Voltage Stability Enhancement of Radial Distribution System Using Distributed Generators

K. Vinothkumar#, B. Santosh Kumar# and M.P.Selvan*

*Assistant Professor, #, *Department of EEE, National institute of Technology, Tiruchirappalli, Tamilnadu, India – 620015. (e-mail: selvanmp@nitt.edu)

Abstract - This paper presents an approach for enhancement of voltage stability of radial distribution system employing distributed generators (DG). Among various indices reported in the past, a superlative index is identified and utilized for determination of distribution system voltage stability by reducing the radial distribution system into two bus equivalent. Thereafter, suitable locations for DG placement are identified to enhance the voltage stability and reduce system power loss. The simulation study is carried out on 31 bus and 33 bus radial distribution systems using the software program developed in MATLAB environment. Key words – Voltage Stability Index, Radial Distribution System, Distributed Generation

I. INTRODUCTION An electric power system can be classified in accordance with the operating voltage levels as generation, transmission and distribution systems. The distribution system widely varies from the transmission system in respect of its operation and characteristics and is generally radial in nature.

The power distribution network is constantly experiencing an ever growing load demand. The load on the system is not constant and varies over a wide range within the same day. Hence, the system stability is of great concern under severe loading conditions in the distribution system. System stability is characterized by an initial slow variation in system operating point until a sharp accelerated change occurs with load increase. If the system loading increases beyond this point then the distribution system will experience a voltage collapse.

Research efforts have yielded different tools and

methodologies for the prediction of system voltage collapse or instability [1] – [3]. These indices are the measure of distribution system voltage stability following any variations in the connected loads, which can have a maximum value of one at the verge of point of voltage collapse and a minimum value of zero when there is no load present in the system.

Owing to fast depleting conventional energy sources and the need for achieving reduced emission levels, the penetration of renewable energy sources as distributed generation (DG) into distribution grids is gaining significant importance. Moreover, the distribution system losses are also reduced with DG placement [4].

In this paper, the radial distribution system

(RDS) is represented by its two bus equivalent system and a superlative index is identified for the determination of its voltage stability. With the help of this superlative index and employing DG placement, an attempt to enhance the voltage stability of the considered distribution system is proposed in this paper. Finally, the suitable location for DG placement is identified based on achieved levels of voltage stability index and system power loss reduction.

II. TWO BUS EQUIVALENT OF RDS The two bus equivalent of radial distribution

system is derived in [3]. The reduced single line network is shown in Fig. 1.

sV rV

eq eq eqr jx z θ+ = ∠

eq eqP jQ+ r rP jQ+

Fig. 1 Single line diagram of two bus equivalent of RDS

In Fig.1,

( )2 2

eqeq

eq eq

Rr

P Q=

+ and

( )2 2

eqeq

eq eq

Xx

P Q=

+ (1)

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 6

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

where eqr and eqx are the equivalent resistance and

reactance of the line respectively, eqR and eqX are

the total real and reactive power loss, eqP and eqQ are the total real and reactive powers injected at the first node.

III. IDENTIFICATION OF SUPERLATIVE VOLTAGE STABILITY INDEX

In the past, several indices were proposed to evaluate the voltage stability of RDS. Among all, the indices given below [1-3] are considered in the present analysis based on the reduced two bus equivalent of RDS:

( )( )( )2

4

coseq r

p

s

r PL

V θ δ

+=

− (2)

( )

[ ]22

4 coscos

rv

s

SL

Y Vθ φδ+⎡ ⎤⎣ ⎦= (3)

( ) ( )( )1

2 2 24 eq r eq r eq r eq rL x P r Q x Q r P= − + + (4)

where θ , φ and δ are the impedance angle, power factor angle and angle difference between the voltages sV and rV The above indices are computed for 31 bus system (single line diagram and data are given in the Appendix) with different load levels at bus-20, which is shown in Fig. 2. The index values are zero when there is no load available in the system and as the system load is increased (at bus-20), the indices value increases until it approaches unity at the point of voltage collapse or voltage instability.

