Interview Questions for Power Curve Analysis and Validation

A power curve in renewable energy, specifically for wind turbines, is a graphical representation of the relationship between wind speed and the power output of the turbine. Think of it like a car’s speedometer – it shows you how much power you get at different wind speeds. It’s a crucial tool for assessing turbine performance, predicting energy production, and optimizing wind farm layouts. The curve typically shows a gradual increase in power output as wind speed increases, reaching a peak (rated power) before plateauing and eventually shutting down due to safety limits at very high wind speeds.

Several key parameters significantly influence a wind turbine’s power curve. These include:

• Wind Speed: This is the primary driver, directly impacting the power generated. The curve maps power output against varying wind speeds.
• Air Density: Denser air contains more kinetic energy, leading to higher power output at the same wind speed. Temperature and pressure influence air density.
• Turbine Blade Pitch Angle: The angle of the blades affects how much energy they capture from the wind. Adjusting the pitch allows for optimized energy capture at various wind speeds, even limiting it at high wind speeds to prevent damage.
• Rotor Speed: The rotational speed of the rotor is connected to the power generated. Optimum speeds vary with wind speeds for maximum efficiency.
• Generator Efficiency: The generator’s ability to convert mechanical energy (from the rotating blades) into electrical energy influences the overall power output.
• Turbine Condition and Maintenance: A well-maintained turbine will show a power curve that aligns closely with its design specifications. Wear and tear, or component failures, can significantly alter the shape of the curve.

Validating a power curve involves comparing the predicted power output (from the theoretical or initial curve) with actual measured power output. Several methods exist:

• SCADA Data Comparison: This is the most common method. Supervisory Control and Data Acquisition (SCADA) systems continuously monitor turbine performance, providing detailed data on wind speed and power output. This data is used to generate a measured power curve which can be compared to the expected curve.
• Statistical Analysis: Techniques like regression analysis can be employed to fit a curve to the SCADA data, providing a best-fit representation of the turbine’s actual performance. This allows for a quantitative comparison with design specifications.
• Expert Review: Experienced engineers can visually inspect the measured curve against the expected one, identifying major discrepancies that may indicate issues.
• A/B Testing (for multiple turbines): If multiple turbines of the same model are available, comparing their measured power curves can highlight inconsistencies that might indicate specific issues in individual turbines.

The validation process typically involves identifying deviations, quantifying their significance, and understanding the underlying reasons for discrepancies.

Outliers in power curve data, points significantly deviating from the overall trend, require careful handling. Ignoring them can lead to inaccurate conclusions. Strategies for handling outliers include:

• Visual Inspection: First, visually inspect the data to identify outliers. This helps understand if the outlier is a true anomaly or due to data acquisition error.
• Data Cleaning: Check for data errors (e.g., sensor malfunctions, recording mistakes). Correct or remove erroneous data.
• Robust Regression Techniques: Employ regression methods less sensitive to outliers, like robust linear regression or quantile regression, which give less weight to outliers in curve fitting.
• Winsorizing or Trimming: Replace outliers with values closer to the edges of the data distribution, or remove them entirely, but only after careful justification.

It’s crucial to document the methods used for outlier handling and justify the decisions made to ensure transparency and reproducibility of the analysis.

Using a single power curve to represent turbine performance over all operating conditions is a simplification. Limitations include:

• Neglect of Environmental Factors: A single curve doesn’t account for variations in air density due to temperature and pressure, impacting power output.
• Ignoring Turbine Degradation: Turbine performance degrades over time due to wear and tear. A single curve cannot capture this temporal variation.
• Oversimplification of Complex Interactions: Turbine performance is affected by many factors beyond wind speed, like yaw misalignment, blade damage, or grid limitations. A single curve fails to represent these interactions.
• Limited Applicability to Varying Conditions: A single curve is usually created under specific conditions. Extrapolating it to vastly different conditions can be unreliable.

For more accurate performance assessment, advanced models that consider these factors are often necessary. For instance, using a family of power curves or more complex models that explicitly incorporate environmental parameters and operational conditions.

Binning in power curve analysis is the process of grouping wind speed data into intervals or ‘bins’. Instead of analyzing each individual wind speed measurement, we average power output within each wind speed bin. This process smooths the data, reducing the noise caused by random fluctuations and improving the clarity of the relationship between wind speed and power.

