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Unit Commitment With continuous-time Generation and Ramping Trajectory Models

IEEE TRANSACTIONS ON POWER SYSTEMS 2016年第4期31卷 3169-3178页

作者： Parvania, Masood Scaglione, Anna Univ Utah Dept Elect & Comp Engn Salt Lake City UT 84112 USA Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85287 USA

There is increasing evidence of shortage of ramping resources in the real-time operation of power systems. To explain and remedy this problem systematically, in this paper we take a novel look at the way the day-ahead unit commitment (UC) problem represents the information about load, generation and ramping constraints. We specifically investigate the approximation error made in mapping of the original problem, that would decide the continuous-time generation and ramping trajectories of the committed generating units, onto the discrete-time problem that is solved in practice. We first show that current practice amounts to approximating the trajectories with linear splines. We then offer a different representation through cubic splines that provides physically feasible schedules and increases the accuracy of the continuous-time generation and ramping trajectories by capturing sub-hourly variations and ramping of load in the day-ahead power system operation. The corresponding day-ahead UC model is formulated as an instance of mixed-integer linear programming (MILP), with the same number of binary variables as the traditional UC formulation. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of events of ramping scarcity in the real-time operations.

关键词： continuous-time function space generation trajectory mixed-integer linear programming ramping trajectory unit commitment

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Generation Ramping Valuation in Day-Ahead Electricity Markets 49

Generation Ramping Valuation in Day-Ahead Electricity Market...

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49th Hawaii International Conference on System Sciences (HICSS)

作者： Parvania, Masood Scaglione, Anna Univ Utah Dept Elect & Comp Engn Salt Lake City UT 84112 USA Arizona State Univ Sch Elect Comp & Energy Engn Tempe AZ 85287 USA

ISBN: (纸本)9780769556703

In this paper, we first introduce a variational formulation of the Unit Commitment (UC) problem, in which generation and ramping trajectories of the generating units are continuous time signals and the generating units cost depends on the three signals: the binary commitment status of the units as well as their continuous-time generation and ramping trajectories. We assume such bids are piecewise strictly convex time-varying linear functions of these three variables. Based on this problem derive a tractable approximation by constraining the commitment trajectories to switch in a discrete and finite set of points and representing the trajectories in the function space of piece-wise polynomial functions within the intervals, whose discrete coefficients are then the UC problem decision variables. Our judicious choice of the signal space allows us to represent cost and constraints as linear functions of such coefficients;thus, our UC models preserves the MILP formulation of the UC problem. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day ahead and real-time operation cost, and the number of ramping scarcity events in the real-time operations.

关键词： Unit commitment generation trajectory ramping trajectory ramping cost continuous-time function space mixed-integer linear programming

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Generation Ramping Valuation in Day-Ahead Electricity Markets

Generation Ramping Valuation in Day-Ahead Electricity Market...

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Hawaii International Conference on System Sciences

作者： Masood Parvania Anna Scaglione Department of Electrical and Computer Engineering University of Utah School of Electrical Computer and Energy Engineering Arizona State University

ISBN: (纸本)9781509019816

In this paper, we first introduce a variational formulation of the Unit Commitment (UC) problem, in which generation and ramping trajectories of the generating units are continuous time signals and the generating units cost depends on the three signals: the binary commitment status of the units as well as their continuous-time generation and ramping trajectories. We assume such bids are piecewise strictly convex time-varying linear functions of these three variables. Based on this problem derive a tractable approximation by constraining the commitment trajectories to switch in a discrete and finite set of points and representing the trajectories in the function space of piece-wise polynomial functions within the intervals, whose discrete coefficients are then the UC problem decision variables. Our judicious choice of the signal space allows us to represent cost and constraints as linear functions of such coefficients;thus, our UC models preserves the MILP formulation of the UC problem. Numerical simulation over real load data from the California ISO demonstrate that the proposed UC model reduces the total day-ahead and real-time operation cost, and the number of ramping scarcity events in the real-time operations.

关键词： Unit commitment Generation trajectory Ramping trajectory Ramping cost continuous-time function space Mixed-integer linear programming

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