Posts Tagged ‘energy storage’








We could see that a reversible Isothermal compression is,



Efficiency of Processes.


  • Pure adiabatic or isothermal processes are not possible.
  • Air is not an ideal diatomic gas
  • Mechanical parts are subject to friction and other inefficiencies.

A few examples



Example 1:





Example 2:



Example 3:
Like Example 2, but with 4 stages


What could we see from this





1. Compressed Air Energy Storage – How viable is it?


3. Wikipedia for general information on different thermodynamic processes



Universal Gas Law

PV = nRT

The Heat Capacity Ratio

\gamma = C_p/C_v
C_p - C_v = R

Adiabatic Compression

PV^\gamma = K_a
T_f could also be computed using Universal Gas Law
\delta S_{system} = 0
\delta S_{surroundings} = 0

Isothermal Compression


Isochoric Cooling

\delta Q = n C_v \delta T

Isobaric Heating

\delta U = n C_v \delta T




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Lead Acid battery is touted as the cheapest battery available. In fact, Lead Acid is the family name for a collection of closely related battery types, from simple vented/flooded to advaned Valve Regulated ones. Depending upon the type of usage, there are shallow and deep cycle batteries. Typical examples of shallow cycle batteries are the ordinary car starter batteries, where as deep cycle batteries are used for prolonged deep discharge operations like electric propulsion, UPS etc. For a comparison, some reasonable Deep Cycle flooded batteries are available for around $120 per name plate KWh. This “lowest cost” has given a lot of advantage for Lead Acid batteries in renewable energy applications. But before getting deep into the deep cycle lead acid batteries there are a lot of interesting facts to consider.

The Fine Prints

Both capacity and the state of charge depend heavily upon a factor named Vpc which is nothing but Voltage per Cell. Normally all standard battery manufacturers quote their capacity to 1.75 Vpc with a discharge time of 20 hours. In simple language, it is the capacity until the voltage of the cell reaches 1.75V with a discharge period of 20 hours. 1.75 V is considered as 0% State of Charge. As Depth of Discharge (DoD) is just the opposite of State of Charge, it is nothing but 100% Depth of Discharge. But discharging up to that level puts a lot of stress on the battery, so that, the battery could only handle very limited number of cycles in that manner. In short, 100% DoD is not at all preferred for lead acid batteries.

All Capacities are equal, but some are more equal than others

Another interesting parameter is the “name plate” capacity mentioned on the battery. Normally a “120AH” battery gives an implication that, it could give 1A for 120 hours, or 120 A for 1 hour, or 20A for 6 hours or whatever combination of that which gives 120AH as the multiplication output. But, in reality this is not the case. Faster discharging try to reduce the available capacity of the battery drastically. As stated above in the previous section the “name plate” capacity is quoted at C/20 which means at a very slow pace of 20 hours to discharge the battery. Many standard discharge applications using inverters do require much higher discharge rate. Available capacity of a battery could be computed using an empirical law named “Peukert’s law”. The following figure shows the available capacity of a typical Lead Acid battery against discharge time. 100% capacity is stated for 20 hours.

Lead Acid Capacity and discharge time

See the interesting fact, if the battery is discharged in 100 hours it could give 145% (actually 45% more than the nameplate) capacity whereas if it is discharged in 6 hours, it could give 75.7% capacity only.

Number of cycles

Total usable cycles of the battery is very much related to the regular depth of discharge. For a regular 80% DoD, a typical battery lasts for around 600 cycles, but if we use 50% DoD, it lasts for around 1200 cycles. There are many telecom batteries which are advertised for 20 years, but they have a rating of 5% to 10% DoD which is ridiculously low(fine prints again). The following graph from windsun.com and Concorde batteries shows the relation between available cycles and Depth of Discharge
Number of Cycles vs DoD of Lead Acid Battery

Apart from that, there are a few “solar batteries” which could give around 2100 cycles at 80% DoD, like the HuP Solar battery. But they also cost a lot, somewhere between $200 to $300 per KWh
HuP Solar Information

There is a clear disadvantage of the better cycle life and lower DoD. More batteries have to be kept in parallel to store the same amount of electrical energy. That means at 80% DoD, 125% capacity is required whereas at 50% DoD, the requirement would become 200%. If the above mentioned telecom battery is used, the requirement would go more than 1000% !!

