# Circulating Current Reduction in MMC-HVDC System Using Average Model
## 1 Introduction  
Among the voltage-source-power converters (VSCs), the modular multilevel converter (MMC) is emerging as a potential candidate for high voltage DC transmission systems [1]. It offers several advantages, such as the absence of large power supplies at each module, lower harmonics, less switching losses, modular structure, and scalable output voltage [2]. However, the working principle of MMC is different from other VSC (two levels and three levels converters) as it is based on the physical insertion and bypassing of its sub-modules (SMs) in a discrete pattern, making its control mechanism and overall structure complex [3]. Electromagnetic Transients Program (EMTP)-type programs, like PSCAD/EMTDC, are normally applied to study the dynamics of such a complex power converter system [4]. MMCs introduce a big challenge for its modeling in electromagnetic transient (EMT) simulation programs due to the increased number of switches and modules. The complete details about thedifferent versions of MMC models are available in Reference [5]. To model switch behavior, the total number of nodes in a network representing an admittance matrix must be re-triangulated during switching operation [6]. In detailed models (DMs), thousands of semiconductor switches are accurately modeled to study the dynamics of MMC-based high-voltage direct-current (HVDC) systems, but computational burden becomes very high. The simplified models, or average-value models (AVMs), have been used to overcome this problem, but they did not reflect the actual dynamics, as switch functions are simplified using controlled voltage and current sources [7]. AVMs also neglect switching details and make system dynamics approximate, leading to fast computation speeds [8].To study slow dynamics of large systems like DC grids, the AVM-based models are more computer-efficient than detailed MMC models [9]. Details of the different types of models are already explained in Reference [10] and can be classified as (1) detailed model; (2) arm equivalent circuit (The vein equivalent) model; (3) arm switch model; and (4) average model. A comprehensive review of these models for EMT-type studies is reported in Reference [11], focusing on transient conditions. Different methods of MMC control and its application are highlighted in Reference [12] without considering modeling techniques. Implementing detailed models is unrealistic for EMT-type computer simulation programs due to the computational complexity. The arm/the venin's equivalent model is computer-efficient but less accurate. The arm switch and average models are computer-efficient but cannot be used for the balancing control of sub-module capacitors (SMs). The continuous model of MMC is developed in Reference [13], which is based on the equivalent branch model of an arm comprising resistance, inductance, and an ideal voltage source. The stability analysis framework of continuous model is discussed in Reference [14]. In Reference [15], interaction between arm current and capacitor voltages are documented using the direct modulation approach. The drawback of this approach is the presence of a circulating current inside the arm current, since it assumes average SM capacitor voltage, which results in arm voltage oscillations and circulating current generation inside MMCs. A compensated modulation technique is used to eliminate the circulating current by considering the voltage ripple estimation that will compensate arm voltage oscillations based on the measurement of amplitude and phase of the output current [16]. In Reference [17], the analytical expressions for circular current interaction with arm voltage and arm current of MMCs was developed. The grid-side AC current and circulating current is controlled separately using proportional resonant (PR)and proportional (P) or gain controllers, which ultimately minimizes SM capacitance fluctuations as proposed in Reference [18].