Imagine trying to draw a line through a scatter plot with many scattered points. Binning groups the points, making it much easier to see the overall trend and fit a meaningful power curve.

Appropriate bin size is crucial. Bins that are too narrow might retain too much noise, while bins that are too wide might obscure important variations in the power curve.

Environmental factors, primarily temperature and pressure, significantly influence air density, directly impacting wind turbine power output. To account for these factors in power curve analysis:

• Data Correction: Use standard meteorological formulas to correct measured wind speeds and power outputs to standard conditions (e.g., 15°C and 1013.25 hPa). This ensures that data from different days/times with varying weather conditions can be directly compared.
• Density Correction Factor: Incorporate a density correction factor into the power curve calculations. This factor adjusts the power output based on the deviation of air density from the standard value.
• Advanced Modeling: Use more advanced statistical models that explicitly incorporate temperature and pressure as independent variables, enabling a more nuanced understanding of their effects on power production. These models can help separate the impact of these environmental factors from turbine performance itself.

Accurate accounting for environmental factors is essential for unbiased evaluation of turbine performance and for accurate predictions of energy yield.

Power curve validation relies on various statistical methods to assess the accuracy and reliability of the measured power output of a wind turbine or other energy generation system across a range of wind speeds. These methods help quantify uncertainty and identify potential biases.

• Regression Analysis: This is the most common method. We typically use least-squares regression to fit a curve (often a parametric curve like a Weibull or a piecewise linear function) to the measured data points. The goodness-of-fit is assessed using metrics like R-squared, which indicates how well the model explains the variation in the data. A high R-squared suggests a good fit.

• Uncertainty Quantification: We use methods like bootstrapping or Monte Carlo simulations to estimate the uncertainty associated with the power curve parameters. These methods involve resampling the data and refitting the curve multiple times to obtain a distribution of parameter estimates. The spread of this distribution quantifies the uncertainty.

• Statistical Hypothesis Testing: We can use hypothesis tests to compare the validated power curve to a reference curve (e.g., the manufacturer’s curve) to determine if there are statistically significant differences. Tests like t-tests or ANOVA (Analysis of Variance) can be used for this purpose.

• Residual Analysis: We examine the residuals (the differences between the measured data and the fitted curve) to check for patterns or outliers. Patterns in the residuals might indicate systematic errors in the measurements or an inappropriate choice of curve fitting function. Outliers need investigation for potential measurement errors.

Several factors can introduce errors into power curve measurements. These errors can be categorized into measurement errors and systematic errors.

• Measurement Errors: These are random errors that arise from the limitations of the measurement instruments. For example, inaccuracies in anemometer readings (wind speed measurement) and power meter readings can lead to scatter in the data. These are often addressed by using high-quality instruments and averaging multiple readings.

• Systematic Errors: These are consistent, non-random errors that can bias the results. Examples include:

  • Calibration Issues: Incorrect calibration of anemometers or power meters will lead to consistent overestimation or underestimation of power output and wind speed.

  • Data Acquisition Problems: Issues with data logging or data transmission can result in missing data or erroneous data points.

  • Environmental Factors: Air density variations, turbulence, and shear (change in wind speed with height) can affect the accuracy of measurements. For example, higher turbulence can make wind speed measurements less reliable and influence the power output at given wind speed.

  • Turbine Condition: Mechanical issues or degradation in the turbine’s components can systematically reduce its power output at all wind speeds. We account for this by considering the turbine’s operational history.

Assessing the accuracy and uncertainty of a power curve is crucial for reliable performance assessment. We use a combination of approaches:

• Goodness-of-fit statistics (e.g., R-squared): As mentioned earlier, a high R-squared value from regression analysis indicates a good fit. However, a high R-squared alone isn’t sufficient; we must also examine the residuals.

• Residual Analysis: Plotting residuals against wind speed and fitted power helps identify patterns indicating model inadequacy or systematic errors.

• Uncertainty Quantification: Confidence intervals or prediction intervals around the fitted power curve are crucial. These intervals reflect the uncertainty in the power curve estimate at specific wind speeds.

• Comparison to Reference Curves: If a manufacturer’s or previously validated power curve is available, we can compare our measured curve against it using statistical hypothesis tests. This helps determine if there’s a statistically significant difference.

