by Robert T. Bullard
Storing excess electrical power has been a problem that has dogged utilities for years. Pumping water that comes out of a hydroelectric dam back to its reservoir was one power storage solution. Wind power seems to highlight the problem because unused wind power is just lost. But it need not be.
A variation on the idea, whether it is pumped air or water, boasts of a few impressive projects around the world. For the most part, it’s still big, expensive, and often excessively challenging to Mother Nature. The potential, however, is too good to ignore and prompts the question: What possibilities are there to store excess wind power?
Many wind farms are along ridges with rather significant topographic relief affording sufficient head difference between adjacent basins. These farms are usually in remote areas where the extraction of ground water for pumped storage is not in conflict with other users. In effect, various pumped storage reservoirs may provide beneficial secondary uses (such as irrigation, recreation, and aquaculture) when appropriately blended into the primary use.
Let’s first review a brief summary of pumped-storage basics before getting into specifics. It consists of two impoundments (reservoirs), and usually two dams. Conventional hydroelectric uses a single dam across a river to form an upstream reservoir. When the upper reservoir is full and electricity is in high demand, water flows down through water turbines which spin generators, thereby producing power for distribution to the electrical grid.
When the electricity demand is low and there is available excess electrical power on the grid, water can be pumped from the lower to the upper reservoir, ready for the next round of high demand power generation. When the electricity can be sold to the grid at a sufficiently high rate during high demand (compared to the price at which the pumped storage operator may purchase electricity from the grid) the pumped-hydro operator will purchase the lower-cost electricity from the grid to recharge (add to or refill) the upper reservoir. When the pumped-storage operator also generates electric power from a secondary source (such as a wind farm) that person has the option of recharging the upper reservoir by purchasing low-cost power for pumping from his own facility instead of selling the electricity at less-than-premium rates to the grid.
There is another big advantage to storing power this way. Because pumped storage recycles water, a well built pumped-storage project needs far less water to produce the same amount of net electricity generation than a conventional once-through hydroelectric dam. Hence, pumped storage can be built in areas where water availability is far less than would be needed for a conventional hydro project.
There are other opportunities. For instance, sites for pumped storage in the size range comparable to wind farms (50 to 500 MW) are considerably more available than those for conventional hydro. With such flexibility in siting, smaller pumped-storage projects may be located closer to existing load centers (cities), power lines and even, among wind farms producing the variable electric power. When a wind farm produces power at low demand or period of low-selling price, the cheap power could drive the upper reservoir’s recharging pumps. Most small, pumped-storage reservoirs can be located in such a fashion as to not substantially reduce historical dry weather flow conditions downstream of the project.
Just as with a conventional hydroelectric facility, pumped storage may also include provisions for site-specific ancillary uses for irrigation, recreation, flood control, aquatic-habitat development, and local industrial water users. The notion of incorporating pumped storage into a proposed or existing wind farm is intriguing, presenting an enhancement of income opportunity for the project developer and land-owner alike.
One problem with renewable electric power generated by a variable source is that it is hard to know how much electricity will be available at any particular time and place. With pumped storage, the system (grid, pumped storage, and wind farm) operators always know how much water is available at what time and at what location, so the pumped-storage generators may be operated up to their peak power rating, dispatching an almost instantaneously varying amount of energy toward stabilizing the electrical variables of the grid. The more pumped storage capacity on the grid, the more the grid operators can depend on it as an on-call source of clean, renewable energy generation, and the less they have to worry about when and where the wind may blowing or the sun shining.
The following and former Mathcad presentation, from an actual candidate wind farm site, gives a look at the calculations to consider when designing pumped hydro facility. By supplying values for the variables, we were able to run dozens of scenarios for how well a proposed pumped hydro project would work. The equations were originally in MathCAD and so can be introduced to any of several math programs or even a spreadsheet. A summary follows the equations and reports on what we learned.
