The purpose of this study is to elucidate under which circumstances, how, and to what extent market power on a Tradable Green Certificates (TGC) market can be used to affect an entire electricity market. There are basically two reasons for being concerned with this. One is that a small number of companies may have exclusive access to first rate sites for wind power generation. The other is that withdrawal of a small number of TGCs implies a multiple reduction of electricity consumption, with corresponding increases of end user prices. We formulate both an analytical model to investigate economic principles and a numerical model based on that to investigate the Swedish TGC market operating in a setting of a common Nordic electricity market. The analysis shows that Swedish producers may exercise market power using the TGC-market but that this problem will be eliminated by opening the TGC-market for other Nordic countries.