• Cross-validation: We can divide the data into training and validation sets. The power curve is fit to the training set and then evaluated on the independent validation set. This approach helps prevent overfitting.

By combining these methods, we can obtain a comprehensive understanding of the power curve’s accuracy and uncertainty, along with identifying potential sources of error.

While both power curves and performance curves describe the output of a wind turbine or energy system, there’s a key difference:

• Power Curve: This depicts the relationship between the wind speed and the *electrical power* output of a wind turbine. It’s a fundamental characteristic of the turbine under ideal conditions, typically representing the maximum power it can generate at each wind speed.

• Performance Curve: This is a broader term that represents the relationship between wind speed and *actual power* output, considering all factors impacting performance including availability, curtailment (deliberate reduction in power), and losses. The performance curve can be viewed as the power curve ‘in action’ in a real-world setting. It typically incorporates operational data over longer periods.

In essence, the power curve is an idealized representation, while the performance curve is a real-world representation.

The shape of a power curve provides valuable insights into the turbine’s performance. A typical power curve starts at zero power at low wind speeds (cut-in speed), increases steadily to a maximum power output at rated wind speed, and then plateaus or slightly decreases (due to power limitations or protection mechanisms) as wind speed increases beyond the rated speed (until the cut-out speed is reached).

• Deviations from this ideal shape can indicate problems: A consistently lower output at all wind speeds suggests general turbine degradation, while a dip in power at a specific wind speed could suggest a mechanical issue or control system problem at that speed.

• The slope of the curve at different wind speeds reflects the turbine’s efficiency at those speeds: A steeper slope implies better energy capture.

• The cut-in and cut-out speeds define the operational range of the turbine: These points are important for operational planning and safety.

By carefully analyzing the shape of the power curve and its parameters, we can diagnose potential issues and optimize turbine performance.

I’m proficient in several software tools and programming languages commonly used for power curve analysis:

• MATLAB: This is a powerful tool for data analysis, statistical modeling, and curve fitting. I utilize its curve-fitting toolbox and statistical functions extensively for regression analysis, uncertainty quantification, and residual analysis.

• Python (with libraries like Pandas, NumPy, SciPy, and Matplotlib): Python provides a flexible and versatile environment for data manipulation, statistical analysis, and visualization. I’ve used these libraries to process large datasets, perform regression, and create visualizations of power curves and residuals.

• R (with packages like ggplot2 and lmtest): R is another widely used statistical software package. I have experience using it for statistical modeling, hypothesis testing, and creating publication-quality graphics of power curves.

• Specialized Wind Energy Software Packages: I have familiarity with commercial software packages specifically designed for wind turbine data analysis, such as those offered by some wind turbine manufacturers or independent consulting firms. These often provide specialized tools for power curve analysis and performance assessment.

SCADA (Supervisory Control and Data Acquisition) systems are essential sources of data for power curve analysis. My experience involves:

• Data Extraction and Preprocessing: I’m experienced in extracting relevant data (wind speed, power output, etc.) from SCADA systems, often using database query tools or APIs. Preprocessing steps include handling missing data, identifying and correcting outliers, and ensuring data quality.

• Data Cleaning and Validation: This critical step involves identifying and addressing inconsistencies or errors in SCADA data before performing power curve analysis. This might involve removing data during periods of turbine maintenance or anomalous operation.

• Data Analysis and Modeling: Once the data is clean, I use statistical methods and software tools (as described in previous answers) to analyze the data, fit power curves, and assess their accuracy and uncertainty. This includes considering the impact of environmental conditions on power output.

• Reporting and Visualization: I generate reports and visualizations (e.g., power curves, residual plots, uncertainty bands) to communicate the results of the power curve analysis to stakeholders. This includes interpreting the findings and making recommendations for improving turbine operation or maintenance.

I’ve worked with various SCADA systems from different manufacturers, adapting my approach as needed to ensure compatibility and data quality.

Inconsistencies in power curve data can stem from various sources, including faulty sensors, data logging errors, or even environmental factors like unexpected turbulence. Identifying these inconsistencies requires a multi-pronged approach.

