Carbon Intensity Weighting | Worked Example

A particular problem in carbon pricing is that a one-size-fits-all carbon price is a blunt instrument for encouraging behavioural change.  A set of prices based on impact and fuel/energy type would be more effective.

The Energy Transition Equation – EefyN

To summarise, to fully address the consequences of CO2 emissions, a carbon pricing system is needed that accounts for the long-term impact of those emissions.  As things stand today, ‘cap and trade’ schemes do not and by definition cannot go far enough: they only trade carbon, so when fossil fuel usage abates they die out.

With a damage-based pricing scheme a similar problem would arise, so from the outset it is essential that energy, not carbon, be used as the accounting basis (for convenience the carbon price can still be considered in terms of CO2 if it is referred to coal that has 0.979kg-CO2/kWh).

Finally, a weighting factor we call must be introduced to appropriately weight the carbon prices for each form of energy, whether a fossil fuel or not. The reciprocal of f gives us the weighted average ‘carbon intensity’ (today, 1/ f is roughly 0.345 kg-CO2/kWh in the United States).

The logic here is that in the future, when fossil fuels usage has died out, but the consequences of their use are all too obvious (and probably growing), somebody has to pay for the damages.  Partly that will be our generation, if we finally accept carbon pricing, and partly it will be future generations.  So when it comes to damage payments, it should be those who now and in the future use the most energy, who should pay the most.  In 50 years time, even the profligate use of solar power should attract a lot of tax.  A king with a solar-powered, air-conditioned palace should pay much more than one of his citizens running a couple of solar light-bulbs.

In order to achieve a seamless transition, from carbon intense energy to low carbon energy, the term weighting factor f is defined as follows:

f = Σ Ei / Σ ( Ei × ei )

where[1] the subscript i denotes each energy type: coal, gas and so on – there can be as many as required, and the list can be updated at anytime.  Ei is the amount of fuel/energy type i used globally (expressed in GWh so the total numbers are comprehendible).

It should be noted that a problem would arise if the World completely decarbonised and all the ei numbers became zero.  In practice that is unlikely to happen, but to avoid the chance of shall we say spurious decarbonisation of wind turbines, for example, it is suggested that ei = maximum of ei or 0.05 (the e-value for today’s solar panels).  This approach is echoed by Bryony Worthington[2], Director of Sandbag, UK, who commented: “The CO2 intensity of our electricity supply is not getting the attention it deserves.  By 2030, we need the total power supply to be around 50g/kWh, whilst the current average hovers around 400g/kWh.  Quick gains can be made by preventing the UK’s old, inefficient and unabated coal stations providing anything other than a short term back-up role.”

If the global carbon price, and it should be global, is denoted as y (US$/tonne-CO2) then we have all the terms except two in the energy transition equation EefyN.  Firstly, E = Σ Ei.  Secondly, the term N applies if there are multiple energy suppliers, as there normally would be, of the same fuel/energy type i – each supplier would pay a proportionate part of the overall tax required and pass on those costs downstream.

Let us consider an example: suppose we have one low carbon energy source (solar, e = 0.05, as above) and one carbon intense fuel (coal, e ~ 1).  Furthermore, to keep things simple, let us assume that there are just two suppliers; the Solar Co. and the Coal Co., so N = 1 in each case.

To begin with, let us assume that there is no solar power, so all the energy E is coal energy, thus f = 1.  The tax to be paid by the Coal Co. will be EefyN = Ey, thus their end-use customers will experience a tax of y $/tonne (with a measure of mark up, no doubt).

