Modeling Gaps in Hydropower Cascading System Models: A Systematic Review of Rule-Based Formulations

Abstract

The coordination of cascading hydropower systems represents a fundamental challenge in modern energy systems engineering, requiring a sophisticated balance between multi-reservoir physics, stringent environmental regulations, and dynamic market participation. As intermittent energy sources increase, the transition to high-fidelity hydropower modeling has become a core requirement for ensuring power system reliability, long-term energy resilience and affordability. This review provides a comprehensive analysis of 131 seminal articles through the exclusive lens of optimization-based approaches, intentionally omitting pure simulation and heuristic methods to focus on rigorous mathematical formulations. A generalized 10-equation mathematical framework is established as a formal baseline, capturing the full physical and hydraulic behavior of cascading systems, including spatiotemporal inflow routing, storage-to-elevation relationships, head-dependent power generation, and prohibited operating zones. Each article is evaluated against every equation of this Standard Model in a systematic census documenting which physical relationships are included, simplified, or omitted, providing an empirical measure of modeling fidelity across the field. Modeling simplifications are evaluated through the lens of grid reliability rather than water management performance alone. The review makes a focused technical case for mixed-integer linear programming with piecewise linear approximations as the optimal balance between physical accuracy and computational tractability, highlighting recent optimal regression techniques that minimize combinatorial overhead. Finally, a bibliometric analysis of solver usage identifies the near-absence of high-performance open-source solvers as a critical reproducibility barrier, and a promising avenue for broader adoption of high-fidelity cascading hydropower models.