This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination. IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY 1 Feed-Forward Control of an HVDC Power Transmission Network Christian Schmuck, Frank Woittennek, Albrecht Gensior, and Joachim Rudolph, Member, IEEE Abstract— An efficient and well-established technology for power transmission across long distances is high-voltage direct current transmission (HVDC). However, HVDC is currently almost completely limited to peer-to-peer connections or net- works with peers situated closely to each other. This contribution introduces the flatness-based design of a feed-forward control of HVDC transmission networks comprising two or more converter stations. The resulting control concept allows for a flexible determination of the power distribution within the network. Furthermore, effects such as power losses and delays due to wave propagation, which are related especially to long transmission lines, can be easily considered. Numerical simulations for an example network are included to prove the value of the results. Index Terms— Flatness-based control, multiterminal high- voltage direct current transmission (HVDC), power grid, power sharing, travelling waves on transmission lines. I. I NTRODUCTION E LECTRIC power transmission by means of AC is not feasible for transmission distances larger than 1000km due to high reactive currents and undesired wave reflections. High-voltage direct current transmission (HVDC) is an effi- cient alternative to overcome these limitations [1], [2]. The well-established standard configuration of an HVDC system is a peer-to-peer link connecting two conventional AC networks as depicted in Fig. 1. The AC network and the DC link are coupled by a converter terminal equipped with a power converter [3], which works as an inverter or as a rectifier depending on the direction of the power flow. Although, currently the vast majority of all implemented HVDC systems are in standard peer-to-peer configuration, there has been increasing interest in HVDC networks with more than two converter terminals, the so called multiterminal HVDC [1], [4]–[6]. As a result of the evolving technology for power converters and the increasing exploitation of renewable energy resources such networks have been put into practice, Manuscript received June 7, 2012; revised October 30, 2012; accepted February 12, 2013. Manuscript received in final form March 14, 2013. Recommended by Associate Editor P. Korba. C. Schmuck is with the Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg 39106, Germany, and also with Fachgebiet Regelungssysteme, Technische Universität Berlin, Berlin 10587, Germany (e-mail: schmuck@mpi-magdeburg.mpg.de). F. Woittennek is with the Institut für Regelungsund Steuerungstheorie, Technische Universität Dresden, Dresden 01187, Germany (e-mail: frank.woittennek@tu-dresden.de). A. Gensior is with the Professur für Leistungselektronik, Technische Uni- versität Dresden 01187, Germany (e-mail: albrecht.gensior@tu-dresden.de). J. Rudolph is with the System Theory and Control Engineering, Saarland University, Saarbrücken 66123, Germany (e-mail: j.rudolph@ lsr.uni-saarland.de). Digital Object Identifier 10.1109/TCST.2013.2253322 3 ∼ 3 ∼ DC transmission line Converter terminal Converter terminal AC network AC network Fig. 1. Peer-to-peer HVDC link with two converter terminals and a DC transmission line connecting them. e.g., for offshore wind farms [7]–[9]. A central goal for the control of an HVDC multiterminal network is to keep the power balance between the electrical power fed into and taken from the DC network by the connected converter stations. Simultaneously, one desires to adjust the power distribution between the converter terminals flexibly during the operation of the system. Furthermore, time delays due to traveling waves can become considerable for long transmission distances [6] and should then be considered. This paper proposes a control method that reaches these goals taking a flatness-based approach. For the discussed transmission system, whose description involves partial dif- ferential equations (PDEs), this means that the solution of the system equations is parametrized by the trajectories of a special set of system variables, called a flat output of the system [10]–[12]. The number of the components of the flat output equals the number of the control inputs. This contribution recalls the control design approach proposed in [13] and extends it to a more general class of networks. Section II describes the mathematical model of the HVDC transmission networks investigated. Section III focuses on tree- like, that is cycle-free, networks to explain the derivation of a flat output and the flatness-based control design. The results are illustrated by a numerical example in Section IV. Section V extends the control design approach introduced for tree-like networks to the general network case. This is further clarified in Section VI through a simple example network. Finally, Section VII gives some remarks on practical issues and on potential extensions to be considered for future work. II. MODEL OF THE HVDC NETWORK This section introduces the mathematical model of the HVDC networks, which the control design is based on. A. General Network Structure A general transmission network is assumed to consist of n P uniquely numbered nodes P μ ,μ ∈ P where P is the set of all node indices existing in the network. Two arbitrary nodes P μ and P ν can be connected by an electric transmission line L ν μ where the notations L ν μ and L μ ν coincide, see Fig. 2. 1063-6536/$31.00 © 2013 IEEE