Constitutive equations and configurational torque for PhotoVoltaic panels, related to intrinsic times of noncircular orbits and...

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1 See discussions, stats, and author profiles for this publication at: Constitutive equations and configurational torque for PhotoVoltaic panels, related to intrinsic times of noncircular orbits and... Technical Report March 2017 DOI: /RG CITATIONS 0 2 authors, including: Lena J-T Strömberg own 24 PUBLICATIONS 143 CITATIONS SEE PROFILE Some of the authors of this publication are also working on these related projects: Bending of thin beams View project Noncircular orbits: Analogies, Cohomologies, Analysis View project All content following this page was uploaded by Lena J-T Strömberg on 12 March The user has requested enhancement of the downloaded file. All in-text references underlined in blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.

Constitutive equations and configurational torque for PhotoVoltaic panels, related to intrinsic times of noncircular orbits and striped fur.

2 Constitutive equations and configurational torque for PhotoVoltaic panels, related to intrinsic times of noncircular orbits and striped fur. Lena J-T Strömberg* and Adel Soualmia** *previously Dep of Solid Mech, Royal Inst of Techn, KTH, ** former president of the Assembly at Samsung Electronics Abstract: Creation and collection of current in PhotoVoltaic are modelled assuming Sun Light energy as electromagnetic radiation with certain frequencies. The interaction is discussed in terms of couplings through frequency and (rate of) power. Discrete frequency ratios determined by intrinsic times and analogies with the geometry in a HVDC transmission line pole, are used to describe details of the scenario which gives current. Keywords: partial shade, darker light, multi junction, higher order model, frequency, angular velocity, noncircular orbits, nco, solar cell, photovoltaic, Schottky diode, HV transmission line pole 1. Introduction In Soualmia and Chenni (2016), partial shade on a PV system is analysed, and relations for Voltage-Current and Power-Voltage are given for various shading distributions on the panel. Here, two of these dependencies, will be scrutinised in terms of modeling, namely the instantaneous power of solar radiation and relative shading rate (or difference in Sunlight between shaded and exposed areas). The results assuming possibilities to collect both light and lower energy light, are elaborated for a multi junction with a geometry similar to that in a HV transmission line pole [3]. The dynamics and propagation are compared to the general results obtained for frequency ratios and intrinsic times, presented in Strömberg (2016). 2. Interaction with Sunlight into partial shade Distribution. For brevity, and since it is a possible spectral distribution, the partial shade are assumed as stripes, similar to those on a tiger. This may be accomplished by different types of Schottky diodes, described below. A tiger named Rayé, (from French for striped), with a pattern, suitable to organize energy from Sun light.

3 In [1], Appendix 1, it is assumed that sunlight energy enters the diode as photons, characterised by frequencies, w. There are other possibilities, e.g. in mechanics, kinetic energy for rotating systems is given by Jw 2 /2, where J is the moment of inertia. Here, we will adopt the frequency interaction, and assume the format from Strömberg (2016), elaborated in Appendix 2, with intrinsic times and certain ratios. With analogies to nco, shade(dark light) and light correspond to the large frequency ratio 2.8, at f=1, and the formation into stripes is due to the high eccentricity, giving elongated distributions as stripes while pasting over the panel, c.f. Figure 2. Then, other frequencies and fine scale distribution may appear, according to the schemes provided by Figures 3-5. With control, if two types of diodes are located in stripes, this may divide the light in either dark shade or light. 3. Coupling with configurational torque The resulting illumination catched by the device is then distributed and this is controlled by intrinsic properties. The coupling to Sunlight may be with a so-called configurational torque. This equalizes the power provided by light input, for a short time, such that the behaviour of the panel is mostly governed by internal dynamical properties. Such behaviour is found at e.g. MC-vehicle wobbling, Strömberg (2013), Appendix 3. In [1] and Appendix 1, the function of a multi junction is explained in terms of band gap. The idea is to use the entire spectrum of Sunlight, i.e. also lower energy photons, by putting several n-substrates on top of each other. Although it is pointed out in [1], c.f. Appendix1, that the physics (i.e.band gap) of the n- substrate determines the absorbed radiation, it is possible that also the distance between metal and the absorbing point, is relevant. This was cast into a formula by Schottky [3]. Another way to capture collection of light with both high and low photon energy could be to put two different types of cells as neighbors in the same plane, instead of a cascade. If the light distributes naturally in stripes of dark and intense, such a panel may be efficient to collect different spectral content. The arrangement could also be beneficial to eliminate the risk of a hot-spot grilling, c.f. Soualmia and Chenni (2016), Strömberg and Soualmia (2017), and for curved designs e.g. at the shadow side of a spherical solar cell panel, Strömberg and Soualmia (2017) Multi junction in a high voltage transmission pole According to the animation in [3], the electromagnetic field is an almost round orbit, around the point B and then moves to C, and then to A and B again, and so on, by increasing and distorted orbits, c.f. Figure 1.

