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Chapter 3 · 5 hours

Planning of Hydropower Projects

IOE past exam questions

Past questions and answers

19 questions set from this chapter, 1 of them more than once. Most asked first.

  • Asked 3 times
  • 2080 Chaitra · 8 marks
  • 2081 Asoj · 8 marks
  • 2071 Magh · 8 marks

In what stages study of a hydropower project are completed? What parameters do you investigate in each stage? Discuss with hydropower development cycle.

Answer

A hydropower project is studied in stages of increasing detail, so that money is spent on detailed work only for projects that prove worthwhile. Together with construction and operation these form the hydropower development cycle.

 Identification / desk study
            |
 Reconnaissance study
            |
 Pre-feasibility study
            |
 Feasibility study  (+ EIA, licences)
            |
 Detailed design & tender
            |
 Construction & commissioning
            |
 Operation & maintenance  --> rehabilitation

1. Desk study / identification

Using maps (1:50 000 topo), existing hydrological records and reports, possible sites are identified and rough power potential P=9.81 QHηP = 9.81\,QH\eta is computed. Several alternatives are listed.

2. Reconnaissance study

A short site visit and study to screen alternatives.

  • Rough layout: headworks, waterway, powerhouse locations.
  • Approximate head (altimeter/GPS) and spot flow measurement.
  • General geology, access, land use, settlements.
  • Rough cost and power; ranking of sites.

3. Pre-feasibility study

Selects the best scheme and decides whether a full feasibility study is justified.

  • Topographic survey at larger scale; hydrological analysis (flow duration curve, floods).
  • Preliminary geology (surface mapping), sediment and seismic data.
  • Comparison of layouts and capacities; preliminary design and cost estimate.
  • Initial environmental examination, power market and economic indicators (B/C, IRR).

4. Feasibility study

Detailed enough for financing and licensing decisions.

  • Detailed topographic surveys; long-term hydrology, design flood, sediment study.
  • Subsurface investigation: drilling, test pits, seismic refraction, lab tests of construction materials.
  • Optimisation of installed capacity, firm/secondary energy; final layout.
  • Design of main structures, construction schedule, detailed cost estimate.
  • Full EIA, social and resettlement study; power market and transmission; financial and economic analysis (NPV, IRR, B/C, cost per kWh).
  • In Nepal, the generation licence (DoED) and PPA with NEA are based on this stage.

5. Detailed design and tender

Final engineering drawings, specifications, bill of quantities, tender documents; further investigation where needed.

6. Construction and commissioning

Access roads, river diversion, civil works, electro-mechanical and transmission works; testing and commissioning.

7. Operation and maintenance

Power generation, monitoring of sediment, structures and equipment; later upgrading or rehabilitation, which restarts the cycle.

StageMain outputAccuracy of cost
ReconnaissancePromising sites±40–50%
Pre-feasibilityBest alternative±25–30%
FeasibilityGo / no-go, financing±10–15%
Detailed designDrawings, tender±5–10%
  • 2082 Chaitra · 10 marks

The monthly power output (in kW) for a proposed hydropower plant is given below. The interest rate is 10%, energy price is US40/MWh,variablecostisUS 40/MWh, variable cost is US 800/kW, annual operation and maintenance cost is 2.5% of variable cost, and the economic life of the project is 40 years. Determine the best-installed capacity, firm energy, secondary energy, total energy, and plant factor.
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Power (kW)806595200320400510650560270140110

Answer

The best (optimum) installed capacity is the capacity at which the net annual benefit (value of energy sold minus annual cost of the capacity) is maximum. Equivalently, the last increment of capacity added should earn at least as much as it costs.

Data and assumptions

  • Each month is taken as 8760/12=7308760/12 = 730 h.
  • Energy price = 40 $/MWh = 0.04 $/kWh.
  • Capital recovery factor (10%, 40 years):
CRF=i(1+i)n(1+i)n−1=0.10(1.10)40(1.10)40−1=0.10226\begin{aligned} CRF &= \frac{i(1+i)^n}{(1+i)^n-1} = \frac{0.10(1.10)^{40}}{(1.10)^{40}-1} = 0.10226 \end{aligned}
  • Annual cost per kW of capacity = capital charge + O&M:
Ca=800 (0.10226+0.025)=101.81 $/kW/yr\begin{aligned} C_a &= 800\,(0.10226 + 0.025) = 101.81\ \text{\$/kW/yr} \end{aligned}

Power duration (descending order)

650, 560, 510, 400, 320, 270, 200, 140, 110, 95, 80, 65 kW. A capacity PcP_c produces min⁡(Pi,Pc)\min(P_i, P_c) in each month.

Annual energy for capacity PcP_c: E=730∑min⁡(Pi,Pc)E = 730 \sum \min(P_i, P_c) kWh.

Benefit–cost table

Capacity (kW)Energy (kWh/yr)Benefit ($)Cost ($)Net ($)
65569,40022,7766,61816,159
1401,073,10042,92414,25328,671
2001,379,70055,18820,36234,827
2701,686,30067,45227,48839,964
3201,868,80074,75232,57842,174
4002,102,40084,09640,72343,373
5102,343,30093,73251,92241,810
5602,416,30096,65257,01239,640
6502,482,00099,28066,17533,105

Benefit = E×0.04E \times 0.04; Cost = Pc×101.81P_c \times 101.81.

Incremental check: going from 320 to 400 kW adds 80 kW (cost $8,145) and 233,600 kWh (benefit $9,344): worth it. Going from 400 to 510 kW adds 110 kW (cost $11,199) but only 240,900 kWh (benefit $9,636): not worth it. A kW is worth installing only if it runs at least 101.81/(8760×0.04)=29%101.81/(8760 \times 0.04) = 29\% of the year (about 3.5 months); the 400–510 kW band runs only 3 months.

