Lognormal Probability Distribution Function Research Articles

Incorporating flowpaths as an explicit measure of river-floodplain connectivity to improve estimates of floodplain sediment deposition

Variation in floodplain topography can lead to gradual flooding and increase river-floodplain connectivity. We show that incorporating flowpaths as an explicit measure of river-floodplain connectivity can improve estimates of floodplain sediment deposition. We focus on the floodplain of the South River, downstream of Waynesboro, Virginia, where measurements of mercury accumulation have been used to estimate decadal-scale sedimentation rates. We developed a two-dimensional Hydrologic Engineering Center's River Analysis System (2D HEC-RAS) hydrodynamic model and used simulated model results with sediment deposition data to create regression models describing sedimentation across the floodplain. All of our statistical models incorporated a flowpath length from the location on the floodplain downstream to the riverbank as an explicit measure of river-floodplain connectivity that improved our estimates of floodplain sediment deposition (r2 = 0.514). We applied our best regression model to our hydrodynamic model results to create a map of floodplain sedimentation rate and discuss differences of three separate sections of floodplain. We found that floodplains with variable topography had wider, bimodal probability distribution functions (PDFs) of sedimentation rate (aggregated spatially) than floodplains without this topographic relief (with narrower log-normal PDFs). Our work highlights how floodplain topography and river-floodplain connectivity affect sedimentation rates and can help inform the development of floodplain sediment budgets.

Hydrological drought assessment using the standardized groundwater index and the standardized precipitation index in the Berg River Catchment, South Africa

Study regionBerg River Catchment (BRC), South Africa (SA). Study focusHydrological droughts threaten water security and climate Change and groundwater abstractions may exacerbate their impact. Thus, early detection and prediction of droughts is essential. The integration of the Standardised Groundwater Index (SGI) with the Standardised Precipitation Index (SPI), has been applied worldwide, it but not explored in South Africa (SA). The aim of this study was to evaluate the integration of the SGI and SPI for hydrological drought assessment within the BRC, SA. New hydrological insights for the regionThe sensitivity of the SGI to selected Probability Distribution Functions (PDFs) was examined, resulting in the Gamma and Log-Normal PDFs being preferred in the BRC. SGI-Gamma and SPI-Gamma comparisons validated the SGI method and shed light on the key factors influencing groundwater-related droughts in the BRC. The following was revealed: Hydrological droughts in the BRC are influenced by climate factors, surface and groundwater interactions, and groundwater abstractions. When conducting hydrological drought assessments using the SGI and the SPI, the initial focus should be on catchment-scale assessments before expanding to national-scale evaluations. Groundwater in the BRC exhibit significant resilience to droughts induced by climate factors, and thus useful to mitigate the risk of future droughts. Finally, The SGI performed satisfactorily in the BRC with limited groundwater level data.

Optimal stochastic power flow using enhanced multi-objective mayfly algorithm

For the classical multi-objective optimal power flow (MOOPF) problem, only traditional thermal power generators are used in power systems. However, there is an increasing interest in renewable energy sources and the MOOPF problem using wind and solar energy has been raised to replace part of the thermal generators in the system with wind turbines and solar photovoltaics (PV) generators. The optimization objectives of MOOPF with renewable energy sources vary with the study case. They are mainly a combination of 2–4 objectives from fuel cost, emissions, power loss and voltage deviation (VD). In addition, reasonable prediction of renewable power is a major difficulty due to the discontinuous, disordered and unstable nature of renewable energy. In this paper, the Weibull probability distribution function (PDF) and lognormal PDF are applied to evaluate the available wind and available solar power, respectively. In this paper, an enhanced multi-objective mayfly algorithm (NSMA-SF) based on non-dominated sorting and the superiority of feasible solutions is implemented to tackle the MOOPF problem with wind and solar energy. The algorithm NSMA-SF is applied to the modified IEEE-30 and standard IEEE-57 bus test systems. The simulation results are analyzed and compared with the recently reported MOOPF results.

