The new challenges to transmission expansion planning. Survey of recent practice and literature review

Electric Power Systems Research 134 (2016) 19–29

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The new challenges to transmission expansion planning. Survey of recent practice and literature review Sara Lumbreras ∗ , Andrés Ramos Institute for Research in Technology, Universidad Pontificia Comillas, Santa Cruz de Marcenado, 26, Madrid 28015, Spain

a r t i c l e

i n f o

Article history: Received 9 February 2015 Received in revised form 3 September 2015 Accepted 11 October 2015 Keywords: Transmission expansion planning Optimization Stochastic Mathematical programming Heuristics, Metaheuristics

a b s t r a c t Transmission Expansion Planning (TEP), the problem of deciding the new transmission lines that should be added to an existing transmission network in order to satisfy system objectives efficiently, is one of the main strategic decisions in power systems and has a deep, long-lasting impact on the operation of the system. Relatively recent developments in power systems, such as renewable integration or regional planning, have increased considerably the complexity and relevance of this problem. This is particularly true in the case of the European Union. These issues have motivated the appearance of a vast array of projects that propose specific development plans for the required transmission, together with academic literature that deals with the different theoretical aspects of the problem. It seems, therefore, pertinent to review these recent works and put them into context. This paper performs a critical review on TEP focusing on its most recent developments. It analyzes the current challenges to transmission planning and illustrates them with some instances of TEP in a European context. Then, it proposes a taxonomy of modeling decisions and solution methods for this problem, linking them to some of their main representative works in the literature with an emphasis on the most recent advances. These alternatives are critically compared, providing with insights that can guide researchers or practitioners when undertaking this kind of studies. © 2016 Elsevier B.V. All rights reserved.

Contents 1. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 The new challenges of transmission expansion planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.1. Deregulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2. Renewable penetration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3. Large-scale generation projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4. Market integration and regional planning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.5. Long permitting processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Transmission expansion planning practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.1. The TYNDP (ten year network development plan) (2014, every 2 years) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.2. E-Highway (from 2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3. Desertec (from 2009) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.4. MedGrid (from 2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.5. RealiseGrid (2007–2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.6. Irene-40 (2008–2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.7. Offshore grid (2009–2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.8. WindSpeed (2009–2011) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.9. SUSPLAN (2008–2010) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 3.10. Roadmap 2050: A practical guide to a prosperous, low-carbon Europe (2013) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

∗ Corresponding author. Tel.: +34 91 542 28 00. E-mail address: [email protected] (S. Lumbreras). http://dx.doi.org/10.1016/j.epsr.2015.10.013 0378-7796/© 2016 Elsevier B.V. All rights reserved.

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4.

5.

6. 7.

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Modeling TEP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 4.1. Just transmission? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.2. Treatment and scope of uncertainties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.3. Decision dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.4. Market considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 4.5. Mono vs. multi-criteria studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.6. Level of detail on the operation of the system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.7. Consideration of special elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Solving the TEP problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.1. Interactive search approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 5.2. Automatic planning approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2.1. Automatic searches based on heuristic rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 5.2.2. TEP by optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

1. Introduction Electric power transmission is the long-distance transfer of electricity from generation plants to substations. From these substations, electricity is subsequently delivered to consumers through the distribution network. The transmission grid is therefore the basic infrastructure that enables the large physical power flows that make the power system possible. It imposes physical constraints to the power flows that traverse it (Kirchhoff’s Laws) and therefore to generation and demand. The main consequence of this is that not all dispatch solutions are feasible. Consequently, Transmission Expansion Planning (TEP), that is, “deciding which new lines will enable the system to satisfy forthcoming loads with the required degree of reliability” [1], is one of the key strategic decisions in power systems. Table 1 provides some context on the decisions that concern the transmission network, with TEP being one of the most important, highest-impact problems . Transmission investments are very capital intensive and have extremely long useful lives (of up to 40 years), so transmission investment decisions have a long-standing impact on the power system as a whole. This is reflected on the relatively large sums dedicated to this purpose: for instance, ENTSO-e members have a joint budget over EUR 100 bln for their 2012–2022 investments [2]. This long-term impact on the power system is particularly relevant for the integration of new generation. In some cases, it is only necessary to connect a new power plant to a nearby node, which is relatively inexpensive compared to the long-distance connections and wide-range reinforcements that are required when generation is located in remote areas. The later case is increasingly relevant given that renewable generation largely determines its location based on the availability of the resource, particularly wind and solar, which often abound in remote areas far away from the main demand centers. In addition, the European Union has set very aggressive emission reduction targets, establishing a 20% reduction in greenhouse gases with respect to 1990 levels by 2020 and endorsing an objective of 80% reductions and 100% clean electricity by 2050 [3,4]. Although considerable amounts of renewable power have been installed in the past couple of decades, most of the member countries are still far from meeting these targets [5]. Therefore, vast amounts of new generation are expected to be built in the medium-term future. These ambitious projects depend critically on the transmission network to integrate the new generation. The necessary expansion can emerge in the form of isolated reinforcements, an extensive HVDC overlay to the existing network or an entirely new grid. The latter case, known as greenfield expansion, applies to the particularly interesting case of offshore grid design, where