Results

  • Best installed capacity = 400 kW (maximum net benefit $43,373/yr).
  • Firm energy (minimum power 65 kW available all year):
Ef=65×8760=569,400 kWh=0.569 GWhE_f = 65 \times 8760 = 569{,}400\ \text{kWh} = 0.569\ \text{GWh}
  • Total energy at 400 kW = 2,102,400 kWh = 2.102 GWh.
  • Secondary energy = 2,102,400 − 569,400 = 1,533,000 kWh = 1.533 GWh.
  • Plant factor:
PF=2,102,400400×8760=0.60=60%PF = \frac{2{,}102{,}400}{400 \times 8760} = 0.60 = 60\%

Answer: Installed capacity = 400 kW; firm energy = 0.569 GWh; secondary energy = 1.533 GWh; total energy = 2.102 GWh; plant factor = 60%.

  • 2082 Kartik · 10 marks

Determine the best-installed capacity of a hydropower plant based on the given power duration data. Interest rate = 12%, Energy price = US36/MWh,Variablecost=US 36/MWh, Variable cost = US 750/KW, Economic life of the project = 50 years.
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Power (KW)70059053530025518015010580706050

Answer

The best installed capacity is the one that gives the largest net annual benefit (revenue from energy minus annualised cost of capacity). It is found by trying each power level of the power duration data as the plant capacity.

Annual cost of capacity

No O&M cost is given, so only capital recovery is used.

CRF=0.12(1.12)50(1.12)50−1=0.12042Ca=750×0.12042=90.31 $/kW/yr\begin{aligned} CRF &= \frac{0.12(1.12)^{50}}{(1.12)^{50}-1} = 0.12042 \\ C_a &= 750 \times 0.12042 = 90.31\ \text{\$/kW/yr} \end{aligned}

Energy price = 36 $/MWh = 0.036 $/kWh. Each month = 730 h.

Power duration (descending order)

700, 590, 535, 300, 255, 180, 150, 105, 80, 70, 60, 50 kW.

For capacity PcP_c: E=730∑min⁡(Pi,Pc)E = 730\sum \min(P_i,P_c), Benefit =0.036E= 0.036E, Cost =90.31Pc= 90.31P_c.

Capacity (kW)Energy (kWh/yr)Benefit ($)Cost ($)Net ($)
50438,00015,7684,51611,252
105803,00028,9089,48319,425
1501,032,95037,18613,54723,639
1801,164,35041,91716,25625,660
2551,438,10051,77223,03028,742
3001,569,50056,50227,09429,408
5352,084,15075,02948,31726,712
5902,164,45077,92053,28424,636
7002,244,75080,81163,21917,592

Incremental check

  • 255 → 300 kW: +45 kW costs $4,064; extra energy 131,400 kWh (4 months) earns $4,730. Worth adding.
  • 300 → 535 kW: +235 kW costs $21,223; extra energy 514,650 kWh (3 months) earns $18,527. Not worth adding.

Break-even running time = 90.31/(8760×0.036)=28.6%90.31/(8760\times0.036) = 28.6\% of the year (3.4 months). The band above 300 kW runs only 3 months, so it does not pay.

Results at 300 kW

  • Firm energy =50×8760=438,000= 50 \times 8760 = 438{,}000 kWh
  • Total energy = 1,569,500 kWh; secondary energy = 1,131,500 kWh
  • Plant factor =1,569,500/(300×8760)=59.7%= 1{,}569{,}500/(300\times8760) = 59.7\%

Answer: Best installed capacity = 300 kW (net benefit ≈ $29,408 per year).

  • 2080 Asoj · 8 marks

The mean monthly flow of a river in Nepal is given in the below table. Calculate the primary and secondary energy that can be generated from the river if the plant capacity is fixed at power corresponding to the flow available for 45% of the time. Consider the plant's overall efficiency as 85% and the Net head as 170 m.
MonthsJanFebMarAprMayJunJulAugSepOctNovDec
Flow (m³/s)302824291837659074564239

Answer

Primary (firm) energy is the energy that can be produced all year from the minimum (dependable) flow. Secondary energy is the extra energy produced when flow is above the minimum, up to the plant capacity.

Step 1: Flow duration (Weibull plotting position P=mN+1×100P = \frac{m}{N+1}\times100, N = 12)

Rank mQ (m³/s)% time exceeded
1907.69
27415.38
36523.08
45630.77
54238.46
63946.15
73753.85
83061.54
92969.23
102876.92
112484.62
121892.31

Step 2: Flow at 45% time (linear interpolation)

Q45=42−45−38.4646.15−38.46(42−39)=39.45 m3/sQ_{45} = 42 - \frac{45-38.46}{46.15-38.46}(42-39) = 39.45\ \text{m}^3/\text{s}

Step 3: Plant capacity

P=γQHη=9.81×Q×170×0.85=1417.55 QP = \gamma Q H \eta = 9.81 \times Q \times 170 \times 0.85 = 1417.55\,Q kW

Pinst=1417.55×39.45=55,922 kW≈55.9 MWP_{inst} = 1417.55 \times 39.45 = 55{,}922\ \text{kW} \approx 55.9\ \text{MW}

Step 4: Primary energy (minimum flow 18 m³/s, May)

Pf=1417.55×18=25,516 kWEp=25,516×8760=223.52 GWh\begin{aligned} P_f &= 1417.55 \times 18 = 25{,}516\ \text{kW} \\ E_p &= 25{,}516 \times 8760 = 223.52\ \text{GWh} \end{aligned}

Step 5: Total energy (flow used = smaller of Q and 39.45; 730 h per month)

MonthQQ usedPower (kW)
Jan303042,526
Feb282839,691
Mar242434,021
Apr292941,109
May181825,516
Jun373752,449
Jul–Nov≥ 4239.4555,922 each
Dec393955,284

∑Qused=402.25\sum Q_{used} = 402.25 m³/s-months.

