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Estimation of Investment Model Cost Parameters for VSC HVDC Transmission Infrastructure

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Estimation of Investment Model Cost Parameters for VSC HVDC Transmission Infrastructure Estimation of Investment Model Cost Parameters for VSC HVDC Transmission Infrastructure Til Kristian Vranaa, Philipp Hartel¨ b aSINTEF Energi, Trondheim, Norway bFraunhofer IWES, Kassel, Germany Abstract Investment model cost parameters for VSC HVDC transmission infrastructure continue to be associated with high uncertainty and their validity remains a crucial challenge. Thus, it is the key objective of this analysis to identify a new cost parameter set providing better investment cost estimates than currently available cost parameter sets. This parameter estimation is based on a previously conducted review of investment model cost parameters including its collection of existing cost parameter sets and project cost reference data. By using a particle swarm optimisation, the overall error function of the review’s evaluation methodology is minimised to obtain an optimal parameter set. The results show, however, that the optimised parameter sets are far from being realistic and useful, which is why an improved overall error function is developed. Effectively penalising negative and near-zero cost parameter coefficients, this new overall error function delivers a realistic and well-performing cost parameter set when being minimised. In fact, the new parameter set produces better cost estimates for back-to-back, interconnector, and offshore wind connection projects than any of the existing cost parameter sets. Therefore, it is a valuable contribution and shall be considered in future grid investment analyses involving VSC HVDC technology. Keywords: Offshore grids, Transmission expansion planning, Cost model, HVDC, VSC, Parameter estimation, Particle swarm optimisation 1. Introduction parameter set based on the reference cost data for realised projects is needed to improve the validity of future Voltage Source Converter (VSC) High Voltage Direct grid investment and evaluation studies. Therefore, by Current (HVDC) is the most suitable technology for drawing on the collected parameter sets and reference future super grids and offshore grids in Europe [1][2]. project cost data in [4], a new parameter estimation While multiple investment analyses of future offshore approach will be explored in this context to determine grid topologies have already been conducted (e.g. [3]), a new investment cost parameter set for VSC HVDC the subject of implementing integrated power grids projects which can be used in transmission expansion continues to be an important research topic. As the studies. optimisation algorithms used for assessing investment In the remaining part of this article, Section 2 decisions in offshore grid infrastructure rely on a cost summarises the cost model and parameter information model and corresponding parameter sets, the validity of for the following parameter estimation. Section 3 those parameter sets plays a crucial role. introduces the particle swarm optimisation methodology However, it has been established in [4] that the cost which is used to compute the new parameter sets through parameter sets which have been widely used by academia error minimisation. Two optimised cost parameter sets and policymakers show significant variations from study based on the error function from [4] are presented in to study. They indicate a high level of uncertainty both Section 4. Section 5 develops an extended overall when comparing them against each other and when error function including the new realness category. evaluating them against reference cost data from realised In Section 6, the final cost parameter set obtained VSC HVDC projects. Acknowledging the fact that from minimising the new overall error function is there are multiple and valid reasons for diverging cost presented. Section 7 discusses the obtained comparison estimates obtained with those parameter sets, a new and evaluation results and Section 8 concludes the study. Preprint submitted to Electric Power Systems Research 2018–02–19 This is the accepted version of an article published in Electric Power Systems Research DOI: 10.1016/j.epsr.2018.02.007 Nomenclature Abbreviations Technical parameters and variables B2B Back-to-Back Pˆ j Maximum power rating for a single installation within ITC Interconnector category j (GW). In case of a back-to-back system, this OWC Offshore Wind Connection is twice the system rating (two fully rated converters at PSO Particle Swarm Optimisation one node). QEF Quadruple Error Function lOHL; f Overhead line section length of branch f (km) R Realness lSMC; f Submarine cable section length of branch f (km) TEF Triple Error Function lUGC; f Underground