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Approximating input-output curve of Pumped Storage Hydro Plant: A Disjunctive Convex Hull Method

IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第1期38卷 63-74页

作者： Wang, Siyuan Liu, Jian Bo, Rui Chen, Yonghong Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA Midcontinent Independent Syst Operator Inc Carmel IN 46032 USA

Pumped storage hydro (PSH) plant is a valuable resource with storage and fast ramp capabilities, which can manage the intermittency of renewable energy. An accurate model for the input-output curve of PSH plant can capture its varying efficiency feature and enable accurate evaluations of available generating/pumping capability. However, the trade-off between approximation accuracy and computation time poses a significant challenge for input-output curve modeling. In this paper, we develop a hypograph-relaxation-based input-output curve modeling framework, wherein sufficient conditions for exact hypograph relaxation are defined, proved, and analyzed for fixed-speed PSH considering the value of water in the upper reservoir. Under this framework, a novel disjunctive convex hull model is proposed to balance the aforementioned trade-off. Our model can take advantage of high accuracy in time-consuming piece-wise approximation models, and acceptable computation burden in less-accurate convex hull models. To divide a given input-output curve into various components that can be approximated by their respective convex hulls, we propose to use an approximate convex decomposition (ACD) based approach. The proposed model is tested for profit maximization problems using real-world Ludington PSH station data. Numerical results demonstrated the superior computational advantage of the proposed approach.

关键词： Pumped storage hydro input-output curve hypograph relaxation disjunctive convex hull mixed-integer linear program

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Hysteresis effects on the input-output curve of motor evoked potentials

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CLINICAL NEUROPHYSIOLOGY 2009年第5期120卷 1003-1008页

作者： Moeller, Caroline Arai, Noritoshi Luecke, Joerg Ziemann, Ulf Univ Frankfurt Dept Neurol Motor Cortex Grp D-60528 Frankfurt Germany Univ Frankfurt Frankfurt Inst Adv Studies D-60528 Frankfurt Germany

Objective: input-output (IO) curves of motor evoked potentials (MEP) are widely used to assess corticospinal excitability by transcranial magnetic stimulation (TMS). Here we sought to determine hysteresis effects on IO curves, i.e. their short-term dependence on prior corticospinal activation. Methods: IO curves were measured from the first dorsal interosseous (FDI) muscle of 14 healthy volunteers in three different conditions of stimulus intensity order: increase from lowest to highest, decrease from highest to lowest, and random. Intensities ranged from 80% to 170% of the resting motor threshold (RMT). IO curves were measured in the resting vs. active FDI and at two different intertrial intervals (ITI, 5 s and 20 s). Results: In the resting FDI and at ITI = 5 s, the IO curve in condition "decrease" shifted significantly to the left compared to condition "increase". The IO curve in condition "random" ran in between the other two curves. Hysteresis was most pronounced in the high intensity part of the IO curves. Hysteresis did not occur at ITI = 20 s or in the active FDI. Conclusions: Findings implicate that hysteresis can influence IO curves significantly. One possible underlying mechanism might be short-term synaptic enhancement. Significance: Consideration of IO curve hysteresis effects is important to avoid systematic data bias in clinical and research TMS applications. (C) 2009 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

关键词： Motor evoked potential input-output curve Hysteresis Corticospinal system Transcranial magnetic stimulation Human

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Pulse width dependence of motor threshold and input-output curve characterized with controllable pulse parameter transcranial magnetic stimulation

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CLINICAL NEUROPHYSIOLOGY 2013年第7期124卷 1364-1372页

作者： Peterchev, Angel V. Goetz, Stefan M. Westin, Gregory G. Luber, Bruce Lisanby, Sarah H. Duke Univ Dept Psychiat & Behav Sci Durham NC 27710 USA Duke Univ Dept Biomed Engn Durham NC 27710 USA Duke Univ Dept Elect & Comp Engn Durham NC 27710 USA Tech Univ Munich D-80290 Munich Germany Univ Calif Davis Sch Med Davis CA 95616 USA Duke Univ Dept Psychol & Neurosci Durham NC 27710 USA

Objective: To demonstrate the use of a novel controllable pulse parameter TMS (cTMS) device to characterize human corticospinal tract physiology. Methods: Motor threshold and input-output (IO) curve of right first dorsal interosseus were determined in 26 and 12 healthy volunteers, respectively, at pulse widths of 30, 60, and 120 mu s using a custom-built cTMS device. Strength-duration curve rheobase and time constant were estimated from the motor thresholds. IO slope was estimated from sigmoid functions fitted to the IO data. Results: All procedures were well tolerated with no seizures or other serious adverse events. Increasing pulse width decreased the motor threshold and increased the pulse energy and IO slope. The average strength-duration curve time constant is estimated to be 196 mu s, 95% CI [181 mu s, 210 mu s]. IO slope is inversely correlated with motor threshold both across and within pulse width. A simple quantitative model explains these dependencies. Conclusions: Our strength-duration time constant estimate compares well to published values and may be more accurate given increased sample size and enhanced methodology. Multiplying the IO slope by the motor threshold may provide a sensitive measure of individual differences in corticospinal tract physiology. Significance: Pulse parameter control offered by cTMS provides enhanced flexibility that can contribute novel insights in TMS studies. (C) 2013 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