A Two-Component Probability Distribution Function Describes the Mid-IR Emission from the Disks of Star-forming Galaxies

High-resolution JWST-MIRI images of nearby spiral galaxies reveal emission with complex substructures that trace dust heated both by massive young stars and the diffuse interstellar radiation field. We present high angular (0.″85) and physical resolution (20–80 pc) measurements of the probability distribution function (PDF) of mid-infrared (mid-IR) emission (7.7–21 μm) from 19 nearby star-forming galaxies from the PHANGS-JWST Cycle 1 Treasury. The PDFs of mid-IR emission from the disks of all 19 galaxies consistently show two distinct components: an approximately lognormal distribution at lower intensities and a high-intensity power law component. These two components only emerge once individual star-forming regions are resolved. Comparing with locations of H ii regions identified from Very Large Telescope/MUSE Hα mapping, we infer that the power-law component arises from star-forming regions and thus primarily traces dust heated by young stars. In the continuum-dominated 21 μm band, the power law is more prominent and contains roughly half of the total flux. At 7.7–11.3 μm, the power law is suppressed by the destruction of small grains (including PAHs) close to H ii regions, while the lognormal component tracing the dust column in diffuse regions appears more prominent. The width and shape of the lognormal diffuse emission PDFs in galactic disks remain consistent across our sample, implying a lognormal gas column density N(H) ≈ 1021 cm−2 shaped by supersonic turbulence with typical (isothermal) turbulent Mach numbers ≈5−15. Finally, we describe how the PDFs of galactic disks are assembled from dusty H ii regions and diffuse gas and discuss how the measured PDF parameters correlate with global properties such as star formation rate and gas surface density.

Modelling diameter at breast height distribution of jack pine and black spruce natural stands in eastern Canada

Individual tree diameter at breast height (DBH) distribution is an important information for forest management planning. Forest managers obtain the DBH data either by field measurements or estimations using predictive models. However, probability distribution models are still lacking or need improvement. Therefore, we aimed to construct and fit diameter distribution models that reflect forest structure and composition change. We evaluated gamma, log-normal, and Weibull probability distribution functions (PDFs) for two commercially important tree species, black spruce ( Picea mariana (Mill) B.S.P.) and jack pine ( Pinus banksiana Lamb), grown in natural stands across Ontario, Canada. We modelled the parameters of the distributions as a function of stand-level variables for these species. We used DBH data from 735 permanent sample plots. Our results showed that all three evaluated PDFs reflected observed DBH distribution. We demonstrated that the moment-based recovered parameters could represent the maximum likelihood-estimated parameters precisely, and parameters of the PDFs can be modelled as a function of stand-level dynamic covariates. The models unbiasedly predicted the PDF parameters DBH means and DBH classes. The R2 of the model fit ranged between 0.35 and 0.98 for the predicted parameters and 0.90 and 0.97 for the predicted DBH.

Integrating renewable energy and V2G uncertainty into optimal power flow: A gradient bald eagle search optimization algorithm with local escaping operator

AbstractHere, a new approach is proposed for solving the optimal power flow (OPF) problem in transmission networks using a Gradient Bald Eagle Search Algorithm (GBES) with a Local Escaping Operator (LEO). The method takes into account uncertainty of the renewable energy sources (wind energy and photovoltaic systems) and Vehicle‐to‐Grid (V2G) in the stochastic OPF problem. To improve the efficiency of the proposed technique and enhance its local exploitation capability, the LEO method's selection features are utilized. Monte Carlo methods are employed to estimate the generation costs of the renewable sources and PEVs and study their feasibility. The uncertainty of the renewable sources and PEVs is represented by Weibull, lognormal, and normal probability distribution functions (PDFs). The GBES approach is experimentally compared with well‐known meta‐heuristics using twenty‐three different test functions, and the results indicate its superiority over BES and other recently developed algorithms. Furthermore, the proposed method's effectiveness is evaluated using IEEE 30‐bus test system under various scenarios, and the simulation results demonstrate that it can effectively address OPF issues considering renewable energy sources and V2G, providing superior optimal solutions compared to other algorithms.

Multi-objective optimal power flow of thermal-wind-solar power system using an adaptive geometry estimation based multi-objective differential evolution

Sustainable energy is a key component of sustainable development. The current grid can be supplied by fossil fuel generators and renewable energy sources (RESs)-based generators, such as solar photovoltaic (PV) and wind power generators. In an electrical network, power generation from several sources must be optimally coordinated to ensure efficient and economical operation. However, the intermittent and uncertain nature of RESs complicate the operation of power systems. In this study, an adaptive geometry estimation-based multi-objective differential evolution (AGE-MODE) method is proposed for multi-objective optimal power flow in a hybrid power system of thermal, wind, and solar energy sources (MOOPF-TWS). In the proposed approach, wind and solar PV power outputs are predicted based on Weibull and lognormal probability distribution functions, respectively. Therefore, the generation costs for solar and wind power can be divided into direct costs, penalty costs for underestimation, and reserve costs for overestimation. Furthermore, the emissions, voltage deviation, and real power loss are considered in particular cases. AGE-MODE is applied to modified IEEE 30-bus and 57-bus systems, where different case studies are simulated with combinations of two-, three-, and four-objective optimizations in MOOPF-TWS problems. Comparisons between AGE-MODE and other recently developed multi-objective methods demonstrate its effectiveness in resolving MOOPF-TWS problems, particularly for cases with more than two objectives.

