The National Energy Modeling System (NEMS) is a large-scale mathematical model that computes equilibrium fuel prices and quantities in the U.S. energy sector and is currently in use at the U.S. Department of Energy (DOE). At present, to generate these equilibrium values, NEMS iteratively solves a sequence of linear programs and nonlinear equations. This is a nonlinear Gauss-Seidel approach to arrive at estimates of market equilibrium fuel prices and quantities. In this paper, we present existence and uniqueness results for NEMS-type models based on a nonlinear complementarity/variational inequality problem format. Also, we document mathematically, for the first time, how the inputs and the outputs for each NEMS module link together.

The Clean Air Act Amendments of 1990 changed the regulations for air pollution by replacing a set of mandated actions with a market mechanism for pollution rights, where electric utilities can buy or sell rights to emit sulphur dioxide (SO2). We implemented the provisions related to the reduction in SO2 in the National Energy Modeling System (NEMS) to assess their impacts on energy markets. Because of the decentralized design of NEMS, the implementation was quite complex. We had to use Lagrangian relaxation, which turned out to be more difficult than first envisioned, and other techniques to arrive at a consistent equilibrium among the relevant energy sectors. As a result of these difficulties, we revised the NEMS model. This exercise illustrates that often an organization should be ready to take a step back from what exists to take a step forward.

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