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Improvement of Voltage Stability Based on Staticand Dynamic Criteria

M. V. Reddy, Student Member, IEEE, Yemula Pradeep, Student Member, IEEE,V. S. K. Murthy Balijepalli, Student Member, IEEE, and S. A. Khaparde, Senior Member, IEEE, C. V. Dobaria

Abstract—This paper aims to reduce the voltage instabilityproblem that occurs due to contingencies in the system bylocation of reactive compensation devices. The exercise is car-ried out in two stages comprising static and dynamic studies.Under first stage, contingency ranking is used to identify severecontingencies, and their effects on the steady state voltage profileis quantified by an index called contingency severity index (CSI)which ultimately determines the location of shunt capacitor. Theapplication of index known as voltage stability margin index(VSMI) is used, which can simulate the voltage stability marginin real-time environment and it is used for validation studies. Inthe second stage, based on the criteria defined by NERC, theseverity of voltage instability is quantified using severity index.The dynamic voltage profile is improved by locating static varcompensator (SVC) as per the severity index. It is observedthat system is stable in steady state, but dynamic simulationresults show that it is not be stable in dynamic state. Theconcept of electrical distance for dynamic analysis is also used tofurther optimize the location. The entire methodology is appliedto improve the voltage stability of standard 39 bus New Englandsystem. The results of steady state analysis, dynamic analysis andimprovement of voltages after installing reactive support deviceand application of VSMI are presented in this paper.

Index Terms—Reactive power compensation, Static voltagestability, Dynamic voltage stability, Contingency severity index,Voltage Stability Margin Index, Electrical distance.

I. INTRODUCTION

RESTRUCTURING of power industry has led to stressingof power system equipment and requiring power systems

to operate at critical loading levels. The operation of powersystem world wide is moving towards increasing stress levelson account of increase in demand, aging generation unitsand transmission infrastructure. The system is subjected tocontingencies which lead the system to further stressed levelsto the extent of collapse. These all problems cause instabilityof power system and are a threat to reliable and secure powerdelivery. During contingency the system may experience se-vere voltage dip, low voltage, voltage instability or completevoltage collapse. Reference [1] gives IEEE definitions forvoltage instability and collapse. During past few decades,power industries all over the world have witnessed voltageinstability related system failures [2].

The static security of the system is improved by locatingreactive support devices considering different criterias. Mostly

M. V. Reddy, Yemula Pradeep, V. S. K. Murthy Balijepalli,S. A. Khaparde, C. V. Dobariya are with the Department ofElectrical Engineering, Indian Institute of Technology Bombay. (e-mail:mvreddy@iitb.ac.in, ypradeep@iitb.ac.in, vsk@ee.iitb.ac.in, sak@ee.iitb.ac.in,chandv@ee.iitb.ac.in)

steady state based approach is available in literature [3]–[11].In reference [12] Static Var compensator device is locatedbased on single contingency voltage sensitivity index. In thispaper, contingency severity index is used for locating the SVCdevice under steady state stability. In reference [13], buseswhich have more reactive power deficiency or voltage dip arechosen for dynamic VAR support [14]. Under dynamic voltagestability, NERC criteria is used [15].

For steady state stability, contingency ranking is carriedout using performance index of voltage. The effect of severecontingencies on bus voltage profile is assessed using con-tingency severity index values. With the increased loading oftransmission lines the voltage stability problem is very criticalissue. Generally, PV curve analysis is widely used for analyz-ing voltage stability issues. But it is time consuming process.So, to analyze voltage stability issues, voltage stability marginindex [16] has been adopted. Similarly for dynamic voltageprofile, severity index and electrical distance calculations arecarried out for locating SVC device to stabilize system fromtransient voltage collapse. This entire premise has been testedon New England 39 bus system [17].

The rest of the paper is organized as follows. Section II de-scribes the methodology for steady state voltage stability anddynamic voltage stability improvement. Section III explainsabout the mathematical formulation used for both steady stateand dynamic voltage studies. Section IV presents the obtainednumerical results on the New England 39 bus test system.Finally, section V concludes the paper.

II. METHODOLOGY FOR VOLTAGE STABILITYIMPROVEMENT

The methodology begins with presenting the criteria forstatic and dynamic voltage stability assessment adopted inthis study. The base case loading levels for the system to bestudied are taken close to the rated capacities of the equipmentin the network. Under steady state conditions the followingcriteria are considered. The changes in the voltage levelsunder post contingency conditions are limited to the rangeof 0.95 p.u to 1.05 p.u. The list of possible contingenciesincluded in the study should be sufficiently significant to affectthe level of voltage security of the system. The probabilitiesassociated with these contingencies are considered. Provisionfor assigning higher priority for voltage stability improvementto any chosen section of the system is also provided in themethodology.