On a Data-Driven Optimization Approach to the PID-Based Algorithmic Trading

This paper proposes an optimal trading algorithm based on a novel application of conventional control engineering (CE). We consider a fundamental CE concept, namely, the feedback control, and apply it to algorithmic trading (AT). The concrete feedback control strategy is designed in a form of the celebrated proportional–integral–derivative (PID) model. The highly fluctuating nature of the modern financial markets has led to the adoption of a model-free realization of the generic PID framework. The control theoretical methodology we propose is combined with the advanced statistics for the historical market data. We obtain a specific log-normal probability distribution function (pdf) associated with the specific quantities associated with the available stock data. The empirical log-normal pdf mentioned above enables the necessary PID gains optimization. For this aim, we apply the data-driven optimization approaches and consider the corresponding Monte Carlo solution procedure. The optimized PID trading algorithm we propose is also studied in the Fourier analysis framework. This equivalent frequency domain representation involves a new concept in financial engineering, namely, the “stock market energy” concept. For the evaluation, we implement the proposed PID optimal trading algorithm and develop a Python-based prototype software. We finally apply the corresponding prototype software to a data set from the Binance BTC/USDT (Bitcoin/Tether) stock market. The experimental result illustrates the implementability of the proposed optimal PID trading scheme and also shows the effectiveness of the proposed CE methods in the modern AT.

A Quasi-periodic Oscillation of ∼4.6 yr in the Radio Light Curves of Blazar PKS 0607-157

We present periodicity search analyses on long-term radio light curves at 4.8, 8, and 14.5 GHz of blazar PKS 0607–157 observed by the University of Michigan Radio Astronomical Observatory telescope. The highly variable radio emissions are approximately distributed as a log-normal probability distribution function. The Power Spectral Density for the radio light curves can be well characterized by a power-law model. Using the Weighted Wavelet Z-transform and Lomb-Scargle periodogram methods, significant Quasi-periodic Oscillation (QPO) of ∼4.6 yr in the radio light curve has been observed above the 3σ confidence level, which presents an interesting case among blazar QPO phenomena. We explore three plausible physical models to explain the observed QPOs: a supermassive binary black hole system, Lense-Thirring precession of the disk, and helical motion of plasma blobs within the jet.

Application of the Standardised Streamflow Index for Hydrological Drought Monitoring in the Western Cape Province, South Africa: A Case Study in the Berg River Catchment

In many regions around the world, drought has been recurrent, more frequent, and more intense over time. Hence, scientific research on drought monitoring has become more urgent in recent years. The aim of this study was to test the applicability of the Standardised Streamflow Index (SSI) for hydrological drought monitoring in the Berg River catchment (BRC), Western Cape (WC) province, South Africa (SA). Using various methods described in this study, the sensitivity of the SSI to the commonly used Gamma, Log-normal, Log-logistic, Pearson Type III, and Weibull Probability Distribution Functions (PDFs) was tested. This study has found that all the tested PDFs produced comparable results for mild to severe drought conditions. The SSI calculated using the Gamma, Log-Normal, and Weibull PDFs is recommended for the BRC because it consistently identified extreme drought conditions during the 1990–2022 study period and identified the 2015–2018 droughts as the worst during the study period. Although more studies are required to test other PDFs not considered, this study has shown that the SSI can be applicable in the BRC. This study has provided a foundation for more research on the application of the SSI in the BRC and other catchments in SA.

