Pumping up hydroelectric power plant

In a pumping up hydroelectric power plant including a main pump/turbine and a booster pump operable in series during the pumping operation of the main pump/turbine, time constants K.sub.1 and K.sub.2 for the pump/turbine and the booster pump, and average torques y.sub.1 and y.sub.2 for the same two machines are selected to satisfy relations EQU (K.sub.1 /K.sub.2)(y.sub.2 /y.sub.1).apprxeq.1.0 and EQU 0.71.ltoreq.K.sub.2 /K.sub.1 .ltoreq.1.42.

BACKGROUND OF THE INVENTION 
This invention relates to a pumping up hydroelectric power plant utilizing 
a reversible pump/turbine and a booster pump operable in series when the 
pump/turbine is operated in the pumping mode. 
Recently, pumping up hydroelectric power plants operable under high heads 
are being constructed widely. However, when the pump/turbine provided 
therein is of a single speed type, the head under which the pump/turbine 
is operated at the maximum efficiency in the pumping mode is considerably 
lower than that in the turbine mode of operation also at the maximum 
efficiency, and therefore it is found difficult to operate the 
pump/turbine in both of the two modes at their highest efficiencies under 
an operating head condition assigned to the pumping up power plant. 
In order to overcome this difficulty, there has been proposed and 
constructed a pumping up hydroelectric power plant wherein a booster pump 
is further provided in a by-pass portion of the suction side tunnel of the 
pump/turbine in such a manner that the booster pump is operated in series 
with the pump/turbine with a portion of the head available at that time 
assigned to the booster pump during the pumping operation of the 
pump/turbine. 
In such an arrangement of the pumping up hydroelectric power plant, during 
the pumping operation since the total head of the power plant is shared 
between the pump/turbine and the booster pump, the actual head under which 
the pump/turbine is operated in the pumping mode can be reduced by an 
amount assigned to the booster pump, and therefore the pump/turbine can be 
operated in both pumping mode and turbine mode at the points of highest 
efficiencies even under the operating head condition assigned to the power 
plant, thus improving the total efficiency of the power plant. 
However, in the above described construction of the power plant, since the 
main pump/turbine and the booster pump, inherently having different 
hydraulic characteristics, are operated in series along a single water 
passage (or suction side tunnel), the two machines tend to interfere with 
each other in their transient conditions, thus rendering the operations to 
be utterly unstable. 
For instance, when the pump/turbine and the booster pump having different 
deceleration characteristics are simultaneously interrupted from the power 
system, a difference in flow-rate due to the different deceleration 
characteristics tends to cause severe variation in water pressure in the 
draft tube. 
More specifically, where the deceleration of the booster pump is larger 
than that of the main pump/turbine, the rotating speed of the latter 
becomes higher than that of the booster pump after their interruption from 
the power system, and a reduction in speed of the booster pump is 
prevented by the water flowing through the main pump/turbine. The 
operation of the booster pump is thus deviated from the designed 
condition, tending to cause a separation of water layers (or cavitation) 
which in turn tends to damage the booster pump and other parts related 
thereto. 
On the other hand, when the deceleration of the main pump/turbine is 
greater than that of the booster pump, the quantity of water pumped up by 
the main pump/turbine per unit time is rapidly reduced. However, since the 
rotating speed of the booster pump is still higher than that of the main 
pump/turbine, an extremely high pressure is inevitably induced at the 
delivery side of the booster pump, with a result that the booster pump and 
other related parts are thereby damaged. 
SUMMARY OF THE INVENTION 
A primary object of the present invention is to provide a pumping up 
hydroelectric power plant including a main pump/turbine and a booster pump 
operable in series along a draft tube, wherein the operations of the main 
pump/turbine and the booster pump are made stable regardless of the 
transient conditions of the operations. 
Another object of the invention is to provide a pumping up hydroelectric 
power plant as described above, wherein the operations of the pump/turbine 
and the booster pump are stabilized without requiring any additional 
electric circuitry for stabilizing the operations. 