So, basically it is a trade-off between capacity, DoD and number of cycles.

That is the story of Lead Acid battery. Let us consider two other types of batteries.

Lithium Ion Battery (Lithium Iron Phosphate)

Like Lead Acid, Lithium Ion is also a family name for, Lithium Cobalt, Lithium Manganese, Lithium Iron Phosphate, Lithium Polymer, Lithium Titanate etc. I am mainly considering Lithium Iron Phosphate for comparison. It has much better cycle life compared to other types of Li-Ion batteries, but a bit lower energy density. Normally Li Ion batteries could handle much better discharge rate compared to Lead Acid batteries. Discharge rate could go more than 2C, that means discharging the battery in 30 minutes. Another advantage of Li Ion battery is that, it has very low dependency on Peukert’s law, that is, even at higher current ratings the battery capacity would not go down like Lead Acid battery. Modern Lithium Iron Phosphate batteries give around 5000 cycles at 70% DoD or 3000 cycles at 80% DoD. The cost has gone down to less than $400 per KWh. Since they have better energy densites, they weigh less and occupy less space compared to Lead Acid batteries.
Specification of Thundersky Lithium Iron Phosphate battery

Sodium Sulphur Battery

Sodium Sulphur could be a very good solution for large scale storage spanning upto MWh range. NGK Insulators of Japan supply these batteries at a price of around $350 per KWh. They are quoted at 2500 cycles at 100% dischange or 4500 cycles at 80% discharge that too at a 6 hour discharge rate. Similar to Lithium Ion, NaS battery has much better energy density compared to Lead Acid, so the weight and volume are also much lower for the same capacity.

Levelized Cost

Let us say that we have to select a battery for renewable energy applications. Since in most cases levelized cost is calculated for a period between 20 to 30 years, we select 9000 cycles which comes very close to 25 years. Assume that the battery has to be discharged in 6 hours. Let us see how these options stand against each other. See the table at the bottom for detailed explanations.

Levelized Cost of different Batteries


It is very easy to jump to conclusions by seeing the nameplate capacity cost, but actual levelized cost/KWh/cycle is an entirely different story. Cheapest lead acid battery is the costliest to operate in the long run. For small and portable storage applications Lithium Iron Phosphate could be an excellent option. For large installations, Sodium Sulphur could give drastic cost and performance advantages.


Peukert’s law:
Capacity of Lead Acid battery is computed using the following eqution, as given by An in depth analysis of the maths behind Peukert’s Equation (Peukert’s Law)
T=C x ((C/R)^n-1) /(I^n)
Here n is taken as 1.3 for Lead Acid Battery.

Battery Levelized Cost:
Total cost of batteries to store 1KWh is computed as follows
Multiplier Factor = (1/DoD) x (1/(6 Hours Capacity Factor)) x (Number of times battery has to be replaced to get 9000 Cycles)
6 Hour Capacity Factor is 75.7% for Lead Acid Batteries. Since the capacity of Lithium Ion does not degrade for 6 hours, the factor is taken as 1. For Sodium Sulphur, the name plate capacity itself is stated for 6 hours, so the factor is 1 for that too.
Number of usable cycles for Lead Acid is taken as 750 and 1500 for 80% and 50% DoD respectively.
Total Cost = Cost/KWh nameplate x Multiplication Factor
Levelized Cost = Total Cost / 9000

This is the summary of all these calculations. All prices are in US Dollars only.