Stochastic Multi-Objective Optimal Reactive Power Dispatch with the Integration of Wind and Solar Generation

The exponential growth of unpredictable renewable power production sources in the power grid results in difficult-to-regulate reactive power. The ultimate goal of optimal reactive power dispatch (ORPD) is to find the optimal voltage level of all the generators, the transformer tap ratio, and the MVAR injection of shunt VAR compensators (SVC). More realistically, the ORPD problem is a nonlinear multi-objective optimization problem. Therefore, in this paper, the multi-objective ORPD problem is formulated and solved considering the simultaneous minimization of the active power loss, voltage deviation, emission, and the operating cost of renewable and thermal generators. Usually, renewable power generators such as wind and solar are uncertain; therefore, Weibull and lognormal probability distribution functions are considered to model wind and solar power, respectively. Due to the unavailability and uncertainty of wind and solar power, appropriate PDFs have been used to generate 1000 scenarios with the help of Monte Carlo simulation techniques. Practically, it is not possible to solve the problem considering all the scenarios. Therefore, the scenario reduction technique based on the distance metric is applied to select the 24 representative scenarios to reduce the size of the problem. Moreover, the efficient non-dominated sorting genetic algorithm II-based bidirectional co-evolutionary algorithm (BiCo), along with the constraint domination principle, is adopted to solve the multi-objective ORPD problem. Furthermore, a modified IEEE standard 30-bus system is employed to show the performance and superiority of the proposed algorithm. Simulation results indicate that the proposed algorithm finds uniformly distributed and near-global final non-dominated solutions compared to the recently available state-of-the-art multi-objective algorithms in the literature.

It takes two to know one: computing accurate one-point PDF covariances from effective two-point PDF models

One-point probability distribution functions (PDFs) of the cosmic matter density are powerful cosmological probes that extract non-Gaussian properties of the matter distribution and complement two-point statistics. Computing the covariance of one-point PDFs is key for building a robust galaxy survey analysis for upcoming surveys like Euclid and the Rubin Observatory LSST and requires good models for the two-point PDFs characterising spatial correlations. In this work, we obtain accurate PDF covariances using effective shifted lognormal two-point PDF models for the mildly non-Gaussian weak lensing convergence and validate our predictions against large sets of Gaussian and non-Gaussian maps. We show how the dominant effects in the covariance matrix capturing super-sample covariance arise from a large-separation expansion of the two-point PDF and discuss differences between the covariances obtained from small patches and full sky maps. Finally, we describe how our formalism can be extended to characterise the PDF covariance for 3D-dimensional spectroscopic fields using the 3D matter PDF as an example. We describe how covariances from simulated boxes with fixed overall density can be supplemented with the missing super-sample covariance effect by relying on theoretical predictions validated against separate-universe style simulations.

The Mixture of Probability Distribution Functions for Wind and Photovoltaic Power Systems Using a Metaheuristic Method

The rising use of renewable energy sources, particularly those that are weather-dependent like wind and solar energy, has increased the uncertainty of supply in these power systems. In order to obtain considerably more accurate results in the analysis of power systems, such as in the planning and operation, it is necessary to tackle the stochastic nature of these sources. Operators require adequate techniques and procedures to mitigate the negative consequences of the stochastic behavior of renewable energy generators. Thus, this paper presents a modification of the original probability distribution functions (PDFs) where the original PDFs are insufficient for wind speed and solar irradiance modeling because they have a significant error between the real data frequency distribution and the estimated distribution curve. This modification is using a mixture of probability distributions, which can improve the fitting of data and reduce this error. The main aim of this paper is to model wind speed and solar irradiance behaviors using a two-component and a three-component mixture of PDFs generated from the integration of the original Weibull, Lognormal, Gamma, and Inverse-Gaussian PDFs. Three statistical errors are used to test the efficiency of the proposed original and mixture PDFs, which are the root mean square error (RMSE), the coefficient of correlation (R2), and the Chi-square error (X2). The results show that the mixture of PDFs gives better fitting criteria for wind speed and solar irradiance frequency distributions than the original PDFs. The parameters of the original and the mixture of PDFs are calculated using the innovative metaheuristic Mayfly algorithm (MA). The three-component mixture of PDFs lowered the RMSE by about 73% and was 17% more than the best original and the two-component mixture distributions.

