POWER January 2020 - 36

HYDROPOWER
Measurement of Surge
Tank Oscillations
The measurement of surge tank oscillations
is done by the logarithmic
decrement:
δ = ln ( x1
/ x2
)
where ln is logarithm to the base e and
x is the amplitude of two successive
surges measured from the new steady
state water surface.
The formula for the equivalent value of
the logarithmic decrement is derived as:
δ = ln [( a1
+ a2 ) / ( a3
+ a4
)]
where a represents the surge heights
sequentially above and below the original
steady state water surface.
In this case, instead of a complete
load rejection, if there is a load change
through which the turbine-generator remains
connected to the grid, the governor
remains in control of the unit. This
will cause a lesser change in the elevation
of the water surface in the surge
tank. However, the governor will read
this as a change in the head differential
across the turbine and seek to readjust
the wicket gate opening from the adjustment
completed to accommodate the
load change. If the governor response
time is in synchronization with the hydraulic
surge tank frequency, the oscillations
will not be dampened, but can
be reinforced. This is referred to as hydraulic
surge tank instability. The oscillations
may grow and remain at a fixed
amplitude in " constrained " oscillation
(see sidebar). In an extreme case, they
may grow until the tank is overtopped,
or even worse, until air is sucked into
the penstock. A sudden hydraulic unloading
of the turbine by air admission
in the penstock can be catastrophic.
Types of Surge Tanks
There are several types of surge tanks
(Figure 2). The basic differences have
to do with the hydraulic losses of fluid
entering and leaving the tank. These differences
are designed into the passive
water hammer protection afforded by
the tank to maintain hydraulic stability.
The most basic type of surge tank
is called a " simple " surge tank. It has
a diameter larger than the penstock so
that the penstock enters the side of the
tank at its base and exits the other side.
36
This type of tank provides the greatest
relief to pressure transients but is the
least stable.
The second type is called a " riser "
tank, which is connected by a smaller
diameter pipe between the penstock
and the bottom of the surge tank. This
type provides less mitigation of the effects
of pressure transients, but the
additional head loss of fluid entering
and leaving the riser and surge tank
adds to the stability. Some riser tanks
are built with orifice plates in the riser.
These are called " restricted riser "
surge tanks. They provide even less
mitigation to pressure transients but
are even more stable.
Finally, there is a class of surge tanks
known as Johnson's Differential or simply
" differential " tanks. These are designed
with different head losses and
elevations for fluid entering and leaving
the tank to disrupt the harmonics of hydraulic
oscillation.
Criteria for Stability
In the early days of hydropower projects,
whenever an unstable surge tank was
encountered, it was observed to be most
unstable under the following conditions:
■ At the lowest head
■ Near full power
■ Where the turbine efficiency droop
was most negative
■ Where the penstock losses were the
lowest
■ Where the conduit losses between
the surge tank and the turbine were
the highest
In 1910, a German professor in Munich,
Germany, D. Thoma, published a
paper that was the first to show that
turbines with automatic governors could
always be stable if the horizontal crosssection
of the tank (As,Th
) exceeds a certain
minimum value. That formula is:
As,Th
= L Ap
/ 2 k g H b
where Thoma's area (As,Th
) equals the
length of the water column (L) times
the cross-sectional area of the penstock
(Ap
) divided by a constant for hydraulic
losses (k), gravity (g), net head to the
surface of the surge tank (H), and resistance
factor of the penstock (b). In
achieving that derivation, Thoma was
forced to assume that generating efficiency
was constant with head. Consequently,
it was standard practice in
Europe to incorporate a safety factor
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The New Melones Project
A number of years ago, the U.S. Army
Corps of Engineers began design work
on a hydroelectric project on the Stanislaus
River in California. Due to endof-year
budget constraints, it opted to
design and build a surge tank for the
New Melones hydroelectric project (Figure
3) at the end of one budget year
and continue the design of the rest of
the project in the following year. It was
noted that in the event of a natural disaster
this project may be called upon to
supply electrical power to a community
as an isolated load. Consequently, the
surge tank was designed as a restricted
POWER | January 2020
2. Four types of surge tanks are shown here.
Surge tanks help to maintain hydraulic stability
by disrupting resonance waves caused by
surges. Source: Lee Sheldon
by increasing the Thoma-derived surge
tank area 25%. In the U.S., it was common
to add 50%.
In the earlier part of the 20th century,
G. Evangelisti, an Italian professor of
Hydraulic Structures in the University of
Bologna, published a paper on hydraulic
stability of any type of surge tank.
He analytically demonstrated that any
hydropower project with a surge tank
that is connected to a grid, which also
carries more than twice the power from
non-surge tank sources, will always be
hydraulically stable.
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POWER January 2020

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