LINE FLOW ANALYSIS OF IEEE BUS SYSTEM WITH THE LOAD SENSITIVITY FACTOR

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 4, Issue 5, May 2014)

898

LINE FLOW ANALYSIS OF IEEE BUS SYSTEM

WITH THE LOAD SENSITIVITY FACTOR

Puneet Sharma

1

, Jyotsna Mehra

2

, Virendra Kumar

3

1,2,3

M.Tech Research scholar, Galgotias University, Greater Noida, India

Abstract—In this paper, line flow analysis coding is been drawn by the help of Newton-Raphson (NR) algorithm for the IEEE 30 bus system. Further in IEEE 30 bus system load has been increased to 135% with an increment of 5% in each step. This change in load gives the node voltage load dependency factor (NVLDF) and line loss load dependency factor (LLLDF). By the help of NVLDF and LLLDF priority list has been made with respect to load sensitivity factor so that system performance index [1] in terms of voltage profile could be obtained. All the system performance study is made under steady- state condition. MATLAB R2013a has been used for calculation purpose. Keywords —Line flow analysis, Newton-Raphson algorithm, Load sensitivity factor, System performance index, Voltage profile.

I INTRODUCTION

Line flow analysis (LFA) is used to make sure that electrical power transfer from generator stations to consumers end through the grid system in reliable and economical form. Conventional techniques [2] for line flow analysis problem are iterative mathematical method like the Newton-Raphson (NR) or the Gauss-Seidel (GS) methods. An engineer is always concerned about economical condition of the system operation. For the mighty interconnected grid system, the power shortage results continuous hike in prices. Thus, it is the priority of engineer to control this continuous hike. Another major problem is economic load dispatch in an optimized manner as it is directly related with load demands. For economically optimized operation of interconnected grid system modern system theory and optimization techniques are being applied with the optimized generation cost function. Through the line flow study, the voltage magnitude and angle at each bus under the steady state can be obtained. The steady state line flow in interconnected network is represented in nonlinear algebraic equations [3]. And, for solving them iterative method is needed. For system to operate in stable condition the voltage has to be maintained within its voltage stability limit.

In this paper, NR method is been used for solution of the line flow equations. By the help of voltage and angle at respective bus, the real and reactive power flow through each line can be computed. And further, the difference between each line flow from the sending end to receiving end is calculated which called as line losses. Furthermore, from increasing the load at each node to 140% with an increment of 5%, the system operation in over-load condition could be studied. Based upon, the over load system the priority list is been created which is very much beneficial to determine the most sensitive node and most sensitive line with respect to change of load.

II LINE FLOW ANALYSIS

Line flow analysis (LFA) is very important tool for analysis of power systems [4] which is used at operational as well as planning stages of the system, like adding and installation of new generation station, load balancing in dynamic running condition and transmission lines site selection. The LFA gives the voltage and phase angle at each bus which is further used to determine the power injection at all the busses along with power flow through interconnected nodes. All these system parameter obtained values are needed for determining the optimal location as well as optimal capacity of proposed generation station, substation and new lines. In order to avoid the system unbalance condition, the voltage should be maintained within its tolerance limit with minimized line transmission losses. In this paper, firstly NR method and its application is been discussed.

2.1 BUS CLASSIFICATION:

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International Journal of Emerging Technology and Advanced Engineering

899 problem. For solving the line flow equation of the system, out of these four variables two are made constant and two are treated as variable. Bus categories are been made on the basis of the constant parameters.

Load bus: No generator is attached to the bus. The real and reactive power is specified at each node. Voltage and phase angle are the uncontrolled variable. It is required to specify only real power demand (Pd) and reactive power demand (Qd) at such bus as at a load bus voltage can be allowed to vary within the permissible values.

Generator bus or voltage controlled bus: Here the voltage magnitude corresponding to the generator voltage and real power (Pg) corresponds to its rating are specified. Reactive power generation (Qg) and voltage phase angle are treated as uncontrolled variable for the line flow analysis.

