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2nd International Conference on Renewable Energy Sources and Energy Efficiency 18 – 21, October 2007, Athens, Greece V pv + I pv ⋅ Rs I pv = I L − I D − I sh = I L − I O ⋅[exp( ) −1] (1) α where I pv , I L , I D , I sh denote the operation current, light current, diode current and shunt current respectively in A, I o the diode reverse saturation current in A, R s the series resistance in Ω, α the curve fitting parameter in Volt and V pv the operation voltage in Volt The above parameters depend on the solar radiation and the cell temperature and can be easily calculated from manufacturer’s data which are provided for the PV-modules. The power from the PV-Array is described as known from: P = V pv ⋅ I ⋅η pv pv conv (2) where η conv denotes the efficiency of the DC/DC converter~90-95% The output power of the Wind Generator is given by the following equation [11]: P m = c ρ ⋅ Α w 3 p ( λ, β ) ⋅ vwind ⋅ηinv (3) 2 where P m denotes the mechanical output of the turbine in W, c p the performance coefficient of the turbine, ρ the air density in kg/m 3 , Α w the turbine swept area in m 2 , v wind the wind speed in m/s, λ the tip speed ratio, β the blade pitch angle in deg and η inv denotes the efficiency of the AC/DC converter~90-95% The relationship for c p is given by equation that is based on the characteristics of the wind turbine and can also be estimated from manufacturer’s data regarding the rotor speed in relation with the wind speed [10]. From the above equations the power from the PV-Array and the Wind Generators is presented in figures 2 and 3 respectively. 5000 1800 Output Power, Watt 4000 3000 2000 1000 Output Power, Watt 1600 1400 1200 1000 800 600 400 200 0 0 200 400 600 800 1000 1200 1400 Time, h 0 0 200 400 600 800 1000 1200 1400 Time, h Figure 2: Output Power from the 5kW p Photovoltaic System Figure 3: Output Power from the 3kW p Wind Generators 3.2 Lead-Acid Accumulator The total power, P RES is calculated by the sum of the power P pv and P m . The power demand for the Load, P load is constant throughout the year at 1kW (or the equivalent energy is 24kWh/day). The shortage or surplus power is calculated as:
2nd International Conference on Renewable Energy Sources and Energy Efficiency 18 – 21, October 2007, Athens, Greece P = P RES − P load (4) Based, on the deficit or shortage of power an Energy Management (EM) strategy was developed and used. Two limits of the State-of-Charge of the Accumulator are introduced: the minimum State-of- Charge, SOC min , where power needs to be provided to the Accumulator and the maximum State-of-Charge, SOC max , where the Electrolyzer is possible to operate. The basic steps of the EM-algortihm are explained below. • If P0 then the surplus power is provided to the Electrolyzer for the production of hydrogen or to charge the Accumulator, depending on the SOC: if SOC≥SOC max then the surplus energy is provided to the Electrolyzer as long as P≥P min,elec . If P≤ P min,elec or if P≥ P max,elec then the spared energy is used to charge the battery. Figure 4 presents the operation current of the Accumulator that has been calculated according to the EM-algorithm. The negative values indicate the charging that takes place while positive values imply the discharging due to lack of power. A very important parameter that needed to be studied in detail was the SOC as it influences the operation of the Accumulator, of the Electrolyzer and of the Fuel Cell. The SOC max limit was assumed to be 91% and the SOC min limit was assumed to be 84%. The State-of-Charge of the Accumulator is given by: SOC( t + 1) = SOC( t) ⋅σ + I ⋅η ⋅ ( ∆t) (5) ac ac ac where SOC is the State-of-Charge of the Accumulator in %, η ac is the efficiency factor ~95%, Ι ac is the charging/discharging current in Α, σ ac is the discharging rate of the Accumulator and t is the time in hr. 30 100 Current, A 15 0 -15 -30 -45 -60 State of Charge, % 98 96 94 92 90 88 86 SOCmax -75 84 SOCmin -90 0 200 400 600 800 1000 1200 1400 Time, h 82 0 200 400 600 800 1000 1200 1400 Time, h Figure 4: Operation Current during the twomonth period Figure 5: State of Charge of the Accumulator during the two-month period
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