Solar Thermal

Create Controlled Function

pandaprosumer.create_controlled_solar_thermal(prosumer, collector_area=2.5, optical_efficiency=0.77, thermal_losses=3.0, second_thermal_losses=0.02, incidence_angle=0.9, flow_rate=72, test_specific_heat=4.18, use_specific_heat=4.18, number_collectors=4.0, series=1.0, piping_length=0.0, piping_diameter=0.028, piping_thickness=0.03, piping_conductivity=0.04, collector_slope=40.0, collector_azimut=0.0, name=None, index=None, in_service=True, level=0, order=0, period=0, **kwargs)[source]

Input Static Data

Parameter	Description	Unit
collector_area	Area of a single collector	m²
number_collectors	Number of collectors in the field	N/A
optical_efficiency (a₀)	Optical efficiency factor
thermal_losses (a₁)	First-order thermal loss coefficient	W/(m²·K)
second_thermal_losses (a₂)	Second-order thermal loss coefficient	W/(m²·K²)
flow_rate	Nominal mass flow rate per collector	kg/h
test_specific_heat	Specific heat used in test conditions	kJ/(kg·K)
use_specific_heat	Specific heat of working fluid	kJ/(kg·K)
piping_length	Length of connecting pipes	m
piping_diameter	Inner diameter of pipes	m
piping_thickness	Pipe wall thickness	m
piping_conductivity	Thermal conductivity of pipe material	W/(m·K)
incidence_angle	Incidence angle modifier at 50°
collector_slope	Slope of the collector field	deg
series	Number of collectors in series	N/A
in_service	Indicates if the solar thermal system is in service	N/A

Input Time Series

Parameter	Description	Unit
beam_solar_radiation_w_m2	Beam solar radiation on collector surface	W/m²
diffuse_solar_radiation_w_m2	Diffuse solar radiation	W/m²
ground_solar_radiation_w_m2	Ground-reflected solar radiation	W/m²
radiation_incidence_angle_deg	Angle of incidence of solar radiation	deg
ambient_temperature_C	Ambient temperature	°C
inlet_temperature_C	Inlet fluid temperature	°C
inlet_mass_flow_rate_kg_h	Inlet mass flow rate	kg/h

Output Time Series

Parameter	Description	Unit
outlet_temperature_C	Outlet fluid temperature	°C
outlet_flow_rate_kg_h	Outlet mass flow rate	kg/h
energy_gain_W	Thermal energy gain of the collector field	W

Mapping

The Solar Thermal model can be mapped using GenericMapping and FluidMixMapping.

Model

class pandaprosumer.controller.models.SolarThermalController(prosumer, solar_themal_object, order, level, in_service=True, index=None, **kwargs)[source]

Definition of the Class for the Controller

Parameters

BasicProsumerController_type_: _description_

Returns

_type_: _description_

The Solar Thermal controller implements the thermodynamic model of a collector field. It accounts for optical efficiency, thermal losses, and correction factors for capacitance, series connection, and piping. The model uses a single temperature to characterize the solar field and relies on the EN12975 standard to characterize the solar thermal collector performance. The approach is based on Chapter 6 and Chapter 10 of “Solar Engineering of Thermal Processes”, by J.A Duffie and W.A. Beckman. The model can simulate the performance of the solar field collector, and then connect it to a thermal storage component or heat exchanger model to incorporate it in a model or a functional system.

Collector Initial Parameters

The effective parameters are derived from test values:

\[FR(\tau \alpha)_n = \frac{a_0}{1 + \frac{3.6 \cdot a_1}{2 \cdot m_{test} \cdot c_{p,test}}}\]

\[FRU_L = \frac{a_1}{1 + \frac{3.6 \cdot a_1}{2 \cdot m_{test} \cdot c_{p,test}}}\]

\[FRU_{L2} = \frac{a_2}{1 + \frac{3.6 \cdot a_1}{2 \cdot m_{test} \cdot c_{p,test}}}\]

Capacitance Correction Factor

\[r_{cap} = \frac{m \cdot c_p}{n_c \cdot a_c} \cdot \frac{1 - \exp\left(-\frac{3.6 \cdot n_c \cdot a_c \cdot f_{finul}}{m \cdot c_p}\right)}{3.6 \cdot FRU_L}\]

with

\[f_{finul} = -\frac{m \cdot c_p}{3.6 \cdot a_c} \ln\left(1 - \frac{3.6 \cdot FRU_L \cdot a_c}{m \cdot c_p}\right)\]

Series Connection Correction Factor

\[r_{series} = \frac{1 - (1 - k)^{n_{series}}}{n_{series} \cdot k}, \quad k = \frac{3.6 \cdot n_c \cdot a_c \cdot FRU_L}{m \cdot c_p}\]

Piping Correction Factor

\[U_p = \frac{2 k_{ins}}{(d_{pipe} + 2 t_{ins}) \ln\left(1 + \frac{2 t_{ins}}{d_{pipe}}\right)}\]

\[U_{ap} = U_p \cdot l_{pipe} \cdot (d_{pipe} + 2 t_{ins})\]

\[r_0 = \frac{1}{1 + \frac{3.6 U_{ap}}{m c_p}}, \quad r_1 = \frac{1 - \frac{3.6 U_{ap}}{m c_p} + \frac{2 U_{ap}}{a_c FRU_L}}{1 + \frac{3.6 U_{ap}}{m c_p}}, \quad r_2 = r_1\]

Radiation Incidence (IAM Effect)

The absorbed solar radiation is corrected by incidence angle modifiers:

\[b_0 = \frac{1 - k_{t,\alpha,50}}{1 - \cos(50^\circ) - 1}\]

\[k_{t,\alpha} = 1 - b_0 \left(\frac{1}{\cos(\theta)} - 1\right)\]

\[k_{t,\alpha,diff} = 1 - b_0 \left(\frac{1}{\cos(\theta_{diff})} - 1\right)\]

\[k_{t,\alpha,gr} = 1 - b_0 \left(\frac{1}{\cos(\theta_{gr})} - 1\right)\]

\[G_t = k_{t,\alpha} I_{beam} + k_{t,\alpha,diff} I_{diff} + k_{t,\alpha,gr} I_{gr}\]

Energy Gain

Finally, the useful thermal energy is:

\[\dot{Q}_{gain} = \dot{m} \cdot c_p \cdot (T_{out} - T_{in})\]