansions and upgrades of domestic transmission networks that are coupled with generation planning may relieve the load on cross-border interconnections and increase bulk international electricity trade. The impacts of domestic generation patterns on trans-national lines are discussed in detail in recent reports concerning transmission systems in Europe and US (EC Directorate General Energy and Transport, 2001; Hirst and Kirby, 2001). Altogether these issues place the focus on the need to analyze generation and transmission investment plans together such that de-congestion, enhanced market trade and cleaner energy generation can be achieved. In this paper, a model is developed for obtaining a dynamic long-term investment plan involving strategic decisions on the expansion of electric power infrastructure including generation and high voltage transmission. The model is tested using data pertaining to a highly industrialized region in Turkey and investment scenarios are developed for a planning horizon that covers the years 2000–2010. The proposed model takes into account the restrictions of the region’s high voltage interconnected transmission network explicitly. It assumes that transmission investment plans are centralized and generation is not yet fully privatized. This reflects the current situation in Turkey where generation plants are built under ‘‘Build, Operate and Transfer’’ contracts. The model aims to minimize the net present worth of generation and transmission investment costs and generation operating costs while satisfying energy demand. The output of the model provides the optimal selection of the locations and sizes of new generation facilities on the interconnected network and the transmission network expansions required to satisfy future load. The model also gives a foresight on the return on investment for building new generation plants in different regions because it specifies the optimal future utilization rates of generation capacity in existing and planned facilities. An extension of this model could be to incorporate competitive electricity market policies in investment strategies. In the following sections, the problem background is discussed briefly and the mathematical formulation of the model is conveyed. Then, a practical procedure used to identify feasible and improved solutions is described, and the investment scenarios developed for Marmara region (Turkey) are illustrated.

2. Problem background Power systems planning research is mainly focused on operational issues such as minimizing loss in the transmission system and minimizing operational costs of generation (unit commitment problem). Optimal

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power flow models are developed for these purposes. These models represent real time restrictions of the transmission network and the existing portfolio of generation units as system operating constraints and aim at identifying the real time optimal mix of generation units that would satisfy active and reactive power demand with minimum power loss. Operating constraints are represented by power flow equations that consist of equations relating node angles, generations and loads to circuit flows. These are approximations of Kirchoff’s first and second laws and they balance energy flow among load and generation nodes (buses). Power flow models optimize the parameters of controllable devices such as reactive devices, generator voltages and phase shift angles (see for instance, Ruzic and Rajakovic, 1991; Batut and Renaud, 1992; Wang et al., 1995; Hewlett et al., 1998). Optimal power flow models deal with the real time and short-term system optimization problem and do not take transmission and generation investment decisions into account. More recently, models involved with optimizing long term power transmission expansion investments are proposed (Romero and Monticelli, 1994; Tsamasphysrou et al., 1999; Bahiense et al., 2001; Gil and da Silva, 2001). These researches analyze the interconnected network design problem under system operating constraints. They use linearized power flow equations in planning studies of high voltage meshed networks, providing good approximations for circuit flows. Investments on candidate circuits are optimized under these constraints respecting flow upper bounds on transmission lines. In this context, the objective would include the minimization of transmission investments as well as operational costs (loss of load). These models are linear mixed integer problems that are difficult to solve by conventional approaches and attempts are made to obtain tight formulations that can be solved by iterative decomposition methods and Lagrangean Relaxation. Another approach in this field is to use system simulators that run on the principles of optimal power flow models to identify transmission bottlenecks. In this approach, different network re-enforcement alternatives are investigated by scenario analysis (EC Directorate General Energy and Transport, 2001). In transmission network investment models, only the capacity value of generation plants are considered. In other words, the effects of different production levels are analyzed in real time with constraints on transmission system stability and security (Wang et al., 1995; Rajamaran et al., 1997). Researchers working on the transmission network expansion problem have to deal with the network infeasibility issue that is inherent to the network design problem (NSP). In general terms, the NSP is a binary programming problem where transmission lines and their load capacities are selected to form a connected tree of supply and demand nodes such that flow conservation equations are satisfied. Given the existing network, it might not be possible to identify a feasible solution that satisfies demand due to line capacity constraints. Gallegro et al. (2000) show that NSP is strongly NP-Complete when load capacity is defined by a discrete function. In fact, this is the situation dealt with in high voltage circuit design problems. NSP is also applicable in areas other than high voltage circuits, such as telecommunications (Amiri and Pirkul, 1997; Frantzeskakis and Luss, 1999; Gendreau et al., 2000), fluid distribution (Castillo and Gonzales, 1998) and low voltage electricity networks (Bousba and Wolsey, 1991). In transmission network investment models, the emphasis is not particularly on the energy value of generation facilities, namely, their annual output forecasts. The energy value is used in long-term generation investment plans and policies (US DOE, Annual Energy Outlook, 1997). Unfortunately, generation and transmission planning are still treated as separate entities even in countries where market liberation is well established. Models that integrate long-term generation and transmission investment decisions are few. An early contribution in this field is made by Iwayemi (1978), who optimizes transmission and generation investment costs as well as generation operation costs. Here, transmission constraints are simplified by including line upper bounds on power flow and rather than including the whole interconnected transmission network, the author only considers regional transfer of bulk energy. More recently, Chatuverdi et al. (1999) propose a model for expanding the transmission network of India and follow the same framework as Iwayemi (1978) by including inter-state bulk energy transfer. The model selects the optimal number of additional