关键词： Transcranial magnetic stimulation Pulse width Motor threshold Strength-duration curve Time constant Rheobase input-output curve Slope

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A formalism for sequential estimation of neural membrane time constant and input-output curve towards selective and closed-loop transcranial magnetic stimulation *

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JOURNAL OF NEURAL ENGINEERING 2022年第5期19卷 056017-056017页

作者： Alavi, S. M. Mahdi Vila-Rodriguez, Fidel Mahdi, Adam Goetz, Stefan M. Univ British Columbia Dept Psychiat Vancouver BC Canada Univ Surrey Surrey Inst People Centred Artificial Intelligenc Guildford Surrey England Univ Oxford Oxford Internet Inst Oxford England Univ Cambridge Dept Engn Cambridge England Duke Univ Dept Psychiat & Behav Sci Durham NC USA Duke Univ Dept Elect & Comp Engn Durham NC USA Duke Univ Dept Neurosurg Durham NC USA

Objective. To obtain a formalism for real-time concurrent sequential estimation of neural membrane time constant and input-output (IO) curve with transcranial magnetic stimulation (TMS). Approach. First, the neural membrane response and depolarization factor, which leads to motor evoked potentials with TMS are analytically computed and discussed. Then, an integrated model is developed which combines the neural membrane time constant and IO curve. Identifiability of the proposed integrated model is discussed. A condition is derived, which assures estimation of the proposed integrated model. Finally, sequential parameter estimation (SPE) of the neural membrane time constant and IO curve is described through closed-loop optimal sampling and open-loop uniform sampling TMS. Without loss of generality, this paper focuses on a specific case of commercialized TMS pulse shapes. The proposed formalism and SPE method are directly applicable to other pulse shapes. Main results. The results confirm satisfactory estimation of the membrane time constant and IO curve parameters. By defining a stopping rule based on five times consecutive convergence of the estimation parameters with a tolerances of 0.01, the membrane time constant and IO curve parameters are estimated with 82 TMS pulses with absolute relative estimation errors (AREs) of less than 4% with the optimal sampling SPE method. At this point, the uniform sampling SPE method leads to AREs up to 16%. The uniform sampling method does not satisfy the stopping rule due to the large estimation variations. Significance. This paper provides a tool for real-time closed-loop SPE of the neural time constant and IO curve, which can contribute novel insights in TMS studies. SPE of the membrane time constant enables selective stimulation, which can be used for advanced brain research, precision medicine and personalized medicine.

关键词： transcranial magnetic stimulation input-output curve neural membrane time-constant closed-loop TMS selective stimulation

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input-output slope curve estimation in neural stimulation based on optimal sampling principles

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JOURNAL OF NEURAL ENGINEERING 2021年第4期18卷

作者： Alavi, Seyed Mohammad Mahdi Goetz, Stefan M. Saif, Mehrdad Cardiff Metropolitan Univ Sch Technol Dept Appl Comp & Engn Llandaff CampusWestern Ave Cardiff CF5 2YB Wales Duke Univ Dept Psychiat & Behav Sci Duke Brain Initiat Durham NC 27708 USA Duke Univ Dept Elect & Comp Engn Duke Brain Initiat Durham NC 27708 USA Duke Univ Dept Neurosurg Duke Brain Initiat Durham NC 27708 USA Univ Cambridge Dept Engn Cambridge CB2 1PZ England Univ Windsor Dept Elect Engn Windsor ON N9B 3P4 Canada

