Stability Margin Research Articles

Stability of mass oscillations in hydropower plants with brook intakes

The need for more energy storage in the transition to a renewable energy system leads to increasing interest in upgrading existing hydropower plants to pumped storage plants. Such upgrades result in stronger hydraulic transients in the tunnel system, including increased mass oscillation amplitudes. In this study, a generalized tunnel system with multiple brook intakes/surge tanks is analysed to assess the influence of the brook intakes on the mass oscillation stability. The variables that are assessed are the number of brook intakes, cross section area, the amount of inflow, and throttling of the brook intakes/surge tanks. The study is carried out using frequency-response analysis, where the excitation is the oscillation of the guide vane position, and the response is the product of the measured head and discharge (equivalent to the hydraulic power). The results show that brook intakes are generally beneficial for the stability of the mass oscillations. Existing hydropower plants with brook intakes may have sufficient stability margins to allow upgrade and reconstruction without the need for upgrading of the surge tank with regard to mass oscillation stability.

Statistical evaluation of stability margin of a multi-stage compressor with geometric variability using adaptive polynomial chaos-Kriging model

Compressed air energy storage systems must promptly adapt to power network demand fluctuations, necessitating a high surge margin in the compression system to ensure safety. It is challenging to completely eliminate blade geometric variations caused by limited machining precision, the important effects of which should be considered during aerodynamic shape design and production inspection. The present paper explores the uncertainty impact of geometric deviations on the stability margin of a multi-stage axial compressor at a low rotational speed. Initially, an adaptive polynomial chaos expansion-based universal Kriging model is introduced, and its superior response performance in addressing high-dimensional uncertainty quantification problems is validated through rigorous analytical and engineering tests. Then, this model is used to statistically evaluate the stability margin improvement (SMI) of the compressor due to the Gaussian and realistic geometric variabilities separately. The results show that the mean and standard deviation of SMI are −0.11% and 0.5% under the Gaussian geometric variability, while those are 0.33% and 0.39% under the realistic variability. For both the geometric variabilities, the stagger angle and maximum thickness deviations of the first-stage rotor are the most influential parameters controlling the uncertainty variations in the stability margin. Finally, the underlying impact mechanism of the influential geometric deviations is investigated. The variation in the stability margin caused by the geometric deviations primarily results from the alteration of inlet incidences, affecting the size of the tip leakage vortex blockage and boundary-layer separation regions near the blade tip of the first-stage rotor.

Corrective-Link Calculation in a Control System of Two-Mass Systems with Specified Stability Margins

Corrective-Link Calculation in a Control System of Two-Mass Systems with Specified Stability Margins

Review of Grid Stability Assessment Based on AI and a New Concept of Converter-Dominated Power System State of Stability Assessment

Artificial intelligence (AI) has been increasingly used for power system stability assessment due to its fast evaluation speed compared to conventional time-domain methods. This paper reviews four types of classic grid stability assessment (GSA) methods based on AI in the recent literature firstly where different AI algorithms from the literature are summarized and compared. Moreover, as the number of power converters using grid forming control intensively increases in the modern system, the influence of the converter parameters on grid stability needs to be investigated. In this context, the concept of the converter-dominated power system state of stability (CDPS-SOS) assessment based on AI is qualitatively discussed. The CDPS-SOS assessment can reveal the system stability margin by considering the converter control parameters and grid bus voltages. Overall, this paper aims to give an overview of AI-based stability assessment for the traditional grid and to provide a new stability assessment concept and inspiration for solving the challenges of future converter-dominated grids.

