Data-Driven Continuous-Time Framework for Frequency-Constrained Unit Commitment

The conventional approach to solving the unit commitment problem involves discrete intervals at an hourly scale, particularly when integrating frequency dynamics to formulate a frequency-constrained unit commitment. To overcome this limitation, a novel continuous-time frequency-constrained unit commitment framework is proposed in this paper. In this approach, Bernstein polynomials represent continuous variables in the unit commitment problem and enable the calculation of frequency response-related metrics such as the rate of change of frequency, quasi-steady-state frequency, and frequency nadir. Notably, startup and shut-down trajectories are meticulously considered, transforming the formulation into a fully continuous-time model and simplifying constraints related to variable continuity. To address the complexities associated with integrating the obtained non-linear frequency nadir constraint into a mixed-integer linear problem, an alternative data-driven frequency nadir constraint is proposed, which accurately constrains frequency nadir deviations throughout the time interval. To validate the proposed model, it is applied to the real-life network of the Spanish Island of La Palma. The results demonstrate the effectiveness of the proposed formulation, indicating that the model is solved timely while mitigating the impact of intra-hour real-time power fluctuations on system frequency

Unit commitment with analytical underfrequency load-shedding constraints for island power systems

This letter presents a corrective frequency-constrained UC (C-FCUC) for island power systems implementing analytical constraints on underfrequency load shedding (UFLS). Since UFLS is inevitable for sufficiently large disturbances, one can argue that less spinning reserve could be held back since UFLS takes place anyway. Congruently, the reserve criterion should consider UFLS likely to occur under disturbances. The C-FCUC can be converted into a preventive frequency-constrained UC (P-FCUC) or the standard unit commitment (UC) and the C-FCUC is thus a generalization. The proposed formulation is successfully applied to a Spanish island power system

Data-driven Estimation of Under Frequency Load Shedding after Outages in Small Power Systems

This paper presents a data-driven methodology for estimating Under Frequency Load Shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic System Frequency Response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine Learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a Mixed Integer Linear Programming (MILP) problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the Mean Absolute Error (MAE) as small as 0.213 MW for the whole process, with a model that is representable as a MILP for use in scheduling problems such as unit commitment among others

Multiobjective Congestion Management and Transmission Switching Ensuring System Reliability

Congestion in transmission lines is an important topic in power systems and it continues to be an area of active research. Various approaches have been proposed to mitigate congestion especially immediate ready ones such as Congestion Management (CM) and Transmission Switching (TS). Using either of the two or their combination (CMTS) may have undesirable consequences like increasing operational costs or increasing the number of switching of transmission lines. More switching aggravates system reliability and imposes extra costs on the operator. In this paper, a multi-objective model is introduced which reduces overall operation costs, the number of switching in transmission lines, and the congestion of lines, compared to available approaches which employ congestion management and TS simultaneously. To verify the performance of the proposed model, it is implemented using GAMS and tested on 6- and 118- bus IEEE test systems. A benders' decomposition approach was employed.© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.fi=vertaisarvioitu|en=peerReviewed

Security-constrained unit commitment problem with transmission switching reliability and dynamic thermal line rating

In security-constrained unit commitment (SCUC) problems, one approach to decrease operation costs is using a transmission switching (TS) tool. In SCUC problems with TS, one of the main challenges is that there is no limitation for the number of switching of circuit breakers (CB) in the system. In this article, the reliability of CB is merged into the SCUC problem with the TS and is considered as a limiting factor for switching. With a more reliable CB, the overall reliability of the system will be increased. So, it can be concluded that the reliability of a CB affects the amount of load shedding. Reliability of a CB is a nonlinear equation based on the number of switching in a period. An approach is presented to linearize the switch reliability equation. In this article, the power flow model uses an improved linear ac optimal power flow and a dynamic thermal line rating (DTLR) model, which considers the weather conditions. Other than CB reliability, DTLR in SCUC problems affects the number of switching and, as a result, operation costs will be significantly decreased. The proposed model is empowered by Bender's decomposition and is tested on 6-bus and 118-bus IEEE test systems.fi=vertaisarvioitu|en=peerReviewed

Data-driven estimation of the amount of under frequency load shedding in small power systems

This paper presents a data-driven methodology for estimating under frequency load shedding (UFLS) in small power systems. UFLS plays a vital role in maintaining system stability by shedding load when the frequency drops below a specified threshold following loss of generation. Using a dynamic system frequency response (SFR) model we generate different values of UFLS (i.e., labels) predicated on a set of carefully selected operating conditions (i.e., features). Machine learning (ML) algorithms are then applied to learn the relationship between chosen features and the UFLS labels. A novel regression tree and the Tobit model are suggested for this purpose and we show how the resulting non-linear model can be directly incorporated into a MILP problem. The trained model can be used to estimate UFLS in security-constrained operational planning problems, improving frequency response, optimizing reserve allocation, and reducing costs. The methodology is applied to the La Palma island power system, demonstrating its accuracy and effectiveness. The results confirm that the amount of UFLS can be estimated with the mean absolute error (MAE) as small as 0.213 megawatts for the whole process, with a model that is representable as a mixed integer linear programming (MILP) for use in scheduling problems such as unit commitment among others

Liquid Air Energy Storage Model for Scheduling Purposes in Island Power Systems

Moving towards clean energy generation seems essential. To do so, renewable energy penetration is growing in the power systems. Although energy sources such as wind and solar are clean, they are not available consistently. Using energy storage will help to tackle variability. Liquid air energy storage is gaining attention among different energy storage technologies, as it is a promising option for grid-scale energy storage. This paper presents a detailed mixed integer linear model of liquid air energy storage to be used in scheduling and planning problems. A comprehensive cycle diagram of different processes of liquid air energy storage is presented, and a model has been developed accordingly. Simulations of the proposed model are carried out for the power system of Tenerife island and compared with the basic models. Basic models overlook specific characteristics of liquid air energy storage systems, such as charging and discharging start energy. Results confirm that the use of simple models will lead to misleading conclusions and overestimate the economic benefits of liquid air energy storage