Journal articles: 'Uncertain power flow analysis'

1

Laib, Khaled, Anton Korniienko, Florent Morel, and Gérard Scorletti. "LMI based approach for power flow analysis with uncertain power injection." IFAC-PapersOnLine 51, no. 25 (2018): 310–15. http://dx.doi.org/10.1016/j.ifacol.2018.11.125.

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Coletta, Guido, Alfredo Vaccaro, and Domenico Villacci. "Fast and reliable uncertain power flow analysis by affine arithmetic." Electric Power Systems Research 175 (October 2019): 105860. http://dx.doi.org/10.1016/j.epsr.2019.04.038.

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Luo, Jinqing, Libao Shi, and Yixin Ni. "Uncertain Power Flow Analysis Based on Evidence Theory and Affine Arithmetic." IEEE Transactions on Power Systems 33, no. 1 (January 2018): 1113–15. http://dx.doi.org/10.1109/tpwrs.2017.2691539.

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Lerche, I., and F. Rocha-Legoretta. "Risking Basin Analysis Results." Energy Exploration & Exploitation 21, no. 2 (April 2003): 81–164. http://dx.doi.org/10.1260/014459803322362459.

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The work presented here uses a basin analysis code, developed for Excel, to handle burial history, fluid flow, fracturing, overpressure development with time, erosion events, kerogen breakdown to oil and gas, hydrocarbon volumetrics for both oil and gas including source retention, migration loss, and area changes with time of source rocks for each formation. The code is remarkably fast, requiring about 0.2 seconds on a laptop to perform all the above calculations for ten formations as well as producing pictorial representations of all variables with space and time. The code seamlessly interfaces with the Monte Carlo risking program Crystal Ball so that a total uncertainty analysis can be done with as many uncertain inputs as required and as many outputs of interest as needed without increasing the computer time needed. A thousand Crystal Ball runs take only about 200 seconds, allowing one to investigate many possible scenarios extremely quickly. We show here with four basic examples how one goes about identifying which parameters in the input (ranging from uncertain data, uncertain thermal history, uncertain permeability, uncertain fracture coefficients for rocks, uncertain geochemistry kinetics, uncertain kerogen amounts and types per formation, through to uncertain volumetric factors) are causing the greatest contributions to uncertainty in any and all outputs. The relative importance, relative contributions and relative sensitivity are examined to show when it is necessary to know more about the underlying distributions of uncertain parameters, when it is necessary to know more about the dynamic range of a parameter to narrow its contribution to the total uncertainty, and which parameters are necessary to first focus on to narrow their uncertainty in order to improve the dynamical, thermal or hydrocarbon outputs. An interface of such a coupled pair of very fast Excel codes with an Excel economics package can also now easily be undertaken so that one ties scientific uncertainty and economic uncertainty together for hydrocarbon exploration and identifies the global parameters dominantly influencing the combined economic/basin analysis system.

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Ray, Shashwati, and Shimpy Ralhan. "Reliable power flow and short circuit analysis of systems with uncertain data." International Journal of Reliability and Safety 12, no. 1/2 (2018): 166. http://dx.doi.org/10.1504/ijrs.2018.092519.

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Ray, Shashwati, and Shimpy Ralhan. "Reliable power flow and short circuit analysis of systems with uncertain data." International Journal of Reliability and Safety 12, no. 1/2 (2018): 166. http://dx.doi.org/10.1504/ijrs.2018.10013806.

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Liao, Xiaobing, Kaipei Liu, Yachao Zhang, Kun Wang, and Liang Qin. "Interval method for uncertain power flow analysis based on Taylor inclusion function." IET Generation, Transmission & Distribution 11, no. 5 (March 30, 2017): 1270–78. http://dx.doi.org/10.1049/iet-gtd.2016.1344.

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Ouyang, Bin, Lu Qu, Qiyang Liu, Baoye Tian, Zhichang Yuan, Peiqian Guo, Hongyi Dai, and Weikun He. "Calculation and Analysis of the Interval Power Flow for Distributed Energy System Based on Affine Algorithm." Energies 14, no. 3 (January 25, 2021): 600. http://dx.doi.org/10.3390/en14030600.

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Due to the coupling of different energy systems, optimization of different energy complementarities, and the realization of the highest overall energy utilization rate and environmental friendliness of the energy system, distributed energy system has become an important way to build a clean and low-carbon energy system. However, the complex topological structure of the system and too many coupling devices bring more uncertain factors to the system which the calculation of the interval power flow of distributed energy system becomes the key problem to be solved urgently. Affine power flow calculation is considered as an important solution to solve uncertain steady power flow problems. In this paper, the distributed energy system coupled with cold, heat, and electricity is taken as the research object, the influence of different uncertain factors such as photovoltaic and wind power output is comprehensively considered, and affine algorithm is adopted to calculate the system power flow of the distributed energy system under high and low load conditions. The results show that the system has larger operating space, more stable bus voltage and more flexible pipeline flow under low load condition than under high load condition. The calculation results of the interval power flow of distributed energy systems can provide theoretical basis and data support for the stability analysis and optimal operation of distributed energy systems.

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Kinias, Ioannis, Ioannis Tsakalos, and Nikolaos Konstantopoulos. "Investment evaluation in renewable projects under uncertainty, using real options analysis: the case of wind power industry." Investment Management and Financial Innovations 14, no. 1 (March 31, 2017): 96–103. http://dx.doi.org/10.21511/imfi.14(1).2017.10.

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Investment analysis is a crucial process for any investment’s success. This process can be supported by both the discounted cash flow analysis and the real options analysis. Many researchers have point out restrictions for the first one, in cases of uncertainty in the entrepreneurial environment. The main types of uncertainty, concerning the wind energy sector, include uncertainties related to the price of electriticity by RES, the public policy regulatory policies, the demand, the initial capital costs, the technological progress, the weather conditions, the political and economical situations and generally the RES market structure. In this paper, we try to find the optimal investment strategy in a liberalized global electricity market, where the price of electricity is uncertain while the other parameters are configured separately in each country. The authors consider about the factors of the time for investment and the electricity’s price level, in wind energy by using the real options theory. The authors select a variety of data for the wind energy industry from different countries in several continents, and also create a model for the investment analysis in this entrepreneurial sector.

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Chen, Yue, Zhizhong Guo, Hongbo Li, Yi Yang, Abebe Tilahun Tadie, Guizhong Wang, and Yingwei Hou. "Probabilistic Optimal Power Flow for Day-Ahead Dispatching of Power Systems with High-Proportion Renewable Power Sources." Sustainability 12, no. 2 (January 9, 2020): 518. http://dx.doi.org/10.3390/su12020518.

