The constraint solving techniques are the mechanisms that ensure all transactions in a competitive electricity market can be achieved without violation of operating limits. It becomes a very important issue in a competitive electricity market, because an improper handling of these can segment the electrical market and will have a significant impact on the ability to exercise market power. The main purpose of this paper is to develop a methodology to solve the power system constraints (both in normal operation and after contingencies) that arise after the daily energy market has been cleared. All this based on a competitive market environment, increasing and decreasing the generation of connected units, and connecting offline ones, all within different time scenarios.