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transmission lines between pairs of states while minimizing transmission investment costs and generation operation costs in the long-term. However, although plans are developed for long-term investments and include the energy value of generation capacity, investment decisions on generation facilities are omitted from the model and the impact of the interconnected network on generation capacity is not considered. However, Chatuverdi et al. (1999) explicitly acknowledge the existence of infeasible solutions for their model and express a penalty term in the objective function for unmet demand. An example where only generation investments are taken into account is the comprehensive energy planning model implemented in US (US EMM, 2001). This model omits transmission investment decisions completely while including transmission line capacity limits only at the level of inter-state bulk energy transfer. The overview given above shows that in currently available planning models, there is a gap between long-term power generation investment models that omit the restrictions of the transmission network, and transmission investment models that are based on real time power flows. The latter incompatibility creates a conflict between the two analysis approaches, because transmission constraints are not accounted for in developing long-term energy investment plans, and, in optimal power flow models where they are accounted for, the projection of generation capacity is only instantaneous. Thus, the two modeling frameworks for generation and transmission investment planning are at different detail levels and have different temporal dimensions. The proposed integrated transmission and generation investment model takes the restrictions of the interconnected transmission network at its energy value level. In this approach, the actual transmission network is represented in the model by a node-incidence matrix and energy flow through each transmission line is bounded from above on an annual basis. This ‘‘spatial’’ perspective enables the planner to analyze the impacts of transmission constraints on generation investments where generation capacity is also represented in terms of its energy value. The optimal choices made on the location, type and size of generation plants are affected by transmission bottlenecks resulting in a more realistic representation of the problem. This approach can also facilitate dealing with restricted electricity trade and congestion pricing discussed in liberalized markets (Eynon et al., 2000). The model’s outputs are the spatial locations and sizes of new generation capacity additions to the interconnected network and their scheduled investments during the planning horizon. Furthermore, the output also includes the time schedule of transmission network upgrades and expansions plus new substations. The generation facility investment part of the model extends the capacitated network location problem (CNLP) that is NP-Hard (Mateus and Thizy, 1999) and the transmission investment part is the NSP with discrete load capacity selections, which is strongly NP-Complete as discussed above. The complexity of this integrated modeling approach (a much simpler version where a static problem is solved with uncapacitated links and capacities of facilities are decided a priori) is analyzed by Melkote and Daskin (2001), who test the solvability of the integrated model on small hypothetical transportation networks. Gupta and Pirkul (2000) also adopt the integrated approach in dealing with the design of a restrictive treelike network for Fiber Co-axial CATV. Their model is simplified by the special structure of the network and the fact that link capacities are fixed. The authors provide a proof for the NP-Completeness of this problem. The integrated power system investment model proposed here is more complex than the ones described in the latter references. However, the tests conducted on the network of Marmara region, Turkey, show that the integrated model is solvable, and that, the increase in problem complexity is compensated by the advantages of integrating transmission and generation investment decisions.

3. Mathematical formulation The mathematical formulation of the integrated model and the notation are given below.

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Sets D G I N A K K0ij

453

set of load centers and buses where power stations exist for stepping up or down voltages of different transmission lines (demand nodes and transshipment nodes) set of existing and potential generation facilities set of import–export nodes set of all nodes, N ¼ fD [ G [ Ig set of all transmission lines (arcs) including proposed lines and voltage levels set of all transmission voltage levels (transmission load capacities) set of new propositions for voltage level of transmission line fi; jg
A, K0ij
K

Parameters T length of the planning horizon Dit energy equivalent of predicted load (GWh) at load center i 2 D in period t energy equivalent of installed power (GWh) available at generation facility i 2 G Si expansion limit for additional/new generation capacity at facility i 2 G Li 0 quota for imported energy from node i 2 I in period t Lit quota for exported energy to node i 2 I in period t L00it R reserve margin for keeping redundant generation capacity in the system for contingencies (R < 1:0) per period transmission capacity (in GWh) of line fi; jg
A at voltage level k Cijk maximum percentage of transmission capacity that can be used to enable operation of lines below R0 thermal limits (R0 < 1:0) (estimated or known) price of imported/exported energy (per GWh) in period t Uit Vi fixed cost for building additional installed power at facility i 2 G (per GWh), discounted to the starting period of construction operating cost per GWh of energy generated at facility i 2 G in period t (fuel and variable operOit ating costs) building/upgrading cost of transmission line fi; jg to voltage level k 2 K0ij , discounted to the Eijk starting period of the construction approximate cost of additional equipment (e.g., transformer) required for voltage step up/step Pk down from voltage level k time required to build additional generating capacity at facility i 2 G ti tij0 time required to build transmission line fi; jg at voltage level k 2 K0ij a capital discount factor B a sufficiently big number binary parameter, Niqt ¼ 1, if t  q P ti , zero otherwise Niqt binary parameter, Mijqt ¼ 1, if t  q P tij0 , zero otherwise Mijqt binary parameter, A0ijk ¼ 1, if fi; jg
A and k 2 K0ij , zero otherwise A0ijk Variables fijt amount of energy transferred by transmission line fi; jg
A in period t xit generation capacity (in GWh) added to facility i 2 G in period t yijkt binary variable indicating if transmission line fi; jg
A of voltage level k is used in period t wikt binary variable indicating if a transmission line of voltage level k incident to node i 2 N is used in period t

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Mathematical model Min

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A; k 2 K0ij ; t; X ½A0jik yjikt þ A0ijk yijkt  6 Bwikt 8i 2 N; k 2 K; t;

ð8Þ ð9Þ

j2N

wikt P wik;t1 8i 2 N; k 2 K; t; yijkt ; wikt ¼ 0; 1 and integer; fijt ; xit P 0:

ð10Þ ð11Þ

The objective function minimizes the net present value of generation investment and operating costs, costs of imported energy, transmission investment costs and costs of additional equipment required at power stations where lines with different voltage levels meet. The return obtained from exported energy is zdeducted. Constraints (1) ensure that energy requirements are satisfied at load centers and constraints (2) impose upper bounds on energy supplied by generation facilities. The upper bound in any period t consists of the currently available generation capacity (it is zero for potential facilities) and the sum of capacity expansions carried out up to the given period. Construction lead times are accounted for at all times. The third set of constraints limit the total amount of generation capacity expansion for each facility. In Turkey, these limits are determined by the Energy Resources and Mineral Research Directorates considering natural reserve availability, site conditions and environmental issues for all types of facilities including fossil fuel fired facilities. The next pair of constraints enforces contract based quotas on imported and exported energy. Constraints (6) restrict energy flow by transmission line capacity at the selected voltage levels. In the next set of constraints, a transmission line is restricted to a single voltage level in each period. Whether or not alternative voltage levels are proposed for an existing line, the variables yijkt corresponding to the line and its alternatives can all be zero if there is no flow passing through that line. In the objective function, only the costs of building the alternatives are accrued. Constraints (8) make sure that a new transmission line preserves its selected voltage level once it is constructed. This constraint is required so that building cost of

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a new transmission line in the objective function is charged only in its period of construction. In the last two sets of constraints, binary variables are triggered when there is a need for additional equipment for stepping up or stepping down voltage levels due to new lines incident to power stations. Constraints (1)–(5) comprise the multi-period CNLP where facility capacities are not fixed a priori, but are optimized along with their locations on the network. Constraints (6)–(10) describe a NSP with additional fixed costs for accurate voltage level switches at buses. In this integrated model, the restrictions of the NSP causes the CNLP to invest on excessive additional generation capacity, because restricted transmission capacity prevents energy transfer to load centers and demand remains unsatisfied unless such uncalled-for investments are realized. Despite excessive investment on generation capacity, it may not be possible to find a feasible solution to the problem unless appropriate transmission network expansions are carried out.