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With the increasing proportion of uncertain power sources in the power grid; such as wind and solar power sources; the probabilistic optimal power flow (POPF) is more suitable for the steady state analysis (SSA) of power systems with high proportions of renewable power sources (PSHPRPSs). Moreover; PSHPRPSs have large uncertain power generation prediction error in day-ahead dispatching; which is accommodated by real-time dispatching and automatic generation control (AGC). In summary; this paper proposes a once-iterative probabilistic optimal power flow (OIPOPF) method for the SSA of day-ahead dispatching in PSHPRPSs. To verify the feasibility of the OIPOPF model and its solution algorithm; the OIPOPF was applied to a modified Institute of Electrical and Electronic Engineers (IEEE) 39-bus test system and modified IEEE 300-bus test system. Based on a comparison between the simulation results of the OIPOPF and AC power flow models; the OIPOPF model was found to ensure the accuracy of the power flow results and simplify the power flow model. The OIPOPF was solved using the point estimate method based on Gram–Charlier expansion; and the numerical characteristics of the line power were obtained. Compared with the simulation results of the Monte Carlo method; the point estimation method based on Gram–Charlier expansion can accurately solve the proposed OIPOPF model

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Palahalli, Harshavardhan, Paolo Maffezzoni, and Giambattista Gruosso. "Gaussian Copula Methodology to Model Photovoltaic Generation Uncertainty Correlation in Power Distribution Networks." Energies 14, no. 9 (April 21, 2021): 2349. http://dx.doi.org/10.3390/en14092349.

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Deterministic load flow analyses of power grids do not include the uncertain factors that affect the network elements; hence, their predictions can be very unreliable for distribution system operators and for the decision makers who deal with the expansion planning of the power network. Adding uncertain probability parameters in the deterministic load flow is vital to capture the wide variability of the currents and voltages. This is achieved by probabilistic load flow studies. Photovoltaic systems represent a remarkable source of uncertainty in the distribution network. In this study, we used a Gaussian copula to model the uncertainty in correlated photovoltaic generators. Correlations among photovoltaic generators were also included by exploiting the Gaussian copula technique. The large sets of samples generated with a statistical method (Gaussian copula) were used as the inputs for Monte Carlo simulations. The proposed methodologies were tested on two different networks, i.e., the 13 node IEEE test feeder and the non-synthetic European low voltage test network. Node voltage uncertainty and network health, measured by the percentage voltage unbalance factor, were investigated. The importance of including correlations among photovoltaic generators is discussed.

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Sivakumar, P., and D. Poornima. "Uncertainty Modelled Power Flow Analysis for DG Sourced Power Systems." Advanced Materials Research 768 (September 2013): 298–300. http://dx.doi.org/10.4028/www.scientific.net/amr.768.298.

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For growing of electrical demand in the modern world energy requirement is tremendously increased day to day power market. Nowadays the non-conventional energy sources are utilized to meet out the current power demand through PV, wind and other non-conventional resources etc. In this concern the energy drawn from the other non-conventional energy sources is highly variable due to the nature of uncertainties. Hence the optimal load dispatch of the power is highly difficult, one of the attempts is to eradicate this difficulty by adding developed uncertainty model of PV and wind sourced power generation in power system network. Uncertainties of PV irradiation and wind speed models are developed by using generic probabilistic approach. By using this hybrid system, instantaneous power flow of a DG system is obtained through Monte carlo simulation (MCS) in the MATLAB/SIMULINK packages. Enhancement of optimal power flow (opf) and system reliability due to addition of uncertainty variables in DG sourced power systems.Index TermsLoad flow analysis, Monte Carlo simulation (MCS), integration of Photovoltaic generator and wind (PVG and WEG).

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Wang, Shouxiang, and Shuangchen Yuan. "Interval Energy Flow Analysis in Integrated Electrical and Natural-Gas Systems Considering Uncertainties." Energies 12, no. 11 (May 28, 2019): 2043. http://dx.doi.org/10.3390/en12112043.

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As integrated electrical and natural-gas systems (IENGS) are popularized, the uncertainties brought by variation of electrical load, power generation, and gas load should not be ignored. The aim of this paper is to analyze the impact of those uncertain variables on the steady-state operation of the whole systems. In this paper, an interval energy flow model considering uncertainties was built based on the steady-state energy flow. Then, the Krawczyk–Moore interval iterative method was used to solve the proposed model. To obtain precise results of the interval model, interval addition and subtraction operations were performed by affine mathematics. The case study demonstrated the effectiveness of the proposed approach compared with Monte Carlo simulation. Impacts of uncertainties brought by the variation of electrical load, power generation, and gas load were analyzed, and the convergence of energy flow under different uncertainty levels of electrical load was studied. The results led to the conclusion that each kind of uncertainties would have an impact on the whole system. The proposed method could provide good insights into the operating of IENGS with those uncertainties.

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Zhang, H., and P. Li. "Probabilistic analysis for optimal power flow under uncertainty." IET Generation, Transmission & Distribution 4, no. 5 (2010): 553. http://dx.doi.org/10.1049/iet-gtd.2009.0374.

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Laowanitwattana, Jirasak, and Sermsak Uatrongjit. "Probabilistic power flow analysis based on arbitrary polynomial chaos expansion for networks with uncertain renewable sources." IEEJ Transactions on Electrical and Electronic Engineering 13, no. 12 (June 22, 2018): 1754–59. http://dx.doi.org/10.1002/tee.22737.

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Adusumilli, Bala Surendra, Vinod Raj, and Kalyan Kumar Boddeti. "Modified Affine Arithmetic-Based Power Flow Analysis with Uncertainty." Electric Power Components and Systems 46, no. 6 (April 3, 2018): 728–37. http://dx.doi.org/10.1080/15325008.2018.1465143.

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Aien, M., R. Ramezani, and S. Mohsen Ghavami. "Probabilistic Load Flow Considering Wind Generation Uncertainty." Engineering, Technology & Applied Science Research 1, no. 5 (October 17, 2011): 126–32. http://dx.doi.org/10.48084/etasr.64.

