Design and Optimization of the Arm Inductor for Modular Multilevel Converter

The modular multilevel converter (MMC) is one of the most promising topologies for high- and medium-voltage applications. However, the conventional MMC relies on large arm inductance and complicated feedback control to maintain submodule (SM) capacitor voltages balanced, which requires a large number of voltage sensors and complicated arm current control loops. In contrast to the conventional perspective, the MMC can be regarded as a derivative from the general multilevel topology based on switched-capacitor (SC) structure. The SC structure endows excellent properties to the MMC, such as minimum or no arm inductor and automatic SM capacitor voltage balancing capability. This MMC with minimum or no arm inductor is named as SC-MMC. Since the arm inductances are very small, the SM capacitor voltages can be balanced automatically. Small stray/parasitic inductance is enough to limit inrush current during SM's switching instants to the rated current level. To unleash the automatic SM capacitor voltage balancing capability of the SC-MMC, a Y-matrix modulation (YMM) has been proposed, which does not require closed loop control or any sensor, has no limitations on the number of SMs, and works for both half-bridge and full-bridge SMs. An unresolved issue of the emerging YMM is that, in the published literature, the existence of the Y matrix with full rank has not been proved theoretically beyond the observation for the SC-MMC when the number of SMs is large. In this paper, an analytical proof of the existence of the full rank Y matrix is provided, which implies the automatic voltage balance of SMs for the MMC with arbitrary number of SMs in each arm. Simulation results using the YMM on a 21-level SC-MMC with minimum arm inductance are provided to verify the voltage balance theory/observation of the SC-MMC using the YMM.

Arm inductor in a modular multilevel converter (MMC) is used to limit the circulating current and dc short circuit fault current. The circulating current in MMC is dominated by second-order harmonic, which can be largely reduced with circulating current suppressing control. By analyzing the mechanism of the circulating current suppressing control, it is found that the circulating current at switching frequency becomes the main harmonic when suppression control is implemented. Unlike the second-order harmonic that circulates only within the three phases, switching frequency harmonic also flows through the dc side and may further cause high-frequency dc voltage harmonic. This article develops the theoretical relationship between the arm inductance and switching frequency circulating current, which can be used to guide the arm inductance selection. The experimental results with a downscaled MMC prototype verify the existence of the switching frequency circulating current and its relationship with arm inductance.

— The modular multilevel converter (MMC) is considered to be emerging multilevel topology for medium to high power applications due to its modularity and highly reliable structure. However, large submodule (SM) capacitor voltage ripple and higher circulating current during variable frequency operation is the major drawback of the MMC. In the literature, higher-order harmonic elimination technique is presented to reduce SM capacitor voltage ripple and circulating current. In this article, effect of lower-order harmonics on circulating current is investigated. The effect of second-order fundamental frequency current harmonic I2f on arm inductor is analyzed. Based on detailed analysis, an optimal design method for selection of arm inductor is proposed. Proposed optimal design is capable of reducing the circulating current under variable frequency range as well as SM capacitor voltage ripple remains under specified limit during entire variable frequency operation. A detailed MATLAB model of MMC fed high power medium voltage drive is developed. Experimental setup is also developed to check the effectiveness of proposed optimal design method. Reduction in circulating current and control of SM capacitor voltage ripple is observed for entire range of frequency.

This paper presents deeply analysis and comparison of different modulation techniques for the modular multilevel converter without using arm inductor. In case of PWM, losses are more and Total Harmonic Distortion (THD) performance is very poor. With the introduction of delta modulation in MMC, the losses will reduce and THD will improve. It can be seen that the THD is 4.9% for delta modulation and 3.82% for adaptive delta modulation without using arm inductance but THD is 13.15% for delta modulation with arm inductance. It means THD has been improved without using arm inductance. It has been observed that the adaptive delta modulation has better THD response as compared to delta modulation due to its several advantages. The THD performance has been calculated and mentioned at different modulation indexes. It has been also observed that the THD performance is better with delta and adaptive delta modulation.

The differential current in Modular Multilevel Converters (MMCs) is inherently subjected to even order harmonics, which are mainly caused by the voltage mismatch between phase legs and dc bus. This issue may exist in both single-phase and multi-phase MMC systems and can be eased by repetitive control based active harmonic suppression methods, which regulate the circulating current through legitimate adjustment of the voltage applied on the arm inductance. Nevertheless, conventional repetitive controllers have relatively slow dynamic response because of the presence of one fundamental period delay, and all the sampled errors in the past one cycle have to be stored for closed-loop control. This paper presents an improved even-harmonic repetitive control scheme that requires less data memory with faster dynamic response. The steady state performance can also be enhanced if system disturbances e.g. frequency deviation are considered. In order to verify its practicality and effectiveness, PLECS simulation and experimental results are presented to show the excellent dynamic response and disturbance rejection of the proposed even-harmonic elimination scheme.

