Toward sustainable and resilient power infrastructure : operation and evaluation strategies under exogenous and endogenous uncertainties

Abstract

With the proliferation of renewable energy sources (RESs), as well as ever-increasing extreme weather events (EWEs), the operation of power infrastructure nowadays have been replenished with new tasks. Beyond economical concerns, sustainability and resilience are two novel objectives that should be seriously accounted when making optimal schedules under normal and stressed conditions. However, a major obstacle in this new context is the significantly increased uncertainty caused by exogenous environments or endogenous decisions. Therefore, novel modeling and evaluation techniques capable of accurately and tractably capturing these uncertainties are necessary for mitigating the risk of suboptimal schedules and unforeseen retrospective regrets. Inspired by these considerations, this thesis will address four critical issues associated with sustainable and resilient power system operation in the presence of endogenous and exogenous uncertainties.

First, to improve the RES integration in the presence of erroneous modeling of their exogenous uncertainties, risk-based stochastic economical dispatch (ED) and unit commitment (UC) models are established, based on which a contamination-based technique (CBT) is used to analytically evaluate the robustness of the obtained dispatch strategies against inaccurate RESs distributions. By stress testing, the sensitivities of risks with regard to RESs' penetration level and system flexibility are revealed.

Second, to further incorporate the exogenous distributional uncertainty induced by data scarcity of RESs, a data-driven two-stage distributionally robust UC (TS-DRUC) model is proposed to minimize the worst-case operating cost among an ambiguity set of distributions of RESs' outputs. Non-parametric kernel density estimation (KDE) and total variation distance are combined to establish the data-driven ambiguity set. Tractable reformulation is derived through exploring its strong duality properties and solved by combining the sampling average approximation (SAA) and column \& constraint generation (C\&CG) algorithm. Furthermore, the explicit relationship between the data number and the size of ambiguity set enables the quantifiable value of data.

Third, to maximally boost power system resilience under stressed conditions such as EWEs, a novel decision-dependent distributionally robust resilience enhancement (DD-DRRE) model is proposed for active distribution systems (ADSs) by systematically modelling the endogenous uncertainty associated with contingencies under EWEs. Through developing scenario-wise decision-dependent ambiguity sets (SDD-ASs), both the endogenous uncertainty of contingencies and exogenous uncertainty of EWEs are captured. Strong duality properties and exact linearization technique are utilized to get the reformulation, which can be conveniently solved by a customized C\&CG algorithm. Additionally, potential risks induced by contingency model misspecificiation of the robust and stochastic counterparts are quantitatively revealed through two novel metrics.

Finally, to assist resilient ADNs in recovering power supply after major blackouts under stressed conditions, a two-stage stochastic decision-dependent service restoration (SDDSR) model is constructed. The endogenous uncertainty residing in the cold load pickup (CLPU) phenomenon is captured by the mixture distribution technique. To leverage the computational burdens introduced by mixed-integer recourse, the progressive hedging algorithm (PHA) is utilized to decompose the original model into scenario-wise subproblems that can be solved in parallel. The numerical test verifies the efficiency of our proposed SDDSR model and provided fresh insights into the monetary and secure values of quantifying the endogenous uncertainties.