The economic operation of a power system is studied using an approximation of the active power losses for estimating the penalty factor of the generation nodes while the generation cost is taken as a quadratic function of the active power. Then, the optimum allocation of active power generation can be calculated for minimum generation cost. It was shown that using approximate active power losses of a power system the penalty factors in the Lagrangian can be estimated and thus the optimum values of the active power of the generation nodes can be calculated for a minimum total generation costs of the power system, i.e., for its optimal economic operation.