Several interconnected power systems worldwide have largely thermal and hydro production along with CO2 cap-and-trade (C&T) systems and variable renewable energy sources (VRES). C&T policies increase VRES generation, and socially optimal storage deployment could integrate VRES output. However, hydro reservoirs may be used strategically due to market power. We investigate these distortions and assess measures for their mitigation via a bottom-up equilibrium model of New York and Québec. In particular, we find evidence that hydro producers shift water between seasons to manipulate electricity prices even under a net-hydro production constraint. Alternative regulation covering net imports as well as net-hydro production limits such temporal arbitrage but enables firms with both thermal generation and pumped-hydro storage to exercise spatial arbitrage. We demonstrate that these distortions will be exacerbated under more stringent C&T policies because price-taking thermal producers are less able to respond to price signals.