Simple model for the energy supply of a house using hybrid wind-solar power system Tamás Beke Our Lady Catholic Grammar School Kalocsa, Hungary Eötvös University Physics Education PhD Program
Research project for secondary school students • The problem to be solved is whether and how a typical house can be supplied with energy off-grid, based entirely on renewable energy sources. • To this end our students carried out a long term measurement series in order to assess typical energy consumption of houses. 2
1. Introduction • Renewable energy sources are becoming increasingly important in energy supply. • Their contribution covered an estimated 19% of the global final energy consumption in 2011 [1]. • They may not completely substitute fossil fuels and atomic energy in the near future, yet they offer an attractive alternative in the long term. 3
Solar and wind energy • Among renewables, solar and wind power are widely available on the Earth. • The locally available solar energy and wind power substantially depend on meteorological conditions and are highly variable in time. 4
• Due to their significance and perspective, it is desirable to give renewable energy sources an appropriate share in physics teaching. • In this lecture a related research project designed for and accomplished by secondary school students is presented. 5
1st stage • Our ‘ Renewable energy sources: stand-alone house with hybrid wind- solar power generator’ project has been carried out in three stages. • For the first stage the daily energy consumption of an average house was investigated. 6
2nd and 3rd stage • For the second stage a mathematical model for an off-grid house with hybrid wind-solar power generator and accumulator system was developed. • For the third stage a computer simulation program was developed, based on the mathematical model and the data collected by students. 7
• Wind power has significant variation over shorter time scales therefore it is used generally in conjunction with other sources to give a reliable supply. 8
2. Gathering data • All the students taking part in this project live in the same town, Kalocsa, in self-contained detached houses with insulated walls and central heating systems. • The number of student houses was N =31. 9
• We monitored the temperatures on every day during the project. • I have chosen 4 days from 4 different seasons to present the data: –the ‘winter day’ is 2014 -Jan-1, –the ‘spring day’ is 2014 -Apr-1, –the ‘summer day’ is 2014 -Jul-1, –the ‘autumn day’ is 2014 -Oct-1. 10
Outside temperatures • We can see in figure 1 the outside temperatures on the days chosen. T [°C] T [°C] 7 Temperature (2014-Jan-1) 25 Temperature (2014-Apr-1) 6 20 5 15 4 3 10 2 5 1 time time 0 0 0:02 2:02 4:02 6:01 7:54 9:45 11:45 13:45 15:45 17:45 19:45 21:45 23:45 0:00 2:00 4:00 6:00 7:54 9:54 11:54 13:54 15:54 17:54 19:54 21:55 23:55 T [°C] T [°C] 25 Temperature (2014-Oct-1) 30 Temperature (2014-Jul-1) 25 20 20 15 15 10 10 5 5 time time 0 0 0:01 1:55 3:55 5:53 7:50 9:46 11:45 13:45 15:49 17:45 19:44 21:42 23:36 0:01 2:02 4:02 6:01 7:58 9:58 11:58 13:58 15:59 17:59 20:01 22:01 11
Energy consumption • Students collected the data of the daily energy consumption of their own houses: – the energy consumption of the electric appliances was monitored; – the natural gas consumption was monitored by gas meter; – the wood and coal burned in furnaces were measured in weighing-machines (scales). E N A N total , i , j ave ave E , total , i N A N j 1 j j 12
• The ‘heating season’ spans from 1st October to 15th April; between 16th April and 30th September the period was designated as ’non - heating season’. • The average daily electricity consumption of students’ household was circa : – 37 MJ in the heating season – and about 35 MJ in the non-heating season. 13
3. Modelling • Now a model of an off-grid hybrid wind-solar power generating system is presented. • In this model we assume that the users cannot (or do not want to) rely on the electric grid system, therefore the energy produced by the hybrid wind-solar system is stored locally in accumulators. 14
Model setup • The model setup is depicted schematically in figure 2. • The parts of the system are the power generating system (photovoltaic modules and wind turbines), the energy storage unit. 15
