A PHES system (refer to Figure 11.2) equipped with a reversible pump–turbine and motor–generator units is operating under the following conditions: • Static head, that is, elevation difference between upper and lower reservoirs H = 600 m • Volumetric water flow rate in pumping mode Vp = 90 m³/s

Question

A PHES system (refer to Figure 11.2) equipped with a reversible pump–turbine and motor–generator units is operating under the following conditions:

• Static head, that is, elevation difference between upper and lower reservoirs H = 600 m
• Volumetric water flow rate in pumping mode [latex]V_{p}[/latex] = 90 m³/s
• Daily duration of pumping period [latex] au_{p}[/latex] = 8.5 h
• Overall pumping efficiency [latex]\eta_{p}[/latex] = 0.83
• Volumetric water flow rate in generating mode [latex]V_{t}[/latex] = 135 m³/s
• Daily duration of power generation period [latex] au_{gen}[/latex]= 6.5 h
• Overall power generation efficiency [latex]\eta_{gen}[/latex] = 0.92

Calculate (a) the plant power output in generating mode, (b) the daily electricity generation, (c) the pumping power input, (d) the daily pumping energy demand, and (e) the turnaround efficiency of the energy storage.

Accepted Answer

1. Plant power output in generating mode

[latex]P_{\mathrm{gen}}\,=\,g\mathbf{r}\,V_{t}H\mathbf{h}_{\mathrm{gen}}\,=\,9.8 1 imes1 000 imes1 35 imes600 imes0.92\,=731\,\mathrm{MW}[/latex]

2. Daily electricity generation

[latex]E_{\mathrm{gen}}\,=\,\mathbf{t}_{gen}P_{\mathrm{gen}}\,=\,6.5 imes731\,=\,4751.8\,\,\mathrm{MW\,h/day}\,[/latex]

3. Pumping power input

[latex]P_{p}\,=\,g\,\mathbf{r} V_{ ho}H\,/\,\mathbf{h}_{p}\,=\,9.81 imes1 000 imes90 imes600\,/\,0.83\,=\,638.24\,\,\mathrm{MW}[/latex]

4. Daily pumping energy demand

[latex]E_{\mathrm{p}}\,=\,\mathbf{t}_{p}P_{\mathrm{p}}\,=\,8.5 imes638.24\,=\,5425~\mathrm{MWh/d}[/latex]

5. Turnaround efficiency of PHES system based on energy output [latex]E_{gen}[/latex] and energy input [latex]E_{p}[/latex]

[latex]\eta_{s}=E_{\mathrm{gen}}/E_{p}=4751.8/5425=0.876=87.6\%.[/latex]

Question 11.1: A PHES system (refer to Figure 11.2) equipped with a reversi......

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