Fig. 2. Voltage stability index of bus-20 in 31 bus system

Fig. 3. Voltage stability index of bus-33 in 33 bus system

It can be inferred from Fig. 2 that the vL index performs better compared to the other two in indicting the voltage collapse point. This inference is confirmed by performing similar study on 33 bus system [5] and the results are presented in Fig. 3. Based on the above study, the vL index is identified as a superlative index for determination of voltage stability of the distribution system.

IV. VOLTAGE STABILITY ANALYSIS

A. Voltage Stability under Base Case Loading

Fig. 4 vL indices with loading at all buses in 31bus system

The vL index curves for 31 bus system with varying loading conditions at each bus are shown in Fig. 4. It can be observed that the buses nearer to substation can be loaded slightly more compared to the nodes farther from the substation. This is attributed to the line loss and subsequent reduced voltages at these nodes. This inference can also be taken from vL index shown in Fig. 4. From the above analysis, three locations are identified as discussed below for DG placement in the distribution system in order to enhance the voltage stability of the distribution system.

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 7

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

Location 1: Bus with lowest slope for vL index curve - bus 29 Location 2: Bus with medium slope for vL index curve - bus 27 Location 3: Bus with highest slope for vL index curve - bus 11 The size of DG unit to be connected is considered to be equal to 25% of the total load in the network and for simplicity of the analysis, DG is modeled as negative constant power load. B. Voltage Stability Analysis with DG at Location 1(Bus 29)

Fig. 5. vL index with DG at bus - 29 in 31 bus system

The vL Index curves for 31 bus system with DG at bus 29 are shown in Fig. 5. The slopes of the curves are similar to that of base case. The voltage stability index vL has the lowest slope at the considered location, which indicates that the considered location is highly stable. No significant changes in the index values are observed after placement of DG units also. C. Voltage Stability Analysis with DG at Location 2 (Bus-27) The vL index curves for 31 bus system with DG at bus-27 are shown in Fig. 6. This location is geographically at the middle of the network and hence power fed by DG flows in both the directions and thereby reduces the line losses. It is observed from Fig. 6 that vL index shows a slightly reduced slope compared to the base case. This indicates that an increased loading with enhanced stability can be achieved using DG placement at this location.

Fig. 6. vL index with DG at bus – 27 in 31 bus system

D. Voltage Stability Analysis with DG at Location 3(Bus-11)

Fig. 7 vL index with DG at bus-11 in 31 bus system

The vL index curves for 31 bus system with DG at bus-11 are shown in Fig. 7. Substantial reductions in the steepness of the curves compared to the base case are observed. This shows that bus-11 is ideally suitable for placement of DG units as increased loading without losing stability of the system can be achieved. E. Voltage Stability Analysis with equal distribution of DG at all three locations The total capacity of the DG considered in the previous cases is equally distributed at all the three locations and the corresponding vL index curves are shown in Fig. 8. The results are similar to that obtained by placing DG at bus-27.

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 8

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

Fig. 8 vL index with DG at all three locations in 31 bus system

Fig. 11 vL index with DG at bus-6 in 33 bus system

Fig. 9. vL index with loading at all buses in 33 bus system

Fig. 12 vL index with DG at bus-17 in 33 bus system

Fig. 10 vL index with DG at bus-22 in 33 bus system

Fig. 13 vL index with DG at all three locations in 33 bus system

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 9

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

Thus it is understood that the suitable location for DG placement is the node with large slope for vL curve. In order to ensure the validity of this observation, similar analysis is carried out with 33 bus system. The vL index curves for the base case are shown in Fig. 9. Based on this, the locations identified for DG placement are: Location 1: lowest slope - bus 22 Location 2: medium slope - bus 6 Location 3: highest slope - bus 17 Considering DG at the above identified locations, the vL index curves with DG placement at the identified locations are given in Figs. 10-13.

V. POWER LOSS ANALYSIS The total power loss without and with DG are furnished in Tables. I and II for 31 and 33 bus systems respectively.

