"George, I need some help." Carlos was calling from South America, where the 225 meter-head Molinos plant, which contains four Francis turbine-generator units, had recently been commissioned. Carlos was operating engineer for the utility that owned the plant. The turbines were encountering a vibration problem between 55% and 65% wicket gate opening that was so severe, the units would occasionally shut down because of excessive shaft shaking. At the most severe operating point, shaft vibration amplitude exceeded 800 μm, compared to normal amplitude of less than 70 μm.1 Power surges ranged from 2 MW to 6 MW.
George, a hydro industry consultant, immediately suspected the cause of the vibration to be an exciting frequency induced from a combination of harmonics of the natural vibration frequency of the generator, draft tube rope frequency and penstock sound wave return time, the usual culprits. He asked Carlos to provide details on the power plant, including drawings and any reports or tests undertaken to detect the source of the vibration.
A few days later, George received a package containing all the information requested. It indicated that a calculation of the natural vibration frequencies revealed the generator natural frequency was five times the draft tube rope frequency, and the penstock sound wave return frequency was four times the draft tube rope frequency. The shaft vibrated at the same frequency as the draft tube rope.
It is sometimes possible to reduce vibration induced by the draft tube rope by injecting air into the draft tube.2 The plant operator tried this, and it produced some smoothing of the vibration, but not enough to warrant continuing the experiment. At high tailwater, the vibration reduced significantly, due to the additional back-pressure on the draft tube, reducing the volume of air in the draft tube rope.
Eventually, utility management decided that with four turbines in the plant, operation in the rough zone could be avoided. When loading a unit, the operator passes through the rough zone as quickly as possible, and the units are operated only above or below the rough zone.
There are two types of vibrations likely to be encountered in a power plant. One is high frequency, usually associated with turbine blade to wicket gate passing frequency, causing fatigue failures. The other is low frequency vibration, usually associated with the draft tube rope frequency, likely to cause power surges and shaft vibration.
Avoiding all high-frequency vibrations in power plants is difficult. There are just so many combinations of harmonics that avoiding all exciting frequencies is almost impossible. This is illustrated by the fatigue failures of a penstock in Japan, investigated by Dr. C. Jaeger in the 1960s, where it was found that the exciting frequency was a combination of two harmonics. Another example would be vibration of one of the penstocks at the 2,078 MW Hoover plant in Arizona and Nevada in the USA, with the exciting source being the turbine blade passing frequency.3 In this case, the turbine runner had 16 blades, another reason to avoid runners with an even number of blades.4
Avoiding lower-frequency vibrations is possible, if measures are taken early in the design process. The best approach is to calculate all possible exciting frequencies after completion of the pre-feasibility report, when project parameters are well-established but can still be changed. A list of the expected frequencies and formulae for calculating their value is available.5 Of these, the most important is draft tube rope frequency, as it is implicated in most Francis turbine vibration problems.
Missing from this list is the generator natural frequency, which has a value obtained by the following equation:
24.3 x √ (system frequency / H)
— H is the generator constant value.
The plant operator must then check to see if the first to fifth harmonic of any of the frequencies matches another frequency or harmonic thereof. If so, measures could be taken before the project proceeds to the detailed design phase, such as avoiding certain turbine speeds, changing the number of runner blades, or changing the length of water passages by moving the powerhouse or surge tank. This may seem an onerous task, but once it is programmed into a spreadsheet, it can be re-programmed to see the effect of changes.
Many papers were published on vibration problems in hydro plants before about 1970. Unfortunately, this was before the digital age. Hence, references to such papers are almost impossible to find, and the papers are difficult to obtain.
— By James L. Gordon, B.Sc., hydropower consultant
1. Pejovic, Stanislav, "Understanding the Effects of Draft Tube Vortex Core Resonance," HRW, Volume 8, No. 4, September 2000, pages 28-33.
2. Falvey, Henry T., "A Primer on Draft Tube Surging," Hydro Review, Volume 12, No. 1, February 1993, pages 76-86.
3. Todd, Robert V., "Investigating Penstock Vibrations at Hoover Dam," Hydro Review, Volume 20, No. 3, June 2001, pages 34-38.
4. Gordon, James L., "Lessons Learned: Nintendo Engineers," HRW, Volume 14, No. 4, September 2006, pages 46, 51.
5. The Guide to Hydropower Mechanical Design, ASME Hydro Power Technical Committee, PennWell Corporation, Tulsa, Okla., Table 3-4, pages 3-65, www.pennwellbooks.com/gutohymede.html.