Slack (swing) bus: For the Slack Bus, it is assumed that the voltage magnitude |V| and voltage phase angle (



)

are known, and real generated power (Pg) and reactive generated power (Qg) are treated as uncontrolled variable.

2.2 Bus Admittance Matrix Formation [7]

Step1 – Numbering of the buses is done from ‘1’ to ‘n’. Bus 1 is the reference node (or ground node).

Step2 -Replace all generators with equivalent current sources connected in parallel to the equivalent admittance.

Step 3- Replace all lines, transformers and loads to equivalent admittances wherever possible.

Step 4- Now by inspection: Yii (diagonal element) = sum of admittances connected to node, and Yij(off diagonal element) = Yji = -(sum of admittances connected from node ‘i’ to node ‘j’).

Step 5-Source current is determined between the nodes 1 to ‘n’.

Step 6- Final node voltage equation:

 

   

*

bus bus bus

I



Y

V

2.3 NR method and line flow analysis (LFA) [5][7]:-

Step1: Assume, initial point

V

_p=1+j0.0 for p= 1, 2….n,

p≠ s, 𝑉𝑠= 1+j0.0.

Step 2: Predefined tolerance value till which the iteration process is followed for the convergence of the system equation.

Step 3: Iteration count is set to K=0.

Step 4: Bus count is set to p=1.

Step 5: Case check when p is slack bus, if yes skip to step 10.

Step 6: Real power (Pp) and reactive powers (Qp) is measured from solving the power flow equations,

1

{ (

)

(

)}

{

(

)

(

)}

n

p p q pq p pq p q pq q pq

q n

p p q pq q pq p q pq q pq

q

P

e e G

f B

f

f G

e B

Q

f e G

f B

e

f G

e B















Step 7: Measure the active power correction factor

k k

p sp p

P







Step 8: Case when then bus is generator bus, then

check for reactive power limit. If

Q

_gen



Q

_max

set

max

gen

Q



Q

else if

Q

_gen

<

Q

_min

set,

Q

_gen

=

Q

_min

and

otherwise, no change is made in Qp and voltage

residue is evaluated as,

2 2 k2

p p _spec p

V







and

then go to step 10.

Step 9: Measure the reactive power correction

factor

k k

p sp p

Q

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International Journal of Emerging Technology and Advanced Engineering

900

Step 10: Bus count is incremented by 1, i.e. p=p+1

and check if all buses have been accounted else,

move back to step 5.

Step 11: Determine the largest of the absolute

value of residue.

Step 12: If the largest of the absolute value of the

residue is less than

tolerance

then go to step 17.

Step 13: Jacobian matrix elements are evaluated.

Step 14: Voltage increment factor Δ

𝑒

𝑝𝑘

and

Δ𝑓

𝑝𝑘

is

calculated.

Step 15: Calculate new bus voltages

𝑒

𝑝𝑘+1

=

𝑒

𝑝𝑘

+

Δ𝑒

𝑝𝑘

and

Δ𝑓

𝑝𝑘

=

𝑓

𝑝𝑘

+

Δ𝑓

𝑝𝑘

. Evaluate cosine

𝛿

and

sin

𝛿

for all voltages.

Step 16: Advance iteration count is K =K+1, then

go to step 4.

Step 17: Finally bus and line powers flow are

evaluated and results printed.

2.4 Load and line flow analysis (LFA):-

Load is the term used for the power sink [10], which consumes the power either in the form of active power or reactive power. For the stable operation [6] of the power system the load should be resistive in nature so that system’s reactive component could be reduced. But in real world most of the loads either they are residential load, commercial load or industrial load is inductive in nature. It’s a characteristic of the inductive load to consume the reactive power. And, with the increase of load demand the generation should also be increased in order to matchup the power demand. But in real world generation increment asks for huge investment and for engineers minimizing the cost function is the main objective. So in order to match up the generation to demand, engineer need to determine the effect of load change on the line flow of the power system on which this paper is based upon.

This effect of load on the power system line flow is termed as load sensitivity factor. With the change in the load the node voltage also get change, this termed as node voltage

load dependency factor (NVLDF). Also with the change of load results change in the line flows of the system, this termed as line loss load dependency factor (LLLDF). This NVLDF and LLLDF is used to determine the most sensitive node and sensitive line with in the power system on which the effect of change of load is observed to be most.

