J. David Fuller

Accuracies of Optimal Transmission Switching Heuristics Based on DCOPF and ACOPF

This paper considers optimal transmission switching (OTS) to reduce generation cost by removing lines from service. A mixed integer program (MIP) has been proposed to solve the OTS problem, based on the linear direct current optimal power flow (DCOPF) model. Because of excessive computation times for large, real systems, the MIP model has been followed by some heuristics, also based on the DCOPF, to obtain near-optimal solutions quickly. However, the approximations in the DCOPF model may lead to poor choices of lines to remove from service. We assess the quality of line removal recommendations that rely on a previously published, DCOPF-based heuristic, by estimating actual cost reduction with the exact ACOPF model, using the IEEE 118-bus and 300-bus test systems with several demand levels. We also extend this heuristic to be based on the ACOPF and compare the quality of its recommendations to those of the DCOPF-based heuristic. The DCOPF-based heuristic performs very poorly in several cases, even leading to cost increases sometimes. There is a need for approximations to the ACOPF which are accurate enough to produce reliably good results for OTS heuristics, but fast enough for practical use.

Backpropagation in Hydrological Time Series Forecasting

One of the major constraints on the use of backpropagation neural networks as a practical forecasting tool, is the number of training patterns needed. We propose a methodology that reduces the data requirements. The general idea is to use the Box-Jenkins models in an exploratory phase to identify the “lag components” of the series, to determine a compact network structure with one input unit for each lag, and then apply the validation procedure. This process minimizes the size of the network and consequently the data required to train the network. The results obtained in four studies show the potential of the new methodology as an alternative to the traditional time series models.

Long-Term Effects of Feed-In Tariffs and Carbon Taxes on Distribution Systems

In deregulated electricity sector climates, such as in Ontario, the production of clean or renewable energy by small power producers through distributed generation (DG) is encouraged. This paper examines the policies that can be used to encourage DG investment and incorporates them into a mathematical model. This model is then used to create scenarios for examining the economic and environmental supply-side effects of policies to a distribution system over a ten-year period. The policies analyzed include a combination of feed-in-tariffs, CO2 tax, and cap-and-trade schemes. The results are discussed in the context of the Ontario market and its Standard Offer Program, implemented on a 32-bus radial distribution system.

A Stochastic Programming Model for a Day-Ahead Electricity Market With Real-Time Reserve Shortage Pricing

We present a multi-period stochastic mixed integer programming model for power generation scheduling in a day-ahead electricity market. The model considers various scenarios and integrates the idea of reserve shortage pricing in real time. Instead of including all the possible scenarios, we parsimoniously select a certain number of scenarios to limit the size of the model. As realistic size models are still intractable for exact methods, we propose a heuristic solution methodology based on scenario-rolling that is capable of finding good quality feasible solutions within reasonable computation time.

Impact of Energy Storage Systems on Electricity Market Equilibrium

Integration of large-scale energy storage systems (ESSs) is desirable nowadays to achieve higher reliability and efficiency for smart grids. Controlling ESS operation usually depends on electricity market prices so as to charge when the price is low and discharge when the price is high. On the other hand, the market-clearing price itself is determined based on the net demand, i.e., including energy storage output, at every hour. Therefore, it is crucial to develop a mathematical model to determine the optimal ESS operation as well as the market-clearing prices. The problem is formulated as a mixed complementarity problem (MCP) that allows the representation of special (incentive) prices, which cannot be represented in a single optimization model. The proposed model is useful for power system operators to determine the optimal storage dispatch simultaneously with the market-clearing price in addition to the conventional generation dispatch. The impact of energy storage size and location on market price, total generation cost, energy storage arbitrage benefit, and total consumer payment is further investigated in this paper. The latter analysis provides some guidelines for power system planners to identify the optimal size and location for installing large-scale ESSs.