• Visual Inspection: Start by plotting the raw data. Look for outliers – data points significantly deviating from the general trend. These might be single points or clusters. A simple scatter plot of wind speed vs. power output is a good starting point.
• Statistical Analysis: Employ statistical methods to detect anomalies. Techniques like box plots can highlight outliers, while moving averages can smooth out random noise and reveal underlying trends. Consider using robust statistical methods less sensitive to outliers.
• Data Cleaning: Once inconsistencies are identified, you need to decide how to address them. Outliers might be removed if they’re clearly due to errors. Alternatively, you could replace them with interpolated values or use techniques like Winsorization (capping outliers at a certain percentile).
• Root Cause Analysis: It’s crucial to understand *why* the inconsistencies occurred. Was there a sensor malfunction? Was there an unusual weather event? Addressing the root cause prevents future errors.

For example, I once worked on a project where a sudden drop in power output was initially attributed to a turbine malfunction. However, further investigation revealed a temporary data acquisition system failure, causing the drop in the data log. Careful investigation prevented costly and unnecessary maintenance.

An inaccurate power curve has significant implications for energy yield estimations, potentially leading to substantial financial consequences.

• Overestimation/Underestimation of Production: An inaccurate curve can lead to either overestimating or underestimating the energy a wind farm or turbine is expected to generate. Overestimation leads to unrealistic project financial models and potential investor disappointment. Underestimation can lead to missed revenue opportunities.
• Impact on Asset Valuation: Accurate power curves are crucial for assessing the value of wind energy assets. Inaccurate curves skew asset valuations, making it difficult to make sound investment decisions.
• Suboptimal Operations and Maintenance: Inaccurate power curves can result in inadequate or unnecessary maintenance actions. If the curve shows lower performance than expected, this might prompt unnecessary investigations or repairs, leading to unnecessary costs. Conversely, a falsely optimistic curve might delay necessary maintenance, leading to increased downtime and repair costs.
• Incorrect Capacity Factor Calculations: The capacity factor, a key performance indicator representing the actual output relative to the maximum possible output, is directly impacted by the accuracy of the power curve. An inaccurate power curve translates into an inaccurate capacity factor, making it difficult to assess the true performance of the turbine or wind farm.

Imagine a scenario where a power curve significantly underestimates the true output. This could mean millions of dollars in lost revenue over the lifetime of a wind farm.

Power curve analysis plays a vital role in wind turbine asset management. It provides a fundamental understanding of the turbine’s performance and allows for proactive maintenance and optimization strategies.

• Performance Monitoring: Regular power curve analysis allows for continuous monitoring of turbine performance against expected values. Deviations from the baseline curve can indicate developing problems like blade damage, gearbox issues, or generator faults.
• Predictive Maintenance: By tracking changes in the power curve over time, asset managers can predict potential failures and schedule preventive maintenance, reducing downtime and repair costs. For example, a gradual decrease in power output at higher wind speeds could indicate blade degradation.
• Optimization: Analyzing the power curve helps identify areas for optimization. For example, if the curve shows suboptimal performance at specific wind speeds, adjustments to the turbine’s control system might improve efficiency.
• Financial Planning: Accurate power curves are essential for accurate forecasting of energy production and revenue streams, enabling better financial planning and investment decisions.

In essence, the power curve serves as a health indicator for wind turbines, allowing asset managers to make data-driven decisions to maximize efficiency and minimize costs.

Determining the optimal bin size for power curve analysis involves balancing the need for sufficient data points in each bin with the desire to capture the detailed shape of the power curve. Too few data points per bin increase uncertainty and might obscure trends, while too many bins can lead to a noisy curve and reduce the statistical significance.

• Data Availability: Start by considering the amount of data available. More data allows for smaller bin sizes.
• Wind Speed Distribution: Consider the distribution of wind speeds. If wind speeds are clustered around certain values, you might need smaller bins in those regions.
• Iteration and Evaluation: Begin with a reasonable bin size and iteratively adjust it, evaluating the resulting curve’s smoothness and statistical significance. Tools like regression analysis can aid in assessing the fit.
• Statistical Considerations: Ensure enough data points within each bin to obtain reliable average power outputs. A common rule of thumb is to aim for at least 30 data points per bin, but this can vary based on data quality and analysis goals.

I often use an iterative approach, starting with a relatively large bin size and progressively reducing it until I observe a reasonable balance between curve detail and statistical robustness. Visual inspection and statistical measures such as the standard error of the mean for each bin are useful tools in this process.

Several Key Performance Indicators (KPIs) are used to evaluate a power curve. These provide a quantitative assessment of the turbine’s performance.

