the impact of facts devices on generation reallocation and load shedding of a power

8/13/2019 The Impact of Facts Devices on Generation Reallocation and Load Shedding of a Power

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THE IMPACT OF FACTS DEVICES ON GENERATION REALLOCATION AND LOAD SHEDDING OF A

POWER

www.BEProjectReport.com Page 2

CHAPTER 1

INTRODUCTION

1.1LOAD FLOW ANALYSISThe operational feature of a composite power system can be determined by symmetrical steady

state. But three major problems encountered in this mode of operation are listed.

Load flow problem

Optimal load flow scheduling problem

System control problem.

Load flow study is the steady state solution of the power system network. The solutions provides

magnitude & phase angles of load bus voltage, creative power at generating bus real and reactive

power flow on transmission line. It also gives the initial conditions of the system when the transient

behavior of the system is to be studied. The load flow study of a power system is essential to decide

the best operation of existing system and for planning the future expansion of the system.

1.2DEVELOPMENTS IN LOAD FLOW ANALYSISBefore the advent of digital computers, AC calculating board was the only means of carrying out

load flow studies. These studies were therefore, tedious and time consuming. With the availability of

fast and large size digital computers, all kinds of power system studies, including load flow, can now

be carried out conveniently. In fact some of advance level sophisticated studies which were almost

impossible to carry out on the AC calculated boards have now become possible by MAT lab

software.

There are different types of iterative algorithm for solving load flow studies in MAT lab

software as follows:

Gauss method

Gauss-Seidel method

Newton-Raphson method

Decoupled Newton method

Fast Decoupled load flow

New Power flow method

Gaussmethod is a simplest method to calculate load flow analysis. The number of iterations in

this method is more and it is much slower to converge, sometimes fail to do so Gauss Seidelmethod

is used. In Gauss Seidel method calculations are simple and programming task is lesser and its

memory requirement is less but there are many disadvantages in this method they are:


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Require large number of iterations to reach convergence

Not suitable for large systems

Convergence time increases with size of system

The above problems can be rectified in Newton-Raphson method. It is a powerful flow method of

solving non- linear algebraic equations. It has the following advantages.

This method is faster, more reliable and the results are accurate

Require less number of iterations for convergence.

The number of iterations are independent of the size of the system

Suitable for large systems

Its only drawback is the large requirement of computer memory. To reduce the memory

requirements decoupled load flowmethod is used. It is not much of an advantage from the point ofview of speed. Since the time per iteration of the DLF is almost the same as that of NR method and it

always takes more number of iterations to converge because of the approximation. A Fast Decoupled

Load Flow is carried out to achieve some speed advantage without much loss in accuracy of solution

using the DLF model. In above all the methods frequency is not considered but during abnormal

conditions frequency changes occurs so a new method has been developed called New Power Flow

Method. This method has the following advantages:

Used for the steady state behavior of large complex power systems

It allows study power flow in normal as well as abnormal conditions.

Demandsupply unbalance is distributed between among all generators

Get exact and accurate results.

1.3 CONTRIBUTIONS TO PROJECT WORK

The load flow calculations for 3-bus, 5-bus and 24-bus are performed by using Newton-

Raphson method and new power flow method.

In order to avoid the over-load on the generators and to reduce the losses generation re

allocation is performed.

Even after the generation reallocation the load does not met the demand so the load is

curtailed by doing load shedding.

To increase the voltage profile facts devices are placed like SVC and TCSC for the 3-bus, 5-

bus and 24-bus systems and results are obtained.

1.4 ORGANIZATION OF PROJECT WORK


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Chapter-2, it deals with the New power flow method mathematical modeling and its basic

equations. Comparisons of Newton-Raphson method and New power flow method for all the

3,5,24 bus systems has been done.

Chapter-3 deals with generation reallocation mathematical equations and comparison with

Newton-Raphson method for all the 3,5,24 bus systems.

Chapter-4 includes load shedding problem formulation, its advantages and disadvantages.

Comparison with Newton-Raphson method for all the 3,5,24 bus systems has been done.

Chapter-5 deals with impact of FACTS devices on power systems and different types of

FACTS devices, their circuit representation & description. This chapter also includes the

effect of facts devices placed in different lines for each bus. The comparison with Newton

method also obtained.

Chapter-6, it discuss with the overall conclusion of the project work.


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CHAPTER 2

NEW POWER FLOW METHOD

2.1 INTRODUCTION

Power flow calculations for determining the steady state of power systems have

conventionally been solved by assuming that system frequency remains constant, that supply demand

unbalances would be regulated by an ideal generator, called slack bus and by neglecting the voltage

characteristics of loads. Since this method of solution neglects frequency discrepancies and voltage

characteristics, i.e., the control characteristics of various generators and system load characteristics,

it is not suited to analyzing a new steady state following a disturbance, or a major supply outage.

It is necessary, however, from the point of view of the security of increasingly large

and complex power systems, to be able to determine the frequency, voltage, presence or absence of

overload, and local supply bottlenecks following a sudden major supply outage or tripping of tie-line

breakers. Thus the need is clear for a calculation model that takes account of generator control

effects, and the voltage and frequency characteristics of load.

The classical methods of solving Load flows assume that system frequency remains

constant, an ideal generator, called slack bus, would regulate that supply - demand unbalance. The

voltage and frequency characteristics i.e. the control characteristics of various generators and system

load characteristics are not considered in these classical power flow models. The conventional GaussSeidel, NR Power Flow Models etc. are not suitable to study the system during dynamic condition

as these models are intended to give solution for a pre-defined static operating point.

2.2 NECESSITY OF NEW POWER FLOW METHOD

A new power flow model is used for the steady state behavior of large complex power systems. It

allows the study of power flow under abnormal conditions as well as normal conditions.

It is necessary to take account of system frequency deviation

While system frequency is maintained relatively constant under normal conditions, changes

will occur in the event of supply-demand unbalance resulting from a major supply outage or

tie-line tripping. It is thus necessary to establish new steady state values by checking for the

magnitude of frequency deviation.

Demand-supply unbalance must be distributed among allgenerators

If the whole unbalance is absorbed by a single swing bus, there maybe major distortions

in load flow distribution, and the model fails to match reality. Thus it is necessary to develop

a model which distributes and absorbs the unbalance on the basis of the governor

characteristics, load characteristics, of each generator.

Voltage characteristics of the system cannot be neglected

Load usually depends on voltage, and system voltages are controlled by generators,capacitors, reactors, transformers.


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2.2.1 Generator real power output

Generator real power output is adjusted by the static response of the prime mover shown in the fig

2.1 which may be expressed as

fR

PPP R

GsetG (2.1)

And

GmaxGGmin PPP (2.2)

WhereG

P : Real power output of generator

GsetP : Scheduled real power output of generator

RP : Rated output of generator

R : Speed regulation in per unit

f : Change in frequency

maxGP , minGP : Real power limits of generator.

Figure 2.1: Generator Governor Model


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2.2.2 Generator Reactive Power Output and Terminal Voltage

In this new model, different types of generator buses are considered.

Bus type 1:

A generator bus is specified by theirG

P andG

Q , or operated under constant power factor.G

Q is

adjusted according to the characteristic as shown in the Fig. 2.2.2

GQGQGsetG PbPaQQ

(2.3)

fR

1PP RG (2.4)

WhereG

Q : Reactive power output of generator

GsetQ : Scheduled reactive power output of generator

Qa ,

Qb : Coefficients of reactive generation control characteristics

Figure 2.2 Characteristics of Generator Reactive Power.