Etotal=1417.55×402.25×730=416.25 GWhEs=416.25−223.52=192.73 GWh\begin{aligned} E_{total} &= 1417.55 \times 402.25 \times 730 = 416.25\ \text{GWh} \\ E_s &= 416.25 - 223.52 = 192.73\ \text{GWh} \end{aligned}

Answer: Plant capacity ≈ 55.9 MW; primary energy ≈ 223.5 GWh/yr; secondary energy ≈ 192.7 GWh/yr (total ≈ 416.3 GWh/yr).

(If P=m/NP = m/N is used for the duration curve, Q45≈40.8Q_{45} \approx 40.8 m³/s and the secondary energy rises slightly; the method is the same.)

  • 2070 Bhadra · 10 marks

Estimate primary and secondary energy from the data given below. Net head available = 102 m, Discharge capacity = 55 m³/s, Overall efficiency = 76%.
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Flow (m³/s)302824291837659074564239

Answer

Primary energy is generated by the flow available 100% of the time (minimum flow). Secondary energy is the additional energy from flows above the minimum, limited by the plant (design) discharge of 55 m³/s.

Power per unit discharge

P=9.81 Q H η=9.81×Q×102×0.76=760.47 Q kWP = 9.81\,Q\,H\,\eta = 9.81 \times Q \times 102 \times 0.76 = 760.47\,Q\ \text{kW}

Installed capacity =760.47×55=41,826= 760.47 \times 55 = 41{,}826 kW ≈ 41.8 MW.

Primary energy

Minimum flow = 18 m³/s (May).

Pf=760.47×18=13,688 kWEp=13,688×8760=119.91×106 kWh=119.91 GWh\begin{aligned} P_f &= 760.47 \times 18 = 13{,}688\ \text{kW} \\ E_p &= 13{,}688 \times 8760 = 119.91 \times 10^6\ \text{kWh} = 119.91\ \text{GWh} \end{aligned}

Monthly energy (flow used ≤ 55 m³/s, 730 h per month)

MonthQ (m³/s)Q usedPower (kW)Energy (GWh)
Jan303022,81416.65
Feb282821,29315.54
Mar242418,25113.32
Apr292922,05416.10
May181813,6889.99
Jun373728,13720.54
Jul655541,82630.53
Aug905541,82630.53
Sep745541,82630.53
Oct565541,82630.53
Nov424231,94023.32
Dec393929,65821.65
Total467259.25
Etotal=760.47×467×730=259.25 GWhEs=259.25−119.91=139.34 GWh\begin{aligned} E_{total} &= 760.47 \times 467 \times 730 = 259.25\ \text{GWh} \\ E_s &= 259.25 - 119.91 = 139.34\ \text{GWh} \end{aligned}

Answer: Primary energy ≈ 119.9 GWh/yr; secondary energy ≈ 139.3 GWh/yr; total ≈ 259.3 GWh/yr.

  • 2079 Chaitra · 8 marks

Following table shows the mean monthly flow of a typical river in Nepal. Calculate annual firm and secondary energy if design discharge selected is 900 m³/s. Take overall efficiency = 90% and head 100 m.
MonthJanFebMarAprMayJunJulAugSepOctNovDec
Discharge (m³/s)120100901503501800200025002000900650500

Answer

Firm energy comes from the minimum flow, which is available throughout the year. Secondary energy is the extra energy from flows above the minimum, up to the design discharge (900 m³/s).

Power per unit discharge

P=9.81×Q×100×0.90=882.9 Q kWP = 9.81 \times Q \times 100 \times 0.90 = 882.9\,Q\ \text{kW}

Installed capacity =882.9×900=794,610= 882.9 \times 900 = 794{,}610 kW ≈ 794.6 MW.

Firm energy

Minimum flow = 90 m³/s (March).

Pf=882.9×90=79,461 kWEf=79,461×8760=696.08 GWh\begin{aligned} P_f &= 882.9 \times 90 = 79{,}461\ \text{kW} \\ E_f &= 79{,}461 \times 8760 = 696.08\ \text{GWh} \end{aligned}

Total energy (flow used = smaller of Q and 900; 730 h per month)

MonthQ (m³/s)Q usedPower (MW)
Jan120120105.95
Feb10010088.29
Mar909079.46
Apr150150132.44
May350350309.02
Jun1800900794.61
Jul2000900794.61
Aug2500900794.61
Sep2000900794.61
Oct900900794.61
Nov650650573.89
Dec500500441.45
Sum6460
Etotal=882.9×6460×730=4163.58 GWhEs=4163.58−696.08=3467.50 GWh\begin{aligned} E_{total} &= 882.9 \times 6460 \times 730 = 4163.58\ \text{GWh} \\ E_s &= 4163.58 - 696.08 = 3467.50\ \text{GWh} \end{aligned}

Answer: Annual firm energy ≈ 696.1 GWh; annual secondary energy ≈ 3467.5 GWh (total ≈ 4163.6 GWh).

  • 2078 Chaitra · 7 marks

Following are the mean monthly flow of the river. Where head (H) = 100 m, overall efficiency = 90% and design discharge selected is 900 m³/s. Calculate the annual firm and secondary energy.
MonthJanFebMarAprMayJunJulyAugSepOctNovDec
Flow (m³/s)1001201403003201800200025102000900100300

Answer

Firm energy is the energy from the minimum flow (available all year). Secondary energy is the extra energy from flows above the minimum, limited by the design discharge of 900 m³/s.