Battery Cost Comparisons

% DoD Usable
Number of
Total Cost/KWh Levelized Cost/KWh
per cycle
Lead Acid
120 80 750 12 19.80 $2376 $0.264
Lead Acid
120 50 1500 6 15.84 $1900 $0.211
Lead Acid
200 80 2100 5 8.25 $1650 $0.183
Li-Ion 400 80 3000 3 3.75 $1500 $0.167
Li-Ion 400 70 5000 2 2.86 $1144 $0.127
NaS 350 100 2500 4 4.00 $1400 $0.156
NaS 350 80 4500 2 2.50 $875 $0.097

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In my last article, I was concentrating more about the Specific Capacity of different cathode materials. But this is only one part of the story when a complete cell is concerned. To find the Specific Capacity of a particular battery chemistry the whole chemical reaction has to be analyzed.

Essentially the method used here is similar to that of previous analysis. Instead of just the cathode material, we have to consider the complete chemical reaction taking place in both cathode and anode. But the rest of the calculation is nearly the same. In short,
Specific Capacity = (N x F) / (Total weight of all components)
N = Change in oxidation state or the number of electrons released.
F = Faraday constant, 26801mAh/Mole

In this article I will be discussing about three popular battery chemistries.

Lead Acid:
This is one of the oldest rechargeable batteries invented, yet ubiquitous. The following is the chemical reaction happening in both Cathode and Anode during discharge process.
-ve Electrode: Cathode: Pb + H2SO4 = PbSO4 + 2H+ + 2e
+ve Electrode: PbO2 + H2SO4 + 2H+ = PbSO4 + 2H2O
The total chemical reaction is,
Pb + PbO2 + 2 H2SO4 = 2 PbSO4 + 2H2O (with 2 electrons through circuit)
Finding the total molar weight, 643g of reactants produce 2 Moles of electrons.
Specific Capacity = 2 * 26.801/643 = 83mAh/g
Total Energy Density, assuming 2V per reaction = 166 Wh/g

Lithium Ion (Lithium Ferrous Phosphate):
This is one of the variants in the family of Lithium Ion Battery.
Overall Chemical reaction during reaction is as follows
LiC6 + FePO4 = LiFePO4 + 6C (with 1 electron through circuit)
That means 230g of reactants produce 1 Mole of electrons, at 3.3V
Calculating both Specific Capacity and Energy Density
Specific Capacity = 26.801/230 = 117mAh/g
Energy Density = 385Wh/kg

Links: http://spinnovation.com/sn/Batteries/Recent_developments_and_likely_advances_in_lithium-ion_batteries.pdf and http://plaza.ufl.edu/csides/Publications/LiFePO4-Carbon.pdf

Sodium Sulphur:
Mainly used in grid scale energy storage application, Sodium Sulphur is a variant of molten metal battery.
To give the overall chemical reaction,
2Na + 4S = Na2S4 (with 2 electrons through circuit)
The cell gives out 2V.
In this case, 174g of reactants, give out 2 Mole of electrons.
So Specific Capacity and Energy Density are
Specific Capacity = 308mAh/g
Energy Density = 616Wh/kg

It could be easily seen that Lead Acid battery, even though most widely used has a very low theoretical capacity. An interesting finding is that, the current practical capacities of both Lithium-Ion and Sodium Sulphur batteries are reaching very near to the theoretical capacity of Lead Acid technology.
Energy Density of Lead Acid, Li-Ion, NaS batteries

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Recently I read some news about Lithium Ion batteries and the author mentioned that Lithium has the highest Specific Capacity of 3861mAh/g. I was very curious to know where this magic number came from. After trying to understand more about that, finally I found the answer. That was 12th class electrochemistry. The calculation is given below.

Specific Capacity = (N x F) / (Atomic Weight)
N = Valency of the Material
F = Faraday constant = 96485 Coulombs/Mole

If this has to be expressed in terms of current, divide that by 3600
F = 26.801Ah/Mole

This is how the equation works for Lithium. Faraday constant is nothing but the total charge of Avogadro number of electrons. Since Lithium has a Valency of 1 and atomic weight of 6.94g/Mole, every 6.94g of Lithium would give out Valency times Avogadro number of electrons when ionized. So, to find out the Specific Capacity

Specific Capacity = (1 Valency x 26.801Ah/g x 1000mA/A) / 6.94g/Mole
= 3861mAh/g

That means, when 1 gram of Lithium metal ionizes to Li+ ions, it gives out 3.861Ah of electricity. This is just the current, but not the energy. If we are interested to calculate the energy density of reaction, it is required to know the Standard Electrode Potential of each material. Since it is 3.03V for Lithium, the total energy density of ionization of Lithium is
3.03V x 3.861Ah/g * 1000g/kg = 11701Wh/kg.
This comes very close the values of hydrocarbons.

