Small Signal Stability Research Articles

Modified PSO tuned two stage lead lag STATCOM control action for small signal stability enhancement of variable wind integrated power system

In this work Modified PSO (MPSO) is proposed to tune two stage lead lag control action based on STATCOM for enhancing small signal stability of an intermittent wind source penetrated power system. The Modified PSO has been compared with standard PSO and fractional PSO to tune controller parameters of STATCOM based control action. Multi machine system subjected to sudden and intermittent wind variations have been considered in this work. Subject to this wind penetration the lead lag control action with only PSO and two stage lead lag control action with fractional PSO and modified PSO has been implemented to damp the system oscillations pertaining to initial operating condition. It was found that subject to intermittent nature of wind penetration the rotor angle small signal stability is being hampered and subject to this when the modified PSO tuned two stage lead lag STATCOM control action is applied, it damps the oscillations heavily and the results have been compared with only PSO and fractional PSO control algorithms.

Analysis of Additional Damping Control Strategy and Parameter Optimization for Improving Small Signal Stability of VSC-HVDC System

The voltage source converter based high voltage direct current (VSC-HVDC) system is based on voltage source converter, and its control system is more complex. Also affected by the fast control of power electronics, oscillation phenomenon in wide frequency domain may occur. To address the problem of small signal stability of the VSC-HVDC system, a converter control strategy is designed to improve its small signal stability, and the risk of system oscillation is reduced by attaching a damping controller and optimizing the control parameters. Based on the modeling of the VSC-HVDC system, the general architecture of the inner and outer loop control of the VSC-HVDC converter is established; and the damping controllers for DC control and AC control are designed in the phase-locked loop and the inner and outer loop control parts respectively; the state-space state model of the control system is established to analyze its performance. And the electromagnetic transient simulation model is built on the PSCAD/EMTDC simulation platform to verify the accuracy of the small signal model. The influence of the parameters of each control part on the stability of the system is summarized. The main control parts affecting stability are optimized for the phenomenon of oscillation due to changes in operation mode occurring on the AC side due to faults and other reasons, which effectively eliminates system oscillation and improves system small signal stability, providing a certain reference for engineering design.

Optimal fractional SSSC damping action for variable wind penetrations

An optimal fractional SSSC based control action has been proposed in this work for enhancing small signal stability of power system pertaining to intermittent variations in wind penetrations. The parameters of controllers are tuned by sailfish algorithm and ITAE based objective function has been chosen for minimization problem. A three machine system has been considered in this work with different operating conditions and step with random variations in wind penetrations have been executed with different machines and subject to which the system response and eigen values are analyzed. Based on system response it is observed that subject to intermittent variations in wind source the small signal stability is hampered due to increased power system oscillations and by properly tuning the fractional lead-lag control action based on static synchronous series compensator. These oscillations can be damped efficiently. The performance of proposed sailfish algorithm (SFA) tuned SSSC controlled action has been compared with PSO and DE algorithms subject to different case studies.

Evaluation of Inherent Damping Introduced by Thyristor Controlled Series Compensators

Series compensation of transmission lines increase the risk of Sub-Synchronous Resonance (SSR) problems. Use of Thyristor Controlled Series Compensators (TCSC) in place of Fixed Series Capacitors (FSC) has benefited in terms of damping SSR. SSR Damping with TCSC can be achieved with supplementary controls or through its inherent damping capability. Use of discrete time models for small signal stability analysis of TCSC is well established. This paper uses a simplified Dynamic Phasor (DP) model of the TCSC for an in-depth evaluation of the inherent SSR damping capability through small signal stability analysis. Source of inherent damping in open loop operation and the representation of it in the DP model is elaborated and the small signal model is validated against Electro Magnetic Transient (EMT) simulations. Effect of inductive-resistive nature of the TCSC on Induction Generator Effect (IGE) and Torsional Interactions (TI) is shown through small signal stability assessment. It is shown that the network resonant frequency exists only in a narrow range of firing angles of the TCSC and thus IGE and TI are avoided in most part of its operating range. IEEE first benchmark system for SSR studies is used to demonstrate the inherent damping capability of a TCSC.

