Sequence Impedance Model Research Articles

Improved sequential impedance modeling and stability analysis of virtual synchronous generators considering frequency coupling effects

With the increasing penetration rate of distributed power supply, the interaction between grid-connected inverters and power grid is prone to harmonic oscillation, which will seriously threaten the stable operation of power grid. At present, impedance analysis has been proved to be an effective tool to study the stability of grid-connected systems. However, few studies have considered the influence of frequency coupling effect on the output impedance characteristics of grid-connected inverters. To solve this problem, the sequence impedance model of a three-phase grid-connected inverter controlled by a virtual synchronous generator is established by harmonic linearization method based on the frequency coupling effect. In addition, an improved method of sequence impedance modeling based on grid impedance is proposed to effectively eliminate the influence of coupling terms. Finally, the correctness and practicability of the proposed simplified sequence impedance model are verified by simulation and experiment.

Sequence impedance modeling of grid-following LC-type voltage source converter

Sequence impedance modeling of grid-following LC-type voltage source converter

LQR control strategy for virtual synchronous generator adapted to stiff grid

Virtual synchronous generators (VSG) exhibit good small-signal stability in low short-circuit ratio (SCR) grids. However, the small-signal stability of the grid decreases as its SCRs increase, and there is even a risk of sub-synchronous resonance (SSR). The VSG sequence impedance model considering the frequency coupling effect is developed. The reasons for SSR caused by VSG integration into a stiff grids are analyzed using the sequence impedance analysis method and the Nyquist criterion. To enhance the grid-connected stability of VSG under stiff grids conditions, a linear quadratic regulator (LQR) control strategy with full-state feedback was proposed. The control strategy of LQR can effectively improve the phase margin of VSG output impedance in the low-frequency region, and it also exhibits strong robustness to variations in grid short-circuit ratios. It can also significantly improve the stability margin of the grid-tied system consisting of VSG and stiff grid, and effectively suppress the occurrence of SSR. Finally, the effectiveness and reliability of LQR control strategy are verified by OPAL-RT experimental platform.

Parameter identification of PLL for grid‐connected inverter based on parameter sensitivity analysis

AbstractUnder the condition of weak grid, the phase‐locked loop (PLL) is one of the main reasons for the sub‐synchronous oscillation of the grid‐connected inverter. Therefore, it is necessary to identify the PLL parameters of the grid‐connected inverter for the analysis of the inverter operating performance. This paper uses the sequence impedance model and measured impedance data of grid‐connected inverter to construct the identification function for parameter identification of PLL, and the function is calculated by particle swarm optimization algorithm to overcome the nonlinear problem of sequence impedance model. In addition, the identification frequency band is selected based on PLL parameter sensitivity to improve the parameter identification accuracy under the same impedance measurement error. At different frequencies, the positive correlation between the sensitivity of the PLL parameters and the identification accuracy is proven to determine the definite frequency band for PLL parameter identification of grid‐connected inverter. Finally, the feasibility and effectiveness of the above research are verified by simulation and semi‐physical experiments.

Comparison Study of the Wideband Oscillation Risk of MMC between Grid-Following and Grid-Forming Control

Currently, research on the small-signal stability of grid-forming converters under two control modes, grid-following and grid-forming, mainly focuses on low-level converters. However, studies on the differences between grid-following modular multilevel converters (MMC) and grid-forming MMC are limited. A comprehensive analysis of the wideband oscillation risk differences in MMC-HVDC systems under these two control modes from the perspective of impedance characteristics is necessary. Therefore, based on the harmonic state-space (HSS) modeling theory, this article establishes wideband sequence impedance models for grid-forming and grid-following MMC. Subsequently, this article identifies key control parameters affecting the impedance characteristics of MMC under two control modes. The wideband oscillation risks of MMC-HVDC systems under both control modes are compared. The study indicates that when the grid strength weakens, grid-following MMC faces instability risks, while grid-forming MMC can maintain stability. In instances where high-frequency resonance peaks exist in the impedance of the grid, both control modes of MMC may face instability risks. Furthermore, by adjusting the obtained key control parameters of MMC, this article effectively suppresses the oscillation risk discussed above. Finally, the analysis results are verified through an electromagnetic transient simulation.

