Category Control of Solar Energy Systems

Simulation Experiments

All the models mentioned in the previous sections can be used for daily plan­ning of electricity production. As a simple example, a simulation experiment is shown in this section on applying the hierarchical daily production planning struc­ture shown in Fig. 8.2. This application can use real data from the installation or a model of direct solar irradiance shown in Chap. 2, the hot oil storage system model briefly explained in Sect. 8.2.4.1, the distributed parameter model of the solar field explained in Chap. 4, Sect. 4.3.2, the optimizing reference governor explained in Chap. 5, Sect. 5.12.1.2, and the feedback linearization controller developed in Chap. 5, Sect. 5.8.1, to regulate the outlet temperature...

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PCS Start-up

The energy needed to start up the plant depends on the time elapsed since it was in operation and the required energy is between 200 and 1200 kWh;. The start-up phase includes the following steps:

1. Increase the pressure to 25 bar.

2. Preheat the pipes and turbine.

3. Start the turbine and reach the nominal rotating speed (100% rpm).

Подпись: Fig. 8.2 Scheme of elements and their interconnection to perform diary planning of electricity production (courtesy of C.M. Cirre, [103])
image290

The energy needed to start up the plant is given by

Pstart = 1200 – 1000e(°’3°4-0-307’i°-4t2) [kWt] (8.21)

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Performance-Based PCS Model

Table 8.1 shows efficiency data of the elements: solar collector field, storage tanks and power conversion part. The yearly efficiency coefficients have been obtained from the monthly efficiency data.

This type of information is useful to evaluate the best and worst cases for making decisions taking risks into account. The steam turbine can be operated at 290°C or at 280°C. The return temperature of the generator is about 70°C lower than the inlet temperature PCS operating temperatures between 287°C and 292°C, which are considered to be in the high range while operating temperatures between 277°C and 282°C are considered low range. The gross process efficiency (in Eq. (8.19)), denoted by ngross, was computed (Eq. (8.14)) by a least squares fitting...

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Power Loss Model

Losses are important when designing a plant-wide control scheme. Overall losses can be computed as the difference between the input and the output power. The input power to the PCS is the thermal power of the hot oil (Phtf), which depends on the inlet oil temperature (Ti„Tur), outlet oil temperature (ToutTur), and flow (qT) as indicated by Eq. (8.14):

Phtf = qT [1-882 ■ 10-3(T^ – – 0.795{TmTur – ToutTur)] (8.14)

The gross output power of the PCS (Pgross) can be obtained as the difference between the thermal power delivered to the steam generator (Phtf), the thermal power delivered to the refrigeration systems (Prs) and the thermal losses inside the PCS (Lpcs).

The steady state energy balance equation is given by Eq. (8.15):

pgross = Phtf – Ln – Lpcs (8.15)

The following equation was obta...

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Power Conversion System

There are different methods for modeling the power conversion systems. The model presented in this section has been obtained from data taken from the power conver­sion system of the DCS project [190]. The PCS is composed of the steam generator, preheater, steam turbine, and refrigeration tower. The steam generator is fed by ther­mal hot oil coming from the hot oil storage tank. The steam powers the turbine and electrical generator (Stal-Laval) with a nominal power of 577 kW.

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Hot Oil Accumulators

In other cases, hot oil is directly stored in a tank (thermocline). Thermal stratification of the oil in the tank allows energy to be stored at different temperatures. As an example, in the ACUREX field, the storage tank is connected to the solar field and to the PCS by means of two pipe circuits placed at the top and bottom of the tank (see Fig. 8.1). The heated oil stored in the tank is used to generate the steam needed to drive the steam turbine of the PCS.

The storage system can be used in different modes; the first mode of operation is only used when there is not enough solar radiation, then hot oil is taken from the tank to the steam generator...

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Storage System

Molten Salt Accumulators

Different thermal energy storage systems are used in solar plants. In some cases molten salt tanks are used. The basic idea is to use the heat from salt fusion; that is, the amount of heat required to melt a solid salt at its melting point into a liquid without increasing its temperature. The heat capacity of a body is defined as the heat needed to increase the temperature of the body by one degree and since the temperature is not increased during melting, the heat capacity is very high at this stage. The liquid salt releases the same amount of heat when it solidifies.

The energy stored at a molten salt energy storage system can be modeled by the following equations:

, . -Tst

C^EAt))-^ — ps+ – ps – – Lst(Tst – Ta)

0 < Ps+< Ps+

0 < Ps-< Ps-

Ps+ — Hst+(qst, Tstin —...

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Prediction Models

This section analyzes some prediction models needed for scheduling production and optimal control of solar power plants.

The most important variable in a solar plant is solar radiation. Different models for solar radiation prediction and forecasting have been explained and developed in Chap. 2, both for short and long term forecasting. Different models of solar collector fields have been developed in Chap. 4 that are useful for optimization purposes (mainly those based on first principles).

Ambient temperature affects the thermal losses of the solar field, heat storage tanks and turbines. Ambient temperature also affects electrical demand. Low am­bient temperature increases the need for heating and, therefore, electrical demand...

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