Optimal Operation Of Hydrothermal System

The input-output relationship for a hydro plant in the simplest form is as shown in  fig.(9-1) with the conventional formula given by:

Where h is the effective water head, q is the rate of water discharge through the turbine, c is a dimensional conversion coefficient, Pn is the output power of hydro plant, and t is the efficiency that is dependent on h and q. Eq. (3-121a) can be put as product of two function one, fh(h) is function of h and d the second fq(q) is function of q, then one can write :

For cases of head variations is negligible (when the hydro plant has large storage reservoirs), the common model of qi   as function of output power Phi for plant I may be written as:

Which is similar to the fuel cost function for thermal plant now, for system has n of power plants divided into m thermal power plants and (n-m) of hydro plants operating at constant head, if the optimization interval in (O, T) (period of operation T may be one year, one month, or one day, depending on the requirement), then the problem is to determine the water discharge rate, q(t), so as to minimize the cost of thermal generation with performance index J defined as:

Under the following constraints:

1) The power balance equation where the generators output matches the system demand P_D(t) plus the system loss P_L (t)   then:

2) The volume of water at each hydro power plant which is available for generation is equal to a certain amount b_i for plant I ,then:

The problem formulation for optimization is:

Where the power balance constraints are included in L using multiplier function

 and the volume of water is included using constant multiplier V_i which is

named water conversion coefficient of plants, the optimality conditions of model   (6-7):

1)   For thermal power plant:

2) For hydro power, plants:

Eq ' s (9-8) and (9-9) can be rewritten as :

and

Where f_i   is the penalty factors and the equations (9-6), (9-7), (9-10) and  (9-11) are named the coordination equations.

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Ahmad Atiia

Hi. I’m Designer of Engineering Topics Blog. I’m Electrical Engineer And Blogger Specializing In Electrical Engineering Topics. I’m Creative.I’m Working Now As Maintenance Head Section In An Industrial Company.

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