Bus type 2:

GP and

GV are specified, and the bus is operated under constant terminal

voltage. Line drop compensation can be applied to the Automatic Voltage Regulator (AVR), and

exciter capability can be taken in to account.

The model for this bus can be expressed by

IjXVV LCGsetG (2.5)

IjXVE fG (2.6)

maxmin EEE (2.7)


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WhereG

V : Generator terminal voltage

setGV : Scheduled voltage

fX : Direct axis synchronous reactance

E : Voltage proportional to field voltage

minE ,

maxE : Limits of field voltage

Bus type 3:

Same as Type 1, with the addition of excitation capabilityG

Q as in equations (2.3) and (2.4) as in

equations (2.6) and (2.7).

Bus type 4:

Same as Type 2, with the addition of reactive power generation limits.

GQ is as in equations (2.3) and (2.4), and

GmaxGGmin QQQ (2.8)

WhereminG

Q ,maxG

Q : Reactive power limits of generator

2.3 LOAD MODEL

Load normally depends on voltage and frequency, and study of emergency system control must take

into account of frequency and voltage characteristics of the load.

Loads may be expressed by:

21

)1(LB

z

N

LB

cpPLsetLV

Vp

V

VppfkPP (2.9)

22

)1(LB

z

N

LB

cpQLsetLV

Vq

V

VqqfkQQ (2.10)


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WhereL

P ,L

Q : Power input of load

setLP , setLQ : Rated power of load

Zp , Zq :Portion of total load proportional to constant impedance load

Cp ,

Cq : Portion of total load proportional to Nthpower of voltage

Pp ,

Pq : Portion of total load proportional to constant power load

PK ,

QK : Frequency characteristics of load

BLV : Normal-operating voltage at load bus

2.4 SOLUTION METHOD

In order to study power flow, taking into account of system frequency deviation, it is

necessary to introduce frequency characteristics into traditional power flow equations. There are

expressed as follows:

The balance of real and reactive power at a node i the following equations one for real power

balance and the other for reactive power balance are shown by equations (2.11) and (2.12.)

0 LiGiipi PPPf (2.11)

0 LiGiiQi QQQf (2.12)

Wherepi

f ,iQ

f : Error of power flowing into node i

n

j

jiji VYI1

(2.13)

n

j

jijiiiii VYVQjPIV1

**

*

(2.14)

Whereii : current flowing into node i

iP,

iQ : injected power into node i.

In traditional load flow studies, a single node or bus is considered to be a slack bus to make up for

the difference between scheduled load, system loss and generation. In this new model, however,

system frequency changes according to the supply demand difference so that a balance among

load, generation and system loss is obtained automatically, and there is no need for a slack bus. It

is however, necessary to specify the voltage phase angle of one of the buses as reference node in


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order to find the voltage angles of the other nodes. All the generators participate in picking up the

entire load and system losses.

2.4.1 Basic equations

We can represent the bus voltage of node i as,

ij

ei

ViV (2.15)

Then Eq. (2.14) becomes

n

1j

j

ij

ej

Vi

VijYijQ

iP (2.16)

And Eq. (2.11) and (2.12) can be represented as functions of V1,

1,V

2,

2,., V n ,

n ,

and f, where f is also one of the variables representing change in the system frequency, i.e.,

fVVVff nnPP ,,,......,,,, 2211 (2.17a)

fVVVff nnQQ ,,,......,,,, 2211 (2.17b)

The New power flow problem to be solved is represented as a set of simultaneous non linear

equations as follows:

(a) For nodes for which real and reactive power are specified:

0,,,......,,,, 2211 fVVVf nnPl (2.18a)

0,,,......,,,, 2211 fVVVf nnQl (2.18b)

(b) For nodes for which power and voltage magnitude are specified:

10

0,,,......,,,, 2211 fVVVf nnPm (2.19)

Where n is the number of nodes for which real and reactive powers are specified and m is the

number of nodes for which real and voltage magnitude are specified.


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Given approximate results for the unknown variables kV , k , kf in equations (2.18) and

(2.19), corrected values V , , f can be obtained from the matrix.

ll

l

n

ijiij

ijiij

Qll

Ql

Pn

nP

P

V

V

f

LGJ

NFH

f

f

f

f

f

.

.

.

)(

.

.

.

||

||

||

||

||

||

||

||

||

||

||

.

.

.

.

.

.

1

1

1

1

1

1

(2.20)

Where1

l , . . . .l

l are the number of nodes for which voltage is not specified andn

is taken for the

phase reference bus. The total number of variables in equation (2.20) is

(2n-m), where n is the total number of buses and m is the number of P-V buses Values forP

f ,Q

f ,

and the Jacobian matrix in equation (2.20) can be obtained by substituting the approximations kV ,

k , kf , solutions for which can be obtained by solving a system of linear equations. The new

values for 1kV , 1k , 1 kf are calculated from equations (2.21a), (2.21b)

)()()1(

)()()1(

kkk

kkk

vvV

(2.21a)

)()()1( kkk fff (2.21b)

The elements of equation (2.20) are defined in equation (2.22)

,j

Pi

ij

fH

j

Qi

ij

fJ

; ,

j

Piij

v

fN

j

Qi

ijv

fL

,f

fF Piij

f

fJ

Qi

ij

(2.22)

Terms of equations (2.22) are given and the computational procedure is given in the

flow chart shown in Appendix(B). 11


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2.5 RESULTS AND DISCUSSIONS

Table 2.1 Results for 5-bus system using Newton method

GENERATION LOAD SHUNT

Bus

Name

Type V Delta MW MVAR M

W

MVAR MVAR

1 bus-

1

slack 1.060 0.00 131.1 90.8 0.0 0.0 0.0

2 bus-2 PVbus 1.000 -2.06 20.0 -71.6 0.0 0.0 0.0

3 bus-3 PQbus 0.987 -4.64 0.0 0.0 0.5 0.1 0.0

4 bus-4 PQbus 0.984 -4.96 0.0 0.0 0.4 0.1 0.0

5 bus-5 PQbus 0.972 -5.76 0.0 0.0 0.6 0.1 0.0

Forward Power Flow Power Losses

Name Name MW MVAR MW MVAR

bus-2 bus-1 -86.840 -72.9105 2.4857 1.0864

bus-3 bus-1 -40.271 -17.5109 1.5176 -0.6928

bus-3 bus-2 -24.112 -0.3493 0.3595 -2.8709

bus-4 bus-2 -27.250 -0.8277 0.4608 -2.5547

bus-5 bus-2 -53.439 -4.8241 1.2147 0.7278

bus-4 bus-3 -19.343 -4.6884 0.0401 -1.8230

bus-5 bus-4 -6.553 -5.1703 0.0431 -4.6526

*************** SYSTEM-GRID TOTALS ******************

Total Generation 151.11MW 19.21 MVAR

Shunt(inductive) 0.00 MVAR


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Total P - Q Load 145.00 MW 30.00 MVAR

