Nonlinear Modeling and Transient Stability Analysis of Grid-Connected Voltage Source Converters during Asymmetric Faults Considering Multiple Control Loop Coupling

A three-phase three-wire shunt active power filter based on a H-bridge three-level converter as its main circuit is presented. The dc-link voltage stable conditions and the effects of the fundamental sequence components on the input active power of the inverter are described in details. Then a dc-link voltage control strategy based on the negative sequence current control method is proposed. The dc-link voltage controller is composed of two parts, the first one is to maintain the dc-link average voltage at its reference value, and the second is to achieve the balance of the dc-link voltage by controlling the output negative sequence current. To eliminate the ill effect of the negative sequence fundamental components in load current, a novel harmonic detection algorithm implemented in dual- dq axis is proposed. Finally, experiments are implemented to verify the proposed control strategy, which demonstrate the excellent performance of the new control algorithm.

With widespread application of voltage source converter (VSC) as a key energy-conversion power electronic device by using the phase-locked loop (PLL) technique for synchronization, the system dynamics has become much complicated. In this paper, the nonlinear dynamics and transient stability of the PLL-based VSC system are investigated, within a unified framework of the (normalized) generalized swing equation. It is found that there are three different types of bifurcation, including the generalized saddle-node, Hopf, and homoclinic bifurcations. Within the coexistence parameter region, the basin boundary of the stable equilibrium point shows either a closed-loop or a fish-like pattern. With the help of the equal area criterion (EAC), the transient stabilities under different transient disturbances including short circuit, voltage dip, and power rise are analyzed. Because the equivalent damping of the VSC is state-dependent, the theoretical results based on the EAC are examined. Furthermore, based on the analytical results from the generalized swing equation, the principle for all major transient stability enhancement methods is uncovered. All these findings are well verified by extensive electromagnetic transient simulations. Therefore, the generalized swing equation provides a deeper physical insight and plays a crucial role in transient stability problems in power-electronic-dominated power systems, similar to the swing equation in traditional power systems.

This paper investigates the influence of a high voltage direct current (HVDC) overlay grid on the transient voltage and rotor angle stability with respect to HVDC converter fault ride-through behavior. For this purpose, the studied meshed hybrid AC/DC transmission grid is established in MATLAB/Simulink with user defined dynamic models of voltage-source converters (VSC) considering fault ride-through requirements of the German Technical Connection Rules for extra high-voltage (VDE-AR-N 4130). The voltage profile during three-phase short-circuit faults as well as bus voltage relative entropy after fault-clearing as stability indices are analyzed. The influence of k-factor and power system stabilisers on transient stability is also investigated.

ABSTRACTIn light of the exponential growth in renewable energy generation, voltage source converters (VSCs) have garnered extensive attention, particularly concerning control methodologies and steady‐state operation analysis. Nevertheless, the comprehensive transient operation analysis under large disturbances remains a critical issue, owing to the challenges in the analysis and characterisation of high‐order nonlinear VSC systems. In this regard, a coupling‐factor‐based nonlinear decoupling (CFND) method is proposed in this paper. Firstly, by evaluating the correlation degree between state variables with coupling factors, the original nonlinear high‐order system can be divided into multiple decoupled first‐ or second‐order cubic modes, which can facilitate the transient stability analysis. Secondly, with the proposed CFND method, the full‐order large‐signal model of LCL‐filtered grid‐connected VSCs is created to analyse the transient stability under grid fault conditions. It is revealed that increasing phase‐locked loop (PLL) bandwidth and decreasing current loop bandwidth are unfavourable to the transient stability. Besides, decreasing the active current reference or increasing the reactive current reference is beneficial for transient stability during the low voltage ride‐through (LVRT) process. Finally, the effectiveness of the stability analysis results is verified through hardware‐in‐loop (HIL) experiments.

This paper formulates the relation between the Phase-Locked Loop (PLL) dynamics of a grid-connected distributed source and the impedance of the grid. Conventionally the design of the PLL for a grid following inverter is performed independently of the grid impedance. With the advent of micro-grids, these design procedures require modification. Microgrids are characterized by higher grid impedances which severely impact the PLL dynamics. The grid voltage in a microgrid is not a stiff variable and thus cannot be assumed to be independent of its interaction with a distributed source. The PLL dynamics in these cases affect the voltage at the point of common coupling (PCC) and vice-versa. In this paper, the relation between the grid impedance and the PLL parameters is analytically derived using dynamic phasors. A distributed resource connected to the grid via a 3-phase inverter is considered for the analysis. Grid synchronization is achieved using a synchronous reference frame (SRF) PLL. It is shown that under weak grid conditions, the PLL can get de-synchronized if the magnitude of grid impedance or the current levels are higher than the thresholds derived in this paper. Microgrids with higher grid impedance are highly susceptible to such situations. The design of SRF-PLL for grid-connected inverters thus needs to include an estimate of the maximum system ratings and the grid impedance.

