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Chapter 6 6.3 Operation Strategy 6.3.1 Reference Operation Strategy The model described in §6.2 can be used to predict the performance of the considered solar tower plant when the reference operation strategy, defined following Refs. [25, 26] is applied. This ap- proach aims at satisfying the nominal power cycle demand, by making use of the available re- sources, namely of the solar field (SF) and the TES system, in a prioritized order. A sequence of logical statements is used to determine whether the power cycle demand can be met with only the SF, or with the SF and the TES, always in this order, while ensuring that the operative constraints (Eqs. 6.10-6.13) are satisfied. In other words, the algorithm aims at running the power block at the maximum possible load for every time step, defocusing the solar field when its output QREC,inc,av ex- ceeds the sum of the nominal thermal power input of the power block and of the maximum storage charging rate that fulfills the capacity limits over a one-hour horizon. In this way, the values of the decision variables mPB and Qdef are determined disregarding any information about the electricity price and of future availability of solar irradiation. The SAM software approximates the differential-algebraic equations of the model by assuming that all variables are constant within each hour of operation, i.e., by using the forward Euler’s method. As there is no feedback from xTES to any other variable of the model, the forward and backward Euler’s methods give the same results in this case, only shifted by one time step, which is irrelevant when determining yearly revenues. 6.3.2 Optimal Control The model described in §6.2 can be adopted to assess the potential of an optimized operation strat- egy for the considered plant, aimed at maximizing the revenue deriving from the sold electricity. The control objective is an integral cost to be minimized over the integration interval from time tin to tfin, i.e., tfin min −W PB du2 dt mPB P + c + g s (u − f min ) dt . (6.14) tin The first term in the integral accounts for the normalized instantaneous revenue from the sale of electricity. The second term, with c > 0, is introduced to penalize fast changes and oscillations of the control variable, as well as repeated re-starts of the plant during the same day. This provision, which aims at avoiding stressful operating regimes for the power block, is implemented in order to coherently follow the approach programmed into SAM. The third term, with g > 0, is introduced to avoid power block operation below the minimum load, along with the additional constraints u=mPB +s, (6.15) 0≤s≤u. (6.16) The free control variable u, which is the output of the dynamic optimization problem together with Qdef, is the unconstrained normalized value of the HTF flow to the power block, while s is a slack variable. If u > f min , the term is minimized by taking the lowest possible value of s ( s = 0), so that mPB m = u. Conversely, if u < f min , the term is minimized by taking the highest possible value of s PB mPB (s = u), so that mPB = 0. The values of c and g are empirically chosen to be the smallest possible, which actually succeeds at avoiding control oscillation, restarting of the power block in the same day, and operation below the minimum load, while perturbing as little as possible the optimization of the first term, i.e., the economic revenue of the plant. An additional constraint might be added to 156PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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