Power per unit discharge

P=9.81×Q×100×0.90=882.9 Q kWP = 9.81 \times Q \times 100 \times 0.90 = 882.9\,Q\ \text{kW}

Installed capacity =882.9×900=794.61= 882.9 \times 900 = 794.61 MW.

Firm energy

Minimum flow = 100 m³/s (January and November).

Pf=882.9×100=88,290 kWEf=88,290×8760=773.42 GWh\begin{aligned} P_f &= 882.9 \times 100 = 88{,}290\ \text{kW} \\ E_f &= 88{,}290 \times 8760 = 773.42\ \text{GWh} \end{aligned}

Total energy (730 h per month)

MonthQQ usedPower (MW)
Jan10010088.29
Feb120120105.95
Mar140140123.61
Apr300300264.87
May320320282.53
Jun1800900794.61
Jul2000900794.61
Aug2510900794.61
Sep2000900794.61
Oct900900794.61
Nov10010088.29
Dec300300264.87
Sum5880
Etotal=882.9×5880×730=3789.76 GWhEs=3789.76−773.42=3016.34 GWh\begin{aligned} E_{total} &= 882.9 \times 5880 \times 730 = 3789.76\ \text{GWh} \\ E_s &= 3789.76 - 773.42 = 3016.34\ \text{GWh} \end{aligned}

Answer: Annual firm energy ≈ 773.4 GWh; annual secondary energy ≈ 3016.3 GWh (total ≈ 3789.8 GWh).

  • 2075 Baisakh · 10 marks

Determine the primary and secondary energy if the hydrograph as shown below is given net head = 200 m and efficiency = 80%. What is the volume of the pondage required if the firm capacity is increased by 150%.
MonthJanFebMarAprMayJunJulyAugSeptOctNovDec
Discharge (m³/s)1001201403003201800200025102000900500300

Answer

Primary energy is produced by the minimum flow that is available all year; secondary energy is produced by the flow above this minimum. No design discharge is given, so the plant is assumed to use all the river flow (secondary energy is then the maximum possible). Each month is taken as 730 h (2.628×1062.628 \times 10^6 s).

Power per unit discharge

P=9.81×Q×200×0.80=1569.6 Q kWP = 9.81 \times Q \times 200 \times 0.80 = 1569.6\,Q\ \text{kW}

Primary energy

Minimum flow = 100 m³/s (January).

Pf=1569.6×100=156,960 kW=156.96 MWEp=156,960×8760=1374.97 GWh\begin{aligned} P_f &= 1569.6 \times 100 = 156{,}960\ \text{kW} = 156.96\ \text{MW} \\ E_p &= 156{,}960 \times 8760 = 1374.97\ \text{GWh} \end{aligned}

Total and secondary energy

MonthQ (m³/s)Power (MW)Energy (GWh)
Jan100156.96114.58
Feb120188.35137.50
Mar140219.74160.41
Apr300470.88343.74
May320502.27366.66
Jun18002825.282062.45
Jul20003139.202291.62
Aug25103939.702875.98
Sep20003139.202291.62
Oct9001412.641031.23
Nov500784.80572.90
Dec300470.88343.74
Total10,99012,592.43
Es=12,592.43−1374.97=11,217.46 GWhE_s = 12{,}592.43 - 1374.97 = 11{,}217.46\ \text{GWh}

Pondage for firm capacity increased by 150%

"Increased by 150%" is read as new firm capacity = 1+1.5=2.51 + 1.5 = 2.5 times the original.

Pf,new=2.5×156.96=392.4 MWQf,new=2.5×100=250 m3/s\begin{aligned} P_{f,new} &= 2.5 \times 156.96 = 392.4\ \text{MW} \\ Q_{f,new} &= 2.5 \times 100 = 250\ \text{m}^3/\text{s} \end{aligned}

Months with flow below 250 m³/s must be supplied from storage:

MonthQDeficit (250 − Q)
Jan100150
Feb120130
Mar140110
Total390 m³/s-month
V=390×2.628×106=1.025×109 m3\begin{aligned} V &= 390 \times 2.628\times10^6 \\ &= 1.025 \times 10^9\ \text{m}^3 \end{aligned}

This storage is easily refilled in the monsoon months, when flows are far above 250 m³/s.

Answer: Primary energy ≈ 1375.0 GWh/yr; secondary energy ≈ 11,217.5 GWh/yr; storage (pondage) required ≈ 1.025 × 10⁹ m³ (1025 million m³).

(If "increased by 150%" is taken as 1.5 times, i.e. firm flow 150 m³/s, the deficits are 50 + 30 + 10 = 90 m³/s-month and the storage is 90×2.628×106=2.37×10890 \times 2.628\times10^6 = 2.37\times10^8 m³.)

  • 2075 Bhadra · 8 marks

Determine the firm and secondary energy for the following set of data of average monthly flows of river over a year.
MonthsJanFebMarAprMayJunJulAugSepOctNovDec
Q (m³/s)15025030042550010012501100100013001600500

Answer

Firm energy is produced by the minimum flow (available 100% of the time); secondary energy is the extra energy from flow above the minimum.

Assumptions

The head, efficiency and plant capacity are not given, so assume:

  • Net head H=100H = 100 m, overall efficiency η=0.85\eta = 0.85
  • The plant can use all the river flow (no spilling)
  • Each month = 730 h

Note: the June flow (100 m³/s) is taken as printed, so June is the minimum-flow month.

