The complexity of communication and the size of different areas of power systems are increasing, and the development of the power system requires the optimal allocation of electric power produced by a large number of system generators. Electric energy production in power systems is one of the most important issues in modern systems, along with minimizing the total production cost of the generator units in the power system. Economic load distribution is a common optimization problem in power systems. In this article, the economic distribution of the load between the production units has been done by limiting the minimum and maximum power range between the generator units. To carry out the economic distribution of the load, the repetition method of the Lagrange coefficient is used. To show the study data, the simulation results for a power system with two production units and taking into account losses and a power system with three production units and without losses are presented. Distinct fuel functions are considered for the units in the study. Manuscript profile

The load of consumer demand is constantly changing. Therefore, controlling the generating units is the first issue for designing the power systems. In this paper, the steam generation unit and hydraulic generation unit are studied and simulated. The steam turbine has a re-heater and the hydraulic turbine has a transient droop compensation. The linearized math-ematical models of the first-order system of two generating units are expressed in the state space. The transient dynamic behavior of two generating units is investigated and com-pared with small changes in load demand. Also, the transfer function of the ratio of fre-quency deviation which changes with the changes in the load demand is shown for each unit. MATLAB software is used for simulation. Manuscript profile