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Proc. of Int. Conf. on Control, Communication and Power Engineering 201010

Proposed Procedure for Determination of Heavily Loaded Branch of a Power Network Using Novel Voltage Stability Indicator on the Verge of Voltage Collapse Point Sumit Banerjee, Member IEEE 1, C.K. Chanda2, Pratap Sekhar Puhan2, Prosit Ghosh 1 ,Ruchira De 1 1

Dr B.C. Roy Engineering College/ Department of Electrical Engineering, Durgapur , India Email: sumit_9999@rediffmail.com, prosit_714@yahoo.com, ruchira.de@gmail.com 2 Bengal Engineering and Science University /Department of Electrical Engineering, Howrah, India Email: ckc_math@yahoo.com, puhan_samal@rediffmail.com Abstract— This paper presents a novel approach for determining the weakest branch or the heavily loaded branch of a power network on the verge of voltage collapse point. The proposed procedure for determination of heavily loaded branch of a power network using novel and unique voltage stability indicator at the proximity of voltage collapse point was tested on the simple IEEE 14 bus interconnected systems and significant results are observed to be in very good agreement.

load bus voltage of a power system within reactive loading index range [8].

II. THEORY We consider a simple 2-bus system as shown in figure 1.

V S = V S ∠δ S

Index Terms— Interconnected systems, Local voltage stability indicator, voltage collapse, voltage stability, weakest branch.

G

IS

VL = VL ∠δ L

Z S = Z S ∠α

IL

Z L = Z L ∠φ

I. INTRODUCTION Figure 1

Voltage stability [1,2] is a major concern for proper control and assessment of security of large power systems in contingency situation, specially in developing countries because of unusual growth of load demand and lacuna in the reactive power management side. It is mostly associated with ultimate voltage collapse which can appear in a distribution system [3-6] operating under the most heavy loading condition, so that the voltage decreases monotonically leading the system to be blackout. The problem of voltage collapse generates due to the inability of the power system to cope with its reactive power supply and demand , i.e., mismatch of reactive power generation and voltage [7,8].

Most of the low voltage distribution systems [3,4] having single feeding node and the structure of the network is mainly radial with some uniform and nonuniform tapings.

Radial distribution systems [4,9] having a high resistance to reactance ratio, which causes a high power loss. Hence, the radial distribution system is one of the power systems, which may suffer from voltage instability. For a low voltage distribution system, the conventional Newton-Raphson method normally suffers

r Here a load having an impedance of Z L = Z L ∠φ is connected to a source through an impedance of r Z S = Z S ∠α . If line shunt admittances are neglected, the current flowing through the line equals the load current.

From figure1, the current flowing through the line is given by,

IL =

VS ∠δ S − VL ∠δ L RS + jX S

(1)

The complex power is written as

S L = PL + jQL = VL I L* P − jQ P − jQ L or, IL = L * L = L VL ∠ − δ L VL

(2)

From (1) and (2)

VS ∠δ S − VL ∠δ L PL − jQL = VL ∠ − δ L RS + jX S

R from convergence problems due to high ratio of the X

[RS PL + X S QL ] + j[X S PL − RS QL ] = 2 VS VL [cos(δ S − δ L ) + j sin (δ S − δ L )] − VL

branches.

This paper has developed a novel and new voltage stability margin indicator [10] of a low voltage distribution system to estimate the maximum permissible

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A simple equivalent 2-bus system of interconnected type of power system.

(3)

(4)

Proc. of Int. Conf. on Control, Communication and Power Engineering 201010

III. ABOUT THE PROPOSED MODEL

Equating real and imaginary part of (4), we get

[RS PL + X S QL ] = VS VL

cos(δ S − δ L ) − V L

2

(5)

Neglecting the line shunt admittances of simple two bus system we have calculated the voltage stability indicator (VSI) from (10). This procedure of VSI determination can be extended to all the branches of the system from (10). In interconnected system, we have considered two bus systems for determining the VSI of branch connected between the two buses and for determining VSI, the greater of two voltages are taken as source voltage and other as load voltage. Now we have calculated the magnitude and the phase angle of the line impedance in per unit and degree respectively of all the branches of the interconnected system. After that we have calculated the VSI of all the branches of the interconnected system.