VSG Sequence Impedance Modeling and Stability Analysis of Dead-Beat Control

Virtual Synchronous Generator uses dead-beat predictive control in the voltage and current loop to improve the dynamic response speed of the system, but the presence of zero-order hold and computation time can lead to system instability. To address this issue, this paper adopts an improved dead-beat predictive control strategy for VSG. This is achieved by linear interpolation to forward predict voltage-current reference values to reduce the impact of delay, while introducing error compensation coefficients to enhance the stability of the voltage-current inner loop of VSG. The selection of error compensation coefficients is based on closed-loop impulse response functions. A harmonic linearization method is used to construct a complete sequence impedance model of VSG, and it's stability is analyzed. The results indicate that VSG's negative sequence impedance exhibits instability in the low-frequency range. To address this, a method of introducing a virtual resistor into VSG is proposed to improve stability. By constructing a sequence impedance model of VSG that includes virtual resistance, the variations in system stability under different virtual resistances and grid impedances are analyzed. The effectiveness of the proposed method is verified by building a VSG model.

Sub-synchronous oscillation suppression strategy for virtual synchronous generators based on dual-loop sliding mode control

The virtual synchronous generator (VSG) has synchronous voltage source characteristics that can effectively improve the stability of high-penetration renewable energy power systems. However, the output impedance of VSG using traditional voltage–current inner-loop control has lower damping in the sub-synchronous frequency range. Therefore, when the VSG is connected to a grid with series compensation for long-distance transmission of renewable energy, in the sub-synchronous frequency range, there is a potential interaction between the inductive output impedance of VSG and the capacitive impedance of the line, leading to the occurrence of sub-synchronous resonance (SSR). To address this challenge, the stability of a series-compensated grid-connected system employing voltage–current inner-loop control was analyzed using VSG sequence impedance modeling. A dual-loop sliding mode control strategy (SMC-DL) was proposed to suppress SSR occurrence. This control strategy can significantly enhance the damping of VSG’s output impedance in the sub-synchronous frequency range, and effectively suppress SSR. Compared to traditional control strategies, this control strategy does not require the addition of virtual impedance, avoids voltage offset issues, adapts to grids with different series compensation levels. Finally, the effectiveness of this approach was verified through simulations and experiments.

Sequence Impedance Modeling and Analysis of Modular Multilevel Converter Considering DC Port Characteristics

The extensive deployment of Modular Multilevel Converters (MMCs) in AC/DC systems can lead to complex resonance issues. Impedance modeling forms the foundation for analyzing the stability of interconnected system. Existing investigations primarily address resonance concerns on the AC side of MMC. In the process of impedance modeling, the DC system is generally approximated as an ideal voltage source, thereby neglecting its dynamic impact on the impedance characteristic of MMC. Such simplification may result in inaccuracies within stability analysis findings. Based on the multi-harmonic linearization method, this paper introduces an impedance modeling approach that takes into account the characteristics of the DC port. Taking DC voltage control as a case study, the impedance model for the AC side of the MMC is established. The results of programming calculation and simulation measurement of sequence impedance are mutually verified. Finally, the MMC impedance responses determined by different DC port characteristics are analyzed. Significant alterations in MMC impedance characteristics are introduced by DC side resistance and capacitance, which may result in negative damping effects and a decrease in system stability margins. The DC side inductance has a relatively minor impact on MMC impedance responses. The analysis results show that the sequence impedance model of MMC considering DC port characteristics can improve the accuracy of stability analysis results.

High‐frequency resonance in HVDC and wind systems: Root causes and solutions

AbstractThis paper presents methods to model and solve high‐frequency resonance problems in HVDC and wind power systems. Control and digital PWM delays are identified as a common root cause for such resonances. A systematic method to include such delays in small‐signal sequence impedance models is presented. The developed models are fully validated and used to characterize the effects of delay on system stability. In addition to full models that can predict the associated impedance and negative damping behaviour accurately, simplified approximate models are also presented to gain insights. The method is applied to type‐III and type‐IV turbines as well as HVDC converters based on modular multilevel converters (MMC). In addition to resonance of MMC and wind turbines with overhead transmission lines, the paper also identifies several other modes of high‐frequency resonance, including resonance between wind turbines and MMC HVDC converters, among different wind turbines, and between MMC HVDC converters and cables. Different methods to damp high‐frequency resonances are also discussed and demonstrated.