Total Power Losses 6.12 MW -10.78 MVAR

Fig 2.3: Voltage profile of Newton method for 5-bus system

Table 2.2 Results for 5-bus system using new power flow method

GENERATION LOAD

Bus Name Type V Delta MW MVAR MW MVAR

1

2

3

4

5

Bus-1

bus-2

bus-3

bus-4

bus-5

slack

PVbus

PQbus

PQbus

PQbus

1.000

1.000

0.971

0.971

0.967

0.000

-3.394

-5.740

-6.119

-7.058

120.00

20.00

0.00

0.00

0.00

-9.80

-1.80

0.00

0.00

0.00

0.00

0.00

45.00

40.00

60.00

0.00

0.00

15.00

5.00

10.00

Forward Power Flow Reverse Power Flow Power Losses

SB EB MW MVAR MW MVAR MW MVAR

1

1

2

2

2

3

4

2

3

3

4

5

4

5

89.68

40.64

24.82

28.08

55.03

18.73

6.26

-29.97

-1.99

6.22

5.27

9.08

-7.22

-2.81

-87.93

-39.32

-24.41

-27.57

-53.78

-18.69

-6.22

29.23

1.09

-8.87

-7.64

-8.22

5.46

-1.78

1.75

1.32

0.41

0.50

1.26

0.04

0.03

-0.74

-0.89

-2.66

-2.37

0.87

-1.76

-4.60


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Total Generation :

Shunt (inductive) :

Total P - Q Load :

Total Power Losses :

140.0009 MW

145.0254 MW

-5.3123 MW

-11.6066 MVAR

0.00 MVAR

30.0000 MVAR

-12.1529 MVAR

From the table 2.1 and table 2.2, it is observed that at constant load, there is a decrement in

total power loss of 13.07% in new power flow method when compared with Newton method.

As losses have decreased, the generation decreases from 151.11MW to 140.0009MW.

Fig 2.4: Voltage profile of Newton & New power flow method for 5-bus system

From fig 2.4, the voltage profile of new power flow method is decreased by 1.6% when

compared with Newton Raphson method .

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6

newton method

new power flow

method

voltage

profile

bus number


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Table 2.3 Results for 24-bus system using Newton method


Bus Name Type V delta MW MVAR MW MVAR MVAR

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1.060

1.000

1.000

1.000

0.898

0.918

0.886

0.993

0.942

0.938

1.030

1.039

1.000

1.026

1.024

0.968

1.021

0.972

0.966

0.940

0.982

1.003

0.987

0.00

-12.49

-9.29

-21.54

-19.72

-35.34

-34.65

-36.37

-27.50

-37.66

-20.33

-23.70

-37.07

-32.83

-5.76

-14.06

-16.11

-36.15

-31.72

-30.24

-27.52

-34.19

-24.54

1654.1

160.0

350.0

520.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

576.9

-54.7

-0.6

93.3

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

4.3

2.8

3.2

1.8

1.2

0.6

0.0

0.0

4.5

0.0

7.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.7

0.9

1.1

0.7

0.4

0.2

0.0

0.0

1.8

0.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-60.7

-48.9

0.0

-47.7

-95.0

-42.5

-47.2

-96.8

-169.1

-120.1

0.0

-103.2

-88.3


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24 bus-24 PQbus 0.999 -13.28 0.0 0.0 0.0 0.0 -283.4

Table 2.4 Results for 24-bus system using new power flow method

GENERATION LOAD

Bus Name Type V delta MW MVAR MW MVAR

1

2

3

4

5

6

7

8

9

10

11

12

13

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1

1

1

1

0.844

0.844

0.829

0.825

0.876

0.88

0.968

0.953

0.821

0

-12.621

-10.914

-19.1

-22.155

-33.569

-34.222

-35.256

-27.431

-25.582

-19.76

-22.717

-35.359

1655.87

160

350

520

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

523.53

36.25

197.07

305.51

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

430.01

280.00

320.00

180.00

120.00

60.00

0.00

0.00

450.01

0.00

0.00

0.00

0.00

170.00

90.00

110.00

70.00

40.00

20.00

0.00

0.00

180.00

SYSTEM-GRID TOTALS

Total Generation :

Shunt (inductive) :

Total P - Q Load :


2684.06 MW

2620.00 MW

64.06 MW

614.98 MVAR

-1203.00 MVAR

980.00 MVAR

-784.08 MVAR


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14

15

16

17

18

19

20

21

22

23

24

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

bus-24

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

0.877

0.966

0.917

0.984

0.913

0.892

0.884

0.939

0.873

0.921

0.96

-31.455

-6.494

-15.797

-16.269

-23.871

-29.303

-29.216

-25.219

-30.945

-24.022

-14.947

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

780.01

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

300.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00


Total Generation :

Shunt (inductive) :

Total P - Q Load :


2685.8702 MW

2620.0000 MW

65.8720 MW

1062.3602 MVAR

1048.9373 MVAR

980.0000 MVAR

85.5636MVAR

From the table 2.3 and table 2.4, it is observed that at constant load, there is a decrement in total

power loss of 13.33% in new power flow method when compared with Newton method. As losseshave decreased, the generation decreases from 2684.06MW to 2685.8702MW.


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CHAPTER 3

GENERATION REALLOCATION

3.1 INTRODUCTION

Generation reallocation is also called as optimum power flow. The generation reallocation is a power

flow problem in which certain variables are adjusted to minimize an objective function such as cost

of the active power generation or the losses, while satisfying physical operating limits on various

controls, dependent variables and function of control variables. Because the objective includes

losses, and controls include reactive devices, the problem is characterized by a non-separable

objective function. The characteristic, which sets the classical OPF apart from similar optimizationproblems, also makes it more difficult to solve. It was first discussed by Carpentier in 1962 [7] and

took a long time to become a successful algorithm that could be applied for everyday use.

The OPF method is based on load flow solution by the Newtons method [8], a first order gradient

adjustment algorithm for minimizing the objective function and use of penalty functions to account

for inequality constraints on dependent variables. The types of controls that an optimal power flow

must be able to accommodate are active and reactive power injections, generator voltages,

transformer tap ratios and phase-shift angles. In the given OPF study, active power controls, reactive

power controls or a combination of both may be optimized.

Practical solutions for OPF problems with separable objective functions have been obtained with

special linear programming methods, but the classical OPF has defined practical solutions, the

Newton approach is a flexible formulation that can be used to develop different OPF algorithms

suited to the requirements of different applications. In other words, the optimal power problem seeks

to find an optimal profile of active and reactive power generations along with voltage magnitudes in

such a manner as to minimize the total operating costs of a thermal electric power system, while

satisfying network security constraints.

There are many applications of the OPF including The calculation of the Optimum generation pattern, as well as control variables, to active the

minimum cost of generation together with meeting transmission system limitations.

In an emergency, that is when some component of system is overloaded or a bus is

experiencing a voltage violation, the OPF can provide a corrective dispatch, which tells the

operation of system, the adjustments to be made to relieve the overload or voltage violation.

The OPF can be used periodically to find the optimum setting for generation voltages,

transformer taps and switched capacitors or static VAR compensators.

The OPF is routinely used in planning studies to determine the maximum stress that a

planned transmission system can withstand. For example, the OPF can calculate themaximum power that can safely be transferred from one area of network to another.


20/95


POWER


3.2 SOLUTION OF THE OPTIMAL POWER FLOW:

The optimal power flow is a very large and difficult mathematical programming problem.

