Environmental Engineering Reference
In-Depth Information
P = Q × H × ρ × g × η
(3.2)
where P = generated output power in watts (W), Q = fluid flow in cubic
meters per second (m
3
/s), H = hydraulic head height in meters (m), ρ = fluid
density in kilograms per cubic meter (kg/m
3
) = 1000 (kg/m
3
) for water, g =
acceleration due to gravity (m/s
2
) or 9.81 (m/s
2
), and η = efficiency.
As shown in Equation (3.2), the changeable variables are the volumetric
flow, the head, and the facility efficiency. Assuming that the head and a great
deal of the efficiency will be dictated by the location of the facility, the flow
becomes a significant design point of a PHES facility. The head and the flow
have an important relationship: if the head is larger, the water utilization can
be minimized. The reverse is also true: if the flow can be maximized, the head
can be reduced. Examples of PHES facilities that use the tradeoffs between
head and flow can be found. The facility in Ludington, Michigan, maximizes
flow to accommodate a moderate head.
3
In locations with high head and lim-
ited water, it would be desirable to maximize head to reduce the water needed.
The water needed in a PHES facility is not consumed; it is reused (less losses
for evaporation and seepage) by multiple up and down pumping. In many
cases, the water is releasable back into the system when needed.
As seen in Equation (3.2), to derive the energy of a facility one must input the
volumetric flow of water. One way to derive the appropriate flow is to assess
the potential sizing for the limiting reservoir. Ascertain the total volume of
water available in the limiting reservoir. Assess the energy market to which
the PHES facility will be interconnected and ascertain a desirable energy stor-
age time for that market. Knowing the volume of fluid and the time desired
for storage, one can suggest a flow rate by dividing the storage volume by the
storage time desired. The flow rate may also be dictated by the economics of
penstock construction or limitations of current or developable waterways.
Continuing to assess the tradeoffs between flow and head requires assess-
ment of the total energy available in the raised volume of water. By ascer-
taining the energy available, one can dictate the dispatch of that energy by
varying the power of the specific system. For a simple rule of thumb, assume
that for each acre foot of water raised 1 meter, 3 kWh are stored for later
dispatch or, for each acre foot of water raised 1200 feet, 1 MWh of energy is
stored for later dispatch. Figure 3.3 depicts energy potential over the volume
of water needed at increasing heads.
Development
Sites for PHES development are challenging to locate but this should not
infer that no sites are available for development. Alternative development
approaches should be considered. In addition, one should consider current