Suppression Strategy of Subsynchronous Oscillation Based on Dynamic Voltage Compensation Control for Grid-Forming D-PMSG in Weak Grid

The virtual impedance can suppress the low-frequency oscillation effectively caused by the power coupling effect for the grid-forming direct-drive permanent magnet synchronous generator (D-PMSG). However, there are few studies on the influence of virtual impedance on the subsynchronous oscillation caused by the interaction between the grid-forming D-PMSG and the weak grid. In this paper, the mechanism of virtual impedance improving the stability of virtual synchronous generator (VSG) control for the converter is revealed from the perspective of power coupling, and the influence of virtual impedance on the system stability in subsynchronous frequency range was analysed based on the sequence impedance model. The analysis results show that the virtual inductance cannot effectively improve the oscillation suppression effect, but the virtual resistance can greatly improve the damping characteristics of the system which has a good oscillation suppression effect. However, excessive increase in virtual resistance will cause power coupling oscillation, even subsynchronous oscillation, which shows limitations in subsynchronous oscillation suppression. To solve the problem, a dynamic voltage compensation control method based on active disturbance rejection control (ADRC) was proposed, and the parameters are designed by bandwidth method. The method can suppress the subsynchronous oscillation effectively in a certain frequency range under different grid strength and disturbance conditions. And it shows strong adaptability and good system robustness in weak grid. Finally, the effectiveness of the proposed oscillation suppression strategy was verified by time domain simulation.

Detailed Wideband Impedance Modeling and Resonance Analysis of Grid-Connected Modular Multilevel Converter

Modular multilevel converter (MMC) tends to cause resonance instability in interconnected systems. Current studies on the stability of MMC mainly focus on high-voltage and large-capacity power systems, while the impedance modeling process of MMC ignores the harmonics of the submodule (SM) capacitor voltages and the influence of voltage feedforward control. The applicability of the MMC impedance model with fewer submodules is doubtful. According to the circuit structure and control mode, the AC-side sequence impedance model of the MMC is established, which takes into account the capacitor voltage balance control of submodules and voltage feedforward control. Based on the RT-Lab control hardware-in-loop (CHIL) test platform, the MMC impedance frequency scanning was carried out to verify the accuracy of the impedance modeling method. The influence of control parameters in different frequency bands on the impedance characteristics of MMC was studied. The AC terminal voltage feedforward causes phase lag in the mid-/high-frequency range and increases the risk of resonance. In the low-frequency range, the dynamics and control of capacitor voltages reduce the impedance magnitude of MMC. Using the resonance phenomenon of an MMC connected to a weak grid as an example, the high-frequency resonance mechanism caused by control parameters is analyzed from the perspective of the negative damping effect. The simulation results show that the detailed wideband impedance model can improve the accuracy of the stability analysis results.

Impedance Shaping Effects and Stability Assessment of Circulating Current Control Schemes in Modular Multilevel Converters

Control of circulating current can help modular multilevel converters (MMCs) improve the internal performance, but only the conventional circulating current suppression control has been considered in impedance models to investigate MMC-grid interactions. In this paper, the sequence impedance responses of circulating current injection methods based on instantaneous information are modeled for stability analysis. Compared with circulating current control schemes based on predefined references, the circulating current injection methods based on instantaneous information introduce couplings among circulating current, output current and capacitor voltage control loops, which influence the MMC impedance in the low frequency range. This paper reveals that injection of second harmonics in the circulating current reduces the capacitor voltage ripples, but the system stability is compromised due to the couplings. The MMC stability boundaries for different circulating current controllers are defined with the help of sequence impedance model and Bode-plot-based analysis. The impedance model and stability assessment are validated by frequency scan results and case studies.