4 The distances agrees to some extent with the ratios in Figure 2-5, Appendix 2, and an interpretation as propagation with noncircular orbits, c.f. Strömberg and Soualmia (2017) 3, and Section 2, above. If this is valid also at smaller scales, such a geometry could be realised as a multi junction, to collect solar light more efficient.

5 Figure 1. Upper. HV Transmission line pole with a specified geometry for the inplane magnetic field given below. Lower. A snap-shot from an animation of the dynamic field around points A,B,C from [3]. 5. Instantaneous power of solar radiation The coupling above was assumed in terms of frequency determined by energy. In Soualmia and Chenni (2016), it is suggested that also the instantaneous power is significant. Since power is the time differentiation of energy, the instantaneous power may be characterized by rate of rate of energy. With a linear relation between energy and angular velocity, this is proportional to rate of angular acceleration. Remark. For the characteristics of wave propagation, such higher order differential may correspond to a more remote (and etheric) spatial interaction, than that of a homogenization with a spatial mean value. For MC-wobbling, harmonic oscillators can be derived, and invokes angular velocity and time-derive of angular acceleration, c.f. Strömberg (2013) and Appendix 3. There is a coupling to the torque between ground and the wheel, and the action of the driver provides a boundary angular velocity at certain occasions. From this, an analogy with frequency from Sun radiation may give a dependency on the rate of power. However, it is also likely to couple with a certain value of a lower derive at the boundary. If this gives heat flux, a non-desirable behavior may begin, causing high temperature and hot-spot c.f. Soualmia and Chenni (2016), instead of producing current.

6 Concluding remarks It was suggested that incoming Sun light is such that partial shade appears as stripes on a Photo Voltaic panel. Constitutive equations for partial shade invokes assumptions for light and non-light; i.e. certain parts of light that appears as shadows. Since shadows are created by an object, it may contain light that followed a path around the object. This is also accomplished when the object is a wave guide, as e.g. the Rayleigh wave at Earth quakes. We assumed partial shade not as darkness but as the minimum value of an alternating frequency, equation (1). Then the ratio r e /r 0 gives noncircular orbits that spreads in one direction, which may correspond to a pasting into stripes. In an elaboration, for a multi junction in a Schottky diode, a possible geometry of the collection points was compared with the scenario for electromagnetism at a HV transmission line pole. Remark. The concept for transmisson in [3], is one of many solutions to transportation of voltage and current. The Figure below shows a configuration where the three cables are located with a distance also between the poles. See also HVDC and HVAC. Acknowledgements To Mr Elouhabi for valuable guidance in high voltage ac, with control systems and to Dr:s at Researchgate for sharing ref 3. Appendix 1 Multijunction from

7 Today's most common PV devices use a single junction, or interface, to create an electric field within a semiconductor such as a PV cell. In a single-junction PV cell, only photons whose energy is equal to or greater than the band gap of the cell material can free an electron for an electric circuit. In other words, the photovoltaic response of single-junction cells is limited to the portion of the sun's spectrum whose energy is above the band gap of the absorbing material, and lower-energy photons are not used. One way to get around this limitation is to use two (or more) different cells, with more than one band gap and more than one junction, to generate a voltage. These are referred to as "multijunction" cells (also called "cascade" or "tandem" cells). Multijunction devices can achieve a higher total conversion efficiency because they can convert more of the energy spectrum of light to electricity. As shown below, a multijunction device is a stack of individual single-junction cells in descending order of band gap (Eg). The top cell captures the high-energy photons and passes the rest of the photons on to be absorbed by lower-band-gap cells. Much of today's research in multijunction cells focuses on gallium arsenide as one (or all) of the component cells. Such cells have reached efficiencies of around 35% under concentrated sunlight. Other materials studied for multijunction devices have been amorphous silicon and copper indium diselenide. As an example, the multijunction device below uses a top cell of gallium indium phosphide, "a tunnel junction," to aid the flow of electrons between the cells, and a bottom cell of gallium arsenide. Appendix 2 Summary of results from Strömberg (2017), where intrinsic time is derived for a system with varying frequency. The frequency is given by an angular velocity, Strömberg (2015) (t)= 0 exp(-2(r e /r 0 )sin(f 0 t)) (1) The format provides a possibility to derive relations assuming that time is determined by in terms of ratios. This will give 3 different functions depending on how time is created. i) From (1), we obtain that min(abs(r e /r 0 ))=0.5ln(w/w 0 ). The function is shown in a graph for frequency ratios embracing those common in acoustics, Figure 3 and 4. Preliminaries. Assume, similar to the establishment of the sine circular map that time is determined by the other frequency. ii) Time from the new frequency. Then, the relation for spatial ratio reads r e /r 0 =0.5ln(w/w 0 )/(sin(w 0 /w)). iii) As in ii), but with an updated format, and time from the first frequency. Relation for spatial ratio r e /r 0 =0.5ln(w/w 0 )/(sin(w/w 0 )). The functions are shown in Figure 2-6, for different f, and it is seen that the curves coincide at certain ratios.

