Grid-Forming IBRs Under Unbalanced Grid Conditions: Challenges, Solutions, and Prospects

This paper proposes an improved three-stages cascading passivity-based control (PBC) for a grid -connected LCL converter in unbalanced weak grid condition. In general, the traditional double-loop control based on positive and negative sequence transformations is used in grid-connected converter control in unbalanced weak grid condition. However, it is time consuming for second harmonic filtering, and positive and negative sequence currents need to be controlled separately. The PBC has strong robustness to interference, and the line voltage based PBC can deal with the voltage unbalance effectively and easily without negative sequence transformation. But the traditional PBC needs six variables and three damping coefficients for the grid-connected LCL converter in unbalanced grid condition, and it has the disadvantage of difficult implementation. The improved PBC can realize the same control effect with three-stages cascading PBCs of two variables and one damping coefficient, and it has the advantages of easy implementation, good performance and high stability. First, the modeling and controller design are detailed described. Then the SIMULINK simulation results demonstrate the benefits of the improved control strategy. Finally, a grid-connected LCL converter prototype of 5kW is built and the experimental results verify the correctness and effectivity of the improved three-stages PBC strategy.

In order to integrate renewable energy into the utility grid with high penetration, AC/DC hybrid microgrids have obtained much attentions in recent years since they feature both advantages of AC microgrids and DC microgrids. In an AC/DC hybrid microgrid, the parallel-operated AC/DC bi-directional interfacing converters (IFCs) are key elements to connect AC bus and DC bus. When unbalanced grid faults occur at the AC bus, the active power transferred by the parallel-operated AC/DC interfacing converters is desired to be maintained constant and oscillation-free to ensure the stable operation of DC bus. However, with conventional control strategies in unbalanced grid conditions, the active power transfer capability of IFCs will be affected due to the current rating limitations. Therefore, the parallel operation of IFCs in a hybrid microgrid under unbalanced AC grid conditions is studied, and a control strategy, which enhances the active power transfer capability with zero active power oscillation, is proposed. Adjustable reference current coefficients for parallel IFCs are introduced in the proposed control strategy to enable the flexible current sharing among IFCs. By utilizing the proposed control strategy, only one IFC needs to be designed and installed with higher current rating to ensure the constant and oscillation-free output active power. Simulations and experiments have verified the feasibility and effectiveness of the proposed strategy.

As a common interface circuit for renewable energy integrated into the power grid, the inverter is prone to work under a three-phase unbalanced weak grid. In this paper, the instability of grid-connected inverters under the unbalanced grid condition is investigated. First, a dual second-order generalized integrator phase-locked loop (DSOGI-PLL)-based inverter under balanced and unbalanced conditions is modeled. A fourth-order impedance model is established to describe its impedance characteristics under the unbalanced grid condition. To analyze this multi-input multi-output system, a simplified stability analysis method based on the generalized Nyquist stability criterion and matrix theory is proposed. Then, the influences of circuit and control parameters on the stability of the grid-connected inverter system under the unbalanced grid condition are investigated. Finally, the accuracy of the derived frequency-coupled impedance model is verified via simulations, and the effectiveness of the proposed simplified stability analysis method on the system stability analysis is verified via both simulations and hardware experiments.

This paper presents a control scheme for the regulation of cell capacitor energy balancing of a Modular Multilevel Converter (MMC) for HVDC transmission systems, considering the unbalanced AC grid conditions. It is essential that the MMC balancing control should be valid not only for the balanced normal operations but also for the asymmetrical grid fault conditions. This paper proposes the control scheme that has the ability of seamless mode change between balanced and unbalanced grid condition. Applying the proposed method, the capacitor energy balancing operation is successfully realized with improved dynamic responses. Finally, the simulation results verify the validity of the proposed method.

Today, interests on hybrid ac/dc microgrids, which contain the advantages of both ac and dc microgrids, are growing rapidly. In the hybrid ac/dc microgrid, the parallel-operated ac/dc bidirectional interfacing converters (IFCs) are increasingly used for large capacity renewable energy sources or as the interlinking converters between the ac and dc subsystems. When unbalanced grid faults occur, the active power transferred by the parallel-operated IFCs must be kept constant and oscillation-free to stabilize the dc bus voltage. However, under conventional control strategies in unbalanced grid conditions, the active power transfer capability of IFCs is affected due to the converters’ current rating limitations. Moreover, unbalanced voltage adverse effects on IFCs (such as output power oscillations, dc-link ripples, and output current enhancement) could be amplified by the number of parallel converters. Therefore, this paper investigates parallel operation of IFCs in hybrid ac/dc microgrids under unbalanced ac grid conditions and proposes a novel control strategy to enhance the active power transfer capability with zero active power oscillation. The proposed control strategy employs a new current sharing method which introduces adjustable current reference coefficients for parallel IFCs. In the proposed control strategy, only one IFC, named as redundant IFC, needs to be designed and installed with higher current rating to ensure the constant and oscillation-free output active power of parallel IFCs. Simulation and experimental results verify the feasibility and effectiveness of the proposed control strategy.

