On-Line Voltage Stability Based Contingency Ranking Using Fast Voltage Stability Index

(FVSI) Ismail Musirin. Student Member, IEEE, and 'Titik Khawa Abdul Rahman , Member, IEEE i

Abslracf-Voltage instability is one phenomenon that could happen in a power system due to its stressed condition. The result would be the occurrence of voltage collapse which leads to total blackout to the whole system. Therefore voltage collapse prediction is important in power system planning and operation so that the occurrence of voltage collapse due to voltage instability could be avoided. Line outage in a power system could also lead to the event of voltage collapse which implies the contingency in the system. Line outage contingencies are ranked so that the line which highly effects voltage stability of the system when there is an outage occurs in this line could be identified. The contingency ranking process can be conducted by computing the line stability index of each line for a particular line outage and sort them in descending order. The contingency which is ranked highest implies that it contributes to system instability. This paper presents a new voltage stability index refers to a line namely fast voltage stability index (FVSI). The values of the line indices indicate the voltage stability condition in the system and it is used to rank the line outage contingency. The information from the contingency ranking denotes the severity of the voltage stability condition in a power system due to line outage. The proposed contingency ranking technique was tested on an IEEE reliability test system.

Index Terms- Voltage stability, contingency ranking, voltage collapse.

1. INTRODUCTION

Voltage violation in a system could be caused by the stressed load and unpredictable events in the power system termed as contingencies. Contingencies can be resulted by the outage of lines and generator in the system. Line outages could occur in the form of single or multiple. Contingency analysis is a division in the voltage stability analysis. Since contingency is one of the contributing factors in voltage violation in the system, therefore contingency analysis and voltage collapse prediction are conducted concurrently. The procedures in the voltage collapse prediction and contingency analysis are quite similar with line outage simulation included

off-line or on-line [6 ] making it beneficial to the power system operators. Most of the voltage stability condition was conducted using voltage stability index or proximity as the measuring instrument. Various indices [ 1]-[5] have been proposed in the literature in order to predict the occurrence of voltage collapse. New technique using neural network was also adapted as reported by D Sutanto et al.[5] and other artificial intelligent techniques [7].

This paper presents a novel Fast Voltage Stability Index (FVSI) used to predict the occurrence of voltage collapse and contingency analysis caused by line outage in a power system. It proposed a simple mathematical formulation which in turn speeded up the process of voltage stability analysis. The voltage stability and contingency analyses were conducted consecutively on the IEEE 24-bus reliability test system and produced promising results. In the voltage stability analysis, the line that gives index value closest to 1.00 will be taken as the most critical line corresponds to a bus that may lead to the whole system instability. At this point, the reactive load that could be connected to the bus is considered as the maximum permissible load and bus ranking in the system could be done by sorting the maximum permissible load in ascending order. The smallest maximum permissible load is ranked the highest implying that the bus is the weakest bus in the system and vice versa. Subsequently, contingency ranking caused by line outage is ranked based on its severity. FVSI for each outage are sorted in descending order in which the highest FVSI implies the most critical outage in the system and vice versa. The proposed technique was verified by examining the test system using line stability index, L, proposed by M Moghavemmi el al. [ I ] and line stability factor, LQP formulated by A Mohamed el aL[2]. Results showed that the developed FVSI exhibit an indicative tool in predicting the occurrence of voltage collapse and ranking the contingencies. It is possible to be implemented practically.

in the continaency analysis. Throughout the years simulation TI tNnFY FORM1 11 A T l n N __. .. .I-_. . - -. . . . studies are progressively carried out to investigate further impact of contingencies caused by line or generator outages. The advancement of t e c ~ o l o g y has aided the computation to be faster. The analysis can be conducted either

Fast voltage stability index abbreviated by FVSI referred to a line is formulated in this study as the measuring instrument in predicting the voltage stability condition in the system. The mathematical formulation is very simple that could speed up the computation. The proposed index made used the same

set to be greater or equal thadto zero to achieve stability. If ' Ismail Musirin can be contacted through: ismailbmu.elec1.itm.cdu.m I Khawa Abdul Rahman is an AsSoc. prof, at ,; Faculty afEle&ical concept as the existing ones [I], 121 in which discriminant is Engineering, Universiti Teknolagi MARA, MALAYSIA. (e-mail:khawa(3ener.uitmedu.mv)

0-7803-7525-4/02/$17.00 0 2002 IEEE. 1118

p,-ie, V*L - 6

the discriminant is small than zero, the roots for the voltage or

could cause instability in the system. The indices proposed by M Moghavemmi et al. [ I ] and A Mohamed et a/ [2] are taken in the comparison since these indices also referred to a line