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Renewable energy sources, such as wind, solar and hydro, are increasingly incorporated into power grids, as a direct consequence of energy and environmental issues. These types of energies are variable and intermittent by nature and their exploitation introduces uncertainties into the power grid. Therefore, probabilistic analysis of the system performance is of significant interest. This paper describes a new approach to Probabilistic Load Flow (PLF) by modifying the Two Point Estimation Method (2PEM) to cover some drawbacks of other currently used methods. The proposed method is examined using two case studies, the IEEE 9-bus and the IEEE 57-bus test systems. In order to justify the effectiveness of the method, numerical comparison with Monte Carlo Simulation (MCS) method is presented. Simulation results indicate that the proposed method significantly reduces the computational burden while maintaining a high level of accuracy. Moreover, that the unsymmetrical 2PEM has a higher level of accuracy than the symmetrical 2PEM with equal computing burden, when the Probability Density Function (PDF) of uncertain variables is asymmetric.

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Nogueira, Wallisson C., Lina Paola Garcés Negrete, and Jesús M. López-Lezama. "Interval Load Flow for Uncertainty Consideration in Power Systems Analysis." Energies 14, no. 3 (January 27, 2021): 642. http://dx.doi.org/10.3390/en14030642.

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Modern power systems must deal with a greater degree of uncertainty in power flow calculation due to variations in load and generation introduced by new technologies. This scenario poses new challenges to power system operators which require new tools for an accurate assessment of the system state. This paper presents an interval load flow (ILF) approach for dealing with uncertainty in power system analysis. A probabilistic load flow (PLF), based on Monte Carlo Simulation (MCS), was also implemented for comparative purposes. The ILF and PLF are used to estimate the network states. Both methods were implemented in Python® using the IEEE 34-bus, IEEE 69-bus and 192-bus Brazilian distribution system. The results with the proposed ILF on the aforementioned benchmark test systems proved to be compatible with that of the MCS, evidencing the robustness and applicability of the proposed approach.

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He, Jincong, Jiang Xie, Pallav Sarma, Xian-Huan Wen, Wen H. Chen, and Jairam Kamath. "Proxy-Based Work Flow for a Priori Evaluation of Data-Acquisition Programs." SPE Journal 21, no. 04 (August 15, 2016): 1400–1412. http://dx.doi.org/10.2118/173229-pa.

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Summary Data-acquisition programs, such as surveillance and pilot, play an important role in reservoir management, and are crucial for minimizing subsurface risks and improving decision quality. Optimal design of the data-acquisition plan requires predicting the performance (e.g., in terms of the expected amount of uncertainty reduction in an objective function) of a given design before it is implemented. Because the data from the acquisition program are uncertain at the time of the analysis, multiple history-matching runs are required for different plausible realizations of the observed data to evaluate the expected effectiveness of the program in reducing uncertainty. As such, the computational cost may be prohibitive because the number of reservoir simulations needed for the multiple history-matching runs would be substantial. This paper proposes a framework on the basis of proxies and rejection sampling (filtering) to perform the multiple history-matching runs with a manageable number of reservoir simulations. The work flow proposed does not depend on the linear Gaussian assumption that is a common, yet questionable, assumption in existing methods. The work flow also enables both qualitative and quantitative analysis of a surveillance plan. Qualitatively, heavy-hitter alignment analysis for the objective function and the observed data provides actionable measures for screening different surveillance designs. Quantitatively, the evaluation of expected uncertainty reduction from different surveillance plans allows for optimal design and selection of surveillance plans.

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Memon, Zain Anwer, Riccardo Trinchero, Paolo Manfredi, Flavio Canavero, and Igor S. Stievano. "Compressed Machine Learning Models for the Uncertainty Quantification of Power Distribution Networks." Energies 13, no. 18 (September 17, 2020): 4881. http://dx.doi.org/10.3390/en13184881.

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Today’s spread of power distribution networks, with the installation of a significant number of renewable generators that depend on environmental conditions and on users’ consumption profiles, requires sophisticated models for monitoring the power flow, regulating the electricity market, and assessing the reliability of power grids. Such models cannot avoid taking into account the variability that is inherent to the electrical system and users’ behavior. In this paper, we present a solution for the generation of a compressed surrogate model of the electrical state of a realistic power network that is subject to a large number (on the order of a few hundreds) of uncertain parameters representing the power injected by distributed renewable sources or absorbed by users with different consumption profiles. Specifically, principal component analysis is combined with two state-of-the-art surrogate modeling strategies for uncertainty quantification, namely, the least-squares support vector machine, which is a nonparametric regression belonging to the class of machine learning methods, and the widely adopted polynomial chaos expansion. Such methods allow providing compact and efficient surrogate models capable of predicting the statistical behavior of all nodal voltages within the network as functions of its stochastic parameters. The IEEE 8500-node test feeder benchmark with 450 and 900 uncertain parameters is considered as a validation example in this study. The feasibility and strength of the proposed method are verified through a systematic assessment of its performance in terms of accuracy, efficiency, and convergence, based on reference simulations obtained via classical Monte Carlo analysis.

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Bernards, Raoul, Werner van Westering, Johan Morren, and Han Slootweg. "Analysis of Energy Transition Impact on the Low-Voltage Network Using Stochastic Load and Generation Models." Energies 13, no. 22 (November 21, 2020): 6097. http://dx.doi.org/10.3390/en13226097.

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The energy transition poses a challenge for the electricity distribution network design as new energy technologies cause increasing and uncertain network loads. Traditional static load models cannot cope with the stochastic nature of this new technology adoption. Furthermore, traditional nonlinear power methods have difficulty evaluating very large networks with millions of cables, because they are computationally expensive. This paper proposes a method which uses copulas for modeling the uncertainty of technology adoption and load profiles, and combines it with a fast linear load flow model. The copulas are able to accurately model the stochastic behavior of solar irradiance, load measurements, and mobility data, converting them into electricity load profiles. The linear load flow model has better scalability and stability compared to traditional load flow models. The models are applied to a case study which uses a real-world dataset consisting of a realistic technology adoption scenario and a low-voltage network with millions of cables, which considers both voltage and current problems. Results show that risk profiles can be generated for all cables in the network, resulting in a valuable map for the district network operator as to where to focus their efforts.

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Ke, Song, Tao Lin, Rusi Chen, Hui Du, Shuitian Li, and Xialing Xu. "A Novel Self-Healing Strategy for Distribution Network with Distributed Generators Considering Uncertain Power-Quality Constraints." Applied Sciences 10, no. 4 (February 21, 2020): 1469. http://dx.doi.org/10.3390/app10041469.

