Grid-connected Voltage Source Converters Research Articles

Impedance modeling and quantitative stability analysis of grid-connected voltage source converters under complex unbalanced conditions

The stability issues caused by voltage source converters (VSCs), which are commonly used in renewable energy systems, are investigated in this paper. Much literature has investigated the impedance models and quantitative stability analysis for converters under the weak and unbalanced grid. However, on the one hand, harmonic-transfer-function (HTF)-based modeling methods are complex, and the established infinite-order models may suffer from unreasonable truncation. On the other hand, these existing impedance models without considering all unbalance factors are inaccurate. Both of these may bring wrong stability analysis results. Therefore, this paper proposes a simple impedance extension method and considers all unbalance factors to derive the impedance model of the converter. However, due to the established higher-order impedance model, the traditional impedance-ratio based stability analysis method is not applicable to multi-input multi-output (MIMO) systems. The commonly used eigenvalue-based GNC and diagonalization-based methods applicable to MIMO systems are cumbersome and not suitable for quantitative analysis. Therefore, in this paper, a quantitative analysis tool of system stability based on the phase-frequency characteristics of determinants is developed. Then, stability regions in the multi-parameter space are obtained. Finally, the established impedance model and the quantitative analysis results are validated via both simulations and hardware experiments.© 2017 Elsevier Inc. All rights reserved.

Linear Time-Periodic theory-based novel stability analysis method for voltage-source converter under unbalanced grid conditions

Small-signal stability analysis is essential for the safe operation and parameter design of power electronic-dominated grids. Unbalanced conditions introduce more frequency-coupling terms, which are unneglectable in the stability assessment. This paper proposes a novel Linear Time-Periodic (LTP) theory-based stability analysis method and focuses on grid-connected voltage-source converters (VSCs) without improved unbalancing controls. Firstly, the analysis of fundamental solutions of the LTP system reveals that each LTP mode is characterized by a unique damping factor and multiple oscillation frequencies, defined by LTP eigenvalues and related transformation vectors, i.e., (λi,Vi(t)). Then, a method for calculating (λi,Vi(t)) is proposed using the characteristic matrix of the Harmonic State-Space (HSS) model. An iterative sorting method based on the time-domain interpretation of HSS eigenvalues/eigenvectors is proposed to determine accurate (λi,Vi(t)) in the case of the minimum truncation order. Finally, generalized definitions and calculation methods of the widely used indicators for modal analysis are presented to assess system stability and guide the parameter design. Numerical and simulation results verify the proposed stability analysis method and indicate its advantages compared to the existing Floquet and HSS methods.

Robust Current Control for Grid-Connected VSC: Nonlinear Adaptive Control with Perturbation Estimation

This paper introduces a robust control strategy for grid-connected voltage source converters using Nonlinear Adaptive Control (NAC) enhanced by a perturbation observer (PO). This approach precisely regulates grid current and adapts to unknown dynamics, time-varying parameters, and disturbances impacting the system. By estimating and compensating for these perturbations, the strategy achieves adaptive feedback linearization, effectively managing the system’s inherent nonlinearity without requiring an exact model or extensive measurements. The NAC offers substantial improvements over traditional vector control and feedback linearization, particularly under conditions where grid voltage significantly deviates from normal levels. Simulation results confirm the superior performance of the proposed method.

Direct Transient Stability Assessment of Grid-Connected Voltage Source Converters: A Transient Energy Functions Perspective

Direct Transient Stability Assessment of Grid-Connected Voltage Source Converters: A Transient Energy Functions Perspective

Grid Synchronization Control for Grid-connected Voltage Source Converters Based on Voltage Dynamics of DC-link Capacitor

Grid Synchronization Control for Grid-connected Voltage Source Converters Based on Voltage Dynamics of DC-link Capacitor

Conditions of Existence and Uniqueness of Limit Cycle for Grid-Connected VSC With PLL

This paper investigates the large disturbance stability of single voltage source converter (VSC) connected to the infinite bus system through the transmission line. One conservative stable region is obtained via the direct method of Lyapunov. Based on the Poincaré Theorem, it is interesting to find there might exist limit cycle between the obtained stable boundary and the angle of unstable equilibrium point (UEP). Accordingly, the nonlinear damping effect on the system stability is defined, and one limit cycle exists when the positive and negative damping effect over one period is mutually balanced. A conservative existence condition of limit cycle is further derived by constructing a proper piece-wise curve to approximate one specified unstable system trajectory. The derived analytical existence condition can directly predict the limit cycle without numerical simulations. Finally, the paper also proves that the studied dynamic system has at most one limit cycle, and if it exists, it is unstable.