• R-squared (R²): This statistical measure indicates the goodness of fit of the regression model used to represent the power curve. A higher R² suggests a better fit, indicating that the model accurately reflects the relationship between wind speed and power output.
• Root Mean Square Error (RMSE): RMSE quantifies the difference between the actual power output and the values predicted by the power curve model. A lower RMSE indicates better accuracy.
• Mean Absolute Error (MAE): Similar to RMSE, MAE measures the average absolute difference between actual and predicted power output. It is less sensitive to outliers compared to RMSE.
• Capacity Factor: While not directly a power curve KPI, the capacity factor calculation heavily relies on the power curve. A well-defined power curve is vital for accurate capacity factor estimation.
• Turbine Availability and Uptime: Although not directly part of the power curve itself, turbine availability and uptime are closely related. Consistent performance indicated by a well-defined power curve supports high availability.

The selection of relevant KPIs depends on the specific objectives of the analysis. For example, in a performance monitoring context, RMSE and MAE are crucial, while during model development, R² is often more important.

Missing data in power curve analysis is a common challenge. Several methods exist to handle this, each with its own advantages and limitations.

• Deletion: If the amount of missing data is small and randomly distributed, simple deletion might be acceptable. However, this is generally not recommended as it can introduce bias.
• Imputation: More sophisticated methods involve imputing missing values. This could involve using the mean, median, or mode of the available data for that wind speed bin or using more advanced methods such as k-nearest neighbors or multiple imputation.
• Interpolation: Linear or spline interpolation can be used to estimate missing values based on the surrounding data points. This approach is better than simple imputation if data shows a clear trend.
• Model-Based Imputation: If a regression model is used to fit the power curve, missing values can be predicted using the fitted model itself.

The best method depends on the nature and extent of the missing data. For instance, if missing data is concentrated in a specific wind speed range, imputation methods might introduce bias. In such cases, caution is needed, and potentially, more advanced techniques, such as model-based imputation, or even discarding data from the affected range, might be necessary.

Throughout my career, I’ve extensively worked with power curve modeling and simulation using various software packages and statistical techniques.

• Software Proficiency: I’m proficient in using software like Python (with libraries like Pandas, NumPy, Scikit-learn), MATLAB, and specialized wind energy software packages for data processing, statistical analysis, and model fitting. I’m comfortable using various regression techniques, including linear regression, polynomial regression, and spline interpolation to create power curves.
• Data Analysis and Preprocessing: My experience encompasses all aspects of power curve analysis, from initial data cleaning and quality control to the selection of appropriate statistical models and the interpretation of results. I’m adept at handling missing data, outliers, and other data irregularities.
• Model Validation and Uncertainty Quantification: I rigorously validate the developed power curves using appropriate statistical metrics and uncertainty quantification methods. This is critical for reliable energy yield estimations and decision-making.
• Real-world Applications: I have applied my expertise in various projects involving power curve analysis for performance monitoring, asset management, and financial modeling for wind farms of varying sizes and technologies.

For example, I recently worked on a project that involved developing a sophisticated power curve model that incorporated environmental factors, such as air density and temperature, improving the accuracy of energy yield predictions by 15%. This reduced the uncertainty associated with financial planning for the project significantly.

Communicating complex power curve analysis results to non-technical stakeholders requires translating technical jargon into clear, concise language, focusing on the implications rather than the methodology. I typically start with a high-level overview, using visuals like charts and graphs to illustrate key findings. For example, instead of saying ‘the power curve exhibits a significant deviation from the expected Weibull distribution,’ I’d say something like ‘the turbine’s energy production is lower than initially projected due to variations in wind conditions.’ I then break down the results into digestible chunks, focusing on the business impact. This might involve discussing potential revenue loss, the need for operational adjustments, or the implications for project financing. Finally, I always ensure there’s ample opportunity for questions and discussion to address any concerns or misunderstandings.

A good analogy would be explaining the results of a medical test. The doctor doesn’t usually explain the intricate biochemical processes; they focus on the diagnosis and treatment plan. Similarly, I focus on the actionable insights from the power curve analysis, enabling stakeholders to make informed decisions.

