Abstract—
Due to uncertainty of wind velocity, wind power
generators don’t have deterministic output power. Utilizing wind
power generation and thermal power plants together creat e new
concerns for operation engineers of power s ystems. In this paper, a
model is presented to implement the uncertainty of load and
generated wind power which can be utilized in power system
operation planning. Stochastic behavior of parameters is simulated by
generating scenarios that can be solved by deterministic method. A
mixed-integer linear programming method is used for s olving
deterministic generation scheduling problem. The proposed approach
is app lied to a 12-unit test system including 10 thermal units and 2
wind farms. The results show affectivity of piecewise linear model in
unit commitment problems. Also using linear programming causes a
considerable reduction in calculation times and guarantees
convergence to the global optimum. Neglecting the uncertainty of
wind velocity causes higher cost assessment of generation
scheduling.
Keywords—
Load uncertainty, linear programming, scenario
generation, unit commitment, wind farm.
I. I
NTRODUCTION
UE to increasing cost of fuels, there is a profound trend
in using wind power. As the amount of wind power
generation increases, concerns due to its effects on power
system operation and expenses increases. As the wind is an
intermittent power supply, developing forecasting tools is so
useful. Though the forecasting tools become more accurate
day by day, in the absence of a perfect estimation, decision
about unit commitment should be done with uncertainties.
Researchers have considered uncertaint y of imprecise
parameters using one of these two methods: fuzzy systems
approach and probabilistic (stochastic) approach. Stochastic
programming considers stochastic variables and uncertainty in
conventional linear and nonlinear programming. Discussed
randomness and uncertainty are generally represented using a
probability density function (PDF).
Unit commitment problem is an important optimization
process to determine on/off scheduling of units in power
system operation. The purpose is to minimize the total cost of
system operation in order to satisfy system load demand and
other constraints. Unit commitment problem is generally a
nonlinear, large scale, and mixed integer combinatorial
problem. This problem has been a dynamic research topic in
the recent decades because of potential savings in operation
M. Esmaeeli Shahrakht is with Department of Electrical Engineering, Iran
University of science and technology, Tehran, Iran. (Corresponding author to
provide phone: +98-915-5623937; e-mail: m[email protected]).
A. Kazemi is with Department of Electrical Engineering, Iran University of
science and technology, Tehran, Iran. (e-mail: kaz[email protected]).
costs. As a result numerous methods including heuristics
methods [1], [2], dynamic programming [3], genetic algorithm
[4], Neural Networks, Fuzzy Systems [5], mixed integer linear
programming [6], and Lagrangian relaxation [7]-[10] have
been suggested. Among these methods Lagrangian relaxation
is the most widely used approach because of its capability in
solving large scaled problems. The most important defect of
this approach is that it is required heuristics methods to
achieve feasible solutions which might be suboptimal, due to
nonconvexities of unit commitment problem. In contrast,
mixed integer linear programming guarantees convergence to
an optimal solution in a few steps. Moreover, it provides
precise and flexible modeling framework [11]. One of the first
efforts for solving unit commitment problem using stochastic
optimization approach is presented in [12]. In this work the
possible future result for the demand are shown with a
scenario tree. In this method, it is assumed that only a limited
number of scenarios are possible because using all the possible
scenarios is computationally impossible. Authors have tested
their method using 100 scenarios and a 48-hour time horizon.
A stochastic model for long-term security constrained unit
commitment is used in [13], which outage of generating units,
transmission lines and load prediction errors are considered.
In this paper, stochastic unit commitment of thermal power
plants and wind farms is implemented with constraints for
wind power generation. Wind speed uncertainties during each
period of operation time is implemented through several
scenario based on the wind speed PDF. To employ the mixed
integer linear programming method and achieving global
optimum, fuel cost function of thermal units is approximated
by a set of piecewise block such that it is not distinguishable
from the nonlinear model.
The main contributions of this work are as follows:
1. Presenting a stochastic scheduling method for solving
stochastic wind-thermal unit commitment problem.
2. Presenting a linear model of unit commitment problem to
solve the problem using linear programming tools.
3. Appropriate envelopment of forecasting error using
application of Monte Carlo simulation for scenario
generation.
The rest of this paper is organized as follows. In Section II,
the proposed approach to model stochastic unit commitment is
introduced. In Section III, problem formulation and problem
constrained are discussed. As a sample problem, 12-unit test
system (including 10 thermal generating units and 2 wind
farms) is employed to be solved using optimization method in
Section IV. Conclusions are given in Section V.
M. Esmaeeli Shahrakht, A. Kazemi
Linear Programming Application in Unit Commitment
of Wind Farms with Considering Uncertainties
D
World Academy of Science, Engineering and Technology
International Journal of Electrical, Computer, Energetic, Electronic and Communication Engineering Vol:7, No:2, 2013
242International Scholarly and Scientific Research & Innovation 7(2) 2013 scholar.waset.org/1999.5/9996930
International Science Index, Electrical and Computer Engineering Vol:7, No:2, 2013 waset.org/Publication/9996930
