Small Disturbance Stability Analysis Research Articles

Analysis of the Stability and System Participation Factors of Grid-Connected Converters

When the sources of renewable energy and numerous power electronic gadgets are introduced into the power system, which is related to the negative resistance features of power electronic gadgets, the power system with high power electronics often exhibits weak inertia. Also the stability of multi-converter grid-connected systems is adversely affected. To address these issues, a process of small disturbance stability analysis is proposed in this paper for the grid-connected systems of multiple grid-forming converters based on impedance ratio criterion. The Nyquist trajectory map of the system ratio of impedance in the complex plane is used in the suggested analytical method to estimate the quantity of RHPs in the right half-plane of the system, and the stability at the common points of the system is evaluated against the Nyquist criterion. In addition, the instability of grid-forming converters in grid-connected systems is reproduced by using grid-forming converters state space equation. Unlike the traditional methods of analysis, the method proposed in this paper can be applied to specifically judge the key equipment or control link of instability of the system, which provides guidance on optimizing the parameters of the system. Finally, simulation analysis is conducted to confirm that the model is accurate and that the proposed approach is applicable.

Small-disturbance stability analysis and control-parameter optimization of grid-connected virtual synchronous generator

Small-disturbance stability analysis and control-parameter optimization of grid-connected virtual synchronous generator

Aggregation Equivalence Method for Direct-Drive Wind Farms Based on the Excitation–Response Relationship

The grid interconnections for direct-drive wind farms have triggered multiple new sub-synchronous oscillation events, which can prevent the power system from operating safely and stably. However, the excessively high order of the detailed model for large-scale wind farms with multiple direct-drive permanent magnet synchronous generators (PMSGs) connected to power systems poses a challenge when investigating small disturbance stability and instability mechanisms. This study establishes a model of the grid-connected PMSG system based on the voltage/power excitation–response relationship to describe the dynamic characteristics of the port of the PMSG, and the analysis of active and reactive response characteristics of PMSG lays the foundation for model simplification. Based on the unit model, a direct-drive wind farm aggregation equivalence method based on the excitation–response relationship is proposed. The equivalent model obtained by this method is suitable for the small disturbance stability analysis of direct-drive wind farms grid connected system, with good accuracy. The simulation verified the effectiveness of the aggregation model.

Small Disturbance Stability Analysis of Onshore Wind Power All-DC Power Generation System Based on Impedance Method

The Onshore Wind Power All-DC Generation System (OWDCG) is designed to integrate with renewable energy sources by modifying the grid structure. This adaptation supports the grid infrastructure and addresses the challenges of large-scale wind power AC collection and harmonic resonance during transmission. Crucially, small disturbance stability parameters are essential for ensuring the system’s stable operation. Unlike conventional power systems, the OWDCG exhibits strong coupling between subsystems, accentuating the small disturbance stability issue due to the dynamic nature of its converter control system. The impedance method facilitates the decomposition of such systems into subsystems, offering insights into the destabilization mechanism through the lens of negative impedance contribution. This approach is conducive to conducting small disturbance stabilization analyses. To tackle this issue, the initial step involves deriving the input and output equivalent impedance models of the subsystem, considering the topological structure, control features, and operational dynamics of the OWDCG. Subsequently, the impact of circuit and control parameters on the system’s impedance characteristics and small-disturbance stability is examined through Bode diagrams and Nyquist curves. This analysis identifies critical parameters for small-disturbance stability, guiding the stable operation and parameter optimization of the OWDCG. The analysis highlights that the main control strategies for stability are the Modular Multilevel Converter (MMC) DC voltage control and the inner-loop current control gain. Validation of the theoretical findings is achieved through simulation results using PSCAD/EMTDC.

Power system small-disturbance stability analysis and control design: A characteristic locus method

A characteristic locus method developed from the celebrated generalized Nyquist criterion is proposed for power systems small-disturbance stability analysis and control design in this paper. First, a loop transformation is introduced to re-formulate the familiar Heffron-Phillips model. The new model has a feedback control structure so that the generalized Nyquist criterion is applicable when concluding the stability of the closed-loop system. Subsequently, the relationship between generalized Nyquist curve and characteristic loci is utilized to acquire a new stability margin. The effectiveness of the stability margin is demonstrated using Cassini Oval Theorem. An analytical expression of the stability margin is derived as well. It is convenient to quantify the effects of control loops on stability margin by applying this expression. Moreover, the analytical relationship between stability margin and frequency responses of controllers provides information for the design of the controllers. The utility of the proposed method is confirmed through case studies.

Analytic Interval Prediction of Power System Dynamic under Interval Uncertainty

With widespread access to renewable energy sources and active loads such as electric vehicles, uncertainty problems have gradually become a prominent problem in the power system. However, the conventional stochastic differential equation (SDE) model is not comprehensive in describing the randomness of disturbances, and the solution of novel models generally relies on numerical calculations. To improve the modeling accuracy and the calculation effectiveness, this paper utilizes intervals to model stochastic continuous disturbances and proposes an analytic method based on Taylor series expansion to predict the dynamic response of the power system under interval uncertainty, which may provide a reference for the small disturbance stability analysis of the power system. Furthermore, in order to apply to a more general situation, the case of continuous intervals is considered, and the analytic results are obtained, by which the superposition principle applicable to intervals is summarized. The comparison with the Monte Carlo method and the responses from actual wind power data verify the effectiveness and rationality of the proposed method.

