Polish energy sector is (almost from its origin) dominated by fossil fuel feed power. This situation results from an abundance of relatively cheap coal (hard and lignite). Brown coal due to its nature is the cheapest energy source in Poland. However, hard coal which fuels 60% of polish power plants is picking up on prices and is susceptible to the coal imported from neighboring countries. Forced by the European Union (EU) regulations, Poland is struggling at achieving its goal of reaching 15% of energy consumption from renewable energy sources (RES) by 2020. Over the year 2015, RES covered 11.3% of gross energy consumption but this generation was dominated by solid biomass (over 80%). The aim of this paper was to answer the following research questions: What is the relation of irradiation values to the power load on a yearly and daily basis? and how should photovoltaics (PV) be integrated in the polish power system? Conducted analysis allowed us to state that there exists a negative correlation between power demand and irradiation values on a yearly basis, but this is likely to change in the future. Secondly, on average, daily values of irradiation tend to follow power load curve over the first hours of the day.

International trends clearly indicate an increasing role of renewable energy sources in covering current and future demand on electric energy. Since the year 2004, Poland has been a member of the European Union. One of the main obligations of the EU members is to reduce their impact on the natural environment by increasing RES share in the energy mix. Polish energy system is based on domestic fossil fuels, particularly hard and brown coal, which enable Poland to generate over 83% of its electric energy [

According to the URE (Energy Regulatory Authority) [

Development of RES in Poland is a response to the EU regulation and the increasing social awareness of the global climate change.

Variable energy sources are a serious challenge for the power grid operator and people responsible for energy system development [

Solar Radiation Data (SoDa) [

Global irradiation incident on optimally inclined PV modules in Europe. Key: Polish border outline: red line; dots: selected cities. Map source: [

Data concerning aggregated electrical energy demand in Poland was obtained from Polish Power Lines (PSE pol. Polskie Sieci Elektroeneretyczne) [

Mean monthly power load and the ratio of its minimal to maximal values of for a given year.

First of all, a correlation coefficient between all pairs of time series was calculated in order to determine whether or not energy generation from PV installations in Poland will follow the same patter. In total, 741 values were obtained. Secondly mentioned correlation coefficients were assigned to the corresponding distance between pairs of sites. It is important to note that, prior to calculating correlation coefficients, selected irradiation values equal to zero were removed from time series. Basically, the site with earliest occurrence of sunlight and that with latest sunset determined the time span for all time series for a given day.

The relation of irradiation to power load values was investigated on annual and daily time scales. In case of yearly variability, mean monthly values of irradiation and power load were calculated for each month separately. After that, they underwent a normalization procedure to 0-1 range. In order to assess mentioned relation on a daily time scale, irradiation time series from each site were summarized, thus yielding an aggregated time series which covered the period from 2010 to 2014 with a 15-minute time step. In this part of analysis, only those hours of the day when irradiation may occur were investigated. Average monthly timeframe for each day was estimated based on sunrise and sunset hours. Finally, based on the 2010–2014 time series, a typical pattern of a power load and irradiation, for given timeframe over day, was calculated.

An analysis of the PV systems integration into the polish energy system concentrated on their potential to cover current and minimize maximal energy demand and their impact on energy demand variability. In order to answer those research questions, the following assumptions have been made. Photovoltaic systems nominal power will be equally distributed among 39 previously selected locations. Energy yield from PV power units will be calculated in a 15-minute time step for the years 2010–2014 based on methods described in papers [

In this part, we present results of conducted calculations, in the same order as they were described in previous section.

We begin by analyzing the values of correlation coefficients between irradiation time series. Figures

Values of correlation coefficients between irradiation time series (2010–2014 with a 15-minute time step); the uncertainty of the slope parameter is −0.88% whereas that of the intercept parameter is 0.11%.

Values of correlation coefficients between irradiation time series (June 2005 with a 1-minute time step); the uncertainty of the slope parameter is −3.68% whereas that of the intercept parameter is 0.9%.

In case of a 15-minute time step (Figure ^{−2} ^{−1}) and variability index for normalized (0-1) Warsaw time series were equal to 0.249 and 0.953% whereas for a source distributed among 39 sites, they were 0.238 and 0.861%. This gives a decrease by, respectively, 4.13% and 9.61%. Decrease in both metrics points to the fact that the energy generation curve from such distributed sources will be smoother, meaning with smaller sudden ups and downs in available energy. This proves the existence of spatial distribution smoothing effect.

Power load in Poland varies and reaches it maximal values usually in December or January, whereas minimal values can be observed in May. Due to the geographical location of Poland, maximal sums of irradiation are observed in June and almost 80% of annual irradiation is observed from May to August. This leads to a conclusion that irradiation and power load are strongly anticorrelated. The value of CC which was calculated for data presented in Figure

Normalized mean monthly values of irradiation and load in Poland over the years 2002–2015.

In ideal weather conditions, irradiation is following patterns which can be calculated for each day, or even seconds over given year, based on the so-called clear-sky model [

Figure

Normalized (0-1) values of irradiation and power load over the course of each month ((a), January).

Based on description in Section

Increasing share of photovoltaics on covering energy demand leads to a picking-up value of variability index (Figure

Considering current annual energy demand and its patterns (which was on average equal to 157 TWh in period 2010–2014), the largest increase in PV share in covering current energy demand is observed when installed capacity of PV ranges from 0+ to 50 GWp (see Figure

Further analysis of increasing installed capacity in PV systems has shown (according to the considered data) that it is not physically possible to cover more than 53% of current energy demand from PV, without energy storage devices. See on Figure

When the share of PV covering the current energy demand exceeds 11-12% (55–60 GWp of installed capacity), greater and greater energy surpluses start to occur. For example, when installed capacity reaches 97.5 GWp then 39% of generated energy is perceived as a surplus and must be stored or exported, not mentioning the fact that in the same time other energy sources are not generating energy at all.

Energy generation from photovoltaic installations does not lead to a decrease in maximal energy demand. This is due to the fact that peak energy demand in Poland occurs after sunset. However, an increasing energy consumption resulting from greater demand for air-conditioning may be effectively covered from PV, especially BIPV (Building Integrated Photovoltaics) [

Photovoltaics impact on energy demand variability.

How does energy demand covered from PV and resulting energy surpluses change for different values of installed capacity in PV. Key: D_PV_1 and so forth (denoted by square, triangle, and circle) represent current demand covered from PV; in respective ranges they were approximated by linear regression equation.

Overall, similarly as in the paper presented by De Jong et al. [

This study concludes that photovoltaics have huge potential to contribute to covering energy demand in Poland. Additionally, conducted analysis has shown that there are some boundaries which should not be crossed when it comes to the maximal capacity installed in PV plants in Poland (however, current trends show that exceeding even 1 GWp in the immediate future is rather unlikely). This study unveiled several interesting directions for future research. First of all, there is a need to perform the thorough analysis of air conditioners impact on power demand and how it correlates with irradiation values. Secondly, a more detailed analysis of regional energy demand patterns is essential to create a model which will aim at optimally distributing variable energy sources whilst taking into the consideration limited capacities of transmissions networks. Finally, a regional potential for energy storage in form of pumped-storage or run-of-river power plants with pondage coupled with photovoltaics should be investigated and estimated.

The authors declare that they have no competing interests.