Extra Objective Research Articles

Normal boundary intersection method for suppliers’ strategic bidding in electricity markets: An environmental/economic approach

In this paper the problem of developing optimal bidding strategies for the participants of oligopolistic energy markets is studied. Special attention is given to the impacts of suppliers’ emission of pollutants on their bidding strategies. The proposed methodology employs supply function equilibrium (SFE) model to represent the strategic behavior of each supplier and locational marginal pricing mechanism for the market clearing. The optimal bidding strategies are developed mathematically using a bilevel optimization problem where the upper-level subproblem maximizes individual supplier payoff and the lower-level subproblem solves the Independent System Operator’s market clearing problem. In order to solve market clearing mechanism the multiobjective optimal power flow is used with supplier emission of pollutants, as an extra objective, subject to the supplier physical constraints. This paper uses normal boundary intersection (NBI) approach for generating Pareto optimal set and then fuzzy decision making to select the best compromise solution. The developed algorithm is applied to an IEEE 30-bus test system. Numerical results demonstrate the potential and effectiveness of the proposed multiobjective approach to develop successful bidding strategies in those energy markets that minimize generation cost and emission of pollutants simultaneously.

Multi-objective market clearing of joint energy and reserves auctions ensuring power system security

A model and solution approach to day-ahead market clearing of joint energy and reserves auctions is proposed in this paper. The model represents the clearing system used by ISO in charge of both the market operation and system security. A Multiobjective Mathematical Programming (MMP) formulation is implemented for provision of ancillary services (Automatic Generation Control or AGC, Spinning, Non-spinning and operational reserves) as well as energy in simultaneous auctions by pool-based aggregated market scheme. System security is taken into account in the market clearing procedure as the extra objective functions of the optimization problem. So, in the MMP formulation of the market clearing process, the objective functions (generation cost and security indices) are optimized while meeting AC power flow constraints, system reserve requirements and lost opportunity cost (LOC) considerations. The model is applied to the IEEE 24-bus Reliability Test System (IEEE 24-bus RTS), and simulation studies are carried out to examine the effectiveness of the proposed method.

Incorporating power system security into market‐clearing of day‐ahead joint energy and reserves auctions

AbstractThis paper is intended to introduce a technique for incorporating system security into the clearing of day‐ahead joint electricity markets, with particular emphasis on the voltage stability. A Multiobjective Mathematical Programming (MMP) formulation is implemented for provision of ancillary services (Automatic Generation Control or AGC, spinning, non‐spinning, and operating reserves) as well as energy in simultaneous auctions by pool‐based aggregated market scheme. In the proposed market‐clearing structure, the security problem, as an important responsibility of ISO, is addressed and a nonlinear model is formulated and used as the extra objective functions of the optimization problem. Thus, in the MMP formulation of the market‐clearing process, the objective functions (including augmented generation offer cost, overload index, voltage drop index, and loading margin) are optimized while meeting AC power flow constraints, system reserve requirements, and lost opportunity cost (LOC) considerations. The IEEE 24‐bus Reliability Test System (RTS 24‐bus) is used to demonstrate the performance of the proposed method. Copyright © 2008 John Wiley & Sons, Ltd.

SU‐FF‐T‐166: Different Method of IMRT Planning for Breast Treatment

Purpose: To compare three different methods of IMRT planning for breast treatment. Method and Material: Breast IMRT plans are conducted for several Patients using Pinnacle PHILIPS system. Three IMRT methods have been utilized; the first is Forward Planning (FP) technique using segment weight optimization for selected set of objectives such as GTV, PTV, lung, heart, etc. The second method is Inverse planning (IP) technique using Direct Machine Parameters Optimization (DMPO) with same objectives used in FP plus an extra segment to account for flash. The third is IP technique using DMPO with same objectives used in FP plus an extra objective called “Flash Planning Target (FPT)” defined by expanding the PTV by 2.5–3.0 cm in the interior direction of the breast depending on the required amount of flash. The “FTP” objective is defined as a uniform dose with 80% or higher of the prescribed dose with an extremely minimum dose in the order of 1E‐15. “FPT” objective is included in the DMPO to generate sufficient flash (due to breathing parameter) which could not have happen without including this objective in the IP optimization. Comparing all methods, IP technique using the two DMPO methods will allow having a Flash for most of the treatment without defining segments and they will give better coverage of the breast from the superior and inferior direction with better controlling the dose to the surrounding organs. Results: Using the “FPT” objective along with DMPO techniques provide the open segment higher percentages for each beam with some other segments generated by Pinnacle not by the planner are superior over FP method. Conclusion: Inverse planning techniques using DMPO technique mentioned above will give a better coverage of the breast from the superior and inferior direction with better controlling the dose to the surrounding healthy tissues.