Wednesday, December 31, 2014

On Renewables and compromises, Intermission: Energy Density and Power Density

So I want to get to the obvious next steps in the world of renewables: solar, wind and tide. Don't get excited though because before I do I have to introduce you to a couple important topics in any discussion of renewable energy: the difference between power and energy. The reason I need to do this is that in order to talk about the strengths and limitations of various renewable energy technologies we need to understand the difference between power density and energy density.

Energy is defined as the ability to do work. It is power integrated over time. Power is the rate at which work is done (energy is transmitted). The difference is that energy can be stored/transmitted while power cannot. The reason I make this distinction is that confusing the two is so surprisingly easy. I do it all the time. In the SI system energy is measured in joules and power is measured in joules/sec which is called a watt. In the units we are used to seeing 1 Megajoule (MJ) can generate 0.28 kilowatt hours (kWh) (source Wikipedia). 

So why am I wasting your time talking about power versus energy? Because our society is power-hungry and we supply that power using energy sources. In order to power our appliances, hospitals and automobiles, we need energy. Ultimately all our energy is sourced either from the sun (solar energy, biological and fossil fuels - which represent historical solar energy stored in chemical form), from the earth (geothermal and radioisotopes) or from physical phenomena (gravity, wind and tide). You probably think I missed hydro, but hydro is simply the effect of gravity on water. Technically, both hydro and wind are partially derived from solar (and we will ignore raw chemical power) because for the purposes of this discussion we are not going that deep.

So now that we understand the difference between energy and power we need to understand energy density. Energy density is defined as the amount of energy stored in a unit of mass or volume. The thing that makes fossil fuels so attractive to our society is that they represent a very dense energy source. Ignoring radioisotopes, fossil fuels represent one of the most energy dense power sources out there. The reason that fossil fuels are so energy dense is that mother nature has done the all-important job of converting solar power into this easily transportable power source. Consider that gasoline has an approximate energy density of 45 MJ/kg. Natural gas has a higher energy density (about 56 MJ/kg) but due to its form (it is a gas) its use is limited to places where it can be shipped via pipelines, also its density in its natural form is much lower (its per liter energy density is much lower than gasoline  0.036 Mj/L versus 37 Mj/L). Alternatively, it can be liquified (LNG) but the cooling process uses a lot of power and the product must be transported in specially equipped rail cars/transport trucks/transport ships.

Wait, wait, I hear some of you suggesting that hydrogen is a better power source than fossil fuels, but I would beg to differ. Hydrogen is extremely energy dense 142 MJ/kg but unlike fossil fuels we have to input a tremendous amount of power to create that energy. In order to get hydrogen in a form that can be combusted it must be converted from a source material (like methane or water). That takes a major input of power, which typically comes from whatever power grid in which the hydrogen generation unit is located. When coupled with a nuclear power plant (which produces power regardless of demand) hydrogen is a useful fuel but most of the time hydrogen is a lot more trouble than one would expect. See the attached link for a detailed discussion (hydrogen article).

When it comes to renewables the issue is power density. Most renewable power sources are very diffuse (they have a low power density). An article prepared by Robert Wilson of provides some useful numbers, specifically, he reports that solar, the highest density renewable, has a theoretical power density of up to 200 W/m2 but that the best solar collection systems seldom do better than 20 W/m2 (in desert solar photovoltaic farms). The further north (or south) you go the lower the theoretical maximum, and thus the lower the resultant systems. A truly exceptional visualization of this is presented by David Mackay at As for the remaining renewables, the best biofuels can achieve about 2 W/m2  while wind can achieve a maximum of about 3 W/m2. As Dr. Wilson points out, since Germany and the United Kingdom consume energy at a rate of approximately 1 W/m2 in order to supply either country with power using wind they would need to cover half of their total land mass with wind turbines which is not a realistic option in a country with cities, farms and forests. Similarly, no combination of biomass, wind, solar and tide has the power density to supply a developed country like Germany with its entire power supply. At best a countries like Germany and the United Kingdom may be able to supply a proportion of the power they need through these sources while importing power and energy from other areas/regions. Germany does this through the importation of wood pellets and also uses offshore wind (which effectively expands its power base) and supplements it all with fossil fuels (notably coal). For political, not scientific, reasons the Germans have forsaken nuclear which in a world of climate change represents the least carbon intensive power source out there. 

Portability is a particularly important feature for energy products. Airplanes and transport ships need energy dense power sources that are relatively light. Batteries can store tremendous amounts of energy but at a very steep cost in weight. Thus a battery powered car is a possibility but a battery powered jumbo jet is not. The problem with solar, wind and tidal power is that they are not sufficiently portable. The power is typically generated at a distance from where it is consumed, but that is a topic for another post.

1 comment:

  1. The German renewables program is somewhat of an economics and emissions reductions failure. Post appraisal will show it to be a poorly engineered and badly planned effort. It's enviromental impact statement was Mickey mouse quality.