Hydro impulse turbine speed regulation

The methodology outlined in a previous paper (1) on this subject, covering reaction units, was used to determine whether the same procedure is applicable to impulse units. It was found that isolated impulse units could operate effectively with a fraction of the minimum inertia previously suggested. This is primarily due to the dual mode of flow control, by needle valve, and by a deflector on the jet which rapidly cuts off flow when the speed rises above synchronous. This is clearly illustrated in Figure 1, where the plant characteristics are plotted on the chart applicable to reaction units, and most impulse units fall into Area A, designated for units which cannot provide any form of frequency control. Frequency control, derived from reaction unit data, can only commence when unit characteristics have a Tm/Tg ratio in excess of about 1.0.

Based on this analysis, it was decided to determine whether an improved methodology could be developed for impulse units which could more precisely define their ability to control frequency. Finding isolated impulse turbine powered utility systems is difficult, and there are very few examples to study. However, lessons can be learned from early experience with three isolated systems in Bolivia, providing electricity to the cities of La Paz, Oruro, and Cochabamba. The principal characteristics of units associated with these systems are shown in Table 1, along with one Canadian development at Cat Arm in Newfoundland.

The first hydro power development in Bolivia was at La Paz, where a small single jet horizontal axis 1,200 HP impulse unit was commissioned in 1909 within the city at Achachicala. At the time, there was no industrial load. Speed regulation was reasonable. The first development in the Zongo valley was also constructed at the same time, but due to the excessively high penstock velocity of 9.08m/sec, the unit had to be operated on base load.

Over time, further units were added at Achachicala, Zongo and downstream at Botijlaca, which had to be operated manually to avoid excessive frequency fluctuations. More power plants were added downstream at Cuticucho and Santa Rosa (2), but speed regulation was difficult, as the units all had slow needle jet opening times. When a district dropped off line due to a fault, the only way to re-connect was to manually intercept the jet flow with the deflector at the largest unit, the 9,000HP Santa Rosa #2, and then let the governor take over by releasing manual control, on a telephone command, the instant the district was re-connected. The weighted needle jet effective opening time of all the hydro units on the La Paz system at that time was 9.2 seconds, far too slow to accommodate a significant load-on due to re-connection of a district.

The isolated Oruro system provides power for the tin mines around Catavi. In 1931, two units of 2,000HP were installed at Miguilla, and the speed regulation capability was much improved from that experienced with Achachicala in La Paz. However, as the mining load increased, a unit was added downstream at Angostura, but the governing had to be manual, due to excessive speed deviations during load-on demand from the mining equipment.

In 1968, two 18,500HP units were installed at Corani for the Empresa Nacional de Electricidad, to provide power for the isolated system at Cochabamba, where there is light industrial development, (3). Speed regulation was found to be satisfactory.

From an inspection of Figure 1, it is evident that speed regulation with impulse units improves as the ratio of unit start time to governor opening time increases, as was experienced with reaction units. In Table 1, the units are ranked according to their speed regulation capability, based on the unit mechanical start time to jet opening time ratio. However, this measure is not sufficiently accurate for design purposes.

Impulse unit speed control

Impulse units have two flow controls – by the needle valve(s) which control flow, and by the jet deflector(s) which deflect the jet off the runner. The needle valves can open rapidly, but always close slowly, in order to limit penstock waterhammer. The jet deflector(s) move very rapidly, usually in about 1.5 to 3 seconds to fully deflect the jet(s) off the runner. The result is that speed rise on a full load-off is very small compared to the speed rise in reaction units. Speed rise on full load-off is usually less than 20%. Part load-off speed rise will be much smaller. This is the main reason why impulse units can control frequency with much smaller unit inertia than that required in reaction units.

Speed drop on a 10% partial load-on from 50% to 60% load can be calculated from the following equation derived from (4) -

N / N₂ = [1 - T / T_m {1.2 -1.1 (1 - h_w)^1.5}]^0.5 [1]

The unknowns in Equation 1 are the part-load jet opening time T and the negative waterhammer hw. The jet opening time can vary considerably, is usually in the order of 4 to 60 seconds, and calculated to produce a negative waterhammer between 40% and 20% or less. The limiting criterion is the penstock profile. If it has a “knee”, the negative waterhammer may be limited to only a few percent, and the jet opening time will be very long. In such cases, the unit will not be capable of operating in an isolated mode. When there is no limitation imposed by the penstock profile, the negative waterhammer can be large, and a fast opening time can be used.

The jet needle discharge characteristic has an “S” shape, with a slow increase in flow relative to stroke at the beginning and end of the stroke. The slow start is imposed by the gradual curve of the needle, required to avoid cavitation. The slow end is due to the smaller inner diameters being opened at the end of the opening stroke. The most rapid change in flow with respect to stroke is in the middle range, between about 20% and 70% stroke, and the relationship between the effective opening stroke in the middle is about 0.6 times the full stroke (Te = 0.6 Tg). However, this relationship will vary slightly with head and between manufacturers. The time required to complete a 10% increase in flow from half-load will then be, including an allowance of 0.2 seconds to start the movement -

T = 0.2 + 0.1T_e [2]

Combining equations 1 and 2 produces –

10% load-on = N / N₂ = [1 - (0.2 + 0.1T_e)/ T_m {1.2 - 1.1 (1 - h_w)^1.5}]^0.5. [3]

To calculate the negative waterhammer, the short time for the load change must be taken into account; hence the instantaneous or regular waterhammer value may need to be used.

