Stability Margin Research Articles

Interval analysis of the small‐signal stability of grid‐connected voltage‐source converter system considering multiparameter uncertainty

AbstractGrid‐connected voltage source converters (VSCs) have been broadly applied in modern power system. However, instability issues may be triggered by the integration of grid‐connected VSCs, jeopardising the operation of the power grid. Conventional stability analysis methods can be utilised to derive system stability margins under nominal conditions. Whereas grid‐connected VSCs inevitably operate under multiparameter uncertainty, which may result in overly optimistic or even incorrect estimations of stability margins, thereby posing potential risks to system operation. To address this issue, an interval small‐signal stability analysis approach is proposed to investigate the system stability under multiparameter uncertainty. First, the interval state‐space model of the grid‐connected VSC system is constructed based on interval symbolic linearisation. Furthermore, the interval eigenvalue decomposition is introduced to calculate the interval eigenvalue distribution of the interval state‐space model. Eventually, the upper bounds of the real part of the dominant interval eigenvalues are utilised for deriving interval stable parameter regions. Results of Monte Carlo analysis and time‐domain simulations of the grid‐connected VSC system are utilised to verify the effectiveness of the proposed interval stability analysis method.

DYNAMIC CHARACTERISTICS OF TIME-VARYING CONTROL SYSTEM OF THE ROCKET’S ROTATIONAL MOVEMENT

The rocket motion control system is time-varying, because its parameters during flight depend on the trajectory point and fuel consumptions. In the available sources, due attention is not paid to the development of a mathematical apparatus of an applied value for the quan- titative assessment of the dynamic characteristics of a time-varying system.
 The purpose of the work is to justify the possibility of an algorithm building for calcu- lating the parameters of a link with constant parameters, which is equivalent to a time- varying system in terms of dynamic characteristics at the selected trajectory section.
 The link’s parameters are found by using the criterion of equivalence of the array of values of the motion model’soutput signal and the analytical solution of the link’s differential equation for a given sequence of input signals. This makes it possible to use the mathematical apparatus of stationary systems to determine the indicators of the disturbances compensation.
 The model of the control system of the rocket’s rotational movement in one plane is taken as a linear differential equation with time-varying parameters without taking into ac- count the executive device inertia and other disturbances. The link with constant parameters is a fractional-rational function of the second order, for the determination of which a se- quence of signals is applied to the input of the system model, the duration of which depends on the desired stability margin on the roots plane of the characteristic polynomial.
 Using the example of a time-varying system for controlling the rocket’srotational movement in the yaw plane, the possibility of determining the parameters of the transition process of compensation for the disturbances characteristic of it is shown for the selected tra- jectory section.
 The obtained results can be used in the design of a motion control system with time- varying parameters.
 The next stage of the research is an assessment of the complexity level of the calcula- tion algorithm when increasing the order of the system’smathematical model.

Individuals with knee osteoarthritis show few limitations in balance recovery responses after moderate gait perturbations

BackgroundKnee osteoarthritis causes structural joint damage. The resultant symptoms can impair the ability to recover from unexpected gait perturbations. This study compared balance recovery responses to moderate gait perturbations between individuals with knee osteoarthritis and healthy individuals. MethodsKinematic data of 35 individuals with end-stage knee osteoarthritis, and 32 healthy individuals in the same age range were obtained during perturbed walking on a treadmill at 1.0 m/s. Participants received anteroposterior (acceleration or deceleration) or mediolateral perturbations during the stance phase. Changes from baseline in margin of stability, step length, step time, and step width during the first two steps after perturbation were compared between groups using a linear regression model. Extrapolated center of mass excursion was descriptively analyzed. FindingsAfter all perturbation modes, extrapolated center of mass trajectories overlapped between individuals with knee osteoarthritis and healthy individuals. Participants predominantly responded to mediolateral perturbations by adjusting their step width, and to anteroposterior perturbations by adjusting step length and step time. None of the perturbation modes yielded between-group differences in changes in margin of stability and step width during the first two steps after perturbation. Small between-group differences were observed for step length (i.e. 2 cm) of the second step after mediolateral and anteroposterior perturbations, and for step time (i.e. 0.01–0.02 s) of first step after mediolateral perturbations and the second step after outward and belt acceleration perturbations. InterpretationDespite considerable pain and damage to the knee joint, individuals with knee osteoarthritis showed comparable balance recovery responses after moderate gait perturbations to healthy participants.

