Calculation of the Number of Parallel Rows

Подпись: M Подпись: Qrow image229 Подпись: (eq.4)

The next step is the calculation of the number of parallel rows, M. This value is a function of the thermal power required by the power block, Qt. The number of rows is the integer rate of this demanding thermal power, Qt, by the thermal power generated in a row, Qrow, which is given by the useful thermal power supplied by every collector, Qutil, colc, multiplied by the pre-design number of collector per row, Npredesign, i. e.,

2. Solar field optimization

In the northern hemisphere, the solar incidence angle in winter is larger than in summer. So the solar irradiation available on the solar field is smaller (due to the cosine effect) and then the generated power decreases too. To reduce this winter effect, the designer could increase the

number of rows, but it would add an overproduction of thermal energy in summer that can not be used by the power block. This wasted thermal energy is known as dumping of energy.

With the methodology proposed in this paper, the optimum size of the solar field is the one that produces the highest electrical power generation with the lowest dumping of energy (below 3%, [5]). To determine this optimum, simulations with several sizes of the solar field are run along a real year (i. e., introducing ambient temperature and solar irradiation data from a typical meteorological year). The sizes are around the already calculated number of rows, M, in the pre­design. A model of the solar thermal power plant is, therefore, necessary.

The model of the solar thermal power plant has two independent components: the solar field model and the power block model (Fig.1).

Подпись: Metheorological data. Fig 1. Scheme of the solar thermal power plant model.

For the solar field model the simulation program TRSNYS (TRansient SYstem Simulations), [6], has been used. This program has a modular structure, which allows of programming in blocks. The different blocks considered for the solar field models are (Figure 1): a thermal and hydraulic model of a parabolic trough collector, a thermal and hydraulic model of a pipeline connection between two collectors in a row, a solar incidence angle calculator and a block reporting the general arrange of the solar field (number of collectors per row and number of rows in the solar field).

It is advisable that the direct normal irradiance and ambient temperature data are mean values in 10 or 15-minute time periods, in order to account transient clouds. The maximum time step to record these meteorological data being considered useful enough is 1 hour. The hydraulic and thermal models of the parabolic trough collectors and their interconnecting pipelines are stationary models.

The thermal model uses the corresponding heat balance, while the hydraulic model calculates the pressure drop using the Bernoulli equation. The mass flow of the heat transfer fluid in the solar field is the one which assures at every moment (i. e., under typical beam irradiance and ambient temperature) a fixed solar field outlet temperature. This temperature is always below the maximum bulk temperature of the thermal oil used as working fluid in the solar field and is previously defined for the solar field pre-design, taking into consideration the efficiency of the oil to water heat exchanger and the steam temperature needed at the inlet of the turbine. At the inlet of the turbine, the temperature — and pressure — is considered to be constant, unlike the steam mass flow, which varies depending on the oil mass flow in the solar field.

The power block model considers the influence of steam mass flow variations at the inlet of the turbo-generator on its electric output. This influence is handled by a fitting curve obtained from the data given by the turbine manufacturer. A conventional fossil fuel boiler may be introduced if hybridization is considered.

The main results of the plant simulation are the incident solar energy onto the solar field, the useful thermal energy produced in the solar field and in the conventional boiler — if any-, the electrical energy generated in the turbine and the dumping of energy, all these results integrated along one year.

3. Example

As an example, let’s consider a parabolic trough solar power plant of 50 MWe somewhere in the South of Spain without storage. It is assumed that there are no restrictions or limitations in the size and orientation of the plot for the solar plant. The heat transfer fluid considered in this example is Therminol VP1 and the parabolic trough collector model is the ET-II (5.76m aperture width, 142.8m useful length). The orientation of the collectors is North-South. The Rankine cycle is assumed to have 38% gross efficiency (thus 131.6 MWth have to be supplied by the solar field at nominal conditions). The power block specifications determine that the temperature of the oil at the inlet and outlet of the solar field are 296°C and 393°C, respectively. 12% conventional fossil fuel energy supply is allowed in a yearly basis.

