[Paper Review] Nonintrusive Uncertainty Quantification of Dynamic Power Systems Subject to Stochastic Excitations

Yiwei Qiu, Jin Lin+3 more|arXiv (Cornell University)|Jan 19, 2020

Probabilistic and Robust Engineering Design31 references4 citations

TL;DR

This paper proposes a nonintrusive, efficient method for uncertainty quantification in dynamic power systems subjected to continuous-time stochastic excitations—common in renewable-integrated grids—by modeling disturbances via Itô processes and using spectral representation with polynomial chaos expansion (PCE) via adaptive sparse probabilistic collocation. The approach enables accurate, high-order statistical characterization of system responses using commercial software like PSS/E, overcoming limitations of intrusive methods and slow Monte Carlo simulations.

ABSTRACT

Continuous-time random disturbances (also called stochastic excitations) due to increasing renewable generation have an increasing impact on power system dynamics; However, except from the Monte Carlo simulation, most existing methods for quantifying this impact are intrusive, meaning they are not based on commercial simulation software and hence are difficult to use for power utility companies. To fill this gap, this paper proposes an efficient and nonintrusive method for quantifying uncertainty in dynamic power systems subject to stochastic excitations. First, the Gaussian or non-Gaussian stochastic excitations are modeled with an Itô process as stochastic differential equations. Then, the Itô process is spectrally represented by independent Gaussian random parameters, which enables the polynomial chaos expansion (PCE) of the system dynamic response to be calculated via an adaptive sparse probabilistic collocation method. Finally, the probability distribution and the high-order moments of the system dynamic response and performance index are accurately and efficiently quantified. The proposed nonintrusive method is based on commercial simulation software such as PSS/E with carefully designed input signals, which ensures ease of use for power utility companies. The proposed method is validated via case studies of IEEE 39-bus and 118-bus test systems.

Motivation & Objective

• Address the lack of efficient, nonintrusive methods for quantifying dynamic uncertainty in power systems due to continuous-time stochastic excitations from renewable generation.
• Overcome the limitations of traditional Monte Carlo simulations, which are computationally expensive for online applications.
• Develop a method that preserves nonlinearity and captures non-Gaussian uncertainty and high-order moments, unlike many existing intrusive approaches.
• Ensure compatibility with commercial power system simulation tools (e.g., PSS/E) to enhance usability for power utility companies.
• Enable accurate quantification of system dynamic response and performance index distributions using only standard simulation outputs with designed input signals.

Proposed method

• Model stochastic excitations (e.g., from renewable generation) as Itô processes using stochastic differential equations (SDEs), enabling continuous-time representation.
• Apply Karhunen-Loève expansion (KLE) to spectrally decompose the continuous-time stochastic processes into a finite set of uncorrelated random variables.
• Represent the system dynamic response using polynomial chaos expansion (PCE) in terms of these random variables, capturing nonlinearity and non-Gaussian features.
• Use an adaptive sparse probabilistic collocation method to efficiently compute the PCE coefficients, reducing computational cost in high-dimensional spaces.
• Calibrate the Itô process parameters using maximum likelihood estimation based on historical data, ensuring accurate stochastic modeling.
• Integrate the entire framework with commercial power system simulation software (e.g., PSS/E) by generating appropriate input signals, enabling nonintrusive operation without modifying internal solvers.

Experimental results

Research questions

• RQ1 How can dynamic power system uncertainty due to continuous-time stochastic excitations be quantified accurately and efficiently without modifying commercial simulation software?
• RQ2 Can a nonintrusive method preserve the non-Gaussian nature and high-order statistical moments of system responses while maintaining computational efficiency?
• RQ3 To what extent can the combination of Itô processes, KLE, and adaptive sparse PCE improve the accuracy and speed of uncertainty quantification compared to Monte Carlo or intrusive methods?
• RQ4 How well does the proposed method perform in large-scale power systems, such as the IEEE 118-bus system, under realistic stochastic excitation scenarios?
• RQ5 Can the method be calibrated effectively from real or synthetic data to ensure reliable stochastic modeling of renewable generation fluctuations?

Key findings

• The proposed method enables accurate, nonintrusive uncertainty quantification of dynamic power system responses using only standard commercial simulation software, without code modification.
• The adaptive sparse probabilistic collocation method significantly reduces computational cost compared to full tensor-based PCE, especially in high-dimensional random spaces.
• The method successfully captures non-Gaussian probability distributions and high-order moments of system responses, which are often missed by Gaussian-approximation-based methods.
• Validation on the IEEE 39-bus and 118-bus systems confirms the method's accuracy and efficiency, with results closely matching reference Monte Carlo simulations but in substantially less time.
• The Itô process modeling of stochastic excitations, calibrated via maximum likelihood estimation, provides a robust and data-driven representation of renewable generation variability.
• The spectral representation via KLE and PCE ensures that the nonlinearity of the power system dynamics is preserved, enabling precise uncertainty propagation.