This paper presents a new mixed-integer linear formulation for the unit commitment problem of thermal units. The formulation proposed requires fewer binary variables and constraints than previously reported models, yielding a significant computational saving. Furthermore, the modeling framework provided by the new formulation allows including a precise description of time-dependent startup costs and intertemporal constraints such as ramping limits and minimum up and down times. A commercially available mixed-integer linear programming algorithm has been applied to efficiently solve the unit commitment problem for practical large-scale cases. Simulation results back these conclusions.Index Terms-Mixed-integer linear programming (MILP), thermal generating units, unit commitment.

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This paper presents a new approach for the contingency-constrained single-bus unit commitment problem. The proposed model explicitly incorporates an security criterion by which power balance is guaranteed under any contingency state comprising the simultaneous loss of up to generation units. Instead of considering all possible contingency states, which would render the problem intractable, a novel method based on robust optimization is proposed. Using the notion of umbrella contingency, the robust counterpart of the original problem is formulated. The resulting model is a particular instance of bilevel programming which is solved by its transformation to an equivalent single-level mixed-integer programming problem. Unlike previously reported contingency-dependent approaches, the robust model does not depend on the size of the set of credible contingencies, thus providing a computationally efficient framework. Simulation results back up these conclusions.

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This paper analyzes some unresolved pricing issues in security-constrained electricity markets subject to transmission flow limits. Although the notion of separate reserve types as proposed by FERC can be precisely and unambiguously defined, when transmission constraints are active, the very existence of separate reserve prices and markets is open to question when the prices are based on marginal costs. Instead, we submit here that the only products whose marginal costs can be separately and uniquely defined and calculated are those of energy and security at each node. Thus, under marginal pricing, at any given network bus all scheduled reserve types should be priced not at separate rates but at a common rate equal to the marginal cost of security at that bus. Furthermore, we argue that nodal or area reserves cannot be prespecified but must be obtained as by-products of the market-clearing process. Simulations back up these conclusions.Index Terms-Contingency-constrained scheduling, demand-side reserve, electricity markets, security and energy pricing, transmission constraints, up and down-spinning reserve.

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