no existing network can be used as the starting point for the developments. The design of large-scale network expansions poses considerable challenges that have been addressed in a vast array of both projects and academic literature. Existing reviews on this topic can be found in references [6,7]. However, the current context of the problem, together with the extension of the recent works, makes it interesting to review it again. This paper contributes to the literature with the following: • A high-level perspective of the present conditions for practical TEP problems and the challenges they face. Given its special interest, we will focus on a European context. However, most of the issues have a more general scope of application. • A review of some of the most interesting instances of TEP carried out in the recent past, highlighting the scope of each study and its main features. • A taxonomy of modeling decisions and solution methods for this problem, linked to some of their main representative works in the literature, with an emphasis on the most recent works. • A critical evaluation of these modeling decisions and solution methods. These alternatives are compared in the light of the type of problem under consideration. This article, therefore, has the final aim of providing the reader with an overview of the problem and its current circumstances, together with comments that have the aim of serving as a guide to select appropriate modeling features and solution methods. This paper is structured as follows. First, Section 2. discusses the current challenges to TEP, which are illustrated with recent project examples in Section 3. Then, Sections 4 and 5. describe the main modeling choices and solution approaches. Finally, Section 6. extracts conclusions.

2. The new challenges of transmission expansion planning Having such a deep impact on the power system as a whole, it is not surprising that TEP has been studied in an academic context for decades. In addition, it has long been recognized that the uncertainties present in the problem, together with its combinatorial nature, constitute a considerable burden to its resolution [8]. However, relatively recent changes have substantially increased this complexity. This is particularly true in the case of the European Union, as will be explained below. Because of this, this paper takes a predominantly European focus, but it should be stressed

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Table 1 Problems related to the transmission grid. Strategic (over 10 years)

Tactical (several months to 10 years)

Operational (from one day to one month)

Liberalized Network Activities

Merchant line investment

Transmission rights trading

Centralized Network Activities

Evaluation of transmission investments (particularly, interconnections) Evaluation of the impact of TEP on market agents Transmission Expansion Planning

Valuation of transmission rights and network contracts Network contracting Network adequacy assessment

that most of the issues described apply to other regions in a more general way. 2.1. Deregulation The deregulation of the power sector has meant that Generation Expansion Planning (GEP), which was once centrally performed, is now a decision taken privately by the companies participating in the generation market [9]. This is especially important considering that, while building a power plant can take around one to three years for some technologies, transmission projects have a much longer lead-time (see Section 2.5). Therefore, TEP must anticipate generation investments, but there is no longer a binding, coordinated generation expansion plan that can guide transmission decisions. In addition, there are new objectives of transmission expansion that have been brought by deregulation, the most important one being facilitating competition. 2.2. Renewable penetration The European Union has set aggressive targets for greenhouse gas (GHG) emission reductions [4] that should lead to large amounts of renewable generation being installed in the coming decades. A large part of this new generation will be installed in the areas were its resource (namely, wind and solar) abounds. This often coincides with relatively remote areas for which connection capacity to the bulk system should be either reinforced or built altogether. A particularly good example of this is offshore wind, which requires the greenfield design and construction of a new transmission system from the plant to the onshore grid. In addition, an important part of this generation will be noncontrollable, which brings additional problems to the operation of the system. When performing TEP, several operation situations should be considered when assessing the possible benefits of network reinforcements—an average scenario is not sufficient. Moreover, long-distance flows are needed in order to export any excess generation or provide a backup when renewables are not available. This means that the transmission network should increase the connection capacity between different zones in order to even their unbalances. 2.3. Large-scale generation projects Usually in relation to renewable, there is currently a wide arrange of extremely ambitious projects that contemplate the installation of large amounts of new generation capacity, such as Desertec or Medgrid, described in Section 3. These schemes extend across borders and require large transmission investments in order to support the long-distance flows they would cause.

Network maintenance Network cost allocation Determination of payments for network use

Introduction of network constraints into the economic dispatch Determination of nodal prices and losses Network operation

2.4. Market integration and regional planning The European Union established three main objectives in its energy policy: affordable and competitive pricing, sustainability and reliability. It has been said that “A well integrated internal energy market is a fundamental pre-requisite to achieve these objectives in a cost-effective way. “The fundamental rules for this market are set out in the Internal Market in Electricity Directive [10]. One of the main obstacles to the creation of the internal electricity market is the lack of sufficient interconnection capacity among the Member States. It is necessary to study how to increase this connection capacity in a cost-efficient way, therefore performing TEP at a joint level. This is the aim of the ten year network development plan, described in Section 3. 2.5. Long permitting processes Building a new transmission line requires licenses that, in Europe, are increasingly difficult to obtain. Growing concerns about environmental impact, together with aesthetic considerations, are responsible for some of the public opposition that can stop a license process. In addition, the negotiations to expropriate the right-ofway where the line will be physically built can take several years. All together, this means that, quite often, ten years will pass before construction can be started—and, in some cases, the license can be even denied, so that construction never starts at all. This increases the impact of general uncertainty, as there will be a 10-year long evolution of the system before the benefits derived from a new transmission line start to be collected. The issues described above have a double effect on TEP decisions: • Increasing the size of system under optimization, from countries to regions. This has two main consequences. Very straightforwardly, the size of the problem grows. This means that any optimal TEP implementation should be either able to deal with very large problem sizes or apply reduction techniques to the original system. In addition, the fact that planning is performed at a regional level means that the expertise of individual TSOs on identifying interesting transmission lines for their relevant areas is not necessarily accurate when identifying lines that stretch across wider regions. This leads to more emphasis on automatic methods that are independent from the planner’s experience. • Extending the scope of uncertainty in the form of different operation scenarios that should be taken into account due to the non-controllable nature of some renewable power or, in a wider sense, to the future of generation expansion.

