# Pumped hydoelectric storage equation problem

1. Sep 10, 2015

### Erik S

I am trying to figure out the efficiency of a reversible hydraulic generator/pump station that will generate electricity when the price is high, and pump water up into the reservouar with power from the grid when electricity is cheap.

I have calculated the following information for the pump and turbine:

Ppump= 10 MW
Qpump= 7.5 m^3/s

Pturbine= 96 MW
Qturbine= 72.5 m^3/s

How can I figure out what percentage of the bought energy can be delivered back to the net?
I am having trouble figuring out how to set up an equation I can use to solve this problem, No matter what I go I get really high effeciency like 99% which must be wrong.

2. Sep 10, 2015

### insightful

Typical efficiencies are 70-80% overall. Why is pumped capacity only 10% of turbine capacity?

3. Sep 10, 2015

### Erik S

The pump is rated at 10MW, the produced flow is calculated using Mannings equation with given Mannings constant.

This is because I don't have any information on the volumetric displacement/ rpm of the pump

4. Sep 10, 2015

### insightful

So this system has open-conduit flow? Can you post a sketch of your system?

5. Sep 10, 2015

### Staff: Mentor

You can easily just ratio all of those numbers against each other to find the efficiency.

...however, just by looking at them I can see that your 99% efficiency is about right. So your problem is in how you came up with those performance points.

By the way, this is engineering, not math. Moving thread...

6. Sep 10, 2015

### Baluncore

Maybe because water is pumped for longer periods while some power is available at low cost, than the shorter periods of peak turbine flow that generate power when the demand and price are higher.

Erik S, You need to find the efficiency of the motor, pump, turbine and alternator.
The penstock will need to be designed to operate with the higher flow expected during turbine operation.

7. Sep 11, 2015

### insightful

Pumping and generating power are usually close:

https://en.wikipedia.org/wiki/Pumpe...ty#/media/File:Pumpspeicherkraftwerk_engl.png

For a 10:1 difference, you'd need a separate pump and turbine for high efficiency.

8. Sep 11, 2015

### Baluncore

But not in this case.

As you can see, there is a separate pump and turbine for the different flow rates.

9. Sep 11, 2015

### Baluncore

Where does that fact come from ? Do you have a reference ?

10. Sep 11, 2015

### Legolaz

Easy, Net Work rate =Net Powerhydroplant= Pturbine-Ppump
If you are interested with Hydro Plant Efficiency = Net Powerhydroplant/Pturbine

Efficiency means what you get from the total effort you exert or gain over capital.
I hope this helps.

11. Sep 11, 2015

### insightful

12. Sep 11, 2015

### anorlunda

Re: Pump versus generate powers.

Insightful didn't say always, he said usually.

It is simply that the number of hours in the day for high-peak power and low-peak power are similar. That alone means you want pumping power and generating power to be of similar magnitude.

It also has to do with the cost of power transmission. Transmission capacity is unnecessarily expensive for high power flows (plus or minus direction) for short periods of time. Both plus and minus flows are typically spread over several hours.

13. Sep 11, 2015

### insightful

14. Sep 11, 2015

### anorlunda

Sure, but remember that the energy stored is proportional to the quantity of water pumped, and the vertical height difference. You might need 200 meters of height to make it worth the trouble. I question the efficiency of a Archemedes Screw at that height.

Consider an example: The Blenheim-Gilboa Pumped Hydro Plant, has 19 million cubic meters of water storage, at 348 meters vertical head, to make 1134 MW electric.

15. Sep 11, 2015

### insightful

Cannot an Archimedes screw be very efficient at low head and high volume for both pumping and generating?

(Edit: Admittedly, this system would require a huge surface area reservoir.)

Last edited: Sep 11, 2015
16. Sep 11, 2015

### Legolaz

Archimedes Screw is ideally applicable to Low Head, High flow reservoirs. For high heads and high flow reservoir, ideal is the impulse and mix flow type of turbine. 200 m is very high elevation indeed.