{'fraction_non_alphanumeric': 0.015332197614991482, 'fraction_numerical': 0.0, 'mean_word_length': 5.791907514450867, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A Linear Envelope for the Maximum Energy Storage Model of Cascade Hydropower Groups

With the rapid improvement of the utilization of hydropower resources, the optimal operation of cascade hydropower groups has been proposed and developed. The paper proposes a linear envelope for the maximum energy storage model of cascade hydropower groups, which comprises the generation of tetrahedron convex envelope of hydropower generation function, three-stage step-by-step linear processing of hydraulic head-water storage relation, deletion of invalid constraints, and the reduction of the maximum energy storage criterion under time delay approximation. The method can effectively realize convex relaxation of the cascade hydropower short-term optimal dispatch model with non-convex nonlinear characteristics, prevent the solution from falling into local optimum and improve the solving speed, thereby being beneficial to the efficient formulation of the cascade hydropower short-term dispatch plan with promising benefits. The effectiveness and the validity of the proposed model are verified using numerical examples from the Wujiang River cascaded hydropower systems in China.