4. A practical heuristic for achieving feasible and improved solutions The model is first solved as a multi-period CNLP omitting constraints (6)–(10). Thus, flows are not restricted by the transmission network. The resulting objective function value, that only comprises of generation investment and operating costs and costs of imported energy, is a lower bound (LB) for the integrated model and serves as a basis of comparison. Next, the model is solved with the existing transmission restrictions and possible upgrade propositions that do not require exception handling. Here, it is assumed that converting a single circuit of a given voltage level to a double circuit at the same voltage level (with tower re-enforcement) does not need exception handling. On the other hand, constructing a new line on the same path with a different voltage level requires exception handling. Constructing a new line that does not follow an existing path is even more difficult due to geographical and demographical reasons. The latter not only requires building new towers, but it involves the acquisition of new land to minimize health hazards. The rules applicable for classifying upgrade alternatives should be developed according to the official and legal procedures adopted by the authorities in each country. A given set of upgrade propositions does not guarantee a feasible solution due to the NP-Complete property of the problem. Furthermore, in case the solution is feasible, there might always be transmission line alternatives to improve a given solution. Consequently, a practical and efficient iterative procedure is developed to handle bottlenecks and exceptions in order to achieve feasibility, and when the result is feasible, to improve the solutions obtained. The iterative procedure is called ConsTruct, CT. In CT, each time an infeasible or feasible solution is obtained, critical transmission lines that require capacity upgrades are reported. If the solution indicates that energy flow is fully utilizing a line’s maximum permissible capacity among all existing and proposed voltage levels for that line (i.e., there is no slack in Eq. (6) for the highest voltage level among existing and proposed levels for the line), then the line is labeled as critical. This analysis is conducted in all time periods of the planning horizon, starting with the period where the gap between generation and load is maximum. CT identifies all critical paths that start from a source succeeded by a set of critical arcs ending at a sink node. These critical paths are bottleneck sub-nets in the interconnected network and if these sub-nets are dealt with, there would be room for improving generation investment and operating costs. The source nodes of critical paths are often generation facilities with cheaper expansion and/or operating costs than the ones utilized in the current solution and sinks might be load centers or sub-stations that are on paths to load centers. There might also be singular arcs that become critical if they are on the supply paths of more than one generation facilities. In these cases, the critical path consists one of critical arc. In any iteration, after all critical paths are identified, CT decides if an alternative should be proposed for a given critical path. If the critical path was also critical in the previous iteration and the alternative proposed in the previous iteration has not been accepted at the maximum proposed voltage level in the

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current iteration, then that specific critical path is ignored. Otherwise, alternatives are formulated for relieving the critical paths as described below. When it is decided that a critical path should be upgraded, CT generates alternatives by proposing to upgrade the voltage levels of the critical lines on the path to their corresponding next higher voltage levels. These alternatives require exception handling and need to be confirmed by the decision-maker (DM). When the DM confirms the alternatives, or adds new alternatives, the model is solved again. CT then starts another iteration by identifying new critical paths. CT’s alternative generation procedure is restricted to lines in the existing network. New lines that do not exist in the current network are proposed by the DM after he/she analyses the energy flow through the network and facility utilization rates. This process might be supported by a GIS aided decision support system (GIS-DSS) that links the network’s database to GIS tools. GIS would provide information on urban development, geographical and geological properties in the areas where alternatives should be proposed (Church, 2002). The model and CT procedure proposed here would be a guide to GIS-DSS in identifying network expansion alternatives in the search for the optimal generation investment strategy. All alternatives proposed by CT and the DM are accumulated during the iterations, i.e., each time the model is solved again, the transmission network contains all default alternatives entered at the initialization step, CT’s propositions and the DM’s contributions to resolve bottlenecks up to that iteration. The relief of a critical path at a given iteration affects all other critical paths in the network, and therefore, all relief alternatives are preserved throughout the iterations. CT terminates the iterations either when there are no critical lines in the solution, or no viable alternatives exist, or, all critical paths in the solution should be ignored due to their existence in the previous iteration. It may also be stopped when the current solution is close enough to the LB in terms of costs. Procedures CT and Critical_Path are given below with the additional notation used. Notation aijt binary parameter indicating if maximum voltage level capacity of line fijg
A is fully utilized in period t, aijt ¼ 1, if fijt ¼ R0 ½maxk2K fCijk g in the current solution (line is critical) 00 A set of critical arcs in the current solution, A00
A p critical path consisting of nodes linked by consecutive critical arcs in A00 P set of critical paths in the current solution, p 2 P P0 set of critical paths in the previous iterations v source vertex of a critical path p, aivt ¼ 0 for 8i 2 N, t and avjt ¼ 1, for at least one fvjg
A00 Ap set of new lines and upgraded voltage levels suggested as upgrade/expansion alternatives for p 2 P0 0 C temporary set of critical lines stored while constructing paths from a given source vertex V set of live source vertices V0 temporary set of live source vertices Procedure CT 0. Initialization: (a) Include all non-exceptional upgrade proposals in the network, A. (b) Determine LB by solving the model with Eqs. (0)–(5). (c) Initialize set of stored critical paths, P0 ¼ £. 1. Solve model with all equations included. 2. Identify the set of critical arcs, A00 in the current solution. 3. Call procedure Critical_Path to identify set of all critical paths, P. 4. If P ¼ £ or any other termination criterion is satisfied, then stop. Else, select a critical path p 2 P and continue.