Stability assessment and parametric sensitivity analysis based on extended Gershgorin Theorem for multiple grid-connected converters

• A multiple grid-connected converters is modeled as a medium and high dimensional negative feedback system with a stable open-loop function in unified dq frame, which fills in the limitations of traditional impedance ratios for the small disturbance stability analysis of multiple grid-connected converters system. • In terms of estimating eigenvalues for the multiple grid-connected converters system, a stability assessment method based on extended Gershgorin Theorem is proposed in frequency domain. Moreover, the algebraic form of the criterion is further simplified to quantify the oscillatory stability, which has the lower complexity compared with generalized nyquist criterion. The proposed method is of great potential in analyzing the stability issue for large-scale new energy power systems. • The reshaped eigenvalue estimation area based on extended Gershgorin Theorem is smaller than traditional Gershgorin Theorem, which can reduce its conservatism to improve system stability margin. • Compared to observe the changed trend of system stability by the change of the related parameters, the parameter sensitivity analysis based on equivalent impedance network model is used to quantify the impact factors on stability, which can be given to guide the parameter optimization of the multiple grid-connected converters system. The large-scale integration of power electronic based systems is bringing new oscillatory stability issues, further threatening the safe and stable operation of power system. Early researches are focused on stability analysis of single grid-connected converters to simple networks. Instead, there have been growing interests in studying the small signal stability of multiple grid-connected converters nowadays, whose main method is to apply traditional stability assessment with high complexity and conservatism. To address this problem, a simplified criterion based on extended Gershgorin Theorem to assess the stability of multiple grid-connected converter. The proposed method has less conservatism than tradition Gershgorin Theorem-based criteria, and has the lower computational complexity with simple algebraic operation compared to generalized nyquist criteria. Moreover, the parametric sensitivity analysis is used for analyzing the impact factors to promote system stability based on the proposed criteria. Theoretical results as well as electromagnetic transient simulations have verified the validity. The proposed method has the potential to assess the high-order system, and provides guidance on system parameters optimization based on the sensitivity.

Stability Analysis of the Parachute System with a Data-Driven Approach

The large-angle pendulous motion of the parachute system, which increases the touchdown impact loading to the structure and saturates the control system, is very disadvantageous to the security of the system. To determine the root cause of the pendulum motion and provide improved design to mitigate the risk, there is an urgent need for stability analysis of the parachute system. In this work, a novel data-driven approach is presented for the stability analysis of the parachute, which could not only determine the stability of system at the glide point but also extract the dynamic characteristics like frequency and amplitude when the system runs into the large amplitude coning or pitching motion. The data-driven method is shown to have a good agreement with the small-disturbance stability analysis of the classic five-degree-of-freedom parachute system. The dominant Koopman modes used to yield a finite linear representation of the nonlinear pendulum dynamics are extracted; these Koopman modes are shown to be the intrinsic components of the parachute system after a large amount of simulation data is analyzed. At last, a two-main multibody parachute system is included to demonstrate the ability of the data-driven method in stability and modal analysis of complex parachute system.

An Improved Prony Prediction Compensation‐Based Wide‐Area Damping Control Approach for Power System Low‐Frequency Oscillation Suppression

Currently, wide‐area damping control has been considered one of the most effective and promising methods to solve the problem of interval low‐frequency oscillation in power systems. In order to reduce adverse affection caused by time delay in acquisition and transmission of wide‐area signals, an improved Prony prediction compensation‐based wide‐area damping control approach for power system low‐frequency oscillation suppression is proposed in this paper. Firstly, the influence of communication time delay on power system stability is analyzed by a small disturbance stability analysis method. An algorithm based on the improved Prony prediction algorithm is designed to predict the acquired signals with time delay. A second derivative‐based order determination algorithm is used to obtain the best effective order of the prediction model, and the parameter prediction step size of the prediction model is determined by the actual situation of time delay change. Finally, design of a wide‐area damping controller based on the improved Prony prediction compensation is presented in detail. The proposed control approach is conducted in a four‐machine and two‐zone power system, and the experiment results show that the proposed approach can effectively compensate for the signal under the conditions of fixed time delay and variable time delay and has better adaptability advantages than the traditional Prony prediction compensation method.

