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the general GAPEX framework is presented that allows us to generalize the models and
to overcome some limitations and simplifications that characterized preliminary ver-
sion of the framework ([7], [13] and [19]). In this paper, attention is devoted to model
design and developing within GAPEX. This has direct implication on the features of
the intelligent agents (i.e. Gencos) as well as on the mechanism of the power exchange.
In particular, in order to properly model the decision process of the economic agents,
an enhanced version of the classical Roth-Erev reinforcement learning algorithm [20]
is described so to apply reinforcement learning in case of negative payoffs. Further-
more, due to its complex high-voltage transmission network, the Italian power exchange
(IPEX) is taken as case of study. Results point out that GAPEX is an adequate frame-
work to model and to simulate power exchanges. In particular, the agent-based model
of the Italian Electricity Market is able to replicate market historical results during both
peak- and off-peak load hours as well as to give insights on Genco behaviors. More-
over the proposed enhanced version of the classical Roth-Erev reinforcement learning
algorithm points out effective learning properties with respect to existent variants in the
literature.
The structure of the paper is as follows. In the next Section, the computational design
and architecture of the GAPEX framework is presented. In Section 3 the Italian Elec-
tricity Day-Ahead Market agent-based model is described. In Section 4 the Enhanced
Roth-Erev reinforcement learning algorithm is presented and studied. In Section 5 we
present main results of the agent-based model of the Italian Power exchange, while
Section 6 summarizes main results and remarks.
2
GAPEX Framework Overview
GAPEX is an agent-based framework developed in MATLAB that is suitable for study-
ing the dynamic performances of many electricity markets. The simulator is imple-
mented using OOP programming capabilities of MATLAB, which allows one to de-
fine classes using a Java/C++ like syntax, thus creating a flexible and extensible ABM
framework which can run local simulation and also exploits the Parallel Computing
Toolbox provided with MATLAB. Detailed computational models of the power techno-
socio economic systems can be realistically simulated by means of the agent-based
modeling (hereafter ABM) approach. Agents can range from entities with no cognitive
function (e.g., transmission grids) to sophisticated decision makers capable of commu-
nication and learning (e.g., electricity traders). According to this research paradigm,
we designed and implemented a versatile software framework for studying electricity
markets. Indeed, the philosophy of the project and the modularity of its implementa-
tion provide a valuable computational framework for easily implementing other critical
infrastructure systems relevant to energy markets, e.g., a natural gas market. In order
to properly address the agent behaviors in different economic environments, we have
used a multi-agent learning (MAL) approach so to define appropriate algorithms able
to implement sophisticated decision-making rules. This represents one of the standards
in the ACE literature and some common features characterize the learning models. The
framework is composed by three main classes:
 
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