# Circulating Current Reduction in MMC-HVDC System Using Average Model
## 1 Introduction
The important tasks for the operation of MMCs is to control output voltages and currents while keeping balance between SM capacitor voltages and the control of circulating currents. The circulating current can influence the proper functioning of converters by increasing its overall ratings and power losses. The advantages of circulating current elimination or minimization is already discussed in References [19; 20]. The double-carrier phase disposition pulse width modulation (PWM) technique is discussed in Reference [21], which eliminates the AC component of the circulating current using a high pass filter and differential current control using a proportional integral (PI) controller to minimize power losses at the cost of capacitor voltage ripple. A plug-in repetitive controller was implemented in Reference [22], which also reduces circulating current by eliminating lower order harmonics. To regulate AC side currents and eliminate circulating currents from arm currents, two separate controllers are normally adopted in MMC-HVDC systems; however, three separate current controllers are proposed in Reference [23] to control arm currents without implementing an AC side controller. To reduce converter losses, higher order harmonics can be eliminated from the circulating current but increases voltage ripples in SM capacitors; whereas injecting harmonics in circulating currents reduces cell capacitance, as proposed in Reference [24], but increases RMS values of arm currents. In Reference [25], SM capacitor voltage ripple is minimized by adding higher order harmonics inside the circulating current at the cost of increasing the RMS value of arm currents. It is evident that existing circulating current control methods can be divided in two groups: (1) elimination of higher order harmonics, which in turn increases SM capacitor voltage ripples but reduce the RMS value of arm currents; and (2) injecting higher order harmonics inside circulating currents reduces the capacitor voltage ripple but increases the RMS value of the arm current unless circulating current injection ratio is calculated accurately, further increasing the burden on the system [26]. The objective of this research work is to implement an MMC-HVDC system based on the average model developed in References [13; 14]. It is a nonlinear average model, which can capture circulating current phenomena by inserting SMs in a continuous manner. It can also be used as a bench mark circuit [27]; however, unlike Reference [14], which implements a circulating current suppression controller to reduce differential current inside MMC, a new method is proposed for reducing the circulating current. In this proposed method, a new technique is used for the addition of higher order harmonics in the upper and lower arm currents in each leg of an MMC; which will lead to a decreased inflow of excessive negative currents in a period. A reduced capacitor energy variation is obtained as arm voltage oscillations is the sum of all the capacitor voltages, which ultimately reduces the flow of the circulating current in each leg of a three-phase MMC. Furthermore, it will not affect the input and output current waveforms of the MMCs. The direct and proposed methods were tested on a common MMC-HVDC system using the PSCAD simulation program based on nonlinear AVM models. To the best of the author's knowledge, the key contributions are summarized as follows:  
1. The existing direct modulation technique generates sinusoidal arm currents that cause variations in capacitor energy, leading to capacitor voltage fluctuations. In the past, different approaches were adopted to minimize capacitor voltage fluctuations. 2. In some papers, harmonics were injected inside the circulating current, which reduced voltage fluctuations but led to increases in RMS values of arm currents, causing excessive power loss. 3.