In the pre-design it is assumed a Direct Normal Irradiance of 850W/m2 and an ambient temperature of 25°C. The temperature difference at the outlet and inlet of the solar field and the used collector features determines that every row needs to have 4 collectors. The required thermal power defines that 74 rows are necessary if the calculation procedure explained in section 2 is applied.

In the optimization of the solar field, the meteorological data available are given in 1-hour time steps. An interpolation procedure has been followed to obtain 5-minute data sets. The accumulated annual direct normal irradiation is 2286 kWh/m2. Simulations are run for ±10% of number of rows to have a dumping of energy lower than 3%. Having in mind a central feed configuration of the solar field piping, an even number of rows are necessary, so the annual performances of the plant with 66, 74 and 82 rows are carried out.

The annual solar energy onto the collector field (insolation), the thermal energy it produces, the electricity output of the power plant and the percentage of wasted energy is shown in Fig. 2 for different sizes of the solar field. As with 82 rows the dumping of energy was lower than 1%, the corresponding results for a plant with 90 rows are also obtained and shown. Running the plant simulation model with typical meteorological data for 74 rows a small dumping of energy is observed, becoming zero with 66 rows. Increasing the solar field size from 74 rows to 82 rows (10.8 %) the electric energy production increases 10%: from 94GWh to 103GWh. When the performance with 74 rows is compared with the one of 90 rows (21.65% of increase in size), the increase of the annual electric production is 17.2 % (from 94GWh to 110GWh), but with 3.37 % of dumping of energy. Thus the electricity production does not increase/diminish in the same percentage as the increase/reduction of the solar field size.

Подпись: 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 Подпись: n° rows of collectorsimage2340s

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Incident energy

 

Thermal energy

 

Electrical energy

 

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Fig 2. Incident, thermal, electrical and wasted energy as function of solar field size.

Keeping the criterion of being below 3 % dumping of energy, the optimized size of the solar field will be between 66 and 88 rows. The next step must be the economical evaluation of these few options.

4. Conclusions

In order to better design a parabolic trough power plant, simulation tools for finding out the optimal solar field size are necessary. Up to now, these simulation tools have an economical criterion as the only figure of merit, requiring a new optimization process every time there was any variation in the economical situation to apply. A way to reduce the number of cases to consider is by including another energetic criterion. This paper presents a methodology to optimize parabolic solar fields where an energetic criterion is applied prior the economical one. A first estimation of the solar field is obtained with a simple calculation, assuming representative meteorological conditions (pre-design). Taking this pre-designed solar field size as reference, annual evaluations of the performance of the plant with different sizes are analyzed. The limits where this size range stays are determined keeping the wasted energy (dumping), due to the oversizing of the solar field in summer, below 3%.

An example to illustrate how to proceed with a specific case is explained. After the methodology

presented here, the economical optimization that would follow is reduced to just a few cases.

References

[1] Greenpeace, SolarPACES, ESTIA: “Concentrated Solar Thermal Power Now — Exploiting the Heat from the Sun to Combat Climate Change”, September 2005

[2] X. Garcia Casals “La ene^a solar termica de alta temperatura como alternativa a las centrales termicas convencionales y nucleares”, 2001

[3] V. Quaschning, R. Kistner, W. Ortmanns, “Influence of Direct Normal Irradiance Variation on the Optimal Parabolic Trough Field Size: A Problem Solved with Technical and Economical Simulation”. ASME Journal of Solar Energy Egineering, 124 (2002) 160-164

[4] FLAGSOL, 2008, http://www. flagsol. com/FLAGSOL. htm, visited on August 2008

[5] J. I. Ajona, “Electricity Generation with Distributed Collector Systems”. Course: “Solar Thermal Electricity Generation”. Plataforma Solar de Almeria (13th-17th July, 1988).

[6] TRNSYS. A Transient System Simulation Program. Solar Energy Laboratory. University of Wisconsin. USA. (1994)