Because of the stochastic nature of wind turbines, the output power management of wind power generation (WPG) is a fundamental challenge for the integration of wind energy systems into either power systems or microgrids (i.e., isolated systems consisting of local wind energy systems only) in operation and planning studies. In general, a wind energy system can refer to both one wind farm consisting of a number of wind turbines and a given number of wind farms sited at the area in question. In power systems (microgrid) planning, a WPG should be quantified for the determination of the expected power flows and the analysis of the adequacy of power generation. Concerning this operation, the WPG should be incorporated into an optimal operation decision process, as well as unit commitment and economic dispatch studies. In both cases, the probabilistic investigation of WPG leads to a multivariate uncertainty analysis problem involving correlated random variables (the output power of either wind turbines that constitute wind farm or wind farms sited at the area in question) that follow different distributions. This paper advances a multivariate model of WPG for a wind farm that relies on indexed semi-Markov chains (ISMC) to represent the output power of each wind energy system in question and a copula function to reproduce the spatial dependencies of the energy systems’ output power. The ISMC model can reproduce long-term memory effects in the temporal dependence of turbine power and thus understand, as distinct cases, the plethora of Markovian models. Using copula theory, we incorporate non-linear spatial dependencies into the model that go beyond linear correlations. Some copula functions that are frequently used in applications are taken into consideration in the paper; i.e., Gumbel copula, Gaussian copula, and the t-Student copula with different degrees of freedom. As a case study, we analyze a real dataset of the output powers of six wind turbines that constitute a wind farm situated in Poland. This dataset is compared with the synthetic data generated by the model thorough the calculation of three adequacy indices commonly used at the first hierarchical level of power system reliability studies; i.e., loss of load probability (LOLP), loss of load hours (LOLH) and loss of load expectation (LOLE). The results will be compared with those obtained using other models that are well known in the econometric field; i.e., vector autoregressive models (VAR).

The use of renewable energy sources on university campuses is crucial for sustainable development, environmental protection by reducing greenhouse gas emissions, improving energy security, and public education. This study addresses technical and economic aspects of the newly designed photovoltaic system on the campus of the Bialystok University of Technology. The first part of the article presents the results of 9 years of research on an experimental photovoltaic system that is part of a hybrid wind and PV small system. The article proposes five variants of the arrangement of photovoltaic panels on the pergola. A new method was used to determine the energy efficiency of individual options selected for analysis. This method combines energy simulations using DesignBuilder software and regression analysis. The basic economic indicators NPV and IRR were applied to select the most appropriate arrangement of PV panels. In the recommended solution, the panels are arranged in three rows, oriented vertically, and tilted at 37°. The photovoltaic system, consisting of 438 modules, has a peak power of 210 kWp and is able to produce 166,392 kWh of electricity annually. The NPV is 679,506 EUR, and the IRR is over 38% within 30 years of operation.