Transient Stability Analysis and Improvement for the Grid-Connected VSC System With Multi-Limiters

As a widely configured controller, the limiter is essential to ensure the security of the voltage source converter (VSC), which affects the stability characteristics of the grid-connected VSC system under severe faults. However, due to limiters' hard algebraic constraints, the existing methods have yet to reveal the stability mechanism related to the multi-limiters thoroughly. In this paper, the stability mechanism of the grid-connected VSC system with multi-limiters is investigated, and an improved Filippov Theorem is proposed to study the dynamic characteristics. Two kinds of points are essential to the stability, namely, the fixed switching point(FSP) and the fixed ending point(FEP). Expressly, transient stability can be guaranteed by the condition that FSP is in the region of attraction(ROA), even if other parts of the trajectory are outside the ROA. Moreover, the existence of FEP contributes to some control loop failure, which does not induce instability but may cause the power into the grid to be inconsistent with the reference value. This paper presents the analytical methods for these crucial points, which avoid time-domain simulation. What follows illustrates how to enhance the stability characteristics by configuring the FSP and FEP. Another advantage of the proposed method is easily extended to the VSC with multi-limiters and different control structures.

Large-signal Stability Analysis of Grid-connected DC Microgrid with VSC

The grid-connected DC microgrid under the background of high penetrations of renewable energy sources and high penetrations of inverter-interfaced devices has the characteristics of strong nonlinearity and poor immunity, which leads to the problems of large-scale voltage fluctuation and instability when the grid-connected DC microgrid suffers large disturbances, and it seriously influences the security and stable operation of the system. Therefore, a large disturbance stability criterion which is based on the mixed potential theory (MPT) for the DC microgrid model with a grid-connected voltage-source converter (VSC) is proposed. This paper also analyzes the mechanism of the conservatism of the stability criterion, verifies the accuracy of the large disturbance stability standard, and analyses the influencing elements and basic mechanism of the large-signal stability (LSS) of the nonlinear systems, which provides a benchmark to design the parameters of the control of VSC and main circuit. Finally, the effectiveness and accuracy of the analysis are verified by electromagnetic transient simulation.

Control of Grid-Forming VSCs: A Perspective of Adaptive Fast/Slow Internal Voltage Source

Grid-forming (GFM) capability requirements are increasingly imposed on grid-connected voltage-source converters (VSCs). Under large grid disturbances, GFM-VSCs need to remain stable while providing GFM services. Yet, such objectives, as pointed out in this paper, inherently lead to conflicting requirements on the dynamics of internal voltage source (IVS) of GFM-VSCs, i.e., the fast IVS dynamics is needed to avoid the loss of synchronism with the grid, whereas the slow IVS dynamics is preferred for maintaining GFM capability. To tackle this challenge, an adaptive fast/slow IVS control is proposed, which switches GFM-VSC between fast and slow IVS dynamics based on system needs. The proposed method enhances the transient stability of GFM-VSC, whilst maximizing its capability of providing GFM service. Further, the approach is robust to different grid strengths and different types of grid disturbances. The experimental results verify the theoretical findings and the effectiveness of the proposed control method.

Stability analysis of limit cycle oscillators synchronised with the grid based on a large signal nonlinear method

The grid synchronisation block is a key component of power electronics converters and their control systems. In some cases, synchronisation algorithms are based on non-linear oscillators and, therefore, their stability boundaries should be analysed by using non-linear techniques. However, as this topic is relatively novel, it has been seldomly addressed in the literature. This article investigates the transient stability of limit cycle oscillators for grid-connected voltage source converters. The analysis is based on the Krasovskii theorem, which is derived from the Lyapunov theory. Numerical results are used to calculate the regions where stability is guaranteed for specific states of the synchronisation system such as the frequency, phase and voltage error. Experimental results obtained from the Power-Hardware-In-the-Loop laboratory are used to validate the theoretical developments.

Re-examination of small-signal instability in weak grid-connected voltage source converters

Weak grid sub-synchronous oscillation (SSO) is an important research topic. Although some analysis and mitigation schemes have been conducted, misperceptions still exist. This paper first aims to update the understanding of weak grid instability of voltage source converters (VSCs) and then points out that instability risks originate in the super-synchronous frequency range rather than in the sub-synchronous frequency range. Moreover, the resonance frequency can be even larger than the double fundamental frequency under certain parameter conditions. This paper also refines the impacts of VSC control parameters on weak grid instability mechanism and resonance frequency. Based on the results, the classification of this phenomenon should be revised.