In the second stage of this paper, load on each bus is been firstly increased to 140% of initial load with an increment of 5% of initial load so that system overloaded condition could be studied.

III CASE STUDIES System data is obtained from [11-12]

3.1 GENERAL 5 BUS SYSTEM:-

Fig. 2 connection diagram of general 5 bus system

3.3 IEEE 30 BUS SYSTEM:-

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International Journal of Emerging Technology and Advanced Engineering

901

GENERAL 5 BUS SYTEM

No. of lines No. of buses No. of generator buses

Tolerance

7 5 1 .0001

IEEE 30 BUS SYTEM

No. of lines No. of buses No. of generator buses

Tolerance

41 30 6 .0001

TABLEI BUS CONNECTION DATA

GENERAL 5 BUS SYTEM

Total shunt loss

0+j0

Slack bus power

Total generation

Total load

Total System loss

1.2945-j0.074

1.695+j0.225 1.650+ j0.400

0.046-j0.174

Total shunt loss

0 + j0

Slack bus power

Total generation

Total load

Total System loss

0.987- j0.074

2.888+j1.083 2.834+ j1.262

0.053+j0.059

TABLEII

NRLINEFLOWANALYSISRESULT

GENERAL 5 BUS SYSTEM

Bus number NODE VOLTAGE LOAD

DEPENDENCY FACTOR(NVLDF)

1 0.000

2 0.000

3 -0.008

4 0.008

5 -0.009

TABLEIII NVLDFFOR5BUSSYSTEM

GENERAL 5 BUS SYTEM REACTIVE POWER LINE FLOW STUDY Line

number

Line from bus

Line to bus

Reactive power line loss load dependency factor

1

₁

₂

_-0.0239

2

₁

₃

_-0.0219

3

₂

₃

_-0.0050

4

₂

₄

_-0.0065

5

₂

₅

_-0.0179

6

₃

₄

_-0.0009

7

₄

₅

_-0.0014

TABLEIV

REACTIVE LINE LOSS LOAD DEPENDENCY FACTOR FOR5BUSSYSTEM

IEEE 30 BUS SYSTEM

Bus number NODE VOLTAGE LOAD DEPENDENCY

FACTOR(NVLDF)

1 0

2 0

3 -0.004

4 -0.005

5 0

6 -0.0039

7 -0.0042

8 0

9 -0.0067

10 -0.0147

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International Journal of Emerging Technology and Advanced Engineering

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12 -0.0071

13 0

14 -0.0107

15 -0.0119

16 -0.0104

17 -0.0122

18 -0.0144

19 -0.0152

20 -0.0144

21 -0.0140

22 -0.0139

23 -0.0142

24 -0.0164

25 -0.0150

26 -0.0190

27 -0.0121

28 -0.0046

29 -0.0168

30 -0.0195

TABLEV

NVLDFFORIEEE30 BUSSYSTEM

REACTIVE POWER LINE FLOW STUDY Line

number

Line from bus

Line to bus

Reactive power line loss load dependency factor

1

₁

₂

_3.3202

2

₁

₃

_1.8712

3

₂

₄

_0.7851

4

₃

₄

_0.5004

5

₂

₅

_2.5338

6

₂

₆

_1.3979

7

₄

₆

_0.3477

8

₅

₇

_0.1543

9

₆

₇

_0.5081

10

₆

₈

_0.0275

11

₆

₉

_2.8063e-16

12

₆

₁₀

₀

13

₉

₁₁

_-3.083e-16

14

₉

₁₀

_2.4671e-15

15

₄

₁₂

_1.2890e-15

16

₁₂

₁₃

_6.1679e-16

17

₁₂

₁₄

_0.1134

18

₁₂

₁₅

_0.3314

19

₁₂

₁₆

_0.0738

20

₁₄

₁₅

_0.0097

21

₁₆

₁₇

_0.0148

22

₁₅

₁₈

_0.0547

23

₁₈

₁₉

_0.0064

24

₁₉

₂₀

_0.0275

25

₁₀

₂₀

_0.1293

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International Journal of Emerging Technology and Advanced Engineering