Sequence Impedance Modeling and Optimization of MMC-HVDC Considering DC Voltage Control and Voltage Feedforward Control

The dynamic performance of the DC bus significantly influences the impedance characteristics of MMC and the system stability in a high-voltage direct current system. However, most of the existing MMC-HVDC system stability research simplifies the DC side as an ideal voltage source and ignores the impacts of voltage feedforward control, which affects the accuracy and practicability of stability analysis. In this paper, a sequence impedance model considering both DC voltage control and voltage feedforward control is developed, and the necessity of considering DC control and voltage feedforward control for MMC-HVDC stability analysis is illustrated. Then, the impact of control parameters on MMC-HVDC impedance is discussed, and the boundary conditions of control parameters are also derived. Finally, a method of control parameters design and impedance optimization for MMC-HVDC based on the stability boundary is proposed. Compared to the traditional optimization method, the system stability is further improved by the impedance optimization method proposed this paper.

Research on the influence of switching frequency on the stability of large-scale distributed generation system

Wind power generation is generally a large-capacity low-switching frequency power station, and photovoltaic power generation is generally a small-capacity high-switching frequency power station. Large-scale access of different types of new energy power stations increased risk of grid voltage fluctuations. Therefore, in order to analyze the variation law of the stability of different types of new energy sources connected to the weak grid, it is very important to analyze the stability of inverters with different switching frequencies, but there are few studies on this issue. In this paper, the detailed sequence impedance model of the current-controlled inverter is firstly established, and its correctness is verified by frequency sweeping. Secondly, considering the control bandwidth, ripple suppression and filtering performance, the filtering parameters of inverters with different switching frequencies are designed using a unified standard. On this basis, the stability criterion based on impedance ratio is used to analyze the stability variation law of inverters with different switching frequencies under strong and weak grid conditions. Finally, the correctness and accuracy of the theoretical analysis are verified by simulation experiments.

Impedance modelling and stability assessment for grid‐connected dual‐PWM adjustable speed drives with motor torque oscillations

The grid-connected dual-PWM adjustable speed drives (ASDs) modulate the energy of the motor torque oscillation and inject it into the power system, potentially causing low-frequency oscillation (LFO) in the grid. In this study, considering the motor torque oscillation and harmonic common-modulation of the both-side converters, the precise sequence impedance models are derived for dual-PWM ASDs using the harmonic linearisation method. Based on the derived impedance of dual-PWM ASD, the torque oscillation, which is equivalent to the time-varying impedance, causes a series of discontinuities at the torque-oscillation-related frequencies on its amplitude-frequency curve. Moreover, these discontinuous drops make it more likely to intersect with the amplitude-frequency curve of the grid impedance, which may lead to LFO of the grid. Then, by applying the proposed impedance model and Bode plot, the stability of the grid-ASD cascade system with motor torque oscillation is assessed. The conclusions of stability analysis demonstrate the exact mechanism that the mechanical system oscillations lead to the grid-converter cascade system instability through the common-modulation and coupling of the dual-PWM ASD. Finally, experimental results on a 3 kW ASD system in the laboratory and measured results on the distribution grid in the Shanghai Yangshan Deepwater Port area verify the correctness and effectiveness of the proposed model and stability assessment.

High-Frequency Stability Analysis and Impedance Optimization for an MMC-HVDC Integrated System Considering Delay Effects

Delay generated by digital control will inevitably lead to negative damping of Modular Multilevel Converter (MMC), which also has significant impacts on the high-frequency stability of the integrated system. Controller parameter optimization is an effectively method for MMC impedance optimization and high-frequency resonance suppression. This paper firstly extends the sequence impedance model of MMC by considering delay effects, and analyzes the high-frequency impedance characteristics as well as the stability of the MMC integrated system. Then, the effect of delay on the frequency range of MMC shows negative damping can be analyzed quantitatively by a vector diagram. Based on the quantified frequency range, the boundary of controller parameters can be derived. Finally, an MMC impedance optimization method that traversal all the values within the derived parameter boundaries to obtain the optimal controller parameters that maximize the phase margin of the system.