For dynamic conditions, NERC has defined certain criteriaon which the current practices for assessment of transient

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voltage dip/sag are derived. In this study, severity indexused to quantify voltage limit violations under the abovecriteria is adopted. Severity index is derived from the transientvoltage response observed at all the buses. The mathematicalbackground is further explained in section III. In the caseof multiple reactive support devices, their locations have toconsider the overlap effects of var support in the near by buses.

The rest of the section presents the methodology for steadystate voltage and dynamic voltage stability assessment used toaddress the above criteria.

A. Methodology for Steady State Stability ImprovementInitially A.C load flow study has been carried out using

N-R method to get steady state voltage profile under basecase. Initial list of contingencies for further study are prepared.Then multiple load flows are carried out, by incorporatingone contingency at a time. From this information voltageperformance index is calculated by substituting the post outagevoltage magnitude into the equation (1). Voltage performanceindex can be penalized when voltage drop is more thanmaximum allowed voltage deviation from the nominal voltage.Based on PIV values, a list of severe contingencies is prepared.Contingency severity index (CSI) for each bus is calculatedfor each contingency. The bus which has highest CSI is mostsuitable for locating reactive support device. To confirm thelocation of the devices, a continuous load flow based constantpowerfactor changing load at a given bus incorporating VSMIindex are carried out. After placing reactive support deviceat the identified location, again A.C load flow study has beencarried out for both base case and contingency case. The aboveprocedure is explained through block diagram which is shownin Fig. 1.

Fig. 1. Outline of work done: Steady-state.

B. Methodology for Dynamic Voltage Stability ImprovementFor the same system considered in the steady state case,

dynamic simulation has done by adding exciter data and

generator data. The transient voltage profiles of each busare calculated for a severe contingency. From these voltageprofiles, dynamic severity index calculation has been done.According to NERC (N-1) contingency criteria, the buseswhich have voltage dip more than 0.25 p.u during the transientperiod, following a fault in the system are considered assevere buses. To reduce the number of locations for reactivesupport devices, concept of electrical distance is used. Thebus which has high severity index and high electrical distancewith respect to line, is most suitable location for reactivesupport device. After placing reactive support device, againdynamic simulation has been carried out. The above procedureis explained through block diagram which is shown in Fig. 2.

Fig. 2. Outline of work done: Dynamic study.

III. MATHEMATICAL FORMULATION

A. Steady State Voltage Stability

The idea of the approach presented in this section is toidentify a bus that is most sensitive for large list of singlecontingencies. This section will describe the definition andcalculation of the contingency severity index (CSI).

To find out, severe contingencies contingency ranking hasbeen done. This contingency ranking is based on the valuesof performance index of voltage(PIV). According to [18], thevoltage performance index is defined as

PIv =N∑

i=1

ωm

2n

(|Vi| − |Vi|sp

∆|Vi|lim)2n

(1)

Where |Vi|= Voltage magnitude at busbar i, |Vi|sp= Specifiedor rated voltage magnitude at busbar i, ∆|Vi|lim = Voltagedeviation limit above which voltage deviations are unaccept-able. n = Exponent of PIv function (n = 1 for second orderPIv), ωm = Real non-negative weighting factor. ωm is used forassigning higher priorities to a section of buses in the network.

The contingency severity index(CSI) for bus j is definedas the sum of sensitives at node j to all considered singlecontingencies and expressed as

CSIj =m∑

i=1

PiUijWij (2)

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Where m is the total number of contingencies considered, Uis the participation matrix, W is the ratio matrix, and P is thecontingency probability array matrix.

According to CSI values, corresponding buses are ranked.The bus which has high value of CSI will be more sensitive forsecurity system margin. The bus with the largest value of CSIis normally considered as the best location for SVC device.The same has been validated by using VSMI [19] basedcontinuous load flow. In the continuous load flow module ofVSMI, the load flows is run by changing the loads at sensitivebuses and the essence of index is captured. Here, VSMI isdefined as

V SMI =θrmax − θ

θrmax(3)

Where θrmax is maximum angular difference between sendingend and receiving end voltages and θ is the angular differencebetween sending and receiving end buses. The VSMI valueindicates how close the angle θ is from θrmax. Therefore ahigher value of VSMI implies that θ is farther away from theθrmax.

B. Dynamic Voltage Stability

In this section, we addresses the contingency assessmentbased on NERC (N-1) contingency criteria [20]. So, severityindex values are calculated based on this criteria. Powersystem abnormal state during contingency is reflected byvoltage dip. Thus a severity index, SIv is used to quantifyvoltage limit violation.

Let D = {V (t)|t ∈ [tcl, tf ]} for V0 ∃ Vdev ∈ D such that

|V0 − Vdev| ≥ |V0 − V (t)| ∀ V (t) ∈ D

Where Vdev is the maximum voltage deviation and V0 isthe nominal voltage.