Almost every mathematical programming approach that can be applied to this problem has been

attempted and it has taken developers many decades to develop computer codes that will solve the

OPF reliably.

There are different methods of solving the optimal power flow problem.

Lambda Iteration Method

Gradient Method

Newtons Method

Linear Programming Method

Interior Point Method

In the Lambda Iteration method, losses are represented by a [B] matrix, or the penalty factors may be

calculated outside by a power flow. Gradient methods are slow in convergence and are difficult to

solve in the presence of inequality constraints. The Linear Programming method and Interior Point

method easily handle the inequality constraints.

The problems with the Gradient method lie mainly in the fact that the direction of gradient must be

changed quite often and this leads to a very slow convergence. To speed up this convergence,

Newtons method is used. It has got very fast convergence characteristics. Efficient and robust

solutions can be obtained for problems of any practical size or kind. Solution effort is approximately

proportional to network size, and is relatively independent of the number of controls or bindinginequalities. A direct simultaneous solution for all of the unknowns in the Lagrangian function in

each iteration is obtained.

The objective function for minimizing the operating cost is

)(1

2

1

igi

NG

i

gi

NG

i

i cPbPaFF ii

Rs/hr (3.1)

Subject to

(a) Active power balance in the network

0),( ii dgi PPVP (i=1,2 n) (3.2)

(b) Reactive power balance in the network

0),( ii dgi

QQVQ (i= nv+1,nv+2,., n) (3.3)

(c) Security related constraints called the soft constraints

(i) Limits on real power generationsmaxmin

iii ggg PPP (i= 1, 2,., n) (3.4)

(ii) Limits on voltage magnitudesmaxmin

iii VVV (i= nv+1,nv+2,., n) (3.5)

(iii) Limits on voltage anglesmaxmin

iii (i= 1, 2, n) (3.6)


21/95


POWER


(d) Functional constraint which is a function of control variables

Limits on Reactive powermaxmin

iii ggg QQQ (3.7)

The Real Power Flow equations are

n

j

jiijjiijjii BGVVVP1

))sin()cos((),( (3.8)

The Reactive Power Flow equations

n

j

jiijjiijjii BGVVVQ1

))cos()sin((),( (3.9)

Where,

n is the number of buses

ng is the number of generator buses

nv is the number of voltage controlled buses

iP is the active power injection into bus i

iQ is the reactive power injection into bus i

diP is the active load on bus i

giP is the active generation on bus i

giQ is the reactive generation on bus i

iV is the voltage magnitude at bus i

i is the voltage phase angle at bus i

jijiji jBGY (are the elements of admittance matrix)

The initial values ofgP and are calculated using the formula given in the equation (3.10). In

addition,pi is initialized to for all buses and qi is initialized to zero for load buses. Voltages for

all the buses are taken as flat voltages and the voltage angles are initialized to zeroes. The

constrained minimization problem can be transferred into an unconstrained one by augmenting the

load flow constraints into the objective function.

The additional variables are known as Lagrangian multiplier functions or incremental cost functions.

n

i i

n

i

n

i i

id

a

a

bP

i

1

1 1

2

1

2 and

i

i

ga

bP

i 2

(i=1,2 ng) (3.10)

The Lagrangian function becomes

n

i

dgiqi

n

i

dgiPiigi

ng

i

gig iiiiiiQQVQPPVPcPbPaVPL

111

2 )),(()),(()(),,(

(3.11)

The optimization problem is solved, if the following equations of optimality are solved.


22/95


POWER


q

p

g

qq

qp

ppgp

qp

pggg

V

p

q

p

g

V

VVVVV

Vp

V

PPP

V

P

000

0

00

0

000

(3.12)

To solve the above equation, Jacobian and Hessian matrix elements are to be calculated. Then the

values of qpg VP ,,, , are calculated by multiplying the Jacobian matrix with the inverse of

Hessian matrix. The convergence is checked using the formula given below, which must be less than

or equal to a pre-specified tolerance value. Otherwise, the values qpg VP ,,, , are updated.

2

1

1

2

1

2

1

2

2

2

1

2 )()()()()(ng

nvi

q

n

nvi

i

n

i

p

n

i

i

ng

i

g iiiVP (3.13)

The limits are also checked, if any variable violates the limit, then a penalty function is imposed on

it.


23/95


POWER


3.3 RESULTS AND DISCUSSIONS

An OPF program by Newtons approach has been written using MATLAB, and the results for 3-bus

system, 5-bus system and 24-bus system are obtained.

Table3.1: Newtons Method results for 3-Bus System


Bus Name Type V Delta MW MVAR MW MVAR MVAR

1

2

3

bus-1

bus-2

bus-3

slack

PVbus

PQbus

1.0500

1.0100

1.0217

0.0000

0.1520

-2.3762

83.3333

96.6667

0.0000

145.2480

-102.4507

0.0000

0.00

0.00

1.80

0.00

0.00

0.30

0.00

0.00

0.00



bus-2

bus-3

bus-3

bus-1

bus-1

bus-2

5.626

-88.960

-91.040

-80.793

-55.951

25.951

0.000

0.000

-0.000

3.215

5.290

4.292


Total Generation :

Shunt (inductive) :

Total P - Q Load :


180.00 MW

180.00 MW

-0.00 MW

42.80 MVAR

0.00 MVAR

30.00 MVAR

12.80 MVAR


24/95


POWER


Table3.2: OPF results for 3-Bus System

Fig 3.1: Voltage profile of Newton and Opf for 3-bus system

From table 3.1 and 3.2 it is found that the 3-bus system has two PV buses and one PQ bus.

The burden on the slack is reduced by 61MW (42.5%) and it is shared by PV bus.

