Technical calculations for the production of energy from renewable sources


The official unit for energy or work is the joule, marked J. This unit is small, so kJ and MJ are used, a thousand or a million joules.

For power, a watt unit, W, is used, ie a thousand times increased kW. The power of one watt is one joule per second, J / s. If the power in kW is realized in one hour, x, work or energy of 1 kWh is obtained. It is common to use this unit for electricity, and heat MJ, etc. Recently, in publications intended for a wide range of users, kWh is increasingly used as a unit for thermal energy, so it will be used in this publication as well. Earlier, a unit of calories, cal, or a thousand times higher kcal, was used for energy. The connections of the units are shown in the following table.

To express the annual consumption of the state, the derived unit, the equivalent of a ton of oil, toe (a ton of oil equivalent) is also used. It means the energy contained in a ton of oil. The lower thermal power of oil is about 41,868 MJ / kg, so one 1 ton corresponds to 41,868 thousand MJ or about 42 GJ. The most commonly used is a million tons of oil, hence Mtoe. For example, the annual consumption of primary energy in Serbia is about

4 Mtoe (primary energy is the energy contained in the fuel. The amount of energy used after the conversion depends on the degree of efficiency of a particular device and/or process and is obtained by multiplying the primary by the real degree of efficiency.


Watercourses (electricity)

Biomass/biogas, biomethane, biodiesel (thermal energy, electricity, vehicle fuel)

Municipal waste/incineration (thermal energy, electricity)

Landfill gas and gas from municipal wastewater treatment plants (electricity)

Wind (electricity)

Sun (electricity, heat)

Geothermal energy (electricity, heat)


Support in the investment phase

Loans with a stimulative interest rate, longer repayment period and grace period, which has a favourable effect on financial justification, but these loans are only occasionally current.

Support in the plant operation phase


Feed-in tariffs for the production of electricity from renewable sources.

European Union

Feed-in tariffs for the production of electricity from renewable sources.

Green certificates to stimulate electricity production (each user of renewable energy sources receives certificates, about 5 € / Mwh), and users of fossil fuels must buy the appropriate number of certificates each year, or pay some kind of penalty, which is higher than the value of purchased certificates. Certificates are sold and bought on the green certificate exchange.

CO2 certificates (Carbon credits), to encourage reduced carbon dioxide emissions In order for a plant to be licensed to emit one tonne of carbon dioxide, it needs to buy them on the CO2 certificate market. Users of renewable energy sources are “rewarded” with a certain number of loans, in accordance with the amount of carbon dioxide they save through their activities.

Note: Each country regulates this area in the way it deems most efficient, and certificates can be traded, ie sold or bought outside the borders of countries, and their price varies depending on supply and demand.

The lower thermal power of the fuel is the amount of heat that is released during the complete combustion of a unit of mass or the amount of fuel, while the water vapour generated during combustion remains in the vapour state in the mixture of combustion products.


Energy efficiency classes:

The Energy required for space heating (E)

E = area of ​​space in m2 x specific consumption in kWh / m2 / year * =… kWh / year

* Classic facade and carpentry 150 kWh / m2 / year, Classic facade and insulated carpentry 100 kWh / m2 / year, Styrofoam facade 5 cm and insulated carpentry 60 kWh / m2 / year, For district heating + losses in transport (pipeline)


E = surface heating m2 x isol (60 – 90 W / m2 * / 1000) x no. Days gr x no hours per day

* Power per m2:class facade without insulated table 90 W

Key facade with iso table 75 W

Fas.stirop 5 cm, izo st 50 W

Through the above equivalents, it is possible to calculate the amount of fossil fuels or biomass, taking into account the degree of boiler efficiency, ie the degree of utilization of thermal fuel power, ranging from 40% for biomass to 95% for natural gas.

Required plant power (P)

P (kW) = m2 x cm x 0.3) / 860 = boiler power.

Example: area 220m2 x height 260cm x 0.3) /860=19.95kW

Note: the coefficient 0.3 changes and refers to the insulation of the heating space

0.3 ……… ..good insulation of the house, good carpentry

0.4 ………… house only plastered, medium good carpentry

0.5 ………… house without mortar and insulation. bad carpentry

RenewableEnergyPro – technical calculations


The Energy required for water heating (E)

E = water volume… m3 x Dt ° C (40 to 60) / 0.86 =… kWh

Example required heater power for boiler 50 lit = 0.05m3 x 45 ° C / 0.86 = 2.6 kW).

Through the above equivalents, it is possible to calculate the amount of fossil fuels or biomass. If fossil fuels or biomass are used, the amount of energy and the power of the boiler should be increased depending on the energy efficiency of the boiler.


