(215d) Integrated Hedging and Operations for Complex Energy Utilities

The economic operation of complex energy utilities involves a tradeoff among operational constraints, energy costs, and the financial risks due to price and demand uncertainty. Examples of complex energy utilities are campus and industrial scale facilities co-generating power, heat, chilling, and possibly other commodities. Such utilities often have some degree of flexibility in energy sources and operating conditions, and normally operators hedge at least a portion of their financial risk through trading in the energy markets. The market hedging operations, however, are generally executed separately from actual process operations, and without the benefit of more detailed process models. Here we wish to explore methods and the benefits that accrue from integrating operational and financial hedging for complex energy utilities.

In this work we propose a novel framework for integrating financial and process operations for complex energy utilities using thermodynamically consistent models. This work demonstrates four specific ideas:

1. We propose a modeling framework for energy conversion networks applying principles from finite time thermodynamics. By incorporating finite resistances to heat transport, and non-isentropic energy conversions, these models have been shown accurately bound the behavior of complex utilities. In this work, we generalize the existing literature by extending finite time thermodynamics to “energy conversion networks.” We show energy conversion networks can be modeled with a system of bilinear matrix inequalities in which entropy fluxes associated with energy conversion devices constitute a system of decision variables. We have developed a library of model elements, and demonstrate application to a realistically scaled model of a campus energy utility.

2. We show the problem of optimal economic operation over a single period is a non-convex, bilinear optimization problem. Global optimal solution of these problems is found using convex relaxations with a branch-and-bound strategy exploiting the thermodynamic origin of these problems. Of independent interest, there are several interesting special cases leading to bilinear eigenvalue problems, and even conventional generalized algebraic eigenvalue problems.

3. In order to provide valuation of energy utilities subject to price uncertainty, we extend the model to multiple periods. Using standard stochastic models for the prices of commodity goods, we discretize on trinomial lattices to capture the behavior and correlations among prices of multiple fuels. For utilities without storage, we show valuation is also a bilinear optimization problem.

4. Finally, we consider the optimal hedging of energy utilities. We define an optimal hedge as the purchase of a cash flow that minimizes the expected value of a convex utility function in the presence of price and demand uncertainty. From second-law considerations, we show that such a cash-flow is not a linear function of underlying commodity pricing.