- - power quadratic equations will have imaginary roots that

Equating (1 ) and (4) we obtained,

V , L O - V ; L ~ P? - .iQ? K + j X - V z L - 8

that makes the comparison possible. __

(4)

A Derivation of Fast Voltage Stability Index (FVSI) ViV2L-rj - VzZLO=(R+)X)(P~ - jQ) ( 5 )

The condition of voltage stability in a power system can be characterized by the use of voltage stability index. This index can either be referred to a bus or a line. The voltage stability index developed in this research is referred to a line. Generally, it started with the current equation to form the power or voltage quadratic equations. The criterion employed in this paper was to set the discriminant of the roots of voltage or power quadratic equation to be greater than zero. When the discriminant is less than zero, it causes the roots of the quadratic equations to be imaginary which in turn causing the voltage instability that may cause voltage collapse in the system. The line index that is evaluated close to 1.00 will indicate the limit of voltage instability.

separating the real and imaginary parts yields,

and, Vi L ’ Z C O S ~ - Y:’ = R P ? + ( 6 )

-V,V2sin6 =XP2-RQ2 (7)

Rearranging quadratic equation of V2;

(7) for P2 and substituting into (6 ) yields a

The roots for V2 will be;

To obtain real roots for V2, the discriminant is set greater than or equal to ‘0’; i.e; bu5 2

I

C l (10) 4ZQ>X Fig. I . 2-bus power system model

Fig. 1 illustrates a 2-bus power system model where the proposed FVSl is derived from. The symbols are explained as follows:

V, , V2 PI, QI P2, Q2

(VI)’(Ksind +Xcos8)’ -

Since 8 is nomally very small then,

6 a 0, R s i n 6 S O and Xcos&=X = voltage on sending and receiving buses = active and reactive power on the sending bus = active and reactive power on the receiving

Taking the symbols ‘i’ as the sending bus and ‘j’ as the receiving bus. Hence, the fast voltage stability index, FVSl can be defined bv:

bus

buses 6 = S I - & *

SI, S I = apparent power on the sending and receiving

= angle difference between sending and receiving

4Z2Q, v, zx FVSi,, = __

where: Z = line impedance X = line reactance

buses Qi = reactive power at the receiving end

The line impedance is noted as Z = R+jX with the current that V; = sendingend voltage

The value of FVSl that is evaluated close to 1.00 indicates that the particular line is closed to its instability point which

/ = U 1 (‘1 may lead to voltage collapse in the entire system. To maintain

flows in the line IS given by;

rI 1.0 - v.,Ld 1, 7 ,A

a secure condition the value of FVSl should be maintained V I is taken as the reference, and therefore the angle is shifted lPrr ,hnn 1 00 ..-.. ._I“ I.. I..

into 0. The apparent power at bus 2 can be written as;

s2 = V 2 i

Rearranging (2) yields;

(2) B. Line Stability index

M Moghavemmi et a/. [3] derived a line stability index based on a power transmission concept in a single line. A single line in an interconnected network is illustrated in Fig. 2. (3)

1119

'S 4

I r+j x - \h SSFpS+jQs Yb S,=P,+jQ,

Fig. 2. Typical one-line diagram oftransmission line

Using the R model, the roots for the voltage quadiatic equation can be derived as;

where, 6, - S2 = 6 and e is the line impedance angle

Setting the discriminant to be greater than zero, the line stability index can he reproduced as;

4Qr x ~ K I sin(^-^)]^

L," =

where: x = line reactance Q, V, = sending end voltage e = line impedance angle 6

= reactive power at the receiving end

=the angle difference between the supply voltage and the receiving voltage

C. Line Srabilify Factor

A Mohamed er al. [2] derived a line stability factor based on a power transmission concept in a single line. The formulation begins with the current equation in a power system. Fig. 3 illustrates a single line of a power transmission concept.

2

Fig. 3. Single line of power transmission concept

The power equation can be derived as;

X 7 ", Q,' - Q, +($e * + Q,]

The line stability factor is obtained by setting the discriminant of the reactive power roots at bus 1 to be greater than or equal to zero thus defining the line stability factor, LQP as,

where: X = line reactance

Qj = reactive power at the receiving end Pi = sending end power Vi = sending end voltage

LQP must be kept less than 1 .OO to maintain a stable system

load bus = 1

3

determine the weaker1 bus

Wfy mth her tnhnque

Fig. 4. Flow chart for voltage stability analysis

111. VOLTAGE STABILITY ANALYSIS

Voltage stability analysis is mainly conducted to predict the point of voltage collapse using the proposed fast voltage stability index (FVSI). It is performed on the lEEE 24-bus reliability test system that consists of 11 generator buses and 13 load buses with 38 interconnected lines. Initially, a load flow program was developed to obtain the power flow solution in the system. The results from the load flow computation are used to calculate the FVSI values for each line in the system. The load flow computation is run from the base case, gradually increased until it stops converging. All load buses in the system are consecutively tested in order to determine the overall system performance accurately. Results from this experiment indicate the point of voltage stability condition, weak bus and critical line in the system. The voltage stability condition and the critical line referred to a particular bus are determined by the FVSI value close to 1 .OO while the weak bus is determined by the maximum permissible load for the individual bus in the system. Load ranking is done by sorting the maximum permissible load in ascending order. The lowest value of maximum permissible load characterizes the highest rank of bus which is the

