In this work, greenhouse gas (GHG) emissions were calculated from reported fuel consumption data reported for electricity generation for the 2017–2022 period (Additionally, the consumption of natural gas was also determined through the consistency requirement ; see below for more explanations.). However, no fuel consumption data are available for 2023 and beyond. Therefore, a method had to be devised which allowed for an estimation of future fuel consumption, using only reported (2023) and projected (2024–2026) electricity generation data for each technology class as an input. This was done based on the technology-fuel matrix method described below.
Appendix A.1. Technology-Fuel Matrix
Writing
for electric energy produced with technology
and
for the fuel equivalent of electricity
, assuming a constant thermal efficiency
for all fuel types used by technology
, we can first relate electricity and fuels by
where
is the amount of fuel of type
,
is the technology-fuel matrix, and
is the number of fuels used in the power sector;
is the dimensionless heat rate of technology class
. Note that the
are normalized:
with
being the number of technology classes, and
. The general structure of the technology-fuel matrix for the Mexican power system is shown in
Table A1.
Table A1.
Technology-Fuel Matrix.
Table A1.
Technology-Fuel Matrix.
Technology | Fuels |
---|
Natural Gas (NG) | Diesel (D) | Fuel Oil (FO) | Coal (C) |
---|
Combined-cycle (CC) plants | | | 0 | 0 |
Single-cycle (SC) gas turbines | | | 0 | 0 |
Conventional steam (CS) plants | | 0 | | 0 |
Coal power plants (CCPs) | 0 | 0 | | |
Internal combustion (IC) plants | | | | 0 |
Table A1 contains 11 unknown variables. The equations include (a) 5 equations relating electricity productions
with fuel consumption
and (b) 4 normalization equations for factors
, leaving us with an underdetermined system of equations. The missing equations can be made up for by providing a special treatment to the contributions from internal combustion (IC) plants, which accounted for only 1.0% of all generation in 2023 and 1.3% of all fossil fuel generation. I first simplify the nomenclature by using the equivalences given in
Table A2.
Table A2.
Simplified notation for the non-zero elements of the technology-fuel matrix.
Table A2.
Simplified notation for the non-zero elements of the technology-fuel matrix.
| | | | | | | | | | |
---|
| | | | | | | | | | |
One can now state expressions for fuel factor elements pertaining to internal combustion (IC) plants by
where
,
, and
are the fractions of electricity generated with IC plants from Diesel (D), fuel oil (FO), and natural gas (NG), respectively. While the values of the fractions are not in the public domain, they can be estimated by the relative capacities corresponding to each fuel type, making the simplifying assumption of constant net capacity factors, which is justified in the light of the small overall contribution of IC plants. Using the database developed in the work of Miranda et al. [
37], we have obtained the following estimates:
,
.
With
,
, and
having been determined, we observe that
, since coal is only burned in coal power plants (CPPs), leaving us with seven unknowns and seven equations (four technology-fuel equations and three balance equations). Three equations can be resolved explicitly and are shown below:
The two variables
and
are coupled through the following matrix equation:
The matrix on the left-hand side can be seen to be of rank 1, leading to the following consistency condition for the elements of the vector on the right-hand side:
which is simply the (energy conservation) requirement that the sum of all fuels burned must equal the weighted sum of electricity generated, with the weights being the inverse efficiencies. Note that Equation (A10) is not automatically satisfied, since the
and
are from independent data sources; see below for discussion.
As it turns out, a first estimate of
can be obtained without knowing
which can be seen readily by using the second of the two equations (A9):
Note that
,
and
are constrained by Equation (A10); however, the following conclusions are largely independent of this constraint. We note that
; e.g., for 2022
, depending on the source, whereas
. The summand between brackets is slightly negative (
for 2022), but of the order of 1. Given that all
values are constrained by 0 and 1, and the high slope of the linear relationship in Equation (A9),
is necessarily confined to a very small interval, i.e.,
Given that the interval is very small, we can choose to use the central value as our predictor:
By the same reasoning,
cannot be determined from the set of equations above, and additional information is required. In order to determine an estimator
, we observe that Diesel fuel use in combined-cycle plants in Mexico is mostly confined to the Yucatán peninsula, where natural gas is not available in sufficient quantities, due to the limitations of the Mayakan natural gas pipeline (The rated capacity of the Mayakan pipeline is 250 MMcfd (or 7.1 Mm
3/day), out of which 240 MMcfd (0.86 Mm
3/day) are tagged for power generation. Actual injection levels are much lower; the annual averages for 2019 to 2022 were
= 71, 102, 142, and 160 MMcfd). Assuming all gas is used in the three combined-cycle plants fed by the pipeline, with a combined firm capacity of about
, and the plants are operated at a net capacity factor
, then
can be estimated as
where the minimum function accounts for Diesel fuel consumed in internal combustion plants and
is the annual flow of natural gas over the Mayakan pipeline. I have assumed NCFs to be close to the national average of combined-cycle plants by setting
. The exact value of
is not critical to the results of this study, which is why a national average is considered a good approximation.
