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This study aims to plan a cost-minimizing charging schedule for electric buses with fast charging stations. The paper conceptualizes the problem as a three-stage procedure, which is oriented around the participation of an electric bus aggregator in a day-ahead energy auction. First, the aggregation stage determines the bid parameters of buses. With bid parameters, aggregated cost-minimizing charging plans are obtained in the second stage conceived as the hourly day-ahead auction. The disaggregation of hourly plans into feasible minutely charging schedules is the third stage. The main contribution is the formulation of mixed-integer linear programming aggregation models to determine charging availability expressed as minimum and maximum hourly energy requirements taking into account detailed, minutely characteristics and constraints of the charging equipment and the buses. No price forecasts are required, and the plans adjust to the wholesale prices of energy. Defining only a few aggregated bids parameters used in linear programming constraints and incorporating them into the auction model is another contributing factor of this paper, allowing the scheduling of storage-based participants economically. The proposed methodology has been verified on a recently published case study of a real-world bus service operated on the Ohio State University campus. We show that the auction-based charging of all 22 buses outperforms as-soon-as-possible schedules by 7% to even 28% of daily cost savings. Thanks to the aggregated bids, buses can flexibly shift charges between high- and low-price periods while preserving constraints of the charging equipment and timetables.

Auctions with non-convexities, as considered in this paper, use a multi-period optimal power flow (OPF) model based on generators' offers to calculate efficient schedules. The standard locational marginal prices (LMPs) may not support these schedules and uplifts are needed to help the generators break even. This paper presents a direct minimum-uplift (DMU) pricing model, which is formulated as a mixed integer linear programming problem with uplift minimization objective. New DMU prices are major variables constrained with decomposition formula based on shift factors, similar to the actual practice of developing LMPs. The remaining constraints reflect the generators' profits and uplifts modeled as functions of the DMU prices. The main feature of the DMU model is individual rationality attained in pool-based auction, under prices properly reflecting network constraints, complemented with minimum uplifts. The model is validated on several cases, including the IEEE 24-node system.

As an active participant of a competitive energy market, the generator (the energy supplier) challenges new management decisions being exposed to the financial risk environment. There is a strong need for the decision support models and tools for energy market participants. This paper shows that the stochastic short-term planning model can be effectively used as a key analytical tool within the decision support process for relatively small energy suppliers (price-takers). A self-scheduling method for the thermal units on the energy market is addressed. A schedule acquired for given preferences can be used as a desired pattern for bidding process. The uncertainty of the market prices is modeled by a set of possible scenarios with assigned probabilities. Several risk criteria are introduced leading to a multiple criteria optimization problem. The risk criteria are well appealing and easily computable (by means of linear programming) but they meet the formal risk aversion standards. The aspiration/reservation based interactive analysis applied to the multiple criteria problem allows us to find an efficient solution (generation scheme) well adjusted to the generator preferences (risk attitude).

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