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These challenges lead to transmission expansion problems that are increasingly difficult to solve, and that should be treated carefully. This paper aims at reviewing the work that has been done to solve the TEP problem, both in practice and in the literature, from the perspective of these challenges. The next section summarizes some recent TEP practice. It starts with a general idea of the regulatory regimes that define it from a global perspective. After that, we review some of the most interesting TEP projects that have been undertaken in the recent past, this time, with a European focus.

3. Transmission expansion planning practice Most regulations acknowledge that only centralized planning results in building all necessary transmission investments. In the most followed approach, the Transmission System Operator (TSO) proposes plans that the regulator later approves, possibly introducing competitive bidding to assign their construction. Alternatively, the regulator can award transmission licenses to private companies and consider them a monopoly. Usually, these companies are remunerated based on reliability indices, so that they are incentivized to invest in the network to guarantee the reliability of supply. In some cases, we can find examples of decentralized TEP, which is not intended to substitute but rather to complement centralized planning. Mixed planning is developed as a collaboration between market agents and regulatory institutions. For instance, coalitions of users can propose reinforcements that the regulator can later approve. The remuneration of the project can either be regulated or bear the risk of investment—the so-called merchant lines. An exhaustive review of the regulation of the transmission activity and these regimes can be found in reference [11]. Particularly interesting examples of decentralized planning can be found in South America. In Argentina, the National Regulatory Authority (ENRE) determines whether the transmission projects proposed by different parties will bring enough benefits to the system. The beneficiaries of the project are identified and, if a highenough part of them agrees to build the project, they pay for its cost in proportion to their anticipated benefit. In Peru, groups of users can propose projects that will be built if they are approved by the regulator. In Chile, TEP is performed in a co-operative way by the National Regulatory Authority (NRA) and the users of the system, which submit the future scenarios and projects that the NRA considers when determining the future expansion plan. A more detailed description of South-American experiences can be found in Ref. [12]. In Europe, merchant line projects can be authorized by the Agency for the Cooperation of Energy Regulators (ACER) [13]. So far, several interconnectors have been built, such as BritNed (between the UK and the Nederlands), Estlink (between Estonia and Finland) or the East–West Cables (between Ireland and the UK). In the United States, merchant line projects can also be built with the permission of the regulator. We can find examples like the privately-owned line from Sayreville to Newbridge or Path15 in California [14]. In Australia, Basslink stretches between Tasmania and Victoria. Previously, Directlink and Murraylink were also built as merchant lines but have been converted into regulated interconnectors. It has been acknowledged that regulating the construction and exploitation of these merchant lines entails considerable challenges [15]. Although merchant lines can be interesting in some cases, mainly for the development of high-risk investment projects, they can only be considered a complement to national-wide central planning. Moreover, there are some examples of planning that extend across borders for cross-national, regional planning, with some relevant examples in the European Union. This type of projects presents a special interest given the current trends in the

