M1: Energy production

The M1 model answers the two questions:

(a) “How much fossil energy can we access, at which costs?”

(b) “How much clean energy could be made available in the future, at which costs?”.

As mentioned earlier, CCEM distinguishes between three fossil fuels: oil, gas and coal, while regrouping all “clean” sources (wind, solar, hydro, nuclear) into one. For M1, we only consider primary sources of energies (M3 will take secondary forms and usage of energy into account).

For fossil fuels, the key “known unknown” is the inventory of accessible resources (such as oil reserves). This is not a value, it a monotonic increasing function of the market price at which the energy may be sold. Between the time when CCEM started, 15 years ago, and now, the inventory has increased significantly due to shale oil and shale gas. This is less relevant for coal since the known reserves cover many centuries of usage, but it is a key parameter for the next 100 years as far as oil and gas are concerned.  For clean energy, the “known unknown” is the speed at which we may grow (our solar and wind farms, the hydroelectric potential, the nuclear facilities …). There are many reasons for which this is hard to forecast: availability of material resources, evolution of technology efficiency, capacity of financing, etc. As a key belief of M1, this is represented as a yearly forecast (a monotonic increasing function that associate to each year the total capacity for clean energy). Energy is measured in PWh, since electrification is one of the key strategic questions.

M1 uses the following state variables to describe the energy system year after year (the parameter y represents the current year):

•       Oe(y): output (production) in PWh for energy e at year y

•       Ce(y): max capacity in PWh for energy e

•       Ae(y): added capacity for energy e through transfers (M3)

•       tOe(y): total output in PWh from years 1 to y

•       Pe(y): price in $ for 1 MWh for energy e at year y

•       UDz(y): demand (unconstrained consumption) for zone z of energy e

•       Gz(y): GDP for zone z on year y

There are three key steps for fossil fuels:

·         Compute the expected capacity: its evolution is planned to match the demand forecast based on the previous 3-years history (obviously, this is a gross simplification that does not reflect the delay between market price, drilling decisions and exploitation).

·         Adjust the current capacity if the reserves (inventory) are lower than a threshold value (80% of the initial known reserves). The adjustment is made with a piece-wise quadratic function so that the capacity is proportional to the fossil reserves below half of the threshold.

·         The production (“supply” function) uses a piecewise affine function that cannot exceed the current capacity (cf. Figure 3) and reflects price elasticity.

The case of clean energy is simpler (right part of Figure 4) with only two steps:

·         The capacity Ce(y) is computed to match the expected demand

·         The supply function is proportional to the proposed price up to the max capacity, with a price sensitivity that reflects a price increase that should follow the world GDP.

The logic of M1 can be described with the following numbered equations (see “blue box” below):    

(1)    Supply(e,p,Cmax) tells the production of fossil energy e at price p, knowing the max capacity Cmax (that was computed earlier). The formula reflects the chart of Figure 4 (piece-wise linear formula named PriceAdjust). The default production is based on the initial production O(1), adjusted for capacity.

(2)    There are two separate sections for Fossil and Clean energies. Supply(e:Clean,p,Cmax,y) reflects the chart on the right of Figure 4. The production grows linearly according to the proposed price until Cmax, with a price sensitivity adjusted so that the nominal capacity is reached to a price that follows the economic growth (G(y – 1) / G(y)) modulo a sensitivity linear factor.

(3)    For fossil energies, capacity evolution is determined by ExpectedCapacity(e,y), but the yearly evolution is the average between existing and forecasted capacities, as a way to smooth oscillations. The expected capacity tries to follow the expected consumption (see equation 5), modulo the maximum yearly growth defined by maxGrowthRate(e). This expected capacity is then reduced according to the current level of reserves (inventory minus past consumption).

(4)    For clean energy, capacity is driven directly by ExpectedCapacity(e,y) which also attempt to follow the expectedGrowth modulo the maxYearlyGrowth constraint that also takes additions into consideration (Ae(y): when other sources of energies are transformed into clean energy – cf M3)

(5)    The two previous formulas use expectedGrowth, which is a linear regression of the past 3 years consumptions. This function returns growth expressed as a ratio of previous volume.

These equations use additional parametric functions associated to M1 (the bold functions represent the “known unknown” that are the “parameters” of CCEM):

•       maxCapacityGrowth(e,y) : for clean energy y, expected max capacity in Gtoe that may be added during year y (yearly production)

•       inventory(e,p) : expected reserves (at year 1) for fossil fuel e with a market price p

•       threshold(e): part of current reserve when suppliers of e reduce their output to match the decline of reserves (strong influence on PeakOil date)

•       targetMaxRatio(e): expected ratio between (max) capacity and output (constant depending on the type of energy)

•       maxGrowthRate(e): percentage of capacity that can be added at most in a year for fossil energy e. (similar to the growth of clean energy but plays a minor role because fossil energies have been around for a long time).

•       sensitivity(e): price factor for energy e. Here we need to repeat that the function shown in Figure 4 is simplistic because we do not try to model the pricing strategy of fossil-fuel-producers, and because prices are dominated by the demand side (prices increase until the demand declines enough to match the possible supply).

•       co2perTon(e): CO2 emissions to produce one toe of energy e