But, remember this is just a half reaction taking place in the cell. We did not consider the anode reaction at all. So, total Specific Capacity of a complete cell would be much lower and it also depends upon the anode, electrolyte, other chemicals used in the cell etc.

Table1: Specific Capacity of Cathode Materials

Reaction Atomic No: Atomic Weight Valency Specific Capacity (mAh/g)
H/H(+) 1 1.008 1 26588
Li/Li(+) 3 6.94 1 3861
Na/Na(+) 11 22.990 1 1166
Mg/Mg(2+) 12 24.310 2 2205
Al/Al(3+) 13 26.980 3 2980
K/K(+) 19 39.10 1 685
Ca/Ca(2+) 20 40.08 2 1337
Zn/Zn(2+) 30 65.39 2 820
Pb/Pb(2+) 82 207.2 2 259

The following bar graph summarizes the specific capacity of all Metals given above.
Specific Capacity of Metals

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There have been a lot of focus about energy storage these days coupled along with solar and wind. As a coin has two sides, Energy Storage has both pros and cons.

Some of the main concerns I could gather are:

  • Prohibitively Expensive Capital Cost:
    Energy Storage systems are expensive to own. Cheapest solutions like Lead Acid Battery itself costs around $200 per KWh.
  • Usage of exotic Chemistries and Rare Materials:
    Many of the materials used are rare and expensive, for example Platinum is used as a catalyst in Fuel cells, usage of composite materials in flywheels, rare earths in superconductors etc.
  • Environmental issues:
    Batteries use environmentally unfriendly chemicals. Prime examples are the usage of Lead and Cadmium. Extremely reactive metals like Sodium and Lithium also are used.
  • Safety Issues:
    Many of the fuel cells and batteries should be operated at high temperatures. Reactive metals like Sodium and Lithium have safety concerns.
  • Limited Cycles:
    Most of the batteries could only be used for a limited number of cycles, for example Lead Acid Batteries have a limit of around 800 cycles.
  • Bad Depth of Discharge:
    They could not be 100% discharged, Deep Cycle Batteries could go to around 20% charge
  • Low Energy Density:
    Energy Densities are very low compared to both fossil fuels and biofuels.
  • Geographic location dependence: Especially for CAES and pumped hydro storage

Does that mean that we could dump the whole idea of energy storage itself? Hold on for a second, let us see what are the alternatives available.

What about maintaining the current status quo?
We are using fossil fules like petroleum, coal and natural gas to meet majority of our energy requirements. They have many advantages which could not be ignored for now, mainly comparatively cheap, excellent energy density, easy to store/carry wherever required etc. Most of the infrastructure required are already there.

To give an overview, currently huge amounts of fossil fuels are getting used. World usage of petroleum is around 86 Million Barrels per Day. To make it simple, 1000 barrels of oil is getting burnt every second !!!!! Coal usage is an astouding 6 Billion Metric Tonnes per year, that is 1 Metric Tonne per person. India alone uses around 3 Million Barrels of oil per day and 250 Million tonnes of coal every year.

So, if are ready to forget about pollution, climate change and expendable nature of fossil fuels, we still would be able to continue drinking petrol, eating coal and breathing natural gas. That is the only way to maintain current status quo.

