haldia institute of technology

8/8/2019 Haldia Institute of Technology

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HALDIA INSTITUTE OF TECHNOLOGY

ECONOMIC LOAD DISPATCH PROBLEMCONSIDERING TRANSMISSION LOSS

BY

Abhishek Basu(06/EE/14)

Prithwiraj Roy(06/EE/19)

Kalyanbar Sarkar(06/EE/20)

Rajib Manal(06/EE/28)

Under

Mr.Budhaditya Biswas

DEPARTMENT OF ELECTRICAL ENGINEERING

HALDIA INSTITUTE OF TECHNOLOGY


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The Head

Department of Electrical Engineering

Haldia Institute of TechnologyHIT/ICARE Complex

PO-Hatiberia,HaldiaMidnapore (E),West Bengal-721 657

Respected Sir,

In accordance with the requirements of the degree of bachelor of Technology in the department

of Electrical Engineering , Haldia Institute of Technology. I present the following thesis entitled

ECONOMIC LOAD DISPATCH PROBLEM CONSIDERING

TRANSMISSION LOSS.

This work was performed under the supervision of Mr.Budhaditya Biswas.

.

We declare that the work submitted in this thesis is our own except as acknowledge in the text

and references ,and has not been previously submitted for a degree at the Institute or any other

Institution.

Your Sincerely, Guided by

Abhishek Basu (06/EE/14) (....)

Prithwiraj Roy(06/EE/19)

Kalynbor Sarkar(06/EE/20)

Rajib Mandal(06/EE/28) Mr.Budhaditya Biswas


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CERTIFICATE

This is to certify that the thesis entitled ECONOMIC LOAD DISPATCH PROBLEM

CONSIDERING TRANSMISSION LOSS

.is a bona fide work carried by mukesh kumar layak in partial fulfillment of the requirement for

the degree of BACHELOR OF TECHNOLOGY in ELECTRICAL ENGINEERING under

supervision of Mr.Budhaditya Biswas

during the academic year 2008-2009 & this has not been submitted elsewhere for a similardegree.

Countersigned by

Dr. Prithwiraj Purkait

Head

Department of Electrical Engineering

Haldia Institute of Technology

Haldia


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ACKNOWLEDGEMENT

Apart from the efforts of ours, the success of this project depends largely on the encouragement

and guidelines of many others. I take this opportunity to express our gratitude to the people who

have been instrumental in the successful completion of this project.

I would like to show my greatest appreciation to Mr. Budhaditya Biswas

I cant say thank you enough for their tremendous support and help. I felt motivated and

encouraged every time when they came for helping me. Without their encouragement and

guidance this project would not have materialized.

The guidance and support received from other sir in department to this project, was vital for the

success of the project. I am grateful for their constant support and help.


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INTRODUCTION

Economic operation and planning of electric energy generating systems have always been given

proper attention in the electric power system industry. A saving in the cost of generation

represents a significant reduction in the operating cost (including the fuel cost) and this area has

warranted a great deal of attention from operating and planning engineers. The original problem

of economic dispatch of thermal power generating system used to be solved by numerous

methods. However, with the development of mathematical tools and advanced computational

methods, the economic scheduling of generators has become more accurate and can be applied

even in complex networks. Thermal scheduling being the prime importance, hydrothermal

coordination scheduling has emerged as another aspect of economic scheduling.

The basic purpose of economic operation of power system is to reduce fuel cost

for the operation of power system, economic operation is achieved when the generators in the

system share load to minimize overall generation cost. The main economic factor in the power

system operation is the cost of generation real power. In any power system, this cost has two

components, viz.,

The fixed being determined by the capital investment, interest charged on the moneyborrowed, tax paid, labour charge, salary given to staff and any other expenses thatcontinue irrespective of the load on the power system, and

The variable cost, a function of loading on generating units, losses, daily loadrequirements and purchase or sale of power.

The present text relating the economic operation of a power system is concerned about

minimising the variable cost factor only as the persons responsible for the operation of a

power system have little control over the fixed costs.

A power system is a mix of different modes of generation out of which thermal, hydro

and nuclear contribute a major share. However, economic operation has conventionally been

considered by proper scheduling of thermal or hydrogenation only or both, as, for the safety of

nuclear station, these types of stations are required to be operated at a fixed load only and there

is little scope to schedule the generation of nuclear type in practice.


