PROBLEMS OF MATHEMATICAL MODELING OF SOLAR STATION

Аннотация

The article presents information that the mathematical model of the operation of a solar power plant of an energy station is simplified by the fact that its parameters are grouped as if the parameters responsible for the territorial location of the plant are used as permanent parameters, and the average values of solar insolation are variable parameters. Keywords. Photovoltaic cell, shunt resistance, mathematical model, photovoltaic panels, solar radiation, temperature, simulation of operating modes, voltage-ampere and voltage-watt characteristic. Introduction. When analyzing domestic and world experience in the field of solar panel modeling, two approaches can be distinguished. One of them considers the photovoltaic panel as a separate component of the power supply system and examines the parameters of the output power depending on various input factors. Procedure. For this, a classical circuit for replacing a photovoltaic cell with one diode can be used, shown in Fig. 1. This photoelectric cell replacement scheme is widely used and is used to assess the effect of the illumination degree and temperature of the photoelectric cell on its characteristics. Such a model is used in the calculation of generating plants with both serial and parallel connection of elements. Fig. 1 - Single-ion photovoltaic cell replacement scheme In this scheme, the diode VD and the current Id passing through it are connected in parallel with a branch containing a current source Iph, this circuit is a p-n transition model, to which a resistor Rs is connected in series, characterizing the active 250 International scientific journal “Interpretation and researches” Volume 2 issue 2 (24) | ISSN: 2181-4163 | Impact Factor: 8.2 resistance of the connecting contacts and the photopanel itself and a branch with a shunt resistance Rsh simulates the reverse p-n junction resistance and the resistance of the conductive films of the element. Accordingly, the load current equation I can be written as follows: 𝑞(𝑈 + 𝐼 × 𝑅 ) (𝑈 + 𝐼 × 𝑅 ) 𝑠 𝑠 𝐼 = 𝐼 − 𝐼 [ − ] 𝑝ℎ 𝑠 𝑁 𝑇 𝑅 𝑘 𝑠ℎ where: 𝐼𝑝ℎ is a photocurrent dependent on solar radiation, defined as: 𝐵 𝐼 = [𝐼 + 𝐾 (𝑇 − 𝑇 )] × 𝑝ℎ 𝑠𝑐 𝑖 𝑟𝑒𝑓 1000 𝐼𝑠 is the saturation current of the diode, which is expressed by the cubic dependence on temperature as follows: 𝐼 𝑞𝑈 𝐼 𝑇 = 𝐼 ( )3 × 𝑁 × 𝑁𝑘( 𝑡 ) 𝑠 𝑅𝑆 𝑇 𝐼 𝐼 𝑟𝑒𝑓 − 𝑇 𝑇 𝑟𝑒𝑓 Here T is the temperature of the photoelectric cell, Isc is the short-circuit current, k is the Boltzmann constant, Ki is the temperature coefficient of the short- circuit current, Tref is the reference temperature, B is the solar insolation value in W/m2, N is the diode ideal coefficient, N is the number of solar panels, Ut is the diode thermal voltage. The reverse saturation current of the diode 𝐼 in this relation for standard 𝑅𝑆 conditions can be approximated as follows: 𝐼 𝑠𝑐 𝐼 = 𝑅𝑆 𝑞𝑈 𝑁𝑘𝑇𝑁 𝑖 Analysis. Due to the dependence of the load current equation on the parameters Rs and Rsh, the current Ish through the shunt resistance is sometimes neglected due to the large value of the shunt resistance. The implementation and testing of such a mathematical model is given in, where for photovoltaic panels, depending on the level of solar radiation and temperature, modeling of operating modes and further construction of voltage-ampere and voltage-watt characteristics are performed, and the following expression is obtained, which determines the relationship of the output power of the solar panel with the temperature of the photovoltaic module and solar radiation: 100 + 0,759 · (25 − t) 𝑃 = (0,2465G − 0,1378)× ( ) 100 A similar approach using a single-ion substitution scheme has been proposed, but it should be noted the importance of investigating the photovoltaic power supply system as a complex consisting of a set of interconnected elements whose main task 251 International scientific journal “Interpretation and researches” Volume 2 issue 2 (24) | ISSN: 2181-4163 | Impact Factor: 8.2 is to convert the energy of the sun into electricity. As a rule, such systems are represented by a photovoltaic installation, an electric energy storage, a controller, an inverter and a load. In addition, for the photovoltaic panel, the importance of modeling these components under various solar insolation data and temperature modes of operation is noted. Methods. A model is considered that estimates the voltage and current potential of a photovoltaic panel under given operating conditions (solar insolation and temperature) and uses a single-ion replacement scheme, but excludes from it a parallel branch with shunt resistance and the expression connecting the load current reduces to: 𝑞(𝑈 + 𝐼 × 𝑅 ) 𝑠 𝐼 = 𝐼 − 𝐼 [ − 1] 𝑝ℎ 𝑠 𝛼 where α is the thermal stress measurement completion factor, B. This method allows you to take into account the intensity of solar radiation, ambient temperature, technical characteristics and the degree of spatial orientation of the photoelectric converter. In operation, the output power of the photovoltaic mod