2014-Economic dispatch.pdf

8/9/2019 2014-Economic dispatch.pdf

1/24

Economic Dispatch of Thermal

Unit


2/24

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.


3/24

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


4/24

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


5/24

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


6/24

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


7/24

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.


8/24

Example


9/24

Example Solution


10/24

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.


11/24

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


12/24

When we recognize the inequality constraints,then the necessary conditions may be expanded

slightly


13/24

Example (2)


14/24


15/24


16/24

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:


17/24

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


18/24

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


19/24

Example (3)


20/24


21/24


22/24


23/24


24/24

Task

Do Problem 3.1. and 3.3Book : Power Generation Operation and

Control, Allen J. Wood.

Documents

2014-Economic dispatch.pdf