Fig 3.1 shows that the voltage profile is improved by 1%

0

0.2

0.40.6

0.8

1

1.2

0 1 2 3 4

VoltageP

rofile

Bus Number

Newton-Raphson Method



1 bus-1 PQbus 1.022 -2.92 0.0 0.0 1.8 0.3 0.0

2 bus-2 PVbus 1.010 -0.96 35.0 -102.9 0.0 0.0 0.0

3 bus-3 slack 1.050 0.00 145.0 146.6 0.0 0.0 0.0



bus-2 bus-1 70.608 -22.3868 0.0000 2.6893

bus-3 bus-1 109.392 62.2611 0.0000 7.1851

bus-3 bus-2 35.608 84.2989 0.0000 3.7978


Total Generation : 180.00 MW 43.67 MVAR

Shunt (inductive) : 0.00 MVAR

Total P - Q Load : 180.00 MW 30.00 MVAR

Total Power Losses : 0.00 MW 13.67 MVAR


25/95


POWER





1 bus-1 slack 1.060 0.00 131.1 90.8 0.0 0.0 0.0

2 bus-2 PVbus 1.000 -2.06 20.0 -71.6 0.0 0.0 0.0

3 bus-3 PQbus 0.987 -4.64 0.0 0.0 0.5 0.1 0.0

4 bus-4 PQbus 0.984 -4.96 0.0 0.0 0.4 0.1 0.0

5 bus-5 PQbus 0.972 -5.76 0.0 0.0 0.6 0.1 0.0



bus-2 bus-1 -86.840 -72.9105 2.4857 1.0864

bus-3 bus-1 -40.271 -17.5109 1.5176 -0.6928

bus-3 bus-2 -24.112 -0.3493 0.3595 -2.8709

bus-4 bus-2 -27.250 -0.8277 0.4608 -2.5547

bus-5 bus-2 -53.439 -4.8241 1.2147 0.7278

bus-4 bus-3 -19.343 -4.6884 0.0401 -1.8230

bus-5 bus-4 -6.553 -5.1703 0.0431 -4.6526


Total Generation 151.11MW 19.21 MVAR

Shunt(inductive) 0.00 MVAR

Total P - Q Load 145.00 MW 30.00 MVAR

Total Power Losses 6.12 MW -10.78 MVAR


26/95


POWER





1

2

3

4

5

Bus-1

bus-2

bus-3

bus-4

bus-5

slack

PVbus

PQbus

PQbus

PQbus

1.0600

1.0000

0.9875

0.9843

0.9717

0.0000

-0.1127

-3.2069

-3.4231

-3.9535

66.7022

83.6080

0.0000

0.0000

0.0000

110.30

-93.52

0.00

0.00

0.00

0.00

0.00

0.45

0.40

0.60

0.00

0.00

0.15

0.05

0.10

0.00

0.00

0.00

0.00

0.00



bus-2

bus-3

bus-3

bus-4

bus-5

bus-4

bus-5

bus-1

bus-1

bus-2

bus-2

bus-2

bus-3

bus-4

-33.128

-30.705

-28.471

-30.725

-55.153

-14.153

-4.847

-91.954

-21.358

1.471

0.615

-4.165

-6.758

-5.835

1.802

1.067

0.506

0.589

1.292

0.024

0.030

-0.965

-2.045

-2.432

-2.172

0.960

-1.872

-4.692


Total Generation :

Shunt (inductive) :

Total P - Q Load :


150.31 MW

145.00 MW

5.31 MW

16.78 MVAR

0.00 MVAR

30.00 MVAR

-13.22 MVAR


27/95


POWER


The burden on slack bus is decreased by 50% by performing optimal power flow method.

The real power generation is reduced by 1MW, while reactive power generation is reduced

by 2.5MW.

Real power losses are decreased by 0.8MW for 5-bus system with two PV buses and one PQ

bus.

From fig 3.2 it is inferred that voltage profile is improved.