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(a) If p 2 P0 and yijkt ¼ 0, for 8fijkg
Ap , k ¼ maxfK0ij g, 8t, and then, P ¼ P  fpg and go to Step 5. Else, continue. (b) Report p and higher voltage level alternatives. Confirm/receive upgrade alternatives from DM. Store alternative links in Ap and update network, A ¼ A þ Ap . (c) P0 ¼ P0 þ fpg, P ¼ P  fpg. 5. If P 6¼ ;, go to Step 4. Else, go to Step 1. The Critical_Path procedure that is called by CT identifies all critical path-source nodes and generates all critical paths emanating from every source node. The pseudocode is given below. Procedure Critical_Path 0. Set time period, t ¼ 0. 1. Increment time period, t t þ 1. 2. Identify all source vertices, v 2 N such that avjt ¼ 1 for at least one line fv; jg 2 A00 and ajvt ¼ 0 for 8fj; vg 2 A00 and place them in V. 3. Select a source vertex, v 2 V. Initialize V0 ¼ fvg and C0 ¼ ;. Store source vertex: v ¼ v. 4. Select a line fv; jg 2 A00 and fv; jg 62 C0 . (a) If there is no such line, then kill vertex v : V0 ¼ V0  fvg and go to Step 5. Else, continue. (b) Store line fvjg, label node j and update temporary set: C0 ¼ C0 þ fv; jg, Lj ¼ Lj þ fvg, and V0 ¼ V0 þ fjg. 5. If V0 6¼ £, select a vertex v 2 V0 and go to Step 4. Else, construct and store all critical paths emanating from v using C0 and Lj . Add critical path to P. Delete: V ¼ V  fv g. If V 6¼ £, then go to Step 3. Else, if t < T , then go to Step 1, else stop.

5. Implementation of the model: Investment scenarios for Marmara region (Turkey) 5.1. Description of the current system The model and the CT procedure are implemented on the electricity transmission and generation system of Marmara region in Turkey. The investment plan consists of 3 macro planning periods (years 2000, 2005, 2010), each representing 5 years. The data is collected from the publications of the Turkish Electricity Agency (1997) and the Turkish Planning Agency that updates parameters such as geographical and sectoral energy consumption rates every 5 years. The transmission network map is dated 1998, therefore, while evaluating the scenarios described here, one should keep in mind that some upgrades might have been carried out on the network. This region has the highest network complexity in Turkey’s transmission network. It includes industrial, commercial and residential load centers with high consumption rates such as Istanbul, Izmit (refineries, sugar cane, etc.), Bursa (automotive and textile industries), Tekirda
g(textile, plastics, chemicals, etc.). About 25% of Turkey’s population lives in Marmara region and the region’s electricity consumption is about 35% (39,798 GWh in 2000) of the total national electricity consumption (114,000 GWh in 2000). The transmission network of Marmara region involves 10 major load centers, 17 existing generation facilities, 12 proposed generation facilities, 1 import source (Bulgaria), and 20 buses where major lines meet. Marmara receives a substantial amount of energy from other regions of Turkey, particularly hydro-power in East-Anatolia that is transmitted to different regions in Turkey by eight 380 KV lines. This inter-regional energy is called here ‘‘internal imported energy’’ whereas the energy received from Bulgaria is called

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‘‘external imported energy’’. In order to represent the generation capacity feeding Marmara from other regions, 9 exterior nodes are connected to the network. The connections are positioned in accordance with Turkey’s overall transmission network, their load capacities are set as in the original transmission network, and their total generation export capacity is calculated based on the proportion of Marmara’s energy consumption to that of Turkey’s. The variable operating cost for internal import is calculated as a weighted average of the operating costs pertaining to the production mix in all regions in Turkey, except Marmara. In Fig. 1, the topology of load centers, existing and proposed generation facilities, internal and external imported energy source nodes are partially illustrated. The partial network in Fig. 1 consists of high voltage transmission (154 and 380 KV) lines. In Fig. 1, 154 KV lines are drawn in light colour and 380 KV lines in dark. Small load centers, such as counties, are added to nearby towns and small auto-producers are clustered into larger facilities. The reduced network analyzed consists of 94 nodes and 115 links. The details of demand (circles in Fig. 1) and supply nodes (triangles in Fig. 1) are shown in Table 1 where existing and proposed generation facilities are listed with their installed capacities in GW, average annual generation capabilities in GWh, operating (per GWh) and investment costs (per GW). The average annual efficiency is 45% for a hydropower plant and 75% for fossil fuel-fired plants. The safety margin, SS, for generation capacity is assumed to be 92.5%. Due to fact that a period is defined as 5 years, all construction lead times are assumed to be equal to one period even if they take less time than 5 years to be completed. The costs of external and imported energy are also indicated in Table 1 (last two rows). The capital discount factor is taken as 6% per annum, and investment costs for generation facilities are included in the model by discounting the construction expenditures to the start time of the construction. Existing generation facilities in Marmara are of three types: natural gas and coal-fired facilities and a small hydropower plant. The locations and types of proposed generation facilities (4 hydropower, 4 coalfired, 4 natural gas plants) and expansion limits of major existing facilities (the hydropower plant cannot be expanded) are acquired from Turkey’s Energy Resources and Mineral Research Directorates, and the maximum permissible installed capacities of new facilities are obtained from the Turkish Electricity Agency. In fact, the construction of the proposed plant #203 has started in 2002 and that of #204 is officially announced to start in 2003. Plant #205 is planned to start in the near future. These three facilities

Legend:

75

Existing plant

Bulgaria

201

7 5

Black Sea

11

12

88 90

93

13

6 91 10 208

15

16

35

36

118

380 KV 18 21

37

19

17

77

26

3

8 23

78

1

22

20

206

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Load center 154 KV

92 205

Marmara Sea

202

Power station

203, 204, 207

76 96

14

Proposed plant

116

24

2

I

internal I

internal Fig. 1. Partial network of Marmara region.

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Table 1 Major existing and proposed generation facilities Generation facility (#ID)

Type of facility

Existing facilities Hamitabat (#11) Aksa Enerji 1 (#12) Ak Enerji (#13) S ß ahinler (#14) Ambarlı (#15) B€ uy€ uk C ß ekmece (#16) C glu (#17) ß olako Kartonsan (#18) _ ß (#19) Ipras Seka2 (#20) Aksa-Ak Enerji (#21) S ß eker Fab (#22) Do gancßay (#23) Bis Enerji (#24) Orhaneli (#26) Trakya Elektrik (#201) Marmara Ereglisi (#202)

Natural gas Natural gas Natural gas Natural gas Natural gas Natural gas Natural gas Natural gas Coal-fired Coal-fired Natural gas Natural gas Hydro power Natural gas Coal-fired Natural gas Natural gas

