Photovoltaic Thermal (PV/T) Hybrid Solar Panel
This example shows how to model the cogeneration of electrical power and heat using a hybrid PV/T solar panel. The generated heat is transferred to water for household consumption.
It uses blocks from the Simscape™ Foundation™, Simscape Electrical™, and Simscape Fluids™ libraries. The electrical portion of the network contains a Solar Cell block, which models a set of photovoltaic (PV) cells, and a Load subsystem, which models a resistive load. The thermal network models the heat exchange that occurs between the physical components of the PV panel (glass cover, heat exchanger, back cover) and the environment. Heat is exchanged through conduction, convection, and radiation. The thermal-liquid network contains a pipe, a tank, and pumps. The pumps control the flows of the liquids through the system.
To model the reflection, absorption and transmission of light in the glass cover, an optical model is embedded in a MATLAB® Function block.
Open the model to view its structure:
The thermal network is in red, the electrical network in blue and the thermal liquid network in yellow. There are subsystems for the solar and pump inputs. There is also a subsystem that contains scopes for visualizing the simulation results. Another subsystem contains the function for the optical model.
The inputs of the model are the pump flows and the solar variables for irradiance and incidence angle. A repeating sequence block is used to define the inputs because they follow a 24-hour periodic cycle.
open_system(‘sscv_hybrid_solar_panel/Pump flow inputs’);
The sun rises at 6:00 and sets at 19:00. The irradiance follows a bell curve that peaks at 12:30. The incidence angle changes from pi/3 to 0.
There are three pumps. One pump models user demand, another models source supply, and a third models internal flow that forces convection in the pipe. The demand is constant and only non-zero from 10:00 to 22:00. The supply is constant and only non-zero from 18:00 to 6:00. The internal flow is also constant and only non-zero from 6:00 to 22:00. This model is used for the internal flow because it is not efficient to force heat exchange during the night when the ambient temperature is low.
You can use the hybrid_solar_panel_plot_inputs.m script to plot the inputs:
Optical model for the glass cover
The optical model is inside a subsystem:
It consists of a MATLAB® Function block, with the 2 solar inputs, and 3 outputs: the transmitted irradiance on the PV cells, the heat absorbed by the glass, and the radiative power absorbed by the PV cells. Part of it will be transformed into electrical power (VI) and the rest will be heat absorbed by the PV cells.
From an optical point of view, the glass consists of 2 parallel boundaries (air-glass, glass-air), each one of those reflects and transmits light. The reflection coefficient in a boundary is obtained from the Fresnel equations. is for P-polarization and for S-polarization. The total reflection is the average of both, and the transmittance is as there is no absorption so far:
^2 \cos(\theta_i). \sqrt^2. \sin(\theta_i)^2#xA;^2 \cos(\theta_i) \sqrt n_^2. \sin(\theta_i)^2 \right) ^2 /
^2. \sin(\theta_i)^2#xA;^2. \sin(\theta_i)^2 \right) ^2 /
\left( r_p r_s \right) /
This is an example of the optical coefficients rp, rs, r and t in function of incidence angle:
nrel = 1.52; %Optical index from air to glass theta = linspace(0, pi/2, 100); rp = ( nrel^2cos(theta). sqrt(nrel^2. sin(theta).^2) ).^2./. ( nrel^2cos(theta) sqrt( nrel^2. sin(theta).^2 ) ).^2 ; rs = ( cos(theta). sqrt(nrel^2. sin(theta).^2) ).^2./. ( cos(theta) sqrt( nrel^2. sin(theta).^2 ) ).^2 ; r = 0.5(rp rs); t = 1. r; figure; plot(theta180/pi, rp, ‘Color’, [0 1 1], ‘LineWidth’, 1.5); hold on plot(theta180/pi, rs, ‘Color’, [0 0.5 1], ‘LineWidth’, 1.5); plot(theta180/pi, r, ‘Color’, [0 0 1], ‘LineWidth’, 1.5); plot(theta180/pi, t, ‘Color’, ‘m’, ‘LineWidth’, 1.5); legend(‘rp’,’rs’,’r’,’t’); xlabel(‘Incidence angle (deg)’); grid on box on
This is what happens in one boundary, but the glass has 2 parallel boundaries separated by. The angle after the 1st boundary is the incidence angle on the 2nd boundary and is calculated from Snell’s Law:
When the light enters the glass, it absorbs part of it with a constant probability per unit length (alpha_g), resulting in an exponential decay from distance travelled for the transmittance coefficient in the glass:
Then, when it arrives at the 2nd boundary, it reflects and transmits again with Fresnel equations. The reflected light is trapped inside the glass, reflecting infinite times between the 2 boundaries until completely absorbed. The total reflection and transmission coefficients of the system are then the sum of an infinite geometrical series, for which the result is:
Heat-driven photovoltaic device hits 40 percent efficiency
- John Timmer
- 04/14/2022 11:00 am
- Categories: Science
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As installing renewable generating sources continues to set annual records, we’re reaching the point where storing the power they generate becomes essential. Proper storage can provide a way to cover temporary drops in production due to changing weather and can potentially offer a way to use power at times when renewable sources aren’t producing at all.
So far, attention has focused on batteries as a storage technology that already works and on hydrogen as a technology that could work. But both options have problems with scaling to meet our needs. And there’s one technology that’s already in use that might be more flexible: heat. Heat created from concentrated solar power already allows solar plants to keep producing long after the Sun sets (some plants can generate around the clock). And we already know how to produce and store heat efficiently.
Now, researchers from the National Renewable Energy Lab and MIT have improved a technology for using the stored heat to produce electricity: a photovoltaic device that’s sensitive to infrared wavelengths. They show that its efficiency is competitive with that of steam boilers, and it avoids the use of moving parts and water that might otherwise be scarce.
Silicon photovoltaic cells—and those made from a range of other materials—can convert infrared light into an electrical current. They just don’t do so efficiently. Other materials are more sensitive to these wavelengths, but the lower-energy photons in the infrared result in a correspondingly lower voltage in the photovoltaic output. That drops the efficiency of any devices targeting these wavelengths.
But since the research team is focusing on energy storage, they assume that they can control the temperature of the hot object that’s acting as their photon source. So the researchers plan to use a relatively high temperature (in the area of 2,000° C) to boost the number of higher-energy photons near the edge of the visible spectrum. This will allow them to use a semiconductor with a higher bandgap, which corresponds to a larger output voltage.
To boost the efficiency further, the cell combines two different materials that absorb different areas of the spectrum in what’s called a two-junction configuration. The team tried two different two-junction setups, one using aluminum/gallium/indium/arsenic and gallium/indium/arsenic and a second that’s gallium/arsenic and gallium/indium/arsenic. The two have slightly different properties in what they absorb most efficiently, which we’ll come back to shortly.
Since this configuration is entirely controllable, the researchers essentially wrap the whole device, which includes both the heating element that produces photons and the thermophotovoltaic cell that converts them to electricity, in highly reflective material. Any photon that emits in the wrong direction gets reflected to either strike the thermophotovoltaic device or be absorbed by the heating element, thus helping maintain its high temperature. The same is true for any photons that reach the thermophotovoltaic material but aren’t absorbed by it. (The researchers dryly note that photovoltaics can’t reflect unabsorbed photons to the Sun to keep it hot.)
The net result is a total device efficiency of around 40 percent, depending on which materials are used and the temperature of the heat source.
How this stacks up
A 60 percent loss sounds pretty horrific compared to a battery, where the round-trip efficiency is more than 90 percent. But the researchers note the efficiency is already higher than that of the average steam turbine generator in the US. The thermophotovoltaic devices are relatively new, and it’s expected that there will be plenty of room to boost the efficiency above 40 percent; by contrast, turbines are about as mature as a technology gets.
