36 OCTOBER 2009 INTERNATIONAL WATER POWER & DAM CONSTRUCTION
ance 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 / N
2
= [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 regu-
lar waterhammer value may need to be used.
S P E E D R E G U L A T I O N A N A L Y S I S .
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 inter-
esting to note that the new regulation ranking is identical to the rank-
ing 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 confi rming 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 avail-
able. 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 profi le, the limit is reached at about 40% negative
waterhammer. Cost will be negligible.
2. Increase inertia. This could easily be accomplished by adding a fl y-
wheel 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 / N
2
)
2
– 1}
-1
{1.2 - 1.1 (1 - h
w
)
1.5
} [4]
With a defi ned 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 –
U 49 or more for industrial loads,
U between 24 and 49 for light industrial loads,
U between 12 and 24 for isolated units with no industrial loads.
U 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 fl ow is maintained at a constant level.
C O N C L U S I O N S
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 defi nes 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
fi rst decrease the needle jet opening time as much as possible, and
then increase inertia with a fl ywheel 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
TURBINES
References
(1) Gordon, J. L. and Whitman, D. H. 1985 Generator inertia for isolated
power systems. Canadian Journal of Civil Engineering, 12(4): 814-820.
(2) Encinas, L. and Ebenstein, G. L. Una cascada de plantas intercepta at
Zongo en Bolivia. Ingenieria Internacional Construccion, 1968, (12): 53-58.
(3) Zenteno, M., Williams, A. W. and Gordon, J. L. 1982. The expansion of
two Bolivian plants. Water Power and Dam Construction, Vol. 34 (2): 26-31.
(4) Gordon, J. L. and Smith, W. G. 1961. Speed regulation for hydraulic
turbines. The Engineering Journal, 44 (10): 92-97.
List of symbols
a sound wave velocity in meters per second.
g acceleration due to gravity, in meters per second squared.
GD
2
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 coeffi cient defi ning the required speed regulation for an impulse unit.
kW generator rating, in kilowatts.
N synchronous speed, in revolutions per minute.
N
2
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
N
2
/ (kW)
T
w
water column start time, in seconds = LV/(gh)
IWP& DC