Power System Stability With a High Penetration of Inverter-Based Resources

Inverter-based resources (IBRs) possess dynamics that are significantly different from those of synchronous-generator-based sources and as IBR penetrations grow the dynamics of power systems are changing. This article discusses the characteristics of the new dynamics and examines how they can be accommodated into the long-standing categorizations of power system stability in terms of angle, frequency, and voltage stability. It is argued that inverters are causing the frequency range over which angle, frequency, and voltage dynamics act to extend such that the previously partitioned categories are now coupled and further coupled to new electromagnetic modes. While grid-forming (GFM) inverters share many characteristics with generators, grid-following (GFL) inverters are different. This is explored in terms of similarities and differences in synchronization, inertia, and voltage control. The concept of duality is used to unify the synchronization principles of GFM and GFL inverters and, thus, established the generalized angle dynamics. This enables the analytical study of GFM-GFL interaction, which is particularly important to guide the placement of GFM apparatuses and is even more important if GFM inverters are allowed to fall back to the GFL mode during faults to avoid oversizing to support short-term overload. Both GFL and GFM inverters contribute to voltage strength but with marked differences, which implies new features of voltage stability. Several directions for further research are identified, including: 1) extensions of nonlinear stability analysis to accommodate new inverter behaviors with cross-coupled time frames; 2) establishment of spatial–temporal indices of system strength and stability margin to guide the provision of new stability services; and 3) data-driven approaches to combat increased system complexity and confidentiality of inverter models.

All-in-One Control Framework for Distributed Drive Electric Buses Path Tracking Subject to Uncertain Crosswind and Varied Passenger Mass

This paper proposes an all-in-one control framework for distributed drive electric buses (DDEBs) that can effectively attenuate the effects of uncertain crosswind and varied passenger mass in path tracking, while minimizing the electricity consumption of battery. To track the desired path and ensure driving stability, a robust tube-based model predictive control method is proposed considering lateral, yaw and roll motions. Simultaneously, for the longitudinal motion, a robust sliding mode control method is designed to achieve accurate tracking of longitudinal velocity. Meanwhile, the uncertain crosswind and varied passenger mass faced by the DDEBs are decoupled into external disturbances and their effects on the system are eliminated in both controllers. Then, to cope with energy optimization problem in path tracking, a torque distribution controller is constructed by formulating the vehicle stability margin, tracking dynamic requirements and energy efficiency as constrained weighted least squares problem. Finally, a Trucksim-Simulink co-simulation is performed, where the simulation results demonstrated that the proposed control framework is robust and effective, and can achieve better energy saving effect compared to the original control methods.

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Currently, the aviation industry is facing an oil and energy crisis and is contributing much more greenhouse gas emissions to the environment. Aircraft design approaches, such as aerodynamic shape optimization, new configuration concepts, and active control technology, have been the primary and effective means of achieving goals concerning fuel burn, noise, and emissions. For now, the design problems of relaxed static stability (RSS, an active control technique) and truss-braced wing (TBW) configurations with high-fidelity aerodynamic shape optimization methods have been investigated widely to promote aerodynamic performance. Nevertheless, they are studied almost always separately, and the combination of exploration and refined design is rarely presented. Therefore, the purposes of this work are to evaluate the benefits of RSS on a full TBW wing–body–tail configuration under various flight conditions and the effects on multi-components and to further explore the potential and analyze the aerodynamic features with the combination of shape optimization and RSS. To address these issues, on the one hand, a range of seven static stability margins are adopted to evaluate its effects with a high-fidelity Reynolds-averaged Navier–Stokes solver. On the other hand, seven cases of drag minimization multipoint aerodynamic design optimization are performed, which are with 600 shape variables and 13 twist variables, subject to lift coefficient, trim, and thickness constraints. The results indicate that with RSS only, the initial configuration has a 2.39% drag reduction under cruise conditions and a 3.01% and a 5.24% drag reduction under two off-design conditions. Additionally, the effects on the multi-components are observed and analyzed. Moreover, all of the optimized configurations with RSS have 2.13%, 2.42%, and 2.12% drag reductions under cruise conditions, drag divergence conditions, and near-buffet-onset conditions, respectively. The most promising optimized configuration has a lift-to-drag ratio of 24.48 with an aerodynamic efficiency of 17.14. The evaluations with a series of off-design points also present high-level aerodynamic efficiency.