Variability response functions for statically indeterminate structures

The response variability of statically indeterminate beam structures caused by uncertain material properties modeled by random fields is studied in this paper. By solving the governing equations of the statically indeterminate structure, the response bending moment along the length of the beam, M(x), is expressed as a function of its (random) zero-moment location. This approach, combined with a second-order Taylor series expansion of the random zero-moment location, leads to novel Variability Response Function-based integral expressions for the variance of the response bending moment, Var[M(x)]. Variability Response Functions have numerous desirable attributes including the capability to perform a full sensitivity analysis of the response variability with respect to the spectral characteristics of the random field modeling the uncertain material/system properties and establishing realizable upper bounds of the response variability. The proposed expressions are fundamentally different from all currently existing expressions that are based inherently on first-order Taylor series expansions, as they involve: (i) two distinct integrals in the expression for Var[M(x)] and, (ii) an expression for the mean value ɛ[M(x)] that depends on the stochastic field modeling the uncertain material properties. In general, the proposed second-order Taylor series-based formulation is expected to provide more accurate results. Extensive numerical examples are provided where the accuracy of the results obtained using the proposed formulation is validated using Monte Carlo simulations involving stochastic fields that follow truncated Gaussian and shifted lognormal probability distribution functions. These Monte Carlo simulation results indicate that the proposed Variability Response Functions are probability-distribution-independent.

Optimal Power Flow of Renewable-Integrated Power Systems Using a Gaussian Bare-Bones Levy-Flight Firefly Algorithm

This article proposes a Gaussian bare-bones Levy-flight firefly algorithm (GBLFA) and its modified version named MGBLFA for optimizing the various kinds of the different optimal power flow (OPF) problems in the presence of conventional thermal power generators and intermittent renewable energy resources such as solar photovoltaic (PV) and wind power (WE). Several objective functions, including fuel costs, emission, power loss, and voltage deviation, are considered in the OPF problem subject to economic, technical, and safety constraints. Also, the uncertainties of solar irradiance and wind speed are modeled using Weibull, lognormal probability distribution functions, and their influences are considered in the OPF problem. Proper cost functions associated with the power generation of PV and WE units are modeled. A comprehensive analysis of ten cases with various objectives on the IEEE 30-bus test system demonstrates the potential effects of renewable energies on the optimal scheduling of thermal power plants in a cost-emission-effective manner. Numerical results show the superiority of the proposed method over other state-of-the-art algorithms in finding optimal solutions for the OPF problems.

Probability distribution of wind speed and wave height in Nowshahr Port using the data acquired from wave scan buoy

The present study aimed to determine probability density function (Pdf) of wind speed and wave height in Nowshahr Port using the data obtained from wave scan buoy. Three Pdfs, i.e. Weibull, Rayleigh and Lognormal, were adopted for estimation of data frequency. The shape (k) and scale (c) parameters of the Weibull function were calculated by four methods, i.e. Graphical method (Gm), Moment method (Mm), Maximum likelihood method (Mlm) and Empirical method (Em) whereas the parameters of the other two functions were estimated only through Mlm. In order to analyze the efficiency of pdfs root mean square error (Rmse), determination coefficient (R2) and chi-square test (χ2) were considered. The results revealed that Mm, Em and Mlm presented almost similar ‘k’ and ‘c’ values. However, Gm yielded smaller values. Accuracy of Weibull Pdf was generally higher than those in Rayleigh one. However, it was seen in the present study that Rayleigh Pdf is better only when Weibull parameters in wind data were measured via Gm. Lognormal Pdf was the most efficient in both wind and wave data. Finally, cumulative distribution function was estimated based upon Weibull and Lognormal probability models and the former was again found to be stronger and more accurate.

Performance Improvement of Multiobjective Optimal Power Flow-Based Renewable Energy Sources Using Intelligent Algorithm

Producing energy from a variety of sources in a power system requires an optimal schedule to operate the power grids economically and efficiently. Nowadays, power grids might include thermal generators and renewable energy sources (RES). The integration of RES adds complexity to the optimal power flow problem due to intermittence and uncertainty. The study suggests a Multi-Objective Search Group Algorithm (MOSGA) to deal with multi-objective optimal power flow integrated with a stochastic wind and solar powers (MOOPF-WS) problem. Weibull and lognormal probability distribution functions (PDFs) are respectively adopted to describe uncertainties in wind speed and solar irradiance. The MOSGA incorporates crowding distance strategies, fast non-dominated sorting, and an archive selection mechanism to define and preserve the best non-dominated solutions. The total cost, real power loss, and emission were defined as the objectives for the MOOPF-WS problem. In the economic aspect, formulated cost modelling includes both overestimation and underestimation situations related to wind and solar power prediction. Further, uncertainty in load demand is represented by a normal PDF and is considered as a special study case due to its novelty. The effectiveness of MOSGA was validated on the IEEE 30-bus and 57-bus systems considering various combinations of objective functions as well as different loading scenarios. Its performance was comprehensively compared with the other three well-regarded multi-objective optimization algorithms including NSGA-II, MOALO, and MOGOA in terms of Spread metric, Hypervolume metric, and the best compromise solutions for all scenarios. The comparisons showed MOSGA was capable of obtaining well-distributed Pareto fronts and producing better quality solutions compared to the others in all tested scenarios. In addition, MOSGA also obtained better solution quality than significant research in the literature for all the comparable cases. These show the superiority of the MOSGA in dealing with the MOOPF-WS problem.

