Stability Margin Research Articles

Transient Stability of Paralleled Virtual Synchronous Generator and Grid-Following Inverter

The majority of inverter-based resources (IBRs) currently operate as grid-following inverters (GFLIs). However, these inverters exhibit certain stability issues when integrated in low-strength areas of the grid. To enhance the grid strength in a GFLI-dominant area, virtual synchronous generators (VSGs) can be installed. If the VSG and the GFLI are investigated as a paralleled system, despite the benefits brought by the VSG, in some cases, the transient angle instability process, caused by a voltage sag, is accelerated, making the whole system more prone to instability. Therefore, this paper aims to study the transient angle stability of a paralleled VSG-GFLI system via investigating the voltage at a common bus between the two IBRs. Subsequently, a stable region of the voltage angles of the two IBRs is determined. Based on this stable region, the stability margin of the paralleled system can be determined and used to quantitatively evaluate the system stability. Moreover, an additional control loop is proposed to improve the transient stability of the paralleled system in this paper. The proposed controller can adaptively reduce the power set-point of the VSG to avoid a complete failure of the VSG even when no stable equilibrium point exists during a voltage sag. The stability investigation and performance evaluation of the proposed method are conducted in PSCAD/EMTDC and experimentally validated.

Plausibility and Implications of Converter-Driven Oscillations Induced by Unstable Long-Term Dynamics

For decades, synchronous generators have dominated power system dynamics and have been the foundation for the comprehension of the physical phenomena involved in power system stability. This paradigm is rapidly changing; large synchronous generators that contribute to system strength are being replaced by inverter-based generators. Consequently, new kinds of instabilities are emerging. Slow-interaction converter-driven instability is one example in which undamped oscillations occur when inverter-based generators operate in weak areas. Transmission system operators have observed the phenomenon under the scope of short-term dynamics following a disturbance during a weak operating condition. This paper suggests that converter-driven oscillations can occur even in the case when the system's initial operating condition is strong. It concludes that the phenomenon can be triggered by long-term dynamics that slowly weaken the system in which small-signal and short-term simulations show an ample stability margin. The outcome is a combination of unstable long-term dynamics and undamped oscillations. Furthermore, this work suggests that classical emergency controllers that are effective against long-term instability may not be successful if undamped oscillations are also present. A method for instability detection and counteraction is proposed based on Prony analysis and time-domain simulations on the IEEE test system for voltage stability assessment.

Generalized Turbine Model Based Analysis and Simulation of Ultra-Low Frequency Oscillation of Hydropower Units

The occurrence of ultra-low frequency oscillation (ULFO) events in the power grid has a significant number of hydropower units in recent years. Considering this aspect, relevant studies have shown that the turbine model has an important impact on the ULFO behavior of hydropower units. Based on the study of the generalized turbine model, the flow factor closely related to the inherent parameters of the turbine and the variation of the generating flow is defined in this paper. The ULFO model of the hydropower unit with full consideration of the flow factor is established. Based on the frequency characteristics of the system and the Routh stability criterion, the mechanism of the influence of the flow factor on the ULFO behavior of the hydropower unit is analyzed. The simulation results of single-machine and multi-machine systems show that, compared with the ideal turbine model, the generalized turbine model considering the flow factor can increase the stability margin of the system. It can provide greater damping torque and restrain the ULFO behavior of hydropower units. The flow factor is larger, and the suppression effect of the ULFO is more obvious.

PID-Based control of sepic power stage with QS bacterial-based search algorithm for renewable energy applications