Total Proposed facilities Mansurlar (#32) Do gancßay (#33) G€ onen (#34) Manyas (#35) C ß ırpılar (#36) Tuzla (#37) Gebze (#203)* Adapazari (#204)* Silivri (#205)* Canakkale (#206) Kurtkoy (#207) Tekirdag (#208)

Hydro power Hydro power Hydro power Hydro power Coal-fired Coal-fired Natural gas Natural gas Natural gas Coal-fired Natural gas Coal-fired

Total Type of facility

Generation investment cost ($/GW) · 106

Natural gas Coal-fired Hydro power External import from Bulgaria Internal import from other regions

454 1055 1335.00 – –

Facility capacity (GW)

Facility capacity (GWh)

1.200 0.021 0.044 0.012 1.350 0.630 0.123 0.014 0.030 0.018 0.038 0.249 0.019 1.450 0.210 0.500 0.478

7776.00 138.67 281.88 80.35 8748.00 4082.40 799.63 92.10 194.40 118.60 246.24 1612.87 71.00 9386.00 1411.34 3240.00 3097.40

6.387

41,376.89

0.018 0.019 0.019 0.019 0.031 0.031 1.400 0.700 0.500 0.320 1.400 1.000

66.53 70.22 70.22 70.22 200.00 200.00 9072.00 4536.00 3240.00 2073.60 9072.00 6480.00

13.032

84,276.43

Generation operation cost ($/GWh) · 106

Construction lead time (period)

0.049 0.069 0.0037 0.035 0.045

1 1 1 – –

Bold faced facilities are announced to be built.

will add a new energy source of 16,848 GWh by the year 2005. The rest of the proposed plants are placed in locations on the network according to official declarations. Estimates of electrical energy consumption for major load centers are provided in Table 2. The figures in Table 2 reflect the base demand estimation, and at peak hours, these figures increase by approximately 15% (Sahin, 1997). The limits for internally imported energy and the quota for energy import from abroad

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Table 2 Estimated energy consumption of major load centers in Marmara Forecasted consumption (GW h) Years Load center (#ID)

2000

2005

2010

Balıkkesir (#1) Bilecik (#2) Bursa (#3) C ß anakkale (#4) Edirne (#5) _ Istanbul (#6) Kırklareli (#7) Kocaeli (#8) Sakarya (#9) Tekirda g (#10)

1642.20 884.70 5093.70 681.90 803.70 19,517.00 981.10 7645.90 906.20 1641.60

2295.00 1293.20 9089.40 919.20 1181.90 28,247.00 1557.60 10,719.50 1423.40 2645.10

3208.00 1934.90 12,569.00 1256.20 1753.00 38,920.00 2387.40 14,231.00 2277.00 4200.60

Total

39,798.00

59,371.30

82,737.10

Internal import limit (from other regions) Transmission capacity limit on internal import External import limit (from abroad) Net energy deficit

24,390.00

42,275.00

54,645.00

36,046.83

36,046.83

36,046.83

2040.00

2969.00

3500.00

–

–

8521.76

(external import) are also indicated in Table 2. It is observed that transmission capacity limits become binding on internal imported energy in 2005. The amount of energy deficit becomes 8521.76 GWh in 2010. The latter calculation is carried out by deducting the existing supply, external and internal import limits from predicted consumption and allowing for the given safety margin, SS. Some transmission related cost parameters are as follows. The construction costs for new transmission lines are approximately $200,000 and $270,000 per km for 154 and 380 KV lines, respectively. Upgrades of existing lines can be realized by building double circuits that cost $128,000/km and $172,500/km respectively for 154 and 380 KV lines. The transfer capacity of the single circuit 154 and 380 KV lines are respectively, 2102.4 and 7884 GWh, and the load capacity of double circuit lines become approximately twice as much. These capacities are calculated using the standard resistance values of high voltage transmission lines in Turkey. In the implementation of the model, voltage types are given the following classification index, k: k ¼ 1: single circuit––154 KV; k ¼ 2: single circuit––380 KV; k ¼ 3: upgrading single circuit 154 KV to double circuit––154 KV; k ¼ 4: upgrading single circuit 380 KV to double circuit––380 KV. Existing lines are classified under voltage levels k ¼ 1 (154 KV) and k ¼ 2 (380 KV). In the proposed network, each existing 154 KV line has a default upgrade alternative of double circuit (k ¼ 3), and similarly, each 380 KV line can be upgraded to the corresponding double circuit (k ¼ 4). These upgrades are not considered exceptional and they are included in the expanded network by default. However, re-constructing a 154 KV line to a single or double circuit 380 KV line is considered exceptional. Such exceptional upgrades are proposed by CT if the solution contains critical paths. When a double circuit 154 K path becomes critical, CT automatically makes an exceptional proposition of upgrading it to a single or double circuit 380 KV line and requires the DM to confirm or enter his/her proposals. If the optimization package chooses to upgrade existing lines or expand the network with the proposed lines in the previous iteration, this is accompanied by appropriate additional equipment placed at the sub-

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stations to which these lines are incident. The approximate cost of additional equipment is taken as $0.6 · 106 and $1.0 · 106 for k ¼ 3 and k ¼ 4 lines, respectively. 5.2. Implementation of the model and CT procedure As described above, the transmission network is represented with all possible non-exceptional upgrade alternatives, and hence, in the expanded network, each line has two voltage level options. Two consumption scenarios are considered for the planning horizon: base demand and peak demand. First, the model is solved using ILOG Cplex 7.5 without including transmission capacity constraints and the solutions providing the LBs for the base and peak demand scenarios are identified. Then, the model is re-solved with the actual transmission constraints. In both scenarios, in the first iteration with transmission capacity restrictions, a feasible solution is not available. As expected, the infeasible peak scenario results in more critical lines. In Tables 3 and 4, details on the critical paths identified, proposed and accepted upgrades, the amount of generation capacity expansion and the cost breakdown structure (generation and transmission network expansions, operating and internal/external import costs) are given for the solutions obtained in each iteration of the CT procedure. The procedure starts with an infeasible solution (iteration 1). The information in these tables should be analyzed with the utilization rates of existing and proposed facilities that are indicated in Tables 5 and 6 for both scenarios. The capacity utilization rate, uri , of a facility i is calculated as: P P i2N fijt  j2N fijt : uri ¼ RðSi þ Li Þ Hence, the utilization rate considers the total possible capacity of a facility including its expansion limit. For internally and externally imported nodes, the capacity limit is taken as the minimum of available energy and transmission capacity limit. The uri indicated in the tables belong to year 2010 because the last period has the maximum energy deficit and transmission bottlenecks occur then. In the second column of Tables 5 and 6, the cost index of each facility, ci , is indicated for facilitating the analysis of the information. The cost index integrates the capital investment cost per GWh with operating cost and it is calculated as: ci ¼ Vi =li þ oi ;