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INPUT-OUTPUT OPERATIONAL CHARACTERISTICS OF DIFFERENT

POWER PLANTS

Thermal generating unit :

It is a well-established physical principal that with increase in difference between the

temperature and pressure of the input and output of any heat operated device (say, a turbine),

more mechanical power will be developed for the same amount of heat energy input. The

overall efficiency of thermal units is then determined by measuring he heat input, i.e. the

electrical energy output. Conventionally, this represents input-output curves and can be

developed for each generating unit involved. An efficient unit develops a given amount of

power with less fuel input. Hence, it has become the usual practice to load the more efficient

unit before loading the lesser efficient unit.


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Hydel power station:

The input-output characteristics for a typical hydro unit has been shown below. Though

apparently it may seen that the input of a hydro plant costs nothing, but a little thinking reveals

that the input water flow costs are due to capacity of the storage, agricultural requirement and

cost of running the plant during dry season. Also, artificial storage requirement imposes cost to

control the water output from the turbine due to agricultural needs.


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INCREMENTAL FUEL RATE (IFR) CURVES

The input-output curves, obtained from the operating data of power station, can be utilized to

get the incremental fuel rate (IFR or IR) curve from the relation.

IFR = incremental change in input /incremental change in output

Thus, by calculating the shape of the input-output curves at various points of operation, the

profile ofIFR can be obtained. IFR profiles for typical thermal and hydro power stations are

shown below.


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INCREMENTAL FUEL COST (IFC) CURVE

This curve can be obtained from IFR curve by multiplying the IFR by the cost of fuel per Kcal.

As in a power station, fuel cost governs the actual total cost. Hence, IFC is very significant in

economic loading of the generation unit. The IFC curves will be similar to the IFC characteristic

in configuration.

It is obvious that the slopes of the input-output curve and incremental fuel rate curve

do not change for different fuels or change in the cost of the same fuel. This time a multiplying

factor may be used so that the actual cost is a realistic one. The unit ofIFC (or simply the IC) is

unit of cost/MWhr.


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CONSTRAINTS IN ECONOMIC OPERATION OF POWER SYSTEM

Primary Constraints:

These constraints arise out of the necessity for the system to balance the load demand and

generation. They are also called equality constraints. If Pi and Qi are the scheduled electrical

generation, Ploadi and Qloadi are the respective load demands, it is obvious that the following

equation must be satisfied at the load bus.

Real power position at load bus

Pi Ploadi Pl = Mi = 0

Qi Qloadi - Ql = Ni = 0

Where Mi and Ni represents the power residuals at bus-i and Pl and Ql the power flow to the

neighbouring system given by

Pl = j=1N

ViVjYij cos(ij-ij)

Ql = j=1N

ViVjYij sin(ij-ij)


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Secondary Constraints:

These constraints arise due o physical and operational limitations of respective units ands

components and are known as inequality constraints. Power inequality constraints are applicable

for proper operation; for each generator we should have a minimum and maximum permissible

output and the unit production should be constrained to ensure that

Pimin Pi Pimax, i= 1,2,., NP

Qimin Qi Qimax , i= 1,2,.., NQ

NP and NQ being the total number of real and reactive sources in the system.

In addition to their inequality constraints, another constraints Pi2+Qi2(Sirated)2 must be satisfied,

where Sirated denotes the complex power capability of the generating unit without any

overloading.

Dynamic Constraints:

These constraints arise where fast changes in generation are required for picking up the

increasing load demand. Here,

dPi(t)/dtat=min dPi(t)/dt dPi(t)/dtat=max

Similarly, for reactive power constraints,

dQi(t)/dtat=min dQi(t)/dt dQi(t)/dtat=max


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Spare Capacity Constraints:

In order to account for the errors in load prediction, any sudden and fast change in load demands

and the inadvertent loss of scheduled generation, spare capacity constraints are frequentlyutilised. In this constraints, the total generation available at any time should be in excess of he

total anticipated load demand and any system loss by an amount not less than a specified

minimum spare capacity PSPS.

Therefore, Pig i=1N Pl+PSPS+Ploadi

For groups of generators, when all plants are not equally operationally suitable for taking up

additional load, this constraints is then given by

Pig Pl+PSPS+Ploadi

Where PSPS is the spare capacity generation for specified generators.


