Things we don't know how to do: Huge nonconvex smart auctions; combining financial and structural models; and multilevel games
Seminar Room 1, Newton Institute
AbstractThree increasingly important -- and challenging -- mathematical problems in power systems are considered in this talk.
The first is to obtain solutions to the mixed-integer, nonlinear, nonconvex, and stochastic short run operations problem that is the 'smart auction.' The primal solutions must be (near) optimal and feasible in order for the system to run and cost savings promised by liberalisation to be realized. Dual solutions should support the primal solution in order to encourage market parties to bid their costs and benefits honestly into the auction. Preventative control means that possible contingencies must be anticipated and prepared for.
Second, there is presently a gap between the deterministic, primal-solution oriented models that are used to evaluate alternative policies and the financial models and concerns that drive the decisions of risk-averse market actors. Policy models tend to be structural, in that their solutions can account for changes in technology, demand, and other market fundamentals. But they do a terrible job of representing price volatility, the conservatism of investors, or the effect of (non)availability of financial hedges upon investments. Financial methods, on the other hand, cannot represent the structural changes in the market that shift the ground beneath the feet of market participants, nor the reality of market power and price manipulation.
Finally, the interaction of large market players all along the supply chain -- from fuel to generation to transmission and finally to consumption -- represents a complex, multilevel game whose outcomes depend on the intensity of competition, learned collusive behavior, and regulatory threats. The consequences of our inadequate models of these interactions cost California ratepayers $20B in 2000-2001, and such models are needed to design markets that provide incentives for efficient investment and operations while restraining unproductive market manipulation.
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