A Comprehensive Stability Assessment System for EV DC Charging Station Based on Multitimescale Impedance Model

The existing all-in-one impedance-based stability analysis only qualitatively reveal the instability factors by the graphic Nyquist criterion while the stability margin is not considered. In this article, a design-oriented multiattribute and multidimensional based comprehensive assessment system (MAMD-CAS) is proposed to evaluate the stability quantitatively and guide the parameter design as well as ensure the desired dynamic response and stability margin. This MAMD-CAS mainly includes the loop-gain-based multi-timescale impedance estimation to analyze the low-frequency oscillation (LFO), phase margin (PM) calculation of different timescales and dynamic performance indicators as the time-domain quantitative expression of impedance estimation. In detail, the multi-timescale impedance model is established and its loop-gain representation is deduced to implement the impedance estimation. Combined with the known PM, the influence of the parameters on dynamic performance and stability margin can be comprehensively evaluated, then the conflict between dynamic performance and stability margin is explored. It is found that the voltage-loop parameters do not have the coupling problem between dynamic performance and stability margin while <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">vir</sub> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">svr</sub> present a conflicting effect between the inertia-loop LFO dynamic performance and stability margin and their interaction affects the severity of inertia-loop LFO. The appropriate control parameters can be thus selected for a good stability margin while suppressing the impedance peak. This MAMD-CAS analysis result is verified by simulation and experiment and this assessment system provides theoretical fundamental for the online stability monitor of multi-timescale power electronics system.

Notes on the margin of stability

The concept of the 'extrapolated center of mass (XcoM)', introduced by Hof et al., (2005, J. Biomechanics 38 (1), p. 1–8), extends the classical inverted pendulum model to dynamic situations. The vector quantity XcoM combines the center of mass position plus its velocity divided by the pendulum eigenfrequency. In this concept, the margin of stability (MoS), i.e., the minimum signed distance from the XcoM to the boundaries of the base of support was proposed as a measure of dynamic stability. Here we describe the conceptual evolution of the XcoM, discuss key considerations in the estimation of the XcoM and MoS, and provide a critical perspective on the interpretation of the MoS as a measure of instantaneous mechanical stability.

An Online Adaptive Damping Controller for Converter-Interfaced Generation

The increasing integration of converter-interfaced generation within large-scale synchronous power systems is presenting both new challenges and opportunities in how we operate these dynamical networks. One of these challenges is designing and parameterizing the digital control loops that dictate the dynamical behavior of these fast-acting resources. Improperly tuned gains, or unexpected controller couplings through the network, can lead to poorly damped oscillations during disturbance conditions and/or decrease the system stability margin. Within this work, we present an approach for adaptively tuning a damping controller to improve the dynamic response of converter-interfaced generation, based only on local measurements. We show that, with low-amplitude probing, we can identify a subset set of observable system modes. We then propose a linear MISO state-feedback controller to improve the damping ratio and stability margin of the system. We show the effectiveness of the proposed controller through both eigenvalue analysis and time-domain simulations. We first demonstrate the proposed approach on a simple 3-bus system followed by a larger test case, the IEEE 14 bus system, with multiple devices simultaneously probing the network.

Voltage Stability Constrained Economic Dispatch for Multi-Infeed HVDC Power Systems

Multi-infeed LCC-HVDC decreases voltage stability margins due to its current source nature. Moreover, the high penetration of variable renewable energy makes it difficult to reserve enough margins for all periods. Therefore, voltage stability constraints need to be considered in the scheduling stage. However, the challenge is that the voltage stability margin is not analytic with respect to state variables. We propose a sparse support vector machine to extract the nonlinear voltage stability rule. To embed the rule into economic dispatch (ED), we apply a convex reformulating technique to the rule and then formulate a voltage stability constrained ED (VSCED) model by semi-definite programming. The model is tested on a modified IEEE-14 system and a real-world system from Jiangsu Province, China; and it is compared with other typical data-driven-based models in the Jiangsu system. The numerical experiments suggest that the stability margins can be effectively reserved above the required threshold within an acceptable computation time by the proposed VSCED model, which outperforms the other models.

