Pumped Storage Hydropower Calculator
Pumped Storage Hydropower Calculator estimates energy output and recommends a turbine type (Pelton, Francis, or Reversible Pump-Turbine) for pumped storage systems (50–1000 m) based on net head, flow rate, and desired power.
Formulas Used in Pumped Storage Hydropower Calculator
The calculator uses these formulas to estimate energy and select turbines:
Net Head:
\\[ h_{\text{net}} = h_{\text{gross}} – h_{\text{loss}} \\]Power Output:
\\[ P = \eta \cdot \rho \cdot g \cdot Q \cdot h_{\text{net}} / 1000 \\]Daily Energy Output:
\\[ E = P \cdot t \\]Specific Speed:
\\[ N_s = \frac{N \sqrt{P}}{h_{\text{net}}^{5/4}} \\]Suitability Score: Based on head and specific speed ranges.
Where:
- \\( h_{\text{net}} \\): Net head (m)
- \\( h_{\text{gross}} \\): Gross head (m)
- \\( h_{\text{loss}} \\): Head loss (m)
- \\( P \\): Power output (kW)
- \\( E \\): Daily energy output (kWh)
- \\( \eta \\): Turbine efficiency (0 to 1)
- \\( \rho \\): Water density (1000 kg/m³)
- \\( g \\): Gravitational acceleration (9.81 m/s²)
- \\( Q \\): Flow rate (m³/s)
- \\( t \\): Operational hours per day (h)
- \\( N_s \\): Specific speed (metric, rpm)
- \\( N \\): Rotational speed (rpm)
Example Calculation
Pumped Storage System
Input: Gross Head = 300 m, Head Loss = 15 m, Flow Rate = 2.0 m³/s, Rotational Speed = 1500 rpm, Desired Power = 2000 kW, Hours/Day = 8
\\[
h_{\text{net}} = 300 – 15 = 285 \ \text{m}
\\]
\\[
P = 0.90 \cdot 1000 \cdot 9.81 \cdot 2.0 \cdot 285 / 1000 \approx 5032.62 \ \text{kW}
\\]
\\[
E = 5032.62 \cdot 8 \approx 40260.96 \ \text{kWh/day}
\\]
\\[
N_s = \frac{1500 \sqrt{5032.62}}{285^{5/4}} \approx 35.14 \ \text{rpm}
\\]
Pelton (head 50–1000 m, \\( N_s \\) 10–50): Score = 92.
Result: Recommended Turbine = Pelton, Efficiency = 0.85–0.90, Power = 5032.62 kW, Energy = 40260.96 kWh/day.