Modular multilevel converters (MMCs) are widely used in grid scale power electronics. Due to the presence of a dc component in the arm current, the MMC submodules (SMs) show an unbalanced current loading profile. This may lead to some semiconductor chips being more stressed than others, significantly affecting the overall reliability. To level the junction temperatures and improve the SM reliability, this article proposes an asymmetrical power module design in line with the loading profile, allocating more chips to higher current parts. This is shown to be realistic if the power flow is unidirectional. The concept is investigated using simulation backed by experiment. It is shown that the designed power module can significantly reduce the maximum temperature and the total power loss can be reduced by 5%–8%. The chip utilization rate is also improved. The proposed module is applicable in a certain range of power factor and modulation index adjustment. This article provides a guidance for optimum design of the power module for the SMs in an MMC.

The Doubly Fed Induction Motor (DFIM) is essential in Wind Energy Conversion Systems (WECS) for efficient wind energy harvesting. Conventional power converters in WECS often result in high Total Harmonic Distortion (THD) in output voltage and current, affecting wind energy economy. This research proposes replacing conventional converters with Modular Multi-level Converters (MMC) due to their scalable topology, low harmonic distortion, high efficiency, and the elimination of DC link capacitors. The MMC is connected in a back-to-back configuration between the rotor of the DFIM and the grid to enable four-quadrant operation. Circulating current in the MMC is minimized using a Modified Deer Hunting Optimization (MDHO) based Fractional Order PID (FOPID) controller and a Mexican Axolotl Optimization (MAO) based FOPID. Capacitor voltage balancing is achieved using Level-Shifting PWM (LSPWM) and Three-Dimensional Space Vector PWM (3D-SVPWM) techniques with voltage sorting algorithms. The impact of these control and modulation techniques on the DFIM is analyzed in terms of reduced THD, and steady state and transient performance. Simulations are conducted in MATLAB/R2022a, and experimental validation is performed using a 7-level 0.5 kW MMC in a Hardware-In-Loop (HIL) setup.

Model predictive control (MPC) is considered one of the best non-linear control methods for controlling the modular multilevel converter (MMC) due to various advantages, such as no need for direct modelling, high dynamic response, and the ability to manage multiple control targets simultaneously. In this paper, a current closed-loop controller (CCLC) based on the current predictive strategy (CPS) is used to control the circulating and output currents in an MMC. A bilinear mathematical model of the MMC is derived and discretized to predict the states of the MMC for one step ahead. In addition, to reduce the practical costs and reduce the converter sensors, a sensor reduction algorithm has been used to reduce the number of voltage sensors and increase the reliability of the system. The proposed method is implemented in a single-phase MMC with four sub-modules (SMs) in each arm. The accuracy and performance of the proposed method are evaluated with simulation and experimental results.

The main technical challenge of the medium-voltage motor drives with modular multilevel converter (MMC) is the serious low-frequency fluctuation on the capacitor voltages, and the existing suppression methods inevitably inject high-frequency circulating currents in MMC. However, the output currents are evidently distorted by the large injected components, while little research has been done to study and solve this problem. This paper analyzes and proves the essential interactions between the output current distortion and the injected components, and the specific dominant output harmonic groups are derived and summarized, revealing the nature of the problem, and it can be taken as a favorable reference for the controller designing. Based on the derivations, this paper proposes a novel suppression method for the greatly improved harmonic characteristics of the output currents during the low-frequency operation. The output harmonics can be accurately measured by the proposed control and effectively suppressed for much lower current total harmonic distortion, benefiting for the superior output control performances with improved efficiency. The simulation results on PSCAD/EMTDC and experimental verifications on a 2.2 kW MMC-based motor drive prototype prove the validity of the presented harmonic analysis and suppression method.

During the operation of a three line ac link in parallel with a ac-dc-ac link system that employs Back-to-Back (B2B)Medium Voltage Modular Multilevel Converters (MMC), a path for the low frequency zero sequence currents is shown to exist. Apart from causing additional losses, these currents can result in limitations on power capacity. A detailed analysis on the influence of cell capacitance, arm inductance and link conductor length on the circulating zero sequence currents and the means to mitigate them through a simulated control strategy is investigated. The simulations show that the dc link employing B2B-MMC can successfully operate in parallel with ac link without transformer isolation by controlling the zero sequence currents.