Revamped Sine Cosine Algorithm Centered Optimization of System Stabilizers and Oscillation Dampers for Wind Penetrated Power System

The mapping of damping ratios and damping factors by Sine-Cosine Algorithm (SCA) is significant in the analysis of low frequency oscillations generated in an integrated network having multiple conventional and renewable energy sources. Multiple random models with unknown search spaces and uncertain conditions and constraints, which incorporate the fluctuation of solutions towards or outwards at the initial stage for solving real-time problems can be analyzed by a revamped sine-cosine algorithm (RSCA) model. In this paper, the SCA has been revamped to explore the stability threshold for a stable system under dynamic nonlinear operating conditions. It is achieved with the infusion of suitable mathematical functions for optimizing the parameters of Power System Stabilizers (PSSs) and Doubly Fed Induction Generator (DFIG) system-based oscillation dampers to enhance the Small Signal Stability of power systems through effective damping of low-frequency oscillations (LFOs). These LFOs weaken the effective power generation and demand management cycle in conventional power systems when the system faces conditions like intermittent renewable energy sources, overloading conditions, impulsive faults etc. The small-signal and transient stability studies for various disturbances and different operating conditions are investigated, and the performance of the proposed RSCA for optimized parameter tuning of system stabilizers and oscillation dampers are analyzed on the modified benchmarking systems with wind generators using MATLAB Ⓡ simulations. The efficiency and robustness of the proposed algorithm has been verified under selective critical operating conditions, line outages, and load uncertainties to prove that the low frequency modes are damped with an elevated positive damping ratio and rapid settling time with reduced oscillations. The application of system stabilizers and oscillation dampers optimized through the proposed RSCA shows a reduced settling time in the LFOs created and improved damping ratio of 0.22 for an increase in 20% loading and 50% of wind power generation in the case study of Two Area Four Machine System.

Small-signal stability analysis of the asymmetrical DC operation in HVDC networks

• Stability of interconnection of monopolar and bipolar HVDC stations is analysed. • A small-signal stability model for asymmetric DC operation studies is developed. • The model is validated with EMT dynamic simulation. • The findings are useful for systematic design of the HVDC grounding systems. • A controller is designed to enhance stability during asymmetric DC operation. The increase in High Voltage Direct Current (HVDC) projects favors their future interconnection to form regional networks, but this interconnection can be hindered by the lack of standardization in station's configuration and converter's differing grounding schemes. Whilst other studies have studied the effect of Direct Current (DC) asymmetrical operation, they are limited in their scope. This paper proposes a more realistic perspective, considering stations with different topologies, permanent DC asymmetries and the influence of the grounding systems. This more complex point of departure requires the re-examination of the modeling methods, from time-domain to frequency-domain. This paper proposes a small-signal stability model of the system, which is validated with the electromagnetic transient (EMT) dynamic simulations using PowerFactory. This model provides guidelines for designing the grounding impedance and allows the proper design of a specific controller to dampen the asymmetrical DC operation mode.

Online Tracking of Small-Signal Stability Rightmost Eigenvalue Based on Reference Point

Machine learning technologies have been applied to improve the real-time performance of small-signal stability (SSS) assessment, while achieving a high accuracy requires numerous samples, and model performance may degrade if not updated over time. Furthermore, single models tend to learn general features without analyzing specific characteristics within the samples, which may lead to a high frequency of large errors, particularly at operating points (OPs) where the eigenvalue trajectories have sudden changes. Facing such issues, this paper introduces the concept of reference points (RPs) for accurate online tracking of the rightmost eigenvalue (RE), as the RP information reflects the characteristics among its surrounding OPs. The performance of this model is sensitive to RPs, so affinity propagation (AP) clustering is employed to determine the number of RPs and generate corresponding groups, accommodating diverse OP characteristics. This paper generates data-driven networks for each group and combines them into a multi-network for precise RE prediction. Case studies show that the use of RPs improves accuracy by nearly 2% compared to methods without them, with even greater improvements in mixed load type scenarios. To mitigate computational stress, this paper proposes an adaptive partial update strategy based on the dynamic time warping algorithm, avoiding the need to update all networks within each sliding time window. Experimental results verify that the total running time is reduced by more than 10%. Online tracking demonstrates that RPs help decrease the frequency of large errors by 40%, especially at sudden change points of RE trajectories.

