Feasible eigenvalue sensitivity for large power systems

Abstract Dynamic equivalent (DE) is an important process of multi-area interconnected power systems. It allows to perform stability assessment of a specific area (area of interest) at minimum cost. This study is intended to investigate the dynamic equivalent of two relatively large power systems. The fourth-order model of synchronous generators with a simplified excitation system is used as equivalent to the group of generators in the external system. To improve the accuracy of the estimated model, the identification is carried in two stages. First, using the global search Sine Cosine Algorithm (SCA) to find a starting set values, then this set is used as starting point for the fine-tuning made through the Pattern Search (PS) algorithm. To increase the reliability of the model’s parameters, two disturbances are used to avoid the identification based on a specific event. The developed program is applied on two standard power systems, namely, the New England (NE) system and the Northeast Power Coordinating Council (NPCC) system. Simulation results confirm the ability of the optimized model to preserve the main dynamic properties of the original system with accuracy.

Download Full-text

Total variation as a metric for complementarity in energy resources time series

10.36227/techrxiv.14850258.v1 ◽

2021 ◽

Author(s):

Diana Cantor ◽

Andrés Ochoa ◽

Oscar Mesa

Keyword(s):

Time Series ◽

Power Systems ◽

Total Variation ◽

Correlation Coefficients ◽

Mathematical Concept ◽

Large Power ◽

Electric System ◽

Geographical Scale ◽

Auto Regressive ◽

High Degree

Complementarity has become an essential concept in energy supply systems. Although there are some other metrics, most studies use correlation coefficients to quantify complementarity. The standard interpretation is that a high negative correlation indicates a high degree of complementarity. However, we show that the correlation is not an entirely satisfactory measure of complementarity. As an alternative, we propose a new index based on the mathematical concept of the total variation. For two time series, the new index φ is one minus the ratio of the total variation of the sum to the sum of the two series' total variation. We apply the index first to an auto-regressive (AR) process and then to various Colombian electric system series. The AR case clearly illustrates the limitations of the correlation coefficient as a measure of complementarity. We then evaluate complementarity across various space-time scales in the Colombian power sectors, considering hydro and wind projects. The complementarity assessment on a broad temporal and geographical scale helps analyze large power systems with different energy sources. The case study of the Colombian hydropower systems suggests that φ is better than ρ because (i) it considers scale, whereas ρ, being non-dimensional, is insensitive to the scale and even to the physical dimensions of the variables; (ii) one can apply φ to more than two resources; and (iii) ρ tends to overestimate complementarity.

Download Full-text