TABLE – I

POWER LOSS IN 31 BUS SYSTEM

Real Power Loss (MW)

Reactive Power Loss

(Mvar) Base Case

(Without DG) 1.500 0.750

DG at bus – 29 1.250 0.703 DG at bus – 27 1.070 0.575 DG at bus – 11 0.570 0.260

DG of equal size at all three bus 0.797 0.402

TABLE – II

POWER LOSS IN 33 BUS SYSTEM

Real Power Loss (MW)

Reactive Power Loss

(Mvar) Base Case

(Without DG) 0.200 0.140

DG at bus – 22 0.170 0.120 DG at bus – 06 0.120 0.076 DG at bus – 17 0.120 0.088

DG of equal size at all three bus 0.120 0.077

From Tables I and II, it can be observed that the power loss reduction is more, when DG is placed at a location identified in the vL index with highest slope, i.e. bus-11 and bus-17 in 31 and 33 bus systems respectively. Hence, it can be concluded that suitable location for DG placement can be identified with the

vL index so as to enhance voltage stability and reduce power loss in the distribution system.

VI. CONCLUSION A method for placement of DG units in the distribution system is proposed in this paper, in order to enhance the voltage stability and reduce power loss. A superlative index is identified and DG is placed at different locations during the analysis. Based on the results of the analysis, it can be concluded that the location with large slope for the

vL index curve will be the suitable location for DG placement. DG placement at such selected location enhances the voltage stability and reduces system power loss to a great extent.

REFERENCES

[1] M. Moghavvemi, M.O.Farurue, “Technique for assessment

of voltage stability in ii-conditioned radial distribution network”, IEEE Power Engineering Review, January, 2001, pp.58-60.

[2] G.B.Jasmon, L.H.C.C. Lee, “Stability of load flow

techniques for distribution system voltage stability analysis”, IEE Proceedings-C, vol. 138, No. 6, November, 1991, pp.479-484.

[3] Mohamed M. Hamada, Mohamed.A.A. Wahab, Nasser.

G.A. Hemdan, “Simple and efficient method for steady-state voltage stability assessment of radial distribution systems”, Electric power and energy systems, 2009, pp. 152-160.

[4] W.El-Khattam, M.M.A.Salama, “Distributed generation

technologies, definitions and benefits”, Electric Power Systems Research, 71, 2004, pp.119-128.

[5] Selvan M P, and Swarup K S., “Distribution system load

flow using object oriented methodology”, International Conference on Power System Technology, POWERCON – 2004, Singapore, Nov.21– 24, 2004, 1168 – 1173.

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 10

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.

APPENDIX

Fig. 14 Single line diagram of 31 bus system

TABLE III TABLE IV LOAD DATA OF 31-BUS SYSTEM BRANCH DATA OF 31-BUS SYSTEM

Branch impedance Branch Number

Bus i Bus j

Rij(Ω) Xij(Ω) 1 0 1 0.896 0.155 2 1 2 0.279 0.015 3 2 3 0.444 0.439 4 3 4 0.864 0.751 5 4 5 0.864 0.751 6 5 6 1.374 0.774 7 6 7 1.374 0.774 8 7 8 1.374 0.774 9 8 9 1.374 0.774

10 9 10 1.374 0.774 11 10 11 1.374 0.774 12 11 12 1.374 0.774 13 12 13 1.374 0.774 14 13 14 1.374 0.774 15 8 15 0.864 0.751 16 15 16 1.374 0.774 17 16 17 1.374 0.774 18 6 18 0.864 0.751 19 18 19 0.864 0.751 20 19 20 1.374 0.774 21 6 21 0.864 0.751 22 3 22 0.444 0.439 23 22 23 0.444 0.439 24 23 24 0.864 0.751 25 24 25 0.864 0.751 26 25 26 0.864 0.751 27 26 27 1.374 0.774 28 1 28 0.279 0.015 29 28 29 1.374 0.774 30 29 30 1.374 0.774

Maximum load at bus j Bus j P(kW) Q(kVAR)

1 - - 2 522 174 3 - - 4 936 312 5 - - 6 - - 7 - - 8 - - 9 189 63

10 - - 11 336 112 12 657 219 13 783 261 14 729 243 15 477 159 16 549 183 17 477 159 18 432 144 19 672 224 20 495 165 21 207 69 22 522 174 23 1917 639 24 - - 25 1116 372 26 549 183 27 792 264 28 882 294 29 882 294 30 882 294

16th NATIONAL POWER SYSTEMS CONFERENCE, 15th-17th DECEMBER, 2010 11

Department of Electrical Engineering, Univ. College of Engg., Osmania University, Hyderabad, A.P, INDIA.