Probability Density Function Of Power Research Articles

Comparison of power probability density functions for vertical sound propagation

When sound travels through the atmosphere, fluctuations in the wind velocity and temperature generate fluctuations in the sound amplitude and phase, which makes source detection, localization, and identification more difficult. While there are several parametric probability density functions for the signal power, the previous literature has not shown which model performs best in a wide variety of environments. This paper compares the noncentral Erlang, gamma, compound gamma, generalized gamma, and log exponentially modified Gaussian distributions' ability to approximate the signal power distributions collected at the National Wind Technology Center (Colorado, United States) in 2018. This weeklong experimental campaign measured the vertical and slanted sound propagation of a non-moving, sinusoidal source (600-3500 Hz) on the ground using microphones mounted to a meteorological tower up to 130 m high. The dataset included several different atmospheric conditions, which were recorded by the meteorological tower and resulted in a wide range of scattering regimes in the measured acoustic data. When evaluated using the Kullback-Leibler divergence, the gamma distribution was the best two-parameter model, and the log exponentially modified Gaussian distribution was the best three-parameter model.

Probabilistic power curve estimation based on meteorological factors and density LSTM

Wind power curve describes the relationship between wind speed and wind power output, which is useful for wind farm design and wind turbine condition monitoring. However, most research on power curves modeling neglected the effect of historical meteorological factors. Also, the research on probabilistic power curve is still limited. Therefore, this paper proposes a novel probabilistic power curve modeling approach. The effect of both current and historical meteorological variables, such as wind speed, wind direction, ambient temperature and turbulence intensity, on the power curve is studied by binning method and kernel density estimation. Next, instead of forecasting the wind power or its quantiles, a new probabilistic power curve model, Density LSTM with Negative Log-Likelihood Loss, is proposed to forecast the parameters of the probability density function of wind power directly. Finally, different probability distribution of wind power output is studied. Gamma, Laplace and Weibull distributions prove to be more suitable than Gaussian distribution. Based on the datasets of inland and offshore wind farms, it is verified that adding useful historical meteorological variables can improve the forecasting performance of the test dataset. Besides, the proposed probabilistic power curve can effectively improve the prediction performance in the probabilistic prediction task and can improve the prediction precision of the annual energy production.

PROBABILITY DENSITY FUNCTION OF AVERAGE POWER OF REAL SPEECH SIGNALS

It is known that many real signals, such as speech signals, are non-stationary processes that express theirfeature through changes in parameters over time. By observing speech in shorter time intervals, the property ofstationarity can be notice. This characteristic enables the application of techniques for adaptation to local signalcharacteristics in signal processing algorithms. Many of these algorithms are described by standards, and in additionto intensive development in this area in last decades, there is a constant need for the development of new solutionsand standards. One of the most used parameters of the speech signal for adaptation is the mean (average) signalpower. The change of speech in time results in a wide dynamic range of average power. In addition to the predicteddynamics of average power, in the design of systems with adaptive techniques it is important to include otherparameters, among which is the Probability Density Function (PDF) of the average power. The goal of the researchpresented in this paper is the analysis of the probability distribution of the average power of speech signals, based onwhich the adaptability in the development of algorithms in digital processing would be improved, which wouldensure higher quality and less requirements in data transmission and storage. In addition to the theoreticalconsideration, the research was conducted on real speech signals of different speakers. In modern technical systems,where Internet technologies are prominent, processing, transmission and memorization of speech is executed frameby frame. Therefore, an analysis of the probability density of the average power for different frame lengths wascarried out in the experiment. In the experimental part, for each of the speech signals of the speech corpus, theProbability Density Function that best describes the average power values per frame was determined. Experimentalresearch results indicate that the function that best describes the average power is different for different speakers. Inaddition, when observing one speaker, the Probability Density Function is different for different frame lengths. Itcan be concluded that when it comes to adaptive techniques in the digital processing of the speech signal, it isimportant to consider the characteristics of the average power, among which is the Probability Density Function ofthe average power

Interference Aggregation Involving Near- to Far-Field Propagation of Disturbance and its Impact on Emission Limits for Radio Protection