Fig 3.2: Voltage profile of Newton and Opf for 5-bus system

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 1 2 3 4 5 6

VoltageProfile

Bus Number

Newton-Raphson

Optimal Power


28/95


POWER





1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1.000

1.000

1.000

1.000

0.844

0.844

0.829

0.825

0.876

0.880

0.968

0.953

0.821

0.877

0.966

0.917

0.984

0.913

0.892

0.884

0.939

0.873

0.921

0.00

-12.62

-10.91

-19.10

-22.16

-33.57

-34.22

-35.26

-27.43

-25.58

-19.76

-22.72

-35.36

-31.45

-6.49

-15.80

-16.27

-23.87

-29.30

-29.22

-25.22

-30.94

-24.02

1655.9

160.0

350.0

520.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

523.5

36.8

198.2

307.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

4.3

2.8

3.2

1.8

1.2

0.6

0.0

0.0

4.5

0.0

7.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.7

0.9

1.1

0.7

0.4

0.2

0.0

0.0

1.8

0.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-53.5

-41.2

0.0

-34.9

-84.6

-38.1

-43.9

-85.5

-144.5

-106.4

0.0

-78.0

-77.0


29/95


POWER


24 bus-24 PQbus 0.960 -14.95 0.0 0.0 0.0 0.0 -261.4



bus-23

bus-18

bus-12

bus-17

bus-14

bus-24

bus-18

bus-23

bus-20

bus-16

bus-16

bus-24

bus-19

bus-19

bus-20

bus-8

bus-5

bus-6

bus-7

bus-8

bus-9

bus-22

bus-22

bus-11

bus-11

bus-12

bus-17

bus-24

bus-24

bus-23

bus-15

bus-24

bus-15

bus-21

bus-22

bus-21

bus-13

bus-16

bus-19

bus-20

bus-14

bus-23

210.935

169.098

-195.330

197.368

-192.378

38.103

-229.200

-489.071

-156.393

-368.789

-64.182

-484.255

-346.752

65.550

-165.255

11.572

-430.00

-280.00

-320.00

-191.57

-120.00

33.0442

-10.0289

-65.0926

1.0195

-136.2234

-116.3538

-97.4833

-167.4229

-99.3193

-93.6954

-173.9701

-76.0130

-266.9147

8.3169

-150.0760

15.1848

-170.00

-90.00

-110.00

-85.18

-40.00

2.6395

2.2364

0.8599

1.1778

2.9519

0.2018

3.6518

7.7162

1.3291

6.1232

0.7290

6.7514

2.8602

0.2298

1.5220

0.0225

2.97

1.20

1.65

0.81

0.41

-73.2578

-102.3059

-48.8408

-68.7230

-112.3103

-135.1601

-100.7803

-187.1462

-90.1636

-29.5282

-53.9007

-203.3029

-122.2094

-69.1407

-60.1173

-7.0383

59.53

24.10

33.04

16.13

8.27


30/95


POWER


bus-10

bus-13

bus-1

bus-2

bus-3

bus-4

bus-18

bus-22

bus-15

bus-17

bus-24

bus-21

-60.00

-438.45

1655.87

160.00

350.00

520.00

-20.00

-157.78

523.53

36.82

198.20

307.01

0.10

2.03

9.95

0.53

1.60

3.61

2.05

40.23

202.07

10.67

32.10

72.35



Shunt (inductive) : -1048.94 MVAR


Total Power Losses : 65.87 MW -915.54 MVAR


31/95


POWER





1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1.0000

1.0000

1.0000

1.0000

0.8506

0.8371

0.8269

0.8149

0.8812

0.8848

0.9436

0.9279

0.8150

0.8595

0.9714

0.9232

0.9639

0.9179

0.8858

0.8819

0.9332

0.8702

0.9260

0.0000

23.7387

7.1291

6.8282

-11.8111

-11.2051

-13.2050

-14.2063

-9.6755

-8.3635

5.6828

1.8833

-14.9406

-9.3932

-2.9026

-5.5440

10.1380

-6.6703

-6.8720

-8.1734

-1.6160

-10.9149

-6.3034

754.2801

578.8871

642.2324

708.2775

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

407.5732

130.5805

204.3099

352.4880

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

4.3000

2.8000

3.2000

1.8000

1.2000

0.6000

0.0000

0.0000

4.5000

0.0000

7.8000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

1.7000

0.9000

1.1000

0.7000

0.4000

0.2000

0.0000

0.0000

1.8000

0.0000

3.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

-50.8753

-39.0517

0.0000

-33.5014

-85.5977

-38.6492

-42.1324

-86.3588-

142.3511

-105.8237

0.0000

-77.6053

-77.7780


32/95


POWER


24 bus-24 PQbus 0.9613 -0.3660 0.0000 0.0000 0.0000 0.0000 -262.3646



bus-23

bus-18

bus-12

bus-17

bus-14

bus-24

bus-18

bus-23

bus-20

bus-16

bus-16

bus-24

bus-19

bus-19

bus-20

bus-8

bus-5

bus-6

bus-7

bus-8

bus-9

bus-22

bus-22

bus-11

bus-11

bus-12

bus-17

bus-24

bus-24

bus-23

bus-15

bus-24

bus-15

bus-21

bus-22

bus-21

bus-13

bus-16

bus-19

bus-20

bus-14

bus-23

144.906

105.134

-237.356

240.499

-233.185

-325.775

-165.235

-326.899

-61.121

-114.614

-318.312

144.418

-434.588

153.366

-260.537

52.112

-430.000

-280.000

-320.000

-232.112

-120.000

46.228

0.348

-59.660

12.268

-110.838

-11.057

-108.734

-196.443

-125.542

-145.431

-121.845

-182.529

-252.157

-4.684

-123.506

-14.124

-170.000

-90.000

-110.000

-55.876

-40.000

1.563

1.081

1.319

1.825

4.170

5.640

1.962

3.529

0.464

1.011

3.156

0.647

4.078

0.903

2.878

0.134

2.925

1.222

1.658

1.073

0.408

-85.516

-114.428

-40.120

-58.148

-90.229

-74.333

-119.580

-233.243

-101.281

-84.748

-28.782

-270.485

-104.884

-60.011

-42.470

-6.336

58.627

24.490

33.225

21.460

8.177


33/95


POWER


For 24-bus system of constant load there are four PV buses and 20 PQ buses the real power

generated from slack bus is reduced by 55%

The real power losses are decreased by 3%.

From the fig 3.3 it is found that the voltage profile is improved by 1.3%.

bus-10

bus-13

bus-1

bus-2

bus-3

bus-4

bus-18

bus-22

bus-15

bus-17

bus-24

bus-21

-60.000

-398.022

754.280

578.887

642.232

708.277

-20.000

-187.788

407.573

130.580

204.310

352.488

0.101

1.837

2.426

6.973

4.497

6.196

2.027

36.454

49.249

139.456

90.114

124.180

SYSTEM-GRID TOTALS

Total Generation :

Shunt (inductive) :

Total P - Q Load :


2683.68 MW

2620.00 MW

63.68 MW

1094.95 MVAR

-1042.09 MVAR

980.00 MVAR

-1059.96 MVAR


34/95


POWER


Fig 3. 3: Voltage profile of Newton and opf for 24-bus system

3.4 CONCLUSION

As the number of buses increases the burden on the slack bus is decreasing, the real power

losses are found to be decreased.

The real power losses are reduced by 2%.

By using optimal power flow method the power generated was shared among all the

generating units optimally.

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30

VoltageProfile

Bus Number

Newton-Raphson Method

Optimal Power Flow Method


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CHAPTER 4

GENERATION LOAD IMBALANCES

4.1 INTRODUCTIONModern electric power systems are highly interconnected and heavily loaded. A severe emergency

state may occur as a result of insufficient generation to meet load demand. Quite simply, if one unit

is lost, spinning reserve prevents an excessive drop in system frequency. Spinning reserve either

represents a percentage of peak demand or is capable of making up the loss of the most heavily

loaded unit at a given period of time. The reserves must be allocated among fast-responding and

slow-responding units to allow the automatic generation control system to restore frequency and

interchange quickly in the event of the outage of generating unit. Load shedding is one of the

remedial actions to prevent area collapse, alleviate line overloads and voltage violations and relieve

system over-frequency or under-frequency. A large number of research papers are available on the

subject of corrective rescheduling of the generated power and load shedding by linear or non-linear

programs. In almost all the methods, the frequency was assumed to be constant.

4.1.2 DEVELOPMENTS IN LOAD SHEDDING TECHNIQUE

A policy of load shedding in power systems has been discussed by Hajdue (1968). Medicheria

(1979, 1981) and Chan (1979) proposed generation rescheduling or reallocation and load shedding to

alleviate line overloads. Application of under-frequency relays for automatic load shedding has been

studied by Lokay. Anoop Nanda has developed an under-voltage load shedding scheme based on

Lyapunovs energy methods where the derived energy function eliminates the need to calculate the

critical equilibrium points. A power flow model, load shedding and solution method including load

and generator characteristic with effects of system control devices have been presented by Okamura

(1975) and Palaniswamy (1985). El-Hawary (1990, 1985) and Venkataramona (1995) have studied

load models and their effects on power system performance. A real-time simulation of the network

components by Rafian (1987) used to provide more accurate results and a realistic operator training

environment. Under-frequency relays may be used to trip loads, in order to restore the balance

between loads and generation, or generation units for unit protection which is studied by Smaha

(1980).

This chapter presents an optimum load shedding algorithm for generation load

imbalances. The voltage and frequency characteristics of the loads are considered in this dynamic

study. The effects of the frequency deviation, as a result of power mismatch between generation and

load on load, and system components are reported. The effects of system average time constant,

speed drop factor, load reduction ratio, system inertia and load shedding on the system frequency are

studied. A simple proposed load distribution factor of load shedding is used during the iterative

process of this algorithm.


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4.2PROBLEM FORMULATION AND SOLUTION METHODOLOGYThe objective in this problem is to seek a minimum load shedding following the loss of generation in

order to supply the customers with minimum degradation of service for a given generation level. The

performance index or the objective function is

2

*

i li liC K S S i=1,..., NB (4.1)

Where NB is the number of system buses

iK is the weighting factor depending on the demand priorities at bus i

*

liS and

liS are the final and initial apparent power of the load at bus i

This objective function is subjected to the following constraints and proposed conditions:

(1)Active and reactive power flow equations

, cos sinGi li i i j ij i j ij i jP P P v V V G B (4.2a)

, sin cosGi li i i j ij i j ij i jQ Q Q v V V G B (4.2b)

WhereGiP , GiQ is active and reactive generation power.

liP , liQ are active and reactive load power.

iP, iQ are net injected active and reactive power at bus i

f is the frequency

iV and i are bus voltage magnitude and angle of bus i

ijG and

ijB are the real and imaginary parts of the bus admittance matrix.

(2) Generation constraints are specified by

min max min max, ,Gi Gi Gi Gi Gi GiP P P Q Q Q i=1, NG (4.3)

where NG is the number of generation buses

min

GiP , max

GiP are the minimum and maximum generation active power limits.

min

GiQ , max

GiQ are the minimum and maximum generation reactive power limits.

(3) Bus voltage and line angle constraints are


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POWER


min max

i i iV V V iNGmax

| |i j ij for all lines (4.4)

Wheremax

ij is the maximum angle difference of line connected between bus i and bus j

miniV is minimum value of the voltage magnitude at load bus.

max

iV is the maximum value of the voltage magnitude at load bus.

Now, assume a generator is partially or totally outage. The system frequency will vary due to the

imbalance between the system generation and loads.

The frequency variation in turn will change;

(1) The generation at the remaining generators according to their speed regulation constants and

plant reserve and

(2) The loads according to load reduction ratio. The resulting instantaneous operating conditions give

rise to an emergency state. Then, all control and corrective remedial actions are integrated to resume

the normal state of the system and minimize the duration period of this emergency state. Therefore,

the previous problem formulation is adapted to handle voltage and frequency characteristics of the

loads to consider the effect of frequency variation and generator control effects.