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Self-healing of smart distribution networks with distributed generators, which are usually operated as independent islands after fault, can improve power-supply reliability. As a hot research topic, a self-healing scheme is usually treated as the output of a nonlinear optimizuoation model. However, existing strategies have two main shortcomings. The first, high-optimization dimension, results in low-optimization efficiency. The second, the effects of power-quality issues, which are more serious on islands and may further threaten the safe operation of islands, is usually neglected. To quickly obtain a reliable self-healing scheme, a novel strategy is proposed. As the first step, the distribution network after a fault occurrence can be divided into several trouble-free subnets via the connectivity analysis; each subnet is called an initial island. Further, for each initial island, a two-step optimization model of self-healing, which consists of load-shedding optimization and network reconfiguration optimization, is proposed to obtain the self-healing strategy with lower searching space as well as higher solving efficiency. In detail, in load-shedding optimization, by means of heuristic differential evolution algorithm, larger total recovery capacity is achieved by considering the droop characteristic of distributed generators (DGs) within the permissible change in frequency. In network-reconfiguration optimization, based on the improved hybrid particle swarm optimization algorithm, a comprehensive set of power-quality constraints, including constraint of change in frequency, uncertain constraints of node voltage total harmonic distortion (THD), and negative sequence components of DGs, is developed to guarantee the reliability of each island. To evaluate whether the constraints are satisfied during the optimization procedure, an improved flexible power-flow algorithm is developed to calculate the power flow of each island under change in frequency. Further, 2m+1-point estimate method is employed for uncertainty analyses of the distributions of harmonic and negative sequence components caused by the uncertainty of corresponding sources. Finally, via a 94-node practical distribution network, the effectiveness and advantages of the proposed strategy in safety, recovery capacity, and optimization efficiency are verified.

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Beaudry, Jean-Paul, and André P. Langlois. "Multiparametric sensitivity analysis of energy production projects." Canadian Journal of Civil Engineering 13, no. 2 (April 1, 1986): 121–29. http://dx.doi.org/10.1139/l86-020.

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Optimization studies of an energy production project or complex consist in determining the economic general dimensioning of the works during the prefeasibility or the feasibility stage of the studies. As these first studies are part of the iterative system planning process, they should include very exhaustive sensitivity analyses on the accuracy of all technical and economic parameters, although (and even because) so much data is uncertain during this phase.After a review of the mathematics of discounting and of the decision-making economic criteria, a nomographic approach is presented that allows the optimum dimensions of the project to be determined as a function of any combination of the following parameters: imposed discount rate, total investment cost, variations in cash flow pattern, delay in commissioning date, life expectancy of the works, monetary value of energy and power, system load growth, seasonal pattern of energy demand, effect of secondary energy, long-term average river flow, and effect of regulation on downstream developments.

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Ma, Xue Dong, and Jie Teng. "Analysis of Flow Field for Link Rod Butterfly Valve." Advanced Engineering Forum 2-3 (December 2011): 817–21. http://dx.doi.org/10.4028/www.scientific.net/aef.2-3.817.

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The link rod butterfly valve relies on the link mechanism inside the flow channel to realize opening. The flow within flow channel is complex and the flow state is uncertain, so that pressure load of the flow part can't be determined in the butterfly valve designing, and strength of the parts can’t be calculated accurately and the thrust of the hydraulic cylinder can't be determined accurately. Therefore, it is necessary to carry out flow field analysis. In this paper, by adopting the plug-in COSMOSMotion of Solidworks software, the link rod butterfly valve with DN1800 is carried on motion simulation, determining the specific opening. And then the butterfly valve at different opening is carried out the finite element analysis of the flow field, adopting the plug-in COSMOSFloworks of Solidworks of software. The result shows that: the force is the largest when the valve plate is in just opening, it is 230731N, the strength analysis of the flow part and selection of the hydraulic cylinder should be based on the working condition; When full opening, the upward force on the valve plate is 18504N, this force is the power source when the valve plate is over opening. The above mentioned work provides a reliable theoretical basis for the strength calculation and the force and energy parameters calculation of the link rod butterfly valve and the theoretical reference for flow pattern evaluation of the link rod butterfly valve.

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Yao, Jia, Yujia Huang, and Jingwei Hu. "Static Stability Analysis Based on Probabilistic Power Flow Calculation considering P2G Technology." Complexity 2021 (March 10, 2021): 1–11. http://dx.doi.org/10.1155/2021/5536294.

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At present, integrated energy systems have received extensive attention, but there is no basic framework for stability analysis of coupled systems. The injection of a large amount of renewable energy also has a great impact on the stability of the system. This paper focuses on how to analyze the static stability of the coupling system with uncertainty, which mainly considers the uncertainty of wind power generation and photovoltaic power generation and also considers the influence of P2G technology on the whole system. Firstly, this paper analyzes the principles of wind power generation and photovoltaic power generation and constructs the probability model of renewable energy power generation power. Then, the three-point estimation method is used to process the data, and the probability distribution of the unknown quantity is obtained by probabilistic power flow analysis. Finally, the probability distribution of each eigenvalue is obtained by analyzing the sensitivity of the characteristic roots to the voltage. Thus, the static stability of the system is judged. The applicability of proposed methodology is demonstrated by analyzing an integrated IEEE 14-bus power system and a Belgian 20-node gas system in this paper.

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Tan, Yung-Chang, Matthew P. Castanier, and Christophe Pierre. "Approximation of Power Flow Between Two Coupled Beams Using Statistical Energy Methods." Journal of Vibration and Acoustics 123, no. 4 (April 1, 2001): 510–23. http://dx.doi.org/10.1115/1.1399051.

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In this work, an investigation is performed into developing a general framework for predicting the power flow between coupled component structures with uncertain system parameters. A specific example of two coupled beams is considered, in which a torsional spring is attached at the coupling point to adjust the coupling strength. The power flow in the nominal system is formulated using component mode synthesis (CMS). First, the parameter-based statistical energy method, which employs free-interface component modes, is applied to obtain approximations for the ensemble-averaged power flow with each beam length having a uniformly-distributed random perturbation. Then, using fixed-interface component modes and constraint modes, the Craig-Bampton method of CMS is employed to formulate the nominal power flow equation in terms of the constraint-mode degrees of freedom. This fixed-interface CMS method is seen to provide a systematic and efficient platform for power flow analysis. Using this CMS basis, a general approximation for the ensemble-averaged power flow is formulated regardless of the probability distribution of the random parameters or the coupling strengths between the substructures. This approximation is derived using Galerkin’s method, in which each modal response is expanded in locally linear interpolation functions in the random system parameters. The proposed general framework is numerically validated by comparisons with wave approximations from the literature for this two-coupled-beam system.