This paper discusses some of the practical limitations and issues, which exist for the input-output (IO) slope curve estimation (SCE) in neural, brain and spinal, stimulation techniques. The drawbacks of the SCE techniques by using existing uniform sampling and Fisher-information-based optimal IO curve estimation (FO-IOCE) methods are elaborated. A novel IO SCE technique is proposed with a modified sampling strategy and stopping rule which improve the SCE performance compared to these methods. The effectiveness of the proposed IO SCE is tested on 1000 simulation runs in transcranial magnetic stimulation (TMS), with a realistic model of motor evoked potentials. The results show that the proposed IO SCE method successfully satisfies the stopping rule, before reaching the maximum number of TMS pulses in 79.5% of runs, while the estimation based on the uniform sampling technique never converges and satisfies the stopping rule. At the time of successful termination, the proposed IO SCE method decreases the 95th percentile (mean value in the parentheses) of the absolute relative estimation errors (AREs) of the slope curve parameters up to 7.45% (2.2%), with only 18 additional pulses on average compared to that of the FO-IOCE technique. It also decreases the 95th percentile (mean value in the parentheses) of the AREs of the IO slope curve parameters up to 59.33% (16.71%), compared to that of the uniform sampling method. The proposed IO SCE also identifies the peak slope with higher accuracy, with the 95th percentile (mean value in the parentheses) of AREs reduced by up to 9.96% (2.01%) compared to that of the FO-IOCE method, and by up to 46.29% (13.13%) compared to that of the uniform sampling method.

关键词： neural stimulation transcranial magnetic stimulation input-output curve slope curve estimation optimal sampling

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Impaired Glutamatergic Neurotransmission in Migraine With Aura? Evidence by an input-output curves Transcranial Magnetic Stimulation Study

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HEADACHE 2011年第5期51卷 726-733页

作者： Cosentino, Giuseppe Fierro, Brigida Vigneri, Simone Talamanca, Simona Palermo, Antonio Puma, Angela Brighina, Filippo Univ Palermo Dipartimento Biomed Sperimentale & Neurosci Clin I-90100 Palermo Italy

Objective.- An imbalance between activity of inhibitory and facilitatory intracortical circuits could play a central role in migraine etiology. We used input-output curves to achieve further information about intracortical excitability of motor cortex in migraine with aura. Methods.- input-output curves were measured in the right abductor pollicis brevis muscle at rest in 12 patients suffering from migraine with aura and 8 healthy subjects. Stimuli were delivered at intensity ranging from 100% to 160% of resting motor threshold with 10-second inter-stimulus intervals. Seven patients were studied before and during treatment with levetiracetam. Results.- Results showed a greater motor-evoked potential amplitude in response to increasing intensity of stimuli in patients compared to controls (P < .02). This increased facilitatory effect was abolished by levetiracetam (P < .005). Conclusions.- Our findings support the hypothesis of an interictal cortical hyper-responsivity in migraine patients that appears to be normalized by levetiracetam. This effect could support the potential therapeutic role of levetiracetam in migraine with aura prevention.

关键词： magnetic stimulation input-output curve migraine with aura levetiracetam motor cortex excitability

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Reciprocal changes in input-output curves of motor evoked potentials while learning motor skills

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BRAIN RESEARCH 2012年 1473卷 114-123页

作者： Suzuki, Makoto Kirimoto, Hikari Onishi, Hideaki Yamada, Sumio Tamaki, Hiroyuki Maruyama, Atsuo Yamamoto, Jun-ichi Niigata Univ Hlth & Welfare Fac Med Technol Niigata 9503198 Japan Niigata Univ Hlth & Welfare Inst Human Movement & Med Sci Niigata 9503198 Japan Nagoya Univ Sch Hlth Sci Nagoya Aichi 4648601 Japan Niigata Univ Hlth & Welfare Fac Hlth Sci Niigata 9503198 Japan Keio Univ Grad Sch Human Relat Tokyo Japan

Reciprocal inhibition of antagonist muscles is crucial for motor skill learning in humans. However, the changes in reciprocal inhibition function during the motor learning process are unknown. The aim of this study was to systematically observe the changes in reciprocal inhibition function. We investigated the optimal coil position for simultaneously eliciting motor evoked potentials (MEPs) of reciprocal muscles, and the reciprocal changes in input-output (IO) curves during motor skill training. From ten healthy volunteers, the IO curves of MEPs were measured for the midpoint between the center of gravity (CoG) of the extensor carpi radialis (ECR) and the flexor carpi radialis (FCR) muscles, for the CoG of ECR, and for the FCR muscles using transcranial magnetic stimulation (TMS). In addition, the IO curves of the ECR and the FCR muscles were measured before and after the motor skill training of rapid wrist extension. The IO curves measured at the midpoint between the CoGs of the ECR and the FCR muscles and the CoG of each muscle were homogenous. However, after training to perform rapid wrist extension, the IO curve of the agonist (ECR) muscle was increased, while the antagonist (FCR) muscle was decreased. The present findings validate the IO curves simultaneously measured for reciprocal muscles, and suggest that motor skill training could induce reciprocal change in corticospinal excitability. (C) 2012 Elsevier B.V. All rights reserved.

