# Analysis of load factor for fuel diversification

#### Abstract

This study develops an improved mathematical model for analyzing investment portfolios of electricity generation assets to meet long-term future demand for power. Results from such analysis will provide diversified mixes of fuels and generation technologies that achieve a balance between reduced cost and reduced risk where risk is measured by the variability of fuel costs. Fuel Diversification (FD) is important in managing the cost of electricity generation. Past studies have modeled the FD problem using the Mean-Variance (M-V) portfolio approach without explicit considerations of the load duration curve (LDC). Most extant formulations of the M-V approach to the FD problem focus on minimizing the mean construction and other improvements, operating and maintenance costs plus a factor times the variance of the operating and maintenance costs for a representative year. Construction and other improvements are typically levelized to obtain an annuity payment over the life of the plant. In order to levelize the costs, each generating plant requires an assumed capacity factor (CF); therefore, unit costs representing technologies are evaluated in the portfolio assuming a fixed load factor (LF). The M-V portfolio method as seen in the literature fails to capture a significant aspect of the underlying problem—the levelized costs change with the load factor. The upshot is that results from models that ignore the load curve are unreasonably specialized and viewed by practitioners as naïve and inappropriate. This situation can be remedied by classifying loads (e.g. base, peaking, and cycling) and dedicating different technology mixes to serving the different load classes. Using this approach, the LDC is partitioned into contiguous segments. Unlike the standard M-V portfolio method where costs representing technologies ignore load variation, the method proposed in this research can accommodate multiple load types. Separate LFs for each load class are taken into account in balancing the mix of the available fuel/technology candidates. As a result, generating units are evaluated by how they are utilized over the load profile, and thus, the fuel mixes of generation assets are optimized for serving the varying loads. Use of the method was demonstrated with an analysis for the state of Indiana (Gotham et al. (2009)) and the results were assessed to be much more credible than those obtained when the LDC is ignored. However, their approach treated load cutoffs for the LDC as predetermined, exogenous levels. Here, load cutoffs are endogenously chosen in an optimal manner. This formulation called the endogenous-cutoff model is used to show that optimal cutoffs are sensitive to the level of risk aversion and to observe the rate at which solutions improve as the number of endogenous cutoffs increases. This analysis will provide insight into what constitutes a good set of cutoff levels and how many cutoffs are sufficient when considering how to break up the LDC for managing FD. Analysis of this problem leads to an alternative formulation that allows the nonlinearities to be confined to a small number of variables where the cutoffs are exogenous. Instead of solving for optimal load cutoff levels, the LDC is segmented into a large number of equally spaced load cutoff levels. This equally spaced cutoff model is an approximation to the theoretical continuous-cutoff model; hence it is called the continuous model approximation. Numerical results for the state of Indiana are presented via a series of case studies. These include analyses of the impact of the addition of carbon costs, simulating implementation of cap and trade legislation, and zero availability of nuclear power, simulating the situation where the public becomes adamantly opposed to nuclear technology. Sensitivity analyses with respect to problem data (e.g. expected technology cost and variance/covariance of technology cost) are also performed.

#### Degree

Ph.D.

#### Advisors

Morin, Purdue University.

#### Subject Area

Finance|Operations research

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