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Kasturi, Kumari, Chinmay Kumar Nayak, and Ranjan Nayak. "Analysis of Photovoltaic & Battery Energy Storage System Impacts on Electric Distribution System Efficacy." International Journal on Electrical Engineering and Informatics 12, no. 4 (December 31, 2020): 1001–15. http://dx.doi.org/10.15676/ijeei.2020.12.4.18.

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Uncertain nature of renewable energy sources like solar irradiation poses a serious concern of loss of power supply reliability. Battery energy storage (BES) system helps in improving system reliability by storing surplus energy generated and supplying the load in case of energy deficit. Thus BES allows improvement of microgrid performance and reduces operational cost by increasing the utilization of renewable energy sources. This paper presents an energy management strategy (EMS) to dictate the power flow among photovoltaic (PV) panels, BES and the load considering a proposed time-of-use (TOU) pricing as the control factor. Its efficacy in improving power supply reliability as well as power quality issues of a 69-bus radial distribution system (RDS) is evaluated from technical performance indices like power loss, voltage deviation index and security margin and economic performance considering costs of power import from the grid and active power loss and financial benefit from battery discharge. Grasshopper Optimization Algorithm (GOA), is used to optimize the sizes and placements of three PV-BES units to minimize an objective function aptly formulated combining the technical performance indices using weighted sum method. The results are contrasted against another two cases of with only PV and without PV and BES integration. Finally, the proposed system is analysed from economic perspective and the benefits obtained are compared. The results are evident of both technical and economic advantages of integrating both PV and BES units at optimal locations (load bus). The optimization results obtained from GOA have been compared with that from Genetic Algorithm (GA). GOA proves to be fast, effective and reliable in resolving power flow optimization problem.

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Aghili, Sayed Javad, Hadi Saghafi, and Hamze Hajian-Hoseinabadi. "Uncertainty Analysis Using Fuzzy Transformation Method: An Application in Power-Flow Studies." IEEE Transactions on Power Systems 35, no. 1 (January 2020): 42–52. http://dx.doi.org/10.1109/tpwrs.2019.2929712.

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Reyes, Elkin D., and Sergio Rivera. "Algorithms for Optimal Power Flow Extended to Controllable Renewable Systems and Loads." Algorithms 14, no. 10 (September 25, 2021): 276. http://dx.doi.org/10.3390/a14100276.

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In an effort to quantify and manage uncertainties inside power systems with penetration of renewable energy, uncertainty costs have been defined and different uncertainty cost functions have been calculated for different types of generators and electric vehicles. This article seeks to use the uncertainty cost formulation to propose algorithms and solve the problem of optimal power flow extended to controllable renewable systems and controllable loads. In a previous study, the first and second derivatives of the uncertainty cost functions were calculated and now an analytical and heuristic algorithm of optimal power flow are used. To corroborate the analytical solution, the optimal power flow was solved by means of metaheuristic algorithms. Finally, it was found that analytical algorithms have a much higher performance than metaheuristic methods, especially as the number of decision variables in an optimization problem grows.

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Qiao, Zheng, Shangyuan Huang, Rui Li, Qinglai Guo, Hongbin Sun, and Zhaoguang Pan. "Unified Power Flow Analysis in Natural Gas and Electricity Coupled Networks Considering the Uncertainty of Wind Power." Energy Procedia 103 (December 2016): 322–27. http://dx.doi.org/10.1016/j.egypro.2016.11.293.

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Vaccaro, Alfredo, Claudio A. Canizares, and Kankar Bhattacharya. "A Range Arithmetic-Based Optimization Model for Power Flow Analysis Under Interval Uncertainty." IEEE Transactions on Power Systems 28, no. 2 (May 2013): 1179–86. http://dx.doi.org/10.1109/tpwrs.2012.2214405.

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Marin, Manuel, Federico Milano, and David Defour. "Midpoint-radius interval-based method to deal with uncertainty in power flow analysis." Electric Power Systems Research 147 (June 2017): 81–87. http://dx.doi.org/10.1016/j.epsr.2017.02.017.

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Costa, Luís Augusto Nagasaki, Célio Maschio, and Denis José Schiozer. "Evaluation of an uncertainty reduction methodology based on Iterative Sensitivity Analysis (ISA) applied to naturally fractured reservoirs." Oil & Gas Science and Technology – Revue d’IFP Energies nouvelles 74 (2019): 40. http://dx.doi.org/10.2516/ogst/2019013.

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History matching for naturally fractured reservoirs is challenging because of the complexity of flow behavior in the fracture-matrix combination. Calibrating these models in a history-matching procedure normally requires integration with geostatistical techniques (Big Loop, where the history matching is integrated to reservoir modeling) for proper model characterization. In problems involving complex reservoir models, it is common to apply techniques such as sensitivity analysis to evaluate and identify most influential attributes to focus the efforts on what most impact the response. Conventional Sensitivity Analysis (CSA), in which a subset of attributes is fixed at a unique value, may over-reduce the search space so that it might not be properly explored. An alternative is an Iterative Sensitivity Analysis (ISA), in which CSA is applied multiple times throughout the iterations. ISA follows three main steps: (a) CSA identifies Group i of influential attributes (i = 1, 2, 3, …, n); (b) reduce uncertainty of Group i, with other attributes with fixed values; and (c) return to step (a) and repeat the process. Conducting CSA multiple times allows the identification of influential attributes hidden by the high uncertainty of the most influential attributes. In this work, we assess three methods: Method 1 – ISA, Method 2 – CSA, and Method 3 – without sensitivity analysis, i.e., varying all uncertain attributes (larger searching space). Results showed that the number of simulation runs for Method 1 dropped 24% compared to Method 3 and 12% to Method 2 to reach a similar matching quality of acceptable models. In other words, Method 1 reached a similar quality of results with fewer simulations. Therefore, ISA can perform as good as CSA demanding fewer simulations. All three methods identified the same five most influential attributes of the initial 18. Even with many uncertain attributes, only a small percentage is responsible for most of the variability of responses. Also, their identification is essential for efficient history matching. For the case presented in this work, few fracture attributes were responsible for most of the variability of the responses.

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Zhu, Guang, Laurent Maxit, Nicolas Totaro, and Alain Le Bot. "Development of a hybrid SmEdA/SEA model for predicting the power exchanged between low and high modal density subsystems." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 263, no. 3 (August 1, 2021): 3824–32. http://dx.doi.org/10.3397/in-2021-2535.