Control for Grid-Connected VSC With Improved Damping Based on Physics-Informed Neural Network

The rapid penetration of renewable energy sources into the power system makes the grid-connected voltage source converter (VSC) highly dynamic and uncertain. This necessitates designing new adaptive control for VSCs to ensure satisfactory system performance, reliability, and stability. This paper introduces a physics-informed artificial neural network (ANN) controller for the grid-connected VSC to improve the system performance and dampen the voltage oscillation due to the sudden change in power demand. The employed ANN structure is a feed-forward multilayer Neural Network trained offline by the Levenberg-Marquardt-based backpropagation algorithm. Results are presented for different dynamic scenarios to show the satisfactory operation of the proposed controller. The small-signal stability analysis is presented to validate the system's stability. Further, the performance of the proposed ANN controller is compared with the widely-used PI-controller and model predictive controller. The results prove that the proposed controller has a better dynamic performance in damping the voltage oscillation.

Analysis and Damping of Low-Frequency Oscillation for DC-Link Voltage-Synchronized VSCs

For grid-connected voltage-source converters (VSCs), the dc-link voltage control (DVC) can be merged with the power-based synchronization control, leading to the dc-link voltage-synchronization control. This paper analyzes the low-frequency oscillations of dc-link voltage-synchronized VSCs, which is due to the impact of constant power load/source (CPL/CPS) in the dc link. An active damping method, based on the active power-frequency feedforward (PFF) control with a notch filter, is proposed to dampen the oscillations. It is revealed that the PFF control loop exploits the phase angle dynamic to resist the frequency deviation, which can be essentially treated as an active damper against the dynamics of dc-link CPL/CPS. Further, a loop-gain shaping method is developed for designing the notch filter, which dampens the synchronous oscillations that is inherent with active power dynamics. Experimental tests are performed under different grid frequencies and strengths, considering both the rectifier and inverter operation modes. The results validate the theoretical analysis and the effectiveness of the control approach.

Analytical investigation of factors affecting small-signal stability of grid-connected VSC

This paper provides an analytical investigation of the small-signal stability of the grid-connected voltage source converter (VSC) as well as the impacts of the system resistances. The dynamic model of the studied system is first established, and the characteristic function is derived from the linearized model. Based on the characteristic function, the analytical relationships between the system resistances and the dominated pole are obtained utilizing the analytical sensitivity approach. It is found that the line resistance can provide positive damping for the oscillation mode, improving the system stability, while the converter resistance will worsen the system stability. Generally, the line resistance has an evident more substantial impact on the stability of the grid-connected VSC than the converter resistance. The stability analysis results of the grid-connected VSC conducted by ignoring the system resistances are conservative. Ulteriorly, the characteristic function is simplified by neglecting the system resistances, and a sufficient and analytical stability criterion is established from the simplified characteristic function using the Routh Judgement. It exhibits the constraint condition among controller parameters, electrical distance and operation conditions for ensuring system stability. Moreover, the power transmission limitation of the converter affected by the controller parameters and electrical distance is obtained from the derived stability criterion. The small perturbation analysis and electromagnetic transient simulation give a demonstration to the analysis.

The Frequency Spectrum Analysis of Wideband Oscillations of Grid-Connected Voltage Source Converter

With the widespread application of voltage source converters (VSCs) in power systems with high renewable resource penetration, the problem of wideband oscillations caused by interactions between power converters and the power grid has drawn great attention. This paper presents a new methodology for simplifying the mathematical derivations of the impedance model of a VSC. Using the new simplified model, the stability and spectrum characteristics of the performance of the VSC can be clearly analyzed. The proposed second-order d-q impedance model of a grid-connected VSC in the presence of a PLL not only mathematically demonstrates that wideband oscillatory modes always occur in conjugate pairs, but also delivers a clear vision of the physical essence of these wideband oscillations. A classic modal analysis is executed in this paper to demonstrate the stability and frequency spectral characteristics of wideband oscillations in a VSC integrated system. The impact of the control parameters of the VSC on wideband oscillatory stability is thoroughly analyzed by modal analysis using ‘DIgSILENT PowerFactory’ as well as hardware-in-the-loop experiments. This methodology can be considered a powerful tool for the control design of VSCs in the modern power system.

Comparative Stability Analysis of Synchronous Reference Frame Current Controllers Operated at High Fundamental Frequency

Synchronous reference frame (SRF) proportional-integral (PI) current controller (CC) is the most well-established solution for current regulation in AC machine drives and grid-connected voltage source converters. The design of high dynamic performance current control loop has several challenges in high-speed and high-power applications due to the effects of controller gain’s selection, non-linearities, parameters variations, disturbances, digital implementation, and time delays. These become more significant due to high operating frequencies, which severely degrade dynamics and stability of the current control system. Various structures of SRF PI CCs have been reported in the literature. However, the aforementioned effects on the dynamics at high frequency operation have not been thoroughly addressed. Therefore, a comparative analysis of different SRF PI CCs’ structures is proposed in this paper, which addresses the design principles and gains’ selection while also taking into account the heavy computational burden and PWM delays. Additionally, the paper thoroughly analyzes and evaluates the dynamics and stability of the system operating at high fundamental frequencies. The advantages and limitations of each SRF PI CC scheme are studied and reported. The performance of the SRF PI CCs is comprehensively tested to demonstrate the analytical outcome of this study.