Эффективность применения динамического метода оценивания состояния параметров режима электроэнергетической системы

The results of the estimation of power system mode parameters are used to solve important technological tasks by real-time hardware-software packages (HSPs), for instance, the calculation of maximum allowed power flows (MAPFs) via sections by a Control System of Stability Margin (HSP CSSM). Now, in the HSP CSSM the state estimation is realized by the static method. Remote measurements (RMs) obtained from an operative informational complex are used as initial data. With the introduction of Wide-Area Measurement Systems and the possibility to obtain synchronized phasor measurements (SPMs) with a high update rate, it becomes possible to apply and improve state estimation dynamic methods. Even though, many researchers pay attention to the state estimation dynamic method, but practical application of this method and obtained results are presented in papers insufficiently. The goal of the study is to improve the state estimation dynamic method based on the extended Kalman filter and analyze the effectiveness in determining the mode parameters of electric power system. The studies are performed by the developed algorithm of the state estimation dynamic method based on extended Kalman filter. С# is the language for software code. Practical evaluation of the state estimation algorithm has been carried out on the basis of a power system model containing 55 nodes and 76 branches. An improved dynamic method to estimate the state of mode parameters is proposed. The test results show that in steady-state modes, when RMs are not updated on time, the developed dynamic method demonstrates high accuracy for the estimation of mode parameters and MAPFs. The estimation error of a voltage and an active power is low, therefore MAPFs are more specifically than MAPFs obtained by CSSM. Also, this method operates with high accuracy in the post emergency states, but only for that part of the power system, where the topology and mode have not been changed. For the part, where the topology and mode affected, the best result shows the static state estimation method by RMs and SPMs. In post emergency states the static state estimation method offers to form the transfer matrix for the dynamic method, therefore, static and dynamic state estimation methods must be used simultaneously in real-time HSPs. It is an undoubted fact that the use of synchronized phasor measurements as input data increases the accuracy of estimation. These results are expected to implement in the software of HSPs, involving the state estimation component.

Optimal gait planning of bionic lower extremity exoskeleton based on elite mechanism bacterial foraging optimization algorithm

To improve the stability and smoothness of bionic lower extremity exoskeleton walking gait, the elitist mechanism was introduced to enhance the diversity and improve the search ability of the optimal solution. The simulation analyses showed that the improved bacterial foraging algorithm had higher convergence accuracy, and was not easy to fall into local extremum. The improved foraging optimization algorithm was used for the optimization of the bionic lower extremity exoskeleton gait zero moment point stability margin. The simulation results showed that the optimal gait planning method proposed can increase the stability margin and ensure the stable and smooth walking.

BULLDOZER, A FREE OPEN SOURCE SCALABLE SOFTWARE FOR DTM EXTRACTION

Abstract. The paper introduces a software called Bulldozer, designed to extract a Digital Terrain Model (DTM) from a Digital Surface Model (DSM) obtained from various sensors. The software is based on a modified version of the multi-scale Drap Cloth principle to process noisy DSMs of any size, employing a tiling strategy and a stability margin to ensure consistent results. A parameter called max object size is introduced to differentiate objects from the ground during the drap cloth process. Gravity steps and ground distance sampling resolution are adjusted based on the input DSM. No-data and noisy values present in the DSM are detected and converted into no-data values to improve the quality of the Cloth simulation. The paper describes a memory-aware parallel execution strategy using both the multiprocessing and the shared memory Python modules. A benchmark dataset has been created to analyze the results and compare them with alternative approaches and reference datasets. Bulldozer offers an extensive Python API. It is open-source and available on PyPi and GitHub. Additionally, a QGIS plugin has been developed.

A note on the marginal instability rates of two-dimensional linear cocycles

A theorem of Guglielmi and Zennaro implies that if the uniform norm growth of a locally constant -cocycle on the full shift is not exponential, then it must be either bounded or linear, with no other possibilities occurring. We give an alternative proof of this result and demonstrate that its conclusions do not hold for Lipschitz continuous cocycles over the full shift on two symbols.

Gait Analysis and Improvement of Hexapod Mobile Robot Using Tetrahedral-Shaped Pneumatic Soft Actuators

In recent years, the aging of society has led to challenges such as ensuring adequate facility capacity and promoting health maintenance for the elderly. Consequently, there has been a growing demand for rehabilitation and fitness equipment suitable for use in limited spaces such as homes. In a previous study, a hexapod mobile robot, equipped with six tetrahedral-shaped pneumatic soft actuators (TSAs), was developed as a core training device to address these issues. However, the robot’s gait was investigated experimentally via a trial-and-error process. Hence, it is necessary to examine the stability of the gait. In this study, a straightforward model is presented for gait analysis of the mobile robot. Furthermore, the stability of the gait is demonstrated based on the analysis, and a more efficient gait with a sufficient stability margin is introduced.