According to the present invention, there is provided a pumping up 
hydroelectric power plant comprising a main pump/turbine having a draft 
tube, and a booster pump provided in a by-pass conduit of the draft tube, 
so that the booster pump is operated in series with the main pump/turbine 
during the pumping operation of the pump/turbine, the improvement wherein 
the main pump/turbine and the booster pump are constructed to satisfy a 
relation 
EQU (K.sub.1 /K.sub.2) (y.sub.2 /y.sub.1).apprxeq.1.0 
wherein 
K.sub.1 : time constant of the rotating part of the pump/turbine, 
K.sub.2 : time constant of the rotating part of the booster pump, 
y.sub.1 : average torque exerted to the rotating part of the pump/turbine, 
y.sub.2 : average torque exerted onto the rotating part of the booster 
pump. 
The pumping up hydroelectric power plant according to the present invention 
may otherwise be modified so that the ratio of the time constants K.sub.1 
/K.sub.2 is in a range of from 0.71 to 1.42.

DESCRIPTION OF THE PREFERRED EMBODIMENT 
Referring now to the accompanying drawing there is indicated a pumping up 
hydroelectric power plant including a single speed reversible pump/turbine 
1 directly coupled with a reversible motor/generator 2. A penstock 3 
connects the pump/turbine 1 to an upper reservoir (not shown), located 
above the power plant and a draft tube 4 connects the pump/turbine 1 with 
a lower (or tailrace) reservoir 5. A booster pump 7 directly coupled with 
an electric motor 8 is provided in a by-pass conduit 6 extending between 
two branching points spaced apart along the draft tube 4. A transfer valve 
9 is provided at the first branching point near the pump/turbine 1. When 
the main pump/turbine is operated in the turbine mode, the transfer valve 
9 is placed at a position indicated by broken lines shown in the drawing 
for closing the conduit 6. In this state, water is discharged from the 
pump/turbine 1 to the lower reservoir 5 through the draft tube 4. 
On the other hand, when the pump/turbine 1 is operated in the pumping mode, 
the transfer valve 9 is shifted to a position indicated by solid lines so 
that water in the reservoir 5 passes through the by-pass conduit 6, and 
hence through the booster pump 7, to the suction side of the pump/turbine 
1 now operating as a pump. 
According to the present invention, the pump/turbine and the booster pump 
are so constructed that the deceleration characteristics of these machines 
are equal to each other. More specifically, the pump/turbine and the 
booster pump are so designed that when the machines are simultaneously 
disconnected from the power system, the rotating speeds of these machines 
are simultaneously reduced to zero. 
The above described characteristics of the two machines can be obtained 
where a time constant is assumed as described hereinbelow for the rotating 
part of each machine inclusive of the rotating part of the driving motor, 
and the ratio between the time constants for the main pump/turbine and the 
booster pump is brought into a predetermined range. 
Ordinarily, when a hydraulic machine is interrupted from the power source, 
and the rotating speed thereof is reduced, the equation of motion for the 
rotating part of the machine inclusive of the driving motor is expressed 
as 
##EQU1## 
wherein t: time (in sec.) 
x: rotating speed (dimensionless) of the rotating part (N/N.sub.o), 
y: dimensionless torque acting on the rotating part from outside 
(=M/M.sub.o), 
N.sub.o : rated speed of the hydraulic machine (rpm), 
N: rotating speed of the hydraulic machine after it has been interrupted 
from the power system (rpm), 
M.sub.o : operational torque of the hydraulic machine at the time of the 
rated operation (kg.m), 
M: torque exerted to the rotating part from water (kg.m) after the machine 
has been interrupted from the power system, 
K: time constant (sec.) for the entire rotating parts of th- hydraulic 
machine inclusive of that of the driving motor (=.pi..multidot.N.sub.o 
.multidot.GD.sup.2 /120 g.multidot.M.sub.o). 
