## 1 Introduction
In addition, and as presented in [21], a proportional-integral (PI) controller is used to control the circulating current. However, many variables have to be well-adjusted to guarantee a good circulating current cancellation. In particular, a method based on a dual vector current controller for high-voltage direct current systems under unbalanced voltage conditions is presented in [21; 22]. However, under unbalanced voltages, the circulating current is composed of positive sequence component, negative sequence component (NSC), and zero sequence component. Hence, this method is not the most adequate for the SRPC application, since the converter is used for the purpose of active power balancing and reactive power compensation in two-phase V/V connection. On the other hand, a model predictive control for circulating current suppression is proposed in [23]. However, when increasing the number of SMs in an MMC, this leads to a higher number of switching states, which increases the control complexity due to the massive calculations that could overload the digital controller [24]. A new method for reducing the circulating current by adding second and fourth harmonics in the upper and the lower MMC arm currents is presented in [7]. However, this method does not eliminate all the even-order harmonics in the MMC arm currents. In this context, a methodology using the deadbeat predictive current control to reduce the MMC circulating currents is presented in this paper, bearing in mind that, the interrelation between the MMC output currents, the MMC circulating currents, and the SM voltages complicates the MMC control. Moreover, these quantities could affect each other, thus affecting the MMC performance [14]. The deadbeat predictive control uses the model of the SRPC system to compute, during every sampling period, the required reference voltage that the converter needs to reach the reference value in the next sampling instant [25]. Therefore, studying the SRPC model is important to extract the reference voltages. Then, the output voltage signal of the deadbeat predictive controller is compared with a phase-shifted PWM to drive the switching devices. Indeed, the more accurate the parameter values of the SRPC model, the better the performance of the controller. In this framework, the main contributions of this paper are: (a) Proposing a methodology based on a deadbeat predictive current control for the circulating current suppression in MMC; (b) An ample mathematical analysis of the SRPC equivalent circuit to extract the final reference equations; (c) A comprehensive comparison between the deadbeat predictive current control methodology and the conventional PI control approach. This paper is organized as follows: Section 2 explains the SRPC system compensation principle when using the V/V power transformer connection. Section 3 presents in detail the SRPC mathematical analysis based on the MMC equivalent circuit to extract the final reference voltages. Section 4 presents the control algorithm blocks of the SRPC system, including, the MMC voltage balancing control. Section 5 presents the simulation results and, finally, Section 6 summarizes the main conclusions.