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The Future of Energy: Why Power Density Matters

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The Energy Transition

This is the first column in The Energy Transition series by Robert Wilson. This series, exclusive to, will take a critical look at the prospects of a transition away from fossil fuels, and promises to abide by the advice of Richard Feynman that reality must take precedence over public relations.

Hong Kong Wind Farm Wakes

The twenty first century will almost certainly witness a transition to an overwhelming urban human population, and hopefully a transition to a low carbon energy system. The former however will have a significant impact on the latter, because a fundamentally urban species cannot be powered locally.

The  continued, and essentially unabated, accumulation of carbon dioxide in the atmosphere may at times make considerations of the requirements of a de-carbonised energy system appear somewhat self indulgent, but I must ask the reader to indulge me, and at a little length.

What would a low carbon energy system look like? (And let’s avoid such fanciful ideas as “zero carbon,” because that would be truly self indulgent.) In essence we would get as much electricity as possible from some combination of renewable and nuclear energy, and electrify as many aspects of our energy systems as is feasible. Predicting the relative composition of such a system is a largely fruitless exercise. However, we can say something about the extent to which it a low carbon energy system will be distributed and “local”. This confidence comes from the difference between the high physical concentrate of energy use in cities, and the relatively low physical concentration of renewable energy resources.

Power density

There are fundamental physical limits to how much energy we can extract from renewable resources for a given area of land. If we want to rigorously quantify this we calculate an energy source’s power density in watts per square metre (W/m2 ).

To get an understanding of this concept consider the recently opened London Array wind farm to the south of England.This is the world’s largest offshore wind farm and according to its owners will generate “enough energy to power nearly half a million homes.” Its total capacity is 630 MW covering a total of 100 km2, and is expected to have a capacity factor of 39%. In other words the power density of the London Array will be 2.5 W/m2. This number is also very similar to the average calculated by David MacKay for existing UK wind farms. The United Kingdom is windier than a lot of the world, and some research suggests that large extraction wind farms will reduce average power density closer to 1 W/m2, so 2-3 W/m2 can be viewed as an upper limit on the power density of large scale wind power. This power density reflects average output, however peak power density of wind farms will be perhaps three times higher, and minimum power density will be close to zero. And it should be noted that it excludes the requirements for manufacturing steel required for turbine towers and the extraction of fossil fuels for conversion to plastics for wind turbine blades. However inclusion of these factors is not likely to result in a significant reduction to power density estimates.

Globally solar radiation available for conversion to electricity averages 170 W/m2, and in sunnier locations it can reach above 200 W/m2. This solar energy however is currently not converted at anywhere close to 100% efficiency. Commercial solar photovoltaic panels typically average between 10 and 15% efficiency. Power density of solar installations must also account for space between panels, either for servicing in solar farms or for spacing between houses in rooftop solar installation. As a result the highest power density achieved is around 20 W/m2 in desert solar PV farms, whereas solar farms in Germany generally achieve 5 W/m2. Future improvements in panel production will hopefully see significant improvements in panel efficiency. However there will remain a firm physical upper limit of 200 W/m2, which will be significantly lower when only considering large scale deployment of residential rooftop solar, due to obvious physical restrictions on panel placement.

At their best biofuels might be able to produce close to 2 W/m2. However power densities of 0.5 W/m2 and below are more typical, with prominent examples of this being corn ethanol for transport and the burning wood for electricity. We will see later that this is a very important consideration for the scalability and sustainability of biofuels.

In contrast typical generation of fossil fuel and nuclear electricity has a power density of at least an order of magnitude greater than that of renewable energy. Power densities are comfortably above 100 W/m2 after accounting for mining etc. And conventional power plants often have power densites in excess of 1000 W/m2. A simple example of this higher power density is this small propane powered generator, providing in excess of 1000 W/m2. This is far in excess of the power density of any conceivable new method of generating renewable energy.


Why power density matters

A simple thought experiment can demonstrate why power density needs to be a fundamental consideration when evaluating renewable energy. Here it is: Imagine a world where all energy comes from bio-energy. What would be the requirements?