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Statistical modal Energy distribution Analysis (SmEdA) was developed from classical Statistical Energy Analysis (SEA). It allows computing power flow between coupled subsystems from the deterministic modes of uncoupled subsystems without assuming the SEA modal energy equipartition. SmEdA is well adapted in mid-frequency when the subsystems have not a very high modal density. However, for some systems e.g. the plate-cavity system, one subsystem can exhibit a low modal density while the other one a high one. The goal of the paper is then to propose an extension of SmEdA formulation that allows describing one subsystem by its deterministic modes, and the other one as a diffuse field statistically supposing modal energy equipartition. The uncertain subsystem is then characterized by sets of natural frequencies and mode shapes constructed based on Gaussian Orthogonal Ensemble matrix and the cross-spectrum density of a diffuse field, respectively. This formulation permits not only the computation of mean noise response but also the variance generated by the uncertainties and furthermore without bringing in much computation. It is demonstrated that the obtained analytical results from the proposed hybrid SmEdA/SEA are consistent with numerical results computed by FEM with an appropriate degree of uncertainty.

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He, Jincong, Pallav Sarma, Eric Bhark, Shusei Tanaka, Bailian Chen, Xian-Huan Wen, and Jairam Kamath. "Quantifying Expected Uncertainty Reduction and Value of Information Using Ensemble-Variance Analysis." SPE Journal 23, no. 02 (January 9, 2018): 428–48. http://dx.doi.org/10.2118/182609-pa.

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Summary Data-acquisition programs, such as surveillance and pilots, play an important role in minimizing subsurface risks and improving decision quality for reservoir management. For design optimization and investment justification of these programs, it is crucial to be able to quantify the expected uncertainty reduction and the value of information (VOI) attainable from a given design. This problem is challenging because the data from the acquisition program are uncertain at the time of the analysis. In this paper, a method called ensemble-variance analysis (EVA) is proposed. Derived from a multivariate Gaussian assumption between the observation data and the objective function, the EVA method quantifies the expected uncertainty reduction from covariance information that is estimated from an ensemble of simulations. The result of EVA can then be used with a decision tree to quantify the VOI of a given data-acquisition program. The proposed method has several novel features compared with existing methods. First, the EVA method directly considers the data/objective-function relationship. Therefore, it can handle nonlinear forward models and an arbitrary number of parameters. Second, for cases when the multivariate Gaussian assumption between the data and objective function does not hold, the EVA method still provides a lower bound on expected uncertainty reduction, which can be useful in providing a conservative estimate of the surveillance/pilot performance. Finally, EVA also provides an estimate of the shift in the mean of the objective-function distribution, which is crucial for VOI calculation. In this paper, the EVA work flow for expected-uncertainty-reduction quantification is described. The result from EVA is benchmarked with recently proposed rigorous sampling methods, and the capacity of the method for VOI quantification is demonstrated for a pilot-analysis problem using a field-scale reservoir model.

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Cheng, Yueming, W. John Lee, and Duane A. McVay. "A New Approach for Reliable Estimation of Hydraulic Fracture Properties Using Elliptical Flow Data in Tight Gas Wells." SPE Reservoir Evaluation & Engineering 12, no. 02 (April 14, 2009): 254–62. http://dx.doi.org/10.2118/105767-pa.

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Summary Gas wells in low-permeability formations usually require hydraulic fracturing to be commercially viable. Pressure transient analysis in hydraulically fractured tight gas wells is commonly based on analysis of three flow regimes: bilinear, linear, and pseudoradial. Without the presence of pseudoradial flow, neither reservoir permeability nor fracture half-length can be independently estimated. In practice, as pseudoradial flow is often absent, the resulting estimation is uncertain and unreliable. On the other hand, elliptical flow, which exists between linear flow and pseudoradial flow, is of long duration (typically months to years). We can acquire much rate and pressure data during this flow regime, but no practical well test analysis technique is currently available to interpret these data. This paper presents a new approach to reliably estimate reservoir and hydraulic fracture properties from analysis of pressure data obtained during the elliptical flow period. The method is applicable to estimate fracture half-length, formation permeability, and skin factor independently for both infinite- and finite-conductivity fractures. It is iterative and features rapid convergence. The method can estimate formation permeability when pseudoradial flow does not exist. Coupled with stable deconvolution technology, which converts variable production-rate and pressure measurements into an equivalent constant-rate pressure drawdown test, this method can provide fracture-property estimates from readily available, noisy production data. We present synthetic and field examples to illustrate the procedures and demonstrate the validity and applicability of the proposed approach.

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Gjerstad, Kristian, and Rune W. Time. "Simplified Explicit Flow Equations for Herschel-Bulkley Fluids in Couette-Poiseuille Flow—For Real-Time Surge and Swab Modeling in Drilling." SPE Journal 20, no. 03 (June 15, 2015): 610–27. http://dx.doi.org/10.2118/170246-pa.

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Summary Simplified flow equations are developed for Herschel-Bulkley (HB) fluids in laminar Couette-Poiseuille (CP) flow. Such flow problems are encountered in drilling when the drillstring is moved longitudinally (surge and swab operations). The new equations give the frictional-pressure gradient explicitly as a function of the bulk-flow rate. This makes them very well-suited for applications in fast, robust dynamic models for real-time applications. Incorporating these equations in a dynamic model based on ordinary differential equations (ODEs) enables coupling with system identification and control-system theory. This is a great advantage in drilling applications where there are many uncertain parameters and few measurements. Thorough analysis of relevant analytical solutions is performed to replace the most complex (implicit) parts of the solution with simpler approximations. The accuracy of the new equations, in comparison with numerical simulations and available analytical solutions, is shown to be acceptable for most practical applications.

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Raj, Vinod, and Boddeti Kalyan Kumar. "A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty." International Journal of Electrical Power & Energy Systems 107 (May 2019): 395–402. http://dx.doi.org/10.1016/j.ijepes.2018.12.006.

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Adusumilli, Bala Surendra, and Boddeti Kalyan Kumar. "Modified affine arithmetic based continuation power flow analysis for voltage stability assessment under uncertainty." IET Generation, Transmission & Distribution 12, no. 18 (October 16, 2018): 4225–32. http://dx.doi.org/10.1049/iet-gtd.2018.5479.

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Cheng, Weijie, Renli Cheng, Jun Shi, Cong Zhang, Gaoxing Sun, and Dong Hua. "Interval Power Flow Analysis Considering Interval Output of Wind Farms through Affine Arithmetic and Optimizing-Scenarios Method." Energies 11, no. 11 (November 15, 2018): 3176. http://dx.doi.org/10.3390/en11113176.