Speed regulation analysis

Equation 5 was used to calculate the 10% load-on speed drop for the 25 units used in this analysis. For the 10 units listed in Table 1, additional characteristics are provided in Table 2.

In Table 2, the units are ranked according to the speed drop on a 10% load-on, and the ranking from Table 1 is also shown. It is interesting to note that the new regulation ranking is identical to the ranking based on experience with reaction units, for the best 4 units. The speed drops at Miguilla and Corani at less than 2% indicate that this is about the limit for regulation of light industrial loads. Achachicala, with a speed drop between 2% and 4% indicates that this is the range for regulation for no industrial load, and at a speed drop of over 4%, as indicated by Zongo, Angostura and Botijlaca, there is no speed regulation, all confirming early operating experiences.

Another chart was developed to more clearly indicate the level of regulation which could be provided by impulse units. This is shown in Figure 2, where the 10% speed drop is plotted against the unit start time. Two units, with valve opening times of more than 20 seconds are missing on Figure 2, since their speed drop exceeds 10%. This chart indicates that: for industrial loads, speed drop should be less than 1%; for light industrial loads, speed drop should be less than 2%; for systems with no industrial load, speed drop should be less than 4%; and systems with a speed drop over 4% cannot provide any speed regulation.

To reduce the speed deviation, there are three alternatives available. These are listed in order of increasing cost –

1. Shorten the effective governor needle valve opening time as much as possible. Assuming there are no restrictions imposed by a knee in the penstock profile, the limit is reached at about 40% negative waterhammer. Cost will be negligible.

2. Increase inertia. This could easily be accomplished by adding a flywheel in a horizontal axis unit, or by increasing the rotor diameter and weight in a vertical axis unit. Cost will increase slightly. For a horizontal shaft unit, this will require an extra bearing, a longer shaft, and more space will be needed in the powerhouse. For a vertical axis unit, the rotor diameter and weight will increase.

3. Increase the penstock diameter and reduce the effective governor opening time, to produce the same negative waterhammer. This option would be very expensive, but friction would be reduced, and energy increased. It is usually not an economic alternative.

Assuming that the needle opening time is as fast as possible, equation 3 can be re-written to determine the required inertia as -

T_m = (0.2 + 0.1T_e) {(N / N₂)² – 1}-1 {1.2 - 1.1 (1 - h_w)^1.5} [4]

With a defined speed variation of 1%, 2% and 4%, equation 4 can be revised to -

T_m = k (0.2 + 0.1T_e) {1.2 - 1.1 (1 - h_w)^1.5} [5]

Where k is a factor depending on the desired degree of regulation, and has a value of –

• 49 or more for industrial loads,

• between 24 and 49 for light industrial loads,

• between 12 and 24 for isolated units with no industrial loads.

• less than 12, will not provide any speed regulation.

This analysis is not applicable to small units with capacities less than about 1000kW. For such units, speed control can be provided by using a dump load such as water heaters, wherein the power is electronically diverted to the dump load whenever there is a surplus. A governor is not required, since water flow is maintained at a constant level.

Conclusions

A review of operating experience with isolated impulse turbine systems in Bolivia, has indicated that by calculating the speed drop on a nominal 10% load change, from 50% load to 60% load, the extent of speed drop will indicate the unit’s ability to control frequency. A speed drop of 1% or less defines a unit capable of accepting industrial load changes. A unit with a speed drop of between 1% and 2% could be used on an isolated system with light industrial load changes. At a speed drop of between 2% and 4%, the unit would only be suitable for isolated systems with no industrial loads. A speed drop in excess of 4% indicates that the unit would not contribute to frequency regulation.

The most economic method of improving speed regulation is to first decrease the needle jet opening time as much as possible, and then increase inertia with a flywheel in horizontal axis units, or by adding inertia to the generator rotor in vertical axis units.

J. L. Gordon, Hydropower Consultant, 102 Blvd St-Jean, Pointe Claire, Quebec, Canada, H9S 4Z1. Fax/tel: +1 514 695 2884. Email: jim-gordon@sympatico.ca

List of symbols

a sound wave velocity in meters per second.
g acceleration due to gravity, in meters per second squared.
GD² generator inertia, in tonne-meters squared, based on diameter of rotating mass.
h turbine rated head in meters.
h_w water hammer ratio, expressed as a fraction of h.
J ratio of actual to normal inertia, ranges between 0.9 and about 3.0.
k a coefficient defining the required speed regulation for an impulse unit.
kW generator rating, in kilowatts.
N synchronous speed, in revolutions per minute.
N₂ speed at end of load change, in revolutions per minute.
T needle valve opening time required for a part load change, in seconds.
T_e effective needle valve opening time, in seconds.
T_g total needle valve opening time, in seconds.
T_m mechanical start time of unit, in seconds = 0.00274 (GD)² N² / (kW)
T_w water column start time, in seconds = LV/(gh)