Currently the planet consumes energy at a rate of over 16 TW (16 trillion watts). If we include non-commercial biomass energy used in Africa and Asia, an uncertain figure, this number would increase. However for simplicity I will ignore non-commercial sources and will round our figure down to 15 TW. If we got all energy from corn ethanol we would need to convert a total of 75 million km2 to corn ethanol plantations. This is roughly half of the land surface of the entire planet, land which is somehat scarce. So this simple thought experiment shows there very real limits on how much energy we can, and should, get from biofuels. If we want large scale biofuels to become truly sustainable, a questionable prospect, we will need to see significant improvements to their power density, perhaps improvements of at least an order of magnitude.

Physical concentration of energy consumption

How much energy do we consume per unit of land? For ease of comparison this figure again can be calculated in W/m2. On a global level this is 0.1 W/m2, if we only consider land surface area. Global averages however are not very instructive, power density averaged at the scale of countries and cities is much more important. David MacKay has visualised this much better than I can in his “Map of the World.” Here is the average rate at which countries consume energy, in W/m2, compared with the power density of different renewables: Ideally a country wants to have lots of available land for renewable energy, i.e. they want to be in the bottom left of this graph. Being in the top right however may lead to some problems.

Consider first the United Kingdom and Germany. Both use energy at a rate of just over 1 W/m2. So a back of the envelope calculation will tell you that getting all of their energy needs from onshore wind will require covering half of the UK or Germany in wind turbines. If you have ever been confused by why these countries are building wind farms in the North Sea, instead of on land where it is much cheaper, now you know why. Wind energy’s low power density means you need to put it in a lot of back yards. And there are not as many of them in the North Sea.

Things are even worse in Japan and South Korea. If you covered all of South Korea in wind turbines they would generate less energy than is consumed there. Japan has a similar problem. And this ignores another difficulty: trees. Both Japan (68%) and South Korea (63%) have very high forest cover. If we ignore forested land (which should be out of bounds for large scale renewable energy generation, unless large scale biomass plantations are deemed acceptable) energy is used with a power density of almost 6 W/m2 in Japan and 7.5 W/m2 in South Korea. This calculation makes it clear that these countries can only be predominantly powered by renewable energy through the large scale utilisation of the more power dense solar energy. And social and political constraints may mean this can only happen if the efficiency of typical solar panels increases significantly from their current 10-15%.

Local Energy Is Not A Solution

Some environmentalists and renewable energy advocates have an ideological preference for small and community scale renewable energy. However what if your community looks like this: missingTokyo skyline

Some people may like the idea of running Tokyo on local renewable energy. They will have some difficulty actually doing it, and that’s putting it mildly.

Since 2008 the majority of humanity live in cities. And by 2050 it is probable that we will see seventy or eight percent of humanity living in cities. The key energy challenge this century will be providing energy for these cities, and quite clearly local distributed energy is not a solution. To see why this is the case requires untangling some issues.

Here are some considerations. An average North American has an annual energy consumption of just over 7 tonnes of oil equivalent (toe)., which is the equivalent of a rate of 9,000 watts. However, this is almost double what it is in countries such as Germany, France and Japan. A comparison of these countries in terms of key well being measures makes one thing clear: there is no evidence that North Americans have greater well being as a result of their excessive energy use. Americans don’t live longer, aren’t healthier, or better educated than countries that consume half as much energy per capita. That this high per capita energy consumption comes with a very significant environmental cost – global carbon dioxide emissions would drop by almost 10% if North Americans consumed like Europeans – but little gain in terms of human well being, suggests that is is not desirable for other countries to emulate North American consumption patterns.

Further evidence for the desirability to limit, and probably reduce, per capita energy consumption in modernised countries is given by its evolution in recent decades. Instead of increasing in the long term, per capita energy consumption now appears to have peaked in almost all modernised countries. Here are some examples:

Per capita consumption has decline steadily in the United Kingdom for the last decade and is now at its lowest point for over four decades:

United Kingdom

The United States saw peak per capita consumption in the 1970s, with consumption now seeing an apparent decline. And the fact that per capita consumption did not rise in the age of the Hummer suggests significant room for movement.


Germany is also now seeing declines in per capita consumption.


In Japan per capita consumption appears to have peaked in the late nineties and is now in decline:


So, many modernised countries are now seeing reductions in per capita energy consumption, and this is not being accompanied by a reduction in quality of living. Any sensible long term energy and climate policy should include a strong desire to continue this trend. The belief that the world can transition to both American levels of energy consumption and to a low carbon energy system by the middle of this century ignores the vital lessons of previous energy transitions, and given the current position of renewable and nuclear energy it appears delusional. The world therefore must be much more like Japan than America.