That’s where the two different devices come in. One was most efficient at extracting electricity from temperatures at around 2,400° C, the second did better once temperatures dropped below 2,000° C. So it should be possible to design systems where different thermophotovoltaic devices are used to efficiently extract electricity as the temperature of source material progressively drops. And, once the temperature drops below where thermophotovoltaic devices work well, things should still be hot enough to create steam to drive a turbine.
A second benefit is that the system is pretty agnostic about how it generates the heat for storage in the first place. It could come from electricity when wind and solar are overproducing. It could be part of a concentrating solar power plant (although those tend to max out at around 1,000° C). One design for a next-generation nuclear power plant would use heat storage to increase its flexibility. There may even be some industrial processes that produce waste heat at these temperatures (although they’re also well above what obvious things like steelmaking require) that could be stored.
Finally, the team notes that an inexpensive material—graphite—can be used to store heat at these temperatures. So, as long as the cost of the thermophotovoltaic device and supporting hardware can be kept within reasonable limits, this might allow thermal storage coupled with renewables to compete with fossil fuels. The main issue seems to be the extreme temperatures needed to get this to work.
What about solar PV heating systems?
Solar PV panels can power appliances and just about anything else in the home, as long as that appliance or device depends on electricity. This means that domestic solar panels can heat a home only if an electric heating system is in place. This extends to some furnaces, hot water tanks and gas or oil boilers, which might have electrical components.
Yes, you can heat water with solar PV panels by using an immersion optimiser. This technology detects when a surplus of solar PV generation is sent to the grid and diverts that energy into heating the water tank. This enables the occupant to optimise their energy usage and store hot water for use later on during the day.
What else should you know?
You can learn more about PV solar panels and systems in these helpful articles:
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Loss of Heat in PV Modules
We have seen what contributes to the heating up of a PV module. We shall now see how the heat from PV modules is lost. A PV module’s operating temperature is the point of thermal equilibrium between the heat generated in the PV module and the heat that is lost to the environment. Heat loss occurs through three main mechanisms namely conduction, convection and radiation. We shall now have a look at how PV modules lose heat through each of these mechanisms.
1] Conduction: This type of heat transfer occurs when two or more things are in contact. This could also be air. In PV modules, these occur due to the gradient between the modules and the things in contact such as the mount and the air. The thermal resistance and the configuration of the materials that are used to encapsulate PV cells into modules are what determine the ability of a module to transfer its heat to its surroundings. Conductive heat flow can somewhat be visualised using the mechanism of conductive current flow. Just like there is a driving force in a conductive current flow which is a difference in the voltage, there is a driving force in conductive heat flow which is a difference in temperature. Hence, temperature and heat (power) are related using the following equation which is similar to the equation that relates voltage to the current across a conductor:
Here, PHeat is the heat or power generated by the module, f is the emitting surface’s thermal resistance in °C/W and ∆T is the change in temperature. The equation is valid on the assumption that the material of the module is uniform and in a steady state. The ‘f’ depends on the thickness of the material and its conductivity. Thermal resistance is given by:
Here, A is the area of the surface that is conducting the heat, l is the length of the material through which there will be heat transfer and k is the thermal conductivity which is expressed in W/m °C. In order to determine the thermal resistance of a relatively more complex structure, the individual thermal resistances are added up in series or parallel. For instance, both the front and the rear surfaces of a module conduct heat to its environment. The two mechanisms are thought of as being operated in parallel with one another. Thus, the thermal resistance of the front and rear accumulate in parallel. On the other hand, the thermal resistances of the encapsulating material and the front glass would add in series.
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2] Convection: When a material moves across the surface of another material, heat is transported away from the surface of the latter material and this is how convective heat transfer occurs. This happens with PV modules too as the wind blowing across a module transports the heat away. This transferred heat is given by:
Here, A is the area of contact between the two materials participating, h is the convection heat-transfer coefficient and its units are W/m 2 °C, and is the difference in temperature of the two materials. The convection heat transfer coefficient (h) is determined experimentally for each system and its conditions. This is because it is quite complicate to compute.