The graph have plotted for voltage stability indicator of all branches of the system. Here we have tested the above proposed theory for IEEE 14-bus system to establish the said fact.

and

[X S PL − RS QL ] = VS VL sin(δ S − δ L )

(6)

From (5) and (6), we get

VS VL cos(δ S − δ L ) − VL

2

=

⎡ VS VL sin (δ S − δ L ) + RS QL ⎤ RS ⎢ ⎥ XS ⎣ ⎦ + X S QL VL

2

⎡⎧ RS ⎫ ⎤ ⎬ sin (δ S − δ L )⎥ ⎢⎨ + V L VS ⎢⎩ X S ⎭ ⎥ ⎢ − cos (δ − δ ) ⎥ S L ⎣ ⎦

⎡ R2 ⎤ + QL ⎢ S + X S ⎥ = 0 ⎣XS ⎦

IV. SIMULATION AND GRAPHICAL ANALYSIS OF CASE STUDY CONDUCTED

(7)

Case study is conducted on a simple IEEE 14 bus system. The single line diagram, bus data and line data of IEEE 14 bus system are given in [11].

The equation (7) is quadratic in nature and to have real roots, the discriminate must be greater than or equal to zero.

From (7), we get

⎤ 2 ⎡⎧ R ⎫ V S ⎢ ⎨ S ⎬ sin (δ S − δ L ) − cos (δ S − δ L )⎥ ⎦ ⎣⎩ X S ⎭

2

Line No.

⎡R ⎤ − 4Q L ⎢ + XS⎥ ≥ 0 ⎣XS ⎦ 2 S

or,

4QL

TABLE I CALCULATION OF Z S AND

(8)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

{R + X } 2 S

2 S

2

2

VS XS ⎡⎧ RS ⎫ ⎤ ⎢⎨ ⎬sin(δS −δL ) − cos(δS −δL )⎥ ⎣⎩XS ⎭ ⎦

(9)

≤1 Here

4QL

{R

2 S

+ X S2

}

2

VS X S ⎡⎧ RS ⎫ ⎤ ⎢⎨ ⎬ sin (δ S − δ L ) − cos(δ S − δ L )⎥ ⎦ ⎣⎩ X S ⎭

2

is

termed as Local Voltage Stability Indicator (VSI) and to maintain stability, the condition is VSI ≤ 1.

Hence,VSI=

4QL 2

{R

2 S

+ X S2

}

VS X S ⎡⎧ RS ⎫ ⎤ ⎢⎨ ⎬ sin (δ S − δ L ) − cos(δ S − δ L )⎥ ⎦ ⎣⎩ X S ⎭

2

(10)

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VL in p.u.

1.045 1.010 1.019 1.020 1.020 1.010 1.019 1.020 1.019 1.062 1.019 1.056 1.051 1.057 1.055 1.050 1.036 1.051 1.050 1.036

VS in p.u

1.060 1.045 1.045 1.060 1.045 1.019 1.020 1.070 1.062 1.090 1.056 1.062 1.056 1.070 1.070 1.070 1.056 1.057 1.055 1.050

δ L in δ S in degree

degree

-4.98 -12.74 -10.28 -8.76 -8.76 -12.74 -10.28 -8.76 -10.28 -13.34 -10.28 -14.92 -15.08 -14.78 -15.07 -15.15 -16.02 -15.08 -15.15 -16.02

0.0 -4.98 -4.98 0.0 -4.98 -10.28 -8.76 -14.22 -13.34 -13.34 -14.92 -13.34 -14.92 -14.22 -14.22 -14.22 -14.92 -14.78 -15.07 -15.15

α

ZS

in p.u.

