Power Performance Curve Research Articles

Further experimental analysis of undershot water wheels towards the development of a prototype model

ABSTRACT The current research aims to analyse the effect of the number and shape of the blades and the curvature of the flume bottom on the performance curves of undershot water wheels, based on experimental tests conducted in a fully instrumented laboratory facility. Six wheels are tested: four wheels with plane blades (16, 24, 36, 48) and two with 24 curved blades for two flume bottom configurations. Torque, mechanical power and mechanical efficiency performance curves are determined for several rotational speed and flow rate values. Results demonstrate that the maximum efficiency is achieved for the 36-plane blade wheel, the curved flume bottom reduces water losses under the wheel and increases efficiency, and the blades’ shape strongly influences the wheel efficiency. Non-dimensional performance curves are provided to generalise the results. This research provides relevant contributions towards the development of a low-cost energy recovery solution to be applied in water infrastructures.

A Simplified Modeling Approach of Floating Offshore Wind Turbines for Dynamic Simulations

Currently, floating offshore wind is experiencing rapid development towards a commercial scale. However, the research to design new control strategies requires numerical models of low computational cost accounting for the most relevant dynamics. In this paper, a reduced linear time-domain model is presented and validated. The model represents the main floating offshore wind turbine dynamics with four planar degrees of freedom: surge, heave, pitch, first tower fore-aft deflection, and rotor speed to account for rotor dynamics. The model relies on multibody and modal theories to develop the equation of motion. Aerodynamic loads are calculated using the wind turbine power performance curves obtained in a preprocessing step. Hydrodynamic loads are precomputed using a panel code solver and the mooring forces are obtained using a look-up table for different system displacements. Without any adjustment, the model accurately predicts the system motions for coupled stochastic wind–wave conditions when it is compared against OpenFAST, with errors below 10% for all the considered load cases. The largest errors occur due to the transient effects during the simulation runtime. The model aims to be used in the early design stages as a dynamic simulation tool in time and frequency domains to validate preliminary designs. Moreover, it could also be used as a control design model due to its simplicity and low modeling order.

Power performance of BBDB OWC wave energy converters

Abstract This research presents the power performance of the backward-bent duct buoy (BBDB) oscillating water column (OWC) wave energy converters (WECs). To achieve that, following steps are detailed: firstly, power conversion from wave power into pneumatic power by coupling the hydrodynamics and the thermodynamics in the air chamber using a linear air turbine power take-off (PTO), with the calculation of the power response curves for the BBDB OWC device in regular waves; secondly, using the power response curve, a power performance curve is then calculated for irregular waves; thirdly, the power matrices for the device is calculated and the determination of the rated power for the device to meet the target capture factor; and finally, the annual energy production will be assessed as the final indicator for the device's power performance. Using the developed approach, some initial optimisations are made to the original design. It is shown that with some simple optimisations, the BBDB OWC device could increase the annual energy production (AEP) significantly. A simple change in making a uniformed water column for the RM6 device could increase the AEP by about 10%, whilst increasing the horizontal duct length by 10 m could increase the AEP by 58%.

The Effect of Control Strategy on Tidal Stream Turbine Performance in Laboratory and Field Experiments

The first aim of the research presented here is to examine the effect of turbine control by comparing a passive open-loop control strategy with a constant rotational speed proportional–integral–derivative (PID) feedback loop control applied to the same experimental turbine. The second aim is to evaluate the effect of unsteady inflow on turbine performance by comparing results from a towing-tank, in the absence of turbulence, with results from the identical machine in a tidal test site. The results will also inform the reader of: (i) the challenges of testing tidal turbines in unsteady tidal flow conditions in comparison to the controlled laboratory environment; (ii) calibration of acoustic Doppler flow measurement instruments; (iii) characterising the inflow to a turbine and identifying the uncertainties from unsteady inflow conditions by adaptation of the International Electrotechnical Commission technical specification (IEC TS): 62600-200. The research shows that maintaining a constant rotational speed with a control strategy yields a 13.7% higher peak power performance curve in the unsteady flow environment, in comparison to an open-loop control strategy. The research also shows an 8.0% higher peak power performance in the lab compared to the field, demonstrating the effect of unsteady flow conditions on power performance. The research highlights the importance of a tidal turbines control strategy when designing experiments.