8 Figure 2. Ratio of eccentricity and radius versus frequency ratio for case i), ii) and iii) from bottom at right, f=1. Figure 3. Ratio of eccentricity and radius versus frequency ratio for case i), ii) and iii), f=2, continuously and indicated with +, *, o respectively, at the ratios 3/2 and Figure 4. Ratio of eccentricity and radius versus frequency ratio for case i), ii) and iii), f=3/2, continuously and indicated with +, *, o respectively, at the ratios 3/2 and Figure 5. Ratio of eccentricity and radius versus frequency ratio for case i), ii) and iii) Left: f=3, indicated with +, *, o respectively, at the ratios 3/2 and 2. Right: f=1, indicated with +, *, o respectively, at the ratio 1/2.

q=[1:0.1:3]; f=3/2; figure(4) hold on ra1=0.5*log(q); ra2=0.5*log(q)./sin(1./q*f); ra3=0.5*log(q)./sin(q/f); plot(q, ra2) plot(q, ra3) plot(q, 0.5*log(q)) grid q=2; ra2=0.5*log(q)./sin(1./q*f); ra3=0.5*log(q)./sin(q/f); plot(q, ra2, 'm*') plot(q, ra3, 'mo') plot(q, 0.

9 q=[1:0.1:3]; f=3/2; figure(4) hold on ra1=0.5*log(q); ra2=0.5*log(q)./sin(1./q*f); ra3=0.5*log(q)./sin(q/f); plot(q, ra2) plot(q, ra3) plot(q, 0.5*log(q)) grid q=2; ra2=0.5*log(q)./sin(1./q*f); ra3=0.5*log(q)./sin(q/f); plot(q, ra2, 'm*') plot(q, ra3, 'mo') plot(q, 0.5*log(q), 'm+') q=3/2; ra2=0.5*log(q)./sin(1./q*f); ra3=0.5*log(q)./sin(q/f); plot(q, ra2, 'm*') plot(q, ra3, 'mo') plot(q, 0.5*log(q), 'm+') Appendix 3 Details of derivation for wobbling

10 References Soualmia A, Chenni R (2016). Modeling and Simulation of Photovoltaic Production Losses due to Partial Shade. Poster Scetit, Springer IEEE. Strömberg L (2013). Models of dynamical phenomena for certain moons in the solar system. Tsijournals. Strömberg L (2015). Motions for systems and structures in space, described by a set denoted Avd. Theorems for local implosion; Li, dl and angular velocities. Journal of Physics and Astronomy Research, 2(3): Strömberg L (2016). Noncircular orbits and organised chaos exemplified with sine circular map and Arnold's tongues, SCIREA Journal of Physics. 1(2), pp Strömberg L, Soualmia A (2017). Heat distribution and fractals in Photovoltaic panels, report Strömberg L, Soualmia A (2017) 2. Vorticity and rotational motion in Schottky diodes and Photovoltaic, related to nco and footballs. DOI: /RG Strömberg L, Soualmia A (2017) 3. Motions of light and electromagnetism on Schottky diodes in Photovoltaic panels, in analogies with noncircular orbits. Report, Researchgate [1] [2] [3] View publication stats

Electrons are shared in covalent bonds between atoms of Si. A bound electron has the lowest energy state.

Electrons are shared in covalent bonds between atoms of Si. A bound electron has the lowest energy state. Photovoltaics Basic Steps the generation of light-generated carriers; the collection of the light-generated carriers to generate a current; the generation of a large voltage across the solar cell; and