• simon45559

How many wind turbines to save the world?

Updated: Feb 1

It is both an exciting and depressing time to be part of the energy industry. The excitement is that we are witnessing a major technological revolution as energy transitions from carbon-energy to renewable-energy.

We can take offshore wind as an example:

The history of Wind Turbines | The Renewable Energy Hub

The power of wind turbines has doubled since 2010. There are no real physical reasons why wind turbines of the future cannot generate more power than we see today. Who knows what radical new designs are just around the corner:

Future of Wind Turbine Technology | The Renewable Energy Hub

But it can be a little bit depressing when you look at the size of the task in front of us. I am a great believer in the power of the Stockdale paradox:

You must never confuse faith that you will prevail in the end — which you can never afford to lose — with the discipline to confront the most brutal facts of your current reality, whatever they might be.

So, what are the ‘brutal facts’ of our current situation:

Fact 1: Capacity in renewable power has nearly doubled since 2010:

Regional Trends (irena.org)

Fact 2: Despite the growth in renewable power, renewable power as a total % of energy has not changed.

Data & Statistics - IEA

Fact 3: Coal generation increased capacity from 8,700 TWh in 2010 to 10,200 TWh in 2018, an increase of 17%

The brutal fact of the situation is:

Despite a doubling of renewable capacity, coal generation increased capacity by 17% between 2010 and 2018.

I recently pointed this out in a blog, but was taken to task for confusing chemical energy, electrical energy, and heat energy. My friend pointed out:

Finally, Dr Simon Stromberg needs to have his knuckles wrapped for making the primary energy fallacy argument. Comparing electricity to heat as if they're equal is like talking about US dollars and Jamaican dollars because they're both called dollars. We have to stop doing that.

After being chastised (quite rightly) by the Thermodynamic Police, I decided to set my myself a challenge:

How many wind turbines does it take to save the world?

I decided to start with how much electricity does coal currently generate globally to get around the thermodynamic problem. Coal uses chemical energy, which is converted to heat, used to make steam, which is then used to do mechanical work, to turn a turbine to generate electricity. But we can start with the fact that coal-fired thermal power stations generate 10,200 TWh of electricity. So if we were going to replace all those coal power-stations , assuming no demand side efficiency gains, we will need 10,200 TWh of electricity.

Wind turbines take the kinetic energy of wind and turn into mechanical energy (turbine) and electrical energy. Wind turbines can convert about 20% of the kinetic energy of wind into electricity. Again we can ignore the efficiency of wind turbines and look at the power output of wind turbines.

The biggest latest generation of turbines can generate 14 MW of electrical power. I am going to use 12MW, entirely possible with todays technology:

Siemens Gamesa reveals 'world's biggest wind turbine' - Energy Live News

However, we also need to think about the capacity of the turbine. The capacity factor is the average power generated, divided by the rated peak power. UK offshore wind capacity factors for the UK is 40%.

UK offshore wind capacity factors (energynumbers.info)

Capacity depends on location and design, so I will tweak it down a little to 35%.

So how much electricity, in TWh, can a 12 MW turbine generate in a year. The calculation is:

Peak output x capacity factor x hours in day x days in a year

That calculation gives us:

12 MW * 35% * 24 hours * 365 days

Which is 36,792 MWh or 0.037 TWh

So now we can calculate how many giant wind turbines are equivalent to the world's coal electrical power which is:

The total amount of electricity per year from coal / Annual turbine output

10,200 TWh / 0.037 TWh.

This gives 277,234 latest generation giant wind turbines to save the world.

Flushed with success, assuming I have not messed up my numbers (which I may well have). I decided to try another question:

How many giant wind turbines would I need if all the automobiles in the UK convert to electric vehicles powered by a battery (EVs) .

First I need to know the full chain energy efficiency for battery charging, which has already been done for me in the excellent blog by David Cebon:

Blog: Long-Haul Lorries Powered by Hydrogen or Electricity? - The Centre For Sustainable Road Freight (csrf.ac.uk)

From his diagram, we can see that electricity production battery-powered vehicles are 69% efficient from the point of electricity production. Put 100 KWh in and 69 KWh end up driving the wheels of the car. We will call that wind-to-wheel.

Next, there are 21 million cars in the UK and the average mileage is 7,400 miles a year. A total UK mileage of 229 billion miles a year (wow that is a lot of miles). For an EV, according to Tesla, the average electric automobile does about 3 miles per KWh. So assuming all vehicles are converted to EVs and there is no change in driving habits, the amount of electrical energy required for those 229 billion miles is 76 TWh per year.

Remembering that well-to-wheel is 69%, we actually need a primary energy electrical input 110 TWh (76/0.69).

We already know that one large wind turbine can generate 0.037 TWh.

So if we power all cars in the UK as EVS we need 110/0.037, which is 2993 giant wind turbines.

If we convert all automobiles to EVs we need about three thousand 12 MW wind turbines

The problem with wind, it is not dispatchable energy. Unlike coal, we cannot turn wind of/on when we like. So when the wind is not blowing, we are not charging our vehicles. What happens if we all go on holiday the week the wind is not blowing? Maybe we can convert that electricity into something storable. How about Hydrogen, that is a gas, we can store it, we can transport. Also, we can fill up a Hydrogen car in a few minutes. We can produce that Hydrogen from wind-generated electricity using electrolysis.

If we look at David Cebon's efficiency diagram, we discover that Hydrogen wind-to-wheel is 23% efficient. Ultimately Hydrogen Fuel Cell vehicles use Hydrogen fuel cells to produce electricity to drive an electric motor:

Hydrogen fuel cell cars: what you need to know | BMW.com

So we can assume with an electric motor we will get about the same mileage per KWh as an electric car. It might not entirely be accurate, as HFCEV are little heavier than their battery-powered cousins. But about 3 miles per KWh will do for now.

OK so we need to remember that Hydrogen cars wind-to-wheel are 23% efficient, so our 76 TWh becomes 330 TWh (76/0.23).

330 TWh divided by the output of a wind turbine, 0.037 TWh gives 8981 wind turbines. three times as many turbines compared to if all the vehicles were battery powered.

If we convert all automobiles to Hydrogen Fuel Cell Vehicle we need about nine thousand 12 MW wind turbines.

How many wind turbines do we need to save the world:

To replace all the coal-fired power stations, we need about two hundred and eighty thousand latest generation giant offshore turbines
To convert all UK automobiles to battery-powered cars we need three thousand wind turbines
To convert all UK automobiles to Hydrogen, we need nine thousand wind turbines.

Is this task doable? It is a tough challenge, but it feels possible. Also, you can bet that 14 MW is not the limit for offshore wind turbines.

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