Assessing metabolic constraints on the maximum body size of actinopterygians: locomotion energetics of Leedsichthys problematicus (Actinopterygii, Pachycormiformes)

AbstractMaximum sizes attained by living actinopterygians are much smaller than those reached by chondrichthyans. Several factors, including the high metabolic requirements of bony fishes, have been proposed as possible body‐size constraints but no empirical approaches exist. Remarkably, fossil evidence has rarely been considered despite some extinct actinopterygians reaching sizes comparable to those of the largest living sharks. Here, we have assessed the locomotion energetics of Leedsichthys problematicus, an extinct gigantic suspension‐feeder and the largest actinopterygian ever known, shedding light on the metabolic limits of body size in actinopterygians and the possible underlying factors that drove the gigantism in pachycormiforms. Phylogenetic generalized least squares analyses and power performance curves established in living fishes were used to infer the metabolic budget and locomotion cost of L. problematicus in a wide range of scenarios. Our approach predicts that specimens weighing up to 44.9 tonnes would have been energetically viable and suggests that similar body sizes could also be possible among living taxa, discarding metabolic factors as likely body size constraints in actinopterygians. Other aspects, such as the high degree of endoskeletal ossification, oviparity, indirect development or the establishment of other large suspension‐feeders, could have hindered the evolution of gigantism among post‐Mesozoic ray‐finned fish groups. From this perspective, the evolution of anatomical innovations that allowed the transition towards a suspension‐feeding lifestyle in medium‐sized pachycormiforms and the emergence of ecological opportunity during the Mesozoic are proposed as the most likely factors for promoting the acquisition of gigantism in this successful lineage of actinopterygians.

The power performance of an offshore floating wind turbine in platform pitching motion

The platform pitching motion of the Offshore Floating Wind Turbine (OFWT) introduces an additional wind profile to the rotor, which may significantly impact the power performance of the OFWT. In this paper, the power performance of an OFWT in platform pitching motion is investigated using the Free Vortex Method (FVM). Firstly, the pitching and non-pitching cases are compared. Then, the power performance of the OFWT in pitching motions with different amplitudes and frequencies is investigated at the design point (tip speed ratio λ = 7). Afterwards, the reduced frequency k is proposed to integrate the influences of the platform pitching amplitude and frequency. The power performance curves of the pitching OFWT are derived as functions of λ and k in the whole operating region. Results show that as k increases, the mean power output decreases at low λ but increases at high λ. The mean power coefficient declines with the increase of k. The power variation increases with the increases of λ and k. To make up the loss of the mean power coefficient and to mitigate the side effects resulted from the power variation, advanced control strategies and platforms with good motion performances should be developed for OFWTs.

Reliability Analysis of the ongoing 10MW Electricity Generation from Wind in Katsina State, Nigeria

Wind potential assessment for any location is an essential and primary task in any power generation study. The amount of energy produced by a turbine depends on the characteristics of both wind speed at the site under investigation and the turbines power performance curve. Improper sitting for installation of the wind turbines results in loss of huge amount of money. This work investigates the reliability potential of the ongoing 10MW electricity generation from wind in Lambar Rimi, Katsina. The project consists of 37 wind turbines with rated power of 275kW each. Five year period (2006-2010) data for wind speed at 10m height was analysed. The average wind speed and the Weibull parameters at 10m height were extrapolated to the hub height of 55m. Seven models for the power performance curve between cut in to rated speed were compared with the manufacturer’s data. The expected power output of the turbine was determined by combining wind characteristics of the location and the power outputcharacteristics of the turbine using numerical methods. The results show that each turbine is expected to generate energy of about instead of rated energy of . Monthly capacity factor for the turbine ranges from 0.10 to 0.23. This indicates that if the 10MW project is completed, it will be reliably operating in the range of 1MW to 2.3MW power plant on average which indicates that the turbine-site matching is very low.