Stability analysis of two-terminal HVDC transmission systems using SISO open-loop gains

The ports of a three-phase voltage source converter have multiple frequency electrical parameters, which makes HVDC systems with these converters present multiple input multiple output (MIMO) characteristics. The generalized Nyquist criterion of the MIMO model is often used to analyze the system stability. However, this model is more difficult to obtain than the single-input single-output (SISO) model, and the stability margin and the oscillation frequency band are difficult to capture. To solve these problems, this paper took the two-terminal HVDC transmission system as the research object to derive a SISO model that can be measured by a port. Moreover, this study also proposed a method for analyzing the system stability through envelope SISO open-loop gains. Finally, the key port and parameters affecting the system stability were analyzed according to the stability margin, which provided theoretical support for the design of the system parameters. The established model and the proposed analysis method were verified in a MATLAB/Simulink simulation model.

Small-signal stability constrained unit commitment based on decomposition and SQP-GS

This paper proposes a small-signal stability constrained unit commitment(SSSC-UC) model to ensure that the solution of SCUC can provide a sufficient small-signal stability margin. To solve the model, Benders decomposition (BD) is applied to separate the problem into a SCUC master problem, which is a mixed-integer linear programming problem, and a series of subproblems to check the AC power flow constraint and small-signal stability constraint. The small-signal stability check subproblems are non-smooth and non-linear programming problems, which are solved by Sequential Quadratic Programming with Gradient Sampling (SQP-GS). When the subproblem checks do not pass, cuts formed by the sensitivity of the spectral abscissa with respect to generator output are added to the master problem for the next iteration of the SCUC. The iteration process continues until all AC power flow and small-signal constraint violations are eliminated and a SCUC solution is found. Simulations on the New England 10-machine 39-bus system and the IEEE 54-machine 118-bus system show that our proposed SSSC-UC can guarantee small-signal stability for all time periods while SCUC cannot. Furthermore, the proposed parallel technique can speed up the computation up to 5 and 11 times respectively for the two test systems.

Practice walking on a treadmill-mounted balance beam modifies beam walking sacral movement and alters performance in other balance tasks.

The goals of this study were to determine if a single 30-minute session of practice walking on a treadmill mounted balance beam: 1) altered sacral marker movement kinematics during beam walking, and 2) affected measures of balance during treadmill walking and standing balance. Two groups of young, healthy human subjects practiced walking on a treadmill mounted balance beam for thirty minutes. One group trained with intermittent visual occlusions and the other group trained with unperturbed vision. We hypothesized that the subjects would show changes in sacrum movement kinematics after training and that there would be group differences due to larger improvements in beam walking performance by the visual occlusions group. We also investigated if there was any balance transfer from training on the beam to treadmill walking (margin of stability) and to standing static balance (center of pressure excursion). We found significant differences in sacral marker maximal velocity after training for both groups, but no significant differences between the two groups from training. There was limited evidence of balance transfer from beam-walking practice to gait margin of stability for treadmill walking and for single leg standing balance, but not for tandem stance balance. The number of step-offs while walking on a narrow beam had the largest change with training (partial η2 = 0.7), in accord with task specificity. Other balance metrics indicative of transfer had lower effect sizes (partial η2<0.5). Given the limited transfer across balance training tasks, future work should examine how intermittent visual occlusions during multi-task training improve real world functional outcomes.

Voltage Stability Improvement Using Intelligence Technique

Numerous Artificial Intelligence procedures have been anticipated for reactive power dispatch to maintain voltage stability of the power system. This paper presents particle swarm optimization (PSO) approach for framework boundaries improvement and ideal reactive power dispatch. The transformers tap transformers, Generator exciters, switchable VAR sources/Static VAR compensators (SVC) are utilized as control factors for progression of framework boundaries and voltage stability. The recommended procedure depends on the minimization of total of the squares of L-index value at all load bus. The PSO Algorithm is tested on an IEEE 30 bus test system. The presentation of PSO is compared with conventional technique and results are introduced for illustration purpose. The margin of voltage stability is estimated in terms of system parameters.