Unit conversions, constants, and equations
Gallon/min (gpm) were converted to m3/sec: 6.309 x 10-5
Specific weight, Y, of water (Newtons/m3): 30°C, Y = 9.765 x 103
Pool surface areas (m2):
Upper pool full: Auf = 4.5 x 104
Lower pool full: Alf = 4.5 x 104
Lower pool at max drawdown, Ald = 3.5 x 104
Water surface elevation (Engl elev conversion to meters above datum)
Upper pool full: Euf = 1.475 x 10³ x 0.3048
Upper pool at max drawdown: Eud = 1.445 x 10³ x 0.3048
Lower pool full: Elf = 1.38 x 10³ x 0.3048
Lower pool at max drawdown: Eld = 1.345 x 10³ x 0.3048
Gross average energy potential at 25% wind capacity factor, Cf, (SI):
Nominal rated power (W) of wind generation, PW = 1.2 x 108
Equivalent 24 hr energy, J, at nominal rated power:
JW = PW x 60 x 60 x 24
JW = 1.037 x 1013
Cf = 0.25
Equivalent 24hr energy, J, at Cf: Jwc = JwCf For the proposed site: Jwc = 2.074 x 1012
Gross average energy potential (J) between lower and upper pools:
Jh = [[(Auf + Aud)/2]Euf – Eud] x [(Euf+Eud)/2 – (Elf+Eld)/2]Y For the proposed site: Jh = 5.219 x 1012
Round trip available dynamic energy, J, at 75% efficiency: εr = 0.75
Jhr = JhεR For the proposed site: Jhr = 3.914 x 1012
Energy consumed to recharge leakage and evaporation of loss of full drawdown volume by pumpage from on-site well to upper pool with 100m lift* to full stage of upper pool:
Hle = 100m *This lift distance may be excessively conservative for the site, given the observation in site note 1 above.
Jle = [([Auf + Aud]/2)Euf – Eud]HleY For the proposed site: Jle = 1.756 x 1013
Reduction in efficiency due to full drawdown volume recharge every 50 round trip pool pumpage/hydro-power generation cycles.
εle = Jle/50Jh For the proposed site: εle = 0.067
Net round trip available, dynamic energy, J, at combined efficiency
Jhrn = (εr – εle)Jh For the proposed site, Jhrn = 3.563 x 1012
Scenarios for full pumpage recharge of upper pool stage range using on-site generated wind electrical power:
1. Enhance capacity factor, Cfe, due to higher wind speed for a full recharge of the upper pool from the lower pool during 24 hours. In this case, it is appropriate to use the pump electro-mechanical efficiency, εp
εp = 0.85 Cfe = Jh/Jw(εp-εle) For the proposed site: Cfe = 0.643
2. Number of hours, Tcf, at capacity factor, Cf, to fully recharge upper pool from the lower one.
Tcf = 24Jh/Jwc(εp-εle) For the proposed site, Tcf = 77.168
For example, if the purchase prices for wind-farm electricity were less than εp-εle, as a percent of a higher selling price, it would behoove the operator during that period to recharge the system from the source well, or recharge the upper pool from the lower pool, or both.
What we learned
Two pumped storage reservoirs were sized to match the available topography considering elevation differences and the reservoir basin construction opportunities, and to have an electrical generation potential for a draw-down cycle that is between the assumed base capacity factor (in this case 25%) and the rated capacity of the wind farm in which the pumped storage facility is sited.
The design anticipates that all water is extracted from an on-site well and that the basins are properly sealed with a material such as bentonite clay to minimize leakage.
Placing pumped-storage facilities smaller than those that have been historically developed within wind farms, enhances the income opportunity of the wind farm by shifting a portion of its lower value, time-of-day electricity to higher value, peak-usage periods and allows doing so on a dispatchable basis when the pool stages are available. In most cases such pumped storage basins may be entirely removed from riverine or lacassine ecosystem impacts, such as would appear to be the case with the present example.
The basin pair analyzed was sized for a maximum hydroelectric capacity to roughly match the energy production for a typical day of wind generation. The wind farm site has other locations with topographic and geometric features for additional basin pairs, should the electric power economics justify proportionately more dispatchable storage.
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