Maximin and maximal solutions for linear programming problems with possibilistic uncertainty

We consider linear programming problems with uncertain constraint coefficients described by intervals or, more generally, possi-bility distributions. The uncertainty is given a behavioral interpretation using coherent lower previsions from the theory of imprecise probabilities. We give a meaning to the linear programming problems by reformulating them as decision problems under such imprecise-probabilistic uncer-tainty. We provide expressions for and illustrations of the maximin and maximal solutions of these decision problems and present computational approaches for dealing with them

Impact of high wind penetration on variability of unserved energy in power system adequacy

This paper presents results on variability of out-turn shortfalls about the expected value indices which are usually presented in resource adequacy studies, for a range of Loss of Load Expectation (LOLE) levels and installed wind capacities in a test system generally representative of future Great Britain system scenarios. While the details of results will clearly vary between systems, one very general conclusion is possible. In the results presented, for a given LOLE level, the probability of very severe out-turn in a future peak season is much greater at high installed wind capacity. Thus for this system, as the installed wind capacity increases, a constant level of LOLE cannot be taken as an indicator of an unchanging overall risk profile of the system. This further demonstrates that in any system, LOLE cannot be assumed to be a good summary statistic of risk profile as the installed variable generation (VG) capacity increases, and that it might be necessary to reconsider the near-universal use of expected value risk indices as the main headline indices in utility adequacy studies

Bayes linear analysis of imprecision in computer models, with application to understanding galaxy formation.

Imprecision arises naturally in the context of computer models and their relation to reality. An imprecise treatment of general computer models is presented, illustrated with an analysis of a complex galaxy formation simulation known as Galform. The analysis involves several different types of uncertainty, one of which (the Model Discrepancy) comes directly from expert elicitation regarding the deficiencies of the model. The Model Discrepancy is therefore treated within an Imprecise framework to reflect more accurately the beliefs of the expert concerning the discrepancy between the model and reality. Due to the conceptual complexity and computationally intensive nature of such a Bayesian imprecise uncertainty analysis, Bayes Linear Methodology is employed which requires consideration of only expectations and variances of all uncertain quantities. Therefore incorporating an Imprecise treatment within a Bayes Linear analysis is shown to be relatively straightforward. The impact of an imprecise assessment on the input space of the model is determined through the use of an Implausibility measure

Bayes Linear Analysis of Imprecision in Computer Models, with Application to Understanding Galaxy Formation

Imprecision arises naturally in the context of computer models and their relation to reality. An imprecise treatment of general computer models is presented, illustrated with an analysis of a complex galaxy formation simulation known as Galform. The analysis involves several different types of uncertainty, one of which (the Model Discrepancy) comes directly from expert elicitation regarding the deficiencies of the model. The Model Discrepancy is therefore treated within an Imprecise framework to reflect more accurately the beliefs of the expert concerning the discrepancy between the model and reality. Due to the conceptual complexity and computationally intensive nature of such a Bayesian imprecise uncertainty analysis, Bayes Linear Methodology is employed which requires consideration of only expectations and variances of all uncertain quantities. Therefore incorporating an Imprecise treatment within a Bayes Linear analysis is shown to be relatively straightforward. The impact of an imprecise assessment on the input space of the model is determined through the use of an Implausibility measure

Contingency Ranking in Power Systems via Reliability Rates

This paper shows the scope of probabilistic contingency ranking algorithms when applied to transmission systems with high levels of renewable integration. Using our fast screening contingency ranking algorithm, a performance index is calculated through AC power flows. In order to capture the probabilistic behaviour of the system outages, we use the reliability data from the Reliability Test System, and combined with the performance index this yields a different assessment on the contingency ranking task. The contingency ranking is applied in this paper for an N-1 security criterion. The entire model was developed and implemented for steady-state power system simulations using the MATPOWER programme which runs in MATLAB environment

Inclusion of Frequency Stability Constraints in Unit Commitment Using Separable Programming

In this paper we address the problem of frequency stability in the unit commitment (UC) optimisation process. We include a set of appropriately defined frequency stability constraints in the UC problem formulation for operational planning scenarios in advance of real-time operation. Consequently, we cover the system against the loss of the largest infeed under the − 1 security criterion.The main contribution of our work consists of using the method of separable programming to incorporate a linearised Frequency Nadir constraint into the UC problem. In our work, the UC problem is formulated as a mixed-integer linear program (MILP). This renders a fast convergence in the solution for a system such as the the three area IEEE RTS-96 system. Meanwhile, we have included the possibility of synthetic inertia provision from the wind farms, which helps to increase the available inertia in the system before a generation outage. The simulations are run using an extended version of MATPOWER tailored for solving UC problems (MOST) which is run in MATLAB