Power Curve Interpolation, What We’ve Learnt?

Slides:

Advertisements

Similar presentations

DÉJÀ VU: Graphing Linear Inequalities

Advertisements

A control polygon scheme for design of planar PH quintic spline curves Francesca Pelosi Maria Lucia Sampoli Rida T. Farouki Carla Manni Speaker:Ying.Liu.

Flexible smoothing with B-splines and Penalties or P-splines P-splines = B-splines + Penalization Applications : Generalized Linear and non linear Modelling.

Least squares CS1114

Interpolation A method of constructing a function that crosses through a discrete set of known data points. .

Objectives (BPS chapter 24)

ABSTRACT Discrete-time multi-level survival analysis is very useful in prevention research due to the longitudinal and clustered nature of the data. Implementing.

Economics 214 Lecture 7 Introduction to Functions Cont.

LINEAR REGRESSIONS: Cricket example About lines Line as a model:

1 Recent developments on sensitivity calculations Effect of combined le and me running –Is there a statistical advantage over pure le running? Discrimination.

Dr. Marco A. Arocha Aug,  “Roots” problems occur when some function f can be written in terms of one or more dependent variables x, where the.

Business Statistics - QBM117 Least squares regression.

1 (Student’s) T Distribution. 2 Z vs. T Many applications involve making conclusions about an unknown mean . Because a second unknown, , is present,

Copyright © 2006 The McGraw-Hill Companies, Inc. Permission required for reproduction or display. by Lale Yurttas, Texas A&M University Chapter 171 Least.

Linear & Non-Linear Equations & Graphs What do they look like?

Inference for regression - Simple linear regression

Handling Data and Figures of Merit Data comes in different formats time Histograms Lists But…. Can contain the same information about quality What is meant.

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Part 4 Curve Fitting.

1 f ’’(x) > 0 for all x in I f(x) concave Up Concavity Test Sec 4.3: Concavity and the Second Derivative Test the curve lies above the tangentsthe curve.

5.7 – Predicting with Linear Models  Today we will be learning how to: ◦ Determine whether a linear model is appropriate ◦ Use a linear model to make.

Section 2.2 Functions  Functions & Graphs  Function Notation & Equations  Applications: Interpolation & Extrapolation 12.2.

NWS Calibration Workshop, LMRFC March, 2009 Slide 1 Analysis of Evaporation Basic Calibration Workshop March 10-13, 2009 LMRFC.

Curve-Fitting Regression

3.2 Least Squares Regression Line. Regression Line Describes how a response variable changes as an explanatory variable changes Formula sheet: Calculator.

Lecture 8 Simple Linear Regression (cont.). Section Objectives: Statistical model for linear regression Data for simple linear regression Estimation.

Regression Regression relationship = trend + scatter

A New Theoretical Basis for Describing Low Turbulence Wind Turbine Performance Peter Stuart PCWG Meeting – 26 June 2015.

ISCG8025 Machine Learning for Intelligent Data and Information Processing Week 3 Practical Notes Application Advice *Courtesy of Associate Professor Andrew.

5.7 Predicting with Linear Models Objective : Deciding when to use a linear model Objective : Use a linear model to make a real life prediction. 1 2 A.

7-3 Line of Best Fit Objectives

A Review of Benchmarking Methods G Brown, N Parkin, and N Stuttard, ONS.

Logistic Regression Saed Sayad 1www.ismartsoft.com.

Bond Price Volatility. Price Yield Relationship Recall the earlier discussion… –Inverse relationship between Price and Yield Price Yield.

PCWG-Share-01 Initial Results PCWG Meeting Kings Langley 9 th December 2015 Peter Stuart (RES), Lee Cameron (RES), Alex Clerc (RES) & Andy Clifton (NREL),

Section 2.1 How do we measure speed?. Imagine a ball being thrown straight up in the air. –When is that ball going the fastest? –When is it going the.

Global predictors of regression fidelity A single number to characterize the overall quality of the surrogate. Equivalence measures –Coefficient of multiple.

Understanding the Power Curve Interpolation Issue Power Curve Working Group, , Hamburg Axel Albers.

PCWG-Share-01 Current Status PCWG Meeting Hamburg 10 th March 2016 Peter Stuart (RES) and Andy Clifton (NREL), on behalf of the Power Curve Working Group.

Remember the equation of a line: Basic Linear Regression As scientists, we find it an irresistible temptation to put a straight line though something that.

