ECONOMIC AND MATHEMATICAL MODELING OF THE RENEWABLE ENERGY DEVELOPMENT IN UKRAINE
Authors: Yelisieieva O. K. , Lyzhnyk Yu. B. 
Published: August 2024

Objective. The objective of the article is to apply economic and mathematical models for the analysis, modeling and forecasting of the development of renewable energy in Ukraine, assessment of country's renewable energy sources potential.

Methods. The following methods are used to model and forecast the development of renewable energy in Ukraine: correlational and actocorrelational analysis (to identify the relationship between macroeconomic indicators of Ukraine and the development of renewable energy in the country); three-factor autoregressive and multiplicative forecasting and five-factor regression forecasting (for forecasting indicators of renewable energy of Ukraine); the basics of the mathematical apparatus for the analysis of transient processes, the methodology of determining the coefficients of impulse-transient and transient functions, methods of building differential models, Laplace transformation and obtaining transient functions, the basics of the mathematics of imaginary quantities, methods of obtaining the amplitude-phase and frequency characteristics of the object under study, methods of analysis stability of controlled dynamic processes (to present the Total renewable energy indicator in the form of a dynamic transient process and model its future states by obtaining a second-order differential equation with a simple input, a complex transfer function and by determining the amplitude-phase frequency characteristic and constructing a Nyquist frequency hodograph, which showed the stability of the studied process to external disturbances).

Results. Forecasting the installed capacities and production volumes of renewable energy is an important task for the effective development of this industry. A new approach to forecasting is proposed, combining autoregressive and multivariate regression models and dynamic modeling.

The development of the capacity of renewable energy is considered as a dynamic transient process, which is represented by a complex transfer function with its real frequency characteristic and its imaginary frequency characteristic, which are used to construct the Nyquist hodograph, which shows the stability of the researched process of development of the capacity of renewable energy from investment investments.

According to the results of modeling based on the transient process method, a model of changes in the volume of installed capacities of renewable energy of Ukraine depending on the volume of investments in renewable energy is obtained in the form of a differential equation, and it is found out that this process is stable, that is, even with temporary restrictions or reductions of such investment over time it will return to a stable growing trend.

The proposed method of dynamic modeling makes it possible to obtain more accurate and reliable forecasts of the development of renewable energy capacity, compared to traditional methods. This method can be used to make informed decisions regarding the development of solar energy and investment in this industry in Ukraine.