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Wind power belongs to sustainable and clean energy sources which play a vital role of reducing environment pollution and addressing energy crisis. However, wind power outputs are quite difficult to predict because they are derived from wind speeds, which vary irregularly and greatly all the time. The uncertainty of wind power causes variation of the variables of power grids, which threatens the power grids’ operating security. Therefore, it is significant to provide the accurate ranges of power grids’ variables, which can be used by the operators to guarantee the power grid’s operating security. To achieve this goal, the present paper puts forward the interval power flow with wind farms model, where the generation power outputs of wind farms are expressed by intervals and three types of control modes are considered for imitating the operation features of wind farms. To solve the proposed model, the affine arithmetic-based method and optimizing-scenarios method are modified and employed, where three types of constraints of wind control modes are considered in their solution process. The former expresses the interval variables as affine arithmetic forms, and constructs optimization models to contract the affine arithmetic forms to obtain the accurate intervals of power flow variables. The latter regards active power outputs of the wind farms as variables, which vary in their corresponding intervals, and accordingly builds the minimum and maximum programming models for estimating the intervals of the power flow variables. The proposed methods are applied to two case studies, where the acquired results are compared with those acquired by the Monte Carlo simulation, which is a traditional method for handling interval uncertainty. The simulation results validate the advantages, effectiveness and the applicability of the two methods.

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Pappenberger, F., K. J. Beven, N. M. Hunter, P. D. Bates, B. T. Gouweleeuw, J. Thielen, and A. P. J. de Roo. "Cascading model uncertainty from medium range weather forecasts (10 days) through a rainfall-runoff model to flood inundation predictions within the European Flood Forecasting System (EFFS)." Hydrology and Earth System Sciences 9, no. 4 (October 7, 2005): 381–93. http://dx.doi.org/10.5194/hess-9-381-2005.

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Abstract. The political pressure on the scientific community to provide medium to long term flood forecasts has increased in the light of recent flooding events in Europe. Such demands can be met by a system consisting of three different model components (weather forecast, rainfall-runoff forecast and flood inundation forecast) which are all liable to considerable uncertainty in the input, output and model parameters. Thus, an understanding of cascaded uncertainties is a necessary requirement to provide robust predictions. In this paper, 10-day ahead rainfall forecasts, consisting of one deterministic, one control and 50 ensemble forecasts, are fed into a rainfall-runoff model (LisFlood) for which parameter uncertainty is represented by six different parameter sets identified through a Generalised Likelihood Uncertainty Estimation (GLUE) analysis and functional hydrograph classification. The runoff of these 52 * 6 realisations form the input to a flood inundation model (LisFlood-FP) which acknowledges uncertainty by utilising ten different sets of roughness coefficients identified using the same GLUE methodology. Likelihood measures for each parameter set computed on historical data are used to give uncertain predictions of flow hydrographs as well as spatial inundation extent. This analysis demonstrates that a full uncertainty analysis of such an integrated system is limited mainly by computer power as well as by how well the rainfall predictions represent potential future conditions. However, these restrictions may be overcome or lessened in the future and this paper establishes a computationally feasible methodological approach to the uncertainty cascade problem.

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Hsieh, Ru-Lan, Wei-Cheng Liao, and Wen-Chung Lee. "Local and Systemic Cardiovascular Effects from Monochromatic Infrared Therapy in Patients with Knee Osteoarthritis: A Double-Blind, Randomized, Placebo-Controlled Study." Evidence-Based Complementary and Alternative Medicine 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/583016.

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Infrared (IR) therapy is used for pain relief in patients with knee osteoarthritis (OA). However, IR’s effects on the cardiovascular system remain uncertain. Therefore, we investigated the local and systemic cardiovascular effects of monochromatic IR therapy on patients with knee OA in a double-blind, randomized, placebo-controlled study. Seventy-one subjects with knee OA received one session of 40 min of active or placebo monochromatic IR treatment (with power output of 6.24 W, wavelength of 890 nm, power density of 34.7 mW/cm2for 40 min, total energy of 41.6 J/cm2per knee per session) over the knee joints. Heart rate, blood pressure, and knee arterial blood flow velocity were periodically assessed at the baseline, during, and after treatment. Data were analyzed by repeated-measure analysis of covariance. Compared to baseline, there were no statistically significant group x time interaction effects between the 2 groups for heart rate (P=0.160), blood pressure (systolic blood pressure:P=0.861; diastolic blood pressure:P=0.757), or mean arterial blood flow velocity (P=0.769) in follow-up assessments. The present study revealed that although there was no increase of knee arterial blood flow velocity, monochromatic IR therapy produced no detrimental systemic cardiovascular effects.

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Roman, Mihai Daniel, and Diana Mihaela Stanculescu. "An Analysis of Countries’ Bargaining Power Derived from the Natural Gas Transportation System Using a Cooperative Game Theory Model." Energies 14, no. 12 (June 17, 2021): 3595. http://dx.doi.org/10.3390/en14123595.

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A large consumption of natural gas accompanied by reduced production capabilities makes Europe heavily dependent on imports from Russia. More than half of Russian gas is exported by transiting Ukraine, so in the context of the underlying conflict between the two, this is considered uncertain. Therefore, in this article, we modeled the natural gas transportation system using cooperative game theory in order to determine the bargaining power of the major players (Russia, Ukraine, Germany, and Norway) by using a form of the Shapley value. We described the interaction between countries as network games where utilities from transport routes are considered and proposed three scenarios where the gas flow from Russia to Ukraine is either diminished or completely interrupted, with the purpose of finding out how the bargaining power on this market is shifted in case of network redesign. In this context, we included in the analysis the scenario where the Nord Stream 2 pipeline will be finished. Results showed that Russia dominates the market in any scenario, and by avoiding Ukraine, its position is even further strengthened. Moreover, Germany’s position remains stable considering its diverse imports and large storage capabilities, and its bargaining power increases in the case of diminishing or avoiding the Ukrainian gas pipelines.

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Das, Biswarup. "Uncertainty modelling of wind turbine generating system in power flow analysis of radial distribution network." Electric Power Systems Research 111 (June 2014): 141–47. http://dx.doi.org/10.1016/j.epsr.2014.01.025.