Modelling the Incentive to Participate in Open Source Biopharmaceutical Innovation

The open source model provides a valuable framework for collective knowledge production and dissemination. Open knowledge networks and other cooperative strategies (classified as open source discovery initiatives) are enabling biopharmaceutical companies to access disembodied knowledge-based resources critical to downstream drug development. The objective of these cooperative strategic alliances is to preserve the downstream technological opportunities for multiple firms. When upstream discovery research cannot yield commercial products and when the costs associated with excessive upstream competition are too high, companies jointly benefit from cooperative knowledge production and open knowledge dissemination. An analysis of 39 open source initiatives (consortia) provides us with information on: the likely participants in such initiatives, the focus of knowledge production activities, the characteristics of the knowledge generated, and the management of joint knowledge assets. Based on this analysis, we use game models to understand the decision to participate in such strategic alliances better. Our game models provide a simple but elegant framework for understanding the impact of changing knowledge structures on the payoffs associated with cooperation and defection in knowledge production, and therefore on behaviour.

Benders decomposition for a class of variational inequalities

Abstract This paper examines Benders decomposition for a useful class of variational inequality (VI) problems that can model, e.g., economic equilibrium, games or traffic equilibrium. The dual of the given VI is defined. Benders decomposition of the original VI is derived by applying a Dantzig–Wolfe decomposition procedure to the dual of the given VI, and converting the dual forms of the Dantzig–Wolfe master and subproblems to their primal forms. The master problem VI includes a new cut at each iteration, with information from the latest subproblem VI, which is solved by fixing the “difficult” variables at values determined by the previous master problem. A scalar parameter called the convergence gap is calculated at each iteration; a negative value is equivalent to the algorithm making progress in that the last master problem solution is made infeasible by the new cut. Under mild conditions, the convergence gap approaches zero in the limit of many iterations. With a more restrictive condition that still admits many useful models, a zero value of the convergence gap implies that the master problem has found a solution of the VI. A small model of competitive equilibrium of three commodities in two regions serves as an illustration.

Dynamic energy and environment equilibrium model for the assessment of CO2 emission control in Canada and the USA

In this paper, an energy process model with geometric dostributed lag (GDL) demand, called the energy GDL process model, was updated to aid in CO2 emission control policy analysis. An updated energy GDL process model of supplies and demands of oil, gas, electricity and coal in Canada and the USA was constructed to assess the impacts of controls on CO2 emission in Canada and the USA. This model was formulated, constructed and solved with the updated GDL version of the Waterloo energy modelling system (WATEMS-GDL), which uses the new decoupling algorithm, to calculate an intertemporal equilibrium of energy supplies and demands. A comparison of scenarios suggests that delay in launching a CO2 emission control program can be very costly. Furthermore, given the current array of fuels, supply technologies and consumer response, it seems impossible to reach the Toronto conference targets, i.e. reducing to 50% below the 1988 CO2 emission level by 2030; significant changes are required in fuels, technologies or life-styles.

Introduction of geometric, distributed lag demand into energy-process models

In this paper, we introduce the combination of an energy-process model with the geometric distributed lag demand, called the energy-GDL process model, as well as its solution technique. In an energy-GDL process model, the demand is represented by a function of the prices not only in the current time period but also in previous time periods, based on the geometric, distributed lag structure. The supply is a cost-minimizing linear process submodel. The software WATEMS-GDL (the GDL version of the Waterloo Energy Modelling System) is implemented for solving such a model. An example illustrating the procedure of modelling and equilibrium-seeking is given.

Subproblem Approximation in Dantzig-Wolfe Decomposition of Variational Inequality Models with an Application to a Multicommodity Economic Equilibrium Model

We present a modification to Dantzig-Wolfe decomposition of variational inequality (VI) problems that allows for approximation of the VI mapping in the subproblem. The approximation is parameterized by the most recent master problem solution, and it must satisfy two simple requirements. In an electronic companion (online appendix), we show that the proofs of convergence and other important properties go through with subproblem approximation. The approximation procedure is illustrated by an application to a class of multicommodity economic equilibrium models (MCEEMs): the standard Dantzig-Wolfe decomposition by commodity does not allow the subproblem to be decomposed into separate subproblems for each commodity, but we show two ways to approximate the subproblems inverse demand function, and both ways allow the subproblem to be broken into separate single-commodity problems. A further approximation is combined with each of the inverse demand approximations; in effect, an approximate supply or demand curve is introduced into each commoditys subproblem for transfers of commodities between different subproblems, thus allowing the subproblems to produce better proposals. An illustration is included for an MCEEM that represents energy markets in Canada.