Power per unit discharge

P=9.81×Q×100×0.85=833.85 Q kWP = 9.81 \times Q \times 100 \times 0.85 = 833.85\,Q\ \text{kW}

Firm energy

Minimum flow = 100 m³/s.

Pf=833.85×100=83,385 kWEf=83,385×8760=730.45 GWh\begin{aligned} P_f &= 833.85 \times 100 = 83{,}385\ \text{kW} \\ E_f &= 83{,}385 \times 8760 = 730.45\ \text{GWh} \end{aligned}

Total energy

MonthQ (m³/s)Power (MW)
Jan150125.08
Feb250208.46
Mar300250.16
Apr425354.39
May500416.93
Jun10083.39
Jul12501042.31
Aug1100917.24
Sep1000833.85
Oct13001084.01
Nov16001334.16
Dec500416.93
Sum8475
Etotal=833.85×8475×730=5158.82 GWhEs=5158.82−730.45=4428.37 GWh\begin{aligned} E_{total} &= 833.85 \times 8475 \times 730 = 5158.82\ \text{GWh} \\ E_s &= 5158.82 - 730.45 = 4428.37\ \text{GWh} \end{aligned}

In general form: Ef=9.81 ηH×100×8760E_f = 9.81\,\eta H \times 100 \times 8760 and Es=9.81 ηH×(8475−12×100)×730E_s = 9.81\,\eta H \times (8475 - 12\times100) \times 730 kWh, so the answer scales directly with the assumed ηH\eta H.

Answer (H = 100 m, η = 85%): firm energy ≈ 730.5 GWh/yr; secondary energy ≈ 4428.4 GWh/yr.

  • 2074 Bhadra · 10 marks

Mean monthly flow for a Nepalese river is given below, the net head of river 150 m, overall efficiency of 85%. Assume 10% of water of minimum flow is required to be left for environment and downstream user in the river. Determine the primary and secondary energy produced by the plant, if design discharge is set to 950 m³/s. Assume any other data suitably if required.
MonthJanFebMarAprMayJunJulyAugSeptOctNovDec
Q (m³/s)1001201403003501800200025202000900650500

Answer

Primary energy comes from the minimum usable flow; secondary energy from the usable flow above it, up to the design discharge. An environmental flow must first be subtracted from the river flow.

Environmental flow

Minimum river flow = 100 m³/s (January).

Qenv=0.10×100=10 m3/s (released every month)Q_{env} = 0.10 \times 100 = 10\ \text{m}^3/\text{s}\ \text{(released every month)}

Usable flow = Q − 10, limited to the design discharge 950 m³/s.

Power per unit discharge

P=9.81×Q×150×0.85=1250.78 Q kWP = 9.81 \times Q \times 150 \times 0.85 = 1250.78\,Q\ \text{kW}

Installed capacity =1250.78×950=1,188,236= 1250.78 \times 950 = 1{,}188{,}236 kW ≈ 1188.2 MW.

Primary energy

Minimum usable flow = 100 − 10 = 90 m³/s.

Pf=1250.78×90=112,570 kWEp=112,570×8760=986.11 GWh\begin{aligned} P_f &= 1250.78 \times 90 = 112{,}570\ \text{kW} \\ E_p &= 112{,}570 \times 8760 = 986.11\ \text{GWh} \end{aligned}

Total energy (730 h per month)

MonthQQ − 10Q usedPower (MW)
Jan1009090112.57
Feb120110110137.59
Mar140130130162.60
Apr300290290362.72
May350340340425.26
Jun180017909501188.24
Jul200019909501188.24
Aug252025109501188.24
Sep200019909501188.24
Oct9008908901113.19
Nov650640640800.50
Dec500490490612.88
Sum6780
Etotal=1250.78×6780×730=6190.59 GWhEs=6190.59−986.11=5204.47 GWh\begin{aligned} E_{total} &= 1250.78 \times 6780 \times 730 = 6190.59\ \text{GWh} \\ E_s &= 6190.59 - 986.11 = 5204.47\ \text{GWh} \end{aligned}

Answer: Primary energy ≈ 986.1 GWh/yr; secondary energy ≈ 5204.5 GWh/yr (installed capacity ≈ 1188 MW).

  • 2073 Bhadra · 10 marks

Following table shows the mean monthly flow of a typical river of Nepal. Estimate the primary and secondary energies available in the river throughout the year. Assume 10% of minimum flow of the series has to be released for environmental flow to the downstream from the dam. Take overall efficiency of the plant is 80% and effective head is 155 m. Note: The months are as per Nepalese calendar i.e 1 as Baishakh and so on.
Month123456789101112
Discharge (m³/s)11501140145018301700155011501000850400480960

Answer

Primary energy is the energy available throughout the year from the minimum usable flow; secondary energy is the extra energy from usable flows above that minimum. No design discharge is given, so the plant is assumed to use all the usable flow. Each month is taken as 730 h (Nepali months vary from 29 to 32 days, but the yearly total is the same).

Environmental flow

Minimum flow of the series = 400 m³/s (month 10, Magh).

Qenv=0.10×400=40 m3/sQ_{env} = 0.10 \times 400 = 40\ \text{m}^3/\text{s}

Usable flow = Q − 40.

Power per unit discharge

P=9.81×Q×155×0.80=1216.44 Q kWP = 9.81 \times Q \times 155 \times 0.80 = 1216.44\,Q\ \text{kW}

Primary energy

Minimum usable flow = 400 − 40 = 360 m³/s.