Stability-assured design of a full state feedback controller for a three-phase grid-connected converter using disk margin analysis

The paper proposes a tuning procedure for a multioscillatory current controller in a three-phase three-wire grid connected converter operating under distorted voltage conditions. The control system should provide high quality sinusoidal currents. This is achieved by implementing internal models of expected disturbances — multioscillatory terms. Tuning of such systems is challenging if the objective is to guarantee a certain level of stability margins. The multiloop disk margin analysis may be a perfect candidate solution. This analysis combined with a global optimization produces controller gains that can be transferred to the physical system. The paper provides the first complete experimental verification of the multioscillatory full state feedback grid current control system with a designer specified stability margin in the form of disk radius.

Non-axisymmetric design and flow field analysis of boundary layer ingesting fans

The inlet distortion problem exists in a boundary layer ingesting propulsion system, and the distortion position is almost stable, which seriously affects the fan performance and stability margin (SM). To effectively improve the distortion resistance of the fan, three non-axisymmetric stator (NAS) schemes are designed according to the parameter distribution law of the distorted flow field in front of the stator under the design conditions in this study, which are based on the solidity matching method of the optimization of the stator inlet geometric angle, chord length, and pitch. The impact of the NAS on the fan performance and the distorted flow field parameters under distorted conditions are numerically studied. The results indicate that NAS can effectively enhance the SM of the fan. Among the three NAS designs, the third one demonstrates a remarkable increase of 74.91% in SM compared to the original fan. The NAS design can promote the fluid re-distribution in the distortion zone, make the aerodynamic parameters more uniform, and thus improve the flow state in the distortion zone. Among the three NAS schemes that are adopted in this research, the NAS design based on the pitch optimization method has the best effect. This design can effectively improve the stator flow field structure, thus significantly improving the SM and the aerodynamic performance of the fan under distortion conditions.

Dynamics Analysis of a Nonlinear Satellite Attitude Control System Using an Exact Linear Model

This study aims to analyze the nonlinear dynamics of a satellite attitude control system equipped with reaction wheels and a PD controller. Based on the angular momentum conservation theorem for a closed mechanical system, the nonlinear equations of the attitude control system dynamics are presented as a linear system of differential equations with time-varying parameters. The asymptotic properties of the angular momentum of a mechanical system including a satellite and reaction wheels as rigid bodies are investigated. A relation has been established between the dynamic parameters of the attitude control system and the initial value of the angular momentum of the satellite. The issue of asymptotic stability for differential equations with time-varying parameters is simplified to the asymptotic stability problem for the ultimate homogeneous system of linear differential equations with constant elements. The dependencies of the dynamic parameters of the attitude control system on the constant parameters of this ultimate system of linear differential equations, as well as the initial values of the satellite’s angular momentum, enable us to apply proven and effective engineering methods. These methods are used not only for analyzing the stability of the control system but also for synthesizing the parameters of the control law based on the quality requirements of transient processes such as the stability margin, responsiveness, oscillation, transient time, and overshoot. In this case, the calculation of the control law parameters will be grounded in exact equations, not on approximate equations of the control system dynamics obtained by linearization.

Distributed bi-level optimal power flow calculation for SVSM interval of integrated transmission and distribution networks considering the uncertain renewables

To accurately and efficiently calculate the static voltage stability margin (SVSM) interval of integrated transmission and distribution networks (ITDNs) considering the uncertain fluctuation of renewables, a distributed bi-level optimal power flow (OPF) calculation method based on the alternating direction method of multipliers for the SVSM interval of ITDNs is proposed in this paper. Due to the different structure characteristics of transmission network (TN) and distribution network (DN), a hybrid node-branch OPF method for calculating the SVSM of ITDNs is proposed, which has better convergence than the traditional node OPF method. Different reactive power-voltage control modes of renewable energy stations (RESs) are also considered in the calculation. Considering the uncertain fluctuation of RESs, two distributed bi-level OPF models for calculating the upper and lower bounds of the SVSM interval of ITDNs are established. Based on the alternating direction method of multipliers, the SVSM interval bounds of ITDNs can be obtained by solving the sub-optimization models and transmitting the boundary coupling variables and the load growth parameter between the TN and multiple DNs iteratively until the given convergence criterion is satisfied. Test results on two ITDNs, the modified IEEE 39–33 & 69 bus system and an actual 2285-bus ITDNs, demonstrate the high computation accuracy and efficiency of the proposed distributed bi-level OPF method compared with other calculation methods.