The students are asked to carefully
employ the modeling habits illustrated in
Rosenthal’s tutorial (e.g., all of the
model’s entities [power plants] should be
identified and grouped by type in GAMS,
defined as a set). The optimization prob-
lem for this tiny model effectively illus-
trates the power of algebraic modeling
languages like GAMS, as the mathemati-
cal formulation—regardless of the num-
ber of power plants we add—remains un-
changed.
In solving this problem, students learn the concept of marginal costs, which is crucial to a proper
understanding of economics in general and energy economics in particular. Students must explore the
intrinsic meaning of marginal costs in many facets of this course. A general interpretation is as follows:
An infinitely small relaxation of the constraint (i.e., one less unit of load must be met) returns the mar-
ginal savings of not producing that unit; similarly, one more unit of load returns the marginal costs of
producing that unit. The dual variables associated with the market-clearing (demand) constraint are often
used as indicators of the price of electricity in a competitive market [10].
A solution to this exercise is provided in Annex B. The GAMS code for this exercise can be found in
the ESM GitHub repository, see Tutorial 01.
2.2. Weeks 4–6: Setting up a three-node energy dispatch model
We start modeling energy dispatch problems with a very simple example. Despite its limited scale,
the example wields the same approach to modeling as empirically realistic problems. Thus, the example
could be easily extended using actual data for any market or region.
We consider the following. Imagine we are dealing
with a three-node energy network in which each node
has some available generation capacity as well as de-
mand levels per time step. The generators can generally
be classified as belonging to one of two categories: “dis-
patchable” for power plants that can ramp generation up
to nominal capacity on demand and “non-dispatchable”
for renewable generators (e.g., wind turbines, photovol-
taic) with output dependent on weather conditions. The
nodes are interconnected by power lines, the capacity of
which is often approximated by net transfer capacities
(NTCs) in this context.
What is the optimal energy dispatch to satisfy de-
mand in this system? Economists often refer to the “op-
timal dispatch” (i.e., meeting load at minimal operating
cost) when discussing efficient power plant scheduling.
In mathematical terms, the efficient power scheduling problem can be formulated as a “classic” linear
optimization problem (1) in which we search for variable vector that minimizes the objective value
under a set of relevant constraints. In this problem, and are parameter vectors (i.e., known
coefficients), is a matrix of parameters, and denotes a matrix transpose. The inequalities are the
Energy-modeling literature uses the same concept for various purposes. For example, the marginal
costs associated with the CO
2
emission constraint can be interpreted as an indicator of the price of an
emission certificate in the EU ETS.
Explanations related to the NTC concept: https://eepublicdownloads.entsoe.eu/clean-docu-
ments/pre2015/ntc/entsoe_NTCusersInformation.pdf
Fig. 2: The first optimization problem.
Fig. 3: Three-node toy energy network
Electronic copy available at: https://ssrn.com/abstract=4320978