Analysis of Multi-Frequency Oscillation Stability in a Prosumer Power Network

Multi-frequency oscillation is a new type of electromagnetic oscillation issue in power systems caused by the increasing penetration of renewable power and power electronic devices. This study investigates the risks and influencing factors of multi-frequency oscillation in a prosumer power network where a variety of converter-based resources exists. For the feasibility of analysis, the internal and external stability of the study system are defined and analyzed based on sequence impedance models. Analysis results show the impacts of control parameters of prosumers, length of cables, transformer ratios, local grid strength, and power and capacity of prosumers on the risks of oscillation. Accordingly, despite the poorly tuned control parameters, the study system has higher risks of multi-frequency oscillation with longer cables, lower-rated voltage of cables, larger capacity, and inductive power consumption of the neighboring prosumers. Frequency-domain analysis results are demonstrated by EMTDC/PSCAD simulations.

Transfer function-based analysis of harmonic and interharmonic current summation in type-III wind power plants using DFIG sequence impedance modeling

This paper presents a new Transfer Function (TF)-based approach to evaluate the summation of complex harmonic and interharmonic current primary emissions in a wind power plant. A comprehensive impedance modeling of a doubly-fed induction generator including the Phase Locked Loop (PLL), induction generator, and current control loops of the converters is included in the TFs. A small-signal impedance modeling consisting of positive/negative-sequence modeling up to 50th harmonic order is adopted. The updated TF models are then used to calculate the contribution of each wind turbine to the total harmonic and interharmonic current distortions at the point of interconnection. Three phase angle distribution patterns are also presented to assess the stochastic behavior of the harmonic and interharmonic currents using the concept of “aggregation factor”. The variations of the aggregation factor with the PLL bandwidth are also investigated. Besides, the obtained primary emission TFs are used to adjust α-exponent in IEC 61000-3-6 summation rule. Analytical results are presented and compared to the simulation results where it is concluded that the proposed approach is more accurate than the previous approaches of TF modeling and related phase angle distribution patterns.

Impedance Modeling and Analysis of Medium-Frequency Oscillation Caused by VSC-HVDC Connected to Local Weak Grid and DFIG-Based Wind Farms

In the northwest of China, a strategy to transmit the wind-thermal–bundled power from the local grid and doubly fed induction generator (DFIG)–based wind farms through a voltage source converter–based HVDC (VSC-HVDC) can be widely applied. However, since the local grid is usually weak, a new type of electrical oscillation in the medium-frequency region may occur in the sending-end converter (SEC) of VSC-HVDC with PQ-control. The mechanism of this oscillation caused by the interaction between the DFIG, local grid, and SEC is not entirely understood. In this study, the sequence impedance model of the sending-end converter (SEC) of VSC-HVDC with the PQ-control outer loop and PLL is derived with the explicit analytic expression, and then, the oscillation mechanism is explored based on the intuitive analysis of the system impedance frequency characteristics. Compared with the subsynchronous oscillation (SSO) caused by the DFIG or power inverter, the theoretical analysis shows that this medium-frequency oscillation (MFO) mainly originates from the SEC due to its negative damping effect between about 100 and 200 Hz. In addition, the impact of the system controller parameters and operating conditions of the DFIG, local grid, and SEC on the oscillation characteristics is analyzed in detail. Finally, the correctness of the theoretical analysis is validated by time-domain simulation.

Frequency-Coupled Impedance Modeling of Virtual Synchronous Generators

The impedance of the virtual synchronous generator (VSG) is an effective method to analyze the dynamic interactions between the VSG and the grid. For the existence of power controllers and asymmetric inner-loop controllers in the d- and q-axis, there are couplings in the output sequence impedance of VSG. Although the couplings are relatively small, they still have a significant impact on the stability performance. However, there is no result published on this aspect up to now. To bridge this gap, a sequence impedance model based on harmonic linearization is established in this paper, which explicitly reveals the mirror frequency effect (MFE) in VSG. Subsequently, the relationships between the power controllers and the MFE are demonstrated. Finally, simulation results verify the feasibility and correctness of the theoretical analysis presented above.