Legacy protection schemes face new challenges as Inverter Interfaced Distribution Generation (IIDG) significantly changes the transient fault response of the distribution grid. The performance of the protection near the IIDG side is adversely affected by Low Voltage Ride Through (LVRT) and the negative sequence current suppression control characteristics of the IIDG. The operational characteristics of the protection are very different from those of the legacy protection schemes used in the distribution grid. Traditional overcurrent protection schemes cannot meet the requirements of selectivity and sensitivity. This paper analyses the influence of the IIDG on the protection schemes used in the distribution grid. Based on the positive sequence voltage polarization impedance criterion this study proposes a polarizing impedance criterion based on the fault component of positive sequence voltage, which can adaptively follow the fault resistance variation to satisfy the requirements of grid operation. The simulation results show that: (a) the proposed criterion is immune to the adverse effects of the transient characteristics of the IIDG; and, (b) it can adaptively follow the change of fault resistance making it suitable for application in short distribution lines. Using specialized System-on-Chip technology, a new distance protection device has been developed and tested on an industrial site. Simulation results and field tests showed that the new distance protection meets the requirements of the distribution grid with IIDGs.

The transient behavior of DC-link voltage (DCV) significantly affects the low-voltage ride-through for phase-locked loop (PLL)-based grid-connected doubly-fed induction generator (DFIG) systems. This study investigates the DCV transient behavior of a PLL-based DFIG system under asymmetrical grid faults. First, by considering the coupling characteristics of positive and negative sequence (PNS) components, a nonlinear large-signal model of DCV is developed. Furthermore, the transient characteristics of DCV under varying parameters are analyzed using phase trajectory diagrams. In addition, the transient stability (TS) mechanism of DCV during asymmetrical faults is examined through an energy function approach. The analysis indicates that the transient instability of DCV is primarily associated with the control characteristics of PNS PLLs, while the TS level of DCV is mainly determined by the power coordination control between the rotor side converter and grid side converter. Moreover, a coordinated control strategy is proposed to enhance the TS of DCV under asymmetrical grid faults. Finally, both simulation and experimental results are presented to validate the theoretical analysis and the effectiveness of the proposed strategy.

Doubly fed induction generator (DFIG) still shares a large part in today's wind power market. It provides the benefits of variable speed operation cost-effectively, and can control its active and reactive power independently. Crowbar protection is often adopted to protect the rotor-side voltage source converter (VSC) from transient overcurrent during grid voltage dip. But under unbalanced grid voltage condition, the severe problems are not the transient overcurrent, but the electric torque pulsation and dc voltage ripple in the back-to-back VSCs. This paper develops dynamic models in MATLAB/Simulink, validates it through experiments, investigates the behavior of DFIG during unbalanced grid voltage condition, and proposes new controllers in separated positive and negative sequence. Methods to separate positive and negative sequence components in real time are also developed, and their responses to unsymmetrical voltage dip are compared. Simulation results prove that the separated positive and negative sequence controllers limit the torque pulsation and dc voltage ripple effectively.

Stability of wind power is the long-concerned issue especially in the context of high grid-integration level. Different from traditional synchronous generators, the transient synchronization stability of the wind turbine is maintained by the phase-locked loop after being disturbed. This paper mainly discusses the transient stability of the doubly-fed wind turbine. Firstly, according to the principle of doubly-fed wind turbines connected to grid, a doubly-fed wind turbine model under the time scale of transient stability analysis is established. Then, by theoretically analyzing the dynamic process after being disturbed, the acceleration and deceleration area of phase-locked loop analogous to the synchronous generator is proposed. The critical stability region of the system is analyzed, and a calculation method for the transient synchronization stability margin of doubly-fed wind turbines is proposed. Finally, a detailed model of four-machine two-zone system is built on MATLAB/Simulink software, and the correctness of the conclusion is verified by analyzing the influence of key parameters on transient stability.

The fully rated converter of type 4 wind turbines is capable of providing dynamic voltage control during grid faults by injecting controlled reactive currents. This paper describes three different dynamic voltage control options during unbalanced grid faults: 1) the positive sequence voltage control with only a positive sequence reactive current injection and suppression of the negative sequence current; 2) the positive sequence voltage control with limitation of the positive sequence reactive current injection and suppression of the negative sequence current; and 3) the positive and negative sequence voltage control with both a positive and a negative sequence reactive current injection. These different control options are compared in simulations of a wind power plant connected to a meshed power system, including synchronous generators. It is shown that both the positive sequence voltage control with limitation and the positive and negative sequence voltage control can overcome the voltage rise and voltage distortion that can occur with pure positive sequence voltage control without limitation. Both of these options have a distinct fault response, where the positive and negative sequence voltage control results in a fault response that resembles the fault response of a synchronous generator with higher fault current contributions in the faulted phases.