8i 2 fG [ Ig

where li is the lifetime of facility i in macro periods, and oi is its operating cost discounted from future estimates to the present. In Tables 5 and 6, facilities 23 and 24 are highlighted with a star, because they cannot be expanded during the planning horizon (#23 is a hydro plant and #24 is recently completed with no further expansion possibility). When uri is indicated in bold face, it implies that new generation capacity is built for facility i in the solution. It is observed in Tables 5 and 6 that, without transmission restrictions (unbounded column in Tables 5 and 6), and in both base and peak demand scenarios, the new natural gas facilities (#203, #204 and #205) are selected for construction. In the peak demand scenario, an existing natural gas facility (#11) is also expanded almost to its full capacity expansion limit. The capacity expansion required to meet consumption in 2010 is 8522 GWh in the base demand scenario and 22,417 GWh in the peak demand case. An interesting observation here is on the facilities selected for generation capacity expansion in the uncapacitated transmission network case. These facilities (203, 204, 205) are the ones that the Turkish Electricity Agency has actually decided to build. However, when transmission network restrictions are included in the model, this solution becomes infeasible for the year 2010. In the infeasible solution for the base demand scenario, demand at load centers cannot be met despite the fact that new generation capacity of 16,359 GWh is built (6th column in Tables 3 and 4), exceeding the actual deficit of 8522 GWh in year 2010. The same is true for the peak scenario where 26,362 GWh is added to generation including the expansion of facility 11. In fact,

462

Table 3 The implementation of CT procedure on base demand scenario Base

Transmission lines (Exceptional) accepted

(Default) upgraded at k ¼ 3, k ¼ 4

Generation expansion

Transmission expansion

Operation

Import/ export

Total

cpu time (seconds)

Critical paths

(Ap for next iteration) (exceptional) CT proposal

24-78-1 ðk ¼ 3Þ

24-78-1 ðk ¼ 2; 4Þ 24-3 ðk ¼ 2; 4Þ 26-3 ðk ¼ 2; 4Þ 116-3 ðk ¼ 2; 4Þ

16,358.81

712.21

4.67

3094.88 3264.72 7076.48 10.68

15-16-91 ðk ¼ 2; 4Þ 15-92-6 ðk ¼ 2; 4Þ

13,647.89

594.18

15.58

2968.26 3360.56 6938.58 10.02

24-3 ðk ¼ 3Þ 26-3 ðk ¼ 3Þ 116-3 ðk ¼ 3Þ Iteration 2 24-3 ðk ¼ 2Þ

11-12-13-6 ðk ¼ 4Þ

15-16-91 ðk ¼ 3Þ

15-16-91-10 ðk ¼ 3Þ 15-92-6 ðk ¼ 3Þ 207-118 ðk ¼ 4Þ

15-92-6 ðk ¼ 3Þ

204-118 ðk ¼ 4Þ

None

15-96 ðk ¼ 2; k ¼ 4Þ (DM)

8521.76

391.82

10.67

3014.36 3360.56 6777.41 10.55

None

None

None

8521.76

391.82

8.86

3014.36 3360.56 6775.60 17.66

8521.76

391.82

–

3014.41 3360.51 6766.74

Iteration 3 24-3 (k ¼ 2) 15-92-6 ðk ¼ 2Þ Iteration 4 24-3 ðk ¼ 2Þ 26-3 ðk ¼ 2Þ 15-92-6 ðk ¼ 2Þ 15-96 ðk ¼ 2Þ Unbounded transmission capacity 0.89

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Iteration 1 Infeasible

Costs (·$106 )

Generation capacity expansion (GWh)

Table 4 The implementation of CT procedure on peak demand scenario Peak

Transmission lines (Default) upgraded at k ¼ 3, k¼4

Critical paths

(Ap for next iteration) (exceptional) CT proposal

15-16-91-10 ðk ¼ 3Þ 15-92-6 ðk ¼ 3Þ 24-3 ðk ¼ 3Þ 26-3 ðk ¼ 3Þ 24-78-1 ðk ¼ 3Þ 93-6 ðk ¼ 3Þ 116-3 ðk ¼ 3Þ

15-16-91-10 ðk ¼ 2; 4Þ 15-92-6 ðk ¼ 2; 4Þ 24-3 ðk ¼ 2; 4Þ 26-3 ðk ¼ 2; 4Þ 24-78-1 ðk ¼ 2; 4Þ 93-6 ðk ¼ 2; 4Þ 116-3 ðk ¼ 2; 4Þ

118-6 ðk ¼ 4Þ

92-6 ðk ¼ 4Þ

203-118 ðk ¼ 4Þ 207-118 ðk ¼ 4Þ 201-7 ðk ¼ 3Þ, 202-10 ðk ¼ 3Þ 201-7 ðk ¼ 3Þ, 202-10 ðk ¼ 3Þ 207-118 ðk ¼ 4Þ, 118-4 ðk ¼ 4Þ

Iteration 1 Infeasible

Costs (·$106 )

cpu time (seconds)

Generation expansion

Transmission expansion

Operation

Import/ export

Total

26,362.35

1147.73

12.67

4048.39

3330.63

8539.42 26.72

22,416.8

975.96

13.03

4018.21

3360.56

8367.76 14.69

118-6 ðk ¼ 4Þ

15-96 ðk ¼ 2; k ¼ 4Þ (DM)

118-6 ðk ¼ 4Þ

None

22,416.8

975.96

12.42

4018.21

3360.56

8367.15 17.66

22,416.8

975.96

4018.26

3360.51

8354.74 0.89

Iteration 2 15-92-6 ðk ¼ 4Þ 24-3 ðk ¼ 4Þ

Iteration 3 15-92-6 ðk ¼ 4Þ 24-3 ðk ¼ 4Þ 15-96 ðk ¼ 2Þ

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(Exceptional) accepted

Generation capacity expansion (GWh)

Unbounded transmission capacity –

463

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Table 5 Utilization rates of existing and proposed facilities for base demand scenario uri in 2010 Base demand

Cost index, ci

CT iterations Unbounded

1 (Infeasible)

