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Steady-State Modelling of a Parabolic-Trough Concentrating Solar Power Plant

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Concentrating Solar Power and Desalination Plants

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Abstract

This chapter describes the modelling of a parabolic-trough (PT) concentrating solar power (CSP) plant that produces electricity. To do this, the modelling of the solar field itself is explained first and then the power cycle, consisting of a reheat Rankine cycle, with steam as the working fluid. This power cycle will be used subsequently to be coupled to a desalination plant, creating what is known as a dual-purpose solar power/water cogeneration plant.

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Abbreviations

A abs :

Absorber tube area (m2)

A c :

Aperture area of the collector’s reflective surface (m2)

A T :

Total collector area required for the solar field (m2)

C p :

Specific heat (kJ/kg °C)

DCA:

Drain cooler approach (°C)

d i :

Inlet diameter of the absorber tube (m)

DNI:

Direct normal irradiance (W/m2)

d o :

Outlet diameter of the metallic tube (m)

E th :

Thermal energy required by the process (kWh)

E th,stored :

Stored thermal energy (kWh)

E th,row :

Thermal energy supplying a collector row (kWh)

F cond :

Refrigeration water flow rate in the power plant condenser (m3/h)

F e :

Collector foiling factor

F w :

Specific fresh or seawater flow rate (m3/MWeh)

GOR:

Gain output ratio

h :

Specific enthalpy of the steam and liquid in the power cycle (kJ/kg)

h f :

Specific enthalpy of the steam in its final state in the thermodynamic cycle (kJ/kg)

h i :

Specific enthalpy of the steam in its initial state in the power cycle (kJ/kg)

h in :

Specific enthalpy of the working fluid at the collector inlet (kJ/kg)

h out :

Specific enthalpy of the working fluid at the collector outlet (kJ/kg)

K :

Incidence angle modifier

L :

Absorber tube length (m)

ṁ :

Mass flow rate of the steam and liquid in the power cycle (kg/s)

ṁ fluid :

Mass flow rate of the oil inside the collector (kg/s)

\( \widehat{n} \) :

Normal aperture vector plane in a parabolic-trough collector

N C :

Number of collectors

N F :

Number of rows

N T :

Total number of collectors in the solar field

P :

Steam and water pressure in the power cycle (bar or kPa)

\( {P}_{\mathrm{c}} \) :

Thermal power dissipated in the condenser (kWth)

P dry :

Power consumption required for the air condensers (kWe)

P cond :

Power consumption by the pump that draws water from the sea to the power cycle condenser (kWe)

P i,pump1 :

Ideal power required by pump 1 (kWe)

P i,pump2 :

Ideal power required by pump 2 (kWe)

P net :

Net electrical power generated in the power cycle (kWe)

\( {P}_{\mathrm{r}} \) :

Thermal power required in the reheater (kWth)

P r,pump1 :

Actual power required by pump 1 (kWe)

P r,pump2 :

Actual power required by pump 2 (kWe)

P pumps :

Total power consumed by the two pumps in the power cycle (kWe)

P turb :

Total power generated by the two turbines in the power cycle (kWe)

P turb,ST1 :

Power generated by turbine ST1 (kWe)

P turb,ST2 :

Power generated by turbine ST2 (kWe)

P Q,collector→environment :

Thermal PTC losses (Wth)

P Q,collector→fluid :

Useful thermal power supplied by a collector (Wth)

P spec, dry :

Specific power consumed by the air condensers (kW/MWnominal)

P Q,sun→collector :

Available solar radiation on the collectors' aperture plane (Wth)

\( {P}_{\mathrm{PCS}} \) :

Thermal power required in the power conversion system (kWth)

P w :

Specific power consumed by the water pump that circulates water through the power cycle condenser (kWh/m3)

P th,field :

Thermal power supplied by the solar field (kWth)

P th, row :

Thermal power supplied by a row (kWth)

P th :

Thermal power required by the process (kWth)

q e :

Heat transfer per unit of mass of the oil in the power cycle (kJ/kg)

q s :

Heat transfer per unit of mass of the steam in the power cycle (kJ/kg)

Re :

Reynolds number

s :

Entropy (kJ/kg °C)

\( \widehat{s} \) :

Solar vector

\( {\widehat{s}}_{E-Z} \) :

Projection of the solar vector onto the E–Z plane

\( {\widehat{s}}_{\mathrm{N}-\mathrm{Z}} \) :

Projection of the solar vector onto the N–Z plane

S :

Useful pass section of the metallic absorber tube (m2)

S E :

East coordinate of the solar vector

SM:

Solar multiple

S N :

North coordinate of the solar vector

S Z :

Z coordinate of the solar vector

t storage :

Period for which the system can operate with the thermal energy stored in the storage tank (h)

t int :

Time intervals into which the design day is divided (h)

t op :

Period of process operation using thermal energy supplied by the collector field (h)

T :

Steam and liquid temperature in the power cycle (°C)

T abs :

Average temperature of the metallic absorber tube (°C)

T amb :

Ambient temperature (°C)

T i :

Oil temperature at the collector inlet (°C)

T o :

Oil temperature at the collector outlet (°C)

T sat :

Temperature of the saturated liquid (°C)

TTD:

Terminal temperature difference (°C)

U L :

Global thermal loss coefficient from the absorber tube to the environment (W/m2 °C)

v :

Specific volume of the liquid through the pumps present in the power cycle (m3/kg)

V :

Oil velocity inside the absorber tube (m/s)

w e :

Work per unit of mass realised by the steam over the power cycle (kJ/kg)

w s :

Work per unit of mass realised by the steam circulating through the cycle (kJ/kg)

x :

Steam quality

γ c :

Average annual usage factor of the thermal storage charge

γ d :

Average annual usage factor of the thermal storage discharge

γ St :

Annual storage losses factor

δ St :

Fraction of energy absorbed by the solar field that is sent to the storage system

Δh :

Specific enthalpy difference of the oil between the collector inlet and outlet (kJ/kg)

ΔT :

Temperature increase demanded by the process (°C)

ΔT c :

Oil temperature difference between the collector inlet and outlet (°C)

ρ :

Fluid density (kg/m3)

η ST :

Isentropic efficiency of the turbine

η th :

Thermal efficiency of the power cycle

μ :

Dynamic viscosity of the fluid (kg/m s)

π:

Pi number

θ i :

Incidence angle (°)

PTC:

Parabolic-trough collector

FWH:

Feedwater heater

ST1:

High-pressure turbine

ST2:

Low-pressure turbine

References

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Authors and Affiliations

  1. CIEMAT—Plataforma Solar de Almería, Tabernas, Almería, Spain

    Patricia Palenzuela, Diego-César Alarcón-Padilla & Guillermo Zaragoza

Authors
  1. Patricia Palenzuela
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  2. Diego-César Alarcón-Padilla
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  3. Guillermo Zaragoza
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Palenzuela, P., Alarcón-Padilla, DC., Zaragoza, G. (2015). Steady-State Modelling of a Parabolic-Trough Concentrating Solar Power Plant. In: Concentrating Solar Power and Desalination Plants. Springer, Cham. https://doi.org/10.1007/978-3-319-20535-9_4

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  • DOI: https://doi.org/10.1007/978-3-319-20535-9_4

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20534-2

  • Online ISBN: 978-3-319-20535-9

  • eBook Packages: EnergyEnergy (R0)

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