0.0622 0.2034 0.1857 0.2294 0.1829 0.1836 0.0441 0.2520 0.2091 0.1761 0.5561 0.1100 0.0902 0.2204 0.2838 0.1461 0.2987 0.2089 0.2979 0.3877

α in degree 71.87 76.65 71.76 76.39 71.87 68.60 72.40 90 90 90 90 90 69.38 64.47 64.33 63.07 64.82 66.87 42.13 63.84

Proc. of Int. Conf. on Control, Communication and Power Engineering 201010 TABLE II CALCULATION OF VOLTAGE STABILITY INDICATOR Between Buses

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1-2 2-3 2-4 1-5 2-5 3-4 4-5 5-6 4-7 7-8 4-9 7-9 9-10 6-11 6-12 6-13 9-14 10-11 12-13 13-14

A. So our proposed idea for estimation of voltage stability indicator is a good method for the operating personal to bring back the voltage level within the estimated range.

B. The proposed estimation method is helpful in power system voltage stability limit in post contingency conditions.

Voltage stability indicator 0.03156 0.15820 0.02990 0.01480 0.01180 0.14950 0.00700 0.01420 0.02900 0.00000 0.07820 0.06480 0.02000 0.01550 0.01780 0.03370 0.06020 0.04730 0.09280 0.07950

REFERENCES [1] H. K. Clark, “ New challenges: Voltage stability ” IEEE Power Engg Rev, April 1990, pp. 33-37.J. Clerk Maxwell, A Treatise on Electricity and Magnetism, 3rd ed., vol. 2. Oxford: Clarendon, 1892, pp.68–73.

[2] P. A. Lof, G. Anderson and D. J. Hill, “ Voltage stability indices of stressed power system”, IEEE Tran. PWRS vol. 8 No. 1, 1993, pp. 326-335..

[3] M. Chakravorty, D. Das, “ Voltage Stability Analysis of Radial Distribution Networks”, Electric Power and Energy Systems,Vol. 23, pp. 129-135, 2001.

[4] R. Ranjan, B. Venkatesh, D. Das, “Voltage Stability Analysis of Radial Distribution Networks”, Electric Power Components and Systems,Vol. 31, pp. 501-511, 2003.

[5] J.F. Chen, W. M. Wang, “ Steady state stability criteria and uniqueness of load flow solutions for radial distribution systems”, Electric Power and Energy Systems,Vol. 28, pp. 81-87, 1993.

[6] M.H. Haque, “ efficient load flow method for distribution systems with radial or mesh configuration”, IEE Proc.Gener, Transm. Distrib., Vol. 143, No. 1,1996, pp. 33-38.

[7] Ph.D thesis of Dr. C.K. Chanda on “Global voltage stability indicator index” in 2003,BESU [8] T. Van Cutsem: “ A method to compute reactive power margins with respect to voltage collapse”, IEEE Trans. on Power Systems, No. 1, 1991.

[9] F. Gubina and B. Strmcnik, “A simple approach to voltage stability assessment in radial network”, IEEE Trans. on PS, Vol. 12, No. 3, 1997, pp. 1121-1128 [10] M.H. Haque, “On-line monitoring of maximum permissible loading of a power system within the voltage stability limit”, IEE Proc.-Gener , Transm. Distrib. , Vol.150,No.1,2003,pp.107-112.

[11] M. A. Pai, Computer Techniques in Power System Analysis, 2nd ed., Tata McGraw-Hill Publishing Company Ltd., New Delhi,2006, pp. 226-235.

0.2 indicator

Voltagestability

Line No.

CONCLUSIONS

0.15 0.1 0.05 0 1

3

5

7

9

11 13 15 17 19

Line num be r

Figure2

Voltage stability indicator of all branches of the IEEE 14 bus system.

V.

DISCUSSION OF RESULTS

We have determined the voltage stability indicator (see Table II) for all branches of the interconnected system.

Now from the above simulation result, it is observed that line number 10 can be considered as the weakest branch or heavily loaded branch of the system (see Figure 2).

Hence, once the voltage stability indicator is achieved, the operating personnel can have a sufficient knowledge regarding the overstressed or weakest branch of the power network.

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