The urgency in mitigating climate change has led to the establishment of agreements, including the Paris agreement (phase IV) whose implementation will be from 2020 and with this it is expected to reduce greenhouse gas emissions by at least 40% by 2030 compared to 1990. The heart of EU climate policy is the EU's emissions trading system (EU ETS). One of the leading sectors in the emission of CO2, especially in Europe, is the electricity sector. The objective of this paper is to model the operation of the EU ETS under the Paris Agreement and its implications on the short-term market of the electricity sector in Germany. Among the results is a significant reduction in CO2 emissions, mainly caused by changes in the installed capacity of the technologies in the market. The generation of electricity by renewable sources and, consequently, the emissions of the sector, depend on installed capacity of renewable energies and the disinvestment in coal technology. It is also found that under the conditions of phase IV for EU ETS there will still be oversupply of permits, therefore, the secondary market does not operate.