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- All Subjects: Electric power systems--Mathematical models.
- Creators: Lei, Qin
Description
Recently, a novel non-iterative power flow (PF) method known as the Holomorphic Embedding Method (HEM) was applied to the power-flow problem. Its superiority over other traditional iterative methods such as Gauss-Seidel (GS), Newton-Raphson (NR), Fast Decoupled Load Flow (FDLF) and their variants is that it is theoretically guaranteed to find the operable solution, if one exists, and will unequivocally signal if no solution exists. However, while theoretical convergence is guaranteed by Stahl’s theorem, numerical convergence is not. Numerically, the HEM may require extended precision to converge, especially for heavily-loaded and ill-conditioned power system models.
In light of the advantages and disadvantages of the HEM, this report focuses on three topics:
1. Exploring the effect of double and extended precision on the performance of HEM,
2. Investigating the performance of different embedding formulations of HEM, and
3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements.
The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance.
A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems.
The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.
In light of the advantages and disadvantages of the HEM, this report focuses on three topics:
1. Exploring the effect of double and extended precision on the performance of HEM,
2. Investigating the performance of different embedding formulations of HEM, and
3. Estimating the saddle-node bifurcation point (SNBP) from HEM-based Thévenin-like networks using pseudo-measurements.
The HEM algorithm consists of three distinct procedures that might accumulate roundoff error and cause precision loss during the calculations: the matrix equation solution calculation, the power series inversion calculation and the Padé approximant calculation. Numerical experiments have been performed to investigate which aspect of the HEM algorithm causes the most precision loss and needs extended precision. It is shown that extended precision must be used for the entire algorithm to improve numerical performance.
A comparison of two common embedding formulations, a scalable formulation and a non-scalable formulation, is conducted and it is shown that these two formulations could have extremely different numerical properties on some power systems.
The application of HEM to the SNBP estimation using local-measurements is explored. The maximum power transfer theorem (MPTT) obtained for nonlinear Thévenin-like networks is validated with high precision. Different numerical methods based on MPTT are investigated. Numerical results show that the MPTT method works reasonably well for weak buses in the system. The roots method, as an alternative, is also studied. It is shown to be less effective than the MPTT method but the roots of the Padé approximant can be used as a research tool for determining the effects of noisy measurements on the accuracy of SNBP prediction.
ContributorsLi, Qirui (Author) / Tylavsky, Daniel (Thesis advisor) / Lei, Qin (Committee member) / Weng, Yang (Committee member) / Arizona State University (Publisher)
Created2018
Description
Over the years, the growing penetration of renewable energy into the electricity market has resulted in a significant change in the electricity market price. This change makes the existing forecasting method prone to error, decreasing the economic benefits. Hence, more precise forecasting methods need to be developed. This paper starts with a survey and benchmark of existing machine learning approaches for forecasting the real-time market (RTM) price. While these methods provide sufficient modeling capability via supervised learning, their accuracy is still limited due to the single data source, e.g., historical price information only. In this paper, a novel two-stage supervised learning approach is proposed by diversifying the data sources such as highly correlated power data. This idea is inspired by the recent load forecasting methods that have shown extremely well performances. Specifically, the proposed two-stage method, namely the rerouted method, learns two types of mapping rules. The first one is the mapping between the historical wind power and the historical price. The second is the forecasting rule for wind generation. Based on the two rules, we forecast the price via the forecasted generation and the first learned mapping between power and price. Additionally, we observed that it is not the more training data the better, leading to our validation steps to quantify the best training intervals for different datasets. We conduct comparisons of numerical results between existing methods and the proposed methods based on datasets from the Electric Reliability Council of Texas (ERCOT). For each machine learning step, we examine different learning methods, such as polynomial regression, support vector regression, neural network, and deep neural network. The results show that the proposed method is significantly better than existing approaches when renewables are involved.
ContributorsLuo, Shuman (Author) / Weng, Yang (Thesis advisor) / Lei, Qin (Committee member) / Qin, Jiangchao (Committee member) / Arizona State University (Publisher)
Created2019