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Thermal Constraints of Transmission Lines:

These constrains arise when power injection (+S) or power drawl (-S) is allowed such that

[Simax] Str [Simin], i= 1,2,(tr)n

Where (tn)n represents the number of branches and Str the branch power transfer in MVA.

Bus Voltage and Angle Constraints:

These constraints arise in order to maintain voltage profle at load bus and limiting the overload

capacity.

Here,

Vimin Vi Vimax, i= 1,2,., N

imin i imax , j 1 j=2,.., M

whee N represents the number of units and M the number of loads in the system.

Operatonal Constraints:

In case the transformer tap position needs to be included for optimization, the tap position ai

should lie within the range available in the transformer, i.e. aimin ai aimax.


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Optimal Operation

Let us assume that it is known a priori which generators are to run to meet a particular loaddemand on the station. This is, given a station with h generators committed and the active power

load PD given, the real power generation PGi for each generator has to be allocated so as tominimize the total cost.

k

C= 7 Ci (PGi) (Rs/h) (1)

i=1

Subject to the inequality constraint

PGi min< PGi < PGi max i=1, 2... k (2)

Where PGi min and PGi max are the lower and upper real power generation limits of the ith

generator. Obviously,

k

7 PGi max >PD (3)

i=1

Considerations of spinning reserve require that


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7 PGi max > PD

In Eq.1, it is assumed that the cost C is largely dependent on the real power

generation PGi and is insensitive to reactive power generation QGi.

Since Ci (PGi) is nonlinear, and Ci is independent of PGj (j{i), this is a separablenonlinear programming problem.

Only the inequality constraint of Eq. (3) is not effective, and between total power

generation and load demand is

k

7 PGi PD =0 (4)

i=1

The problem can then be solved by the method ofLagrange multipliers, which is used for

minimizing (or maximizing) a function with side conditions in the form of equality constraints.

Using this method we define an augmented cost function (Lagrangian) as

_ k


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C = C -P (7 PGi PD ) (5)

i=1

Where P is the Lagrangian multiplier.

Minimization is achieved by the condition

_

xC /x PGi =0

or dCi/dPGi = P, i = 1, 2,, k (6)

Where dCi/dPGi is the incremental cost of the ith generator (units: Rs/MWh).

Equation (6) can be written as

dC1/dPG1 = dC2/dPG2=.. = dCn /dPGn =P (7)

i.e., optimal loading of generators corresponds to the equal incremental cost point of all the

generators. Equation (4), called the coordination equation numbering n is solved

simultaneously with the load demand in equation 13, to yield a solution for the Lagrange

multiplier P and the optimal generation of n generators.


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Economic allocation of generator between different plants in a

system considering system transmission loss( economic

dispatch) :

Economic allocation of generator between different generating plants has been

considered previously. When considering the economic allocation of generation between

different plants in an integrated system, the transmission losses are to be considered. This

leads to the dispatch of power in an economical way so as to make the overall cost to be

minimum , Let there be N plants in a system interconnected by transmission line and

ties

Let P1, P2,PNrefer to the generation ofN plants, respectively in MW . Let

the total load be Pload(constant)and loss in the lines be Pl.. The constraint equation will be

i=1N -Pi+Pl+Pload=R

(Rbeing the residual power and should approach zero during steady state power system

operation)


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Let the net fuel input cost per hour be F which is the summation of fuel costs per hour of

each of the units governed by the generator powerP,

i.e. F =i=1NFi(Pi) Rs/hr

application of Lagrangian technique in order to optimize real power generation gives

L=F+,be the multiplier , necessary condition for cost function to be minimum has

been obtained by setting the first derivative of the lagrangian with respect to each of the

independent variable to zero, i,e. L/Pi =0.

Here L =F+(i=1N-Pi+Pl+Pload) and with L/Pi=0 we can write

dFi(Pi)/dPi (1-Pi/Pl)=0

or, dFi(Pi)/dPi + Pl/Pi =

this equation represents the modified economic operation criterion for the thermal plants

with transmission losses considered.