2

3

4

Existing facility 11 12 13 14 15 16 17 18 19 20 21 22 23* 24* 26 201 202

0.068 0.068 0.068 0.068 0.068 0.112 0.068 0.068 0.112 0.112 0.068 0.068 0.092 0.068 0.147 0.068 0.068

50.00% 50.00% 50.00% 50.00% 41.56% 85.47% 50.00% 50.00% 50.00% 50.00% 50.00% 50.00% 100.00% 100.00% 50.00% 78.83% 75.91%

50.00% 50.00% 50.00% 50.00% 42.80% 0.00% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 99.99% 87.18% 50.00% 62.79% 75.91%

60.13% 50.00% 50.00% 100.00% 46.77% 0.00% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 100.00% 100.00% 50.00% 100.00% 100.00%

59.77% 50.00% 50.00% 100.00% 64.30% 80.32% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 100.00% 100.00% 50.00% 90.57% 75.91%

51.01% 50.00% 50.00% 100.00% 74.95% 80.32% 100.00% 100.00% 50.00% 50.00% 59.73% 100.00% 100.00% 100.00% 50.00% 100.00% 100.00%

Proposed facility 32 33 34 35 36 37 203 204 205 206 207 208 External import Internal import

0.092 0.099 0.118 0.099 0.124 0.135 0.068 0.068 0.068 0.112 0.068 0.112 0.035 0.044

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 13.50% 100.00% 100.00% 0.00% 0.00% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 0.00% 0.00% 100.00% 0.00% 100.00% 99.60%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 81.54% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 36.68% 0.00% 0.00% 0.00% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 100.00%

Bold face figures imply generation capacity has been expanded.

for the peak scenario the energy deficit is 22,417 in year 2010. Thus, when capacities are expanded without resolving the problems of transmission congestion, it will lead to an inefficient investment or to a worse extent, wasted investment. Obviously, the existing and expanded transmission network fed into the model is insufficient to transport the required energy to load centers and the critical parts of the network need to be analyzed. An official announcement on expansion plans of the transmission network is not available yet, and therefore, a one-to-one comparison with the results of the scenario is not possible at present. In the implementation of CT, let us analyze the base demand scenario first. CT identifies the set of critical paths, A00 in the infeasible solution. These turn out to be the lines linked to load center 3. The set of source vertices, v, are #24, #26 and #16. Procedure Critical_Path identifies two critical paths emanating from source vertex 24, and these are 24-78-1 and 24-3, both critical at k ¼ 3. Facility 24 is a recently expanded generation plant that is linked to 154 KV circuit with two different lines 24-3 and 24-78. Facility 24

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Table 6 Utilization rates of existing and proposed facilities for peak demand scenario uri in 2010 Peak demand

Cost index, ci

CT iterations Unbounded

1 (Infeasible)

2

3

Existing facility 11 12 13 14 15 16 17 18 19 20 21 22 23* 24* 26 201 202

0.068 0.068 0.068 0.068 0.068 0.112 0.068 0.068 0.112 0.112 0.068 0.068 0.092 0.068 0.147 0.068 0.068

89.16% 50.00% 50.00% 50.00% 41.56% 85.47% 51.95% 50.00% 50.00% 50.00% 50.00% 50.00% 100.00% 100.00% 50.00% 78.83% 75.91%

50.00% 50.00% 50.00% 100.00% 46.77% 0.00% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 100.00% 87.18% 50.00% 100.00% 75.91%

55.49% 50.00% 50.00% 100.00% 69.90% 85.47% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 100.00% 100.00% 50.00% 99.54% 100.00%

62.04% 50.00% 50.00% 100.00% 90.92% 85.47% 100.00% 100.00% 50.00% 50.00% 100.00% 100.00% 99.99% 100.00% 50.00% 99.54% 100.00%

Proposed facility 32 33 34 35 36 37 203 204 205 206 207 208 External import Internal import

0.092 0.099 0.118 0.099 0.124 0.135 0.068 0.068 0.068 0.112 0.068 0.112 0.035 0.044

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 100.00% 100.00% 0.00% 0.00% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 100.00% 0.00% 0.00% 100.00% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 0.00% 0.00% 0.00% 55.48% 0.00% 100.00% 100.00%

0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 0.00% 100.00% 0.00% 100.00% 100.00%

Bold face figures imply generation capacity has been expanded.

tries to feed load centers 3 and 8. Load center 8 is supplied via the path 24-78-1-117-106-8. The ‘‘24-781’’portion of this path is a single circuit 154 KV line that needs to be upgraded at least to level k ¼ 2, since 1-117-106-8 path is at voltage level, k ¼ 2. For resolving this problem, CT proposes to upgrade the single circuit 154 KV lines on both critical paths to the next higher voltage levels, k ¼ 2 and k ¼ 4. This is a costly but necessary proposal because facility 24, which has a lower cost index ci than other utilized facilities (Table 5) cannot be fully exploited in the last period (year 2010) when there is a high energy deficit. The other two congested paths are 26-3 and 116-3. The latter congestion results from two internal import nodes (Fig. 1) feeding load center 3. The congestion in 26-3 is not due to facility 26 because its supply quantity is lower than line capacity. The reason is that facility 24 also sends part of its supply to load center #3 through the parallel path 24-78-37  -4-77-26-3. Consequently, the congestion around load center #3 can be relieved by proposing single and double circuit-380 KV lines (k ¼ 2, k ¼ 4) for any of the critical paths.