Pf=1216.44×360=437,918 kW≈437.9 MWEp=437,918×8760=3836.17 GWh\begin{aligned} P_f &= 1216.44 \times 360 = 437{,}918\ \text{kW} \approx 437.9\ \text{MW} \\ E_p &= 437{,}918 \times 8760 = 3836.17\ \text{GWh} \end{aligned}

Total energy

MonthQUsable QPower (MW)
1 Baisakh115011101350.25
2 Jestha114011001338.08
3 Asar145014101715.18
4 Shrawan183017902177.43
5 Bhadra170016602019.29
6 Ashwin155015101836.82
7 Kartik115011101350.25
8 Mangsir10009601167.78
9 Poush850810985.32
10 Magh400360437.92
11 Falgun480440535.23
12 Chaitra9609201119.12
Sum13,180
Etotal=1216.44×13,180×730=11,703.86 GWhEs=11,703.86−3836.17=7867.69 GWh\begin{aligned} E_{total} &= 1216.44 \times 13{,}180 \times 730 = 11{,}703.86\ \text{GWh} \\ E_s &= 11{,}703.86 - 3836.17 = 7867.69\ \text{GWh} \end{aligned}

Answer: Primary energy ≈ 3836.2 GWh/yr; secondary energy ≈ 7867.7 GWh/yr (total ≈ 11,703.9 GWh/yr).

  • 2070 Magh · 10 marks

From the following data of flow at a given site for an average year compute and draw a power duration curve. Assume an average net available head of 100 m and a combined turbine generator efficiency of 89%. Determine the primary and secondary energy available during a year if the plant capacity is fixed at power corresponding to the flow available for 45% of time.
Flow (m³/s)900600500450400360340300280200140100
% time110203040506070809093100

Answer

A power duration curve is the flow duration curve with the flow axis converted to power, P=9.81 QHηP = 9.81\,Q H \eta. Area under it gives energy.

Power for each flow

P=9.81×Q×100×0.89=873.09 Q kWP = 9.81 \times Q \times 100 \times 0.89 = 873.09\,Q\ \text{kW}
% timeQ (m³/s)Power (MW)
1900785.78
10600523.85
20500436.55
30450392.89
40400349.24
50360314.31
60340296.85
70300261.93
80280244.47
90200174.62
93140122.23
10010087.31
P (MW)
 786 |*
     | \
 524 |   *
 437 |     *
 349 |========*======  <- capacity 331.8 MW
 314 |        |  *  *         (45% time)
 262 |        |        *  *
 175 |  secondary          *
 122 |        |               *
  87 |-primary (firm)---------------*
     +---------------------------------
     0   20   45   60   80   93  100  % time

Plant capacity (flow at 45% time)

Q45=400−45−4050−40(400−360)=380 m3/sPinst=873.09×380=331,774 kW≈331.8 MW\begin{aligned} Q_{45} &= 400 - \frac{45-40}{50-40}(400-360) = 380\ \text{m}^3/\text{s} \\ P_{inst} &= 873.09 \times 380 = 331{,}774\ \text{kW} \approx 331.8\ \text{MW} \end{aligned}

Primary energy

Flow available 100% of the time = 100 m³/s.

Pf=873.09×100=87,309 kWEp=87,309×8760=764.83 GWh\begin{aligned} P_f &= 873.09 \times 100 = 87{,}309\ \text{kW} \\ E_p &= 87{,}309 \times 8760 = 764.83\ \text{GWh} \end{aligned}

Total energy (area under capped curve, trapezoidal rule)

Flow used is capped at 380 m³/s from 0% to 45%.

Interval (%)Mean Q usedΔt (%)Area
0–453804517,100
45–5037051,850
50–60350103,500
60–70320103,200
70–80290102,900
80–90240102,400
90–931703510
93–1001207840
Total32,300

Mean flow used =32,300/100=323= 32{,}300/100 = 323 m³/s.

Etotal=873.09×323×8760=2470.39 GWhEs=2470.39−764.83=1705.56 GWh\begin{aligned} E_{total} &= 873.09 \times 323 \times 8760 = 2470.39\ \text{GWh} \\ E_s &= 2470.39 - 764.83 = 1705.56\ \text{GWh} \end{aligned}

Plant factor =323/380=85%= 323/380 = 85\%.

Answer: Installed capacity ≈ 331.8 MW; primary energy ≈ 764.8 GWh/yr; secondary energy ≈ 1705.6 GWh/yr.

  • 2077 Chaitra · 1+7 marks

Define firm power and secondary power. The load on a hydropower plant varies from a minimum of 12,000 kW to a maximum of 35,000 kW. Two turbo-generators of capacities 22,000 kW each have been installed. Calculate: (i) total installed capacity of the plant, (ii) plant factor, (iii) maximum demand, (iv) load factor, and (v) utilization factor.

Answer

Firm and secondary power

  • Firm (primary) power is the power that is available continuously (100% of the time), even in the driest period. It is fixed by the minimum flow.
  • Secondary (surplus) power is the power above firm power that is available only part of the time, when flow is higher than the minimum. It is sold at a lower rate or used for non-essential loads.

Data

Minimum load = 12,000 kW; maximum load = 35,000 kW; two units of 22,000 kW each. The load is assumed to vary linearly (uniformly) between minimum and maximum, so the average load is the mean of the two.

Pavg=12,000+35,0002=23,500 kWP_{avg} = \frac{12{,}000 + 35{,}000}{2} = 23{,}500\ \text{kW}

(i) Total installed capacity

Pinst=2×22,000=44,000 kWP_{inst} = 2 \times 22{,}000 = 44{,}000\ \text{kW}

(ii) Plant factor (capacity factor)

PF=average loadinstalled capacity=23,50044,000=0.534=53.4%PF = \frac{\text{average load}}{\text{installed capacity}} = \frac{23{,}500}{44{,}000} = 0.534 = 53.4\%

(iii) Maximum demand

Maximum demand = peak load = 35,000 kW.

