Alexis L. Motto

Transmission expansion planning: a mixed-integer LP approach

This paper presents a mixed-integer LP approach to the solution of the long-term transmission expansion planning problem. In general, this problem is large-scale, mixed-integer, nonlinear, and nonconvex. We derive a mixed-integer linear formulation that considers losses and guarantees convergence to optimality using existing optimization software. The proposed model is applied to Garvers 6-bus system, the IEEE Reliability Test System, and a realistic Brazilian system. Simulation results show the accuracy as well as the efficiency of the proposed solution technique.

A mixed-integer LP procedure for the analysis of electric grid security under disruptive threat

This paper presents a solution procedure for the mixed-integer bilevel programming model of the electric grid security under disruptive threat problem, here concisely denoted by (ST-MIBLP), that was recently reported. Using results from linear programming theory and some basic linearization of products of binary-binary or binary-continuous variables, we recast (ST-MIBLP) into a standard (one-level) mixed-integer linear program (ST-MILP) with no more binary variables than in the original (ST-MIBLP). This transformation provides a framework for globally solving (ST-MIBLP) using available mixed-integer linear programming solvers. Some numerical results obtained by the new method are compared with those recently published, based on IEEE Reliability Test Systems.

Equilibrium of auction markets with unit commitment: the need for augmented pricing

We discuss issues and methods for attaining equilibrium in electric power auction markets with unit commitment. We consider a generation-side competition whereby producers are profit maximizing agents subject to prices only. For expository purposes, we will consider the single-period unit commitment problem, which is still quite rich for this presentation. We show that it is possible to eliminate the duality gap or cycling that occurs in a decentralized decision-making environment that encompasses discontinuous nonconvex programs. This result extends previous work on coordination of locally constrained self-interested agents, and it has a broad scope of applications that may be of interest to power systems engineers, market designers, economists, and mathematicians.

Reconciling social welfare, agent profits, and consumer payments in electricity pools

Under a common condition called profit suboptimality, market equilibrium cannot be reached in electricity pools; in other words, no system marginal price exists for which the profit-driven independent generators would self-schedule to levels that exactly meet the demand. On the other hand, although a centrally imposed generation schedule satisfies power balance, it may force some agents to operate at a profit below what they could achieve under self-scheduling. This paper examines these incompatible goals and proposes a conflict resolution scheme based on the notion of generalized uplift functions. These functions are defined such that they: (i) change the offered generation cost characteristics so as to increase the system marginal price, thus forcing the consumers to compensate the generators for part of their combined loss of profit; (ii) execute an equitable transfer of revenues among the generators so that these also participate in any loss of profit compensation; (iii) ensure market equilibrium at the centralized minimum cost solution; and (iv) ensure that the net sum of the uplifts adds up to zero.

On walrasian equilibrium for pool-based electricity markets

We present a single time period decentralized electricity market clearing model that includes reactive power and demand responsiveness in addition to the more common framework of generation-side competition for the real power commodity. The approach allows self-interested agents, namely producers and consumers, independently to maximize their individual surpluses subject to prices. This is consistent with the notion of a competitive market as defined in equilibrium theory. An auctioneer computes equilibrium prices that achieve power balance at every network node, as required by Kirchhoffs laws. The overall scheme is justified by duality theory, for which there is a rich theoretical support, and convergence is achieved using a Newton price-updating algorithm.

Decentralized Nodal-Price Self-Dispatch and Unit Commitment

This chapter sets forth a scheme for self-scheduling independent market participants in a power pool. The approach, named DNSA for Decentralized Nodal-Price Self-Scheduling Auction, is proposed as an alternative to centralized Pool auctions and operation. DNSA exploits the intrinsic parallelism of the dual unit commitment problem to decentralize the various scheduling and dispatch functions. Each competing participant (GENCO, DISTCO) maximizes its profit for any set of nodal prices by choosing its level of production or consumption. Similarly, the TRANSCO independently maximizes its merchandising surplus within the network security constraints. The price caller, a centralized entity without access to proprietary cost information, updates prices through an effective Newton algorithm until the power balance at each bus is satisfied. DNSA does not assume a perfect market and accounts for the AC load flow model including transmission losses and line congestion, in addition to integer variables, ramping rates, start-up costs, and minimum up and down times. The convergence of DNSA hinges on the notions of profit optimality and the convexifying market rule. We present several study cases to illustrate the characteristics of DNSA. We conclude that to achieve fairness of treatment for all competing participants, they should be allowed to optimize their profit by self-scheduling. Therefore, to the extent possible, the next generation of unit commitment models should include profit optimality.

Unit commitment with dual variable constraints

A new unit commitment model is proposed for market economies with some form of indivisibilities (nonconvexities). Coordination in electricity pool auction markets with unit commitment is a conspicuous example. This presentation applies to a single-time period unit commitment with no network. The new formulation includes a market coordinator who collects the sale and purchase bids, and determines the optimal solution that balances the total generation with the forecast demand. A solution to the new commitment model is said to be optimal if it maximizes the (monetary) margin of every accepted production unit, while minimizing the sum of the margins of the unaccepted units that would achieve positive margins at the prevailing market price. The new unit commitment model produces a market price that is the system-wide marginal (bid) cost. Some preliminary results are reported, considering the single-period unit commitment problem, which provide some insights into the adequacy of the proposed approach as well as its economic implications as a tool for managing restructured energy systems.

On the exact solution of a class of Stackelberg games

This paper presents a mixed-integer linear reformulation for a subclass of two-level nonlinear discrete-continuous decision problems also known as Stackelberg strategic games. Solving the original (two-level and nonlinear) model is algorithmically challenging. In fact, even global solvers for standard (or single-level) mixed-integer nonlinear programs are difficult to implement and relatively inaccessible. The proposed transformation allows solving this class of Stackelberg games using mixed-integer linear programming theory for which optimized solvers with large-scale computational capabilities have been reported. Furthermore, the proposed reformulation is achieved without adding any new integer variables to the original model, a desired computational property in case a large portion of the search tree has to be enumerated.

Power-Based Segmentation of Respiratory Signals Using Forward-Backward Bank Filtering

We present an automated method for the segmentation of ribcage and abdominal signals measured by noninvasive respiratory inductance plethysmography (RIP) into quiet breathing and artifact-corrupted segments. This procedure, which involves forward-backward filtering, is applicable to the automated off-line analysis of long records of respiratory signals. Examples of applications include home and sleep laboratory studies of cardiorespiratory data. The new procedure was successfully applied to the segmentation of cardiorespiratory signals acquired post-operatively from infants in the recovery room of the Montreal Childrens Hospital (MCH)

A Portable, PC-Based Monitor for Automated, On-line Cardiorespiratory State Classification

We have developed a monitor that acquires, classifies, annotates and displays patient cardiorespiratory data in an on-line and fully automated manner. The monitor is compact, portable and battery-operated; it applies automated methods that detect apnea and classify cardiorespiratory state on-line from non-invasive measurements of patient respiratory movements, blood oxygen saturation and heart rate, logging the raw and processed data. The monitor provides continuous, on-line, objective, standardized cardiorespiratory classification and has a graphical display and interface for patient monitoring by a clinician; it has immediate application in the clinical setting