In response to the growing need for efficient power conversion in renewable energy applications, this study addresses the issue of harmonic distortion and low Power Factor (PF) values caused by non-linear loads, such as electronic devices. Low PF results in reduced efficiency, increased energy consumption, and higher costs for both consumers and utilities. Active correction, typically involving an active circuit implemented using a power converter, provides an optimal solution by offering high performance, precise regulation, and low harmonic distortion. This research proposes a Power Factor Correction (PFC) solution utilizing an Interleaved DC-DC Single Ended Primary Inductance Converter (SEPIC) for the power stage and a Proportional Integral Derivative (PID) controller for the control block, tuned by a Quorum Sensing (QS) bacterial-based search algorithm. The PID controller parameters are derived using a frequency-domain approach, which presents advantages such as reduced design complexity, improved stability margins, and enhanced SEPIC performance. Simulation results indicate reduced overshoot, settling time, rise time, and Total Harmonic Distortion (THD) percentage, as well as increased efficiency and power factor nearing unity. The proposed scheme also demonstrates improved dynamic performance for variations in load, line, and reference voltage. Owing to its high efficiency, precise voltage regulation, and minimized impact on the electrical grid, this solution is well-suited for renewable energy applications, where optimizing energy conversion and ensuring stable operation are crucial for the overall performance of renewable energy systems.

Enhanced Virtual Inertia Controller for Microgrid Applications

Unlike Synchronous Generators (SGs), Virtual Synchronous Generators (VSGs) inertia is not fixed once it is manufactured and only has an upper limit defined by its energy storage components. In this paper, a novel Enhanced Virtual Inertia Controller (EVIC) is proposed. The proposed controller alters the VSG inertia coefficient between two limiting levels in response to a grid transient. The key difference between the proposed controller and the variable inertia controller is that the proposed EVIC causes a smooth transition in the inertia coefficient while the variable inertia controller causes a discontinuous jump in it. The proposed EVIC guarantees an adaptive response to grid dynamics, such that a negligible change occurs at small disturbances and a linear and smooth increase occurs at moderate disturbances. For large disturbances, the proposed controller smoothly oscillates the inertia between two saturation levels, which then quickly returns the converter to its steady-state operating point with minimum oscillations. A qualitative study of the performance and stability margin of the proposed controller was conducted using a large signal model (nonlinear model) of VSG connected to a microgrid. The large signal model provided a complete description of the converter’s behaviour under large disturbances, which is the area of interest of the proposed controller. It also contained the small-signal dynamics (linear dynamic) within the vicinity of the equilibrium (steady-state) point. Thus, a complete description of the proposed controller dynamics is conveyed to prove its validity and adaptability.

Design and Optimization of a PIR Controller for Voltage Regulation in a Synchronous Boost Converter

This paper proposes a proportional-integral-retarded (PIR) controller for a synchronous boost converter to ensure its reliable operation during voltage regulation. The PIR controller is based on the addition of a time-delay as a design parameter. In this approach, we analyze the spectral properties of the closed-loop system and establish a tuning rule that optimizes its dynamic response, thus maximizing the exponential decay rate for the system’s solutions. Inspired by the application field of renewable energy systems such as photovoltaic and fuel-cell systems, we validate the significance of our results via numerical simulations and show that incorporating delays as design parameters improves relative stability margins.

A new index for the assessment of power system strength considering reactive power injection and interaction of inverter based resources

Power system strength evaluation is vital to maintain secure operation in power systems having huge dependence on Inverter Based Resources. This paper reviews the state-of-the-art power system strength assessment methodologies along with their research gaps. Further, this paper proposes a novel power system strength assessment index for power system strength assessment in the presence of Static Var Compensator. A modified IEEE 39 bus system with Inverter Based Resources was used for the validation. The proposed index is validated in positive sequence modelling software using voltage stability margin and is compared with existing indices. To verify the applicability of the proposed index along with other existing indices, Electro Magnetic Transient type simulations are presented, which illustrate the sensitivity of the voltage following a three phase to ground fault followed by transmission line tripping in the power system.

Effect of hip abduction assistance on metabolic cost and balance during human walking.