4.3 GENERATOR MODEL

The use of digital telemetry is becoming common-place in modern automatic generation control

schemes wherein supervisory control (opening and closing sub-station breakers), telemetry

information (measurements of MW, MVAR, MVA, voltage, etc.) and control information (unit raise

lower) are sent via the same channels. The new desired output MW, desGiP , during the disturbance for

unit i can be expressed as follows;

/des baseGi Gi iP t P f t R (4.5)

Where baseGi

P is the base point (reference) generation for unit i

iR is the speed regulation factor for unit i

f (t) is the system frequency deviation at any time t.

4.4 LOAD MODEL

Most mathematical load models (constant power and or constant current and or constant impedance)

now used in power flow, security analysis, system control and transient stability studies do not

represent actual load characteristics because collection of real data is not an easy task. Better

formulations can predict and give power system performance more accurately and bring

improvements in transmission system planning and utilization. The load at any bus is a composite of


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POWER


lighting, resistance heating, arc furnaces, dc converters, and motors of various sizes and types. The

load model in this chapter is

21

z I p pli loi p i p i p F LshediP P K V K V K K f P

(4.6a)

21

z I p qli loi q i q i q F LshediQ Q K V K V K K f Q

(4.6b)

Whereloi

P , loiQ are the case active and reactive load power at bus i

LshediP , LshediQ are the active and reactive load shedding at bus i

f is the frequency deviation

pFK ,

qFK are the active and reactive frequency sensitivity factors,

zpK ,

IpK ,

ppK ,

zqK ,

IqK ,

pqK are the active and reactive voltage sensitivity factors (constant

impedance, constant current and constant power).

4.5 TRANSMISSION LINES AND TRANSFORMER MODEL

Transmission lines are represented using a model where the series impedance of the line connected

between bus i and bus j is ij ijr jX and the shunt admittance at bus i is piY . At frequency f the line

parameters in p.u. (f = 1 p.u) are

0 01 , 1ij ij pi piX X f Y Y f (4.7)

For a transformer k connected between bus i and bus j with tap changing turns ratiok

t , phase shifting

k , winding resistance

kr and winding reactance

kX , the model is as follows referred to the bus i:

With tap changing only

2

, ,1/

ii k k jj k ij ji k k

k k k k k

y t y y y y y t yy G jB r jX

(4.8)

With phase shifter ii k jjy y y

cos sin cos sin

cos sin cos sin

ij k k k k k k k k

ji k k k k k k k k

y G B j B G

y G B j B G

(4.9a)

With tap changing and phase shifter2

, ,ii k jj k y t y y y


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POWER


' '' ' ''

' '' ' ''

' ''

,

,

cos , sin

ij k k k k k k k k

ji k k k k k k k k

k k k k k k

y G t B t j B t G t

y G t B t j B t G t

t t t t

(4.9b)

4.6 LOAD SHEDDING DISTRIBUTION

For load shedding kD LshedP P of the total demand at iteration k, the load shedding at

35

each bus kliP is given by

,k kli Li D

new k

li li li

P P

P P P

i=1,,NB (4.10)

whereLi

are proposed load distribution factors and defined by

Li = /li liP P , i = 1,, NB and li = 1.

The new value of the load reactive power is given by /new newli li li liQ P Q P assuming the power factor

is fixed.

4.7ADVANTAGES OF LOAD SHEDDING

Load Shedding is a process of curtailment of load on power system to avoid collapse of the

system. The advantages of load curtailment are:

Avoids total system collapse.

The consumers affected by supply outage are minimum.


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POWER


4.8 RESULTS AND DISCUSSION

Table4.1 When 3- bus system is overloaded.



1 bus-1 PQbus 0.955 -4.25 0.0 0.0 2.4 2.8 0.0

2 bus-2 PVbus 1.010 -1.53 35.0 33.9 0.0 0.0 0.0

3 bus-3 slack 1.050 0.00 205.0 290.5 0.0 0.0 0.0



bus-2 bus-1 91.522 113.9498 0.0000 10.4700

bus-3 bus-1 148.478 205.7093 0.0000 29.1891

bus-3 bus-2 56.522 84.7533 0.0000 4.7065







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POWER


Table4.2: After load shedding at bus-1 by 25 %( 60MW) on 3-bus system

If a bus system get over loaded the voltage profile violates the limits, so to make the voltage

profile within limits load curtailment is to be performed. For 3-bus system the voltage at bus-3 is reduced to 0.95, so as to maintain the voltage profile

60MW of load is to be curtailed at bus-3



1 bus-1 PQbus 1.022 -2.92 0.0 0.0 1.8 0.3 0.0

2 bus-2 PVbus 1.010 -0.96 35.0 -102.9 0.0 0.0 0.0

3 bus-3 slack 1.050 0.00 145.0 146.6 0.0 0.0 0.0



bus-2 bus-1 70.608 -22.3868 0.0000 2.6893

bus-3 bus-1 109.392 62.2611 0.0000 7.1851

bus-3 bus-2 35.608 84.2989 0.0000 3.7978







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POWER


Table4.3: When 5- bus system is overloaded.



1

2

3

4

5

Bus-1

bus-2

bus-3

bus-4

bus-5

slack

PVbus

PQbus

PQbus

PQbus

1.060

1.000

0.961

0.951

0.879

0.00

-3.81

-7.12

-7.91

-7.84

200.0

20.0

0.0

0.0

0.0

84.2

43.1

0.0

0.0

0.0

0.0000

0.0000

0.4500

0.8000

0.8000

0.0000

0.0000

0.1500

0.0500

0.9000

0.0000

0.0000

0.0000

0.0000

0.0000



bus-2

bus-3

bus-3

bus-4

bus-5

bus-4

bus-5

bus-1

bus-1

bus-2

bus-2

bus-2

bus-3

bus-4

-134.410

-58.293

-33.804

-41.381

-72.444

-46.829

-7.556

-54.2975

-19.3585

-10.6704

-12.6078

-64.1120

-16.0523

-25.8879

4.1395

3.1976

0.7935

1.2137

4.7736

0.2679

0.6541

6.0477

4.4764

-1.4652

-0.1672

11.6629

-1.0233

-2.2278


Total Generation :

Shunt (inductive) :

Total P - Q Load :


220.04 MW

205.00 MW

15.04 MW

127.30 MVAR

0.00 MVAR

110.00 MVAR

17.30 MVAR


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POWER


Table 4.4: After load shedding of 40MW at bus-4 and 20MW at bus-5 for 5-bus system.



1

2

3

4

5

Bus-1

bus-2

bus-3

bus-4

bus-5

slack

PVbus

PQbus

PQbus

PQbus

1.060

1.000

0.987

0.984

0.972

0.00

-2.06

-4.64

-4.96

-5.76

131.1

20.0

0.0

0.0

0.0

90.8

-71.6

0.0

0.0

0.0

0.0000

0.0000

0.4500

0.4000

0.6000

0.0000

0.0000

0.1500

0.0500

0.1000

0.0000

0.0000

0.0000

0.0000

0.0000



bus-2

bus-3

bus-3

bus-4

bus-5

bus-4

bus-5

bus-1

bus-1

bus-2

bus-2

bus-2

bus-3

bus-4

-86.840

-40.271

-24.112

-27.250

-53.439

-19.343

-6.553

-72.9105

-17.5109

-0.3493

-0.8277

-4.8241

-4.6884

-5.1703

2.4857

1.5176

0.3595

0.4608

1.2147

0.0401

0.0431

1.0864

-0.6928

-2.8709

-2.5547

0.7278

-1.8230

-4.6526


Total Generation :

Shunt (inductive) :

Total P - Q Load :


151.11 MW

145.00 MW

6.12 MW

19.21 MVAR

0.00 MVAR

30.00 MVAR

-10.78 MVAR


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POWER


From table 4.3 it is inferred that the voltage at bus-4 and bus-5 is less than 0.96, so 40MW at

bus-4 and 20MW at bus-5 are curtailed.

