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Design of CSP Plants with Optimally Operated Thermal Storage according to P = TOD(t) PPA. (6.2) The power actually reaching the receiver QREC,inc may then be calculated as QREC,inc = QREC,inc,av − Qdef , (6.3) where Qdef is the power dumped by defocusing heliostats, which is a control variable of the problem. The following (normalized) equations QREC,abs = QREC,inc αREC , QHTF = QREC,abs ηREC,th , mHTF = QHTF , WPB=mPBηPB, = mHTF − mPB , complete the model. Eq. (6.4) gives the thermal power absorbed in the receiver QREC,abs and Eq. (6.5) the power QHTF transferred to the HTF. Eq. (6.6) relates the mass flow rate of HTF through the receiver mHTF to QHTF, while Eq. (6.7) establishes the relation between WPB, mPB, and the power block efficiency ηPB, which is assumed to be linear in this work. Finally, the differential equation (6.8) describes the dynamics of the TES system, where hTES is the capacity of the stor- age tank in terms of hours of operation at nominal power block load. The corresponding initial conditions for the state variable are explicitly defined by Eq. (6.9). dxTES dt (6.4) (6.5) (6.6) (6.7) (6.8) (6.9) hTES xTES(0) = xTES,0 , Several constraints need to be enforced in order to ensure feasible operation, namely Q ≤ fmax , REC,inc QREC,inc (6.10) (6.11) (6.12) (6.13) 0 ≤ Qdef ≤ QREC,inc,av , 0≤mPB ≤1, x ≤ x ≤ fmax . xTES TES,min TES The first inequality states the maximum power that can be handled by the receiver, calling for a partial defocusing of the heliostat field if the available power QREC,inc,av becomes too high; the defocused power Qdef (second inequality) is non-negative and less than the available power. The normalized flow rate of HTF to the power block is comprised between 0 and 1 per unit (third inequality), while the storage tank state of charge xTES is limited between a lower and an upper bound. Furthermore, both the solar field thermal power QREC,inc and the power block HTF flow mPB have a minimum operating load, and need to be turned off if the desired load level is lower than that. The first constraint is enforced by substituting Q which is done as a pre-processing task. The second constraint is handled by introducing extra terms in the optimization problem, see §6.3.2. The resulting model has two known, time-varying inputs QREC,inc,av(t) and fTOD(t), and two control variables mPB(t) and Qdef(t). The model is readily encoded using the equation-based, object- oriented language Modelica [32], see also §6.4 and listing 1 in A.3. REC,inc,av REC,inc,av = 0 whenever Q ≤ f min , QREC,inc 155PDF Image | New Concepts FOR Organic Rankine Cycle Power Systems
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