Mind The Power Holes: Sifting Operating Points in Power-Limited Heterogeneous Multicores

Heterogeneous chip multicore processors (HCMPs) equipped with multiple voltage-frequency (V-F) operating points provide a wide spectrum of power-performance tradeoff opportunities. This work targets the performance of HCMPs under a power cap. We show that for any performance optimization technique to work under power constraints, the default set of V-F operating points in HCMPs must be first filtered based on the application’s power and performance characteristics. Attempting to find operating points of maximum performance by naively walking the default set of operating points leads the application to inefficient operating points which drain power without significant performance benefit. We call these points Power Holes (PH) . Contrary to intuition, we show that even using a power-performance curve of Pareto-optimal operating points still degrades performance significantly for the same reason. We propose PH-Sifter, a fast and scalable technique that sifts the default set of operating points and eliminates power holes. We show significant performance improvement of PH-Sifter compared to Pareto sifting for three use cases: (i) maximizing performance for a single application, (ii) maximizing system throughput for multi-programmed workloads, and (iii) maximizing performance of a system in which a fraction of the power budget is reserved for a high-priority application. Our results show performance improvements of 13, 27, and 28 percent on average that reach up to 52, 91 percent, and 2.3 $\times$ , respectively, for the three use cases.

Development of a conceptual design model of a direct ethanol fuel cell (DEFC)

Small fuel cells appear to be appealing solutions to the problem of providing portable energy sources. One promising system is the Direct Ethanol Fuel Cell (DEFC) stacks, which are modular and simple to construct and have certain attributes, such as being a compact and lightweight cell, that make it favorable for portable applications. Nevertheless, there are still many challenges for DEFC commercialization, such as water transport management, EtOH crossover and the sluggish Ethanol Oxidation Reaction (EOR) kinetics on the anode. The phenomena involved with DEFCs are complicated and include transport processes, thermochemical reactions and fluid mechanics that are hard to quantify experimentally. On the other hand, mathematical modeling is a powerful and economical tool that enables us to better understand the physical phenomena that occur during operation. In this study, a conceptual design was developed to obtain a power performance curve. The voltage and current characteristics with the proposed MEA geometry will be used as starting point for more detailed modeling and simulation studies that aim to provide a basic understanding of the internal process of the DEFC. This study is to be used as initial estimations for engineers to design and optimize the DEFC for use in portable applications.

Uncovering wind turbine properties through two-dimensional stochastic modeling of wind dynamics

Using a method for stochastic data analysis borrowed from statistical physics, we analyze synthetic data from a Markov chain model that reproduces measurements of wind speed and power production in a wind park in Portugal. We show that our analysis retrieves indeed the power performance curve, which yields the relationship between wind speed and power production, and we discuss how this procedure can be extended for extracting unknown functional relationships between pairs of physical variables in general. We also show how specific features, such as the rated speed of the wind turbine or the descriptive wind speed statistics, can be related to the equations describing the evolution of power production and wind speed at single wind turbines.

Weighted error functions in artificial neural networks for improved wind energy potential estimation

This paper presents the application of the artificial neural network (ANN) to predict long-term wind speeds of a particular site, and to estimate the annual energy production of wind turbines using the predicted wind speeds. A major finding in this study is that an ANN trained with a conventional error measure may significantly underestimate the annual energy production. An accurate prediction of the mean wind speed does not guarantee an accurate prediction of the energy production when the variance of the wind speed is underestimated. To improve the accuracy in estimating the energy production, we proposed two ANNs that are based on weighted error functions. They use the frequency of the wind speed and the power performance curve to develop the weighted form of the error function. For the site and the turbine studied in this paper, the proposed ANNs showed 8–12% improvement in predicting the annual energy production compared to the conventional ANN.

Comparative Study on Impacts of Power Curve Model on Capacity Factor Estimation of Pitch-Regulated Turbines

The amount of energy produced by a turbine depends on the characteristics of both wind speed at the site under investigation and the turbine's power performance curve. The capacity factor (CF) of a wind turbine is commonly used to estimate the turbine's average energy production. This paper investigates the effect of the accuracy of the power curve model on CF estimation. The study considers three CF models. The first CF model is based on a power curve model that underestimates the turbine output throughout the ascending segment of the power curve. To compensate for the aforementioned discrepancy, the Weibull parameters, c and k, which are used to describe wind profile, are calculated based on cubic mean wind speed (CMWS). The second CF model is based on the most accurate generic power curve model available in open literature. The third CF model is based on a new model of power performance curve which mimics the behavior of a typical pitch-regulated turbine curve. As the coefficients of this power curve model are based on a general estimation of the turbine output at different wind speeds, they can be further tuned to provide a more accurate fit with turbine data from a certain manufacturer.