The severity index is given by the equation

SIv ={ |V0 − Vdev|/V0 if |V0 − Vdev|/V0 ≥ 0.25

0 otherwise

Based on severity index values, a set of severe buses can befound. To reduce the number of locations for reactive powerinjection, electrical distance concept has been introduced [21].Electrical distance between bus and line is defined as

aijk = (zji − zki)yj−k + zjiy

shj−k (4)

Where zji, zki are the impedance matrix elements, yj−k

is the admittance of a branch j − k and yshj−k is the shunt

admittance of a line j − k.Electrical distance represents the propagation of voltage

variation following reactive power injection at a bus. Themagnitude of the ai

jk parameter provides a measure of theelectrical distance between bus i and one point at the beginningof the line j-k.

IV. CASE STUDY: NEW ENGLAND 39 BUS SYSTEM

The New England IEEE 39 bus test transmission networkis used to illustrate the effectiveness of the dynamic andsteady-state methods. The system data of this network isavailable in [17], which consists of 10 generators, 39 buses,and 46 branches. In this study, transient two-axis model forsynchronous generator is used together with excitation control.SVC is used as reactive power device. Loads are modeled ascombination of constant impedance, current and power.

Steady state AC load flow calculations have been doneusing MATPOWER [22] tool. For calculating performanceindex of voltage and contingency ranking MiPower [23] soft-ware is used. Contingency severity index is calculated usingMSExcel. For calculating severity index, electrical distanceand a continuous load flow based VSMI, MATLAB software isused. Dynamic simulation has been done using multi machinetransient stability tool [24].

Here results of steady state voltage stability and dynamicvoltage stability have shown in different cases. Case A, rep-resents steady state voltage stability improvement. Case B,represents short term voltage collapse and improvement ofdynamic voltage profile after placing SVC device.

Case A: For steady state stability, reactive support device isplaced based on CSI values. From the contingency ranking, thedecisive contingencies from a large list of contingencies areranked according to values of performance index of voltages(PIV). Based on PIV values, 15-16 and 21-22 outages arethe most severe contingencies and are shown in Table I. 16-17 outage is also considered for calculation of contingencyseverity index. Since it the outage for which the systembecomes unstable in dynamic case. The voltage response ofbuses under contingency 16-17 is shown in Fig. 5. Fromthe contingency severity index, 15th bus is more sensitive toreactive power injection which is shown in Fig. 3.

Fig. 3. Contingency severity index values for different buses.

While placing SVC at buses, the type of reactive powercompensation required has been investigated, and it is foundthat SVC at bus no.15 is working as a capacitor and suppliesreactive power for 15-16. Before placing SVC, the voltageprofile in the range of 0.92 p.u to 1.06 p.u. But, After placingSVC, the voltage magnitude of a bus is within the limits. Thevoltage response of buses under contingency 15-16 is shownin Fig. 4.

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TABLE ICONTINGENCY RANKING

From Bus To Bus PIV Rank1 39 21.98 222 3 35.87 32 25 21.81 253 4 29.95 63 18 21.77 264 5 21.93 234 14 22.40 205 6 23.59 155 8 22.76 186 7 24.63 106 11 24.25 117 8 21.67 278 9 33.65 49 39 33.22 510 11 23.08 1710 13 23.93 1413 14 23.53 1614 15 22.44 1915 16 37.94 116 17 24.11 1216 19 26.94 816 21 24.06 1316 24 20.01 3417 18 20.32 3217 27 22.04 2121 22 37.06 222 23 20.04 3323 24 24.88 925 26 21.13 2826 27 29.47 726 28 20.68 3126 29 20.97 291 2 20.69 3028 29 21.86 24

Fig. 4. Voltage profiles at 15th bus with and without reactive support.

Fig. 5. Voltage profiles at 16th bus with and without reactive support.

A. System Validation Using Voltage Stability Margin Index

A base case for the 39-bus system was taken and the activeload at bus 15, 16 are increased considering one bus at a timemaintaining power factor constant, in steps from the base case.Based on the bus voltages and angles the VSMI index foreach bus is calculated. The range of Index is from 0 to 1. Ifthe index reaches “0” then it indicates the corresponding busMargin in view of voltage stability is approaching Zero. Thiscan be observed from the graphs. The VSMI values of busno.16 is obtained by increase the loads incrementally. Afterplacing SVC device, the VSMI is increased means it increasesthe stability margin. So, the VSMI for bus no.16 under basecase is shown in Fig. 6.

Fig. 6. Base case VSMI values of a 16th bus

If line 16-17 line outage occurs, then the effect of thiscontingency on VSMI values is shown in Fig. 7. From thefigure, reactive power device improved the VSMI values foreach increment in load.

