# THE STOCHASTIC UNIT COMMITMENT PROBLEM: A CHANCE CONSTRAINED PROGRAMMING APPROACH CONSIDERING EXTREME MULTIVARIATE TAIL PROBABILITIES

Ozturk, Ugur Aytun (2003) THE STOCHASTIC UNIT COMMITMENT PROBLEM: A CHANCE CONSTRAINED PROGRAMMING APPROACH CONSIDERING EXTREME MULTIVARIATE TAIL PROBABILITIES. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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## Abstract

Reliable power production is critical to theprofitability of electricity utilities. Power generators (units) need to be scheduled efficiently to meet the electricity demand(load). This dissertation develops a solution method to schedule units for producing electricity while determining the estimated amount of surplus power each unit should produce taking into consideration the stochasticity of the load and its correlation structure. This scheduling problem is known as the unit commitment problem in the power industry. The solution method developed to solve this problem can handle the presence of wind power plants, which creates additional uncertainty. In this problem it isassumed that the system under consideration is an isolated one such that it does not have access to an electricity market. In such a system the utility needs to specify the probability levelthe system should operate under. This is taken into consideration by solving a chance constrained program. Instead of using a set level of energy reserve, the chance constrained model determines the level probabilistically which is superior to using an arbitrary approximation. In this dissertation, the Lagrangian relaxation technique is used to separate the master problem into its subproblems, where a subgradient method is employed in updating the Lagrange multipliers. To achieve this a computer program is developed that solves the optimization problem whichincludes a forward recursion dynamic program for the unit subproblems. A program developed externally is used to evaluate high dimensional multivariate normal probabilities. To solve thequadratic programs of period subproblems an optimization software is employed. The results obtained indicate that the load correlation is significant and cannot be ignored while determining a schedule for the pool of units a utility possesses. It is also concluded that it is very risky to choose an arbitrary level ofenergy reserve when solving the unit commitment problem. To verify the effectiveness of the optimum unit commitment schedules provided by the chance constrained optimization algorithm and todetermine the expected operation costs, Monte Carlo simulations are used where the simulation generates the realized load according to the assumed multivariate normal distribution with aspecific correlation structure.

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## Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
Ozturk, Ugur Aytunaytunozturk@yahoo.com
ETD Committee:
Committee ChairNorman, Bryan Abanorman@engrng.pitt.edu
Committee MemberRajgopal, Jayantrajgopal@pitt.eduRAJGOPAL
Committee MemberMazumdar, Mainakmmazumd@pitt.eduMMAZUMD
Committee MemberSimaan, Marwansimaan@pitt.eduSIMAAN
Committee MemberIyengar, Satishssi@pitt.eduSSI
Date: 3 September 2003
Date Type: Completion
Defense Date: 1 July 2003
Approval Date: 3 September 2003
Submission Date: 18 July 2003
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Swanson School of Engineering > Industrial Engineering
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Chance Constrained Programming; Lagrangian Relaxation; Multivariate Probability Evaluation; Scheduling; Simulation; Unit Commitment
Other ID: http://etd.library.pitt.edu:80/ETD/available/etd-07182003-142758/, etd-07182003-142758
Date Deposited: 10 Nov 2011 19:51