关键词： input-output curve Motor evoked potentials Reciprocal inhibition Motor learning Transcranial magnetic stimulation

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Modulation of input-output curves by low and high frequency repetitive transcranial magnetic stimulation of the motor cortex

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CLINICAL NEUROPHYSIOLOGY 2002年第8期113卷 1249-1257页

作者： Gangitano, M Valero-Cabré, A Tormos, JM Mottaghy, FM Romero, JR Pascual-Leone, A Harvard Univ Beth Israel Deaconess Med Ctr Sch MedLab Magnet Brain Stimulat Dept NeurolDiv Behav Neurol Boston MA 02215 USA Miguel Hernandez Univ Inst Bioengn Valencia Spain Univ Valencia Dept Med Valencia Spain

Objectives: Exploring the modulatory effects of different frequencies of repetitive transcranial magnetic stimulation (rTMS) on the excitability of the motor cortex as measured by the input-output curve technique (I-O curve). Methods: Sixteen healthy subjects participated in this experiment. On two different sessions, conducted 1 week apart, rTMS was applied either at a frequency of 20 or 1 Hz at 90 k of individual motor threshold (MT) for a total of 1600 pulses each. Before and after rTMS, the cortical excitability was assessed by treasuring MT and the size of motor evoked potentials (MEPs) collected at different intensities of stimulation. Results: The analysis on the whole population showed a significant decrease of cortical excitability after I Hz rTMS and an increase after 20 Hz rTMS. A subsequent cluster analysis pointed out the presence of two distinct groups of subjects with opposite responses at the same frequency of stimulation. Significant variations on MT were found for both groups only for the facilitatory effect irrespective of the frequency of stimulation. Conclusions: The results provide further insight into interindividual differences in the effects of rTMS and suggest the existence of subpopulations with specific patterns of response to rTMS. (C) 2002 Elsevier Science Ireland Ltd. All rights reserved.

关键词： repetitive transcranial magnetic stimulation cortical excitability input-output curve humans

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Parameter estimation using a modified whale optimization algorithm for input-output curves of thermal and hydro power plants

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2020年第2期30卷

作者： Secui, Dinu Calin Hora, Cristina Bendea, Gabriel Bendea, Codruta Univ Oradea Dept Energy Engn Univ 1 Oradea 410087 Romania

This paper presents a modified whale optimization (MWO) algorithm for solving the problem of parameters estimation for input-output curves of thermal and hydro generating units that operates in power plants. In order to improve the MWO algorithm, a chaotic component based on logistic map is added. This new algorithm is called chaotic MWO (CMWO). Both MWO and CMWO algorithms have kept the structure of original whale optimization (WO) algorithm, but some characteristics regarding how the solutions positions are updated inside CMWO and MWO phases were modified. Estimation of curve parameters is an optimization problem. Its objective is to minimize the sum of absolute errors between actual values and estimated values. The efficiency of CMWO, MWO, and WO algorithms is tested either on polynomial models or on models that use nonsmooth functions. The results of CMWO algorithm are then compared with the ones obtained by other recently published algorithms.

关键词： input-output curve optimization parameters estimation thermal and hydro power plant

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Modeling State Transition and Head-Dependent Efficiency curve for Pumped Storage Hydro in Look-Ahead Dispatch

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IEEE TRANSACTIONS ON POWER SYSTEMS 2021年第6期36卷 5396-5407页

作者： Wang, Siyuan Liu, Jian Chen, Haotian Bo, Rui Chen, Yonghong Missouri Univ Sci & Technol Dept Elect & Comp Engn Rolla MO 65409 USA Midcontinent Independent Syst Operator Inc Carmel IN 46032 USA

As one of the most widely installed utility-scale storage facilities, pumped storage hydro (PSH) plays an essential role in providing flexibility for power systems worldwide. Thus, to accurately quantify the flexibility of PSH units in operational optimization problems is important. The conventional PSH models in the literature rarely consider detailed state transitions due to their hourly-based settings. However, it becomes imperative for operational optimization on short-term intervals, especially with increasing shares of renewable energy in power systems. To this end, this paper presents a novel deterministic PSH model that considers the transition time and trajectory between three states of PSH units in look-ahead dispatch. Moreover, to better characterize the varying efficiency of PSH units with water head and flow rate, this paper proposes to model detailed head-dependent efficiency curves (hereafter called input-output curves) in look-ahead dispatch, which encounters heavy computational burdens when short time intervals are applied. In this work, a zig-zag piece-wise linear approximation method is used for input-output curve modeling. This can enable an accurate quantification for variable efficiency and head dependence in a computationally effective manner. Numerical results are presented to show performances of the proposed PSH model in both flexibility quantification and computation time.

关键词： Reservoirs Power systems Optimization Trajectory Linear approximation Generators Wind farms Pumped storage hydro state transition input-output curve look-ahead dispatch

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