Small Signal Stability Analysis Research Articles

Stability Analysis of Grid-Interfacing Inverter Control in Distribution Systems With Multiple Photovoltaic-Based Distributed Generators

A stability-enhancement inverter controller is proposed and its impact on the small-signal stability of distribution systems with multiple photovoltaic-based distributed generators (PV-DGs) is investigated. In specific, the random variation of the power output from multiple PV-DGs is considered. Being different from a single grid-connected PV system, the spatial correlation between PV-DGs and the system stability sensitivity with respect to different PV-DGs among the feeder are also taken into account. The small-signal stability analysis of the distribution system is performed using a probabilistic approach. As the PV-DG power output is randomly variable, the distribution system is not operating in a fixed mode. Consequently, the critical eigenvalues of the system move randomly. Through the Gram–Charlier expansion method, the probability density function of the critical eigenvalues of the distribution system is approximated and the probabilities of the system stability and instability are calculated. Taking the probability of the system instability as the performance metric, the effects of different system parameter settings of the grid-interfacing inverter controller on the distribution system are analyzed. The verification of the analytical results is carried out through Monte-Carlo time-domain simulations of the distribution system. The results suggest several methods to reduce the probability of system instability, including installation of the proposed inverter controller, choosing a large substation capacitor and/or choosing large capacity load and substation transformers.

Mathematical Modeling of the Squirrel Cage Induction Generator based Wind Farm for Sub-Synchronous Resonance Analysis

Background/Objectives: To analyze the SSR phenomenon in a Squirrel Cage Induction Generator based Wind farm connected to series compensated transmission line at varying operating conditions. Methods/Statistical Analysis: There is a remarkable rise in the renewable energy sector in the current energy demand scenario, but their grid integration leads to various power system stability issues. In the case of wind power, wind farms being located far away from the grid, the integration of large scale wind farms to the utility grid requires high transmission line capacity to transport huge amount of wind power. In order to provide the power transfer capability and to improve the system stability, series compensation is the effective solution. But the series compensation may cause SSR oscillations in the system. Eigen value analysis is the method chosen to perform the Small Signal Stability analysis which examines the potential of SSR in the study system. Findings: The study investigates on the application of series capacitor for series compensation which is required during the grid integration. Series compensation of transmission line causes electro-mechanical oscillations at a sub-synchronous frequency which may finally result in serious damages in the system such as shaft failure. In order to perform the Eigen value analysis, detailed mathematical modeling of the system is developed. The pitch angle control is not taken into account while developing the system, whereas the strength of the transmission line is considered. The interconnection of three sub systems provides the complete model of the study system. The identification of system modes and damping of torsional and network modes are analyzed for various wind speed levels, various series compensation levels and various grid impedance levels. It has been observed that different grid impedance levels have a significant effect on the torsional mode oscillations of the system. Application/Improvements: As the overall system model is linearised, optimal control techniques can be developed as an application to mitigate the SSR oscillations and thereby improve the system stability.

Model-Free Closed-Loop Stability Analysis: A Linear Functional Approach

Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex right half-plane, the circuit is unstable. The classic way to detect unstable poles is to fit a rational model on the impedance. In this paper, a projection-based method is proposed which splits the impedance into a stable and an unstable part by projecting on an orthogonal basis of stable and unstable functions. When the unstable part lies significantly above the interpolation error of the method, the circuit is considered unstable. Working with a projection provides one, at small cost, with a first appraisal of the unstable part of the system. Both small-signal and large-signal stability analysis can be performed with this projection-based method. In the small-signal case, a low-order rational approximation can be fitted on the unstable part to find the location of the unstable poles.