Optimal power flow solution of an integrated power system using elephant herd optimization algorithm incorporating stochastic wind and solar power

ABSTRACT In this paper an improved optimization strategy is proposed to address issues related to uncertainty of the optimum power flow (OPF) considering the cost analysis. Elephant Herd Optimization (EHO) method roused by the crowding conduct of elephant gathering has been modified to achieve the minimization of the objective functions. Initially, the OPF is analyzed with the Newton-Raphson (N-R) approach by considering only conventional resources, later on the wind and PV-based power scheduling is performed. The output power of the wind and PV systems is computed from the Weibull probability distribution function (PDF) and Lognormal PDF. Initially, the objective function is defined to analyze the power loss, voltage deviation, carbon emissions and generation cost. The defined multi-objective function is solved for PV and Wind power generation costs, emission, voltage stability, and losses. The considered constraints are the cost of generation and the risks associated with the renewable energy sources apart from voltage and reactive power limits. Moreover, the penalty deviation charges have also been considered during extreme conditions for sustainable power sources. The proposed approach has been applied to IEEE 57 bus system and the resulting emissions, generation cost, losses and voltage deviation are evaluated and the direct, reserve, and penalty costs of wind and PV are analyzed It is contrasted to standard approaches such as Differential Evolutionary (DE) and Firefly Algorithm (FA) to substantiate the efficiency of the EHO method. The proposed approach is deployed in the MATLAB for various cases.

Dynamic optimal power flow with cross entropy covariance matrix adaption evolutionary strategy for systems with electric vehicles and renewable generators

Modern power systems which integrate renewable energy sources (RESs), such as wind or solar energy sources and plug-in electric vehicles (PEVs), need to carry out the uncertainty due to the access of demanded or injected power. Therefore, it is necessary to consider uncertainty costs in optimal power flow problems. To develop the uncertainty cost functions, log-normal probability distribution function (PDF) for solar irradiance, normal PDF for unloading and loading behavior of PEVs, and Rayleigh PDF for wind speed are considered. In this work, a dynamic optimal power flow (DOPF) model is formulated by considering the uncertainties of RESs and PEVs. A newly hybrid metaheuristic algorithm named cross entropy (CE) covariance matrix adaption evolutionary strategy (CMAES) is proposed to evaluate the DOPF problem in a modified IEEE 118-bus system. The application of adaptive step length in the CMAES method improves the local exploitation capability, while the CE method is used in the initial stage for global exploration due to its fast convergence. Simulation results indicate that the proposed technique can solve the DOPF problems with RESs and PEVs effectively and can provide high-quality solutions compared to different techniques. The conventional statistical method called ANOVA test is performed for comparative analysis of different techniques. The results of this test show the validation of CE-CMAES compared to different optimization techniques. Therefore, the proposed method could be easily and efficiently applied by power system operators in real-time optimal power flow operations.

On the width and mean value of bubble size distributions under subcooled flow boiling

In this work, a new comprehensive dataset about bubble sizes in flow boiling of water is presented. The experimental setup basically consists of a lower copper heated plate embedded in a horizontal rectangular channel flow. Several experimental conditions, ranging bulk velocities: 0.1–0.9 [m·s−1]; mass fluxes: 96.9–871.8 [kg·m−2·s−1]; subcooling degrees: 16–36 [°C]; heat fluxes: 200–650 [kW·m−2] and pressures: 110–190 [kPa] were set for three cooper plates of different roughness, with Sa: 0.45, 1.23 and 7.43 [µm], respectively. Based on the current samples, the probability function for the normalized bubble diameter has been described by a lognormal pdf for any plate and experimental condition and a dimensionless correlation for the standard deviation of the bubble size distribution is presented. In order to completely describe the diameter distribution for bubbles in subcooled boiling systems, an improved correlation for the mean bubble diameter value is also presented here, after a deep review of previously published datasets. Further work is required to accommodate different channel configurations and surface morphologies.