Analysis of load factor for fuel diversification

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

Optimization of on-site renewable energy generation for industrial sites

We consider the energy sourcing decision problem faced by industrial power consumers who must determine their long-term electricity procurement plan and need to evaluate various options to meet load requirements for their facilities including those which may involve on-site renewable generation. Other than sourcing from on-site renewable generation such as solar photovoltaic or wind, power can be purchased from spot markets or through a power purchase agreement, i.e. energy supply contract. We develop a mixed-integer linear model to make decisions that include investments in renewable generation, power purchases from spot markets, and amount sourced from supply contracts. Taking into account renewable energy certificates, the model's objective is to maximize revenue from trading renewable certificates minus the expected total costs of investing and operating on-site renewable generation, and purchasing from electricity markets. Real load data from manufacturing plants are used to illustrate a numerical case study for our model

A load factor based mean-variance analysis for fuel diversification

Fuel diversification implies the selection of a mix of generation technologies for long-term electricity generation. The goal is to strike a good balance between reduced costs and reduced risk. The method of analysis that has been advocated and adopted for such studies is the mean-variance portfolio analysis pioneered by Markowitz (Markowitz, H., 1952. Portfolio selection. Journal of Finance 7(1) 77-91). However the standard mean-variance methodology, does not account for the ability of various fuels/technologies to adapt to varying loads. Such analysis often provides results that are easily dismissed by regulators and practitioners as unacceptable, since load cycles play critical roles in fuel selection. To account for such issues and still retain the convenience and elegance of the mean-variance approach, we propose a variant of the mean-variance analysis using the decomposition of the load into various types and utilizing the load factors of each load type. We also illustrate the approach using data for the state of Indiana and demonstrate the ability of the model in providing useful insights.Fuel diversity Mean variance Fuel selection Energy risk management Portfolio choice

A load factor based mean-variance analysis for fuel diversification

Fuel diversification implies the selection of a mix of generation technologies for long-term electricity generation. The goal is to strike a good balance between reduced costs and reduced risk. The method of analysis that has been advocated and adopted for such studies is the mean–variance portfolio analysis pioneered by Markowitz (Markowitz, H., 1952. Portfolio selection. Journal of Finance 7(1) 77–91). However the standard mean–variance methodology, does not account for the ability of various fuels/technologies to adapt to varying loads. Such analysis often provides results that are easily dismissed by regulators and practitioners as unacceptable, since load cycles play critical roles in fuel selection. To account for such issues and still retain the convenience and elegance of the mean–variance approach, we propose a variant of the mean–variance analysis using the decomposition of the load into various types and utilizing the load factors of each load type. We also illustrate the approach using data for the state of Indiana and demonstrate the ability of the model in providing useful insights

Applying Load Factors to the Mean-Variance Analysis for Fuel Diversification

Fuel diversification implies the selection of a mix of generation technologies for long-term electricity generation. The goal is to strike a good balance between reduced costs and reduced risk. The method of analysis that has been advocated and adopted for such studies is the mean-variance portfolio analysis pioneered by Markowitz (1952). However the standard meanvariance methodology, does not account for the ability of various fuels/technologies to adapt to varying loads. Such analysis often provides results that are easily dismissed by regulators and practitioners as unacceptable, since load cycles play critical roles in fuel selection. To account for such issues and still retain the convenience and elegance of the mean-variance approach, we propose a variant of the mean-variance analysis using the decomposition of the load into various types and utilizing the load factors of each load type. We also present examples using real data for the state of Indiana and demonstrate the ability of the model in providing useful insights

Diversification of fuel costs accounting for load variation

A practical mathematical programming model for the strategic fuel diversification problem is presented. The model is designed to consider the tradeoffs between the expected costs of investments in capacity, operating and maintenance costs, average fuel costs, and the variability of fuel costs. In addition, the model is designed to take the load curve into account at a high degree of resolution, while keeping the computational burden at a practical level. The model is illustrated with a case study for Indiana's power generation system. The model reveals that an effective means of reducing the volatility of the system-level fuel costs is through the reduction of dependence on coal-fired generation with an attendant shift towards nuclear generation. Model results indicate that about a 25% reduction in the standard deviation of the generation costs can be achieved with about a 20–25% increase in average fuel costs. Scenarios that incorporate costs for carbon dioxide emissions or a moratorium on nuclear capacity additions are also presented