Admissible Region of Large-Scale Uncertain Wind Generation Considering Small-Signal Stability of Power Systems

The increasing integration of wind generation has brought great challenges to small-signal stability analysis of bulk power systems, since the uncertainty of wind generation may considerably affect equilibria of the systems. In this regard, this paper develops a conceptual framework to geometrically measure the influence of uncertainty of wind power injections (WPIs) on the small-signal stability of bulk power systems. We define a new concept in the WPI subspace, which is referred to as the admissible region of uncertain wind generation considering small-signal stability ( SSAR ). To do this, first the traditional concept of small-signal stability region (SSSR) defined in the nodal power generation injection space is extended to a higher dimensional nodal injection space that incorporates both the deterministic generation injections and the uncertain WPIs. Then the SSAR is obtained by mapping the extended SSSR onto the WPI subspace. The polynomial approximation of the SSAR boundary is given in a closed form. Case studies on the modified New England 39-bus system with multiple wind farms illustrate the SSAR concept and its potential applications.

Interaction of Droop Control Structures and Its Inherent Effect on the Power Transfer Limits in Multiterminal VSC-HVDC

Future multi-terminal HVDC systems are expected to utilize dc voltage droop controllers and several control structures have been proposed in literature. This paper proposes a methodology to analyse the impact of various types of droop control structures using small-signal stability analysis considering all possible combinations of droop gains. The different control structures are evaluated by the active power transfer capability as a function of the droop gains, considering various possible stability margins. This reveals the flexibility and robustness against active power flow variations, due to disturbances for all the implementations. A case study analyzing a three terminal HVDC VSC-based grid with eight different kinds of droop control schemes points out that three control structures outperform the remaining ones. Additionally, a multi-vendor case is considered where the most beneficial combinations of control structures has been combined in order to find the best performing combination.

Small-Signal Stability Analysis for Non-Index 1 Hessenberg Form Systems of Delay Differential-Algebraic Equations

This paper focuses on the small-signal stability analysis of systems modelled as differential-algebraic equations and with inclusions of delays in both differential equations and algebraic constraints. The paper considers the general case for which the characteristic equation of the system is a series of infinite terms corresponding to an infinite number of delays. The expression of such a series and the conditions for its convergence are first derived analytically. Then, the effect on small-signal stability analysis is evaluated numerically through a Chebyshev discretization of the characteristic equations. Numerical appraisals focus on hybrid control systems recast into delay algebraic-differential equations as well as a benchmark dynamic power system model with inclusion of long transmission lines.

Power flow and small signal stability analysis on the interconnected Philippine power grid

Summary The Philippines, as one of the developing nations in south-east Asia, has isolated power system networks which bring forth challenges in its operational systems, especially when subjected to a deregulated environment. This paper presents an analysis on the power flow and small signal stability of the interconnected three isolated Philippine Power Grid. To achieve this, eigenvalue analysis is employed to probe the small signal stability of the main power grids. The free software, Power Systems Analysis Toolbox (PSAT), is used to develop the model using MATLAB®/Simulink®. There have been no publicly available studies regarding stability of the proposed link between the major grid and the Mindanao (south island) grid. Participation factors were further studied to determine which states contributes most with the variety of modes. The lowest oscillatory damping modes are also assessed to better understand the systems characteristics.

Probabilistic Analysis of Small Signal Stability for Power Systems With High Penetration of Wind Generation

Wind generation is growing fast worldwide. The stochastic variation of large-scale wind generation may impact the power systems in almost every aspect. Probabilistic analysis method is an effective tool to study power systems with random factors. In this paper, a systematic nonlinear analytical probabilistic method is proposed to evaluate the possible effect of random wind power generation on power system small signal stability. A second-order polynomial is proposed to approximate the nonlinear relationship between the wind generation and the damping of a particular dynamic mode, such as the dominant mode. Gaussian mixture model formulates wind uncertainty in a uniform way. Spectral theorem is adopted to reshape the second-order polynomial into a form without cross-product terms. Cholesky decomposition is used to eliminate correlations among outputs of different wind farms. Thereafter the cumulative distribution function (CDF) of the damping ratio with respect to random wind power is consequently constructed. Numerical simulations are carried out in the IEEE standard test system. The proposed method is verified with higher accuracy than the traditional linearized method. Meanwhile, it is much more time-saving in calculation than Monte Carlo simulation.

