Power markets are becoming increasingly complex as they move towards (i) integrating higher amounts of variable renewable energy, (ii) shorter trading intervals and lead times, (iii) stronger interdependencies between related markets, and (iv) increasing energy system integration. For designing them appropriately, an enhanced understanding of the dynamics in interrelated short-term physical power and energy markets is required, which can be supported by market simulations. In this paper, we present an agent-based power market simulation model with rule-based bidding strategies that addresses the above-mentioned challenges, and represents market participants individually with a high level of technical detail. By allowing agents to participate in several interrelated markets, such as the energy-only market, a procurement platform for control reserve and a local heat market representing district heating systems, cross-market opportunity costs are well reflected. With this approach, we were able to reproduce EPEX SPOT market outcomes for the German bidding zone with a high level of accuracy (mean absolute percentage error of 8 €/MWh for the years 2016–2019). We were also able to model negative market prices at the energy-only market realistically, and observed that the occurrence of negative prices differs among data inputs used. The simulation model provides a useful tool for investigating different short-term physical power/energy market structures and designs in the future. The modular structure also enables extension to further related markets, such as fuel, CO2, or derivative markets.