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With these additional upgrade proposals, the network is further expanded and CT conducts the second iteration where the model is re-solved resulting in a feasible solution. It is observed that out of the exceptional propositions, only 24-3 line is upgraded to voltage level, k ¼ 2, and this relieves all congested lines linked to load center 3. In the solution, the northern path 11-12-13-6 is upgraded to double circuit in order to enable the expansion of facility 11. However, this path is not critical, but quite loaded in year 2010 due to the fact that energy outflow from facility 15 is following a parallel path, that also includes the path 11-12-13-6. In this iteration, two critical paths are identified, both with the same source vertex, facility 15. These are 15-16-91 and 15-92-6. It is observed in Table 5 that the utilization rate of facility 16, ur16 , is zero in iteration 2. This occurs because path 16-91 is congested, and therefore, out of the two facilities, only facility 15 feeds load center 6 through paths 15-92-6 and the parallel path that starts with 15-16-91 and ends with 13-6. The latter congestion blocks the expansion of facility 15, and leads to over expansion of facility 207. When the new generation expansions are summed up in iteration 2, it is observed that this figure amounts to 13,647.89 GWh that is still greater than the deficit. The costs of over-expanding generation capacity in iterations 1 and 2 can be compared with the expansion costs in subsequent iterations and in the unbounded transmission capacity solution. To relieve the outflow of energy from facilities 16 and 15, higher voltage level upgrades are proposed by CT for paths 15-16-91 and 15-92-6 at voltage levels k ¼ 2 and k ¼ 4. In the third iteration, it is observed in Table 3 that the upgrade proposal for 15-92-6 is accepted at voltage level k ¼ 2 (in the previous iteration, this path was upgraded to voltage level k ¼ 3). Due to this transmission capacity upgrade, in Table 5, we observe that ur16 becomes 80% (facility 16 is utilized but not expanded) and that the expansion of facility 202 is reduced by 25%, and, that of facility 201 reduced by 10%. Furthermore, facility 15 is now expanded by 15%. The main difference between the two solutions lies in the fact that in iteration 2, the capacity of facility 207 is over-expanded (7396.91 GWh) leading to an expansion higher than required, while in iteration 3, it is not utilized at all, and it is replaced by the two expansions of 1663.61 GWh (facility 204) and 2502.68 GWh (facility 15). Hence, over-expansion of generation capacity is completely eliminated in iteration 3. Furthermore, the upgrades of the paths 11-12-13-6 to 380 KV double circuit and 15-16-91-10 to 154 KV double circuit are not required any more in this iteration. Hence, transmission costs diminish significantly due the latter savings. CT stops the iterations here, because there are no other critical paths. It is observed that in this iteration, generation expansion and operating costs (including imports) are identical to those of the LB solution and there can be no improvement over these costs. Yet, transmission costs could be improved by new transmission expansions. To illustrate the latter, an exceptional proposal is made by the DM for constructing a new line joining facility 15 and sub-station 96 to free energy flow from facility 15 towards load center 6 via paths outgoing from node 96. In iteration 4, we observe that this proposal is accepted and it results on the elimination of all new propositions for generation facilities (new facility 204 is not constructed), as well as all upgrades to voltage level k ¼ 3 and k ¼ 4. However, the exceptional proposal 26-3 at voltage level k ¼ 2 made by CT in the first iteration is accepted. The latter shows how previous propositions may be activated when a new expansion is included in the network. The final total costs obtained in iterations 3 and 4 are 0.15% and 0.13% above the LB, respectively. In the peak demand scenario, critical paths in the infeasible solution (iteration 1 in Table 4) involve the paths around both load centers 3 and 6. CT proposes voltage level upgrades of single and double circuit 380 KV for all single circuit 154 KV critical lines. Obviously, the default upgrade of moving from single circuit 154 KV to double circuit 154 KV is insufficient. In iteration 2, the two paths, 15-92-6 and 24-3, are upgraded to voltage level k ¼ 4. This solution is similar to that of Iteration 3 in the base demand scenario. The same pattern of generation expansion exists except for the additional facility 207 in the peak scenario. The observations that are made in the third iteration of the base demand scenario are valid in the second iteration of the peak demand scenario. However, paths 92-6 and 118-6 are critical at voltage level, k ¼ 4. CT can no longer propose upgrades for these paths, because both links are at their maximum possible

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voltage level. Since both paths directly point at load center 6, line 15-96 is proposed by the DM. This proposal is accepted in iteration 4 at voltage level k ¼ 2, however, path 118-6 remains critical. Analyzing the flow through paths 118-76-6 and 118-93-6 the DM observes that these paths are critical at voltage level k ¼ 2 (their original state in the existing network), and that, the default option of upgrading them to a higher voltage level, k ¼ 4, has not been selected by the optimization package. Due to this reason and the fact that the expansion and operating costs of the solution are equivalent to those of the LB solution, CT is terminated. The final solution’s objective value is 0.15% above the corresponding LB. Comparing the final solutions obtained for the base and peak demand scenarios, we observe that the expansion patterns are similar, the peak scenario having larger expansion amounts and the additional expansion of facility 207. It is observed that the general optimal policy is to expand available facilities as much as possible. A substantial amount of investment is required for expanding the transmission network. In the peak demand scenario, with the exception of 24-3 line that has to be built before the year 2005, all other upgrades are required after that year. If there is an economic slowdown like the one the country is facing now, then low consumption might relieve the load on the network in the future. In Tables 3 and 4, in each iteration, CPU times required by CPLEX to solve the integrated model with accumulated network expansion alternatives are indicated. The computation times are taken on an IBM PC with 400 MB RAM and 1.6 GHz processor and they include CT’s retrieval of the output and feeding the input. It is observed that computation times are reasonable, given that the size of the problem is [170,452 · 106,836] in the last iteration of the peak demand scenario where the number of expansion alternatives is maximum. CPLEX reduces the size of this problem to [1829 · 1949] by suppressing constraints and variables on non-existing arcs. The observed computation times imply that the integrated model can be tested on larger networks.

6. Conclusion An integrated mathematical model is developed for planning long-term electric power transmission and generation investments. The model explicitly considers the capacity restrictions of the interconnected transmission network at high voltage levels. In the implementation of the model, it is observed that transmission constraints have significant impacts on the choice among generation expansion alternatives and on plant utilization rates. The proposed model is an intermediary between macro models involving only generation investments, and instantaneous power flow models that consider transmission network expansion subject to technical constraints. The aim in developing the model is to associate the two model categories and guide the power flow models by suggesting viable new transmission alternatives associated with generation investments. The integration of electricity pricing issues within the model constitutes the next step in building this conceptual framework. The proposed model is NP-Complete and therefore may result in infeasible solutions with a given set of upgrade alternatives. To resolve the latter, an iterative procedure that guides the proposal of new transmission upgrades is developed. The procedure may still result in sub-optimal solutions unless all possible network expansions are expressed, which is a difficult task in itself. However, the quality of solutions can be measured by comparing them with an easily computed lower bound. This procedure is tested on data obtained for Marmara region in Turkey and satisfactory results are obtained with the integrated model with respect to the lower bound. A future goal is to embed the model and the procedure in a GIS aided decision support system for planning power infrastructure investments that would also include simulation tools for generation patterns and pricing. In such a framework, the link between the proposed model and power flow models would also be established.

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