In response to Assembly Bill 32, the State of California is considering three types of carbon emissions trading programs for the electric power sector: load-based, source-based, and first-seller. They differ in terms of their point-of-regulation, and in whether in-state-to-out-of-state and out-of-state-to-in-state electricity sales are regulated. In this paper, we formulate a market equilibrium model for each of the three approaches, considering power markets, transmission limitations, and emissions trading, and making the simplifying assumption of pure bilateral markets. We analyze the properties of their solutions and show the equivalence of load-based, first-seller and source-based approaches, when power sales in both directions are regulated under the cap. A numeric example illustrates the emissions and economic implications of the models. In the simulated cases, "leakage" eliminates most of the emissions reductions that the regulations attempt to impose. Further, "contract reshuffling" occurs to such an extent that all the apparent emissions reductions resulting from changes in sources of imported power are illusory.