Improved Vector Control Strategy for Current-Source Converters Connected to Very Weak Grids

This paper investigates the interconnection of current-source converters (CSCs) to a very weak grid using the conventional vector control in the rotating reference frame. It is shown that the system stability is degraded under weak-grid conditions due to the implementation of the synchronous reference frame phase-locked loop (PLL). Supplementary controllers are proposed and integrated to the outermost control loops of the CSC to alleviate the associated negative impacts of the PLL. The proposed compensators do not alter the dynamic characteristics of the conventional vector control. More importantly, they enable the CSC to inject 1.0 per-unit of active power at a unity short-circuit ratio. Small-signal stability analysis and controllers design procedures are presented in details. The design of the proposed compensators is independent of the conventional vector control and hence no extensive coordination and parameters tuning are needed. Time-domain simulations results are presented to validate the effectiveness of the proposed techniques.

Small-Signal Stability, Control and Dynamic Performance of Power Systems [Book Reviews

This book includes 14 chapters and comprehensively covers the topic of small-signal stability and control in power systems. The first three chapters constitute introductory material and provide a primer on various topics related to control analysis and design. These chapters offer readers new to this topic the requisite background to understand the material that follows. The book is an excellent treatise on the topic of small-signal electromechanical stability analysis and therefore a must read for the practicing engineer and for students pursuing the study of small-signal stability in power systems.

Small-Signal Stability Analysis of Large Power Systems With Inclusion of Multiple Delays

The paper focuses on the small-signal stability analysis of large power systems with inclusion of multiple delayed signals. The following four techniques are compared: 1) a Chebyshev discretization scheme of an equivalent partial differential equations that resembles the original delay differential-algebraic equations (DDAEs); 2) an approximation of the time integration operator; 3) a linear multistep discretization of the DDAEs based on an high-order implicit time-integration scheme; and 4) the well-known Pade approximants. These techniques are compared using a GPU-based parallel implementation of the Shur method and QR factorization and tested through a real-world transmission system.

Generalised analytical framework for the stability studies of an AC microgrid

The objective is to address the small-signal stability analysis of a renewable-driven AC microgrid in the context of the practical usage and application. The state-space modelling of the system is generalised over all possible microgrid configurations. It is shown that there exist two simple templates to represent the dynamics of any type of load. The dynamics of any type of source (including the utility grid during the grid-connected operation) can be represented through a single template. Thus, the effective number of the different types of dynamic element is minimised and set fixed irrespective of the actual microgrid composition. In addition, similar loads are represented in the form of a single group to reduce computational complexity. A systematic procedure for constructing the system matrix using the prescribed source and load templates is discussed. The developed framework is applied on a test system having complex loads for both grid-connected and islanded operations. It is a common observation that system stability is influenced by the interactions between inertial and non-inertial components. To overcome this issue, suitable parameters are identified and tuned by performing system level study.

Small-signal Stability Analysis and Control System Design of a Meshed Multi-terminal High-Voltage Direct Current Grid with a Current Flow Controller

A DC current flow controller can provide branch current control in a meshed multi-terminal high-voltage direct current (HVDC) grid. However, the introduction of a DC current flow controller may affect the stability of the multi-terminal HVDC. Hence, the dynamic characteristics of the multi-terminal HVDC with the DC current flow controller should be investigated. This article focuses on small-signal stability analysis of a current flow controller-equipped meshed three-terminal HVDC system. A small-signal model for the multi-terminal HVDC with the DC current flow controller is established. Based on the stability analysis of the small-signal model, a control system is designed for the DC current flow controller, fulfilling the system stability requirement. Finally, non-linear dynamic simulations on the real-time digital simulator are conducted, and simulation results are compared with a theoretical model to validate the proposed controller for the DC current flow controller. In addition, dynamic impacts of the DC current flow controller on the meshed multi-terminal HVDC grid are discussed.

