Category Control of Solar Energy Systems

System Hybrid Model

The different system configuration modes can be defined according to the signal values for every state, as shown in (7.25) and the transitions among states is defined in an FSM (Finite State Machine) such as shown in Fig. 7.31.

s1 = V1 л V3 a^Gh

s2 = —V1 л—V3 a-Gh

s3 = —V1 л V3 л Gh

s4 = V1 л—V3 a—Gh (7.25)

s5 = V1 л V3 л Gh s6 = —V1 л—V3 л Gh s7 = V1 л—V3 л Gh

From

To

Events

From

To

Events

s1

s2

—V1 л —V3

s2

s1

V1 л V3

s1

s3

—V1 л GH

s3

s1

V1 л—GH

s1

s4

—V3

s4

s1

V3

s1

s5

GH

s5

s1

—GH

s1

s6

—V1 л —V3 л GH

s6

s1

V1 л V3 л—GH

s1

s7

—V3 л GH

s7

s1

V3 л—GH

s2

s3

V3 л GH

s3

s2

—V3 л—GH

s2

s4

V1

s4

s2

—V1

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Plant Hybrid Configuration Modes

The space-state model obtained in the previous section only allows the system re­sponse to be simulated when all the cooling system components work together but this model is not valid for all the other plant configuration modes. The on-off valve position and system dynamics change at each different plant configuration mode (Fig. 7.30). The presence of both continuous and discrete dynamics defines the cool­ing process as a hybrid system. Changes in the valve position will cause changes in the system configuration modes and, therefore, in the system dynamics. These tran­sitions among system configuration modes must be ensured to be continuous. More information about the nature of hybrid systems can be found in [33].

image707
image708
Подпись: HEATER
Подпись: /2
Подпись: GAS Подпись: 1/2
Подпись: TANKS

image282ABSORPT ON

MACHINE

Fig. 7...

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Simple Gas Heater Model

The gas heater behavior presents a double stage response when it is turned on. The first stage increases the temperature to 40% of the gas heater performance and after exactly 5 min, the gas flow opens totally, increasing the temperature at a second stage with a higher gas heater performance. This behavior was dealt with using a combination of first-order systems by means of four transfer functions divided into two sets, identifying the relationship between the gas heater inlet and outlet temperature and between the water flow and the outlet temperature when the gas heater is turned on and after 300 s.

image705 Подпись: (7.21)

The global transfer function (7...

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Tank Model

image702 Подпись: Astpfv(t)cf(Tstin(t) — Tstout (t)) + Hst Sst (Ta(t ) — Tstout (O) Подпись: (7.20)

The accumulation system, consisting of two separate tanks connected in series, was simplified by a lumped-parameter model. The tanks can be considered as a buffer and thus, they can be modeled as a transport delay between the inlet and the out­let temperature which depends on the flow. Equation (7.20) models the relationship between the tank outlet temperature and the tank input temperature, ambient tem­perature and fluid flow:

where pf is the water density, cf is the water specific heat, Vst is the tank volume [m3], Tst0ut is the accumulation tank water outlet temperature [°C], Ast is the ac­cumulation tank area [m2], v is the fluid velocity in the system [m/s], Tstin is the accumulation tank water inlet temperature [°C], Ta the ambient temperature [°C], Hst is the tank’s l...

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Solar Field Collector Model

The solar collector model used is the same as that explained in Chap. 4, Sect. 4.3.4.2, calibrated for the specific solar field layout at this plant [284].

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Hybrid Model of the Solar System

The same approach as that has been commented on in Chap. 6, Sect. 6.8.4 in the case of the CRS has been applied to control the overall installation using a hybrid MPC control scheme. As shown in [284], a hybrid model of the system composed of a solar collector field, a gas heater and two tanks connected in series to store hot water can be developed (see Fig. 7.21). These systems are used as energy sources for an absorption machine whose objective is to obtain chilled water for the fan-coil system. All these components are included or excluded from the cooling system by means of switching valves and activating or deactivating signals...

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Multiple Operating Modes

The plant was used as a benchmark within the network of excellence HYCON funded by the European Commission under FP6. The benchmark exercise [412] consisted of comparing the results obtained by each controller under simulation and the results of the controller working for one day at the real plant. The simulation results had to be obtained for two days with the given environmental conditions corresponding to a clear day followed by a day with scattered clouds. The follow­ing quantities were to be measured: mean square error of evaporator temperature tracking, energy consumed by the gas heater, value of the tank temperature at the end of each day...

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Application in the Solar Plant

Although the real process has non-linear behavior, as is the case of many industrial processes, if working variables are kept close to a particular operating point, a linear model computed considering small changes around this point will be sufficient. It will be necessary to model VM1-Tjc and I-Tsc transfer functions. Both VM1-TSc and I-Tsc dynamics are similar to a classic first-order system with a certain de­lay, so an ARX 12 0 structure (with a sampling time of 40 s) is selected to model them. Enough data were obtained from several experiments to identify VM1- Tsc and I-Tsc characteristics. These data are subject to a parametric model identifi­cation process implemented in a well-known software packet [229]. The obtained

image683 image270

VM1-Tsc transfer function is shown in Eq. (7...

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