Stability Enhancement of Grid-Connected Wind Power Generation System Using PSS, SFCL and STATCOM

The stability related issues may occur in a power system due to disturbances in generating or loading conditions, especially in the presence of distributed generation (DG) based on renewable energy resources (RERs). This paper proposes a novel strategy for the stability enhancement of a wind power generation system (WPGS) by using a combination of three devices, namely, a power system stabilizer (PSS), resistive superconductor fault current limiter (R-SFCL) and static synchronous compensator (STATCOM). The small signal (SS) stability of the test system is enhanced by selecting the best PSS type from the different types of PSS. An R-SFCL is used for improving the rotor angle and the frequency stability of the test system. Two indices, namely, transient stability index and sum of maximum deviations (SMD) index are introduced for determining the optimal locations of different sized R-SFCLs for increasing the rotor angle stability. The sensitivity index (SI) based on the power change between areas is applied for determining the optimal locations of different sized R-SFCLs for enhancing the frequency stability. Along with rotor angle and frequency stability, LVRT capability improvement of the wind farm using STATCOM is also considered. Finally, the combined effect of R-SFCL and STATCOM on the rotor angle and the frequency stability, for different fault locations, is also investigated for determining the optimal location of an R-SFCL in the presence of STATCOM. The results presented in the paper show that STATCOM affects both the number of feasible locations and the optimal locations that can be selected for different sized R-SFCLs for augmenting the rotor angle and the frequency stability of the system during faults. Moreover, it is pointed out that an optimal combination between the different sizes and the locations of R-SFCLs and STATCOM exists to enhance the overall stability of the test system under fault conditions.

Dynamics and Stability of Power Systems With High Shares of Grid-Following Inverter-Based Resources: A Tutorial

Electric power systems worldwide are undergoing a foundational transition from mechanical-backed generation technologies dominating the resource mixture, primarily synchronous generators, into a hybrid system consisting of periods of a preponderance of power electronics-backed generation technologies, primarily solar photovoltaics and wind power plants and battery storage systems. Almost all current inverter-based resources integrated into bulk power systems are grid-following technology, and there exists a knowledge gap concerning the impacts of large-scale integration of grid-following inverters on power system dynamics, which is a critical aspect of power system planning and operation. This paper serves as a tutorial and addresses the stability and reliability challenges pertinent to the integration of grid-following interfaced inverter-based resources. While considering both small-signal and large-signal stability problems, it demonstrates and explains the underlying interrelated dynamics of electric angle, frequency, and voltage, as well as the impacts that system inertia can have on system stability. Industry-grade electromagnetic transient simulations in Power Systems Computer-Aided Design (PSCAD) are utilized to demonstrate the concepts presented in this paper, and all the computer models have been made available to the public at no cost.

Small-Signal Angle Stability-Oriented False Data Injection Cyber-Attacks on Power Systems

The small-signal angle stability (SSAS) of a power system is determined by the property of operation points. The widely applied false data injection (FDI) cyber-attack, however, is able to stealthily mislead the optimal power flow (OPF) and thus compromise operation points, leading to damages to the SSAS margin. To provide insights for cyber defenders, this paper proposes and investigates a stealthy SSAS-oriented FDI cyber-attack focusing on two attacking purposes, i.e., the SSAS margin and operation cost, with higher priority on the former one. First, this paper establishes a novel bi-level model with an implicit SSAS constraint based on a structure preserving model to compromise operation points. Then, for the SSAS interarea mode in a typical two-area system, this paper formulates closed-form expressions of how the SSAS margin and operation cost behave with respect to stealthy injections. By comparison, for the SSAS local mode in general power systems, this paper proposes a moving target cyber-attack-based hierarchical solution algorithm. Simulation results on a two-area system, a Kundur 11 bus system, and a modified IEEE 14 bus system demonstrate the significant damaging effects of the proposed SSAS-oriented FDI cyber-attack and the conflict between the two attacking purposes.