Dynamic modeling and control of the tidal current turbine using DFIG and DDPMSG for power system stability analysis

This paper describes the overall dynamic models of tidal current turbine driving either a doubly fed induction generator (DFIG) or a direct drive permanent magnet synchronous generator (DDPMSG) connected to a single machine infinite bus system including controllers to improve system stability. Testing with ranges of controller gains is carried out to establish zones of stability. The overall results show the advantages of using the DDPMSG over the DFIG. In this paper we used two different models for each machine; the full model and the reduced order model. Also IEEE-9 bus system is used in this work for multi-machine system and tested for a small signal stability analysis.

Measurement-based investigation of inter- and intra-area effects of wind power plant integration

This paper has a two pronged objective: the first objective is to analyze the general effects of wind power plant (WPP) integration and the resulting displacement of conventional power plant (CPP) inertia on power system stability and the second is to demonstrate the efficacy of PMU data in power system stability analyses, specifically when knowledge of the network is incomplete. Traditionally modal analysis applies small signal stability analysis based on Eigenvalues and the assumption of complete knowledge of the network and all of its components. The analysis presented here differs because it is a measurement-based investigation and employs simulated measurement data. Even if knowledge of the network were incomplete, this methodology would allow for monitoring and analysis of modes. This allows non-utility entities and study of power system stability. To generate inter- and intra-area modes, Kundur’s well-known two-area four-generator system is modeled in PSCAD/EMTDC. A doubly-fed induction generator based WPP model, based on the Western Electricity Coordination Council (WECC) standard model, is included to analyze the effects of wind power on system modes. The two-area system and WPP are connected in various configurations with respect to WPP placement, CPP inertia and WPP penetration level. Analysis is performed on the data generated by the simulations. For each simulation run, a different configuration is chosen and a large disturbance is applied. The sampling frequency is set to resemble the sampling frequency at which data is available from phasor measurement units (PMUs). The estimate of power spectral density of these signals is made using the Yule–Walker algorithm. The resulting analysis shows that the presence of a WPP does not, of itself, lead to the introduction of new modes. The analysis also shows however that displacement of inertia may lead to introduction of new modes. The effects of location of inertia displacement (i.e. the effects on modes if WPP integration leads to displacement of inertia in its own region or in another region) and of WPP controls such as droop control and synthetic inertia are also examined. In future work, the methods presented here will be applied to real-world phasor data to examine the effects of integration of variable generation and displacement of CPP inertia on inter- and intra-area modes.

Nyquist Stability Analysis of an AC-Grid Connected VSC-HVDC System Using a Distributed Parameter DC Cable Model

In this paper, a two-terminal VSC-HVDC system embedded in a weak grid ac environment is considered, emphasizing modeling, controller design, and small-signal stability analysis. Traditionally, the dc cable is modeled by $\Pi$ -sections, implying that care has to be taken when using the model for higher frequencies or in cases of higher cable impedance density, such as submarine cables. Here, a distributed parameter cable model is used to overcome this problem. The VSC-HVDC system can be described as two cascaded blocks. The first block is a transfer function that will differ depending on what input and output variables are considered, but which is in all realistic cases stable. The second block is a feedback loop, where the forward path is a rational function and the return path is a dissipative infinite dimensional function, remaining the same in all cases. The stability is then analyzed, using the Nyquist criterion, in a straightforward manner. Numerical examples are given by the use of MATLAB. The result is that if the VSC-HVDC system using a single $\Pi$ -section cable model is stable, so is the VSC-HVDC system using a distributed parameter cable model.

