How much energy is stored in a pumped storage power plant?
Reduction of carbon footprint is a key objective of almost all developed countries. To make the transition to a more renewable power generation successful, sufficient energy storage capacity is absolutely crucial. This is especially true in Europe where the generation capacity is limited during winter season (mainly solar power generation due to short daylight and cloudy or fogy weather). So how much energy is stored in a pumped storage power plant? How large are those green batteries?
Proven concept of large scale energy storage
The hydro pumped storage technology is known for many decades. Pumped storage power plants (PSPP) are the most economical large scale energy storage. Basic principle is to pump the water from the lower reservoir into the upper one at times when there is a surplus or electric power. Vice versa, during periods of high demand the water flows into the lower reservoir and turns the turbine-generator.
Operation regime of pumped storage power plants
These power plants are operated in two basic scenarios.
In the first one the power plant is used to balance the power generation and power demand during the day. There is typically a first peak of power demand in the morning hours followed by another one in later afternoon/evening. On the other hand, before the noon or during night time the consumption is usually lower. In such a scheme the pumped storage power plant is operated 2-3 times per day in pump mode and same number of times in turbine mode. With the increased number of renewable power the generation is less predictable and there are tendentially more transitions from pump to turbine mode or vice versa during the day. In this new situation a variable-speed pumped storage is of a great benefit as it can better adjust the power to be pumped or generated.
Second scenario is a hydro power plant with large storage capacity. The purpose is to balance the generation and demand throughout the year, i.e. compensating the seasonal differences. With some simplification we can say that those power plants work mainly in pump mode during summer and fall time filling up the upper lake. Then during winter and spring season the water streams to the lower lake and electricity is generated. It is obvious that tremendous energy needs to be stored in such case.
Energy storage capacity
After this introduction we can finally look at the storage capacity. How to calculate it?
Well, it is quite simple. We just apply basic law of physics. The energy stored in the power plant which can be released for power generation is the potential energy. Thus, it is determined by the mass of water and the height difference between the two reservoirs. Of course, the generation is linked with some losses (as in every power plant regardless of principle). Remember that: it is the combination of water mass and the head between both reservoirs. The height difference is actually changing. It is the highest at the beginning of power generation (upper reservoir almost full, lower reservoir quite empty) and reduces during the turbine mode. Therefore, we shall consider the average head between the reservoirs. Normally the two reservoirs have relatively similar volume (especially in the closed loop systems) so that the relationship is quite linear. In specific cases, however, the volume of each reservoir can be different. Justification for that may be a more complex system with more than two reservoirs.
How to calculate
a) Based on potential energy
The calculation is simple providing you know the basic parameters of the PSPP.
- The reservoir with lower volume determines the maximum water mass. One cubic meter (m³) of water has weight of approx. 1’000 kg (1 ton). Thus the volume in m³ equals the water mass in tones.
- Use the average head (height difference between reservoirs) during one cycle.
- Calculate the potential energy E_potential = m·g·h.
m … mass [kg or t]
g … gravity (9.81 m/s²)
h … height (head) [m]
Above formula allows you to calculate the stored energy. If you want to calculate the electric energy that can be gained, assume realistic value for the system efficiency as a multiplicator.
b) Based on required flow
The second option is to calculate the energy storage capacity from the rated power, rated flow and volume of the reservoir. One can calculate how much it would take to empty the lake using the rated flow. Multiplying this time with the rated power we get the energy storage. In this case the efficiency is already included.
- Time duration: t = V / Q
- Energy: E = P ⋅ t
V … volume of the reservoir [m³]
Q … flow rate [m³/s]
t … time [s]
E … stored energy [MJ]
P … rated power [MW]
In some sources the energy storage is directly stated. It can be used as a reference for the calculations.
Knowing the theory we will now look at few practical examples of European pumped storage power plants.
Energy storage calculations
Example 1: Dlouhe Strane PSPP
Dlouhe Strane [1] is the largest PSPP in Czech Republic, located in Jeseniky mountains. The power plant has its own visitor centre and in combination with beautiful nature it is a popular tourist destination. Dlouhe Strane contain two reversible turbines, each rated 325 MW (among the largest unit power in Europe). The average water head is approx. 510 meters.
Rated power: 2 x 320 MW (motor) / 2 x 330 MW (generator)
Average head: 510 m (turbine) / 534 m (pump)
Volume of upper reservoir: 2’580’000 m³
Flow rate: 68 m³/s (turbine)
Now doing the math:
a) Potential energy
E = 2.58 ⋅ 10^9 ⋅ 9.81 ⋅ 510 [J]
E = 12’907’998 MJ
E = 3’586 MWh
b) Energy based on rated power and rated low rate
t = 2.58 ⋅ 10^6 m³ / 68 m³/s
t = 37’914 s
t = 10.54 h
E = P ⋅ t
E = 320 MW ⋅ 10.54 h
E = 3’373 MWh
Note that indicated flow rate (68 m³/s) is per turbine. If both turbines are running, the reservoir would be emptied in half of the time (approx. 5.2 hours – it corresponds with data stated in [1]).
