• Aleksandra Dedinec Faculty of Computer Science and Engineering, University Ss. Cyril and Methodius, Skopje, Republic of Macedonia
  • Igor Tomovski Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428 1000 Skopje, Republic of Macedonia
  • Ljupčo Kocarev Faculty of Computer Science and Engineering, University Ss. Cyril and Methodius, Skopje, Republic of Macedonia Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov, 2, P.O. Box 428 1000 Skopje, Republic of Macedonia




This paper is motivated by a large tendency of shift towards low emission electricity production, which can be achieved by substituting the conventional energy sources by renewable energy sources. Therefore, a share of renewable energy sources is continually growing. However, large-scale integration of renewable energy sources into the power system is a challenging task, since it depends on a balance between demand and supply at any time and because of the nature of renewable energy sources. The production from some sources such as the photovoltaic and wind power plants fluctuates depending on meteorological conditions, so it cannot be regulated. However, large hydropower plants can be regulated, so they are suitable for electricity balancing. In this paper, an optimization model is set for a system with 100 % renewable energy sources, which includes models for correlation of meteorological data and the production of electricity from different variable renewable energy sources. The resulting model gives an optimal ratio of production of variable renewable energy sources, which depends on the share of these sources in the total electricity production. The objective function of this optimization problem is to minimize the excess and lack of electricity production. For this purpose, hourly data for electricity consumption and hourly meteorological data are included. The results show that if only wind and photovoltaic power plants are considered, for the case of Macedonia, this optimum is found at 72% wind and 28% photovoltaic power production. However, if the already installed capacity of the big hydropower plants and the maximal potential of the small hydropower plants which make together 30% of the total installed capacity is taken into account, the optimal ratio of production from the other sources is: 50% wind power generation and 20% photovoltaic power generation.


R. A. Rodriguez, S. Becker, G. B. Andersen, D. Heide, M. Greiner, Transmission needs across a fully renewable European power system, Renewable Energy, Vol. 63 (2014) 467−476.

REN 21 Steering Committee, Renewables 2013, Global Status Report. Available at: http://www.ren21.net/Portals/0/documents/Resources/GSR/2013/GSR2013_lowres.pdf.

K. Van der Bergh, E. Delarue, W. D'haeseleer, The impact of renewable injections on cycling of conventional power plants, TME WORKING PAPER - Energy and Environment, Last update: May 2013. Available at: http://www.mech.kuleuven.be/en/tme/research/energy_environment/Pdf/wpen2013-05.pdf.

H. Lund, Large-scale integration of op-timal combinations of PV, wind and wave power into the electricity supply, Renewable Energy, Vol. 31 (2006) 503−515.

D. Heide, L. von Bremen, M. Greiner, C. Hoffmann, M. Speckmann, S. Bofinger, Seasonal optimal mix of wind and solar power in a future, highly renewable Europe, Renewable Energy, Vol. 35 (2010) 2483−2489.

M. G. Rasmussen, G. B. Andersen, M. Greiner, Storage and balancing synergies in a fully or highly renewable pan-European power system, Energy Policy, Vol. 51 (2012) 642−651.

G. B. Andersen, R. A. Rodriguez, S. Becker, M. Greiner, The potential for arbitrage of wind and solar surplus power in Denmark, Energy, Vol. 76 (2014) 49−58.

Energy Regulatory Commission of the Republic of Macedonia, Yearly report 2015, Available at: http://www.erc.org.mk/odluki/2015.05.15_Godisen%20izvestaj%20za%20rabota%20na%20Regulatornata%20komisija%20za%20energetika%20na%20RM%20za%202014%20godina_FINAL.pdf

M. Collares-Pereira, A. Rabl, The avera-ge distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values, Solar Energy, Vol. 22 (1979) 155−164.

I. Cvrk, Optimizing the Use of Solar Energy by Photovoltaic Conversion, Graduation paper no.125. [Na hrvatskom: I. Cvrk, Optimiranje korištenja solarne energije fotonaponskom pretvorbom, diplomski rad br. 125], Available at: http://www.ieee.hr/_download/repository/DR08ICvrk.pdf.

B. Y. H. Liu, R. C. Jordan, The interrelationship and characteristic distribution of direct, diffuse and total solar radiation, Solar Energy, Vol. 4 (1960) 1−19.

A. Dedinec, A. Dedinec, N. Markovska, Optimization of heat saving in buildings using unsteady heat transfer model, Thermal Science, Vol. 19−3 (2015) 881−892.

Electricity Transmission System Operator of Macedonia (MEPSO), Daily information. (2010−2013), Available at: http://mepso.com.mk/ListanjeIzveshtai.aspx?categoryID=113

NASA, Surface meteorology and Solar Energy, (2003−2005) Available at: https://eosweb.larc.nasa.gov/sse/

I. Staffell, Wind Turbine Power Curves, 2012, Available at: http://www.academia.edu/1489838/Wind_Turbine_Power_Curves

Macedonian power plants - ELEM. “Инвестициони проекти на А.Д ЕЛЕМ од обновливи извори на електрична енергија”. Недела на енергетиката. (2012). (in Bulgarian) Available at: http://energyweek.mk/Prezentacii%20Finalni/5.%20ELEM%20AD%20Makedonija.pdf

Electricity Transmission System Operator of Macedonia (MEPSO), Dispatch reports (2010−2013), Available at: http://mepso.com.mk/ListanjeIzveshtai.aspx?categoryID=110

Macedonian Academy of Science and Arts, Strategy for utilisation of renewable energy sources in the Republic of Macedonia By 2020, 2010, Available at: http://iceor.manu.edu.mk/Documents/ICEIM/Strategies/Strategy%20for%20utilization%20RES.pdf