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. 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 each fossil fuel, M1 defines its inventory (affine function that returns the accessible capacity as a function of market price), and yearly production capacity. This production capacity is a function of the max (theoretical) capacity, which is proportional to the total accessible inventory, and the possible to grow this capacity (for each fossil fuel, we define the maximal increment, in proportion, that can be build each year).

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 Gtoe (giga tons of oil equivalent) for CCEM v4; we shall use TWh and PWh in future versions, 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 Gtoe for energy e at year y

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

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

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

•       Pe(y): price in $ for 1 toe 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

For the sake of simplicity, the price range is discretized between 0 and Pmax by Pinc increments. There are three key steps for fossil fuels:

·       Compute the max inventory capacity: mostly a function of the inventory “belief”, based on the average market price during the past 3 years (obviously, this is a gross simplification that does not reflect the delay between market price, drilling decisions and exploitation).

·       Adjust the current capacity (bounded by the max inventory)

·       The production uses a piecewise affine function that cannot exceed the current capacity (cf. Figure 8) and reflects price elasticity (calibrated at the decade level).

The logic of M1 can be described with the following equations. There are two separate sections for Fossil and Clean energies. For fossil fuels, we compute the maximum theoretical capacity from the inventory (with the three years average price). This theoretical capacity is an upper bound for the actual “max capacity” that mimics the growth of needs (an input from M2), adjusted to reflect the growth constraint. Since prices in CCEM are signals that do not intend to reflect market prices but rather “aggregated prices over a number of years”, we suppress irrelevant oscillations by a damping factor (the ratio need/output is divided by a constant factor (currently 3). We then compute the supply output vector using the function show in Figure 7 (as seen in the equation below, the MaxCapacity formula is different for fossil (finite) and clean (“infinite”) energies. The code for clean energy max capacity uses the “belief” maxCapacityGrowth(e,y) which gives, for any year in the future, the growth capacity (expressed in output per year) for this year.  Figure 7 may look far too simplistic, which it is, but keep in mind that it applies to situation where energy is abundant and where it simply represents a linear elasticity. When energy is scare the price trend is dominated by “the other half of the equation”, that is how demand decreases with price.

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 sensitivity factor for energy e. Here we need to repeat that the function shown in figure 7 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