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NEP is one of the main strategic decisions in power systems and has a deep, long-lasting impact on the operations of the system. Relatively recent developments in power systems, such as renewable integration or regional planning, have increased the complexity and relevance of this problem considerably. Market integration is the current paradigm to achieve a competitive, sustainable and reliable electric system and the network is a facilitator in this process. This is particularly true in the case of the European Union. These challenges EU. The design of large-scale network expansions poses considerable challenges that have been addressed in a vast array of both projects and papers. Thorough reviews of the academic literature academic literature. Existing thorough academic reviews on this topic can be found in references [11, 12, 13]. These works are a very good starting point to understand the state of the art of the network expansion planning challenges and current approaches.

Among the current challenges to be addressed for the network expansion planning we can mention the following ones:

- Its coordination with GEP, as discussed previously. On the one hand, GEP is a deregulated business activity while NEP is mostly regulated. On the other hand, generation investments can take around three years, while network expansion need to be anticipated longer periods.
- Renewable integration is one of the major drivers for investing in new transmission lines. Onshore and offshore wind power, and solar generation are renewable technologies currently being developed at large scale to meet the low-carbon electricity generation targets. A large part of this generation is located in remote areas far from the load centers requiring transmission reinforcements or new connections. Besides, the intermittent nature of these renewables introduces operational challenges and, from the network planning point of view, many varied operation situations should be considered.
- Market integration is the current paradigm to achieve a competitive, sustainable and reliable electric system and the network is a facilitator in this process. The creation of an European internal market with strong enough interconnection capacity among the member states increases the scope of the planning process, from a national activity to a European scale.

Different mathematical optimization techniques are used for solving the network expansion planning. They can be classified as: classical and non-classical (metaheuristic) methods see references [12, 13].

- Classical methods include linear, nonlinear and mixed integer programming methods. Linear optimization ignores the discrete nature of the investment decisions but still it can be useful is system is too large to be solved with discrete variables or a relaxed solution is good enough. A transportation or a direct-current (DC) load flow fit in this linear formulation. Nonlinear, in particular quadratic, models appear as a way to represent transmission losses. Finally, mixed integer optimization allows considering the integer nature of the decisions. If stochasticity in some parameters is included then models become stochastic and, therefore, decomposition techniques should be used for large-scale systems. Among them, Benders decomposition, Lagrangean relaxation or column generation are frequently used see also the references listed in the section DNEP.
- Non-classical metaheuristic methods include Greedy Randomized Adaptive Search Procedure (GRASP), tabu search, genetic algorithms, simulated annealing, swarm intelligence, ant colony optimization, differential evolution, ordinal optimization, etc.

Network expansion planning is per se a multicriteria decision problem although frequently a single objective function is used by combining and monetizing the multiple criteria under a single one with the weighted-sum method. The main criteria are usually: costs, environmental impact, market integration and other exogenous factors. Costs are measured by the attributes such as investment and operation costs of the transmission decisions but also operation costs of the system. In the cost criterion, it can also be introduced the reliability impact. Environmental impact is determined by attributes as amount of renewable integration or curtailment avoided at system level and impact of the line construction. Market integration is accounted as number of hours of market splitting. Social acceptance is an exogenous criterion and, nowadays, is a major concern of the current planning process and being the cause of many delays.

### Model

A wide variety of models and the corresponding mathematical optimization techniques are used in solving the network expansion planning. Initially, models can be classified as either linear, non-linear, mixed integer linear (MILP), or non-linear (MINLP). Linear models, often based on transportation or direct-current (DC) load-flow, ignore the discrete nature of the investment decisions, but can be useful as an approximation. Nonlinear models, often quadratic, represent transmission losses, but still usually ignore the discrete nature of the investment decisions. MILP approaches allow for the integer nature of the investment decisions to be considered, but are restricted to an approximation of the non-linearity, either using piece-wise linearisations, or linearisations including the DC and transportation load-flow. If stochasticity in some of the parameters is considered, then models may become stochastic challenging to solve already, and decomposition techniques are often used for large-scale instances. Finally, one may consider the the full MINLP model: there, both the discrete and non-linear features of the problem are modelled faithfully, but the problem is challenging.

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We refer to [2,3,4,7,11,12,13] for detailed surveys. See [14] for an illustration of the impact of security of transmission constraints, [8] for an example of the impact of the choice of model (AC vs. PWL vs. DC), and [17] for an example of the impact of the uncertainty. Within multi-stage approaches, there are very well-developed decompositions [1], and for a pro-active Transmission Expansion Planning model by considering related Gencos generation capacity expansion planning.

### Software

Within two-stage approaches, there is a long tradition of work on decomposition methods [2,9], although even a monolithic scenario expansion may be tractable [6,15,6], when AC and security of transmission constraints are ignored and the model of the network [15] is sufficiently coarse. The incorporation of market considerations [10,11] complicates matters considerably.

#### References:

[1] S. Ahmed, A. King, G. Parija, "A Multi-Stage Stochastic Integer Programming Approach for Capacity Expansion under Uncertainty," Journal of Global Optimization, Vol. 26, pp. 3–24, 2003.

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