3] Radiation: We know that any object will emit radiation depending upon its temperature. However, a PV module is not an ideal blackbody. For non-ideal blackbodies, the blackbody equation is modified and this is done by adding a new parameter called the emissivity, ε, of the material. The emissivity of a perfect blackbody is 1. The absorption properties tell a lot about the emissivity of an object since both will usually be very similar. Taking metals for instance, which usually have reduced absorption, have a lower emissivity as well. This is usually around 0.03. Now, to add the emissivity in the equation for emitted power density from a surface gives:
Here, is the emissivity, is the Stefan-Boltzmann constant, and T is the temperature of the cell in K. The net heat lost from the PV module because of radiation is the difference between the heat emitted from the surroundings to the PV module and the heat that the PV module emits to the surroundings. This is given by:
Nominal Operating Cell Temperature
The ratings of a PV module are done in Standard Testing Conditions (STCs) i.e. at 1 kW/m 2 and at 25°C. In reality, however, when they are operating in the field i.e. on the rooftop or in the ground, the temperature is usually higher and the insolation is usually somewhat lower than the STCs. So, to determine the power output of a cell or a module, it is essential to determine the operating temperature (expected) of the cell or module. The Nominal Operating Cell Temperature (NOCT) is the value of temperature reached by open-circuited solar cells in a module under certain conditions. These conditions include an Irradiance level of 800 W/ m 2 on the cell surface, an air temperature of 20°C, the velocity of the wind as 1 m/s and the mounting to provide an open back side for the module(s). The following equation gives the cell temperature as a function of the air temperature, the NOCT and the insolation level in mW/cm 2 :
Heat loss through both, conduction and convection, are linearly related to the insolation that is incident on a PV cell/module. This is verified by the equations for solar radiation and temperature difference between the module and air. However, this is only true for a given wind speed, provided that there is not much considerable change in the thermal resistance and heat transfer coefficient with temperature. The NOCT is the best in the case where the module has fin-like structures made up of aluminium on its rear. These fins are used to cool the module down. This reduces the thermal resistance and increases the surface area for convectional heat loss. The figure below shows the layers of a PV module with fins made up of aluminium at the rear:
There are some other factors also that have an impact on the NOCT of a cell/module. For instance, the design of a module, especially the module materials and packing density of the cells, has a major effect on the NOCT. A lower packing density of the rear surface along with a lower thermal resistance could make a difference in temperature of 5°C or maybe even more. Mounting conditions of modules could also affect the operating temperature by affecting heat transfer. Both conductive and convective heat transfers are affected by the way in which the modules are mounted. If the rear surface is covered with no gap for air to flow (such as the case where the module is directly mounted on a roof) will have an infinite thermal resistance. Convectional transfer is also limited to only the front of the module. Thus, in roof-integrated mounting systems, the operating temperature is usually increased. This often causes the temperature of the modules to increase by 10°C.
Thermal Expansion and Thermal Stresses
Thermal expansion is the expansion of a material upon heating. It needs to be taken into account when making solar modules as cells can expand too. Consider the following animation:
Here, αGC and αCD are the expansion coefficients of glass and the PV cell respectively, D is the width of the cell and C is the distance between two cells’ centres. As shown in the figure above, the connections between cells are looped. There are also double interconnects which are used to protect against the possibility of fatigue failure caused by that kind of stress. Additionally, all module interfaces are subject to temperature-related cyclic stress which may eventually lead to delamination of the module.
In this article, we have seen what the effect of temperature and heat is on photovoltaic cells and modules. We have looked at how heat is generated and lost in PV modules. We also looked at the Nominal Operating Cell Temperature of a PV module and how it is used as a more realistic parameter. We finally looked at thermal expansion and stresses and how they affect PV modules. The effect of different factors such as temperature and heat is an important area of study and research as it can help understanding those effects which would help in researching methods to tackle the negative effects.
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