This paper presents the development of methods and mathematical models to determine the DC/AC average efficiency of inverters that allow to optimize estimates of electricity generation of photovoltaic systems. The adaptive hybrid mathematical model of DC/AC average efficiency of inverters of photovoltaic systems proposed in this paper may be composed of three function settings–Linear, Lognormal, and Polynomial–considering the influence of the relative power, which varies with the sizing factor inverter and the DC input voltage. Determining of the average efficiency with a high degree of accuracy guarantees greater reliability in estimating electricity generation of photovoltaic systems. Depending on the specific behavior of each model and topology of inverter, the adaptive hybrid mathematical model determines the fit functions with highest coefficient R2 , and estimates with accuracy the DC/AC average efficiency that represents the operation and dynamic behavior of the inverters.

Introduction

Interest in the integration of distributed generation units in the electric power system arose from the growth of incentives to using alternative sources of energy, the technological evolution that resulted in the fall of prices of energy generation systems [1,2], and from environmental pressures [3]. Especially, distributed generation photovoltaic systems have technological maturity, performance, reliability, economic competitiveness and harmonious architectural integration. In this scenario of inserting distributed generation photovoltaic systems, the consumer units also become electrical energy generating units (prosumer units). The DC/AC inverter is responsible for converting DC electrical energy generated by photovoltaic modules (photovoltaic array or generator) to AC electrical energy, with characteristics and quality for injection in the power grid. Since the technology was developed, the inverters have considerable increases in DC/AC efficiency and safety in energy conversion, achieving efficiencies of 98% in medium powers [4] and high efficiencies even at load levels of 10 or 20% of power nominal [5]. The inverters used in grid connected photovoltaic systems have a maximum power point tracking, anti-island protection, high conversion efficiency, automatic synchronization with the power grid, low harmonic distortion level and power factor close to the unit [5,6]. Most inverters use a two-stage power conversion topology; the first is a DC/ AC/DC or DC/DC stage, which is needed to increase the voltage to higher values. The second stage is the DC/AC conversion for power grid connection [7,8]. There are two main classifications of inverter topologies for photovoltaic systems, with or without galvanic isolation [9]. The use of inverter with low or high frequency transformer ensures galvanic isolation [10]. Galvanic isolation solutions offer safety, but also losses in the extra components, so the inverters without galvanic isolation, that is, transformersless inverters, can increase efficiencies by 1–۲% [۱۱]. As a safety measure, the first grid-connected photovoltaic systems were designed to operate at low voltages and therefore, required inverters with transformer [12]. Galvanic isolation prevents leakage of current that can cause, for example, degradation of performance, activation of protections, safety difficulties, and problems of electromagnetic compatibility [8]. However, the use of transformerless inverters has some limitations, for example, several thin film modules need protection against leakage currents caused by the parasitic capacitance. In this case, inverters with high frequency transformers are required; thus it is possible to ground the negative pole of the modules avoiding an electrical corrosion, which damages their cells, impairing their performance and service life [13,14].