integration of markets. The rest of this section is dedicated to presenting some pertinent examples along these lines. 3.1. The TYNDP (ten year network development plan) (2014, every 2 years) The European Union’s Third Energy Package was proposed by the European Commission in 2007 and adopted in 2009. One of its core elements is unbundling, which stipulates the separation of the different activities related to the power system, in particular, of the ownership and operation of the transmission network. Most of the network extensions are decided at a national level by the relevant TSO, which according to Directive 2009/72/EC should ensure “the long-term ability of the system to meet reasonable demands for the transmission of electricity” [9]. In addition national TEP, the TYNDP performs European-wide planning. It is carried out by ENTSO-e (the European Network of Transmission System Operators). The TYNDP is an analysis of the electricity grid development in the coming 10 years and is performed every 2 years. As a previous evaluation of the necessary grid reinforcements, the main transmission bottlenecks are identified—around 80% of these bottlenecks are related to RES integration. The bottlenecks are used to propose relevant grid reinforcements, but candidates lines can also be submitted by 3rd parties (non-ENTSO-E members). These candidates are then evaluated under different scenarios, which describe combinations of two drivers: GHG emission reductions and the degree of European market integration [16]. The TYNDP develops an extensive evaluation of the proposed grid reinforcements according to several evaluation criteria (increase in grid transfer capacity, socio-economic welfare, RES integration, improvement of security of supply, losses variation, CO2 emissions mitigation, flexibility or costs [17]. This process is limited in the sense that candidate projects are proposed manually, assessed individually, and no optimization is performed. Other projects have tried to overcome these limitations in the European region, as shown below. 3.2. E-Highway (from 2012) Project E-Highway is a 7th Framework Program (7FP) project aimed at developing a methodology for Pan-European TEP from 2020 to 2050. Its objective is to guarantee a reliable delivery of renewable electricity as well as pan-European market integration. The project will result in a modular development plan for possible electricity high-ways and options for a complete grid architecture, based on various future power system scenarios [18]. The approach followed in the project builds comprehensive scenarios and tests the proposed grid architectures in a multi-criteria setting. In addition, a Work Package 8 is responsible for developing an alternative TEP methodology. The proposed method involves reducing the network to an equivalent system that keeps the same grid limitations as the original one. Candidate investments are proposed automatically [19] and selected by optimization. The results of this project will be available in 2016. 3.3. Desertec (from 2009) Desertec is an initiative proposed by a German-led consortium of companies that aims at installing a large amount of renewable generation (10 GW in 2030 and over 20 GW in 2050) in the Sahara desert and its surroundings. This renewable power would be predominantly solar (photovoltaic and concentrated solar power), with a part of this energy being exported to Europe. In order to be able to support these long-distance power flows, new transmission lines would be built. The proposed transmission investments are the result of an optimization process that focuses on an extensive use of HVDC (for instance, planning for more than 200 km of

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undersea cables). The cost of these transmission investments is taken into account in the economical evaluation of the project [20]. 3.4. MedGrid (from 2010) MedGrid is another project, French-based, that contemplates the exploitation of the renewable potential of the Mediterranean region in a coordinated way, installing over 20 GW of new capacity mostly in North Africa and supporting energy exchanges among the Mediterranean [21]. More than 5 GW of this new capacity would be exported to Europe. The consortiums Desertec and MedGrid are working together to promote an interconnected European supergrid. 3.5. RealiseGrid (2007–2013) RealiseGrid was 7FP project with the objective of promoting an optimal development of the European trans-national transmission grid infrastructure. It accounts for a wide range of uncertainties, considering many issues associated to a deregulated market (such as bidding strategies) and develops extensive economic, social and environmental assessments. Transmission expansion reinforcements are identified by welfare maximizing, engineering and market criteria. After identifying a broad group of possible reinforcement solutions, a cost-benefit analysis is carried out to compare and rank the selected options. No optimization is performed and the investments are only considered in isolation [22]. 3.6. Irene-40 (2008–2012) Irene-40, another 7FP project, created an infrastructure roadmap for energy networks in Europe with a focus on electricity. It analyses future scenarios of electricity generation, consumption and market models, identifies weak network points and elaborates grid development strategies and a roadmap for investment strategies accounting for the different interests of stakeholders. The project develops an extensive review of existing electricity generation and consumption scenarios [23,24]. More detailed scenarios are developed for the three regions of interest: North-Sea, The Iberian Peninsula and Greece. They identify problem areas by using simulation, together with expert knowledge from TSOs or documents such as the Priority Interconnection Plan [25]. The candidate investments are filtered according to investment and operation cost and their impact on reliability. No optimization is performed and the investments are only considered in isolation. 3.7. Offshore grid (2009–2011) The Offshore Grid project is a techno-economic study funded by the EU’s Intelligent Energy Europe (IEE) program. It is an in-depth analysis of a meshed offshore grid in Northern Europe (Baltic, North, Irish Seas) from a comprehensive perspective, addressing technical, economic and policy issues. In pursuit of the optimal offshore grid configuration the study performs a optimal TEP based on detailed generation data, market and grid power flow modeling and infrastructure cost modeling. Wind power evolution is based on EWEA (European Wind Energy Association) offshore wind scenarios [26] and TradeWind onshore wind scenarios [27]. The infrastructure cost model is also based on scenarios. In addition, ensitivity analysis is used to assess robustness against a changes in interconnection capacity, distance to shore or price differences between countries. 3.8. WindSpeed (2009–2011) WindSpeed (SPatial Deployment of offshore WIND Energy in Europe) was funded by the IEE program. The project presents a

