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An electrical system is modelled with a transmission network, customers, central generators, and independent generators. The system is subject to stochastic failures and stochastic demand parameters. Optimal spot prices are derived for the system. They vary stochastically with space and time, and depend on electrical load flow patterns. The price difference between two locations or two voltage levels, and the wheeling charge between them, will change magnitude and sometimes sign over time, as a function of events throughout the network. Current spatial pricing methods are significantly different from the spot-price-based methods derived here.
Bohn et al. (Sun,) studied this question.