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Dynamic energy pricing provides a promising solution for the utility companies to incentivize energy users to perform demand side management in order to minimize their electric bills. Moreover, the emerging decentralized smart grid, which is a likely infrastructure scenario for future electrical power networks, allows energy consumers to select their energy provider from among multiple utility companies in any billing period. This paper thus starts by considering an oligopolistic energy market with multiple non-cooperative (competitive) utility companies, and addresses the problem of determining dynamic energy prices for every utility company in this market based on a modified Bertrand Competition Model of user behaviors. Two methods of dynamic energy pricing are proposed for a utility company to maximize its total profit. The first method finds the greatest lower bound on the total profit that can be achieved by the utility company, whereas the second method finds the best response of a utility company to dynamic pricing policies that the other companies have adopted in previous billing periods. To exploit the advantages of each method while compensating their shortcomings, an adaptive dynamic pricing policy is proposed based on a machine learning technique, which finds a good balance between invocations of the two aforesaid methods. Experimental results show that the adaptive policy results in consistently high profit for the utility company no matter what policies are employed by the other companies

Profit maximization algorithms for utility companies in an oligopolistic energy market with dynamic prices and intelligent users