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development pathway up to 2030 to integrate large offshore wind capacity in the Central and Southern North Sea (Belgium, Denmark, Germany, the Netherlands, Norway and the UK). Some guidelines and candidate areas for offshore power location are established and a grid configuration is obtained with a simplified optimal TEP model. 3.9. SUSPLAN (2008–2010) SUSPLAN (PLANning for SUStainability) is a 7FP project that develops a set of guidelines for the integration of renewable energy sources (RES) into future infrastructures (electricity, gas and heat) in Europe. These guidelines are established on the basis of regional and trans-national studies in the time perspective of 2030–2050. It addresses the problem of the necessary grid infrastructure expansion in order to allow an economically efficient integration of RES. Since 2030 is the starting point of the considered time horizon, the plan builds a transmission system evolution in Europe based on the data contained in several public sources [28–30]. Four scenarios are used to model the broad range of uncertainties, derived from the combinations of two drivers, technology development and public attitude. Within each scenario, the distribution of generation is determined, and TEP is carried out by identifying bottlenecks in interconnection capacity between countries. An additional set of transmission lines, in particular, HVDC links, are defined by experts. No optimization is performed and the investments are only considered in isolation. 3.10. Roadmap 2050: A practical guide to a prosperous, low-carbon Europe (2013) The Roadmap 2050 is a study performed by the European Climate Foundation aiming to assess the feasibility of an 80% GHG emissions reduction in Europe by 2050, which implies a 95% GHG reduction in the power sector without degradation in reliability. They consider different scenarios that describe several possible mixes of fossil fuels with Carbon Capture and Storage (CCS), nuclear and RES. The share of Renewable Energy Sources (RES) by 2050 in each scenario is: 40%, 60% and 80%, respectively. They include proposals for transmission expansion for each of their scenarios. An extensive sensitivity analysis is developed to assess the robustness of the externally-defined transmission expansion plans and to understand their main cost drivers. The analysis considers the impact of extreme weather conditions, different RES portfolios and several possibilities for the operational flexibility of RES. These projects face the challenges described in Section 2., which revolve around the consideration of large problem sizes and vast uncertainties. The literature must respond to these challenges. The next sections present an updated review on TEP. First, we review the different modeling options in the problem. After that, we present the solution methods that have been used to tackle it. These different options are discussed throughout the text so that the reader can use this document as a guide to select the most suitable option for his particular problem. 4. Modeling TEP Transmission expansion is by nature a multi-stage problem where the planner takes decisions at several time horizons. In addition, the expansions have an impact not only on the operation of the system but also on other factors such as its dynamic behavior or market power. The literature adopts different perspectives with respect to the inclusion of these effects, taking a wide spectrum of simplifying assumptions. This section reviews the most important modeling decisions in TEP and discusses their most reasonable

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scope of application. For the sake of convenience, these discussions have been added at the end of each subsection. 4.1. Just transmission? In certain contexts it might be reasonable to undertake Generation Expansion Planning (GEP) and TEP in a joint manner. In deregulated markets it is not possible to establish a centralized generation expansion plan and generators make individual decisions based on price signals. However, even if it cannot be implemented directly, the joint strategic planning of TEP & GEP can give important insights about cost-effective designs, particularly with respect to the efficient allocation of regional renewable generation targets. This has motivated some authors to deal with the two problems simultaneously [31–33]. Therefore, depending on the case it might be worthwhile to include GEP in the problem. 4.2. Treatment and scope of uncertainties As explained above, the large renewable generation capacity that is anticipated for the coming decades has increased dramatically the relevance of incorporating uncertainty into the planning process. The main tools applied for the treatment of uncertainties in transmission expansion are: • Stochastic optimization, which incorporates random uncertainties directly in the decision process to optimize expected objective value [34–37]. Ref. [38] quantifies the cost of ignoring uncertainty instead of solving the stochastic problem. Ref. [39] applies chance-constrained programming to the TEP problem. • Robust optimization and other related techniques focus on a worst-case scenario analysis and can minimize maximum regret [40–42]. • Fuzzy decision analysis deals with the outcomes of different scenarios in an analogous way to the multiple attributes defined in a multi-criteria problem. It identifies non-dominated solutions and works with the decision maker to analyze the relative importance of the objectives [43,44]. Along these lines, probabilitistic power flow [45] and fuzzy power flow tools [46] have also been applied. Many works have focused on deterministic forecasts, ignoring uncertainty. Among the works that do, the most commonly studied uncertainties are generation expansion and generation costs. Among the most commonly incorporated risks (this is, short-term uncertainty that can be modeled with a probability distribution, we can find demand, hydro inputs, renewable energy production or element failures. The latter leads to the inclusion of reliability, which is one of the main objectives of transmission expansion. The N-1 criterion (which considers the failures of single components) is often used [34,47], although alternatively the planner can define the list of contingencies that will be considered, possibly of several elements at once. Meeting demand in these defined contingencies can be included as a hard constraint, although it is also possible to include the different contingency scenarios in a probabilitistic setting, so that penalties for Non Supplied Energy (NSE) are weighted by contingency probability. As an alternative to building a list of contingencies, it is also possible to sample them with Monte Carlo approaches [48]. The inclusion of uncertainty can lead to substantially transmission plans. Therefore, as long as its incorporation does not result in an unmanageable problem, the main sources of uncertainty should be indentified and included. It is reasonable to treat risks using stochastic optimization; the repeated occurrences mean that

positive deviations offset negative ones, so that optimizing the expected value is a sensible strategy. If necessary, risk measures such as Value-at-Risk (VaR) or Conditional Value-at-Risk (CVaR) can be used as the optimization objective or be assigned bounds through a constraint. Long-term uncertainties, on the other hand, might be better approached with robust optimization or fuzzy decision analysis. For instance, in cases such as GEP, there is no possibility for compensation among scenarios. In these cases, minimum-regret approaches can be more reasonable.