Coordinated reactive power planning in an industrial park integrated energy system using support vector regression

In this study, we develop and present a comprehensive multi-objective optimization model for reactive power planning in industrial park integrated energy systems (IPIES), addressing the challenges posed by extensive inductive loads. Our model prioritizes enhancing system resilience through three key objectives: minimizing total costs, improving static voltage stability margins, and enhancing voltage recovery capabilities. We employ support vector regression (SVR) to estimate voltage recovery metrics effectively, using reactive power capacity as input. The optimization process leverages the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) for efficient solution finding. Validation on the IEEE-39 bus system demonstrates the model’s effectiveness, with SVR significantly reducing computational demands while maintaining satisfactory accuracy.

A Novel Decentralized Frequency Regulation Method of Renewable Energy Stations Based on Minimum Reserve Capacity for Renewable Energy-Dominated Power Systems

In this paper, we propose a novel decentralized frequency regulation method for renewable energy-dominated power systems. First, the system is modularized into unified frequency regulation modules composed of synchronous generators(SGs) and renewable energy stations. Then, based on the aggregation model of the module, a renewable energy station frequency regulation method based on robust control barrier functions(RCBFs) is proposed to ensure that the frequency deviation is limited, and an additional switching control strategy is complemented to avoid the long-term suspension of over-high quasi-steady-state frequency. The proposed method is still applicable under the coordination of multiple renewable energy stations. Each renewable energy station deploys decentralized control based on local information, which can support fast frequency response. The robustness of frequency response time constants of renewable energy stations and frequency dead zone are considered, which makes the control method easy to implement. A module transient frequency stability margin index based on reserve capacity is proposed, which can be used to guide the system planning and operation. Finally, simulation results validate the applicability of the proposed method, demonstrating its efficacy in regulating frequency in renewable energy-dominated power systems.

Dynamic-Deep-Ensemble-Learning Scheme for Probabilistic Voltage Stability Margin Estimation to Enhance Resilient Power Grid Monitoring

Modern power grids are characterized by significant penetration of renewable energy sources (RES), variable power demand, and aging transmission infrastructure, all of which contribute to a high degree of operational uncertainty. Such uncertainty complicates the assessment of the static voltage stability in power grids. In response to this challenge, this paper proposes a novel deep ensemble learning-based approach to assess the probabilistic voltage stability margin (PVSM) for strengthening the resilience of power grid monitoring. First, the estimation of the PVSM is formulated as a quantile regression problem. Then, an improved deep quantile regression (iDQR) is utilized to generate a set of quantiles under specific nominal proportions. Next, a dynamic deep ensemble learning (D2EL) scheme based on diverse iDQR models and an improved Choquet fuzzy integral (iCFI) algorithm is proposed to enhance the overall performance of predictive quantiles for the PVSM. The proposed D2EL-based PVSM estimation approach is capable of accommodating system changes in a timely manner, thus providing higher estimation accuracy and stronger adaptability than conventional approaches. A comprehensive numerical study of several test systems is carried out, taking into account uncertain RES and loads, as well as topology changes. The results reveal the impressive performance of the proposed approach in the PVSM assessment.

A Small-Signal Stability Analysis Method Based on Minimum Characteristic Locus and Its Application in Controller Parameter Tuning

A small-signal stability analysis method based on minimum characteristic locus (MCL) was recently proposed by the authors. The method is found to be particularly useful in analyzing various oscillation modes in a unified way. The present work continues this line of research. After providing a brief review of the basic principle of MCL method, the paper proceeds to show the mathematical relationship between the stability margin obtained using an MCL method, and that obtained by traditional modal analysis method. Next, a sensitivity analysis procedure is proposed to study quantitatively the effects of control parameters on the stability of the system. Third, the properties of the so-called exciter mode are explained in detail, in particular, explicit formulas of exciter mode frequency and power system stabilizer (PSS) critical gain are derived. Finally, taking PSS4B as an example, a controller parameter tuning method is proposed. The effectiveness and practicability of the proposed method are verified by case studies of Kundur's four-machine-two-area system and China's Yunnan power grid.

