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Abstract In this work, we intend to solve the equations governing two laminar isothermal or non-isothermal coaxial plane jets with variable density in an ambient fluid at rest in order to study the initial conditions influence (i.e. the nozzles ejection conditions) on the jet characteristic parameters. A finite difference method is developed to solve the dimensionless Navier–Stokes and energy equations resulting from some assumptions. The discussion about the results relates primarily to the concentration core length according to the nozzles thicknesses ratios. The influences of the gas velocity and temperature resulting from the external nozzle are also examined. This made it possible to deduce correlations of practical use between these parameters in order to apply them in engineering processes.

Abstract In this work, we intend to solve the equations governing two laminar isothermal or non-isothermal coaxial plane jets with variable density in an ambient fluid at rest in order to study the initial conditions influence (i.e. the nozzles ejection conditions) on the jet characteristic parameters. A finite difference method is developed to solve the dimensionless Navier–Stokes and energy equations resulting from some assumptions. The discussion about the results relates primarily to the concentration core length according to the nozzles thicknesses ratios. The influences of the gas velocity and temperature resulting from the external nozzle are also examined. This made it possible to deduce correlations of practical use between these parameters in order to apply them in engineering processes.

This manuscript presents performed laboratory studies and the analysis of the impact of current shunt values used in the differential connection on the wideband metrological performance of inductive current transformers. Moreover, a comparison of the accuracy of wideband and 50 Hz-type inductive current transformers in the specified frequency range from 50 Hz to 5 kHz is presented. The main factor which may influence the wideband accuracy of inductive current transformers is the phenomenon of self-generation. This causes rapid changes in the accuracy, and simultaneously causes the most positive and the most negative values of current error and phase displacement. To evaluate the metrological performance in the differential measurement setup for higher harmonics of the distorted current, a digital acquisition board was used. Obtained results show that if proper values of current shunt resistance are chosen, such devices may be used to evaluate the wideband accuracy of inductive current transformers. The results indicate that the typical units designed for the transformation of sinusoidal current with a frequency of 50 Hz can achieve a comparable metrological performance to that of the wideband inductive current transformer.

This manuscript presents performed laboratory studies and the analysis of the impact of current shunt values used in the differential connection on the wideband metrological performance of inductive current transformers. Moreover, a comparison of the accuracy of wideband and 50 Hz-type inductive current transformers in the specified frequency range from 50 Hz to 5 kHz is presented. The main factor which may influence the wideband accuracy of inductive current transformers is the phenomenon of self-generation. This causes rapid changes in the accuracy, and simultaneously causes the most positive and the most negative values of current error and phase displacement. To evaluate the metrological performance in the differential measurement setup for higher harmonics of the distorted current, a digital acquisition board was used. Obtained results show that if proper values of current shunt resistance are chosen, such devices may be used to evaluate the wideband accuracy of inductive current transformers. The results indicate that the typical units designed for the transformation of sinusoidal current with a frequency of 50 Hz can achieve a comparable metrological performance to that of the wideband inductive current transformer.

Abstract The price effect of the rising share of renewable electricity, which is called ‘merit-order-effect’, leads to noticeable changes in the German power industry and debates about the electricity market design. This paper estimates the merit-order-effect induced by variable renewable energy in the German-Austrian electricity sector with a multivariate regression model. The research focus lies on the impact of the estimated effects on the marketability of variable renewable electricity generation. The results show a systematic decline of the average market revenues for wind and photovoltaic plants in the period from January 2011 to December 2013. Current market data shows a continuation of this trend into 2016. According to the German long term goals for the use of renewables, wind and solar power will play a crucial role in the future electricity generation mix. If investments in these technologies will be profitable without any regulatory remuneration mechanisms in addition to the market revenues, depends on the further cost degression and the development of the merit-order-effect.

Abstract The price effect of the rising share of renewable electricity, which is called ‘merit-order-effect’, leads to noticeable changes in the German power industry and debates about the electricity market design. This paper estimates the merit-order-effect induced by variable renewable energy in the German-Austrian electricity sector with a multivariate regression model. The research focus lies on the impact of the estimated effects on the marketability of variable renewable electricity generation. The results show a systematic decline of the average market revenues for wind and photovoltaic plants in the period from January 2011 to December 2013. Current market data shows a continuation of this trend into 2016. According to the German long term goals for the use of renewables, wind and solar power will play a crucial role in the future electricity generation mix. If investments in these technologies will be profitable without any regulatory remuneration mechanisms in addition to the market revenues, depends on the further cost degression and the development of the merit-order-effect.

Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.

Lithium-ion batteries exhibit a dynamic voltage behaviour depending nonlinearly on current and state of charge. The modelling of lithium-ion batteries is therefore complicated and model parametrisation is often time demanding. Grey-box models combine physical and data-driven modelling to benefit from their respective advantages. Neural ordinary differential equations (NODEs) offer new possibilities for grey-box modelling. Differential equations given by physical laws and NODEs can be combined in a single modelling framework. Here we demonstrate the use of NODEs for grey-box modelling of lithium-ion batteries. A simple equivalent circuit model serves as a basis and represents the physical part of the model. The voltage drop over the resistor–capacitor circuit, including its dependency on current and state of charge, is implemented as a NODE. After training, the grey-box model shows good agreement with experimental full-cycle data and pulse tests on a lithium iron phosphate cell. We test the model against two dynamic load profiles: one consisting of half cycles and one dynamic load profile representing a home-storage system. The dynamic response of the battery is well captured by the model.