As is apparent from the above equation (1), the rate of variation in the 
dimensionless rotating speed of the rotating part with respect to time is 
varied depending on the dimensionless torque y and the time constant K. 
Assuming that the time period from the interrupting instant x=x.sub.o =1) 
to an instant where the rotating speed N of the hydraulic machine is 
reduced to 0 (x=0) is represented by t, and by subjecting the equation (1) 
to a definite integration as follows, 
##EQU2## 
the following relation can be obtained. 
##EQU3## 
This equation (3) indicates that the time constant K is defined to be a 
definite integration of dimensionless torque y from the interrupted 
instant to an instant where the rotating part is brought to standstill. 
From equation (3), the mean value y of the torque y is expressed as 
##EQU4## 
It is apparent that the mean value y and the time constant K are values 
specific to each of the hydraulic machines. 
Returning now to the arrangement shown in FIGURE, it is assumed that the 
main pump/turbine 1 and the booster pump 7 are simultaneously disconnected 
from the power system, and that the values related to the main 
pump/turbine 1 are designated by characters suffixed with 1, while the 
values related to the booster pump are designated by characters suffixed 
with 2. Then, the time periods t.sub.1 and t.sub.2 required for bringing 
these two machines from the rated speeds to standstill condition are 
EQU t.sub.1 =K.sub.1 /y.sub.1 . . . (5) 
EQU t.sub.2 =K.sub.2 /y.sub.2 . . . (6) 
From these relations, 
EQU t.sub.1 /t.sub.2 =(K.sub.1 /K.sub.2) (y.sub.2 /y.sub.1) . . . (7). 
Ordinarily, hydraulic machines are classified into Francis type, axial-flow 
type, and a diagonal-flow type. Regardless of whatever types are the two 
hydraulic machines, the mean values y.sub.1 and y.sub.2 of the torques 
y.sub.1 and y.sub.2 applied to these machines are different from each 
other when the "specific speed" of these machines, which is an important 
factor in machine design, is different. 
Furthermore, it has been found that the ratio of these mean values y.sub.1 
and y.sub.2 for the two machines which are operable in series in an 
arrangement as shown in the accompanying drawing is advantageously in the 
following range. 
EQU (y.sub.2 /y.sub.1)=0.71-1.42 . . . (8) 
The lower limit 0.71 corresponds to a combination of the pump/turbine and 
the booster pump, wherein a greatest possible value is selected for the 
torque of the pump/turbine against that of the booster pump, while the 
upper limit 1.42 corresponds to a combination wherein a smallest possible 
value is selected for the torque of the pump/turbine against that of the 
booster pump. 
From the above described relations (7) and (8), the ratio of the two time 
constants K.sub.2 /K.sub.1 causing t.sub.1 =t.sub.2 is expressed as 
EQU K.sub.2 /K.sub.1 =y.sub.2 /y.sub.1 =1.42-0.71 . . . (9). 
When it is assumed that N.sub.o1 and N.sub.o2 represent rated speeds (rpm) 
of the pump/turbine and the booster pump respectively; M.sub.o1 and 
M.sub.o2 represent hydraulic torques (kg.m) of the two machines during the 
rated pumping operations; GD.sub.1.sup.2 and GD.sub.2.sup.2 represent 
moment of inertias (kg.m.sup.2) of the two machines inclusive of the 
rotating parts of the driving motors; .pi. represents the circumference to 
diameter ratio of a circle; and g represents an acceleration coefficient 
of gravity, the time constant K.sub.1 of the main pump/turbine is 
expressed as 
##EQU5## 
while the time constant K.sub.2 of the booster pump is 
##EQU6## 
Thus by adjusting GD.sub.1.sup.2 and GD.sub.2.sup.2, the ratio between the 
time constants K.sub.1 and K.sub.2 for the main pump/turbine and the 
booster pump can be brought into a range of from 0.71 to 1.42.