Which of the following techniques is the basic for extrapolation?

Question

Examoogle · Accepted Answer

Option B: Parabolic extrapolation

Explanation & Concepts:
Parabolic extrapolation is a fundamental technique used in load forecasting and numerical analysis to predict future values based on a quadratic curve fit. It assumes that the relationship between variables follows a second-degree polynomial, providing a better fit for non-linear load growth patterns compared to linear models.

Working Principle: The technique works by fitting a parabola of the form $y = a + bx + cx^2$ to the existing data points using the method of least squares. By solving for the constants $a$, $b$, and $c$, the model can extend the curve beyond the observed data range to forecast future trends. It is more flexible than linear extrapolation because it captures the curvature (acceleration or deceleration) of the load demand growth.

Key Formulas: $y = a + bx + cx^2$ — Standard quadratic equation for parabolic trend fitting; $E = \sum (y_i - (a + bx_i + cx_i^2))^2$ — Least squares error function to be minimized

Key Points: Parabolic extrapolation is used when load growth is non-linear.; It requires at least three historical data points to determine the coefficients $a$, $b$, and $c$.; Effective for short-to-medium term forecasting in power systems.; Higher-order polynomials can lead to Runge's phenomenon if overfitted.

Advantages: Better accuracy than linear models for curved trends; Captures acceleration in demand growth

Disadvantages: Prone to errors if extrapolated too far into the future; Sensitive to outliers in historical data

Applications: Short-term peak load forecasting; Trend analysis in utility planning

Additional Info: Extrapolation is inherently risky because it assumes that the past trend will continue indefinitely into the future, ignoring exogenous shifts.. Option A and C are specific models that do not serve as the foundational category for general polynomial extrapolation techniques.

Answer: B is correct — Parabolic extrapolation provides a second-degree polynomial model that serves as the foundation for fitting non-linear trend curves in load forecasting.

Exam Tip: Always remember that in electrical load forecasting, parabolic models provide a superior fit to rapid growth phases compared to linear models, but they should be used cautiously to avoid unrealistic future projections.

Examoogle · Answer

Option A: Square extrapolation

Examoogle · Answer

Option C: Exponential extrapolation

Examoogle · Answer

Option D: None of the above

Correct Answer

Discussion (0)

Correct Answer

Related Questions

Discussion (0)