(iv) Load factor

LF=average loadmaximum demand=23,50035,000=0.671=67.1%LF = \frac{\text{average load}}{\text{maximum demand}} = \frac{23{,}500}{35{,}000} = 0.671 = 67.1\%

(v) Utilization factor

UF=maximum demandinstalled capacity=35,00044,000=0.795=79.5%UF = \frac{\text{maximum demand}}{\text{installed capacity}} = \frac{35{,}000}{44{,}000} = 0.795 = 79.5\%

Check: PF=LF×UF=0.671×0.795=0.534PF = LF \times UF = 0.671 \times 0.795 = 0.534.

QuantityValue
Installed capacity44,000 kW
Plant factor53.4%
Maximum demand35,000 kW
Load factor67.1%
Utilization factor79.5%

Answer: 44,000 kW; 53.4%; 35,000 kW; 67.1%; 79.5%.

  • 2081 Asoj · 6 marks

Describe flow duration and power duration curves with their significance in estimating power potential of a hydropower project.

Answer

Flow duration curve (FDC)

A flow duration curve is a plot of discharge (on the y-axis) against the percentage of time that discharge is equalled or exceeded (on the x-axis). It is a cumulative frequency curve of the river flow.

How it is drawn

  1. Collect a long record of daily or monthly flows.
  2. Arrange the flows in descending order and give each a rank mm (1 for the largest).
  3. Compute the exceedance probability P=mN+1×100%P = \frac{m}{N+1}\times100\% (N = number of values).
  4. Plot Q against P.

Power duration curve (PDC)

A power duration curve is obtained by converting each flow of the FDC to power:

P=9.81 Q H η kWP = 9.81\,Q\,H\,\eta\ \text{kW}

It shows the percentage of time a given power is equalled or exceeded. Where the head is nearly constant, the PDC has the same shape as the FDC with a different scale.

Q or P
  |*
  | *
  |  **
  |    ***  installed capacity
  |=======*****======   (e.g. Q40)
  |   secondary  ****
  |                 *****
  |--- firm (Q100) -------****
  +---------------------------->
  0        50             100
       % time equalled/exceeded

Significance in estimating power potential

  • Firm power: the power at 100% (or 90–95% in practice) of time gives the firm (dependable) power of a run-of-river plant.
  • Installed capacity selection: the design discharge is chosen at a certain exceedance, e.g. Q40 to Q65 for Nepalese run-of-river projects; the PDC shows the power at that level.
  • Energy estimation: the area under the PDC (capped at the installed capacity) gives the annual energy; the area below firm power is primary energy and the rest is secondary energy.
  • Plant factor: mean power from the capped curve divided by installed capacity.
  • Flow character: a steep curve shows a flashy river (needs storage); a flat curve shows a well-regulated, groundwater-fed river.
  • Storage and pondage: shows how much storage is needed to raise the firm flow.
  • Environmental flow and spill: shows how often water is spilled and how much is left for downstream use.
  • 2071 Bhadra · 2+6 marks

What is the flow duration curve? Describe in brief the parameters influencing planning of hydropower projects.

Answer

Flow duration curve

A flow duration curve (FDC) is a graph of river discharge against the percentage of time that discharge is equalled or exceeded. It is drawn by arranging the recorded flows in descending order and plotting each against P=mN+1×100%P = \frac{m}{N+1}\times 100\%. It is used to find firm flow, design discharge (e.g. Q40, Q65) and annual energy.

Parameters influencing planning of hydropower projects

  1. Hydrology: the amount and variation of river flow (FDC, mean monthly flows, floods, low flows) decides firm power, installed capacity, and spillway size. Long, reliable records are needed.
  2. Topography (head): power depends on Q×HQ \times H. Steep rivers with a short distance between intake and powerhouse give high head cheaply. Valley shape decides dam type, reservoir area and layout.
  3. Geology: the foundation of the dam, tunnel route and powerhouse must be strong and stable. Faults, weak rock, landslides and seismic zones raise cost and risk (very important in the young Himalaya).
  4. Sediment: Himalayan rivers carry heavy sediment, which needs desanders and causes turbine wear and reservoir filling.
  5. Power market and demand: size and type of plant (base load or peaking, run-of-river or storage) must match the load curve, demand growth and possibility of export.
  6. Access and transmission: distance to roads and to the grid; long transmission lines add cost and losses.
  7. Environmental and social factors: land acquisition, resettlement, environmental flow, fish, effect on downstream users; an EIA/IEE is required.
  8. Economic and financial factors: project cost, interest rate, energy tariff, benefit–cost ratio, IRR and payback period.
  9. Legal and institutional aspects: licences, water rights, government policy and royalty.
  10. Construction materials and logistics: availability of sand, aggregate and cement near the site.
  11. Multipurpose use: irrigation, flood control, water supply and navigation needs can change the reservoir operation.
  • 2075 Bhadra · 4 marks

Explain the differences between Pre-feasibility and Feasibility studies in hydropower projects.

Answer

Pre-feasibility study is a preliminary study that compares alternative layouts of a hydropower site and selects the most promising one. Feasibility study is a detailed study of the selected scheme to prove that it is technically, economically, financially and environmentally viable and ready for financing.