4.3. Decision dynamics TEP is a multi-stage problem that implements long-term decisions in discrete phases, with clear milestones where it re-evaluates decisions in the light of the revealed uncertainties. However, the complexity of this dynamic nature has lead most studies to focus on simplifications of the problem: • Static: A vast majority of research studies consider only one snapshot of the future system at a particular moment. This is known in the literature as the Static Transmission Expansion Planning problem (STEP) [49–51]. • Sequential static: Widely used, it consists in modeling several time horizons, taking into account that any investments made will be available from their deployment date to the end of the planning scope. Sequential static planning can be carried out forward (moving in time from the closest to the furthest time horizon) or backward (starting with the final year and moving towards the present) [34,52–54]. • Dynamic planning: It keeps the full dynamic complexity of the problem. Given the computational complexity associated with this option, most research has focused on very small case studies or used heuristic methods [37,55]. Some authors have suggested that TEP can be a promising area for the use of real options theory [56,57]. Static planning is the most reasonable approach when dealing with short time horizons where decisions are not going to be revisited. For longer time horizons, dynamic planning fits more closely the reality of the problem but it cannot be implemented in real problems due to size. Sequential static approaches are more suitable in these cases.

4.4. Market considerations Most works carry out centralized TEP with centralized costbased operation, even in liberalized generation markets [49,58]. In cases where the focus is the medium-term expansion of the system, some references consider centralized TEP in a competitive generation market [43,59]. Ref. [60] presents a sophisticated approach where both competition and uncertainty are incorporated to the GEP problem. Finally, there has been some work done on decentralized expansion [61–63] and the impact of coalitions [64]. The inclusion of market considerations increases complexity considerably, but can support more realistic theoretical results. However, its advantages are limited in practical TEP studies given this complexity and the fact that the long time horizons make it very difficult to build reasonable assumptions on future market structure and behavior. It therefore seems that including competitive behavior is reasonable only when the focus of the study is competition specifically.

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4.5. Mono vs. multi-criteria studies TEP is by nature a multi-criteria problem although most approaches regard cost as the only objective included in the optimization, even if several factors are taken into account within the definition of aggregated cost. These factors usually include: • Investment cost of the transmission assets added to the network. • In a centralized operation context: • Operation cost, defined as the average generation cost across scenarios. • Adequacy penalties, introduced to avoid solutions where demand is not satisfied in normal operating conditions. For some of the simplest studies, the only objective considered is investment cost, but restrictions on adequacy are imposed to ensure acceptable service levels. • Expected Energy Not Supplied (EENS) and other reliability indices penalize plans with a poor behavior under system contingencies. • In a generation market context: • Aggregate social welfare is the main objective considered. It can incorporate elements for the objectives described above, such as EENS penalties. • Facilitating competition. In addition, other relevant objectives are social acceptance of new corridors, environmental impact, renewable generation integration, congestion cost reduction, impact on system stability and geopolitical risk. Most of the reviewed works limit their focus to a single objective that integrates the attributes considered. Within a multi-criteria context, the most widely used tools are Fuzzy Decision Theory [37], Goal Programming (GP) [65] and Analytic Hierarchy Process (AHP) [66]. Any TEP study should include at least investment and operation cost, plus some considerations of reliability. When there is a market focus, other objectives such as facilitating competition should be added as well. The method to consider these objectives should be chosen depending on the availability of information about the decision maker’s preferences. When the relative importance of the objectives are clear, it is easy to define weights and therefore using one aggregate objective is the simplest and most suitable model. On the contrary, when the tradeoffs are not obvious, multicriteria methods are generally more adequate. 4.6. Level of detail on the operation of the system The literature presents different levels of detail in the technical description of the system. In particular, TEP models have a longterm focus that usually results in neglecting medium-term effects such as hydrothermal coordination or short-term constraints like ramps. Most of the details on system operation therefore refer to the description of the power flows The main options that appear in the literature are: • Transportation models, which only take into account Kirchhoff’s First Law (energy/power conservation). This model is normally too simple to generate viable transmission expansion plans. However, using such a simple model reduces the computational requirements of the optimization [67]. Therefore, they can be appropriate either in very large problems that cannot be solved otherwise or as a pre-process to other, more sophisticated approaches. • DC power flow models (DCPF), which consider Kirchhoff’s First Law and a linear version of the second one (voltage balance),