PV modules and wind turbines • This off-grid hybrid wind-solar power generating system consists of N photov pieces of PV modules and N windt pieces of small wind turbines. 16
PV module • A photovoltaic (PV or solar) cell converts the energy of light directly into electricity by photovoltaic effect. • In a PV cell the direct conversion of light to electricity occurs in semi-conducting materials. 17
Power of a photovoltaic module • The power of a photovoltaic module ( P photov ) is proportional to the incoming light power [2]: , η P = P t = A I t photov photov photov photov 18
Power of one PV module • Figure 3 shows the power of one photovoltaic module on the days chosen. 10 Power 1 solar module (2014-Jan-1) 140 Power 1 solar module (2014-Apr-1) P [W] P [W] 120 8 100 6 80 4 60 40 2 20 time time 0 0 0:02 2:02 4:02 6:01 7:54 9:45 11:45 13:45 15:45 17:45 19:45 21:45 23:45 0:00 2:00 4:00 6:00 7:54 9:54 11:54 13:54 15:54 17:54 19:54 21:55 23:55 200 Power 1 solar module (2014-Jul-1) 120 Power 1 solar module (2014-Oct-1) P [W] P [W] 100 160 80 120 60 80 40 40 20 time time 0 0 0:01 2:02 4:02 6:01 7:58 9:58 11:58 13:58 15:59 17:59 20:01 22:01 0:01 1:55 3:55 5:53 7:50 9:46 11:45 13:45 15:49 17:45 19:44 21:42 23:36 19
ith + T day day Energy of PV module 0 Δt E = P t N , photov , i photov photov ith day 0 • In figure 4 the sum-total electrical energy produced by one photovoltaic module on the days chosen is shown. 2,5 Energy 1 solar module (2014-Apr-1) 0,12 Energy 1 solar module (2014-Jan-1) E [MJ] E [MJ] 0,1 2 0,08 1,5 0,06 1 0,04 0,5 0,02 time time 0 0 0:00 2:00 4:00 6:00 7:54 9:54 11:54 13:54 15:54 17:54 19:54 21:55 23:55 0:02 2:02 4:02 6:01 7:54 9:45 11:45 13:45 15:45 17:45 19:45 21:45 23:45 5 Energy 1 solar module (2014-Jul-1) 2 Energy 1 solar module (2014-Oct-1) E [MJ] E [MJ] 4 1,5 3 1 2 0,5 1 time time 0 0 0:01 2:02 4:02 6:01 7:58 9:58 11:58 13:58 15:59 17:59 20:01 22:01 0:01 1:55 3:55 5:53 7:50 9:46 11:45 13:45 15:49 17:45 19:44 21:42 23:36 20
Wind turbines • Wind turbine generates electricity from the kinetic power of the wind. • The power output of the wind turbine is proportional to the area swept by the blades and to the cube of the wind velocity. • The power of wind turbine ( P windt ) is assumed [3]: ρ t , air 3 P = P t = C A v t windt windt po rotor wind 2 21
Power of wind turbine • In figure 5 the power of one small wind turbine can be seen on the days chosen. P [W] 40 Power 1 small turbine (2014-Jan-1) 100 Power 1 small turbine (2014-Apr-1) P [W] 80 30 60 20 40 10 20 0 0 0:02 2:02 4:02 6:01 7:54 9:45 11:45 13:45 15:45 17:45 19:45 21:45 23:45 0:00 2:00 4:00 6:00 7:54 9:54 11:54 13:54 15:54 17:54 19:54 21:55 23:55 time time 20 Power 1 small turbine (2014-Oct-1) 160 Power 1 small turbine (2014-Jul-1) P [W] P [W] 140 15 120 100 10 80 60 5 40 20 0 0 0:01 1:55 3:55 5:53 7:50 9:46 11:45 13:45 15:49 17:45 19:44 21:42 23:36 0:01 2:02 4:02 6:01 7:58 9:58 11:58 13:58 15:59 17:59 20:01 22:01 22 time time
ith + T day day Energy of wind turbine 0 Δt, E = P t N windt, i windt windt ith day 0 • In figure 6 the sum-total electrical energy produced by one small wind turbine on the days chosen is shown. 0,4 Energy 1 small turbine (2014-Jan-1) 1,0 Energy 1 small turbine (2014-Apr-1) E [MJ] E [MJ] 0,8 0,3 0,6 0,2 0,4 0,1 0,2 time time 0,0 0,0 0:02 2:02 4:02 6:01 7:54 9:45 11:45 13:45 15:45 17:45 19:45 21:45 23:45 0:00 2:00 4:00 6:00 7:54 9:54 11:54 13:54 15:54 17:54 19:54 21:55 23:55 2,5 Energy 1 small turbine (2014-Jul-1) 0,10 Energy 1 small turbine (2014-Oct-1) E [MJ] E [MJ] 2,0 0,08 1,5 0,06 1,0 0,04 0,5 0,02 time time 0,0 0,00 0:01 2:02 4:02 6:01 7:58 9:58 11:58 13:58 15:59 17:59 20:01 22:01 0:01 1:55 3:55 5:53 7:50 9:46 11:45 13:45 15:49 17:45 19:44 21:42 23:36 23
Produced energy • During the period of the project the wind speed, the pressure of air, the temperature of air and the sunlight is monitored in every D t =5 minutes automatically by a local weather station, so it is available for us. • The total daily production of electrical energy in our hybrid system on i th day can be determined by knowing, separately, the daily energy production of the solar modules and the daily energy production of the wind turbines: E = E + E , ee , i photov , i windt , i 24
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