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Using Mathematica to Model Deregulation of the Illinois Electric Power Market: Anticipating Deregulation of the Illinois Electric Power Industry

Charles M. Macal
Organization: Argonne National Laboratory

2004 Wolfram Technology Conference
Conference location

Champaign IL

The restructuring of the electric power industry continues to be an important topical area to consumers, investors, policy makers, and the public at large. Electricity prices and grid reliability are performance measures of the greatest concern. This paper describes the use of Mathematica to model the deregulation of Illinois electric power markets using an agent-based simulation modeling approach. An implementation-independent structured modeling approach, similar to object-oriented modeling, is used within the Mathematica programming environment. Abstract data types are defined to represent electric power system objects, in general, and electric power system agents, in particular. The structured modeling approach has several advantages including scalability, reusability, and consistency (with object-oriented models being developed for the electric power market in Java). Mathematica's interactive notebook style allows for the quick exploration and interactive analysis of large-scale databases for the electric power system. Data analysis and verification is an iterative process, as large data sets contain many gaps, inconsistencies, and anomalies. Interactive analysis is used for data cleaning and visualization in support of data verification. Electric power system data and results are exported to 3D graphics for use in Live3D. Manipulation of the complex data sets and networks of the electric power system in 3D space has important benefits for data verification and identification of key simulation results and system behaviors. Mathematica's integrated optimization environment is used to solve an embedded optimal power flow (OPF) problem, which links the electric power generators, generation companies, and electric power loads through the transmission network, for each time period. The OPF solves for spatially distributed, locational marginal prices for electricity and power flows throughout the network. The simulation framework built in Mathematica allows for the easy setup of large-scale parameter sweeps over higher dimensional spaces to explore system behaviors across the realm of all possibilities.

The electric power grid has been described as the most complex system ever developed by humankind. However, the rules of business and social interaction are at least as important as the rules of physics when it comes to the generation, sale, and delivery of electrical power. The electric power market is a natural area for the application of agent-based modeling. Agent-based modeling and simulation (ABMS) is part of computational social science and involves the use of agent-based models to study complex social processes and systems. ABMS is related to a variety of other simulation techniques, including discrete event simulation and distributed artificial intelligence (DAS) or multi-agent systems (MAS). Although many traits are shared, ABMS is differentiated from these approaches by its focus on finding the set of basic decision rules and behavioral interactions that can produce the complex results experienced in the real world.

ABMS consists of a set of agents and a framework for simulating their decisions and interactions. ABMS tools are designed to simulate the interactions of large numbers of individuals so as to study the macro-scale consequences of these interactions. Each entity in the system under investigation is represented by an agent in the model. An agent is thus a software representation of a decision-making unit. Agents are self-directed objects with specific traits and typically exhibit bounded rationality, that is, they make decisions by using limited internal decision rules that depend only on imperfect local information. In practice, each agent has only partial knowledge of other agents, and each agent makes its own decisions based on the partial knowledge about other agents in the system. Agent-based modeling is the best avenue for incorporating some of the corporate, financial, and social interactions that are beyond capture with traditional means of modeling.

This paper describes a series of electric power agent models, implemented in Mathematica, that blend the approaches taken in several disciplines. Electric power market agents are heterogeneous, varying by objectives, available resources, decision-making sophistication, access to information about other agents and the environment, and other factors. Interactions among agents produce emergent market and social structure, which in turn implies market prices, system reliability, and other system-wide parameters. The model includes different types of agents to capture the heterogeneity of restructured markets, including generation companies (GenCos), transmission companies (TransCos), demand companies (DemCos), distribution companies (DistCos), independent system operators (ISOs) or regional transmission organizations (RTOs), consumers, and regulators. Electric power agents are highly specialized to perform diverse tasks ranging from acting as generation companies to modeling transmission lines. To support specialization, the agent models include specific rule sets that represent plausible sets of behaviors. Analysts can define new rules and strategies to be used for the agents and then examine the marketplace consequences of these strategies.

*Business and Economics
*Engineering > Electrical Engineering
*Mathematics > Probability and Statistics
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