Predictive optimized adaptive PSS in a single machine infinite bus

Power System Stabilizer (PSS) devices are responsible for providing a damping torque component to generators for reducing fluctuations in the system caused by small perturbations. A Predictive Optimized Adaptive PSS (POA-PSS) to improve the oscillations in a Single Machine Infinite Bus (SMIB) power system is discussed in this paper. POA-PSS provides the optimal design parameters for the classic PSS using an optimization predictive algorithm, which adapts to changes in the inputs of the system. This approach is part of small signal stability analysis, which uses equations in an incremental form around an operating point. Simulation studies on the SMIB power system illustrate that the proposed POA-PSS approach has better performance than the classical PSS. In addition, the effort in the control action of the POA-PSS is much less than that of other approaches considered for comparison.

A firefly optimized fast extreme learning machine based maximum power point tracking for stability analysis of microgrid with two stage photovoltaic generation system

This paper proposes a new Firefly optimized Ridge Extreme Learning Machine (RELM-FF) algorithm based maximum power point tracking (MPPT) investigation for stability study of photovoltaic (PV) interactive microgrid dynamics. The proposed MPPT study is effective by managing minimum uncertainty limits, during solar uncertainty conditions (i.e., inconsistent irradiation, partial shading, etc.), compared with conventional techniques. A two stage converter dynamics is considered for the proposed grid interactive PV system. To withstand stability during worst grid operating scenario (both PV side and grid side uncertainty), a robust nonlinear Lyapunov based finite time sliding mode (LFSM) control is proposed for PV-VSC (voltage source converter) system. As the proposed multiple distributed energy resources based microgrid is considered as weak (low short circuit ratio), and PV is considered as an active power source, the Q-V based state variables are used for the dynamic control loop. A small signal stability analysis with the two stage PV converters is presented using the proposed RELM-FF algorithm and LFSM control. The performance evaluation of the microgrid operating with the PV array is demonstrated through various case scenarios, in MATLAB/Script environment. A hardware validation with TMS320C DSK board and embedded MATLAB coder is performed to establish effectiveness of the proposed MPPT algorithm, in real time. The superiority of the proposed MPPT over the conventional techniques is validated by comparing the stability improvement performance in grid interactive PV-VSC microgrid.

On small signal stability of an AC/DC power system with a hybrid MTDC network

Multi-terminal HVDC (MTDC) networks are being contemplated for large scale integration of renewable energy sources, as well as for the interconnection of asynchronous AC systems. A hybrid MTDC network that combines line commutated converters (LCCs) and voltage source converters (VSCs) can combine the benefits of both technologies. This paper presents a mathematical model of an AC/DC power system with an embedded hybrid MTDC network interconnection. Small signal stability analysis of the power system is conducted based on the linearization of the model. The impact of VSC controller gains on the dominant modes in the system is investigated. The contributions of the converters and generators to different modes of the system are investigated based on the participation matrix analysis. Auxiliary controllers are applied at the converters for the purpose of damping power oscillations in case of disturbances. The results of small signal stability analysis are validated by time-domain simulations in MATLAB.

Stochastic Small-Signal Stability Analysis of Grid-Connected Photovoltaic Systems

As the penetration level of photovoltaic (PV) generators into the grid is rapidly increasing, the effect of a variable PV power output on the stability of power systems cannot be ignored. Due to the stochastic characteristics of PV power generation, deterministic analysis approaches are not able to fully reveal the impact of high-level PV integration. This paper investigates the impact of the stochastic PV generation on the dynamic stability of grid-connected PV systems by using a probabilistic small-signal analysis approach. The sensitivity of the critical eigenvalue to the variation of solar irradiance is obtained. With the knowledge of the sensitivity relationship and the statistics of solar irradiance data, the probability density function (pdf) of the real part of the critical eigenvalue is approximated by Gram–Charlier expansion. This pdf is then used to calculate the probability of the stochastic small-signal stability of a power system. The impacts of important system parameters on the stochastic stability of the system are also analyzed. It has been found that these system parameters can significantly affect the stochastic stability of the system. Results of Monte Carlo and time-domain simulations of the grid-connected system verify the effectiveness of the proposed stochastic stability analysis method.