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.

Small Signal Stability Analysis of Damping Controller for SSO Mitigation in a Large Rated Asynchronous Hydro Unit

Small Signal Stability Analysis of Damping Controller for SSO Mitigation in a Large Rated Asynchronous Hydro Unit

Adaptive Droop Control for Voltage and Frequency Regulation in Virtual Power Plant under Power System Contingencies

The frequent penetration of distributed energy resources in microgrid environment often faces operational challenges like stability and reliability issues. In order to overcome these challenges, the concept of the virtual power plant is suggested. Practically, the chance of voltage and frequency fluctuation increases in virtual power plant scenarios under critical power system contingencies like faults and sensitive load switching. Therefore, implementation of efficient controllers is required to address this issue. Further, the fixed gain droop control topology reported in literature is insufficient to accomplish seamless voltage and frequency regulation of the virtual power plants. Therefore, this paper proposes an adaptive droop control scheme to regulate system’s frequency and voltage (as per IEEE 1547) in presence of critical power system contingencies under virtual power plant scenarios. Further, a small signal stability analysis is carried out considering the system Eigenvalues to investigate the effectiveness of the proposed adaptive droop controller. Additionally, a comparative analysis between traditional and proposed droop controller is performed considering critical power system contingencies under MATLAB / Simulink environment. The dynamic responses establish the improved performance of the proposed controller over the traditional control scheme in terms of transient and steady-state stability.

Modeling, Analysis, and Design for Small-Signal Stability in Sequence-Decomposed Grid-Forming Control

Modeling, Analysis, and Design for Small-Signal Stability in Sequence-Decomposed Grid-Forming Control

Inertia Estimation of the 60 Hz Japanese Power System From Synchrophasor Measurements

This paper proposes a new approach to estimate the inertia of the 60 Hz Japanese power system from the background signals of phasor measurement units. Regarding the constraint boundaries, the entire system is divided into two control areas, which can be represented by an equivalent two-generator model based on small-signal stability analysis. The ambient inertia of each area, including both generation and demand sides can be estimated by measuring the corresponding phase difference and interchange power with respect to the extracted proportions of the frequency response, inter-area oscillation, and synchronizing power. Then, the sum of the estimated inertia for each area gives the total inertia of the entire 60 Hz system. The method was validated on the benchmark model of the Japan transmission network, and its sensitivity is evaluated by conducting various system operations on generator control effects. The efficiency and robustness were verified through real measurements under diverse system conditions. The results confirm that the developed approach can accurately estimate the system inertia during normal operation, enabling nearly continuous inertia tracking trajectory.

Small-Signal Stability of DC Current Flow Controller Integrated Meshed Multi-Terminal HVDC System

In this paper, the small-signal stability of a DC current flow controller (CFC) integrated meshed multi-terminal HVDC (MTDC) system is investigated with unique contributions: (1) The dynamics of a multi-line CFC, interconnected voltage- source converters (VSCs) and the DC transmission lines are considered in the small-signal modelling. (2) The switching effect of the capacitive components in the π-type DC transmission lines is identified. The comparative studies of modelling the DC transmission lines using π-type/T-type equivalent circuit are conducted. (3) The impact of the CFC on the AC side of the MTDC system is taken into account with analysis of the critical short-circuit ratio (CSCR) through root-locus analysis and participation factors. The relationship of the SCR with VSC outer-loop control and power transfer is analyzed. (4) The influence of the CFC control system/structural parameters on the small-signal stability of the entire system is investigated. The relationship of the CFC integration with the VSC outer-loop control is analyzed. The adjustment of single/multiple parameters for enhancing the system stability and a sequential parameter tuning approach for multiple parameters are explained. The effectiveness of the proposed method applied in different MTDC systems with CFC is verified. It would be useful for the configuration and parametric design of the CFC integrated meshed MTDC systems.