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where angle differences are calculated as the flow across the line divided by its reactance. Hybrid models consider the Second Law only in existing lines. These linear models can only assess losses in an approximate way, and are unable to incorporate stability considerations. They offer a good compromise between modeling detail and computational requirements, and therefore have been extensively applied [68,69]. • The AC power flow (ACPF) is the only model that is capable of incorporating voltage or stability considerations, as well as an accurate evaluation of losses. However, the demanding computational requirements that arise from its nonlinearity mean that it has not been usually applied in optimal plan searches but rather in the evaluation of proposed solutions [70]. The simplicity of the transportation model seems to be unjustified in most real applications. The ACPF is usually too complex to be integrated in an optimal TEP model, but should nonetheless be used to evaluate the solution plan in detail. The DCPF offers a good approximation at a low computational cost and is therefore the preferred option for optimal TEP as reflected in the literature. 4.7. Consideration of special elements Special elements are becoming increasingly relevant in the transmission system: • High-Voltage Direct-Current (HVDC) links are interesting alternatives for long-distance connections, as they avoid the voltage drops created by their AC counterparts. For this reason, they are usually considered the basic building block of a supergrid that would allow large power transfers across long distances. They have been considered in works such as references [57,71–73]. • FACTS (Flexible Alternating Current Transmission Systems), such as Phase-Shifting Transformers (PSTs) or reactive power compensation, can be very useful tools to alleviate some congestions in the system without resorting to an increase in connection capacity [57]. Special elements are becoming more and more relevant. HVDC links offer considerable advantages for long-distance connections or in offshore or underground settings. If the TEP problem under study aims at studying offshore locations or wants to keep the potential for supergrid investments, including HVDC becomes a necessity. FACTS, on the other hand, are interesting when phenomena such as loop flows are relevant. In these cases, PSTs can alleviate congestions at a lower cost than introducing new transmission lines. 5. Solving the TEP problem This article proposes to classify the different solution methods that have been applied to TEP into two main families of approaches: interactive (this is, requiring intervention from the planner) and automatic. Within the automatic techniques, we distinguish between searches by the application of heuristic rules and optimization. This section discusses the main choices and works in this area, and adds a discussion on the most suitable area of application of these techniques. A summary of this can be seen in Table 2. 5.1. Interactive search approaches Traditionally, TSOs have undertaken TEP in a heuristic way that incorporates their experience into the planning process. They usually follow an iterative search that combines a planning module

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Table 2 Solution approaches to TEP.

and an operation module. The planning module is aimed at identifying specific reinforcements to be made to the network. These preliminary expansion decisions are proposed by the TSO based on information calculated by the operation module. The operation module evaluates the performance of the system considering the network architecture resulting from the reinforcements proposed by the planning module. The performance of the proposed reinforcements is assessed according to an agreed set of criteria. The economic dispatch subject to at least the most relevant technical constraints should be incorporated to this calculation. If the proposed network expansion plan generates any technical infeasibilities at the operation stage, they should be tackled depending on their importance. Small and easily solved infeasibilities are corrected by means of minor modifications to the expansion plan. More important infeasibilities are reformulated as constraints that are added to subsequent iterations of the planning module. The most fundamental advantage of this technique is its relative simplicity and ease of use and the fact that it integrates the planners’ experience. This means that this approach and variations on its basic description are the most widely followed in national and regional TEP. Implementations of interactive search approaches can be found in references [74,75]. 5.2. Automatic planning approaches Automatic methods rely on an agreed set of optimization criteria or expansion rules with no further requirement for human intervention. However, they can be included as a step within the planning module of an interactive planning approach, for instance,

to generate relatively good expansion proposals that will be subsequently evaluated in the operation module. These approaches are the ones that appear in most of the academic literature. Within automatic methodologies, two types of methods should be distinguished: • Automatic searches based on heuristic rules apply some predetermined actions in order to improve the existing network. This approach cannot guarantee optimality. • Optimization methods provide with the best possible expansion plans according to the established criteria.

5.2.1. Automatic searches based on heuristic rules Automatic searches rely on a set of pre-defined rules that are applied to generate a suitable expansion plan. There is no a-priori guarantee of the goodness of the final solution or the soundness of the rules applied. However, the relatively simple layout of these tools compared to optimization allows including a high level of modeling detail. The application of rules to guide the expansion is also widespread. Particularly, greedy local searches directed by sensitivity analyses are rather popular [76,77]. In addition, Expert Systems can extract expansion rules by generalizing information from a set of sample systems [78]. This technique generalizes the behavior of smaller systems and, therefore, can miss effects and structures that arise only in larger systems. Notably, although this method might detect suitable reinforcements, it might miss large supergrid investments, resulting in suboptimal solutions. This risk increases with the size of the area under study [19].