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Li, Hang, Zhe Zhang, and Xianggen Yin. "A Novel Probabilistic Power Flow Algorithm Based on Principal Component Analysis and High-Dimensional Model Representation Techniques." Energies 13, no. 14 (July 8, 2020): 3520. http://dx.doi.org/10.3390/en13143520.

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Because the penetration level of renewable energy sources has increased rapidly in recent years, uncertainty in power system operation is gradually increasing. As an efficient tool for power system analysis under uncertainty, probabilistic power flow (PPF) is becoming increasingly important. The point-estimate method (PEM) is a well-known PPF algorithm. However, two significant defects limit the practical use of this method. One is that the PEM struggles to estimate high-order moments accurately; this defect makes it difficult for the PEM to describe the distribution of non-Gaussian output random variables (ORVs). The other is that the calculation burden is strongly related to the scale of input random variables (IRVs), which makes the PEM difficult to use in large-scale power systems. A novel approach based on principal component analysis (PCA) and high-dimensional model representation (HDMR) is proposed here to overcome the defects of the traditional PEM. PCA is applied to decrease the dimension scale of IRVs and eliminate correlations. HDMR is applied to estimate the moments of ORVs. Because HDMR considers the cooperative effects of IRVs, it has a significantly smaller estimation error for high-order moments in particular. Case studies show that the proposed method can achieve a better performance in terms of accuracy and efficiency than traditional PEM.

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Vaccaro, Alfredo, Claudio A. Canizares, and Domenico Villacci. "An Affine Arithmetic-Based Methodology for Reliable Power Flow Analysis in the Presence of Data Uncertainty." IEEE Transactions on Power Systems 25, no. 2 (May 2010): 624–32. http://dx.doi.org/10.1109/tpwrs.2009.2032774.

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Kabir, C. S. S., M. Elgmati, and Z. Reza. "Estimating Drainage-Area Pressure With Flow-After-Flow Testing." SPE Reservoir Evaluation & Engineering 15, no. 05 (September 11, 2012): 571–83. http://dx.doi.org/10.2118/146049-pa.

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Summary Estimating the average drainage-area pressure (pav) of individual wells is a cornerstone to any reservoir-management practice. Yet conventional methods do not always offer reliable solutions to this vexing problem. This study shows that transient flow-after-flow (FAF) testing offers an excellent opportunity to establish pav in a time-lapse mode, when conducted following operational shutdowns. Instrumented wells are natural candidates for FAF testing. Real-time surveillance offers the opportunity to perform rate-transient analysis that results in drainage volume and, consequently, pav. However, gathering quality rate data commensurate with pressure over a long producing period is fraught with uncertainty, which raises questions about the validity of the pav so obtained. In addition, continuous changes in drainage-boundary conditions pose modeling challenges with a given reservoir model. Therefore, the independent estimation of pav cannot be overemphasized. This paper presents a theroretical framework for transient FAF testing and also shows a pragmatic approach to handling pressure/rate data incoherence.

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Li, L., and H. A. Tchelepi. "Conditional Stochastic Moment Equations for Uncertainty Analysis of Flow in Heterogeneous Reservoirs." SPE Journal 8, no. 04 (December 1, 2003): 392–400. http://dx.doi.org/10.2118/87337-pa.

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Kunz, Jan, Jiri Fialka, Stanislav Pikula, Petr Benes, Jakub Krejci, Stanislav Klusacek, and Zdenek Havranek. "A New Method to Perform Direct Efficiency Measurement and Power Flow Analysis in Vibration Energy Harvesters." Sensors 21, no. 7 (March 30, 2021): 2388. http://dx.doi.org/10.3390/s21072388.

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Measuring the efficiency of piezo energy harvesters (PEHs) according to the definition constitutes a challenging task. The power consumption is often established in a simplified manner, by ignoring the mechanical losses and focusing exclusively on the mechanical power of the PEH. Generally, the input power is calculated from the PEH’s parameters. To improve the procedure, we have designed a method exploiting a measurement system that can directly establish the definition-based efficiency for different vibration amplitudes, frequencies, and resistance loads. Importantly, the parameters of the PEH need not be known. The input power is determined from the vibration source; therefore, the method is suitable for comparing different types of PEHs. The novel system exhibits a combined absolute uncertainty of less than 0.5% and allows quantifying the losses. The approach was tested with two commercially available PEHs, namely, a lead zirconate titanate (PZT) MIDE PPA-1011 and a polyvinylidene fluoride (PVDF) TE LDTM-028K. To facilitate comparison with the proposed efficiency, we calculated and measured the quantity also by using one of the standard options (simplified efficiency). The standard concept yields higher values, especially in PVDFs. The difference arises from the device’s low stiffness, which produces high displacement that is proportional to the losses. Simultaneously, the insufficient stiffness markedly reduces the PEH’s mechanical power. This effect cannot be detected via the standard techniques. We identified the main sources of loss in the damping of the movement by the surrounding air and thermal losses. The latter source is caused by internal and interlayer friction.

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Tseng, Li, Sung-Chun Tang, Chun-Yuan Chang, Yi-Ching Lin, Maysam F. Abbod, and Jiann-Shing Shieh. "Nonlinear and Conventional Biosignal Analyses Applied to Tilt Table Test for Evaluating Autonomic Nervous System and Autoregulation." Open Biomedical Engineering Journal 7, no. 1 (September 6, 2013): 93–99. http://dx.doi.org/10.2174/1874120720130905004.

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Tilt table test (TTT) is a standard examination for patients with suspected autonomic nervous system (ANS) dysfunction or uncertain causes of syncope. Currently, the analytical method based on blood pressure (BP) or heart rate (HR) changes during the TTT is linear but normal physiological modulations of BP and HR are thought to be predominately nonlinear. Therefore, this study consists of two parts: the first part is analyzing the HR during TTT which is compared to three methods to distinguish normal controls and subjects with ANS dysfunction. The first method is power spectrum density (PSD), while the second method is detrended fluctuation analysis (DFA), and the third method is multiscale entropy (MSE) to calculate the complexity of system. The second part of the study is to analyze BP and cerebral blood flow velocity (CBFV) changes during TTT. Two measures were used to compare the results, namely correlation coefficient analysis (nMxa) and MSE. The first part of this study has concluded that the ratio of the low frequency power to total power of PSD, and MSE methods are better than DFA to distinguish the difference between normal controls and patients groups. While in the second part, the nMxa of the three stages moving average window is better than the nMxa with all three stages together. Furthermore the analysis of BP data using MSE is better than CBFV data.

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Journal articles on the topic 'Uncertain power flow analysis'

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