As a conclusion we can state that Dlouhe Strane has approx. 3’600 MWh of potential stored energy and approx. 3’400 MWh of effective stored energy considering the turbine efficiency.
We got very similar figure like in the first approach using potential energy of the water stored in the upper reservoir. The calculation b) results in lower energy as it considers the efficiency of the power plant while calculation a) is a theoretical calculation based on 100% efficiency.
Example 2: Kruonis PSPP
For the next PSPP we go to Lithuania. There is pumped storage hydro power plant called Kruonis. The plant is located north of the town Kruonis. Interestingly, it is the only PSPP in the Baltic countries. But it is definitely not a small one. Let’s have a look at the key parameters:
Rated power: 4 x 225 MW
(Total power 900 MW, originally designed for up to 1’600 MW with 8 x 200 MW. Only 4 units have been installed but unit power was increased to 225 MW).
Rated speed: 150 rpm
Water head (average): 103.5 m
Volume of upper reservoir: 48’000’000 m³
(Yes, 48 million m³ of a manmade water reservoir – very impressive)
a) Potential energy
E = 48 ⋅ 10^9 ⋅ 9.81 ⋅ 103.5 [J]
E = 48’736’080 MJ
E = 13’538 MWh
b) Energy based on product of power and time
According to sources [2] and [3], the power plant has storage capacity to run at rated power for approx. 12 hours. Thus, we can simply calculate the energy by multiplying those numbers.
t = 12 h
E = P ⋅ t
E = 900 MW ⋅ 12 h
E = 10’800 MWh
Same as in previous case, the 13’500 MWh is the potential storage energy without reflecting efficiency of the power generation. The 10’800 MWh is the real energy storage when considering the losses of the power components (turbine, generator, step-up transformer etc).
Example 3: Grimsel 2 PSPP
Fo the third example we will visit Swiss alpine power hydro storage power plant Grimsel 2. The construction commenced back in 1973 and in the years 2012-2016 a major modernization was performed. There are four (4) francis turbines and corresponding generators, each rated 100 MVA.
Total rated power: 388 MW (turbine) / 392 MW (pump)
Water head: 430 m
Flow rate: 100 m³/s (turbine) / 77 m³/s (pump)
Volume of main reservoir: 94’000’000 m³
a) Potential energy
E = 94 ⋅ 10^9 ⋅ 9.81 ⋅ 430 [J]
E = 396’520’200 MJ
E = 110’145 MWh
Note: Grimsel power plants create a cascade. Thus, the water from the largest reservoir, Grimselsee, is used in two different power plants. Above calculation considers only the power plant Grimsel 2.
The whole Grimsel region consist of several hydro power plants and a system of water reservoirs. There is a popular visitor centre. It is really worth to take a tour there.
Kindly note that the installed power (MW) has no direct relation to the energy storage capacity. There are pumped storage power plants with installed capacity of several hundred MW. They can provide much needed power during peak loads of the day while consuming power when the demand is low. However, for daily balancing the required storage capacity is not that high (power plant does not need to operate in one mode for more than few hours). On the other hand, power plants for seasonal balancing need huge storage capacity to fulfill their purpose. Their power rating can be smaller than the rating of PSPP for daily balancing.
Summary
Pumped storage hydro power plants have considerable energy storage as shown in the examples in this blog post. The purpose of PSPP is to help balancing the power generation and consumption. Some PSPP are designed to balance the daily fluctuation. They have quite high power rating but the energy storage is limited as the power plant operates in each mode (turbine/pump) not more than few hours. Representatives of those power plants are Dlouhe Strane and Kruonis mentioned above. Other type are PSPPs used for seasonal balancing. They can be characterized by extra large energy storage capacity (combination of large volume and significant head). Example is Grimsel 2 in Swiss Alps.
Remark:
The term ‘green battery’ may be controversial. Any technology, including renewables, has certain impact on the environment and nature. But comparing to other alternatives pumped hydroelectric storage has in our view smaller environmental impact than the competitive solutions.
References
[1] Pumped storage power plant Dlouhe Strane, https://mb-drive-services.com/pspp_dlouhe_strane/
[2] Kruonis Hydro Pumped Storage Power Plant (Ignitis Gamyba), https://www.ignitisgamyba.lt/en/our-activities/electricity-generation/kruonis-hydro-pumped-storage-power-plant/4188
[3] Kruonis pumped storage power plant (wikipedia), https://en.wikipedia.org/wiki/Kruonis_Pumped_Storage_Plant
[4] KWO Grimselstrom – Power plants (in German), https://www.grimselstrom.ch/produktion/strom-aus-wasserkraft/kraftwerke/