The use of wearable robots to provide walking assistance has rapidly grown over the past decade, with notable advances made in robot design and control methods toward reducing physical effort while performing an activity. The reduction in walking effort has mainly been achieved by assisting forward progression in the sagittal plane. Human gait, however, is a complex movement that combines motions in three planes, not only the sagittal but also the transverse and frontal planes. In the frontal plane, the hip joint plays a key role in gait, including balance. However, wearable robots targeting this motion have rarely been investigated. In this study, we developed a hip abduction assistance wearable robot by formulating the hypothesis that assistance that mimics the biological hip abduction moment or power could reduce the metabolic cost of walking and affect the dynamic balance. We found that hip abduction assistance with a biological moment second peak mimic profile reduced the metabolic cost of walking by 11.6% compared with the normal walking condition. The assistance also influenced balance-related parameters, including the margin of stability. Hip abduction assistance influenced the center-of-mass movement in the mediolateral direction. When the robot assistance was applied as the center of mass moved toward the opposite leg, the assistance replaced some of the efforts that would have otherwise been provided by the human. This indicates that hip abduction assistance can reduce physical effort during human walking while influencing balance.

Bus-impedance-based stability improvement of DC power distribution system considering dynamic performance

A direct-current (DC) power distribution system (PDS) enjoys the benefits of flexibility and efficiency. However, increasing stability issues occur due to the interaction among feedback-controlled converters in PDS. For ensuring stability, various impedance-based method is discussed by scholars. Unlike the traditional analysis method based on minor-loop-gain (MLG), Passivity-Based Stability Criteria (PBSC) is a novel bus-impedance-based method. Although PBSC is a promising measure of stability analysis for the distribution system, the difficulty of stability margin calculation and dynamic characteristic analysis limits its application. Therefore, the relative stability margin (RSM) is proposed to assess the damping levels. Based on RSM, the dynamic performance optimization algorithm (DPOA) is presented to optimize the proposed MMC impedance reshaping (MIR) control. Compared with the past stability analysis, dynamic behaviour is considered in this paper when stability improvement is implemented. By means of the MIR and DPOA, the stability and dynamic performance of the distribution system are enhanced. Simulation results confirm the validity of the proposed viewpoints and method.

Growth faults and avalanches: Reconstructing Paleoarchean basins in the Pilbara and Kaapvaal cratons

Four new volcano-sedimentary complexes (VSC's), respectively c. 3510, 3460, 3430, and 3320 Ma old, are identified in the East Strelley, Coongan, and Kelly belts of the East Pilbara craton and compared with the extraordinarily complete c. 3450 Ma Buck Reef-VSC in the southern African Kaapvaal craton. The VSC’s reveal an intricate relationship between volcanic deposition, sedimentation, development of syndepositional fault arrays, both extensional and contractional, and magmatism. The geometry and kinematics of these fault systems were analyzed after restoring the tilt of the stratigraphic sequences back to the depositional horizontal. The growth fault arrays are interpreted to have been generated by lack of lateral support of depositional basin margin prisms as known from present-day deltas and passive margins. This ‘basin margin collapse’ scenario for deformation and kinematics of the topmost section of the crust relies on topographic relief combined with vertical crustal oscillation. The relationship between supracrustal collapse and coeval deformation on deeper-seated detachments within the basement of the Pilbara remains as yet unsolved.The restoration corroborates the (semi-)circular basin architecture we proposed in 2017, which preceded, and is unrelated to, the present-day configuration of granitoid complexes and greenstone belts. The new findings also assess an early, syndepositional presence of the east–west Warrawoona Lineament as a major dividing line of as yet unknown structural character between two areas of basin superposition.For the Coonterunah Subgroup a multistorey architecture is established: the Table Top/Coucal-VSC with its near-water level chert top is overlain by regularly bedded Double Bar Basalt. The ensemble is truncated by the newly introduced tectono-stratigraphic Bergamina Unit, interpreted as a mega-avalanche emplaced somewhere between 3496 and 3466 Ma, possibly time-equivalent to the Duffer Fm.The crustal depths of the detachments below the (water-level) tops of all VSC’s identified, in other words the thicknesses of the VSC’s, are used as proxy for determining minimum basin centre depths ranging from 1000 to 3800 m. The greatest depth was reached in the North and South Coongan Basins, where voluminous bimodal volcanism of the Duffer Fm, maximum subsidence and deposition rates resulted in maximum basin margin instability.

