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We have developed an innovative power generation scheduling method using quadratic programming (QP). The advantage of using our method is that it simultaneously solves unit commitment and economic load dispatch. We relax the binary variables of the unit state into continuous variables to apply QP to this problem. We also add the penalty term to converge the value of those variables to 0 or 1 to the objective function; the sum of fuel costs and start-up costs. This penalty term depends on per-unit fuel cost. The possibility of its variable converging to zero increases as the cost increases. This method was applied to a test system of daily generation scheduling that consisted of 29 thermal units, two pumped-storage units, four cascaded-hydro units, and one transmission. The schedule satisfied all constraints, i.e., load-power balance, operation reserve, power flow, minimum up/down-times, and fuel consumption. This result shows that the developed method is effective.