# How Pumped Hydro Stores Excess Wind Power

Alternative energy is an important topic given the current state of the world. One solution often discussed is wind power. The problem is, unused wind power is typically lost, although there are solutions, most of them are challenging and extremely expensive. Robert T. Bullard recently wrote an article that was posted on Wind Power Engineering & Development explaining how to store wind power, while referencing calculations developed in PTC Mathcad.

Bullard writes, “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.

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

Upper pool at max drawdown:  Aud = 3.5 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 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/Jwple)      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/Jwcple)     For the proposed site, Tcf = 77.168

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.”

Check out the article in its entirety here.

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