Part-Load Operation of a Francis Unit in the Monsoon
Each of the three 60 MW Francis units at a 180 MW station is rated at 100 m head and 70 m³/s at 150 rpm. The runner setting is 2.1 m above the minimum tailwater level, the summer water temperature is 25 °C (vapour pressure head 0.24 m), and atmospheric pressure is taken as 10.3 m of water. During this monsoon the reservoir head has fallen to 78 m and the load despatch centre is running all three units between 30 MW and 45 MW at night for frequency regulation. Since then the draft tube pressure transducer shows a peak-to-peak fluctuation of 9.5 % of head at about 1.1 Hz, the unit is clearly audible at the draft tube access door, and the thrust bearing temperature has risen from 62 °C to 79 °C against an alarm at 80 °C. The last inspection found 3 mm deep erosion pits in a band near the blade trailing edge at the band. The model test gives σ critical = 0.13 at 55 % load and 0.06 at 90 % load. Unit efficiency is 88 % at 60 % load and 93.5 % at 92 % load. The alternative is to run two units at 55 MW each for the same 110 MW total.
1. Calculate the plant cavitation index at the present head and decide whether the night regime is actually cavitating. What does each symptom tell you?
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Plant sigma. Using the turbine setting as positive suction head: σ avail = (H atm − H vap − H setting)/H = (10.3 − 0.24 − 2.1)/78 = 7.96/78 = 0.102.
Comparison with the model test. σ critical is 0.13 at 55 % load and 0.06 at 90 %. Interpolating linearly, σ critical falls to 0.102 at a load of 0.55 + (0.13 − 0.102)/(0.13 − 0.06) × 0.35 ≈ 0.69, i.e. about 69 %. So the whole 30–45 MW band (50–75 %) lies where σ critical exceeds σ available: the unit is cavitating at night, and it is safe above roughly 70–75 % load. Note the trap - the setting itself is fine at full load; it is the part-load operation that has consumed the margin.
Symptoms read together.
- 1.1 Hz on a 150 rpm runner (2.5 Hz) is 0.44 × runner frequency, exactly the part-load vortex-rope range - confirming a hydraulic excitation, not a mechanical one.
- 9.5 % peak-to-peak draft tube fluctuation and audible noise at the access door are the same phenomenon; this is fatigue loading on the runner and draft tube.
- Thrust bearing temperature rising 17 °C with the vibration is vibration-induced, so raising the alarm band would be the wrong response.
- 3 mm pits near the trailing edge at the band are classic cavitation erosion, consistent with hours already logged in this band.
The regime is damaging, and the damage accumulates as a fatigue and erosion problem, not as an immediate trip.
2. Evaluate the two dispatch options quantitatively and recommend an operating policy.
Read the worked answer
Water rate for 110 MW. Power per unit discharge at 78 m: P(MW) = 9.81 × 78 × η × Q/1000 = 0.7652 × η × Q.
- Three units at 36.7 MW, η = 0.88: Q each = 36.7/(0.7652 × 0.88) = 54.5 m³/s → 163.4 m³/s total.
- Two units at 55 MW, η = 0.935: Q each = 55/(0.7652 × 0.935) = 76.9 m³/s → 153.7 m³/s total.
Saving ≈ 9.7 m³/s, about 6 % of the water for the same output, worth roughly 6.9 MW of equivalent generation - over an 8-hour night about 55 MWh, or ₹2.5 lakh at ₹4.5/kWh. Over 300 such nights this is of the order of ₹7 crore a year, before counting the reduction in cavitation damage.
Counter-arguments to weigh. Two-unit running doubles the largest single contingency from 36.7 MW to 55 MW and needs that reserve elsewhere; the system operator may refuse it during a transmission constraint. The third unit on barring gear or standby also reduces the ability to pick up load fast.
Policy I would issue:
- Minimum unit loading 48 MW (80 %), with a hard interlock below 45 MW; the 30–45 MW band is prohibited except with written engineering approval for a short grid emergency.
- At night, run two units at 55 MW whenever reserve is available; revert to three units when the largest-contingency reserve cannot be provided elsewhere.
- Do not simply raise the bearing alarm setting; investigate the vibration source instead.
3. What engineering and monitoring measures would you put in place for the coming months, and how do they compare economically with the dispatch fix?
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Measures, in order of value:
- Operating band interlock - cheapest and most effective. It costs nothing and removes most of the damage; it is the primary measure, not a substitute for the others.
- Air admission under the runner, typically 0.5–1 % of discharge. It cushions the vortex rope and cuts pressure pulsation sharply, at an efficiency penalty of about 1 % - roughly 1.1 MW at 110 MW, about 9 MWh a night, or ₹40,000. That is materially cheaper than the ~55 MWh lost through the poor water rate of 3-unit part-load running, so if part load cannot be avoided, air admission is worth having. Size the compressor for the worst case and interlock admission with the load band.
- Monitoring: a draft-tube pressure pulsation channel with a trend alarm and a high-high trip, plus bearing vibration on the thrust bearing; the 1.1 Hz component is the specific indicator to trend. Signature analysis at each load band, not just at full load.
- Runner repair criteria: pits of 3 mm are repairable but must be ground and weld-repaired before they reach about 10 % of blade thickness or the fatigue life is compromised. Plan the repair in the lean season and record pit depth mapping at each inspection so the erosion rate in mm per 1,000 hours is known.
- Check the sigma curve for the actual head. With head varying through the year, the minimum safe load moves; publish a load-versus-head chart for the operators rather than a single number.
Economic comparison: air admission costs roughly ₹40,000 a night; three-unit part-load running costs about ₹2.5 lakh a night in water plus quantified erosion; the interlock costs nothing. Cost-effective sequence: interlock, then air admission, then repair.