I120

weakest one in the system. Verification of the proposed technique is also performed by carrying out the similar process using I- and LQP as the indicator. The whole process is represented in the flow chart of Fig. 4.

F , + I Fig. 5 . Flow chart for conti ency analysis

IV. CONTINGENCY ANALYSIS

In order to observe the impact of line outage in the system, contingency analysis is performed on the system. Contingency analysis is conducted by removing the lines in the system in sequence for every pre-determined case. The- predetermined cases are as follows; case i: base case, case ii: Q, = 1.0 P.u., case iii: Q5 = 1.0 P.u., case iv: Qlo= 2.0 pu., case v: Q20 = 7.5 PA. The pre-determined cases are set at half of the maximum permissible load obtained from the voltage stability analysis. This is done in order to slow down the divergence of the load flow computation, otherwise the load flow diverged too fast and produced an incorrect result. of contingency ranking. The procedures for contingency analysis is almost similar to the one in voltage stability analysis. The only difference is that, load flow computation is run with a line outage at a time and there is no need to increase the reactive power loading in the system. The buses are randomly

chosen to justify the severity of outages that could occur in the system. FVSI were computed on every outage for all cases. Results from every outage will be sorted in descending order. The outage that resulted the highest index exhibited the most severe contingency. The complete procedures are envisaged in the flow chart appeared in Fig. 5 .

Weakest tine for each bus vs reactive load ru(ation (IEEE ZCbur)

Il..ctnr l0.d ".".110.

: ~ $ ~ , : : ; ~ $ ~ ; * - ~

M e n km= ** Fig 6. Highest Index referred to a bus versus reactive load variation

V. RESULTS AND DISCUSSION

Results for the voltage stability analysis that aimed to determine the voltage stability condition, weak bus and load ranking in the system are shown in Fig. 6 and Fig. 7. Fig. 6 illustrates the response for critical line on each bus against the reactive load variation. These lines are the dominating lines that exhibited the highest FVSI values for every tested bus. The line that exhibits the highest rate of change of FVSI is considered as the critical line referred to a bus while the value of maximum reactive load at FVSI value closed to 1.00 is assigned as the maximum permissible load. The critical lines extracted from every load bus are plotted together on the same graph in order to identify weak bus in the system. Weak bus is determined by looking at the maximum permissible load rather than the FVSl values since beyond this limit system will be already unstable.

From Fig. 6, it is obvious that the line index increases as the reactive power loading increased. Line 6 is the most critical line corresponds to any load change at bus 3. Bus 3 has the smallest maximum permissible load of 2.15 p.u. and it is ranked the highest in the system. On the other hand, line 36 is the most critical line corresponds to load change at bus 20. Since bus 20 has a maximum permissible load at 16.00 P.U., therefore it is the most secure bus in the system according to its large maximum loadability. The bar chart appeared in Fig. 7 is derived from the graph in Fig. 6. It indicates the maximum permissible load for every load bus in the IEEE 24- bus reliability system. From this result, a proper planning can be arranged according to the bus capacity in avoiding voltage collapse in the system.

1121

Uaxirnurn Penniriiblt Load lor PQ buses

2o - Bus No

Fig. 7. Maximum permissible load in IEEE 24-bus system

Table I shows the results for contingency ranking of the IEEE 24-bus system. The contingencies are ranked according to their severity. The FVSI for each line outage are sorted in descending order in which the highest index is ranked the highest and vice versa. The line outage that is ranked the highest implies that the particular line outage is very critical. Experiments were persistently conducted in order to justify the uniformity of the ranking. Results showed that ranking is consistent for all cases indicating that the line outage criticalness is accurately ranked. For instance, line 1 1 is ranked the highest for all cases implying that this line is the most critical one. Line I I is connected between bus 7 and bus 8 in the system. This line becomes very sensitive because the removal of this line could cause the generator at bus 7 floating. As a result, the entire system becomes very unstable even at the base case since the current from bus 7 will be circulating in the bus itself. Table 2 compared the results of contingency ranking using Lm[ I ] and LQP[2]. The results agreed each other with minor misclassification indicating that the proposed technique is reliable. From the table, lines 11, 23, 19, 15, 17, 14, 29, 16, 27 and 7 are the top ten highest ranking in the system for all cases using different techniques which indicates that these lines are the most critical outage in the system. Vice versa, lines 3 I , 5 , 38, 26, 25, 32,33,6, 1 and 2 are the most secure lines in the system. The outage of these lines cause less influence to the stability of the system.