This article investigates the phase-locked loop (PLL) synchronization transient stability (PLL-STS) issue of grid-tied multiple voltage source converters (MVSCs) systems, specifically focusing on transient stability evaluation and transient interaction analysis. First, a novel PLL-STS assessment method for MVSCs systems has been proposed, which considers angular frequency jumps, nonlinear damping, and transient interactions among VSCs. Compared with previous studies, this method can accurately evaluate PLL-STS of MVSCs system since the acceleration and deceleration areas of VSCs can be accurately determined by combining equal-area criterion and numerical integration method. Moreover, it can identify the dominant converters which lead to transient instability. Second, by introducing static and dynamic interaction coefficients, influence of static and dynamic interaction on the transient stability of individual converters is quantitatively analyzed. Finally, the theoretical analysis results are verified by PSCAD/ EMTDC time-domain simulation results and RT-LAB hardware-in-the-loop experimental results.

This paper presents a salient method to find an optimal bandwidth for low noise phase-locked loop (PLL) applications by analyzing a discrete-time model of charge-pump PLLs based on ring oscillator VCOs. The analysis shows that the timing jitter of the PLL system depends on the jitter in the ring oscillator and an accumulation factor which is inversely proportional to the bandwidth of the PLL. Further analysis shows that the timing jitter of the PLL system, however, proportionally depends on the bandwidth of tile PLL when an external jitter source is applied. The analysis of the PLL timing jitter of both cases gives the clue to the optimal bandwidth design for low noise PLL applications. Simulation results using a C-language PLL model are compared with the theoretical predictions and show good agreement.

Phase locked loop (PLL) and Park transformation largely affects the stability of a grid-inverter system. Impedance-based approach is employed to analyze the effect of PLL to stability in this paper. Self-admittance and accompanying admittances are set up to represent the inverter including the PLL effect, and Nyquist criterion is employed to analyze the system stability. An asymmetric current control scheme is proposed to alleviate the PLL effect on stability of the grid-inverter system. The proposed control scheme is simple and practical in the sense that it is derived using the existing current controller. An inverter admittance model including the PLL effect and asymmetric current controller is constructed to evaluate the stability of the inverter-grid system. The relationship between the asymmetric ratio and PLL bandwidth is established to ensure the stability. Experimental results demonstrate that the proposed asymmetric control scheme achieves the stability without sacrificing the PLL bandwidth.

There is a need to develop new control strategies for interconnecting Renewable Energy Sources (RES) to the power system due to the ever increasing penetration of RES and in particular for wind power systems (WPS). The control strategies are typically based on a fast and accurate detection of the phase angle of the grid voltage which may be estimated by using a Phase-Locked Loop (PLL) control circuit. The performance of the PLL under normal and abnormal operational conditions is a crucial aspect, since the RES is desired to operate to support the power system under grid fault conditions. This paper investigates the performance of three different PLLs: a synchronous reference frame PLL (dqPLL), a stationary reference frame PLL (αβPLL), and a decoupled double synchronous reference frame PLL (ddsrfPLL). The results of this investigation motivate to the development of a new hybrid PLL which is a combination of the abovementioned PLLs and uses the advantages of each PLL. The proposed decoupled stationary reference frame PLL (dαβPLL) may be an appropriate solution to use in an interconnected RES with Ride Through Fault (RTF) capability, since it prevails the other PLLs with regards to its accuracy under unbalanced faults. Further, it has a lower deviation of the estimated phase after the fault occurs. The performance of the new hybrid dαβPLL is verified through simulations and experiments. Further the new PLL is used in an interconnected RES through experiments under normal and RTF operation.

Current control in three-phase voltage source converters (VSC) is usually performed in the dq-coordinate system because of its ability to eliminate steady-state tracking errors. For grid-connected VSCs, such as PWM rectifiers and grid-parallel inverters for integration of renewable energy and energy storage devices, a phase-locked loop (PLL) is commonly used to synthesize a set of harmonic-free voltages synchronized to the grid voltages for transformation between the dq and the abc coordinate systems. The multitude of control functions in large systems, such as wind turbines, necessitate the use of multiple digital control devices. In such cases, the PLL output has to be transferred among different devices. To reduce the bandwidth requirements and noise susceptibility of such signal transfer, this paper presents a PLL implementation method that distributes the PLL function into different devices. Instead of transferring directly the synthesized grid voltage angle, the synthesized grid frequency, which has much lower signal bandwidth, is communicated. A binary reset signal is used to eliminate the difference between initial values of the distributed integrators that convert locally frequency into reference angle. An experimental system consisting of a three-phase VSC, a TMS320F28335 DSP, and an Altera DE2 board with a Cyclone II EP2C35 field programmable gate array (FPGA) is used to demonstrate the proposed concept.