Influence of Active Flow Control of Synthetic Jet at Suction Surface on the Performance of a Subsonic Axial Compressor Rotor

In order to investigate the effect of a synthetic jet arranged at the suction surface on the aerodynamic performance of an axial flow compressor, a high-speed subsonic axial flow compressor rotor was numerically simulated in this paper. The results showed that after being excited by the synthetic jet, the flow margin of the compressor decreased by 1.3%, but the peak efficiency increased by 0.47%. After analyzing the internal flow field, it was found that although the alternating blowing and suction effect of the synthetic jet can reduce the separation loss of the suction surface, the radial velocity of the flow is higher when stimulated and converges towards the blade tip, resulting in more severe blockage at the blade tip than in the prototype compressor, leading to a slight decrease in stability margin. To balance the stability margin of the compressor, a coupled flow control numerical simulation combining passive control of the casing treatment and active control of the suction surface synthetic jet was subsequently carried out. The results showed that the coupled flow control could exert their respective advantages, resulting in an increase of 17.84% in the compressor flow margin and a decrease of only 0.2% in peak efficiency.

Influence of diversified dihedral stator on the thermodynamic performance and flow loss characteristics of a variable core driven fan stage

The Variable Cycle Engines (VCE) have emerged as the unequivocal choice for the next generation of aircraft power systems, with the core driven fan stage (CDFS) playing a crucial role in determining its performance. In this study, the variations in performance improvements of CDFS with different dihedral stator schemes are analyzed, and a weight-adjustable comprehensive improvement coefficient is defined. The results indicate that under different modes, a dihedral angle of 10° provides optimal improvements in peak efficiency and maximum pressure rise, while the optimal dihedral angle for stability margin improvement varies depending on the operating mode. The influence of dihedral height on performance is relatively minimal compared to the dihedral angle. By integrating flow field analysis and quantitative loss analysis, it is observed that the dihedral blade can effectively mitigates the interaction between the trailing edge recirculation vortex and other vortex in the stator, resulting in a significant reduction in secondary flow losses and wake losses. However, under near stall conditions, excessively large dihedral schemes in the stator intensify the interaction between secondary flow vortices, leading to premature flow instability.

A novel reinforcement learning policy optimization based adaptive VSG control technique for improved frequency stabilization in AC microgrids

In this paper, an improved Reinforcement Learning (RL) based approach for adaptive Virtual Synchronous Generator (VSG) control of grid-forming inverters is proposed. High penetration of inverter-based resources causes recurrent frequency stabilization issues. For this matter, a novel model-free Actor–Critic policy optimization technique is proposed to improve frequency transients metrics such as frequency nadir and Rate of Change of Frequency (RoCoF). Stability analysis of the VSG controlled system is conducted through small signal modeling to determine the stability margins of both the virtual inertia parameter J and damping coefficient Dp. The control problem is formulated in RL terms using a new technique for state, action and reward construction that improves the learning process of the agents. The proposed approach’s efficiency is tested for three RL algorithms, namely, Deep Deterministic Policy Gradient (DDPG), Soft Actor–Critic (SAC), and Twin-Delayed DDPG (TD3) with special attention given to the latter. Various performance metrics such as training time and maximum cumulative episodic reward are used to compare the three algorithms. The resulting agent based VSG adaptive controllers are simulated and then compared for power quality and frequency stabilization capabilities. Finally, a comparison between non-adaptive VSG and TD3 based VSG is presented to conclude on the efficiency improvements achieved by the proposed approach.

Robust damping control for integrated wind turbine power networks during low inertia condition

AbstractThis paper presents a modal analysis‐based impact analysis of the change in system inertia due to the integration of the large‐scale doubly fed induction generator (DFIG)‐based wind turbine system (WTS) on the power system damping in inter‐area oscillation modes. The impact of replacement of a synchronous generator by WTS of same MVA capacity on system dynamics such as emergence of new critical modes of inter‐area oscillations affecting system stability is studied. Further, a double‐channel scheme‐based wide‐area damping controller (WADC) is proposed for WTS, which provides sufficient damping of prominent oscillation modes and enhanced stability margin to alleviate the negative impact of reduction in system inertia. The comparative assessment of the proposed controller with a PSS‐based WADC on a modified New England 10‐machine system validates the performance and is found to be more effective in mitigating inter‐area oscillation in the system. The real‐time feasibility of the proposed double‐channel WADC is evaluated on the Real‐Time Digital Simulator (RTDS) platform. The simulation results show that the proposed WADC can successfully mitigate various inter‐area modes simultaneously. Furthermore, it provides robust performance for a variety of contingencies, time delays in feedback signals, and uncertainties associated with different operating scenarios of WTS.