903

27

₁₀

₂₁

_0.1764

28

₁₀

₂₂

_0.0850

29

₂₁

₂₂

_0.0006

30

₁₅

₂₃

_0.0056

31

₂₂

₂₄

_0.0864

32

₂₃

₂₄

_0.0150

33

₂₄

₂₅

_0.0071

34

₂₅

₂₆

_0.0689

35

₂₅

₂₇

_0.0252

36

₂₈

₂₇

_3.0839e-16

37

₂₇

₂₉

_0.1338

38

₂₇

₃₀

_0.2519

39

₂₉

₃₀

_0.0521

40

₈

₂₈

_0.0155

41

₆

₂₈

_0.0464

TABLEVI

REACTIVE LINE LOSS LOAD DEPENDENCY FACTOR FORIEEE30BUS SYSTEM

IV. RESULT

By line flow analysis (LFA) of the 5 bus system and IEEE 30 bus system, the system parameters like bus voltage, voltage phase angle, active power generation (Pg) and reactive power generation (Qg) for each type of system are obtained.

Further for over-loaded condition study, in which the load is increased to 140% from 100% with an increment of 5% in each step, the NVLDF and the LLLDF is obtained. The NVLDF is the difference of the average incremental node voltage with standard voltage at 100% load. More is the value of NVLDF more is node sensitive to load increment.

The LLLDF is the difference of the average change in line power loss with the standard load. More is the value of LLLDF more is the line loss sensitive to the load increment.

IV. CONCLUSION

LFA of the general 5 bus system is been studied with IEEE 30 bus system. Along with the study of system parameter NVLDF and LLLDF is also obtained.

By table III, most sensitive bus is 5th.

By table IV, most sensitive line is line number 1and 2. By table V, most sensitive bus is bus number 26th and 30th. By table VI, most sensitive line is line number 1st, 2nd and 5th line.

For this paper, program is been designed in the MATLAB2013a environment.

V. REFERENCES

[1] A.E. Guile and W.D. Paterson, „Electrical power systems, Vol. 2‟, (Pergamon Press, 2nd edition, 1977).

[2] Carpentier “Optimal Power Flows”, Electrical Power and Energy Systems, Vol.1, April 1979, pp 959-972.

[3] W.D. Stevenson Jr., „Elements of power system analysis‟, (McGraw-Hill, 4th edition, 1982).

[4] Hadi Saadat, “Power System Analysis”, Tata McGRAW-HILL Edition.

[5] W. F. Tinney, C. E. Hart, "Power Flow Solution by Newton's Method, " IEEE Transactions on Power Apparatus and systems , Vol. PAS-86, pp. 1449-1460, November 1967.

[6] A. J. Wood, B. F. Wollenberg. Power Generation Operation and Control. 2nd ed. John Willey & Sons Inc

[7] Load flows, Chapter 18, Bus classification, Comparison of solution methods, N-R method–Electrical Power system by C.L.WADHWA.

[8] D.I.Sun, B.Ashley, B.Brewer, A.Hughes and W.F.Tinney, “Optimal Power Flow by Newton Approach”, IEEE Transactions on Power Apparatus and systems, vol.103, No.10, 1984, pp2864-2880.

[9] T.K.A. Rahman and G.B. Jasmon, “A new technique for voltage stability analysis in a power system and improved loadflow algorithm for distribution network,” Energy Management and Power Delivery Proceedings of EMPD '95; vol.2, pp.714 – 719, 1995. [10]P. Kundur, 1. Paserba, V. Ajjarapu, G. Anderson, A. Bose, C.A.

Canizares, N. HatziargYfiou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsem, and V. Vittal, "Definition and Classification of Power System Instability," IEEE Trans. On Power Systems, Vol. 19, No.2, pp.1387-1401, May 2004

[11]A. Bergen and V. Vittal, “Power Systems Analysis,” second edition, Prentice Hall, Upper Saddle River, New Jersey, 2000