Wind energy potential assessment considering the uncertainties due to limited data

A new Bayesian approach is proposed to estimate the annual energy production (AEP) of a site where construction of wind turbines is considered. The approach uses long-term wind speeds of a nearby weather station and short-term wind speeds near the target site. Uncertainties exist due to the limited amount of data in the target site, in addition to the inherent uncertainties in the wind speed, the air density, the surface roughness exponent, and the power performance of the turbine. The proposed method systematically addresses these uncertainties and provides the distribution of the AEP. For illustration, we used the wind speed data near Yeosu, Korea, and the power performance curve of a 3MW turbine. For the site and the turbine studied, the range given by the 95% confidence interval corresponded to 8.9% of the mean AEP, and the range given by the 99% confidence interval corresponded to 11.9% of the mean AEP. Benefits of using the Bayesian approach compared to the classical statistical inference was also illustrated with the case study. The proposed approach provides a more conservative estimation considering the uncertainties due to the limited amount of data. Distributions of parameters of the prediction model are also provided, which enables a more detailed analysis of the prediction.

Optimum turbine-site matching

Abstract This paper presents a new formulation for the turbine-site matching problem, based on wind speed characteristics at any site, the power performance curve parameters of any pitch-regulated wind turbine, as well as turbine size and tower height. Wind speed at any site is characterized by the 2-parameter Weibull distribution function and the value of ground friction coefficient ( α ). The power performance curve is characterized by the cut-in, rated, and cut-out speeds and the rated power. The new Turbine-Site Matching Index ( TSMI ) is derived based on a generic formulation for Capacity Factor ( CF ), which includes the effect of turbine tower height ( h ). Using the CF as a basis for turbine-site matching produces results that are biased towards higher towers with no considerations for the associated costs. The proposed TSMI includes the effects of turbine size and tower height on the Initial Capital Cost ( ICC ) of wind turbines. The effectiveness and the applicability of the proposed TSMI are illustrated using five case studies. In general, for each turbine, there exists an optimal tower height, at which the value of the TSMI is at its maximum. The results reveal that higher tower heights are not always desirable for optimality.

New method for estimating CF of pitch-regulated wind turbines

This paper presents a new formulation for wind turbine capacity factor ( CF) estimation using wind speed characteristics at any site and the power performance curve parameters of any pitch-regulated wind turbine. Compared to the existing model, the proposed formulation is simpler and results in more accurate CF estimation. The accuracy of the proposed model is verified using measured data from an existing wind farm. Four illustrative case studies and parameter sensitivity analysis are presented to test the effectiveness of the model in turbine-site matching applications.

High speed pocketing strategy

Pocketing is most common in aerospace, die and mold machining operations. This paper presents automated selection of feed, speed, and depth and width of cuts by considering torque, power and chatter stability limits of the machine tool. The chatter stability limits are predicted by considering the structural dynamics of the machine and work material's cutting force coefficients. The torque and power performance curves of the machine are also used as limits. A wide range of spindle speeds, feeds, depth and width of cuts are processed through a genetic search algorithm. The most optimal cutting condition set, which gives the shortest machining time while respecting the chatter, torque and power constraints, is determined. The proposed pocketing strategy is experimentally validated.

Uncertainty analysis of wind energy potential assessment

This study presents a framework to assess the wind resource of a wind turbine using uncertainty analysis. Firstly, probability models are proposed for the natural variability of wind resources that include air density, mean wind velocity and associated Weibull parameters, surface roughness exponent, and error for prediction of long-term wind velocity based on the Measure–Correlate–Predict method. An empirical probability model for a power performance curve is also demonstrated. Secondly, a Monte-Carlo based numerical simulation procedure which utilizes the probability models is presented. From the numerical simulation, it is found that the present method can effectively evaluate the expected annual energy production for different averaging periods and confidence intervals. The uncertainty, which is 11% corresponding to the normalized average energy production in the present example, can be calculated by specifically considering the characteristics of the individual sources in terms of probability parameters.