Hydropower is really clean, should we use it?
Hydropwer is the single largest renewable energy source currently under use. It accounts for 20% of both India’s and World’s electricity production. Hydropower has a total potential to supply around 100% of installed capacity (around 3000GW) of the world. So water could barely lift the current load.
Hydro Potential of India
Hydro Potential of World

Nuclear Power Scenario
Nuclear Power provides around 14% of World’s electricity. Nuclear enjoyed lots of interests until recently. But after the Japanese Fukushima Nuclear Crisis, serious safety concerns have been raised.

How about using biomass like agricultural by-products, manure etc.
Biomass has got a huge potential and we should try to utilize them. A study says that India produces around 500 MMT of biomass per year and out of which around 150 MMT is surplus. This gives a potential of around 25000 MW electricity production for India.
Biomass Potential of India
But, looking carefully, biomass is really a low hanging fruit. It looks fantastic until biomass based systems try to go real mainstream. Once they reach the mainstream status, they could potentially create the following problems.

  • Limited amount of biomass availability because they are mainly agricultural by-products. So further scaling up from the above numbers would be really difficult.
  • Direct competition with food production for the availability of land if biomass production becomes a profitable business.
  • Stepping upon forest land for the same reason.
  • Difficult to use in transportation sector.

Can we complement the situation with Biofuels?
There are many different types of biofules available like bioethanol, biodiesel and biobutanol. Current main source of ethanol are sugar cane, and corn. Where as biodiesel could be produced from different oil sources like sunflower, coconut oil, palm oil etc. and also from Jatropha from marginal lands. But the best yield is given by different algae streams.
One study says that Jatropha based biodisel cound supply 22% of India’s petroleum demand.
Jatropha Potential of India

Considering the usage of land, it is essential to look at the overall efficiency from sunlight to biodiesel. It is practically less than 1%
Photosynthesis Efficiency

So, only algae based Biofules could reach sustainability. It is progressing but still it has not reached commercial status.
Other biofuel technologies like sugar cane ethanol, corn ethanol, palm oil and other biodiesel etc. have limited potential to fix the overall energy issues. Apart from that, they also contribute to the above mentioned problems: encroaching upon forest and farm land.

Our Earth is too hot inside. Geothermal energy.
Geothermal is another often discussed (pseudo) renewable energy and it could be considered as a baseload resource with no energy storage requirement. For commerical/quality power generation deep wells are required, on the other hand shallow wells could be used for heating purpose.
All these come with a few drawbacks. As per wikipedia, even though geothermal potential is much more than the current energy requirement, only a fraction of that is recoverable. Also quality varies through geographic locations. Apart from the economics, there are potential environmental drawbacks also. Chances of trapped carbon dioxide, sulphur dioxide etc. getting released to the environment is high. In addition to these gases toxic elements like Mercury, Arsenic etc. could get released. There have been concerns about increased earthquakes due to deep wells.
Environmental Effects of Geothermal Energy
Geothermal Resources

Wave Power, OTEC and Tidal Power
Wave Power, Tidal Power and Ocean Therman Energy Conversion (OTEC) have great energy potential. But they have not reached commercial status yet. Only pilot projects of a few MWs have been carried out so far.

How about Solar and Wind?
As per Harvard University, Wind Energy has a potential of more than 40 times the current World energy consumption. Where as Earth receives around 6000 times Solar Energy compared to the energy consumption. Wind Power has already reached grid parity in many cases and solar is gearing towards that. Lots of reserach and investments are taking place to make them go mainstream.
Global Potential for Windpower
Windpower Potential
Solar Potential

So, Sustainability and Climate Change have defined a clear goal…… Reduce the above oil and coal usage numbers as much and as fast as possible. A very challenging problem, much more than any “Rocket Science” ever achieved.

Considering both the current state of technology development and overall potential to meet the global energy demand completely, only Solar and Wind could be considered for the top positions. But their sustainability depends upon Energy Storage.

So as far as Energy Storage is concerned, apart from biting the bullet no other solution is existing in the long run. There is no other way, but to fix all of the shortcoming of Energy Storage.

Edited on 08/08/2011
I received a comment about Solar Thermal systems. Solar could include both Photovoltaic and concentrated solar thermal systems also.

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