To introduce the interference aggregation effect into the emission-limit-setting model, aggregate interference power arising from randomly distributed disturbance sources is studied considering the near- to far-field propagation of radiated disturbance. It is assumed that point sources are uniformly distributed in a two-dimensional model and that the distance to the victim receiver ranges from the near-field region to the far-field region. A piecewise approximation is applied to the distance attenuation curve with a corner distance that indicates the border between the near and far fields. The mean value, standard deviation, and probability density function (PDF) of the decibel-scaled aggregate interference power are theoretically and numerically analyzed at various source densities. The results show that the shape of the PDF markedly changes as the source density increases because of the mixed contribution of disturbing sources both from the near and far fields. Accordingly, the variations in the mean value and standard deviation of the aggregate interference power are strongly dependent on the distance attenuation at which major interfering sources are found. When introducing the interference aggregation effect into the emission requirements, both the distance attenuation characteristics and the estimated source density in a real environment should be carefully considered.

Dependence of the probability density function of laser radiation power on the scintillation index and the size of a receiver aperture.

Power scintillations of a Gaussian laser beam propagated through a 7 km long horizontal atmospheric path for a wide range of turbulence strengths and different sizes of the receiver aperture were studied experimentally. The probability density function (PDF) and its properties were analyzed for a wide range of scintillation conditions. It was shown that the PDF can be described by the fractional exponential distribution in the strong scintillation regime (scintillation index of power measured on aperture σPIB2>1) for apertures with diameter d < a, where a is the size of the isoplanatic region, and by the gamma distribution in the weak scintillation regime (σPIB2<1), as well as by the lognormal distribution for σPIB2≪1. More than one distribution can be considered as a good approximation for experimental data for some ranges of d/a and σPIB2, but the transition from one distribution to another as the best approximation occurs at certain characteristic values of these parameters. In the strong scintillation regime, the aperture averaging effect resulted in the transition from the fractional exponential distribution to the fractional gamma (FG) distribution when the aperture diameter is about the size of the isoplanatic region (d/a∼1). The FG distribution better approximates the experimental PDF because it accounts for the fact that the probability of zero power values becomes zero due to the averaging effect of the aperture. The fractional gamma distribution is the best approximation of the PDF for a finite aperture when σPIB2>σPIB,crit2=[0.7-0.8], while the gamma distribution is the best approximation for σPIB2<σPIB,crit2.

Performance Analysis of Dynamic Downlink PPP Cellular Networks Over Generalized Fading Channels With MRC Diversity

This paper proposes novel and generalized expressions to characterize the performance of modern cellular networks under realistic user mobility behavior. The η-μ distribution is employed to derive the received power probability density function, the average bit error rate for different modulation schemes, and the coverage probability assuming a Poisson point process spatial distribution of base stations in downlink. The user is assumed to experience fading with Maximum Ratio Combining (MRC) and move according to a random way-point mobility model. The proposed expressions are applicable to different widely-used fading environments, such as Rayleigh and Nakagami-m as particular cases, by an appropriate selection of the η-μ parameters. Monte Carlo simulation was used to show the validity of the proposed expressions. The generalized expressions allow the system designer to quantify the effects of user mobility on the cellular network performance, in different propagation environments, and network topologies as a function of the number of base stations and MRC branches.

Optimal configuration of hybrid‐energy microgrid considering the correlation and randomness of the wind power and photovoltaic power

In this study, an improved method of optimal sizing method for a hybrid-energy microgrid (HEM) is proposed, simultaneously considering the impact of correlation and randomness of the wind power and photovoltaic (PV) power on HEM's sizing. The proposed optimal sizing method is based on the following steps: firstly, in order to obtain a large amount of data for the wind power and PV power in the planned area, a combined method which includes Kendall rank correlation coefficient, non-parametric estimation, Copula theory and Monte Carlo is proposed to generate the joint probability density function of the wind power and PV power and to generate an amount of data. Then, while guaranteeing reliable system operation of energy supply, the optimal sizing objective function with a minimum of operation cost, investment cost and pollution gas treatment cost is established based on the scenario-based approach. Finally, a case study of HEM is presented to verify the advantages of the proposed optimal sizing method.

Wind and solar power probability density prediction via fuzzy information granulation and support vector quantile regression

Uncertainty among wind and solar power affects the stability of power systems. In order to fully describe the uncertainty of wind and solar power, a probability density prediction model is proposed to predict the probability density function of wind and solar power. According to the wind and solar power time series, the original data is processed with fuzzy information granularity to eliminate the fluctuation and uncertainty of data. The Lagrange function is constructed by a support vector quantile regression model to get the quantile of wind and solar power at different points. The conditional quantiles are combined with the Epanechnikov kernel function to acquire complete probability density curves of forecasting results. In order to evaluate the performance of the output results, this paper analyzes the accuracy of the prediction results using point prediction error, prediction interval coverage probability and average bandwidth. The experimental data of wind and solar power with same temporal and spatial resolutions are taken into account. The results show that the method can effectively describe the uncertainty of wind and solar power, and also provide technical support for the safe and stable operation of the power system.