This paper develops a comprehensive dynamic-phasor-based small-signal model for the modular multilevel converter (MMC) system under unbalanced grid conditions, which takes into consideration the dynamics of the MMC system under a balanced grid condition as well as the other emerging internal harmonics produced by the unbalanced grid components and more complex controllers. The small-signal model is validated by comparing the time-domain responses from a detailed electromagnetic transient (EMT) simulation in PSCAD/EMTDC. Based on the eigen-analysis and PSCAD-based time-domain simulation studies, this paper reveals the poorly damped modes that cause unstable oscillations in MMC system under the unbalanced grid conditions. From the results, more poorly damped modes involved in the internal harmonics are emerging under unbalanced grid conditions compared with the modes under the balanced grid conditions, and can highly impact the system dynamic behaviors by the selection of the control parameters. It is also shown that, under the unbalanced grid conditions, the feasible region of the control parameters of the vector current control gets narrowed indicating the reduction of the stability margin, smaller (larger) value of proportional (integral) gain of the circulating current suppressing controller can enhance the system stability, and larger values of the proportional and integral gains of the negative-sequence current suppressing control can result in the harmonic instability of the MMC system. Besides, the parameters of multiple complex-coefficient filters for positive- and negative-sequence components extraction also have a big impact on the small-signal stability of the MMC system and are required to be properly selected.

Analysis and experimental verification of improved two-level converter behaviors under unbalanced AC conditions

This paper investigates space‐vector‐modulation (SVM) technique that uses only rotating space vectors to drive a direct matrix converter (DMC) with zero common‐mode voltage (CMV). Two methods for controlling grid power factor have been proposed in the literature for such a drive. Until now, analysis has been limited to balanced grid conditions. However, total harmonic distortion (THD) of grid currents significantly increases under unbalanced conditions. Hence, the aims of this paper are: (1) derivation of DMC model consisting of general equations for output voltages and input currents, written in the complex form. (2) Analysis and comparison of two existing methods for grid power factor control under balanced grid conditions, by using the previously derived model. (3) Proposal of extended versions of both methods in order to improve converter's performance under unbalanced grid conditions. The proposed control strategy aims to achieve sinusoidal currents and maintain the same power factor on the grid side while completely compensating grid unbalance on the load side. (4) Determination of the maximum transfer ratio under balanced and unbalanced grid conditions. Experimental results with Hardware In the Loop (HIL) are provided to verify the theoretical analysis and effectiveness of the proposed control strategy.

The Vienna rectifier is an excellent Power Factor Correction (PFC) AC–DC converter which has low Total Harmonic Distortion (THD) of input current, resistance to high-voltage, and high efficiency. Based on the structural characteristics of Vienna rectifier under the unbalanced grid conditions, considering the influence of grid voltage negative sequence component, the reference modulation wave of Vienna rectifier will lead or lag the input current, and the input current will be distorted which affects the power quality of Vienna rectifier. In this paper, a novel modulation waves clamping method by modifying the current command of the rectifier is proposed to eliminate the input current distortion under unbalanced grid conditions. By analyzing the distortion mechanism of the input current for a Vienna rectifier in unbalanced grid, the drawback of the conventional modulation waves clamping method for suppressing the input current distortion is illustrated, which shows that the method is ineffective in certain non-ideal grid conditions. Moreover, the proposed method modifies the current command, which realizes adjusting the clamping interval for modulation waves. So signs of the reference modulation wave and the input current are avoided to be inconsistent, and the input current distortion is suppressed. Besides, the quality of the input current is improved effectively. Finally, experimental results show that the proposed method can suppress the input current distortion obviously under the unbalanced grid conditions. Compared with conventional modulation wave clamping method, the THD value of the input current for a Vienna rectifier is reduced effectively (below 2%) with the proposed method.

Small-signal models (SSM) of modular multilevel converter (MMC) based HVDC grid under unbalanced grid conditions in recent literatures do not consider interactions between MMC and dc network. Therefore, it is necessary to correctly model the double-fundamental-frequency zero-sequence circulating currents (DFF-ZSCC) existing under unbalanced grid conditions, although they can be suppressed to avoid penetrating into dc side. In view of that, a general and modular small-signal modeling method of MMC-HVDC grid under unbalanced grid condition is developed. Firstly, a general d-q transformation process for multi-sequence and multi-frequency components is introduced to build the state-space model of MMC electric part in d-q frame. Secondly, the SSM of dc network, which is divided into dc- and double-fundamental-frequency parts, is developed based on the existing frequency-dependent-cascaded-pi (FDC-PI) cable model. Then, to interface MMC stations with dc network under unbalanced grid conditions, a general method to synchronize the variables of double fundamental frequency at dc side of each MMC station is introduced to compose the SSM of the entire HVDC grid from SSMs of each MMC and dc network. Finally, taking a three-terminal MMC-HVDC grid as an example, two SSMs of the MMC-HVDC grid with FDC-PI cable model and single-PI cable model are developed in Matlab, respectively. The small-signal dynamics and stability of both SSMs of the grid under unbalanced grid conditions are compared to validate the accuracy and stability of the proposed SSM of the whole HVDC grid. The simulation results validate the correctness and effectiveness of the proposed modular modeling method.

