2014-economic dispatch.pdf
TRANSCRIPT
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Economic Dispatch of Thermal
Unit
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Economic Dispatch
Economic Dispatch (ED) yaitu menentukankeluaran (dispatch) daya masing-masing unit
pembangkit pada kondisi beban tertentu
sehingga biaya produksi dapat diminimalkan.
Pada Economic Dispatch (ED) beban sistem
dialokasikan diantara unit-unit pembangkit
secara optimal untuk memenuhi persamaan
kesetimbangan daya dan batasan operasisistem dan masing-masing unit pembangkit.
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The Economic Dispatch Problem
Consider a system that consists of N thermal-generating units serving an aggregated electrical
load, Pload
input to each unit: cost rate of fuel consumed, Fi
output of each unit: electrical power generated, Pi
total cost rate, FT, is the sum of the individual unit
costs
Essential constraint:
the sum of the output powers must equal the load
demand
the problem is to minimize FT
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Problem Formulation
Problem Formulation :
Objective Function
Min FT
FT = F1 + F2 + F3 + ... + FN
Subject to constraint :
P P Load
N
i
i
1
)(1
P F i
N
i
iT F
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Solution Methods
Mathematical Programming (Heuristical) based Lagrange Relaxation (LR)
Lambda Iterative method
Gradient Search (projection) method
Newton’s method
Dynamic Programming (DP) method
Linear Programming (LP) or Non Linear Programming (NLP) methods
Artificial intelligent based methods
Genetic Algorithm (GA), Simulated Annealing (SA), Evolutionary
Programming (EP), Differential Evolution (DE), Particle Swarm
Opimization (PSO). Hybrid methods
Combine two or more techniques previously mentioned in order to get
best features in each algorithm
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Lagrange Relaxation Methods
ED Problem may be solved using the Lagrangefunction
In order to establish the necessary conditions for
an extreme value of the objective function, add
the constraint function to the objective function
after the constraint function has been multiplied
by an undetermined multiplier ().
This is known as the Lagrange function
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LR Principle
The Lagrange function establishes the necessary conditionsfor finding an extrema of an objective function with constraints
The necessary conditions for an extreme value of the objective
function result when we take the first derivative of the
Lagrange function with respect to each of the independent
variables and set the derivatives equal to zero.
Thus
The necessary condition for the existence of a minimum costoperating condition for the thermal power system is that the
incremental cost rates of all the units be equal to some
undetermined value.
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Example
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Example Solution
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Exercise
The input - output characteristics of twogenerating units are as follows:
F 1 = 0.0008 P12 + 0.2 P1 + 5
F 2 = 0.0005 P22 + 0.3 P2 + 4 Determine the economic operation point for
these two units when delivering a total of
500 MW power demand.
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LR Principle (2)
We must add the constraint equation that the sum of thepower outputs must be equal to the power demanded by
the load.
In addition, there are two inequalities that must be
satisfied for each of the units. The power output of each unit must be greater than or equal to
the minimum power permitted
and must also be less than or equal to the maximum power
permitted on that particular unit.
Thus
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When we recognize the inequality constraints,then the necessary conditions may be expanded
slightly
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Example (2)
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Economic Dispatch With Network Losses
Consider a similar system, which now has atransmission network that connects the generating
units to the load
The economic dispatch problem is slightly more
complicated The constraint equation must include the network
losses, Ploss
The objective function, FT is the same as before
The constraint equation must be expanded as:
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The transmission network loss is a function of the impedances and the
currents flowing in the network
for convenience, the currents may be considered functions of the
input and load powers
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Solution Procedure
The same math procedure is followed to establish thenecessary conditions for a minimum-cost operating
solution
it is more difficult to solve this set of equations
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Example (3)
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Task
Do Problem 3.1. and 3.3Book : Power Generation Operation and
Control, Allen J. Wood.