Ambient Noise Level and Site Characterization in Northern Egypt

The characterization of the background seismic noise in any seismological network is an essential task for checking the performance of the recording stations. Hence, a funded project from Science and Technology Funding Authority (STDF) was awarded by the National Research Institute of Astronomy and Geophysics (NRIAG) in 2017 to detect the recording capabilities of the Egyptian National Seismological Network (ENSN), established after the Cairo Earthquake which occurred in Egypt on October 12, 1992. This article covers the first output of the project which shows the results of noise assessment for nine broadband stations located in northern Egypt. For a proper assessment of seismic data quality for a part of the ENSN network, the PASSCAL Quick Look Extended (PQLX) software was used, which is based on the calculation of power spectral density (PSD) and probability density function (PDF) for the background noise. The analysis covered almost one year of continuously recorded seismic data. The results show that some stations have very low detectability and higher noise level in some frequency bands which affects the recording of seismic events, while others show good performance. Complete site analysis for all stations was done to illustrate the present site response to be able to recommend whether to keep a station or to relocate it. To achieve this, the seismic noise data extracted from all stations of the considered zone was studied to determine the horizontal to vertical (H/V) spectral ratio method to study the amplification parameters of the recording site. The output of this study is useful for detecting operational problems in the northern part of the Egyptian seismological network and could be relevant for the reconfiguration and optimization of ENSN stations.

A Computationally Efficient Method to Design Probabilistically Robust Wide-Area PSSs for Damping Inter-Area Oscillations in Wind-Integrated Power Systems

This paper proposes an efficient method that tunes wide-area power system stabilizers (WPSSs) to have probabilistic robustness for damping inter-area electromechanical oscillations in power systems with incorporated random wind power. Specifically, the efficiency of this method benefits from unique consideration and deduction of the analytic forms of cumulative distribution functions (cdfs) of two types of random variables and their derivatives with respect to tunable parameters of the conventionally structured WPSSs, based on approximations of wind power probability density functions by Gaussian mixtures. These cdfs then compose the objective function of an optimization that can rapidly solve for optimal parameters of WPSSs by a sequential quadratic programming algorithm. The optimized WPSSs are probabilistically robust because they enhance the probability of two commonly desired control effects. Simulation studies on a modified IEEE 10-machine and 39-bus system validate the superior efficiency of the proposed tuning method and the excellent performance of the derived WPSSs.

Optimization Scheduling Method for Power Systems Considering Optimal Wind Power Intervals

Wind power intervals with different confidence levels have an impact on both the economic cost and risk of dispatch plans for power systems with wind power integration. The higher the confidence level, the greater the bandwidth of corresponding intervals. Thus, more reserves are needed, resulting in higher economic cost but less risk. In order to balance the economic cost and risk, a unit commitment model based on the optimal wind power confidence level is proposed. There are definite integral terms in the objective function of the model, and both the integrand function and integral upper/lower bound contain decision variables, which makes it difficult to solve this problem. The objective function is linearized and solved by discretizing the wind power probability density function and using auxiliary variables. On the basis, a rolling dispatching model considering the dynamic regulation costs among multiple rolling plans is established. In addition to balancing economic cost and risk, it can help to avoid repeated regulations among different rolling plans. Simulations are carried on a 10-units system and a 118-bus system to verify the effectiveness of the proposed models.

