Stability Analysis Of Grid-Connected Converters Research Articles

Reduced-Order Symbolic Admittance Model and Stability Analysis of Grid-Connected Converters

Reduced-Order Symbolic Admittance Model and Stability Analysis of Grid-Connected Converters

Transient Stability Analysis of Grid-connected Converters in Wind Turbine Systems Based on Linear Lyapunov Function and Reverse-time Trajectory

Transient Stability Analysis of Grid-connected Converters in Wind Turbine Systems Based on Linear Lyapunov Function and Reverse-time Trajectory

Design-Oriented Transient Stability Analysis of Grid-Connected Converters: A Comparative Study of Analysis Methods

Design-Oriented Transient Stability Analysis of Grid-Connected Converters: A Comparative Study of Analysis Methods

Settling Angle-Based Stability Criterion for Power-Electronics-Dominated Power Systems

Impedance-based analysis methods are widely applied to the small-signal stability analysis of grid-connected converters. As the initial step to carry out the impedance-based stability analysis, it is critical to select whether to represent the converter as a Norton or Thevenin equivalent circuit. However, there is lack of definition on the representation of converters, and inappropriately selected impedance model choice leads to improper stability analysis. Moreover, existing impedance-based stability analysis methods, e.g., return-ratio matrix (RRM)-based method, only apply to minimum phase systems where the RRM does not contain right-half-plane poles. In complex and power-electronics-dominated power systems, interactions between multiple converters lead to nonminimum phase power systems, where current methods can no longer be directly applied. To address these problems, a stability criterion is proposed by introducing the concept of settling angle. As the main contribution of this article, the settling angle of total admittance is proven as the intrinsic hallmark of power systems and directly reflects the system stability. The proposed settling-angle-based stability criterion is validated by control hardware-in-the-loop experimental results for a three-terminal system that integrates grid-forming and grid-following converters through a common bus.

Domain of Attraction’s Estimation for Grid Connected Converters With Phase-Locked Loop

A large number of non-linear hardware and control units exists in power electronic system used in grid connected devices. The analytical transient stability analysis of grid-connected converters presents numerous difficulties. A common method to tackle this problem is the stability analysis using Lyapunov’s method. By applying this method, difficulties arise not only from finding a suitable Lyapunov function, but also from checking the constraint of Lyapunov stability. If the appropriate Lyapunov function is a high-order polynomial, it is very challenging to test if it meets the constraints of Lyapunov stability in certain regions. In this paper, the sum-of-squares programming method is used to obtain the estimation of a converter’s domain of attraction with a relatively small number of iterations compared to classically applied methods, such as the Monte Carlo method. The estimation of the domain of attraction are verified by time-domain simulations and StarSim’s controller hardware-in-the-loop tests in this paper.

Rapid Multivariable Identification of Grid Impedance in DQ Domain Considering Impedance Coupling

Identifying grid impedance at the point of common coupling is essential for the adaptive control and the online stability analysis of grid-connected converters. A balanced three-phase system is commonly modeled by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> components in the synchronous reference frame. In identification of the synchronous reference-frame impedance components, errors may occur due to the coupling of the system impedances; for example, a measurement injection that is intended to perturb only the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> -channel current may also perturb the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> -channel current, thus distorting the impedance measurements. Traditionally, sequentially performed measurements, where different injections are performed one after another at the same frequencies, have been required to tackle the impedance coupling. However, the sequential measurements are prone to changes in the operating conditions between the measurements. This article proposes a method to simultaneously obtain all the grid-impedance components within a single measurement cycle with no coupling effect. In the method, two orthogonal binary injections are simultaneously injected into the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula> current references of the inverter controller. Then, a frequency-domain interpolation technique is applied to adjust the measured current and voltage responses. As a result, the impedance coupling is avoided in the measured grid impedance. The proposed technique is validated by experimental measurements.

Independent Channel Design Approach for Stability Analysis of Grid-Connected Converters

The independent channel design approach proposes that the stability of a multiple-input multiple output system can be studied through the analysis of single-input single-output (SISO) systems. In the case of the grid-connected converters (GCCs) studied in this paper, two SISO systems are defined as positive and negative sequence channels, PSC and NSC, respectively. Further simplifications for the SISO systems are proposed so that the simplified PSC and NSC are decoupled. The advantage of studying decoupled SISO systems is that the identified instabilities can be given a physical interpretation. For example, it is found that instabilities related to ac-grid resonances are due to the fact that the GCC acts as a negative conductance in the PSC. Instability is less likely to occur in the NSC since resonances take place at a higher resonance frequency where the GCC acts as a positive conductance. It is also argued that the proposed simplification is able to reproduce fairly close instabilities related to ac-grid resonances, while for instabilities of other nature, complete expressions need to be used.

