fault simulation for hardware...

CURENT SUMMER RESEARCH PROJECT, 2016 1

Fault Simulation for Hardware EmulationJohn Curtin

Abstract—This paper describes the details of the research completed by the author at the University of Tennessee atKnoxville during the summer of 2016. It mainly focuses on the attempted software design during the program, includingapplication and implementation. While this simulation had not been completed by the end of the program, manysignificant steps were taken toward completing the software development. The paper also discusses other work done bythe student, specifically his assistance in hardware construction.

Index Terms—Faults, Fault protection, Fault transients, University of Tennessee at Knoxville, Simulink, Hardware TestBed

F

1 INTRODUCTION

Every summer, the Center for Ultra-Wide-AreaResilient Electric Energy Transmission Net-works (CURENT) at the University of Ten-nessee at Knoxville takes in undergraduate col-lege students to participate in an eight weekresearch program. As a part of this program,the student John Curtin spent eight weeks con-ducting research, as well as performing othertasks. The research project assigned to the stu-dent was to create a computer program thatsimulates the effects of a fault on an electricpower transmission system. While the end goalof this project was not met, many significantsteps were taken toward the completion of theproject, which will help in the eventual comple-tion of the project.

2 BACKGROUND

This project was assigned to the student sothat it could be implemented on the hard-ware power system simulation device calledthe Hardware Test Bed (HTB.) This is signifi-cant because the accurate simulation of faultswould improve the overall functionality of theHTB drastically.

2.1 FaultsFaults are important to consider because theinstabilities caused by faults are arguably thegreatest existing threat to an electrical power

grid. The damage that faults are capable ofcausing can easily lead to large-scale blackoutsand equipment damage. This implies that, inthe worst case scenario where a shunted powersystem fault has zero impedance, the currentthat passes through the fault is the parameterthat protection equipment is designed around.This protection equipment, typically consistingof circuit breakers and relays, is what preventslarge-scale blackouts and equipment damage. Itis also worth noting that the fault current is themost significant parameter in fault calculation.

In real power systems, most faults are sig-nificant enough that they cause the protectionequipment in the system to trip, preventingsignificant damage to the system. However, theprotection equipment, consisting of relays thatdetect the faults and circuit breakers that openthe power lines and clear the faults, takes asmall amount of time to trip. In this time, thefault may have a significant effect on the powersystem, which the program made in this projectwould ideally be able to measure.

There are many different kinds of powersystem faults, including Line-to-Line, Line-to-Ground, Three-phase, and Double-Line-to-Ground.[1] These are the four categories offaults that have been considered in this project,and characterize many real-world power sys-tem faults. An example of one of these faults


can be seen in Figure 1, which shows the basiccircuit model of a Line-to-Ground fault.

Fig 1: Circuit model of a Line-to-Ground fault

It can be seen that this fault can be accu-rately characterized by a circuit model. Whilethis is a simple concept, it is important in un-derstanding the analysis that has been used inthis project.

Another important aspect of fault analysisis the complete characteristic current waveformthat is created by a typical fault. This waveformcan be characterized by a DC offset current, asub-transient and transient AC waveform, anda steady-state AC waveform. All of these com-ponents decay over time, typically very quickly,except for the steady-state AC component.[2]This can be visualized in Figure 2.

Fig 2: Fault current with all components

In this figure, it can be seen that there is alarge current spike at the time the fault occurs,in this case time zero, followed by a gradual de-cay into the steady-state stage of the waveform.

2.2 Hardware Test Bed

The Hardware Test Bed (HTB) is, essentially,a hardware device that is used to simulateelectrical power grids. This is done using setsof three-phase AC-to-DC power converters.This works in such a way that back-to-backconverters are used to simulate loads andgenerators. This concept can be visualized inFigure 3.

Fig 3: back-to-back HTB converter model

Once the hardware is put in place, the sys-tem is controlled through software, which iswritten in the C programming language andprogrammed onto the DSP chips that controlthe AC-to-DC converters. This allows for con-trol of the sending and receiving end voltages,as well as the line impedance. These values canthen be used to calculate the line current, whichfully parametrizes the system. This simulationmethod has the advantage of real-world com-ponent variation, in other words, time-variantvoltages and line impedance. This is a muchmore accurate representation of the real powergrid than a computer simulation and can alsobe used to test certain hardware devices to beput into the power grid. This simulation alsoworks completely in time-domain, improvingthe overall accuracy.