VI. CONCLUSION

A thorough study on the voltage stability based contingency ranking has been presented. The voltage stability analysis process carried out using fast voltage stability index (FVSI) is capable in determining the critical line referred to a bus, critical outage, weak bus beside and the load ranking in the system. The FVSI that is evaluated the highest implies the sensitive line referred to a bus, while the lowest reactive power loading indicates the weak bus in the system. Bus ranking is resolute by sorting the maximum permissible load

in ascending order. The smallest maximum permissible load is ranked the highest and vice versa.

Contingency analysis was conducted by simulating the line outage in the system for several pre-determined cases to verify the consistency of the outage contingencies ranking. FVSI was also used as an instrument to indicate the criticalness of a particular line when a line outage occurs in the system. The indices were sorted in descending order for every line outage to indicate the severity of contingencies. Verification through comparison with other existing techniques developed by A Mohamed et al.[2] and M Moghavemmi et aQ31 showed an agreement which indicates that the proposed technique is an acceptable one. From the contingency analysis, the most critical outage and the most secure lines in the system are identified. Voltage stability analysis determined the weak bus, sensitive line referred to a bus and bus ranking, whilst, contingency analysis determined the most critical line outages in the system. Both analyses used the voltage stability index (FVSI) as the measuring instrument with less computation. Verification through the comparison with other techniques are comparable showing that the proposed formulated index is an indicative instrument in evaluating the point of voltage instability and the contingencies ranking caused by the line outages.

VII. ACKNOWLEDGMENT

The authors would like to acknowledge The Staff Development and Training Section, Universiti Teknologi MARA, MALAYSIA for the financial support of this document.

VI11. REFERENCES

[ I ] M Moghavemmi, and F M Omar, ‘‘Technique for Contingency Monitoring and Voltage Collapse Prediction,” IEE Proceeding on Generation, Transmission and Distribution, Vol. 145, pp 634 - 640. No. 6, 1998.

[2] A Mohamed, G B Jasmon and S Yusoff, “A Static Voltage Collapse Indicator Using Line Stability Factors,” Journal of Industrial Technology, Vol. 7, No. I. pp 73-85. Pt C, (1989)

[3] I Musirin and T K Abdul Rahman, “On-Line Voltage Stability Index for Voltage Collapse Prediction. in Power System,” presented at Brunei International Conference on Engineering and Technology 2001 (BICET200 I), Brunei. October 200 I.

[4] D Sutanto, C J Parker and I F Momison, “Fast Prediction of System Instability Using Artificial Neural Networks,” Australian Journal of Intdligent Informarion Processing Systems, pp 67 - 74, 1996.

[ 5 ] I Dobson, H Glavitsch, C C Liu, Y Tamura and K Yu, “Voltage Collapse in Power Systems,” IEEE Transaction on Circuits and Devices, pp 40 - 45, 1992.

I122

[6] A C Zambroni de Souza, J C Stacchini de Souza and A M Leite da Silva, “On-Line Voltage Stability Monitoring,” IEEE Transaction on Power Systems, Vol. 15, No. 4, pp 40 - 45, Nov. 2000.

[7] Y Y Hau and H C Kuo, “Fuzzy-Set Based Contingency Ranking,” IEEE Transaction on Power Systems, Vol. 7, No. 3, pp I189 - 1196, Aug. 1992.

TABLE 1 RESULTS ON CONTINGENCY RANKING

35 36 37 38

Contingency Analysis I ~ a s e ~ : I c a s e 3 I Cased: I cases:

33 33 33 38 38 38 6 6 6 26 26 26 1 1 2 25 25 25 2 2 1 1 1 1

IX. BIOGRAPHIES

lsmail Musirin received his B. Elect. Eng. (Hons) from University of Technology Malaysia on 1990 and MSc from University of Strathclyde on 1992 respectively. He is currently pursuing his

PhD studies in the field of voltage stability analysis and expert system.

Titik Khawa Abdul Rahman received BSc E.E. (Hons) and PhD on 1988 from Loughborough University of Technology and University of Malaya, MALAYSIA on 1996 respectively. She is currently an Assoc. Prof. at the Faculty of Electrical Engineering, Universiti Teknologi MARA. MALAYSIA and holding the S &

T Coordinator at The Graduate Studies Centre of the university. She has written several papers in voltage stability analysis and related field and one of the technical expert panel at the national level. Her research interest includes voltage stability analysis and GA.

1123