Production cost models (PCMs) are widely used in the power sector to plan system operations and evaluate policy scenarios. However, their standard mathematical formulations rely on the assumption of perfectly competitive wholesale electricity markets, where generators are dispatched according to their merit order or bidding price. This assumption neglects the institutional context of regulated markets in which physical Power Purchase Agreements (PPAs) secure the bankability of renewables and constrain system operations. Oversimplifying the representation of contracts prevents models from accurately characterizing true system performance. Meanwhile, modeling systems with high renewables penetration require running numerous hydro-climate scenarios, posing a computational challenge for large-scale systems.This dissertation on power system modeling is a collection of publications and pre-prints built upon one another, covering topics of software design, mathematical formulation, solution algorithms, and applications. First, we introduce PowNet 2.0, an open-source Python framework designed for simulating large-scale systems at high temporal and spatial resolutions. In addition to its core PCM module, PowNet 2.0 includes other tools, such as synthetic time series generation to support scenario analysis and a dedicated hydropower reservoir simulation module to estimate hourly hydropower generation. To address computational tractability, we adopt a strong mathematical formulation of the underlying mixed-integer linear program and exploit the resulting problem attributes with two heuristics, Iterative Rounding and Column Generation. These heuristics are evaluated on country-scale power systems in terms of runtime, solution quality, and scalability. Building on the resulting modeling framework, this research then turns to the challenge of representing PPAs in PCMs. Rather than modeling minimum purchase obligations in isolation, we consider a holistic set of contractual constraints, which includes price premiums, firm-energy delivery requirements, and energy-delivery time window. Benchmarking our modeling approach against prevailing ones in the literature reveals that our proposal yields more operational realism, while maintaining computational tractability. Finally, the modeling framework is applied to study cross-border electricity trade in the Laos-Cambodia-Thailand-Vietnam (LCTV) corridor, the center of regional integration efforts in Southeast Asia. The analysis quantifies the opportunity costs of existing PPAs, highlighting their impact on electricity export and import values, volume of hydropower curtailment, and system vulnerability to hydro-climate-induced price shocks. Our findings highlight the necessity of explicitly representing contractual obligations within techno-economic optimizations to capture real-world operations.