Water heating (water collectors)

Max annual energy savings of 45% if consumption is continuous

Collector area = (1.1 x type of collector x 50 lit per tenant x number of tenants) / 60 =… m2

collector type: plate 1; vacuum 0.8

Example: type of collector: plate, number of occupants 4

Collector area = (1.2 x 1 x 50 x 4) / 60 = 4 m2

Space heating (water collectors)

Collector area = collector type x space area x 0.2 /(Insulation / 100)

Example: Collector area = (1 x 150 x 0.2) / 75/100) = 40 m2.

Isolation of the building:

Facade without insulation 90

Key facade with insulated table 75

Fas.stirop 5 cm, izo joinery 50

Electricity generation (photovoltaics)

E1m2 / year = annual insolation per 1 m2 (in kWh) * x 15% to 20% **

* depends on the geographical area, for NS about 1350 kWh / m2 / year

** depends on the manufacturer

Note: For a power of 1 kW, about 5 m2 of panels are required.


The formula for calculating the wind power for wind turbines with a horizontal axis is:

P = 1/2 x air density * x rotor surface x wind speed³

* Air density is about 1.23 kg / m3


The Rotor diameter of 2 m, wind speed 5 m / s, we get:

Wing width 15-20% of wind wheel radius.

(1 wing covering the surface 100% high sensitivity, low speed and low power, a large number of very narrow wings, the number of revolutions will generally be large, but therefore the sensitivity will be very low).

P = 1/2 x 1.23 x 3.14 x 125 = 241.38 W

However, these are only theoretical values ​​because according to Betz, the maximum power is about 59% of the 241.38 W calculated above, 142.42 W, and in practice from the manufacturer 30% to 40% of 241.38 W,. 72.41 W to 96.55 W. The formula shows that if we double the diameter of the rotor, we can draw 4 times more power, and if we double the wind speed, we can count on 8 times more power.

Annual electricity production can be roughly calculated based on the annual number of wind hours and the average wind speed.

Note: Solanius and Darius wind generators (vertical axes) have different formulas.


The formula for calculating power is simplified:

P = g x η x Q x h =…. kW.


g – gravitational acceleration 9.81 m / s

η – degree of efficiency of turbine and generator (0 <x <1

Q – volume flow (m3 / s)

h – effective drop (m)

Example: 9.81 x 0.83 x 0.1 x 10 = 8.14 kW.

η = 0.83

h = 25 m

Q = 0.1 m3 / sec

Annual energy production (E)

E = P × t = 8.14 kW × 24 h / day × 365 day / year = 70,330 kWh per year


Power KW = potr.en / COP / / br per day

Power consumption e.m. heatpumps = power x br days gr x br hours / day.

Total length of wells in the ground in meters = (power x COP x 0.75) /0.05

The amount of water from the well in sec = surface heating / 100

Quantity of thermal water in sec=(heating temperature / 100) / (temp. Thermal temperature -15) / 6)

COP efik.topl.pump 3,5 – 5

Total length of wells in the ground in meters = (power x COP x 0.75) /0.05

The amount of water from the well in sec = surface heating / 100

Water temperature (sec) = (heating temperature / 100) / (temp. Temperature -15) / 6)


Heating area 500 m2

Number of heating days 150 per year

Number of heating hours per day 18 h

Required energy = surface heating 500m2 x insulator (60 – 90 W / m2 / 1000) x number of days gr

50 x hours per day 18 = 101250 kWh / year

COP (3.5 to 5) = 3.5

Power KW = consumption 101,250 kWh / COP 3.5 / 150 / on day 18 = 10.7 kW.

Total length of wells in the ground in meters = (power 10.7 x COP 3.5 x 0.75) /0.05 = 562 m

The amount of water from the well in sec = surface heating / 100 = 5 lit / sec

Water temperature (sec) = (heating temperature 500/100) / (temp. Temperature 33 ° C-15) / 6) = 1.7 lit / sec


Biomass technology – FTN Novi Sad

Example of home heating:

Family house 200m2, annual energy needs 30,000 kWh.

Before the investment – heating with natural gas from the network

Gas boiler power 24 kW

Natural gas consumption 3,800 Sm3 / year

After investing in a straw bale boiler (10kg)

Strawbale boiler power 30 kW

Required amount of straw: 30,000 kWh / DTM 3.9 kWh / kg / η 0.55 = 14,000 kg / year


An example of cogeneration

Raw material base: agricultural estate, farm of 1200 dairy cows and agricultural land of 1500 ha:

Available substrates: beef manure 27,000 tons / year and 10,000 tons of corn silage / year.

Plant power = 1 Mwel.en + 1 MW topl.en net

Consumption of natural gas from the network for the continuity of energy production around 300,000 Sm3 / year.

Electricity production 8 million kWh / year

Thermal energy production 8 million kWh / year

Solid fermentation residues