Driven by several techno-economic, environmental and structural factors, the electric energy industry is expected to undergo a paradigm shift with a considerably increased level of renewables (mainly variable energy sources such as wind and solar), gradually replacing conventional power production sources. The scale and the speed of integrating such sources of energy are of paramount importance to effectively address a multitude of global and local concerns such as climate change, sustainability and energy security. In recent years, wind and solar power have been attracting large-scale investments in many countries, especially in Europe. The favorable agreements of states to curb greenhouse gas emissions and mitigate climate change, along with other driving factors, will further accelerate the renewable integration in power systems. Renewable energy sources (RESs), wind and solar in particular, are abundant almost everywhere, although their energy intensities differ very much from one place to another. Because of this, a significant integration of such energy sources requires heavy investments in transmission infrastructures. In other words, transmission expansion planning (TEP) has to be carried out in geographically wide and large-scale networks. This helps to effectively accommodate the RESs and optimally exploit their benefits while minimizing their side effects. However, the uncertain nature of most of the renewable sources, along with the size of the network systems, results in optimization problems that may become intractable in practice or require a huge computational effort. Thus, the challenge addressed in this work is to design models, strategies and tools that may solve large-scale and uncertain TEP problems, being computationally efficient and reasonably accurate. Of course, the specific definition of the term “reasonably accurate” is the key issue of the thesis work, since it requires a deep understanding of the main cost and technical drivers of adequate TEP investment decisions. A new formulation is proposed in this dissertation for a long-term planning of transmission investments under uncertainty, with a multi-stage decision framework and considering a high level of renewable sources integration. This multi-stage strategy combines the need for short-term decisions with the evaluation of long-term scenarios, which is the practical essence of a real-world planning. The TEP problem is defined as a stochastic mixed-integer linear programming (S-MILP) optimization, an exact solution method. This allows the use of effective off-the-shelf solvers to obtain solutions within a reasonable computational time, enhancing overall problem tractability. Furthermore, in order to significantly reduce the combinatorial solution search (CSS) space, a specific heuristic solution strategy is devised. In this global heuristic strategy, the problem is decomposed into successive optimization phases. Each phase uses more complex optimization models than the previous one, and uses the results of the previous phase so that the combinatorial solution search space is reduced after each phase. Moreover, each optimization phase is defined and solved as an independent problem; thus, allowing the use of specific decomposition techniques, or parallel computation when possible. A relevant feature of the solution strategy is that it combines deterministic and stochastic modeling techniques on a multi-stage modeling framework with a rolling-window planning concept.
The planning horizon is divided into two sub-horizons: medium- and long-term, both having multiple decision stages. The first sub-horizon is characterized by a set of investments, which are good enough for all scenarios, in each stage while scenario-dependent decisions are made in the second sub-horizon.
One of the first modeling challenges of this work is to select the right network model for power flow and congestion evaluation: complex enough to capture the relevant features but simple enough to be computationally fast. The thesis includes extensive analysis of existing and improved network models such as AC, linearized AC, “DC”, hybrid and pipeline models, both for the existing and the candidate lines. Finally, a DC network model is proposed as the most suitable option.
This work also analyzes alternative losses models. Some of them are already available and others are proposed as original contributions of the thesis. These models are evaluated in the context of the target problem, i.e., in finding the right balance between accuracy and computational effort in a large-scale TEP problem subject to significant RES integration. It has to be pointed out that, although losses are usually neglected in TEP studies because of computational limitations, they are critical in network expansion decisions. In fact, using inadequate models may lead not only to cost-estimation errors, but also to technical errors such as the so-called “artificial losses”.
Another relevant contribution of this work is a domain-driven clustering process to handle operational states. This allows a more compact and efficient representation of uncertainty with little loss of accuracy. This is relevant because, together with electricity demand and other traditional sources of uncertainty, the integration of variable energy sources introduces an additional operational variability and uncertainty.
A substantial part of this uncertainty and variability is often handled by a set of operational states, here referred to as “snapshots”, which are generation-demand patterns of power systems that lead to optimal power flow (OPF) patterns in the transmission network. A large set of snapshots, each one with an estimated probability, is then used to evaluate and optimize the network expansion. In a long-term TEP problem of large networks, the number of operational states must be reduced. Hence, from a methodological perspective, this thesis shows how the snapshot reduction can be achieved by means of clustering, without relevant loss of accuracy, provided that a good selection of classification variables is used in the clustering process. The proposed method relies on two ideas. First, the snapshots are characterized by their OPF patterns (the effects) instead of the generation-demand patterns (the causes). This is simply because the network expansion is the target problem, and losses and congestions are the drivers to network investments. Second, the OPF patterns are classified using a “moments” technique, a well-known approach in Optical Pattern Recognition problems.
The developed models, methods and solution strategies have been tested on small-, medium- and large-scale network systems. This thesis also presents numerical results of an aggregated 1060-node European network system obtained considering multiple RES development scenarios. Generally, test results show the effectiveness of the proposed TEP model, since—as originally intended—it contributes to a significant reduction in computational effort while fairly maintaining optimality of the solutions.
Stockholm: KTH Royal Institute of Technology, 2016. , 221 p.
Transmission expansion planning, uncertainty and variability, optimization, stochastic programming, moments technique, clustering
2016-10-10, Auditorium of Rey Francisco, 4 (Sala de Conferencias), Madrid, 12:00 (English)
Ramos, Andres, Prof.dr.
Söder, Lennart, Prof.dr.Rivier, Michel, Prof.dr.de Cuadra, Fernando, Prof.dr.