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Chapter 5 design calculation. Hence, Equation (5.4) states the relation between mass flow rate and turbine inlet conditions, during off-design operati√on. The off-design isoentropic efficiency is expressed as a function of the flow coefficient Φ = ω/ 2∆hs, with ω being the speed of revolution, and ∆hs the isoentropic enthalpy drop across the expansion [29]. The recuperator is modeled by the counter-current connection of 1D ThermoPower modules, much as the once-through boiler, see Fig. 5.5. The heat transfer on the vapor side dominates, therefore the overall heat transfer coefficient is taken equal to that at the interface between the working fluid and the metal wall. Both the overall heat transfer and the pressure drops, in off-design conditions, are modelled as already detailed for the once-through boiler. The condenser is trivially modeled as a fixed pressure component. This is justified considering the large availability of cooling sea-water, which allows the cooling circuit to be controlled in such a way that the condenser pressure is nearly constant. For simplicity, the condensate is assumed to leave the component in saturated conditions (no subcooling) with no pressure losses. The pump model is based on a head-volume flow curve derived by fitting the data of an existing centrifugal pump designed for similar volumetric flows and heads. The curve is given as a function of α = m ̇ m ̇−1 · ρdes ρ−1, and can be expressed as des α ω2 H=Hdes·(b1+b2e)· ω , (5.6) des where H is the head and, in the present case, the coefficients assume the values b1 = 2.462 and b2 = −0.538. The monotonic exponential functional form increases the model robustness compared to typically adopted polynomial expressions. The isoentropic efficiency of the pump is expressed as a function of χ = α · ωdes ω−1, following Ref. [32]. The off-design electric efficiency of the ORC generator is calculated as for the case of the gas turbine generator, while the electro-mechanic efficiency of the pump motor is evaluated by assum- ing a quadratic dependency on the ratio between the actual the nominal load value. CONTROL SYSTEMS As explained in §5.3, the system under consideration operates off-grid. The alternating current (AC) grid-system of the off-shore platform is powered by the two synchronous generators connected to the gas and ORC turbines, which can be assumed to rotate at the same speed, as the electrical con- nections are very short. The gas turbine features the fastest load response, so it is used to control the network frequency (or, equivalently, the shaft rotational speed). As the low pressure and high pres- sure compressor are not equipped with variable inlet guide vanes, the load can only be controlled by opening or closing the fuel valve. The feedback controller included in the gas turbine sub-system (see Fig. 5.3) replicates the functional model provided by the gas turbine manufacturer, including the controller transfer function, and a simplified model of the fuel-system dynamic response, also given as a transfer function. Note that this controller is embedded in the GT unit and its parameters cannot be changed by the end-user, so the controller parameters are taken as they are in the context of this study. The goal of the ORC control system is to target the maximum possible heat recovery from the GT exhaust, while ensuring that no acid condensation takes place, which might be particularly dangerous since also heavy fuels can be fed to the turbine combustor. This goal is attained by using the feed pump speed to control the temperature of the exhaust gases exiting the OTB at the design point value, which is as low as possible, yet high enough to avoid condensation. During stationary operation, the design of the heat exchanger is such that the highest temperature of the organic fluid, at the turbine inlet, is lower by a safety margin with respect to the thermal decomposition 132PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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