PointPre-feasibility studyFeasibility study
PurposeScreen alternatives and choose the bestConfirm viability of the chosen scheme
StageAfter reconnaissance/desk studyAfter pre-feasibility, before detailed design
DataExisting maps (1:50,000), short or regional hydrologyDetailed survey (1:1000–1:5000), site flow measurement
InvestigationsSurface geological mapping, few testsDrilling, test pits, seismic survey, material tests
DesignConceptual layouts, rough sizesOptimised layout, preliminary design of all structures
Cost estimate accuracyAbout ±25–30%About ±10–15%
EnvironmentInitial screening of impactsFull IEE/EIA
OutputRecommended alternative, go/no-goBankable report: B/C, IRR, financing plan
Cost and timeLow, a few monthsHigh, one to two years

In short, the pre-feasibility study answers "which option is best?", and the feasibility study answers "is this option worth building, and how?".

  • 2077 Chaitra · 6 marks

Explain Power market, Hydrology and Geology as a planning parameter for hydropower development.

Answer

Hydropower planning depends on several parameters. Three of the most important are the power market, hydrology and geology.

Power market

The power market is the demand for the energy and the price it can be sold at.

  • Load demand and growth: the plant size must match present and future demand; an oversized plant spills energy.
  • Load pattern: base-load demand suits run-of-river plants; peak demand needs peaking run-of-river (PROR) or storage plants.
  • Seasonal mismatch: in Nepal, run-of-river plants have surplus energy in the monsoon and a shortage in winter, so storage or export markets (India, Bangladesh) are important.
  • Tariff and power purchase agreement (PPA): the buying rate (e.g. NEA rates, different for wet and dry season) decides revenue and financial viability.
  • Grid access: distance to the grid and transmission capacity.

Hydrology

Hydrology tells how much water is available and when.

  • Mean monthly flows and FDC: fix firm flow, design discharge (e.g. Q40–Q65) and annual energy.
  • Flood flows: design flood (e.g. 1-in-1000 or 10,000-year) sizes the spillway, diversion works and cofferdams.
  • Low flows: decide firm power and environmental flow.
  • Sediment load: sizes the desander and estimates reservoir life.
  • Glacial lakes (GLOF), snowmelt, climate change: need special study in Himalayan basins.
  • Long, reliable records are needed; for ungauged rivers, regional methods (e.g. MIP, WECS/DHM methods) are used.

Geology

Geology decides whether the structures can be safely and economically built.

  • Foundation: dam and powerhouse need strong, watertight rock with low permeability.
  • Tunnelling conditions: rock class, faults, shear zones, squeezing and water ingress control tunnel cost and time.
  • Slope stability: landslides at the intake, headworks and penstock route.
  • Seismicity: Nepal is a high seismic zone; design must include earthquake loads.
  • Construction materials: sand, aggregate, clay for dams.
  • Reservoir leakage and sedimentation depend on geology of the catchment.

Weak geology is the most common reason for cost and time overruns of Nepalese hydropower projects.

  • 2081 Chaitra · 6 marks

Enumerate the advantages and limitations of hydro-electric power.

Answer

Hydro-electric power is electricity produced by using the potential energy of water falling through a head to drive turbines coupled to generators (P=9.81QHηP = 9.81QH\eta).

Advantages

  1. Renewable source: water is renewed by the hydrological cycle and is not used up.
  2. No fuel cost: running cost is very low; only operation and maintenance.
  3. Clean: no smoke, ash or CO₂ during operation.
  4. High efficiency: overall efficiency 80–90%, much higher than thermal plants (30–40%).
  5. Quick start and load following: units can start and take load in a few minutes, so they are ideal for peak load and frequency control.
  6. Long life: 50–100 years for civil works.
  7. Reliable and simple: fewer moving parts, low breakdown rate.
  8. Multipurpose benefits: storage projects also provide irrigation, flood control, water supply, fisheries and tourism.
  9. No import dependence: for Nepal it uses local resources and saves foreign currency; surplus can be exported.

Limitations

  1. High initial cost: dams, tunnels and access roads are costly.
  2. Long construction period: usually 4–10 years.
  3. Dependent on rainfall/flow: output falls in the dry season or drought years.
  4. Site specific: plants are in remote hills, far from load centres, needing long transmission lines.
  5. Environmental and social effects: submergence of land, displacement of people, effect on fish and the downstream river.
  6. Sedimentation: reservoirs fill up and turbines are eroded, especially in Himalayan rivers.
  7. Geological and seismic risk: landslides, weak rock and earthquakes can damage works.
  8. Risk of dam failure and GLOF: large consequences downstream.
  • 2072 Asoj · 2+3 marks

What are the major sources of electric power generation? Discuss the relative merits and demerits of hydropower as compared to thermal power.

Answer

Major sources of electric power generation

  • Conventional: hydropower, thermal (coal, oil, diesel), gas turbine and combined cycle, nuclear.
  • Non-conventional (renewable): solar (photovoltaic and solar thermal), wind, biomass and biogas, geothermal, tidal and wave energy, fuel cells.

Hydropower compared with thermal power

PointHydropowerThermal power
FuelWater, free and renewableCoal/oil/gas, costly and finite
Initial costHigh (dam, tunnel)Lower
Running costVery lowHigh (fuel)
Efficiency80–90%30–40%
Starting timeFew minutes; good for peak loadHours; better for base load
PollutionNone in operationSmoke, ash, CO₂, SO₂
Life50–100 years25–40 years
LocationFixed by site, often remoteNear load centre or fuel source
Construction timeLongShorter
OutputDepends on rainfallSteady, independent of weather

Merits of hydropower: no fuel cost, clean, high efficiency, long life, quick start, multipurpose use.

Demerits of hydropower: high capital cost and long construction time, output varies with season, remote sites need long transmission lines, and dams cause submergence and resettlement.

Questions from Old Question Collection (CE 660) (IOE BEL CE 660 exam papers from 2070 Bhadra to 2082 Chaitra (18 papers)). Answers are written for this site; check them against your class notes.

Chapter titles and hours from the IOE syllabus ↗