The remaining unknown
and
can be calculated from the following balance equations:
The results of the calculations described above are exhibited for six selected variables, as shown in
Figure A1, illustrating how different fuel types are used among the technology classes over time. The error bounds shown were calculated with the methodology described in
Appendix A.2. The fraction
of natural gas (NG) used in combined-cycle (CC) plants can be seen to rise steadily over the years, accounting for about 87% of all natural gas burned in the power sector in 2022, with a corresponding decline in natural gas used in conventional steam (CS) plants. The fraction of natural gas used in single-cycle (SC) gas turbines remained below ten percent for all years and also declined in recent years. An interesting case is the case of fuel oil in coal power plants (CPPs), first reported anecdotally by Barnés de Castro [
48], the consumption of which rose from a value consistent with zero in 2019 to nearly 40% in 2022, with a corresponding decline in conventional steam (CS) plants, the other outlet for fuel oil in the Mexican power sector. (Note that the predicted fuel consumption fraction for fuel oil (FO) in conventional steam (CS) for the year 2019 is slightly higher than 100%; however, this value is consistent with 100% within the margins of error indicated in the figure).
Figure A1.
Main elements of the fuel-technology matrix for the period 2017–2022 determined with the methodology described in the annex. The error margin corresponds to ± one standard deviation.
= fraction of total natural gas (NG) consumption burned in combined-cycle (CC) plants.
= fraction of total natural gas (NG) consumption burned in single-cycle (SC) gas turbines.
= fraction of total natural gas (NG) consumption burned in conventional steam (CS) gas turbines.
= fraction of total Diesel (D) consumption burned in combined-cycle (CC) plants.
= fraction of total fuel oil (FO) consumption burned in conventional steam (CS) plants.
= fraction of total fuel oil (FO) consumption burned in coal power plants (CPPs). Sum rule values were calculated from
and average efficiency values
for each technology class
. See
Appendix A.3 for further explanations. Horizontal dotted lines delimit the range of the fuel-fraction factors (
). Note that all predicted
values fall within the range limits within the margins of error.
Figure A1.
Main elements of the fuel-technology matrix for the period 2017–2022 determined with the methodology described in the annex. The error margin corresponds to ± one standard deviation.
= fraction of total natural gas (NG) consumption burned in combined-cycle (CC) plants.
= fraction of total natural gas (NG) consumption burned in single-cycle (SC) gas turbines.
= fraction of total natural gas (NG) consumption burned in conventional steam (CS) gas turbines.
= fraction of total Diesel (D) consumption burned in combined-cycle (CC) plants.
= fraction of total fuel oil (FO) consumption burned in conventional steam (CS) plants.
= fraction of total fuel oil (FO) consumption burned in coal power plants (CPPs). Sum rule values were calculated from
and average efficiency values
for each technology class
. See
Appendix A.3 for further explanations. Horizontal dotted lines delimit the range of the fuel-fraction factors (
). Note that all predicted
values fall within the range limits within the margins of error.
Appendix A.4. Estimation of Future Fuel Consumptions
After these preparations, the consumption of the four major fuels consumed in the generation of electricity can be determined as follows. First, the total consumption of a given fuel is stated as the sum of consumption values from each technology class. In the case of natural gas (NG), we have the following relationship:
where
,
, and
are the amounts of natural gas consumed in combined-cycle (CC) and single-cycle (SC) gas turbines, and conventional steam (CS) plants, and
,
, and
are the fuel equivalents of the electricity production from CC, SC, and CS plants, respectively. These fuel equivalents are either known (2023) or can be predicted with reasonable accuracy (2024–2026). Note that the structure of Equation (A21) is a direct consequence of the structure of the technology-fuel matrix (
Table A1). Continuing with the case of natural gas, we can now write
where the first part of Equation (A22) is the first line of the technology-fuel Equation (A1), and
is the fraction of the fuel equivalent of the CC-generated electricity which was produced with natural gas. From Equation (A22), we can immediately determine the unknown
:
The remaining unknowns and can be determined in a similar way; this is left as an exercise to the reader. It is important to note that the use of Equation (A21) requires the consistency or sum rule value for the natural gas consumption to be used, rather than the reported consumption for a given year.
Evidently,
and the other free parameters require fuel consumption, fuel equivalents of electricity, and technology-fuel matrix elements as inputs, which is why the last values which can be determined this way correspond to the year 2022. In order to project fuel consumption data into the future, some assumptions have to be made. In this work, I am assuming that
and the other parameters stay at their 2022 values. (Note that one cannot argue that the technology-fuel matrix elements remain at their 2022 values; the proof is left to the reader.)). One can then state the following equality
which is generally called the persistency hypothesis in forecasting applications. In the case of natural gas and combined-cycle plants, this seems to be a very reasonable assumption, based on the reasoning used to derive
(see
Appendix A.1), i.e., the fact that burning Diesel fuel in combined-cycle plants on the Yucatán peninsula is becoming increasingly unnecessary due to the increased transmission capacity of the Mayakan gas pipeline. In the case of the other parameters, other forecast approaches may be proposed, but their influence on the projected results is believed to be minor.