And cities must play a key role in reducing energy consumption. The most important and effective way to do this is simple: make them dense. For a full elucidation of why, I recommend books by Edward Glaeser and David Owen. But the key reasons are easy to understand: a dense city lets you walk or take public transport instead of drive and it lets you live in a more energy efficient apartment building instead of a large inefficient house. Packing people more tightly together in cities may not be to the taste of everyone, but it appears to be one of the most achievable and practical ways to reduce how much energy people consume.

Let us now move forward to 2050, and the world is as I hope it will be. Global population will have peaked below 9 billion as a result of the spread of the demographic transition to modernising countries, and the success in reducing infant mortality and widespread availability of contraception. Perhaps 7 billion of us will live in cities, and they will consume much more like modern day Japanese than Americans.

How will we provide energy for these cities? The answer appears to be large, centralised power plants, whether they are wind, solar or nuclear. Here I assume, wishfully, that we have managed to get rid of fossil fuels, an unlikely prospect. The answer however is almost certainly not local distributed energy, and for simple reasons.

Consider Manhattan, not what many would typically look at as the green ideal. Yet here you will find significantly lower per capita energy consumption than in almost every American city. You will also find energy consumption far greater than can conceivably be provided by local renewables. A recent study managed to map energy consumption in the city that never sleeps right down to the individual city block. This is what it looks like:

A typical block in Manhattan consumes energy at a rate of over 1,000 kWh per square metre each year, a power density of over 100 W/m2. This is almost two orders of magnitude greater than the power density of wind power, and obviously you could not plaster Manhattan in wind turbines. Solar power is not much better. Imagine that we could cover 20% of Manhattan in solar panels. This would give us no better than 5 W/m2. Clearly Manhattan is not getting its energy locally. And as you can see from the above map the other boroughs of New York are not going to fare much better.

How about the rest of North America? If we reduced per capita energy consumption to Japanese levels, a sensible but unpopular idea, could many American cities run largely on local renewables? The graph below shows population density versus energy use density in this lower consumption America: usDensity

Low density Phoenix perhaps has a shot at getting most of its energy from solar power. Covering 25% of Phoenix in solar panels would produce as much energy as is consumed in Phoenix. The practicality of this is of course rather questionable, and getting more than 50% of Phoenix’s energy from local solar will require something that currently does not exist: a cheap way to store energy on a large scale. A system involving more than 50% of energy coming from solar will thus inevitably require the accounting of land requirements for large scale storage, an uncertain prospect, and significant losses of solar panel output due to efficiency losses during storage and curtailment of excess.

The prospects of American cities running largely on local renewables thus seems unlikely, and 83% of Americans live in cities.

A global appraisal

The world’s two hundred largest urban areas are home to over 1.2 billion people, and a quarter of these areas are more densely populated than New York (10,000 people per square kilometre). This is shown below: PopDensity

Before asking if these cities can run on local renewables I must first mention the too real disparities in global energy consumption. Below is a comparison of the population of countries with their per capita energy consumption, with population plotted on a logarithmic scale due to China and India being much larger than other countries. And I include lines showing typical European and North American per capita energy consumption. GlobalEnergyComp

While there are about 350 million North Americans who can, and should, reduce their energy consumption to European levels, there are even more at the bottom who must increase their energy consumption significantly to improve their quality of life. Quantitative comparisons are sobering. Over 35 countries have per capita consumption at less than 10% of North American levels, with populations totalling over 2 billion. Despite the apparent desires of some environmental NGOs (for an example see page 11 of this WWF report) it is therefore undesirable to propose reductions in global energy consumption. The modernised world may consume excessive energy, but energy consumption is much too low in modernising countries to let us decrease global energy consumption without negative humanitarian impacts.

We therefore should have a desire to both reduce excessive consumption in modernised countries and increase energy consumption in modernising countries. I am not going to suggest a prescriptive end point. Instead I will assume that consumption levels in modern day Japan can provide a very good quality of life, and exceeding these levels is unnecessary.

If the populations of the world’s 200 largest cities consumed energy like modern day Japanese energy use density would look like this:


In total 10 cities would have power density greater than 100 W/m2, 56 would have power density greater than 50 W/m2, while 181 would have power density of over 10 W/m2. That is 90% of the planet’s 200 largest cities almost certainly cannot be powered predominantly by local renewable energy. The population densities of these cities are not significantly different than the rest of the world’s cities, so we can conclude that the the vast majority of cities cannot be powered by local renewables. And this suggests very serious limits to the role of local distributed energy in a world where more than 70% of us will probably live in cities.