Recovering whole-body angular momentum and margin of stability after treadmill-induced perturbations during sloped walking in healthy young adults

Although humans are well-adapted to negotiating sloped terrain, balance recovery after a disturbance on slopes is poorly understood. This study investigated how slope affects recovery from unanticipated simulated trips and slips. Eighteen healthy young adults walked on a split-belt treadmill at 1.25 m/s and three slope angles (downhill: − 8°; level: 0°; uphill: + 8°), with slip- and trip-like perturbations applied randomly at heel-strike. We evaluated balance recovery using whole-body angular momentum (WBAM) and perturbation response (PR), for which larger PR values indicate greater deviation of the margin of stability from baseline, therefore, greater destabilisation after perturbation. Overall, trips were more destabilising than slips, producing larger PR and greater range and integral of WBAM across all tested slopes, most significantly in the sagittal plane. Contrary to expectation, sagittal-plane PR post-trip was greatest for level walking and smallest for downhill walking. Heightened vigilance during downhill walking may explain this finding. Recovery strategy in both frontal and sagittal planes was consistent across all slopes and perturbation types, characterized by a wider and shorter first recovery step, with trips requiring the greatest step adjustment. Our findings advance understanding of the robustness of human locomotion and may offer insights into fall prevention interventions.

Nonlinear Optimal Control for Stochastic Dynamical Systems

This paper presents a comprehensive framework addressing optimal nonlinear analysis and feedback control synthesis for nonlinear stochastic dynamical systems. The focus lies on establishing connections between stochastic Lyapunov theory and stochastic Hamilton–Jacobi–Bellman theory within a unified perspective. We demonstrate that the closed-loop nonlinear system’s asymptotic stability in probability is ensured through a Lyapunov function, identified as the solution to the steady-state form of the stochastic Hamilton–Jacobi–Bellman equation. This dual assurance guarantees both stochastic stability and optimality. Additionally, optimal feedback controllers for affine nonlinear systems are developed using an inverse optimality framework tailored to the stochastic stabilization problem. Furthermore, the paper derives stability margins for optimal and inverse optimal stochastic feedback regulators. Gain, sector, and disk margin guarantees are established for nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal Hamilton–Jacobi–Bellman controllers.

The margin of stability is affected differently when walking under quasi-random treadmill perturbations with or without full visual support.

Sensory-motor perturbations have been widely used to assess astronauts' balance in standing during pre-/post- spaceflight. However, balance control during walking, where most falls occur, was less studied in these astronauts. A study found that applying either visual or platform oscillations reduced the margin of stability (MOS) in the anterior-posterior direction (MOSap) but increased MOS in the medial-lateral direction (MOSml) as a tradeoff. This tradeoff induced an asymmetric gait. This study extended the current knowledge to investigate overall stability under unpredictable environments. This study aimed to determine (1) whether quasi-random treadmill perturbations with or without full vision support would result in a significant reduction in MOSap but an increase in MOSml and (2) regardless of whether vision support was provided, quasi-random treadmill perturbations might result in asymmetric gait patterns. Twenty healthy young adults participated in this study. Three experimental conditions were semi-randomly assigned to these participants as follows: (1) the control condition (Norm), walking normally with their preferred walking speed on the treadmill; (2) the treadmill perturbations with full vision condition (Slip), walking on the quasi-random varying-treadmill-belt-speeds with full vision support; and (3) the treadmill perturbations without full vision condition (Slip_VisionBlocked, blackout vision through customized vision-blocked goggles), walking on the quasi-random varying-treadmill-belt-speeds without full vision support. The dependent variables were MOSap, MOSml, and respective symmetric indices. A one-way repeated ANOVA measure or Friedman Test was applied to investigate the differences among the conditions mentioned above. There was an increase in MOSap in Slip (p=0.001) but a decrease in MOSap in Slip_VisionBlocked (p=0.001) compared to Norm condition. The MOSml was significantly greater in both Slip and Slip_VisionBlocked conditions compared to the Norm condition (p=0.011; p<0.001). An analysis of Wilcoxon signed-rank tests revealed that the symmetric index of MOSml in Slip_VisionBlocked (p=0.002) was greater than in the Norm condition. The novelty of this study was to investigate the effect of vision on the overall stability of walking under quasi-random treadmill perturbations. The results revealed that overall stability and symmetry were controlled differently with/without full visual support. In light of these findings, it is imperative to take visual support into consideration while developing a sensory-motor training protocol. Asymmetric gait also required extra attention while walking on the quasi-random treadmill perturbations without full vision support to maintain overall stability.