Symmetric Admittance Modeling for Stability Analysis of Grid-Connected Converters

This paper proposes a novel admittance model for the stability analysis of grid-connected voltage-source converters (VSCs) which features a symmetric structure. On this basis, the grid-connected VSC system can be represented by a reciprocal two-port circuit to explore the oscillation mechanism of the system. Furthermore, the grid-connected VSC system can be modelled as a single-input single-output (SISO) system rather than a multi-input multi-output (MIMO) system. We analytically evaluate the influences of the VSC control parameters and the power factor on the stability of the grid-connected VSC by employing the Nyquist criterion and the stability margin. In addition, we demonstrate that the VSC's current output is in inverse proportion to the system's gain margin. Further, an analytical expression of the current limit constrained by small-signal stability is derived in closed form so as to calculate the admissible current output. All of analysis results are verified by simulations based on Simulink and hardware-in-the-loop (HIL) platform.

Design-Oriented Transient Stability Analysis of Grid-Connected Converters With Power Synchronization Control

The power synchronization control (PSC) has been increasingly used with voltage-source converters (VSCs) connected to the weak ac grid. This paper presents an in-depth analysis on the transient stability of the PSC-VSC by means of the phase portrait. It is revealed that the PSC-VSC will maintain synchronization with the grid as long as there are equilibrium points after the transient disturbance. In contrast, during grid faults without any equilibrium points, the critical clearing angle (CCA) for the PSC-VSC is identified, which is found equal to the power angle at the unstable equilibrium point of the post-fault operation. This fixed CCA facilitates the design of power system protection. Moreover, it is also found that the PSC-VSC can still re-synchronize with the grid after around one cycle of oscillation, even if the fault-clearing angle is beyond the CCA. This feature reduces the risk of system collapse caused by the delayed fault clearance. These findings are corroborated by simulations and experimental tests.

Stability Analysis of Grid-Connected Converters with Different Implementations of Adaptive PR Controllers under Weak Grid Conditions

Adaptive proportional resonant (PR) controllers, whose resonant frequencies are obtained by the phase-locked loop (PLL), are employed in grid connected voltage source converters (VSCs) to improve the control performance in the case of grid frequency variations. The resonant frequencies can be estimated by either synchronous reference frame PLL (SRF-PLL) or dual second order generalized integrator frequency locked loop (DSOGI-FLL), and there are three different implementations of the PR controllers based on two integrators. Hence, in this paper, system stabilities of the VSC with different implementations of PR controllers and different PLLs under weak grid conditions are analyzed and compared by applying the impedance-based method. First, the αβ-domain admittance matrixes of the VSC are derived using the harmonic linearization method. Then, the admittance matrixes are compared with each other, and the influences of their differences on system stability are revealed. It is demonstrated that if DSOGI-FLL is used, stabilities of the VSC with different implementations of the PR controllers are similar. Moreover, the VSC using a DSOGI-FLL is more stable than that using a SRF-PLL. The simulation and experimental results are conducted to verify the correctness of theoretical analysis.

Robust Stability Analysis of Grid-Connected Converters Based on Parameter-Dependent Lyapunov Functions

This paper deals with the problem of robust stability analysis of grid-connected converters with LCL filters controlled through a digital signal processor and subject to uncertain grid inductance. To model the uncertain continuous-time plant and the digital control gain, a discretization procedure, described in terms of a Taylor series expansion, is employed to determine an accurate discrete-time model. Then, a linear matrix inequality-based condition is proposed to assess the robust stability of the polynomial discrete-time augmented system that includes the filter state variables, the states of resonant controllers and the delay from the digital control implementation. By means of a parameter-dependent Lyapunov function, the proposed strategy has as main advantage to provide theoretical certification of stability of the uncertain continuous-time closed-loop system, circumventing the main disadvantages of previous approaches that employ approximate discretized models, neglecting the errors. Numerical simulations illustrate the benefits of the discretization technique and experimental results validate the proposed approach.