Stochastic small disturbance stability analysis of nonlinear multi-machine system with Itô differential equation

The stochastic small disturbance stability is widely recognized as a major issue in the small signal stability of power system due to complex stochastic factors such as increasing large-scale renewable power grid integration, random fluctuations of electrical loads and so on. By the relevant theories of Itô differential equation, this paper proposes a new method to prove the mean stability and mean square stability of the power angle and the angular speed of the nonlinear multi-machine system under small Gauss random disturbances. In this approach, the stability criterion is derived from the system. Simulation results of 4-machine 11-bus system and the 16-machine 68-bus system using MATLAB demonstrate that the proposed method is able to analyze the stochastic small disturbance stability with high effectiveness and accuracy compared with the theoretical proof, and it is suitable for any nonlinear multi-machine system. Based on the application of stochastic differential equation, the influence of intensity and quantity of the random disturbances on the stability of the system is further analyzed.

Modeling and Stability of Microgrids with Smart Loads

A demand-side technology called “electric springs” was recently proposed to stabilize the future smart grid subject to large penetration of renewable energy sources. Based on power flow and basic circuit theory, this paper establishes a comprehensive microgrid model that consists of energy sources interfaced via inverters and smart loads for which electric springs are installed. Modeling it as a controlled voltage source, we can design the high-level control for the electric spring such that the load bus dynamics can be shaped to have desired frequency and voltage dynamics. We conduct the small-disturbance stability analysis on the established microgrid model where both generation and load buses implement frequency and voltage droop control. Finally, a graph-theoretic like stability condition is obtained.

Probabilistic Small-Disturbance Stability Assessment of Uncertain Power Systems Using Efficient Estimation Methods

This paper presents comparative analysis of the performance of three efficient estimation methods when applied to the probabilistic assessment of small-disturbance stability of uncertain power systems. The presence of uncertainty in system operating conditions and parameters results in variations in the damping of critical modes and makes probabilistic assessment of system stability necessary. The conventional Monte Carlo (MC) approach, typically applied in such cases, becomes very computationally demanding for very large power systems with numerous uncertain parameters. Three different efficient estimation techniques are therefore compared in this paper-point estimation methods, an analytical cumulant-based approach, and the probabilistic collocation method-to assess their feasibility for use with probabilistic small disturbance stability analysis of large uncertain power systems. All techniques are compared with each other and with a traditional numerical MC approach, and their performance illustrated on a multi-area meshed power system.

Identification of Electromechanical Modes and Placement of PSSs Using Relative Gain Array

The paper investigates the possibility to use relative gain array (RGA) for power system small-disturbance stability analysis. The RGA has been successfully used in the past as steady state measure of interactions for multivariable, decentralized control in chemical and process engineering. The effectiveness of the RGA in identifying electromechanical modes and selecting the optimal location for placement of PSSs is compared with the conventional approach that uses transfer function residues, eigenvalues and participation factors. Two different multimachine power systems are used for the case studies. Limitations and advantages of the use of RGA in this purpose are clearly indicated in the paper.

Stochastic Approach to Small Disturbance Stability Analysis

Stochastic Approach to Small Disturbance Stability Analysis

A stochastic approach to small disturbance stability analysis

A systematic approach to the construction of stochastic models of electric power systems for small disturbance stability analysis is presented. In this study, the cumulative effects of small-magnitude random fluctuations of electrical loads are considered as sources of eventual loss of stability, and a security measure is derived to determine the small-disturbance stability limits of the stochastic system. The electric power system models were tested on a 30-bus power system and compared according to the relative effects of load fluctuations on the proposed security measure.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A stochastic model for small disturbance stability analysis of electric power systems

As a result of inherent uncertainties directly affecting power system dynamic stability studies, many works have been presented in the field of stochastic modelling of power system parameters. In the past the system was modelled as linear and/or model small disturbances as small zero-mean Gaussian distributed white noises (of infinite bandwidth). In this paper a multi-dimensional power system with a preserved model is studied which is perturbed by small zero-mean Gaussian distributed coloured noises (band-limited white noises). Concerning the system's stability, the region and its boundary are shown more accurately, and sensitivity studies are performed on the proposed model to investigate the effect of coloured noise on the dynamic system behaviour.

A New Coherence Approach of Generators for Investigation of Slow and System Wide Oscillations in Large Power Systems

A new technique is described for aggregation of generators in a large power system. The technique focuses on slow and system wide oscillations. The reduced order models have many applications in analysis of large power systems. The equivalent parameters for the turbine governors and synchronous machines are calculated as weighted mean values of the parameters of included governers and machines in the coherent group. Model parameters for voltage control, power system stabilizers etc., have the same control characteristics as the largest machine in the coherent group.The primary advantage of this procedure is that the definition of coherent machines can easily be interpreted physically and the definition is independent of the excitation of the system. This definition may be used for small disturbance stability analysis, (SDSA). Similar approach is used by Geeves,1988. Other definitions of coherency (Berg et. al.,1983; Oshawa et. al.,1978; Podmore,1978; Zhou et. al.,1985) are not suitable for the analysis of slow and system wide power oscillations. These definitions are mainly used for large disturbance stability analysis, (LDSA). The coherency, based on the LDSA - definition, of generators will depend on where the disturbances are applied in the power system and will also depend the frequency spectrum of the disturbances.