Efficiency and Operational Constraints

When considered in isolation, the objective of a DCSF is to convert as much solar power as possible to thermal energy that can be used, for instance, for energy produc­tion. As shown in Fig. 8.2, the fluid outlet temperature should be closed to the value Topt that yields the maximum efficiency. However, due to the stochastic disturbances discussed in Sect. 1.3, the fluid temperature is not kept at an exact value, but instead randomly varies around its mean value with some probability density function (pdf). Let us call A to this pdf and T* to the corresponding mean value (see Fig. 8.2).

For safety reasons, the percentage of samples of the temperature value that are allowed to be above a certain threshold is limited. This threshold corresponds to an operational constraint (shown in Fig. 8.2) and its value is selected depending on aspects such as the maximum temperature that the fluid to be heated tolerates or the possibility that the pipes and the other fluid containment equipments develop microcracks due to thermal stress. To comply with this constraint, the temperature set-point T* is selected at a value that is lower than the optimum. This choice ensures that the probability of exceeding the operational constraint (given by the area under the pdf A and to the right of the constraint) is according to the specifications.

If a better control algorithm is used, for instance an adaptive controller that opti­mizes the performance in an asymptotic way, the fluctuations around the mean will
be smaller. Therefore, as illustrated in Fig.8.2, where B denotes the pdf in this new situation, the mean temperature Г2* can be increased to become close to, or equal to, the optimum value, while maintaining the probability of exceeding the operational constraint. This aspect provides a direct link between the controller performance (measured by the ability of the controller to reject disturbances and compensate the DCSF dynamics so as to keep the outlet fluid temperature constant) and economic performance (measured by the power drawn from the plant).

In addition to efficiency, a better temperature regulation achievable by a controller with a higher performance has a positive impact on the quality of the energy being pro­duced, in the sense that its physical qualities are closer to the desired specified values.

The operational constraint limit in Fig. 8.2 depends on the useful life considered in the plant design. If this upper bound is often exceeded by the temperature, micro­cracks start to appear in the pipes and in the other plant components that are subject to thermal stress. Ultimately, continuous grow of these micro-cracks will render the equipment unoperational. In life extending control (Kallappa 1997) the controller and the reference are tuned in such a way thjt the temperature fluctuates such as to maximize the plant useful life. The controllers designed under this objective may take advantage of material models (Ray and Tangirala 1996).

Although all the control strategies presented in this book have generally a ben­eficial effect in what concerns all the issues above, the methods of Chap. 3 have a tighter connection to their solution, due to the probabilistic formulation upon which they rely.