This paper proposes a mathematical model for the shading profiles of a PV module with thin, long linear elements. The model includes the brightness distribution over the entire shading region (umbra, penumbra, and antumbra). A corresponding calculation code in the form of m-files has been prepared for the MATLAB environment. The input data for the calculations are the coordinates of the Sun’s position in the sky, the dimensions and spatial orientation of the shading element, and the spatial orientation of the shaded PV module. The correctness of the model was verified by a measurement experiment carried out under actual outdoor weather conditions. Statistical analysis of the comparison between the measurement data from the experiment and the model showed its high accuracy. As part of this research work, it was also checked how shading with thin linear elements affects the current–voltage characteristics of the module. It turned out that even a small linear shading could reduce the power output of the module by more than 6%, with the distribution of this shading across the individual cells of the module being extremely important.

The paper presents the problem of modeling and simulation of thermal energy generation in a batch-fired straw boiler combined with a buffer tank. The batch-fired straw boiler in concern have a combustion chamber and a water jacket. During the combustion process, the combustion chamber heats up and from it the water jacket. Within the boiler, water circulates between the water jacket and the buffer tank.

W artykule przedstawiono problematykę sterowania hybrydowym systemem grzewczym. System ten ma dwa źródła ciepła: sieć miejską oraz kocioł na biomasę ze zbiornikiem akumulacyjnym. Sterowanie tym systemem wymaga odpowiedniej&nbs...

The paper proposes a batch-fired straw boiler model, which is used to control the temperature of the combustion chamber. This model describes a boiler which consists of a combustion chamber and a water jacket. The combustion chamber is blown by the adjustable air mass flow, which is used for straw combustion in the combustion chamber. The combustion chamber heats a water jacket, which in turn transfers heat to the external circulation. The model is nonlinear because of the straw combustion process. Apart from this process, the other components of the model are linear and describe mass and heat transfer. The boiler model has single input and single output (SISO). The input of the model is the air mass flow and the output is the temperature of the combustion chamber. Based on the presented model, one proposed a closed-loop system to control the temperature of the combustion chamber. The closed-loop system consists of the classical PID controller, model of the whole plant and some inverse transfer function of the nonlinear part of the whole model. In this way, there is calculated a time response of the air mass flow, which results a reference value of the temperature of the combustion chamber. The paper presents results of simulation of this closed-loop system in MATLAB/Simulink.