Simplified Modelling of the F2F MMC-Based High Power DC-DC Converter Including the Effect of Circulating Current Dynamics Abel A. Taffese * and Elisabetta Tedeschi † Power Electronics ans Systems Group Department of Electric Power Engineering Norwegian University of Science and Technology Trondheim, Norway Email: * abel.taffese@ntnu.no and † elisabetta.tedeschi@ntnu.no Abstract—The Front-to-Front Modular Multilevel Converter (MMC) is one of the topologies being considered for high- voltage, high-power, dc-dc conversion. Hence, there is a need for the development of simplified models for such a converter in order to study how it behaves in a large power system. Direct interconnection of two MMC models is one option but it leads to high number of states. Moreover, symmetry of the converter offers further simplification opportunities. The use of this fact to develop a simplified models was reported in literature. However, the resulting models are only applicable when compensated modulation is used. Furthermore, these models neglect the effect of Circulating Current Suppression Controllers (CCSCs), which makes the models inaccurate in the presence of such controllers. This paper proposes a more general simplification approach that captures the effect of CCSC while minimizing the number of states. The proposed model is validated by using time domain simulations and modal (eigenvalue) analyses. Index Terms—Modular Multilevel Converter, Front-to-Front, dc- dc, F2F, Simplified Model, Modal analysis I. I NTRODUCTION With the increasing number of installed HVDC links, there is a drive to create a meshed dc grid in order to increase reliability and reduce cost [1]. The high voltage, high power, dc-dc converter plays a vital role in the development of such a grid [2], [3]. In addition to filling the role of the “dc transformer” [4], the converter is also required to provide other services such as power-flow control [2]. The Front to Front (F2F) dc- dc converter composed of two Modular Multilevel Converters connected on the ac side, is one of the promising topologies proposed to meet these requirements [5]. The dc-dc converter is needed when the grid becomes more complex with multiple voltage levels and power-flow paths. This means that it is often studied as part of a large power system. Therefore, it is essential to develop a simplified model of this converter so that it can be used in system level studies. The building block for the converter, i.e. the MMC, is well developed and models of varying level of detail are already available [6]–[13]. However, because of its symmetry, the F2F lends itself to further simplification. This fact was utilized in [14] to develop a simple model of the converter with a single capacitor representing the arm energy dynamics, thus reducing the number of states from 18 to 6. However, as will be shown in this paper, the model is applicable only when using compensated modulation, a special method for calculating the insertion indexes [6]. When using other types of control, such as direct voltage control, there is an uncontrolled interaction between the different harmonic components in the converter, which leads to a poorly damped oscillation at the converter terminals [15]. The existing simplified model of the F2F from [14] fails to accurately capture such modes of oscillation. Additionally, the model neglects the effect of circulating current ripple and the associated suppression controllers. It has been shown that the effect of Circulating Current Suppression Controllers (CCSCs) cannot be neglected because they can interact with external systems [16]. Therefore, the main goal of this paper is to develop a simplified model that can include the circulating current dynamics while keeping the state count to a minimum. The remainder of this paper is organized as follows: A detailed model of the converter is presented in Section II, followed by the proposed simplification in Section III. Validation and analysis of the models are presented in Section IV and Section V, respectively. II. DETAILED AVERAGE MODELLING Since the F2F is built from two MMCs, this section will begin by modelling an MMC connected to a stiff voltage source, v g , on the ac side. The assumptions used to develop the average model are [7]: 1) the insertion indexes are continuous variables, 2) the Sub-Modules are balanced, and 3) the arm capacitance is the same for all the arms. A simplified per- phase equivalent circuit of the F2F, with relevant parameters, is shown in Fig. 1. The following equations can be derived by taking these assumptions into consideration. n u = n c − n s n l = n c + n s i u = i c + 1 2 i s i l = i c − 1 2 i s (1) where n u and n l are the upper and lower arm insertion in- dexes, respectively. n c and n s are the common-mode (dc) and