This equation may be written as

dFi(Pi)/dPi[1/1-Pl/Pi] =

or dF(Pi)/dPi*PFi =


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PFi =[1- Pl/Pi]-1

PFi is known as Penalty factor the equation is known as the exact coordination equation .

in dFi(Pi)/dPi beang the incremental cost Pl/Pi known as the incremental

transmission loss. N number of optimum dispatch equations along with the constraint

suffice for determining (N+1) unknown P1,P2,..Pn and .

[i.e Pi-Pl=Pload

thus dF(Pi)/dPi*PFi = dF(Pi)/dPi*1/1- (Pi-Pl) = dF(Pi)/dPi * Pi-Pload

== dFi(Pi)/dPload

When dFi(Pi)/dPload is the incremental cost of the received power for plant i and the

penalty factor Pi-Pload . this also means that as Piincremental has a longer

proportion dissipated as loss, (Pi-Pload) approaches unity and the penalty factorPFi ,

increases without bound , thus for a larger penalty factor unit-i should be operated at low

increment cost implying a low power output.]

For N number of plants the coordination equation are given as

dF1(P1)/dP1 [1- dPl/dP1]= 0

dF2(P2)/dP2 [1- dPl/dP2]= 0

.

.

.

dFN(PN)/dPN [1- dPl/dPN]= 0


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while the constraints equation is given by

i=1N(Pi)+Pload+Pl= R

If the numerical value f the partial derivative of the line losses with respect to each

generator output (dPl/dPi) is known, the generator output power may be adjusted to

satisfy the following equation

dFi(Pi)/dPi[1/(1-dPl/dPi)]=, i=1,2,3..N

the optimal economy is thus achieved when the products of the incremental fel cost times

the penalty factor is the same for all plants,

i.e.

dF1(P1)/dP1PF1= dF2(P2)/dP2PF2=..= dFN(PN)/dPNPFN =

stands here for the incremental cost f the received power in unit of (currency/MWhr)

and hense during economic operation of plants with losses being considered,

= Incremental fuel cost/(1-Incremental transmission loss)


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Mathematical Calculation:

Consider a simple power system consisting of two generating plants and one load as shown in

below figure

Plant 1 I1 I2 plant 2

A C B

I1+I2

Fig: a simple system connecting two generating plants to one load

Let Rac, Rbc, and Rcd be the resistance of the lines AC,BC and CD respectively. For the given

system we can write the transmission loss as

PL = 3 I1^2 Rac + 3 I2^2 Rbc + 3 I1 + I2^2 Rcd (1)

If we assume that I1 and I2 are in phase,

I1 + I2 = I1 + I2 (2)


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PL = 3 I1^2 (Rac + Rcd ) + 3 I2^2 (Rbc + Rcd ) + 6 I1 I2 Rcd

(3)

Let P1 and P2 be the three-phase power output of plants 1 and 2 at P.F of COS J1 andCOS J2, and V1 and V2 be the bus voltage at the plants.

I1 = P1 / (3 V1 COS J1 ), I2 = P2 / (3 V2 COS J2 )

Substituting the values of I1 and I2 in equation (3) we get

PL = P1^2 (Rac + Rcd ) + 2 P1P2 Rcd + P2^2 Rac + Rcd

V1 ^2 cos J1^2 V1 V2 cos J1cosJ2 V1^2 cos J1^2...(4)

Equation (4) can be written as

PL = P1^2 B11 + 2 P1P2B12 + P2^2 B22

Where, B11 = (Rac + Rcd ) , B12 = Rcd

V1 ^2 cos J1^2 V1 V2 cos J1cosJ2


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B22 = Rac + Rcd .. (5)

V1^2 cos J1^2

The terms B11, B12 and B22 are called loss coefficient

If the voltage in equation (5) is line-to-line voltages in kilo volts and line resistances are in ohms,

the unit for the loss coefficients will be in reciprocal megawatts. Then, in equation (4) with three-

phase powers in megawatts, PL will be in megawatts also. If all the quantities are in per unit, te

coefficients will be in per unit.

It is seen that the loss coefficients depend on source voltages and p.f. The source voltages

and p.f depends on and vary with system conditions. However B coefficients are constants. It is

sufficiently accurate to calculate B coefficient for some average operating conditions use these

value for economic loading for all the load variations. However for large load variation or major

system changes, several sets of loss coefficients are used.


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