Optimal Location And Size of The STATCOM to Enhance The Power System Stability

The importance of power system operation is becoming increasingly significant due to the escalating demand observed in many nations. The exponential growth in load demand exerts substantial stress on electrical power systems, since they run in close proximity to their critical thresholds due to limitations imposed by environmental and economic factors. The basic goal of operating electrical power networks is to efficiently supply energy to users at optimal frequency and voltage levels, with a focus on cost minimization. The main objective of this study is to examine the augmentation of voltage stability margin by deploying Flexible AC Transmission Systems (FACTS) at their ideal positions. In order to determine the most efficient size of a Static Synchronous Compensator (STATCOM), it is necessary to explore the relationship between the loading factor and the capacity of the STATCOM. The case study utilized the Iraqi National Super Grid System (INSGS), which consisted of a 24-bus configuration. The effectiveness of the CPF technique has been assessed in the framework of the Iraqi Super Grid test System. The appropriate place for attaching STATCOM to enhance voltage stability in the Iraqi network system was identified to be Bus (20).

FUZZY LOGIC CONTROLLED STATCOM WITH A SERIES COMPENSATED TRANSMISSION LINE ANALYSIS

The integration of wind farms with transmission networks exhibits several problems. The sub-synchronous resonance (SSR) plays a vital role in those issues, and it must be reduced. Two effective flexible ac transmission system (FACTS) based voltage control devices, namely static synchronous series compensator (SSSC) and static compensator (STATCOM) are proposed in this paper to mitigate the SSR. Detailed eigenvalue analysis was conducted to prove the successful mitigation of SSR by two controllers in a series of compensated wind farms. To find the dominant control scheme, the eigenvalues of the proposed controllers are compared with PSCAD/EMTDC simulations. Finally, a comparison study is carried out between the two proposed SSR controllers.Further, the fuzzy logic control based on STATCOM and SSSC is also developed to enhance the stability margin of the wind turbine. The results have been validated with the IEEE 1st SSR benchmark system. From the results, it is proven that Fuzzy Logic Controller (FLC) based SSSC exhibits better performance than STATCOM.

How should the margin of stability during walking be expressed to account for body size?

When expressing the margin of stability as a distance, it does not directly estimate the perturbation magnitude needed to change stability states. Additionally, it is unknown how body size may influence this measure. Therefore, we propose other expressions of stability margins, including that of an impulse, a change in center of mass velocity, and a scaled, unitless impulse. The purpose of this study was to determine the influence of body size on these margin expressions using walking data from children and adults. We anticipated that margins expressed as an impulse would have strong correlations with body mass and height, as well as large between-group differences. We predicted that scaling this impulse value would result in small correlations and between-group effect sizes. We calculated each stability margin at minimum lateral values and in the anteroposterior directions at mid-swing and foot strike. In the lateral direction, margins expressed as an impulse had strong correlations with body size (r≥0.58, p<0.01) and large between-group differences (|d|≥1.07, p<0.01). The other expressions did not have strong positive correlations (|r|≤0.20) or large between-group effects (|d|≤0.44). In the anteroposterior directions, impulse margins had strong correlations with body size (|r|≥0.83, p<0.01) and large between-group differences (|d|≥1.74, p<0.01). The scaled, unitless impulse margin was the only variable that resulted in small, non-significant differences (|r|≤0.22, p≥0.24) as well as small between-group effect sizes (|d|≤0.46, p≥0.22). We propose expressing stability margins as an impulse. If scaling is needed, we encourage using the scaled, unitless impulse.

