Solar Field Output Temperature Optimization Using a MILP Algorithm and a 0D Model in the Case of a Hybrid Concentrated Solar Thermal Power Plant for SHIP Applications

Simon Kamerling,Sylvain Rodat,Valéry Vuillerme

doi:10.3390/en14133731

Abstract

Using solar power for industrial process heat is an increasing trend to fight against climate change thanks to renewable heat. Process heat demand and solar flux can both present intermittency issues in industrial systems, therefore solar systems with storage introduce a degree of freedom on which optimization, on a mathematical basis, can be performed. As the efficiency of solar thermal receivers varies as a function of temperature and solar flux, it seems natural to consider an optimization on the operating temperature of the solar field. In this paper, a Mixed Integer Linear Programming (MILP) algorithm is developed to optimize the operating temperature in a system consisting of a concentrated solar thermal field with storage, hybridized with a boiler. The MILP algorithm optimizes the control trajectory on a time horizon of 48 h in order to minimize boiler use. Objective function corresponds to the boiler use, for completion of the heat from the solar field, whereas the linear constraints are a simplified representation of the system. The solar field mass flow rate is the optimization variable which is directly linked to the outlet temperature of the solar field. The control trajectory consists of the solar field mass flow rate and outlet temperature, along with the auxiliary mass flow rate going directly to the boiler. The control trajectory is then injected in a 0D model of the plant which performs more detailed calculations. For the purpose of the study, a Linear Fresnel system is investigated, with generic heat demand curves and constant temperature demand. The value of the developed algorithm is compared with two other control approaches: one operating at the nominal solar field output temperature, and the other one operating at the actual demand mass flow rate. Finally, a case study and a sensitivity analysis are presented. The MILP’s control shows to be more performant, up to a relative increase of the annual solar fraction of 4% at 350 °C process temperature. Novelty of this work resides in the MILP optimization of temperature levels presenting high non-linearities, applied to a solar thermal system with storage for process heat applications.

Highlights

The following variables are displayed: Direct Normal Irradiance (DNI) (Figure 7a), the absorbed power on the solar field (Figure 7b), the ambient temperature (Figure 7c), the demand mass flow rate (Figure 7d), and for the 3 dispatch strategies, the solar field temperature (Figure 7(e.x)), the solar field mass flow rate (Figure 7(f.x)), the storage level in percentage (Figure 7(g.x)), the storage temperature (Figure 7(h.x)), the power of the boiler (Figure 7(i.x)), the auxiliary mass flow rate (Figure 7(j.x)), the power losses in the SF (Figure 7(k.x)) and the energy defocused in the solar field (Figure 7(l.x))
The main difference between the three strategies on this day is when the defocus takes place: Mixed Integer Linear Programming (MILP)’s control defocuses in the morning (Figure 7(l.1)) and fills the storage during the afternoon (Figure 7(g.1)), while the two other strategies fill the storage in the morning (Figure 7(g.2,g.3)) and defocus in the afternoon (Figure 7(l.2,l.3))
It can be observed that the MILP doesn’t fill the storage at 100%, as 80% is enough to go through the night: no auxiliary mass flow rate is needed (Figure 7(j.1))

Summary

Introduction

SHIP (Solar for Industrial Process Heat) is gaining more and more attention in research and in industry worldwide. Recent European projects regarding Solar Thermal are oriented towards SHIP such as InSun, SHIP2Fair, ASTEP or FriendSHIP. A dedicated IEA task (task 64) is devoted to Solar Process Heat and entities like Solar Heat Europe are promoting the use of solar thermal technology for renewable heating and cooling. Heat for industry accounts for 34% of the total energy need, and represents. 73% of the total energy needed by industries [1]. Less than 5% of this energy need is met by renewables. Solar thermal energy is one of the most efficient ways to provide

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