Some years later, let us imagine that the size of the energy market E is the same as before, but the Solar Co. has gained a 1 per cent market share, thus

E = Ecoal + Esolar

   = 0.99 × E + 0.01 × E

The weighting factor

f = E / ( 0.99 × × 1 + 0.01 × × 0.05 )

   = 1 / ( 0.99 × 1 + 0.01 × 0.05 )

   = 1.00959

The Coal Co. customers would pay 1 × 1.00959 × y $/tonne while the Solar Co. customers would pay 0.05 × 1.00959 × y $/tonne.  Note the absence of solar subsidy.  It may be that even with a carbon tax the Solar Co. would struggle to compete.  Under those circumstances, governments (within existing subsidy rules) might wish to intervene.  This could be done by temporarily introducing negative ei values until solar panel prices had fallen sufficiently.  However, there is some danger here that the subsidy could be held in for too long or phased out too quickly – like political careers, most government subsidies end badly!  Have we reached the point where solar subsidies are no longer needed?  Apparently so: in the UK, solar subsidies are being phased out (badly[3]) and in Germany, Chancellor Angela Merkel introduced a tax on solar energy to help rein in power costs[4].

Let us continue.  If the market E remains the same but the Solar Co. now has a 50 per cent market share, then

E = Ecoal + Esolar

   = 0.50 × E + 0.50 × E

The weighting factor becomes

f = E / ( 0.50 × × 1 + 0.50 × × 0.05 )

   = 1 / ( 0.50 × 1 + 0.50 × 0.05 )

   = 1.9048

The Coal Co. customers would pay 1 × 1.9048 × y $/tonne and the Solar Co. customers would pay 0.05 × 1.9048 × y $/tonne.  Both coal and solar carbon prices have increased proportionately.  In absolute terms, the coal carbon price has increased the most – but, because of coal’s falling market share, N, the carbon revenue from coal has decreased.

Finally, when there are no coal emissions, then

E = Esolar = 1.00 × E

The weighting factor becomes

f = E / ( 0 + 1.0 × × 0.05 )

   = 1 / ( 0 + 1.0 × 0.05 )

   = 20

Thus the Solar Co. customers would pay all the tax required 0.05 × 20 × y $/tonne = y $/tonne.  As already outlined, the more energy a solar user demands, the more tax they pay.  Yes, of course, the carbon emissions will have stopped but, for the foreseeable future, the damage and hence the need for a carbon tax will continue.

The table below shows how the EefyN strategy would work in practice.  The data is based on the US electricity market with an approximation of the US transport market.


United States based fuel/energy carbon prices with estimated E- and e-values (data sources: US EIA[5], US RITA[6], UK DECC[7]). This data and the form of calculation is the basis of PALcarbon Predict Ability Ltd’s real time carbon pricing phone ‘app’.

Although coal is only 13.9 per cent of the total US energy market it is still a big component of the US electricity market and, because of its high e-value, the tax on coal would be one of the highest; 39 per cent of the carbon revenue would come from coal.  The tax on renewables and the revenue from them would be quite small.  Natural gas and road transport fuels would make up most of the non-coal revenue.

If a lower limit of e = 0.05 were imposed on renewables, as suggested earlier, the picture today would change only slightly and yet that small change would make the energy transition equation EefyN completely future-proof.  The result is shown below.


United States fuel/energy prices with e-values = maximum {e-value, 0.05} grey cells.

In compiling the above tables from various data sources it was clear that there is a need for a globally agreed, self-consistent source of e-values and fuel usage data.  Perhaps if the data is used for carbon pricing, that will focus people’s attention.


There has been much discussion and, indeed, action on divestment since 2013 when the environmental activist Bill McKibben released the film Do the Math[8]; an explosive documentary that triggered the global divestment movement.  Wikipedia states “Fossil fuel divestment is the removal of investment assets including stocks, bonds, and investment funds from companies involved in extracting fossil fuels, in an attempt to reduce climate change”.[9]  Many universities and similar organisations have moved their pension funds out of fossil fuel related investments.  Not all universities agree.  Some believe they are better off investing in oil and gas, notwithstanding the moral dimension.  Overall, there is most agreement about divesting from the most carbon-intense fuels such as tar sands and lignite etc.  EefyN, the energy transition equation, directly conveys the priorities here and the direction of travel that is needed in our energy use behaviour.

[1] Σ means “sum of”, thus Σ Ei means sum of all the energy contributions all the fuel/energy types i.e. the total energy used, E

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Carbon Intensity Weighting | Worked Example was last modified: April 25th, 2017 by admin