The three-phase H-bridge or NPC converters are commonly adopted converter topologies for FACTS devices. Both the converters are classified as multilevel converters capable of producing a three-level AC voltage between the phase and the neutral terminals. Either topology is a good solution in the low voltage environment where it is possible to select a switch capable of blocking the required DC bus voltage. If the converter is designed for a high-voltage application, the design stage of these converters may be challenging due to making composite switches for voltage blocking requirements. Besides, there is a need for a large filter for interfacing these converters with the grid to meet the THD requirements as the operating frequency is the line frequency. Therefore, this paper adopts an MMC as an SSSC to enhance power flow in the transmission network and relieve the transmission line against abnormal situations. Besides, PR-based controllers are presented in αβ0 stationary reference frame to provide reliable operation under unbalanced grid conditions. The effectiveness of the MMC-based SSSC and its controller is modeled in FPGAs and integrated with the RTDS through fiber optic cables.

This paper proposes a sliding-mode direct power control (SMDPC) strategy for doubly fed induction generator (DFIG) under both balanced and unbalanced grid conditions using extended active power. When the traditional power theory is used under unbalanced grid condition, the control strategies usually need to be modified and become more complicated. Therefore, an extended active power is proposed in this paper, which is effective under both balanced and unbalanced grid conditions with a simple control strategy. Based on the extended active power, elaborated analysis of the mathematical model of DFIG is obtained. Furthermore, an SMDPC strategy using the extended active power is proposed, which can obtain sinusoidal stator currents and restrain electromagnetic torque ripples under unbalanced grid condition without the need of decomposition process and phase-locked loop (PLL). Comparative experimental studies of the SMDPC using the extended and traditional active powers for DFIG are conducted to validate the effectiveness of the proposed strategy under both balanced and unbalanced grid conditions. In addition, the dynamic performance and robustness of the proposed SMDPC are also proved to be satisfying by the experimental results.

This paper proposes a cooperated control of the grid side converter (GSC) and rotor side converter (RSC) in doubly-fed induction generator (DFIG) wind power generation system under unbalanced grid condition. Mathematical model of doubly-fed induction generator (DFIG) and GSC under unbalanced grid voltage condition are investigated. Dual-dq current control strategies of the RSC and GSC under unbalanced grid condition are detailed studied. A cooperated control strategy of the GSC and RSC under unbalanced grid condition is proposed to provide enhance operation of DFIG system. The GSC is controlled to remove the total active power fluctuation of the system and RSC is controlled to eliminate the DFIG electromagnetic torque oscillation. Simulation based on Matlab/Simulink of a 1.5 MW DFIG prototype was carried out to validate the proposed cooperated control strategy.

The modular multilevel converter-based unified power flow controller (MMC-UPFC) is able to operate under unbalanced grid conditions with symmetric component decoupling. However, the constraint of the voltage limit of UPFC is not considered and no protection schemes are investigated to protect the UPFC from overmodulation under unbalanced grid conditions. To solve this problem, this paper proposes the cascaded control scheme for MMC-UPFC based on voltage limit control and symmetric component decoupling to balance the ac current of the transmission line. With appropriate transformer connections for MMC-UPFC, the negative- and zero-sequence currents are suppressed by the corresponding inner current loops. Considering the voltage limit of MMC, the operating ranges of UPFC-MMC under balanced and unbalanced grid conditions are investigated in both mathematical derivation and point scanning methods. The results are depicted and analyzed in 3-D vision. Based on the analysis of operating regions, the voltage limit control is proposed to protect the MMC from overmodulation and to maximize the controllable region under unbalanced grid conditions. Finally, the final cascaded control structure is constructed. The simulation results obtained in PSCAD/EMTDC are provided to validate the effectiveness and robust performance of the proposed control strategies.

The unbalanced grid condition is one of common fault in the power system, the performance of electronic equipment will reduce when the controller designer without considering the unbalanced grid input. The traditional controller design methods of three-phase pulse width modulation (PWM) converter, are based on the instantaneous power model and the double-closed loops proportional integral (PI) controller, where the positive- and negative-sequence current components are controlled separately. Thus, there are eight mutual influenced control parameters need to be tuned, it is a difficult task. In addition, the performance of PI controller will degrade when the working point changes in a large scale. In this paper, a constant frequency current model predictive control (MPC) strategy is proposed for the three-phase PWM converter under unbalanced grid condition. In this strategy, the positive- and negative-sequence predictive current values are calculated by the predictive model and the cost function of MPC is designed, the duration times of voltage vectors are produced directly by minimizing the cost function in each sector and the space vector pulse width modulation (SVPWM) is used, thus the constant switching frequency of system is guaranteed. The proposed method has less control parameters need to be tuned and can realize the accurately and quickly current adjustment under unbalanced grid condition, which is proved by the simulation results.