Cognitive Predictors of Responsiveness to Reactive Step Training in People with Parkinson’s Disease at Fall-Risk

Reactive stepping can be improved in people with Parkinson’s Disease (PwPD). However, there is variability in the responsiveness to such training. This study examined if cognition could predict the responsiveness of PwPD to a two-week reactive step training intervention. 25 PwPD (70.52 years ± 7.15; Hoehn & Yahr range 1–3) at risk for falls completed a multiple baseline, open-label, uncontrolled pre-post intervention study. Reactive stepping was trained through a two-week (six-session) intervention with repeated support surface translations. Stepping performance was measured at two baseline assessments (B1 and B2), immediately after the intervention (P1), and two months after training (P2). Primary stepping outcomes were anterior-posterior margin of stability (MOS), step length, and step latency during backward steps. The primary aim assessed whether global cognition (Scales for Outcomes in Parkinson's Disease-Cognition - SCOPA-COG, & Montreal Cognitive Assessment - MoCA) was related to two-month retention of improvements in reactive stepping after practice. The secondary aim explored whether specific cognitive domains predicted retained stepping improvements, including attention/working memory, executive function, language, memory, and visuospatial function. Greater baseline global cognition was related to better two-month retention of step length improvements (SCOPA-COG: p = 0.002, f2 = 0.31; MoCA: p = 0.002, f2 = 0.38). However, only SCOPA-COG retained statistical significance after p-value adjustment for multiple comparisons (p = 0.04). Optimal cut-point analysis revealed that a SCOPA-COG threshold of 31 or higher was optimal for identifying individuals likely to retain improvement. Specific cognitive domains did not predict changes in reactive stepping outcomes. Participants with greater baseline global cognition, particularly as measured by SCOPA-COG, demonstrated greater retention of improvements in reactive stepping. In this cohort, a SCOPA-COG threshold of 31 could predict individuals likely to benefit from the intervention. These findings highlight the potential of cognitive screening to identify people more or less likely to benefit from reactive balance training.

Nonlinear Rigid-Elastic Coupled Modeling and Oscillation Mechanism Analysis of Rotor-Body-Slung-Load System

In order to reveal the mechanism of Category II rotor-body-slung-load coupled oscillation (RBSLCO) with the frequency range of 2.5~8 Hz, a novel nonlinear rigid-elastic coupled model is presented for the helicopter and slung load system (HSLS) with explicit formulation. The slung load system model is coupled with the current rigid-elastic coupled helicopter model, considering fuselage hook point rigid-elastic coupled movements, cable stretching, and hook point force from the slung load system. The results show that carrying the heaviest load is the vital state for Category II RBSLCO. As slung load mass ratio increases, rotor-fuselage coupling becomes stronger and the oscillation frequency shifts slightly, causing a maximum of 15% reduction in stability margin. In addition, even when the load is lightweight, another form of Category II RBSLCO may appear involving fuselage bending and cable stretching. This Category II RBSLCO behaves like the vertical bouncing but is divided into a high-frequency anti-phase oscillation and a relatively low-frequency in-phase oscillation.

Age-related differences in lower limb muscle activation patterns and balance control strategies while walking over a compliant surface

Substantial evidence demonstrates that falls in older adults are leading causes of fatal and non-fatal injuries and lead to negative impacts on the quality of life in the aging population. Most falls in older fallers result from unrecoverable limb collapse during falling momentum control in the single limb support (SLS) phase. To understand why older adults are more likely to fall than younger adults, we investigated age-related differences in knee extensor eccentric control, lower limb muscle activation patterns, and their relation to balance control. Ten older and ten younger healthy adults were compared during balance control while walking on a compliant surface. There was a positive correlation between knee extensor eccentric work in the perturbed leg and the swinging leg’s speed and margin of stability. In comparison to younger adults, older adults demonstrated (1) less eccentric work, reduced eccentric electromyography burst duration in the perturbed leg, (2) higher postural sway during SLS, and (3) impaired swinging leg balance control. The group-specific muscle synergy showed that older adults had a prominent ankle muscle activation, while younger adults exhibited a more prominent hip muscle activation. These findings provide insight into targeted balance rehabilitation directions to improve postural stability and reduce falls in older adults.

FPGA Implementation of IIR Notch and Anti-Notch Filters With an Application to Localization of Protein Hot-Spots.