Stochastic modelling of a wind turbine's power output with special respect to turbulent dynamics

A frequent challenge for wind energy applications is to grasp the impacts of turbulent wind fields properly. The wind turbine power performance curve, usually determined applying the IEC standard 61400-12, provides a functional relation between the measured wind speed u and the corresponding power output P of the turbine. But it is not sufficient to describe the actual dynamics of the power output on small time scales. Recently, we introduced an alternative method to estimate the power curve of a wind turbine based on high-frequency data. The crucial point of this method is that we first reconstruct the wind turbine's entire response dynamics that, then, yields the power curve by a fixed-point analysis. To reconstruct the power conversion dynamics of the wind turbine, we apply a dynamical systems approach, assuming that the variable P(t) follows a diffusion process. Its evolution in time is given by a Langevin equation consisting of a deterministic relaxation term and a stochastic noise term. The coefficients defininig these terms can directly be extracted from the given data sets. On the basis of simulated data, we verified the method and showed that it is more accurate than the standard method. For measured data we reconstructed the deterministic dynamics of a representative wind turbine and estimated the corresponding power characteristics to demonstrate the application of the method. The split of the dynamics into a deterministic and a stochastic part allows to distinguish the actual behaviour of the wind turbine, i.e. relaxation and control effects, from the turbulent effects of the wind. We gain an understanding of something like the turbulent dynamics of wind energy conversion and obtain a method to describe the actual fluctuations in power output.

Influence of Atmospheric Stability on Wind Turbine Power Performance Curves

The impact of atmospheric stability on vertical wind profiles is reviewed and the implications for power performance testing and site evaluation are investigated. Velocity, temperature, and turbulence intensity profiles are generated using the model presented by Sumner and Masson. This technique couples Monin-Obukhov similarity theory with an algebraic turbulence equation derived from the k-ϵ turbulence model to resolve atmospheric parameters u*, L, T*, and z0. The resulting system of nonlinear equations is solved with a Newton-Raphson algorithm. The disk-averaged wind speed u¯disk is then evaluated by numerically integrating the resulting velocity profile over the swept area of the rotor. Power performance and annual energy production (AEP) calculations for a Vestas Windane-34 turbine from a wind farm in Delabole, England, are carried out using both disk-averaged and hub height wind speeds. Although the power curves generated with each wind speed definition show only slight differences, there is an appreciable impact on the measured maximum turbine efficiency. Furthermore, when the Weibull parameters for the site are recalculated using u¯disk, the AEP prediction using the modified parameters falls by nearly 5% compared to current methods. The IEC assumption that the hub height wind speed can be considered representative tends to underestimate maximum turbine efficiency. When this assumption is further applied to energy predictions, it appears that the tendency is to overestimate the site potential.

The power performance curve for engineering analysis of fuel cells

The power delivered by a fuel cell to an external load is controlled by the impedance of the external load. The power performance curve is a new metric that relates the power delivered to the external load to its impedance. The power delivered is 0 for both an open circuit and a short circuit (infinite and zero external impedance) and is a maximum when the external load impedance matches the internal resistance of the fuel cell. Fuel efficiency is 50% at maximum power output. Higher fuel efficiency is achieved when the load impedance is much greater than the internal resistance of the electrolyte. A simple equivalent circuit for the fuel cell consisting of a battery, diode and resistor captures the essential characteristics of a fuel cell as part of an electrical circuit and can be used to analyze of the response to changes in load. Simple circuit analysis can be employed to elucidate the power output and efficiency of large area fuel cells and fuel cell stacks. Non-uniformities in large area fuel cells create internal potential differences that drive internal currents dissipating energy. Non-uniformities in fuel cell stacks can drive low power cells into an electrolytic state, eventually leading to failure. The power performance curve simplifies analysis of control and operation of fuel cell systems.