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5.2.2. TEP by optimization Optimization has been extensively applied to TEP, mainly in academic contexts, so we can find a large array of classical and non-classical approaches that have been applied to TEP. 5.2.2.1. Classical methods. • Linear Programming (LP). The first papers that formalize the TEP problem did so from a perspective of linear programming (LP), where efficient simplex-based algorithms could find optimal solutions in affordable times for the computers available [67]. These approaches ignore the discrete nature of investment (a line of a certain type can be built or not, but it is not possible to build a fraction of a line). This avoids the computational burden of integer variables. Linear formulations can accommodate transportation power-flow models. In addition, most of these works consider only deterministic forecasts for the uncertainties involved and focus on finding optimal plans for those. These simplifications are still useful in a context where the problem is too large to use a discrete model or an approximately solution is good enough. The latest case can include a pre-process aimed at finding a relatively good solution that will be used as starting point for a more sophisticated method. • Quadratic Programming models approximate losses as resistance times the square of the intensity calculated from a DCPF. This model can be found in references such as [72]. • Mixed-Integer Programming (MIP) acknowledges the discrete nature of investment (a transmission line can either be installed or not). This technique can deal appropriately with a DCPF. It is probably the most widely used approach within the classical methods [79,80]. If a stochastic description of uncertainty is used, the application of stochastic optimization techniques can considerably accelerate the process. This has prompted the appearance of studies based on stochastic decomposition such as Benders’ decomposition [68,81], column generation [82], or Lagrangean Relaxation [53]. Ref. [67] compares alternative decomposition approaches. • In a handful of cases, Non Linear Programming (NLP) and MixedInteger Non Linear Programming (MINLP) have been used to accommodate the nonlinearities of an ACPF [83]. However, in most cases these refer to the evaluation of a proposed solution rather than to the search of an optimal expansion plan [65]. 5.2.2.2. Non-classical methods. Metaheuristic algorithms improve a solution iteratively, usually including some form of random evolution: • GRASP (Greedy Randomized Adaptive Search Procedure) consists of iterations made up from successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search [69]. • Tabu Search avoids already visited directions by adding them to a restricted or tabu list [84]. • Genetic Algorithms replicate the principles of Darwinian evolution to solve optimization problems. They are currently a widely popular approach when solving combinatorial problems. This has been reflected in TEP applications [85]. • Simulated Annealing draws a parallel between the thermodynamical evolution of a slowly cooling system and the optimization process [86]. • Swarm intelligence mimics the collective dynamics of selforganized systems [87]. • Ant Colony Optimization is a particular application of these principles [88].

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• Differential Evolution improves a solution pool by combining candidates among them [47]. • Constructive Heuristic Algorithms refine solution proposals locally [89]. • Artificial Immune systems focus on mutation rather than recombination processes [90]. • Ordinal Optimization exploits the lower computational requirements of finding relatively good solutions as opposed to a single optimal one [91,92]. • General artificial intelligence techniques such as Artificial Neural Networks have been also been incorporated to TEP studies [55]. • Other relatively little-known algorithms add diversity to the landscape of techniques that have been used in TEP. Examples of this are invasive weed optimization [93], random leap frog algorithms [94], path relinking [95], mosquitoes mating strategies [96] or hybrids of previously presented approaches [97]. 6. Discussion Interactive approaches have been traditionally applied in most countries. This is the case because they are simple to implement and can integrate relatively sophisticated models in their operation module—for instance, a detailed ACPF. However, the current context calls for methods that do not rely on the planner’s expertise to propose the candidate investment plans. In the same spirit, the larger the area in scope, the larger the potential benefits that can be missed if a suboptimal solution is adopted. Therefore, optimization is needed in order to guarantee a suitable expansion plan. However, the size limitations of optimization methods mean that the plan (or set of plans) obtained must still be evaluated with respect to more detailed objectives that could not be included in the model. Thus, it seems like the most reasonable approach in the current context is to integrate optimization methods within the planning module of an interactive approach. On the other hand, the selection of an optimization technique depends also on the size of the problem, which results from the compound effect of the required level of modeling detail and the size of the network. The latter can vary from tens of nodes in academic case studies to thousands in real systems. Within the classical methods, LP can accommodate the largest case studies, with MIP offering a relatively good compromise and MINLP being too consuming even for small planning problems. This prompted the application of non-classical, heuristic methods that trade off global optimality (that is, they offer only relatively good solutions rather than optimal ones) but are able to deal with large sizes at affordable computation times, with the added advantage of being able to incorporate any level of modeling detail. However, the risk of arriving at suboptimal solutions grows as the size of the problem increases. It is possible to reduce the size of an existing system to a manageable one by applying network reduction techniques that build an equivalent, reduced system that behaves as close as possible to the original one [98]. These reduction approaches can enable the application of an otherwise too resource-consuming method to a network that would be, in principle, too large for its application. However, the expansion plans obtained for the reduced network must be interpreted appropriately in order to apply them to the original system. 7. Conclusions TEP is one of the key strategic decisions in power systems and has a deep, long-lasting impact on the system as a whole. In addition, recent trends have increased considerably the complexity and relevance of this problem. This paper analyzes these challenges

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and identifies, as the main issues faced in a European context, the following factors: deregulation, renewable penetration, large-scale generation projects, market integration and regional planning and long permitting processes. This leads to large problems that need efficient solution methods and to an increasing importance of the uncertainties. These challenges have been illustrated with an array of projects, from the Ten-Year Network Development Plan to ambitious initiatives such as Desertec or Medgrid. From this perspective, the main works in the literature are studied and classified, with a special emphasis on the most recent works. The main modeling choices have been identified. The importance of including uncertainty in the analysis with appropriate tools has been stressed, together with a suitable tradeoff for the decision dynamics or the details of the power flow considered. In addition, the increasing relevance of technologies such as HVDC or PSTs has been discussed. The existing approaches to TEP resolution have been classified as interactive and automatic. Automatic approaches have been described as based on heuristic rules or on optimization, which can in turn be classical or non-classical. A combination of interactive planning and optimization has been proposed as the most suitable solution to getting the advantages of both, also highlighting the increasingly relevant role of network reduction techniques. This catalogue of recent practice and academic literature, together with the discussions in this paper, will hopefully serve as a starting point for researchers or practitioners working on this topic.

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