In this paper, high-speed second-order infinite impulse response (IIR) notch filter (NF) and anti-notch filter (ANF) are designed and realized on hardware. The improvement in speed of operation for the NF is then achieved by using the re-timing concept. The ANF is designed to specify a stability margin and minimize the amplitude area. Next, an improved approach is proposed for the detection of protein hot-spot locations using the designed second-order IIR ANF. The analytical and experimental results reported in this paper show that the proposed approach provides better hot-spot prediction compared to the reported classical filtering techniques based on the IIR Chebyshev filter and S-transform. The proposed approach also yields consistency in prediction hot-spots compared to the results based on biological methodologies. Furthermore, the presented technique reveals some new "potential" hot-spots. The proposed filters are simulated and synthesized using the Xilinx Vivado 18.3 software platform with Zynq-7000 Series (ZedBoard Zynq Evaluation and Development Kit xc7z020clg484-1) FPGA family.

Impact of Time Delay on the Control Link in Small Signal Dynamics of LCC-HVDC System

The time delay in the control link will affect the small signal stability of the line commutated converter based high voltage direct current (LCC-HVDC) system. This paper establishes the small signal model for the LCC-HVDC system considering the time delay in the control link. Then, based on the developed models, the movement feature of the eigenvalue loci with varying time delay under different AC system strength is investigated, the impact of the time delay on the system stability margin is quantitatively evaluated, and the frequency band affected by the time delay is identified. Subsequently, influence mechanisms of time delay on system stability are revealed from the perspective of the system damping characteristic by decomposing different damping paths. Moreover, impacts of time delay on DC current/voltage controller's stability margin are investigated. Theoretical analysis and simulation results indicate that, the increase of time delay at the rectifier-side will continuously deteriorate the system stability, as well as the system dynamic performances, while in most cases the increase of the time delay at the inverter-side imposes a non-monotonic effect on the system stability, which is weakened first and then slightly strengthened. Therefore, in certain scenarios, the larger time delay at the inverter-side may play a positive role in the system stability to some extent. The results can provide certain technical reference for the identification of key influencing factors causing the system oscillation and reasonable selection of control parameters in practical LCC-HVDC projects.

Adiabatic collapse of non-homogeneous self-gravitating gas cloud

In this letter, we find the critical mass of a self-gravitating, spherically symmetric gas cloud, above which the fluid, within the bubble, collapses. Our analysis departs from a non-homogeneous equilibrium density, satisfying the Boltzmann relation. A time scale is defined in terms of the adiabatic index of the gas. Subsequently, a sinusoidal perturbation around equilibrium is regarded, thereby leading to a dispersion relation of frequency with wavelength, which does not depend on geometrical curvature effects. Such a formulation clearly justifies that the collapse occurs much faster than predicted by the well-known Jeans approach. The equilibrium profiles of the density, gravitational field, and potential are obtained as functions of the spherical radius coordinate at marginal instability. Since our theory captures the essential physics of gravitational collapse, it can be used as the starting point for several advancements in galactic dynamics.

Interday Reliability of Upper-limb Geometric MyoPassivity Map for Physical Human-Robot Interaction.

The value of intrinsic energetic behavior of human biomechanics has recently been recognized and exploited in physical human-robot interaction (pHRI). The authors have recently proposed the concept of "Biomechanical Excess of Passivity," based on nonlinear control theory, to construct a user-specific energetic map. The map would assess the behavior of the upper-limb in absorbing the kinesthetic energy when interacting with robots. Integrating such knowledge into the design of pHRI stabilizers can reduce the conservatism of the control by unleashing hidden energy reservoirs indicating a less conservative margin of stability. The outcome would enhance the system's performance, such as rendering kinesthetic transparency of (tele)haptics systems. However, current methods require an offline data-driven identification procedure prior to each operation to estimate the energetic map of human biomechanics. This can be time-consuming and challenge users susceptible to fatigue. In this study, for the first time, we investigate the interday reliability of upper-limb passivity maps in a sample of five healthy subjects. Our statistical analyses indicate that the identified passivity map is highly reliable in estimating the expected energetic behavior based on Intraclass correlation coefficient analysis (conducted on different days and with various interactions). The results illustrate that a one-shot estimate is a reliable measure to be used repeatedly in biomechanics-aware pHRI stabilization, enhancing practicality in real-life scenarios.