By this load shedding the voltage profile maintained within the limits


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POWER




1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

bus-24

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1.000

1.000

1.000

1.000

0.808

0.795

0.781

0.744

0.816

0.701

0.922

0.896

0.740

0.798

0.951

0.882

0.955

0.787

0.844

0.838

0.909

0.793

0.862

0.921

0.00

-17.83

-15.25

-27.62

-25.98

-43.26

-43.18

-45.48

-34.73

-46.69

-25.60

-29.19

-45.91

-40.39

-7.51

-19.07

-21.50

-35.82

-38.47

-37.57

-33.84

-40.74

-30.82

-19.33

1893.3

160.0

350.0

520.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

755.3

111.3

392.8

458.9

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

4.3

2.8

3.2

1.8

1.2

2.6

0.0

0.0

4.5

0.0

7.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.7

0.9

1.1

0.7

0.4

0.8

0.0

0.0

1.8

0.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-48.6

-36.4

0.0

-28.9

-82.1

-35.3

-41.3

-63.5

-129.3

-95.4

0.0

-64.5

-67.4

-240.8


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POWER


Table4.5 When 24- bus system is overloaded.



bus-23

bus-18

bus-12

bus-17

bus-14

bus-24

bus-18

bus-23

bus-20

bus-16

bus-16

bus-24

bus-19

bus-19

bus-20

bus-8

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-13

bus-22

bus-22

bus-11

bus-11

bus-12

bus-17

bus-24

bus-24

bus-23

bus-15

bus-24

bus-15

bus-21

bus-22

bus-21

bus-13

bus-16

bus-19

bus-20

bus-14

bus-23

bus-18

bus-22

257.928

88.140

-215.141

218.118

-210.809

59.308

-351.118

-556.960

-176.810

-434.694

1.449

-642.879

-364.310

82.954

-145.047

29.662

-430.00

-280.00

-320.00

-209.66

-120.00

-260.00

-420.40

74.9175

-61.3606

-97.1439

51.2052

-134.7518

-126.9106

-141.8067

-182.3175

-63.3072

-111.5874

-158.7623

-99.4397

-328.1871

81.7339

-179.3510

12.9175

-170.00

-90.00

-110.00

-82.92

-40.00

-80.00

-161.60

4.7175

0.7544

1.2661

1.7110

4.3324

0.4375

12.1150

11.5405

1.7460

9.2633

0.5445

12.7404

4.0886

0.8123

1.7934

0.0643

3.25

1.36

1.86

1.15

0.48

2.98

2.34

-35.0308

--90.1960

-37.6275

-56.9268

-74.0313

-123.1953

11.3866

-119.6538

-72.7837

8.4212

-51.1314

-124.6345

-93.8333

-51.8849

-50.2689

-5.4865

65.04

27.17

37.23

22.94

9.53

59.69

46.35


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POWER


bus-1

bus-2

bus-3

bus-4

bus-15

bus-17

bus-24

bus-21

1893.29

160.00

350.00

520.00

755.28

111.30

392.84

458.86

13.71

0.75

2.74

4.76

278.38

15.04

54.92

95.42







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Table4.6: After load shedding of 200MW at bus-10 for 24-bus system.



1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

bus-1

bus-2

bus-3

bus-4

bus-5

bus-6

bus-7

bus-8

bus-9

bus-10

bus-11

bus-12

bus-13

bus-14

bus-15

bus-16

bus-17

bus-18

bus-19

bus-20

bus-21

bus-22

bus-23

slack

PVbus

PVbus

PVbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

PQbus

1.000

1.000

1.000

1.000

0.844

0.844

0.829

0.825

0.876

0.880

0.968

0.953

0.821

0.877

0.966

0.917

0.984

0.913

0.892

0.884

0.939

0.873

0.921

0.00

-12.62

-10.91

-19.10

-22.16

-33.57

-34.22

-35.26

-27.43

-25.58

-19.76

-22.72

-35.36

-31.45

-6.49

-15.80

-16.27

-23.87

-29.30

-29.22

-25.22

-30.94

-24.02

1655.9

160.0

350.0

520.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

523.5

36.8

198.2

307.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

4.3

2.8

3.2

1.8

1.2

0.6

0.0

0.0

4.5

0.0

7.8

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

1.7

0.9

1.1

0.7

0.4

0.2

0.0

0.0

1.8

0.0

3.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

0.0

-53.5

-41.2

0.0

-34.9

-84.6

-38.1

-43.9

-85.5

-144.5

-106.4

0.0

-78.0

-77.0


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POWER


24 bus-24 PQbus 0.960 -14.95 0.0 0.0 0.0 0.0 -261.4



bus-23

bus-18

bus-12

bus-17

bus-14

bus-24

bus-18

bus-23

bus-20

bus-16

bus-16

bus-24

bus-19

bus-19

bus-20

bus-8

bus-5

bus-6

bus-7

bus-8

bus-22

bus-22

bus-11

bus-11

bus-12

bus-17

bus-24

bus-24

bus-23

bus-15

bus-24

bus-15

bus-21

bus-22

bus-21

bus-13

bus-16

bus-19

bus-20

bus-14

210.935

169.098

-195.330

197.368

-192.378

38.103

-229.200

-489.071

-156.393

-368.789

-64.182

-484.255

-346.752

65.550

-165.255

11.572

-430.00

-280.00

-320.00

-191.57

33.0442

-10.0289

-65.0926

1.0195

-136.2234

-116.3538

-97.4833

-167.4229

-99.3193

-93.6954

-173.9701

-76.0130

-266.9147

8.3169

-150.0760

15.1848

-170.00

-90.00

-110.00

-85.18

2.6395

2.2364

0.8599

1.1778

2.9519

0.2018

3.6518

7.7162

1.3291

6.1232

0.7290

6.7514

2.8602

0.2298

1.5220

0.0225

2.97

1.20

1.65

0.81

-73.2578

-102.3059

-48.8408

-68.7230

-112.3103

-135.1601

-100.7803

-187.1462

-90.1636

-29.5282

-53.9007

-203.3029

-122.2094

-69.1407

-60.1173

-7.0383

59.53

24.10

33.04

16.13


50/95


POWER







From table 4.5 it is observed that the voltage at buses 8, 10 and 13 violated the limits. By shedding a

load of 200MW at bus-10, the profile is improved and voltage constraints are satisfied.

4.7CONCLUSION To improve the voltage profile for 3, 5 and 24 bus systems load shedding is performed. The load

curtailed for 3-bus system is 25% of the total load, while for 5-bus it is 29% and for 24-bus

system it is 7%. By this method the load has been curtailed to satisfy the voltage constraints. The consumers

affected by supply outage are reduced.

bus-9

bus-10

bus-13

bus-1

bus-2

bus-3

the impact of facts devices on generation reallocation and load shedding of a power

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