On Transient Instability Mechanism of PLL-Based VSC Connected to a Weak Grid

This paper analyzes the transient process of Phase Locked Loop (PLL) based grid-connected Voltage Source Converters (VSCs) under large disturbances by modeling the PLL dynamic model and active power loop model. With a focus on the effect of transient grid voltage changes on the stability of the PLL-based VSCs, it reveals that the mechanism of transient instability of PLL-based VSCs is different under various disturbance levels. It can be concluded that prior to the PLL losing synchronization, the power loop has already become unstable. In addition, the influence of the PLL prefilter used for asymmetrical faults on the stability criterion is analyzed. Moreover, based on the transient instability mechanism, two solutions are proposed to deal with different instability occasions, and the adaptability of these solutions is analyzed. Finally, hardware-in-the-loop experimental results validate the proposed transient instability mechanism and the proposed control strategies.

Analysis of Grid-Connected VSCs Subject to Voltage Harmonic Disturbances: Prediction and Design Tool of Resonant Controllers

The influence of current and voltage harmonics in the power quality of electrical facilities is currently an important topic in discussion. Considering that in Voltage Source Converter (VSC) applications it is common to utilize resonant controllers to mitigate characteristic current harmonics, this work proposes a methodology to allow the tuning of resonant controllers through a power quality criterion during the design process, enabling the designer to select between harmonic content and stability. The disturbance rejection model that relates the output harmonic currents with the grid voltage harmonics is utilized as basis for the methodology, also providing an analytical calculation of the resonant controller gain according to the imposed harmonic limitations, both for VSCs with regular L as with LCL output filters. Simulations and experiments validate the proposal.

Stability Impacts of an Alternate Voltage Controller (AVC) on Wind Turbines with Different Grid Strengths

This paper studies the stability impact of the alternate voltage controller’s (AVC) low-pass filter (LPF) in a wind turbine’s grid-connected voltage source converter (VSC). A small-signal model of the grid-connected converter is designed with a grid-following synchronization control. More specifically, the non-linear state-space model of the grid-connected converter was developed, including the dynamics of both the inner and outer control loops of the converter, the dynamics of the elements of the electrical system, as well as the digital time delay. An eigenvalue-based stability analysis gives insight into the stability impacts of the outer-loop controllers. It is proven that the cutoff frequency of the AVC’s LPF affects the phase-locked loop (PLL) and AVC bandwidths of instability, as well as the corresponding critical oscillation frequencies. This phenomenon is observed in both weak and strong grids. Consequently, the small-signal stability regions of the PLL and AVC bandwidth can be identified for the range of the AVC’s LPF cutoff frequency under study. The stability regions of the PLL and AVC, which are obtained from the small-signal model, as well as the determined critical oscillation frequencies, are validated through time domain simulations and fast-Fourier transformation (FFT) analysis.

Implementation and performance comparison of harmonic mitigation schemes for three-phase grid-connected voltage-source converter under grid voltage distortion: HiL and experimental validation

This paper presents an implementation methodology for a current harmonic compensation technique of three-phase grid-connected voltage-source converter (VSC), which was applied under the grid voltage distortion and frequency variation. The proportional–integral plus multi-resonant controllers (PIMR) were used to mitigate the high-order harmonic current. The harmonic compensators were used in the synchronous reference frame at harmonic orders 6th and 12th for suppression of the grid voltage harmonic orders 5th, 7th, 11th, and 13th with a total harmonic distortion of 4.69%. The PIMR controller was transformed to the discrete-time domain and implemented on a TMS320F28379D digital signal processor. The PIMR controller was compared with the conventional multiple synchronous reference frame (PIMSR) controller. The two control schemes were validated with a hardware-in-the-loop (HiL) and with a 5 kW three-phase LCL-filtered grid-connected VSC. The PIMR and PIMSR controllers exhibited excellent harmonic rejection on the grid current with a total harmonic distortion close to 1%, which complied with the IEEE 1547 standard. The grid current can track the reference command with a fast dynamic response. Moreover, the PIMR controller consumed a computational time of 1.625μs, 35% of the PIMSR controller.