A model has been developed to study the global complex dynamics of blackouts in power transmission systems. This model included a simple level of self-organization by incorporating the growth of power demand and the engineering response to system failures. Two types of critical points have been found. The first critical point is characterized by operation with lines close to their line limits. The second critical point is characterized by the maximum in the fluctuations of the load demand being near the generator margin capability. The identification of this second critical point is an indication that the increase of the generator capability as a response to the increase of the load demand must be included in the dynamical model. When this is done, the model shows a probability distribution of blackout sizes with power tails similar to that observed in real blackout data from North America.