The prospects are even worse in individual countries. Of the world’s 200 largest urban areas, 17 are in India. Below I have isolated these cities.

India power density

120 million people live in these cities. Covering any of them entirely in 10% efficient solar panels will generate less than half of their energy needs. And look at that dot in the top right, that is Bombay. For Bombay to get all of its energy needs from solar in my hypothetical future it would need to harness almost 100% of the solar radiation that strikes it, a remote prospect. This extremely high population density is routinely ignored by western environmentalists calling for distributed energy to be the solution to India’s energy problems. It quite clearly is not.

In this century the bulk of humanity will live in large densely populated cities. If the citizens of of these cities are to attain a high quality of life they will require large centralised energy generation. This is not a matter of ideological preference, but of engineering reality.

energy collective

8 Comments on "The Future of Energy: Why Power Density Matters"

  1. GregT on Tue, 6th Aug 2013 3:35 am 

    Anyone reading this article, with an ability to look at the big picture, we be planning to get out of largely populated areas ASAP.

  2. Arthur on Tue, 6th Aug 2013 4:40 am 

    Why on earth would you aspire to generate Manhattan’s energy needs locally? There is no need to. The global phenomenon of urbanization went hand in hand with increased energy per capita usage, enabling ever more people to abandon agriculture as a necessary means of living. With declining energy supply the trend is likely to reverse. But the energy needs of a city can be supplied by the territory surrounding the city and does not need to be centralized but can be distributed from millions of sources.

  3. GregT on Tue, 6th Aug 2013 4:55 am 

    The electrical energy supply maybe, but not very likely.The food supply, definitely not.

    Electricity is a nicety, not a necessity. Food and water are necessities, and will not be available to millions of people in densely populated areas, without fossil fuels.

  4. deedl on Tue, 6th Aug 2013 7:28 am 

    Shifting to renewables does not work if you only shift the supply patterns, you also have to shift demand patterns. Many city buildings are not designed to be enregy efficient. However they have many features that in principle enable lower energy consumption: they have due to their size a much smaller surface/volume ratio than rural or suburban single homes, which translates to smaller energy losses and they are packed with people which are 100-Watt heaters each. Transitioning cities to renewables means to update the energy patterns of the buildings, which can reduce energy demand by an entire order of magnitude. So a calculation based on current inefficient cities is a bit faulty.

    Implementing the well known technology fo low energy houses is a pure question of political will, not e question of economics or technology.

  5. BillT on Tue, 6th Aug 2013 11:11 am 

    The modern cities are death traps. Historically, cities existed in places and times that had excess energy in the form of slaves, or had armies pillaging neighboring countries. If there would be a solar flare that takes out the world’s electronics, like the one we barely missed 2 weeks ago, cities would turn into the worse type of hell imaginable. Can you see NYC permanently down. Nothing coming in from the out side. No electric, water, food, etc. I don’t want to be within 50 miles of a major city when it happens.

  6. GregT on Tue, 6th Aug 2013 3:40 pm 


    I figure 300 miles away from large population centers to be a much safer bet. Most people would run out of fuel for their cars before that point, and wouldn’t have enough energy to walk that far without food.

  7. energyskeptic on Tue, 6th Aug 2013 4:06 pm 

    Left out: the energy density of oil as a benchmark comparison, the inability of alternative energy resources to be constructed without fossil fuel inputs and their inability to reproduce themselves using their own generated energy, their inability to substitute for oil, gas, or coal, lack of scalability and long time to construct, intermitency, and above all, EROEI. I recommend reading my summary of David Fridley’s “Alternative energy challenges” at energyskeptic “LBNL scientist David Fridley on why alternative energy won’t save us”

  8. rollin on Tue, 6th Aug 2013 7:42 pm 

    “In this century the bulk of humanity will live in large densely populated cities. If the citizens of of these cities are to attain a high quality of life they will require large centralised energy generation. This is not a matter of ideological preference, but of engineering reality.”

    In this century, cities will not have enough energy or food support to survive. Many people will move out to rural areas to produce food. In this century many cities will be devastated by ocean rise combined with increased storm size and strength. In this century the mega-city will disappear to be replaced by a more agrarian and dispersed set of settlements.

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