Design and analysis of optimal AGC regulator for multi‐area power systems with TCPS and energy storage unit in deregulated environment

AbstractIn today's electric power network, fast changes are the norm, and auxiliary services such as automatic generation control (AGC) play a crucial role in maintaining the quality of the power supply. AGC ensures a balance between power generation, demand, and losses to sustain frequency stability and variation in tie‐line power within a set limit, even when the load changes. To accomplish this, it is always beneficial to consider new approaches to controlling the situation. This paper introduces the design of new AGC regulators that consider deviation in DC tie‐line power as an extra control variable for the turbine controller. In this study, three different deregulated power systems (containing two control areas), namely three thermal generations, the combination of one thermal and two hydro generations, and three hydro generations, including two power distribution companies (DISCOs) in each control area. These optimal AGC regulators are implemented in the proposed thermal–thermal–thermal system to carry out the various power contracts. The results have shown that the dynamic outcomes meet the AGC standards. To improve further dynamic results and the proposed systems' stability margins by incorporating redox flow batteries (RFB). In actual operating conditions, the system parameters do not remain constant due to the aging effect, assumptions made in simplifying the mathematical model, etc. Thus, ±50% deviations in the nominal value of system parameters to assess how well the optimal AGC regulators perform in the system under investigation. The suggested realistic AGC system incorporates many parameter fluctuations and works well with the optimal AGC regulators developed for the proposed plans. This study expanded to include a two‐area, thermal‐hydro‐hydro (THH) system under a deregulated framework connected via an asynchronous transmission link with or without a thyristor‐controlled phase shifter (TCPS) and RFB. The genetic algorithm (GA) can solve many issues and has global search, flexibility to varied problem types, intrinsic parallelism, and the ability to handle massive, complex search spaces. Thus, a two‐area deregulated hydro‐hydro‐hydro system with parallel tie‐lines utilizes GA‐PID, GA‐FOPID, and GA‐(1 + PI)‐FOPID controllers. Moreover, a random load disturbance (RLD) is employed in each section of the offered approach to show the resilience and elite performance of the proposed control strategy. To produce various dynamic reactions in the plans, MATLAB software version R2013a is employed.

The optimal allocation of thyristor-controlled series compensators for enhancement HVAC transmission lines Iraqi super grid by using seeker optimization algorithm

Abstract Meta-heuristic approaches evaluate the optimum size and position of flexible alternative current transmission systems power systems. The seeker optimization algorithm (SOA) technique was used to solve power engineering optimization problems with better performance than traditional approaches. This article shows the application of SOA for optimal setting and allocation of thyristor-controlled series compensators (TCSCs) in a transmission line. TCSC devices are used to improve transmission systems’ capacity and voltage profile by controlling the transmission line reactance. The IEEE 30 bus system, as well as the Iraqi Super Grid 400 kV system, is used as a test system to illustrate the technique used. Results showed that the installation of TCSC unites the aims to reduce the voltage deviation, reduce the losses of active/reactive power, and increase transmission line reserves over thermal limits. TCSC devices are very effective for the better use of existing installations without sacrificing the stability margin. SOA is intended to identify the best location and size of TCSC devices that resolve the technological difficulties of reducing the TCSC devices’ costs.