My experience encompasses both parametric and non-parametric power curve modeling. Parametric models, like Weibull or Beta distributions, are statistically efficient and require fewer data points. However, they rely on assumptions about the underlying distribution, which may not always be accurate. I’ve used Weibull fitting extensively, often adjusting the shape and scale parameters to optimize the fit to the measured data. This involves iterative processes and careful consideration of goodness-of-fit metrics. On the other hand, non-parametric methods, such as spline interpolation or kernel regression, are more flexible and can capture complex patterns in the data without making strong distributional assumptions. I’ve applied spline methods to datasets with unusual characteristics or where parametric models failed to capture the true nature of the power curve. The choice between parametric and non-parametric approaches depends heavily on the quality and quantity of the available data and the specific requirements of the project. A robust analysis often involves exploring both methods and comparing their performance.

Validating power curves for offshore wind turbines presents unique challenges compared to onshore installations. Firstly, data acquisition is often more expensive and logistically complex. Weather conditions in offshore environments are harsher and more variable, leading to potential data gaps and measurement errors. Secondly, the operating environment is more dynamic, with significant variations in wave height and currents influencing turbine performance. This needs to be accounted for in the validation process. Thirdly, accessibility limitations make regular maintenance and calibration of measurement equipment more difficult, potentially impacting data quality. Finally, the remote location of offshore turbines can introduce communication challenges and delays in data transmission, potentially affecting the timeliness and accuracy of the validation process. To address these challenges, we typically employ rigorous quality control procedures, use advanced data processing techniques to handle missing data and outliers, and incorporate environmental variables into the validation models.

Ensuring the quality and reliability of power curve data is paramount. This involves a multi-faceted approach starting with meticulous data acquisition planning. This includes selecting appropriate measurement sensors and ensuring their proper calibration and maintenance. Rigorous quality control procedures are implemented throughout the process, including automated checks for outliers and inconsistencies. Data cleaning techniques, such as outlier removal or interpolation, are used cautiously, with careful documentation of any adjustments. Data validation against independent sources, such as meteorological mast data, is crucial. Finally, comprehensive uncertainty quantification is conducted to assess the reliability of the estimated power curve. We use statistical methods to quantify the uncertainty associated with each data point and propagate it through the model fitting process, enabling us to establish confidence intervals around the predicted power output.

Uncertainty quantification in power curve analysis is critical for providing a realistic and reliable representation of turbine performance. Sources of uncertainty include measurement errors (sensor accuracy, calibration), environmental variability (wind speed fluctuations, air density changes, turbulence), model uncertainty (choice of model, parameter estimation), and data limitations (sample size, data gaps). I employ both frequentist and Bayesian methods to assess uncertainty. Frequentist methods, such as bootstrapping, are used to estimate confidence intervals for power curve parameters. Bayesian methods allow the incorporation of prior knowledge and subjective beliefs about the model parameters, providing a more comprehensive assessment of uncertainty. The results are typically presented as uncertainty bands around the power curve, indicating the range of possible power outputs at each wind speed. This allows stakeholders to make informed decisions by considering the range of possible outcomes rather than relying on a single, potentially misleading, point estimate.

Developing a power curve for a new wind turbine technology requires a structured approach. I would begin by defining the project scope, including the desired accuracy, the required data volume, and the time frame. The next step is to design a comprehensive measurement plan, which will specify the sensors to be used, the data acquisition frequency, and the data validation procedures. Next, we would gather data from field testing, carefully documenting all environmental conditions. This data would be rigorously quality-checked and processed. Then, different power curve models would be explored, and the best-fitting model would be selected based on statistical criteria and engineering judgment. Uncertainty quantification would be performed to assess the reliability of the developed power curve. Finally, the results, including the validated power curve and the uncertainty assessment, would be documented and presented to stakeholders.

In one project, we encountered unexpected spikes in the measured power output at low wind speeds. Initial investigation suggested sensor malfunction. However, after careful analysis of the wind data and turbine operational logs, we discovered that these spikes corresponded to periods of significant wind shear near the ground. This shear caused the anemometer to under-report the actual wind speed experienced by the turbine at hub height, leading to artificially high power outputs at low reported wind speeds. We addressed this issue by using a more sophisticated wind speed correction algorithm that accounted for the effects of wind shear. This involved using data from a nearby meteorological mast to estimate the wind shear profile and apply appropriate corrections to the anemometer readings. This ultimately led to a more accurate and reliable power curve.