In this article, we study the integration of high-temperature superconducting arm coils in a mod-ular multilevel converter (Cryo-MMC). With this integration, the fault current can be greatly reduced by the increased resistance of the superconducting arm coils during fault condition. We simulate and compare the performance of the cryo-MMC and a conventional MMC under a DC-side pole-to-pole fault. The simulation results show that the Cryo-MMC reduces the DC-side surge current by 57%, the peak arm currents by 65%, and the peak AC-current by 73.7% during the simulated fault. We also report the construction of the first cryo-MMC prototype that will experimentally validate the integration of superconducting arm coils into a single-phase 6-level MMC.

The occurrence of DC-side bipolar short-circuit faults in flexible DC transmission systems is a serious problem at present. In order to achieve fault clearing, an improved reverse-blocking hybrid submodule (RB-Hybrid-SM) topology of modular multilevel converter with DC-side fault current clearing capability is presented. All submodule (SM) capacitances of the proposed topology are series into the fault circuit and provide back electromotive force (back EMF) with converter valve blocking to clear the fault current. Then the fault clearing mechanism is analyzed, and the fault current analysis expression is pushed according to fault equivalent circuit. Finally, using this topology as an example, an improved reverse-blocking hybrid SM modular multilevel converter (RB-Hybrid-SM-MMC) simulation model was built in the PSCAD/EMTDC software are carried out to verify its effectiveness and feasibility. The simulation results show that the new SM topology proposed in this paper can quickly block the fault current, and always provide 2Uc back EMF during the fault blocking process.

Modular multilevel converter (MMC) based high voltage direct current (HVDC) systems are quite popular in high power transmission systems as it offers low losses, high quality output voltage, modular and scalable structure as compared to the two level voltage source converter based HVDC systems. However, inability to block dc fault current is a major concern of conventional MMC-HVDC system, especially for the overhead HVDC system. In this paper, the performance of conventional MMC with half bridge submodules is analyzed for dc side fault. In the event of a dc side fault, the conventional MMC acts as an uncontrolled diode rectifier and feeds very high current to dc fault. To tackle this problem, different techniques have been discussed in the literature. This paper gives a brief overview of dc fault tolerant techniques discussed in the literature. Moreover, in this paper, a detailed comparison between different hybrid topologies with dc fault tolerant capability is performed on the basis of required number of switches and capacitors. Furthermore, the fault tolerant capability of MMC with bipolar (full bridge) submodule is experimentally validated.

The control complexity of modular multilevel converter (MMC) increases with the number of submodules per arm. In particular, the implementation of a pulsewidth modulation (PWM) scheme and a voltage balancing approach for MMC is a major challenge. This paper proposes a generalized low-cost less computational decoupled sampled average PWM scheme for MMC. In this approach, the reference output voltage is generated by averaging the two nearest voltage levels from the top and bottom arms in each sampling interval. In addition, a simplified voltage balancing approach is proposed for MMC. The proposed approach does not require a sorting technique to select the submodules. Instead, the relative comparison logic is presented. The effectiveness of the proposed modulation scheme and voltage balancing approach is evaluated on a single-phase MMC system with three-level flying capacitor submodules. The proposed approach is extended to a three-phase system, which results in dynamic balancing of the zero-sequence voltage. Hence, the zero-sequence current is minimized. The performance of the proposed three-phase approach is compared with that of the conventional phase-shifted carrier PWM scheme. The simulation and experimental studies show successful voltage balancing among submodule capacitor voltage, low harmonic distortion, and less ripple in output current.

this paper proposes a circulating current elimination controller based on the detailed analysis of sub module capacitor voltage ripple in modular multilevel converter (MMC). When a circulating current suppression controller is embedded in MMC overall controller, the switching function of arms consists of a second harmonic component. The magnitude and phase angle of the second harmonic switching function (SHSF) is dependent on various factors, like, output current, power factor, modulation index, submodule capacitor, average submodule capacitor voltage and submodule capacitance. This paper gives the mathematical analysis of determining the magnitude and phase angle of SHSF. Firstly, the voltage components of submodule capacitor at different frequencies are calculated using average model of MMC. Based on the derived voltages, the magnitude and phase angle of the SHSF is determined. The analytic expressions and proposed control scheme are validated with simulation study.