Nitrogen oxide emission calculation for post-Panamax container ships by using engine operation power probability as weighting factor: A slow-steaming case

ABSTRACTIn this study, the nitrogen oxide (NOx) emission factors and total NOx emissions of two groups of post-Panamax container ships operating on a long-term slow-steaming basis along Euro–Asian routes were calculated using both the probability density function of engine power levels and the NOx emission function. The main engines of the five sister ships in Group I satisfied the Tier I emission limit stipulated in MARPOL (International Convention for the Prevention of Pollution from Ships) Annex VI, and those in Group II satisfied the Tier II limit. The calculated NOx emission factors of the Group I and Group II ships were 14.73 and 17.85 g/kWhr, respectively. The total NOx emissions of the Group II ships were determined to be 4.4% greater than those of the Group I ships. When the Tier II certification value was used to calculate the average total NOx emissions of Group II engines, the result was lower than the actual value by 21.9%. Although fuel consumption and carbon dioxide (CO2) emissions were increased by 1.76% because of slow steaming, the NOx emissions were markedly reduced by 17.2%. The proposed method is more effective and accurate than the NOx Technical Code 2008. Furthermore, it can be more appropriately applied to determine the NOx emissions of international shipping inventory.Implications: The usage of operating power probability density function of diesel engines as the weighting factor and the NOx emission function obtained from test bed for calculating NOx emissions is more accurate and practical. The proposed method is suitable for all types and purposes of diesel engines, irrespective of their operating power level. The method can be used to effectively determine the NOx emissions of international shipping and inventory applications and should be considered in determining the carbon tax to be imposed in the future.

Four-Parameter Models for Wind Farm Power Curves and Power Probability Density Functions

This letter is an additional contribution to the calculation of wind farm power curves and power probability density functions with the help of the logistic function and Jensen's model for wake effect calculation. The goal is to complete a previous formulation based on the use of the 3P-DP logistic function, with two other, called the 4P-DS and the 4P-DP ones.

Small-Scale Fading Statistics of Emerging 3-D Mobile Radio Cellular Propagation Channels

In delivering fifth generation (5G) communication networks, the fundamental advancements in the scale of antenna arrays, density of networks, mobility of communicating nodes, size of cells, and range of frequencies necessitate the derivation of an appropriate and reliable channel model. A tunable three dimensional (3-D) geometric channel model comprehending the mobility of user terminal together with high degree of flexibility in modelling the shape, orientation, and scale of the scattering region is proposed. Characterization of Doppler spectrum, quantization of multipath dispersion in angular domain, and second order fading statistics of the radio propagation channel is presented. Mathematical expressions for joint and marginal probability density function of Doppler shift and multipath power are derived for this advanced 3-D hollow geometric scattering model. Next, an analysis on the Doppler spectrum is presented, where the impact of various physical channel parameters on its statistical characteristics is analyzed. Since, the quantification of multipath dispersion in 3-D angular domain is of vital importance for designing large scale planner antenna arrays with very high directional resolution for emerging 5G communications, therefore, a thorough analysis on the multipath shape factors (SFs) of the proposed analytical 3-D channel model is conducted. Finally, the analysis on SFs is extended for characterization of second order fading statistics of multipath channels.

Performance Evaluation of Wireless Communication Systems over Composite $${\varvec{\alpha}}{-}{\varvec{\mu}}/$$ α - μ / Gamma Fading Channels

The composite $$\alpha {-}\mu /$$ gamma distribution is considered in this paper. Specifically, we derived closed-form expressions for the power probability density function (PDF) and the cumulative density function (CDF). We then use the PDF and the CDF to derive novel closed-form expressions for the outage probability, the average symbol error rate, and the average channel capacity over the composite $$\alpha {-}\mu /$$ gamma fading channels. All derived expressions are valid for integer and non-integer values of the fading parameters. Some representative numerical examples are provided to study the impact of the fading and shadowing parameters on the system performance. Furthermore, the numerical results are compared with Monte-Carlo simulations. Both results demonstrate excellent agreement which validates our analysis.

Analytical Expressions for Joint Distributions in Probabilistic Load Flow

Adopting the Gaussian mixture model, we derive an analytical expression for the joint probability density function of active power on multiple transmission lines, in the presence of non-Gaussian stochastic power injections. The corresponding joint cumulative distribution function is further obtained by multiple integrals. Results of the proposed method coincide with that of Monte Carlo simulations.

