Browsing by Subject "Chance constraint"

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Open Access
A chance constrained approach to optimal sizing of renewable energy systems with pumped hydro energy storage
(2022-08) Kalkan, Nazlı
Burning fossil fuels is responsible for a large portion of the greenhouse gases released into the atmosphere. In addition to their negative impacts on the environment, fossil fuels are limited, which makes the integration of renewable energy sources into the grid inevitable. However, the intermittent nature of renewable energy sources makes it challenging to regulate energy output, resulting in low system flexibility. Adoption of an energy storage system, such as pumped hydro energy storage (PHES) and batteries, is necessary to fully utilize and integrate a larger proportion of variable renewable energy sources into the grid. On the other hand, in investment planning problems, satisfying the demand for certainty for even infrequently occurring events can lead to considerable cost increases. In this study, we propose a chance constrained two-stage stochastic program for designing a hybrid renewable energy system where the intermittent solar energy output is supported by a closed-loop PHES system. The aim of this study is to minimize the total investment cost while meeting the energy demand at a predetermined service level. For our computational study, we generate scenarios for solar radiation by using an Auto-Regressive Integrated Moving Average (ARIMA) based algorithm. In order to exactly solve our large scale problem, we utilize a Benders based branch and cut decomposition algorithm. We analize the efficiency of our proposed solution method by comparing the CPU times provided by the proposed algorithm and CPLEX. The findings indicate that the proposed algorithm solves the problem faster than CPLEX.
Open Access
Systemic risk measures based on value-at-risk
(2023-07) Al-Ali, Wissam
This thesis addresses the problem of computing systemic set-valued risk measures. The proposed method incorporates the clearing mechanism of the Eisenberg-Noe model, used as an aggregation function, with the value-at-risk, used as the underlying risk measure. The sample-average approximation (SAA) of the corresponding set-valued systemic risk measure can be calculated by solving a vector optimization problem. For this purpose, we propose a variation of the so-called grid algorithm in which grid points are evaluated by solving certain scalar mixed-integer programming problems, namely, the Pascoletti Serafini and norm-minimizing scalarizations. At the initialization step, we solve weighted sum scalarizations to establish a compact region for the algorithm to work on. We prove the convergence of the SAA optimal values of the scalarization problems to their respective true values. More-over, we prove the convergence of the approximated set-valued risk measure to the true set-valued risk measure in both the Wijsman and Hausdorff senses. In order to demonstrate the applicability of our findings, we construct a financial network based on the Bollob´as preferential attachment model. In addition, we model the economic disruptions using identically distributed random variables with a Pareto distribution. We conduct a comprehensive sensitivity analysis to investigate the effect of the number of scenarios, correlation coefficient, and Bollob´as network parameters on the systemic risk measure. The results highlight the minimal influence of the number of scenarios and correlation coefficient on the risk measure, demonstrating its stability and robustness, while shedding light on the profound significance of Bollob´as network parameters in determining the network dynamics and the overall level of systemic risk.