CAIMS Prize Award

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Department of Applied Mathematics, University of Western Ontario

Supervisor:  M. Davison

Thesis title:  A Hybrid Model for Electricity Spot Prices


Prior to the deregulation trend, electricity prices were highly regulated and were usually entirely predictable - generators and wholesalers knew their costs of production and revenues, and consumers knew their electricity cos ts. However, deregulation has caused electricity to become the most volatile of the commodities. Not only is the demand for electricity highly variable, but the inability to store electricity in any appreciable quantity requires electricity to be consumed as soon as it is generated. The supply of electricity cannot shift as quickly as the demand. The result is an economic certainty - when demand increases quickly, the price must respond, and as a result, price spikes occur that are orders of magnitude higher than the base electricity price. For example, in the large Pennsylvania-New Jersey-Maryland (PJM) Market, a typical base price might be 30/MWh, while spikes can exceed 1000/MWh. A robust and realistic model for the spot price is required for any type of risk management or investment planning in volatile markets.

The model developed here is a hybrid of the top down data driven approach common in traditional financial applications and the bottom up system driven approach common to regulated electricity markets. The advantage of this innovative approach is that it incorporates the primary system drivers, and clearly illustrates the effects of these drivers on terminal prices. The model contains four primary modules: a model for forced outages, a model of maintenance outages, an electrical load model and finally a price module which combines the results of the previous three modules.

Each of the modules is individually implemented and tested for performance against observed data before being combined into the overall model. The forced outage model is the first of its kind to simulate the system on an aggregate basis using Weibull distributions. The overall spot price model is calibrated to and tested with data from the PJM electricity market. This model performs very well in simulating PJM market prices and has a primary advantage over other models in its ability to adapt to changing system conditions and/or new electricity markets.

A robust and realistic model for electricity prices has many applications. In this thesis, two primary applications are examined. The first is the pricing of derivative contracts on electrical power and the second is the comparison of various portfolio scenarios using a Cash Flow at Risk (CFaR) approach. Both of these applications yield interesting results and observations about the current state of the deregulated electricity markets. In closing, a number of additional improvements and exciting new applications are highlighted.