cable section length of branch f (km) General l f Total equivalent line length of branch f (km) dreale Ceiling of real (dreale = min fn 2 N0 j n ≥ realg) p f Installed power rating of branch f (GW) jsetj Cardinality of set pg=h Installed power rating at node g=h (GW). In case of a Indices and sets back-to-back system, this is twice the system rating (two fully rated converters at one node). f 2 Fi Set of branches within project i Deviations and errors g 2 Gi Set of nodes within project i k Unscaled root-mean-square realness error for cost h 2 Hi Set of offshore nodes within project i R parameter set k (-) i 2 I j Set of projects within category j k q j 2 J Set of project categories (J = fB2B; ITC; OWCg) q;EXP Relative exponential deviation of parameter for cost k 2 K Set of cost parameter sets parameter set k (-) k q 2 Qk Set of cost parameters of parameter set k q;LOG Relative logarithmic realness deviation of parameter q z 2 Z Set of categories including realness (Z = J [ fRg) for cost parameter set k (-) k Cost parameters and variables q;REL Relative realness deviation of parameter q for cost k parameter set k (-) B0 Fixed cost for building a branch with cost parameter set k (Me) A Constant scalar realness error scaling factor (-) k Dk Project investment cost estimation deviation of project i Blp Length- and power-dependent cost for building a branch i with cost parameter set k (Me/GW·km) for cost parameter set k (-) k Dk Category investment cost estimation deviation of category Bl Length-dependent cost for building a branch with cost j parameter set k (Me/km) j for cost parameter set k (-) k k Cest;i Estimated investment cost for project i (Me) EQEF Overall root-mean-square error of four category errors Cref;i Reference investment cost for project i (Me) (Quadruple Error Function) for cost parameter set k (-) con Ek Overall root-mean-square error of three category errors Cref;i Reference contracted cost for project i (Me) TEF (Triple Error Function) for cost parameter set k (-) Nk Fixed cost for building a node with cost parameter set k 0 k (Me) ER Root-mean-square realness error for cost parameter set k (-) Nk Power-dependent cost for building a node with cost p k parameter set k (Me/GW) Eq Realness error of cost parameter q for cost parameter set S k Fixed additional cost for building an offshore node with k (-) 0 k cost parameter set k (Me) E j=z Category root-mean-square error of category j=z for cost k parameter set k (-) S p Power-dependent additional cost for building an offshore node with cost parameter set k (Me/GW) 2. Fundamentals associated with offshore grid HVDC infrastructure and yields a reasonable accuracy regarding long-term This section contains a summary of the most important large-scale transmission expansion studies (e.g. [45]). information, equations, and tables from [4], which are The cost model is based on [46], [47] and [48]. essential for the optimisation approach of this article. In Bear in mind that a mixed-integer linear cost model addition, a new parameter set notation is introduced as it yields significant benefits for long-term large-scale is convenient for all subsequent considerations. transmission expansion planning problems and the optimisation algorithms solving them, as computation 2.1. Cost model time and convergence face severe challenges when more A linear uniform cost model has been defined in [4]. complex cost models are applied. It provides an approximation of the investment cost 2 This is the accepted version of an article published in Electric Power Systems Research DOI: 10.1016/j.epsr.2018.02.007 Since the main equations explained in [4] are for a back-to-back system (contains two fully-rated inevitable for the subsequent calculations, they are converters). This is the reason why Pˆ B2B is twice the repeated in this subsection. The linear uniform cost size of Pˆ ITC and Pˆ OWC. model for VSC HVDC transmission investments is In Equations (2) to (4), the ceiling operators are defined by Equations (1) to (6): needed to enforce the necessary integer investment decisions which have to be made as part of the optimisation problem. Gi Fi Hi k X k X k X k Cest;i = Ng (pg) + B f (l f ; p f ) + S h(ph) (1) g f h 2.2. Parameter set notation It is helpful to combine the seven parameters of a & p ' k k g k cost parameter set in a mathematical set, as denoted in Ng (pg) = Np · pg + N0 (2) Pˆ j Equation (7): & p ' n o k k f k k k k k k k k k k 8 B f (l f ; p f ) = Blp · l f · p f + Bl · l f + B0 (3) Q = Blp; Bl ; B0; Np; N0 ; S p; S 0 k (7) Pˆ j & ' With that in mind, it is the primary goal of this k k k ph k article to identify a new parameter set Q constituting S h(ph) = S p · ph + S 0 (4) Pˆ j an optimal fit for estimating investment costs of VSC HVDC infrastructure. Pˆ = 4 GW Pˆ = 2 GW Pˆ = 2 GW (5) B2B ITC OWC 2.3.
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