Research on Virtual DC Generator-Based Control Strategy of DC Microgrid with Photovoltaic and Energy Storage

With the penetration of a large number of photovoltaic power generation units and power electronic converters, the DC microgrid shows low inertia characteristics, which might affect the stable operation of the microgrid in extreme cases. In order to enhance the “flexible features” of the interface converter connected to the DC bus, a control strategy of DC microgrid with photovoltaic and energy storage based on the virtual DC generator (VDCG) is proposed in this paper. The interface converters of the photovoltaic power generation system and the energy storage system simulates the inertia and damping characteristics of the DC generator to improve the stability of the DC bus voltage. The impedance ratio of DC microgrid was obtained by establishing the small-signal model of photovoltaic power generation system and energy storage system, and the Nyquist curves was applied to analyze the small-signal stability of the system. Finally, the simulation results were verified with MATLAB/Simulink. The results show that the proposed control strategy can slow down the fluctuation of bus voltage under the conditions of photovoltaic power fluctuation and load mutation, thus enhancing the system stability.

Stability Analysis of a Weak-Grid-Connected Voltage-Sourced Rectifier Considering the Phase-Locked Loop Dynamics

The high bandwidth of a phase-locked loop (PLL) can deteriorate the small-signal stability of a voltage-sourced converter (VSC) under a weak grid condition. This instability can occur for a VSC operating as both a rectifier and an inverter, but the root causes can differ for the two. This study, through modal analysis, demonstrates that different approaches are required depending on the power flow direction to resolve the instability. Subsequently, an analysis of the rectifier dynamics is set as the primary target, and the instability characteristic is investigated via a new approach that utilizes the open-loop transfer function of the power control loop. Consequently, it is discovered that the high-bandwidth PLL reduces the reactive power compensation for the AC system and results in a severe voltage drop. A novel parallel voltage filter technique is proposed to overcome this instability. The performance of the proposed method is verified in the frequency- and time-domain analyses. The results indicate that the proposed method effectively improves stability without major modifications to the control system.

Identifying and Assessing Small-Signal Stability of Grid-Tied VSCs Considering Multiple Modes

Identifying and Assessing Small-Signal Stability of Grid-Tied VSCs Considering Multiple Modes

Small-signal Stability Analysis and Improvement with Phase-shift Phase-locked Loop Based on Back Electromotive Force Observer for VSC-HVDC in Weak Grids

Voltage source converter based high-voltage direct current (VSC-HVDC) transmission technology has been extensively employed in power systems with a high penetration of renewable energy resources. However, connecting a voltage source converter (VSC) to an AC weak grid may cause the converter system to become unstable. In this paper, a phase-shift phase-locked loop (PS-PLL) is proposed wherein a back electromotive force (BEMF) observer is added to the conventional phase-locked loop (PLL). The BEMF observer is used to observe the voltage of the infinite grid in the stationary <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha\beta$</tex> frame, which avoids the problem of inaccurate observations of the grid voltage in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$dq$</tex> frame that are caused by the output phase angle errors of the PLL. The VSC using the PS-PLL can operate as if it is facing a strong grid, thus enhancing the stability of the VSC-HVDC system. The proposed PS-PLL only needs to be properly modified on the basis of a traditional PLL, which makes it easy to implement. In addition, because it is difficult to obtain the exact impedance of the grid, the influence of short-circuit ratio (SCR) estimation errors on the performance of the PS-PLL is also studied. The effectiveness of the proposed PS-PLL is verified by the small-signal stability analysis and time-domain simulation.