Numerical assessments of ocean energy extraction from western boundary currents using a quasi-geostrophic ocean circulation model

A single-layer, quasi-geostrophic (QG), large-scale ocean circulation model is developed in this paper to study available ocean current energy potentials harnessed by using the ocean current turbines. Power extraction is modeled by adding a parameterized Rayleigh friction term in the barotropic vorticity equation. Numerical assessments are performed by simulating a set of mid-latitude ocean basins in the beta plane, which are standard prototypes of more realistic ocean dynamics considering inter-decadal variability in turbulent equilibrium. The third-order Runge–Kutta scheme for the temporal discretization and the second-order conservative Arakawa scheme for the spatial discretization are utilized to perform Munk scale resolving high-resolution computations. A sensitivity analysis with respect to the turbine parameters is performed for various physical conditions. Results show that the proposed model captures the quasi-stationary ocean dynamics and provides the four-gyre circulation patterns in time mean. After an initial spin-up process, the proposed model reaches a statistically steady state at an average maximum speed between 1.5m/s and 2.5m/s, which is close to the observed maximum zonal velocities in the western boundary currents. The probability density function of the available power over a long time period is computed for a wide range of parameters. Numerical results shows that 10GW mean power can be extracted from the turbines distributed over a length scale of 100km along the western boundaries. However, it is demonstrated that bigger turbine areas would alter the flow patterns and energetics due to excessive dissipation. An increase in the turbine area results in an increase in the available power ranging from 8 to 22GW depending on the values of turbine modeling parameters. This first step in the numerical assessment of the proposed QG model shows that the present framework could represent a viable tool for evaluating energy potentials in a highly turbulent flow regime.

An application of the ECMWF Ensemble Prediction System for short-term solar power forecasting

Solar energy production is steadily growing in several countries. Depending on meteorological variables such as solar irradiance, cloud cover and temperature, solar power production predictability is limited by the chaotic nature of these parameters. This work presents an application of the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) to produce short-term probabilistic solar power forecasts (SPF). The EPS is based on running a meteorological model multiple times, starting from slightly perturbed initial conditions. The distribution of these different runs allows estimating the prediction uncertainty. We use about two years of power data from three solar farms located in different parts of Italy, characterized by different climatic conditions. We retrieve ensemble members of meteorological variables to build a power probability density function (PDF) for 0–72h forecast horizons. A neural network (NN) is applied to reduce model bias and to generate a PDF of power starting from the ensemble of meteorological variables. Then two statistical methods are applied to calibrate further the ensemble of power predictions, which results in the final probabilistic power forecast. The first technique has been already tested for wind power forecasting (WPF), and it is based on estimating the variance deficit (VD) or “lack of spread” of the ensemble distribution. The second is a well-established method to calibrate probabilistic predictions based on Ensemble Model Output Statistics (EMOS). Also, a persistence ensemble (PE) is used as a baseline technique. PE builds the ensemble members from the most recent power measurements available at the same lead time. It is shown that EPS coupled with VD and EMOS is a valid method to produce skillful probabilistic SPF in different climatic conditions. VD and EMOS show a similar level of statistical consistency and forecast skill for each test case. Overall, the performances of VD and EMOS appear significantly better than those of PE.

Primary User Emulation Attack Analysis on Cognitive Radio

Objectives: For dynamic spectrum sharing and for spectrum scarcity problem solution, Cognitive radio is used. This paper provides Primary User Emulation Attack analysis on Cognitive radio. Methods: This paper presents simulation framework to evaluate the impact of Primary User Emulation Attack on Cognitive radio network. For evaluation of the capability analysis of Cognitive radio networks under Primary User Emulation Attack, a hypothesis test at secondary user based on measured Probability density function of power received has been conducted. Simulation is done with MATLAB 2012b. Findings: For Primary User Emulation Attack analysis on Cognitive radio, the simulation results based on probabilities of miss detection as well as false alarm have been shown. The conclusion is that with increased number of malicious users within the system, false alarm probability also increases. Application: These results are useful for Primary User Emulation Attack analysis on Cognitive radio and are also useful to telecom operators. Keywords: Cognitive Radio (CR), Primary User Emulation Attack (PUEA), Probability Density Function (PDF), Probability of False Alarm

Reformulation of parameters of the logistic function applied to power curves of wind turbines

The current procedure for obtaining the parameters of the logistic function, used as a model for the power curve of wind turbines, provides meaningless values. These values are different for each wind turbine and obtaining them requires an optimization process. This paper proposes a procedure to obtain the parameters of the 4-parameter logistic function based on the features of the power curve, providing a model that is a function of the power curve parameters supplied by the manufacturer. Furthermore, that model can be used to derive another 4-parameter model and a 3-parameter model is proposed for certain conditions. The three models consist of a continuous function which simplifies the implementation of the curve in a computer program compared to piecewise models. In addition, the probability density function of the output power of a wind turbine is derived by using each model.