[Paper Review] A Non-Intrusive Low-Rank Approximation Method for Assessing the Probabilistic Available Transfer Capability

Hao Sheng, Xiaozhe Wang|arXiv (Cornell University)|Oct 18, 2018

Power System Reliability and Maintenance25 references4 citations

TL;DR

This paper proposes a non-intrusive low-rank approximation (LRA) method to efficiently and accurately assess the probabilistic available transfer capability (PATC) in transmission systems with renewable energy uncertainties. By leveraging polynomial chaos expansion and sparse LRA, the method reduces computational cost by ~95% compared to Latin hypercube sampling Monte Carlo simulations while maintaining high accuracy in estimating PATC mean, variance, and CDF for TRM and ATC determination.

ABSTRACT

In this paper, a mathematical formulation of the probabilistic available transfer capability (PATC) problem is proposed to incorporate uncertainties from the large-scale renewable energy generation (e.g., wind farms and solar PV power plants). Moreover, a novel non-intrusive low-rank approximation (LRA) is developed to assess PATC, which can accurately and efficiently estimate the probabilistic characteristics (e.g., mean, variance, probability density function (PDF)) of the PATC. Numerical studies on the IEEE 24-bus reliability test system (RTS) and IEEE 118-bus system show that the proposed method can achieve accurate estimations for the probabilistic characteristics of the PATC with much less computational effort compared to the Latin hypercube sampling (LHS)-based Monte Carlo simulations (MCS). The proposed LRA-PATC method offers an efficient and effective way to determine the available transfer capability so as to fully utilize the transmission assets while maintaining the security of the grid.

Motivation & Objective

• To develop a computationally efficient method for assessing probabilistic available transfer capability (PATC) under uncertainties from large-scale renewable energy sources and stochastic loads.
• To incorporate probabilistic uncertainties from wind and solar generation into the ATC calculation framework using a mathematically rigorous formulation.
• To enable accurate estimation of PATC statistics (mean, variance, PDF, CDF) for reliable TRM and ATC determination without relying on high-cost Monte Carlo simulations.
• To provide a scalable and non-intrusive alternative to traditional sampling and meta-modeling methods for transmission security and market operation planning.

Proposed method

• Formulates PATC as a stochastic response using polynomial chaos expansion (PCE) to represent the system's transfer capability under uncertain renewable generation and load inputs.
• Applies a non-intrusive low-rank approximation (LRA) technique to construct a sparse, statistically equivalent representation of the PATC response using only a small number of system simulations.
• Employs the Nataf transformation and copula-based dependence modeling to accurately capture the statistical dependence between correlated renewable and load inputs.
• Uses continuation power flow (CPF) as the underlying ATC solver to compute deterministic PATC values for each sample in the stochastic collocation framework.
• Constructs low-rank approximations of the PATC response by identifying dominant rank-one components with high-degree polynomials, minimizing the number of required simulations.
• Derives the mean, variance, and cumulative distribution function (CDF) of PATC from the LRA coefficients to enable TRM and ATC calculation under different confidence levels.

Experimental results

Research questions

• RQ1 How can the probabilistic available transfer capability (PATC) be accurately formulated when incorporating uncertainties from wind and solar generation and stochastic loads?
• RQ2 Can a non-intrusive low-rank approximation (LRA) method achieve high accuracy in estimating PATC statistics with significantly reduced computational cost compared to Monte Carlo simulation?
• RQ3 What is the impact of input dependence modeling (via copulas and Nataf transformation) on the accuracy of PATC estimation under correlated renewable and load uncertainties?
• RQ4 How does the proposed LRA-PATC method compare in accuracy and efficiency to established methods such as Latin hypercube sampling (LHS) Monte Carlo and sparse PCE?
• RQ5 To what extent can the LRA method reduce the number of required power flow simulations while preserving the fidelity of PATC statistics for TRM and ATC determination?

Key findings

• On the IEEE 24-bus system, the LRA method achieved a mean PATC of 61.8815 MW and standard deviation of 21.1497 MW at 95% confidence, with only 556 simulations required—compared to 10,000 for LHS-based MCS.
• The LRA method reduced computational time to 480 seconds, achieving ~95% speedup (1/19th of MCS time) while maintaining high accuracy in PATC statistics estimation.
• On the IEEE 118-bus system, the LRA estimated PATC mean as 23.7550 MW and standard deviation as 4.8617 MW, closely matching the MCS result of 23.9278 MW and 4.8779 MW, respectively.
• The LRA method achieved a relative error of only -0.722% in mean estimation and -0.3327% in standard deviation compared to MCS, demonstrating high accuracy with minimal computational overhead.
• For a 95% confidence level, the LRA method determined an ATC of 61.8815 MW on the 24-bus system, with TRM set at 21.1497 MW, enabling secure and efficient transmission utilization.
• The method enables system operators to determine confidence-based TRM and ATC values efficiently, supporting secure and reliable transmission planning under renewable integration.