1. Analyzing patterns in scatterplots 2. Correlation and linearity 3. Least-squares regression line 4. Residual plots, outliers, and influential points.

Global predictors of regression fidelity A single number to characterize the overall quality of the surrogate. Equivalence measures –Coefficient of multiple.

Global predictors of regression fidelity A single number to characterize the overall quality of the surrogate. Equivalence measures –Coefficient of multiple.

PCWG Intelligence Sharing Initiative 10 August 2016 NREL, Colorado, US.

STAR Reading. Purpose Periodic progress monitoring assessment Quick and accurate estimates of reading comprehension Assessment of reading relative to.

PCWG 2016 Update 20th May 2016 Peter Stuart.

PCWG Intelligence Sharing Initiative Update

PCWG Intelligence Sharing Initiative Update 13 December 2016

The simple linear regression model and parameter estimation

Alternative Turbulence Correction Methods

PCWG Intelligence Sharing Initiative

Statistical Data Analysis - Lecture /04/03

Chapter 11: Simple Linear Regression

LSRL Least Squares Regression Line

Some examples Noughts and crosses exercise

Position vs. time graphs Review (x vs. t)

Copyright © Cengage Learning. All rights reserved.

INTERPOLATION Prof. Samuel Okolie, Prof. Yinka Adekunle & Dr

residual = observed y – predicted y residual = y - ŷ

Population and Demographic Data

Steady-State Aerodynamics Codes for HAWTs

Why/When is Taguchi Method Appropriate?

6.3 Modeling Linear Associations

Natural Language Processing on Time Series Presenter: Sara Alaee

Project Team: Mark Buehner Cecilien Charette Bin He Peter Houtekamer

Michael M. Desai, Daniel S. Fisher, Andrew W. Murray Current Biology

Lesson 2.2 Linear Regression.

DETERMINANT MATH 80 - Linear Algebra.

Statistics Time Series

Bonds and Their Valuation Supplement

Presentation transcript:

Power Curve Interpolation, What We’ve Learnt? NREL, Boulder, US 10th August 2016 Peter Stuart (RES), Daniel Marmander (NPC) & Axel Albers (Wind Guard)

PCWG-Share-01: Baseline Error, Inner vs Outer Range Version 0.5.9/10 (cubic interpolation) Version 0.5.8 (linear interpolation) What is causing these errors?

Interpolation Issue: V0.5.8 (Liner Interpolation) Linear Interpolation: v0.5.8 and earlier, improvement for individual data points but noticeable over prediction at low wind speed

Interpolation Issue: V0.5.9 (Cubic Interpolation) Cubic interpolation: introduced in v0.5.9 for PCWG-Share-01. Noticeably reduces error at low wind speed compared to linear.

Typical ‘By Wind Speed’ Signature of Interpolation Issue Normalised Mean Error (NME) by wind speed: Cubic interpolation has similar but smaller errors than linear. Zero-order has 0 error by definition Cubic and linear interpolators over estimate data at the ankle Cubic and linear interpolators under estimate data at the knee

Residual Error Main reason for residual error: Bin averages are used as interpolation points. Unfortunately the bin averages do not lie exactly on the curve when the underlying function is non-linear. Cubic (Convex) Clipped (Concave) Linear The bin average, (avg(x), avg(y)), is below the curve The bin average, (avg(x), avg(y)), is above the curve The bin average, (avg(x), avg(y)), is on the curve

What do we really need? Power Performance Context In order to conduct a power performance test we need a reference curve which can be compared to the measured curve. In this context bin averages work fine as if the reference curve is supplied as bin averages then if can be compared to a bin average measured curve (with consistently defined bins). Resource Assessment Context Ideally we want a continuous power curve which can be used with to determine the power curve for any wind speed. Note: This requirement is particularly pertinent for time series yields.

Interpolation Strategy Bin averages ≠ continuous power curve Bin Averages + Interpolation Strategy = continuous power curve Which interpolation strategy works best?

Does the continuous curve need to intersect the bin averages? Zero order Average of blue curve over bin ≠ bin average Power Curve Interpolation, Daniel Marmander (Natural Power), PCWG Present 15 March 2016.

Average of blue curve over bin = bin average Shifting the interpolation points from the bin averages can be used to minimise errors… Zero order Average of blue curve over bin = bin average Iterative procedure used to determine interpolation points which when interpolated and averaged over the bin give the bin average. Power Curve Interpolation, Daniel Marmander (Natural Power), PCWG Present 15 March 2016.

Comparison Cubic Interpolation vs Modified Method

Questions?