Determination of the optimum power rating of a back-pressure steam turbine in a co-generation system of waste-steam utilization

The utilization of steam from industrial waste-heat boilers in combined heat-and-power generating plants (CHP) is more effective than alternative ways of using the steam. A back-pressure steam turbine is cheaper from the point of view of capital expenditure under the condition that its power rating has been optimized. The base for the determination of the power rating of a back-pressure turbine is a duration curve of waste-steam production. If more than one waste-heat boiler is operated, the duration curve of global waste-steam production is needed. A summarizing duration curve is formed making use of the method of convolution of the distribution functions of random variables. The objective function is the annual profit resulting from the realization of the CHP system. Useful effects are the economic value of heat and electricity estimated by means of the method of avoided costs. It is convenient to assume that the decision variable is the time of utilizing the power rating of a back-pressure turbine. The power rating results from the global duration curve of waste-steam production and the time of its utilization. The decision variable exists also in the limit of integration. For this reason the optimal problem is solved by searching for the extremum of the objective function containing integrals depending on one parameter. The limits of integration also depend on this parameter. This paper contains the aforesaid algorithm, as well as an example for an industrial plant.