Fig. 7. Contingency case VSMI values of a 16th bus

Case B: A three phase fault occurred at the end of line 16-17near bus 16 at t=0.1 sec. The fault was cleared after 6 cyclesby tripping the line 16-17. After fault clearing, generatorexcitation voltage shoots up, to provide reactive power support.But some generators reach its excitation limit lately. Thisleads to significant voltage drop and generators may go outof synchronism. Finally short-term voltage collapse occurred.The bus voltage response due to line contingency 16-17 isshown in Fig. 8.

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Fig. 8. Bus voltage response due to line contingency 16-17

For the same contingency steady state response is within thelimits from Fig. 5. The result showed that although the systemmay have post disturbance equilibrium in steady-state but it isactually unstable in transient frame. This dynamic simulationhas done using a multi- machine transient stability tool [24].

The bus voltage response is shown in Fig. 8, due to linecontingency 16-17 shows short term system collapse aroundt=1.2 sec. So, basically voltage response after t=1.2 sec doesnot mean anything as the system has already become unstable.The voltage response after t=1.2 sec is just to show that thesystem has become unstable.

To improve voltage profile during dynamic state, installationof reactive support device is necessary. Before installation,severity index for each bus has calculated. From severity indexvalues, a set of severe buses has been prepared which is shownin Fig. 9.

Fig. 9. Severity index of buses due to line contingency 16-17

To reduce the number of locations for reactive supportdevices, electrical distance is used. It is highly possible thatbuses in close electrical neighborhood of most sensitive busesare also very sensitive. Thus the values of electrical distancesbetween line and each bus is shown in Fig. 10. This reductionin number of locations reducing the complexity of problem.Another significant advantage is that it avoids small installa-tions at electrically adjacent and likewise sensitive buses.

Fig. 10. Electrical distance distance between bus and line

From the severity index and electrical distance values busno.16 and 17 are the suitable locations for a contingency 16-17. So, After placing reactive support device at bus no.16, thedynamic voltage profile has been improved which is shownFig. 11.

Fig. 11. Bus voltage response due to line contingency 16-17 with SVC

V. CONCLUSION

A comprehensive analysis of both steady state and dynamicvoltage instability phenomenon under contingency conditionsare carried out. For finding severe contingencies, contingencyranking is used. Contingency severity index, VSMI and elec-trical distance concepts are used to locate reactive supportdevices under steady state. The response of system voltage to adisturbance and system behavior during a voltage collapse situ-ation can be considered as dynamic power system phenomena.However as far as reactive long term planning is concerned, asteady state analysis has been shown to be generally adequatefor providing an indicator of the margin from current operatingpoint to voltage collapse point and for determining the locationand MVar rating of any necessary reactive power source.Dynamic analysis is separately used to design the controlsfor system reactive support. Even though, under voltage loadshedding, can improve the dynamic response. but it can takemore time to operate, in that time short term voltage collapsemay occur. From the results obtained during this research, itis observed that only steady state analysis cannot guaranteethe short-term stability because sometimes system may seemstable in long-term but it may not stable in short-term.

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M. V. Reddy has a Masters degree in the Department of ElectricalEngineering at Indian Institute of Technology Bombay, India. His researchinterests include voltage stability, restructured power systems, power systemsimulation studies. He is a graduate student member of the IEEE Bombaysection, and the IEEE power and energy society.

Yemula Pradeep is currently working towards Ph.D. degree in Departmentof Electrical Engineering at Indian Institute of Technology Bombay, India.His research interests include IT applications in power systems and powersystems restructuring issues. He is a graduate student member of the IEEEBombay section, and the IEEE power and energy society.

V. S. K. Murthy Balijepalli is currently a research scholar with theDepartment of Electrical Engineering, Indian Institute of TechnologyBombay, India. He is a graduate student member of the IEEE Bombaysection, and the IEEE power and energy society. His current researchinterests include Transmission System Expansion Planning, data miningapplication to power systems, smart grids and governing standards.

Shrikrishna A. Khaparde (M’87-SM’91) is a Professor in the Departmentof Electrical Engineering, Indian Institute of Technology Bombay, India.He is a member of the Advisory Committee of Maharashtra ElectricityRegulatory Commission (MERC). He is the editor of International Journalof Emerging Electric Power Systems (IJEEPS). He has co-authored bookstitled, “Computational Methods for Large Sparse Power System Analysis:An Object Oriented Approach,” and, “Transformer Engineering: Design &Practice,” published by Kluwer Academic Publishers and Marcel Dekker,respectively. His research areas include distributed generation and powersystem restructuring.

C. V. Dobariya is a Project manager in the Department of ElectricalEngineering, Indian Institute of Technology Bombay, India. His area ofinterest includes renewable energy and power system economics.

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