It should be noted that the HTB uses theshort transmission line approximation to modelpower systems. This approximation does notinclude the shunt capacitance and conductanceseen in the complete transmission line model.As the name implies, this approximation is ac-curate for short, overhead power transmissionlines. It should also be noted that the HTB is al-ready capable of simulating open-circuit faults.


This is done simply by making the variableinductance parameter of the HTB very large,which causes the AC voltage waveform to seethe inductance as an approximate open circuit.

The physical hardware configuration thatmakes this system possible is made up ofseveral hardware cabinets, such as the onesshown in Figure 4.

Fig 4: Several cabinets of the HTB

The cabinets shown in Figure 4 containmany electrical components to make the powersystem emulation possible, such as inductorsand power converters.

During his time here, the student was ableto assist in the construction of one of the trans-mission line cabinets and the inductor cabinetthat will be used in the four area configura-tion of the HTB. It is worth noting here that,while the program does focus largely on pureresearch, the skills required to build these cab-inets are valuable engineering skills that are indemand in both industry and academia. Theseskills include metalwork, soldering, wiring,crimping, and many other fundamental hands-on skills not included in most academic en-gineering programs. With this in mind, incor-porating more practical skills such as these isan idea worth considering for future researchprojects.

3 PROCEDURE

This project was done using a step-by-stepprocedure. The student would begin by re-searching background information he neededfor his project. The student would then go

about putting the useful information he foundinto software using Simulink and testing thatsoftware to obtain the desired end results. Theidea was that this Simulink software could beused as a stepping stone to write the C codethat would be put into the HTB.

3.1 Background ResearchThe student began by finding several read-ings on fault analysis, as he had not takena fault analysis course before attending theprogram. In his research, he found that mostconventional methods of fault analysis use thephasor-domain technique of symmetrical com-ponents.[1] While this is fine for calculating themaximum possible current magnitude, it doesnot incorporate transient effects. This is due tothe lack of a dynamic, changing frequency vari-able in phasor-domain analysis. As the projectassigned to the student was to create a completefault calculation model, this method would nothave been suitable due to the fact that it doesnot include transient effects.

He also found that many assumptions andapproximations in these phasor-domain anal-ysis methods. For instance, the assumption ismade that all currents other than the fault cur-rent are zero, which can be justified by sayingthat those currents are very small relative to thefault current.[1] These assumptions are fine fordetermining how to configure protection equip-ment, as they are made so that the equipmentprepares for the worst-case scenario of a fault.However, this project requires that no assump-tions are made, so that the most accurate resultscan be obtained. This is important for many ofthe research projects that the HTB is used in.

Consequently, the student proceeded to re-search many different areas of power systemsanalysis trying to find some that would helphim solve his problem. These areas of analy-sis include d-q coordinates, the Z-bus method,and generator stability. Unfortunately, a greatdeal of time was spent researching these topics,which, while they are useful in certain areas,turned out to be unhelpful for the researchproject.

After consulting a few of the graduate stu-dents, the research student was able to obtain a


feasible method for completing the project. Thismethod was to model the fault current using s-domain transfer functions and simulate thosemodels using Simulink. The reason that thiswould work can be best explained using thecharacteristic equation of the s variable, shownbelow as Equation 1.

s = σ + jω (1)

In this equation, σ can be thought of as theamplitude variable of the signal. This meansthat a positive value increases the time-domainoscillation amplitude, a negative value de-creases the oscillation amplitude, and a zerovalue causes no change in the oscillation am-plitude. This is complimented by the ω vari-able, which can be thought of as the angularfrequency variable. This variable determinesthe frequency of the sinusoidal time-domainwaveform. Together, these components forma variable, s, that can be used to accuratelycharacterize the time-domain functions used inthis project. The kinds of time-domain wave-forms that this variable can simulate can bevisualized in Figure 5, which shows the time-domain waveform of the current of a faultedpower grid.

Fig 5: Three-phase Fault current

Figure 5 shows both the pre-fault and post-fault steady-state currents as well as the tran-sient current of each phase of a three-phasesystem. It should be noted that, in a real powersystem, the circuit breaker on the line wouldhave most likely tripped. This would cause thesteady-state post-fault current and part of thetransient fault current to have a much smalleramplitude.

It should also be noted that use of the svariable requires that the function start at timezero and that the function is continuous. How-ever, neither of these constraints are an issuebecause the initial time can be set to zero in thesimulation and there is a method for digitizingthe s variable known as a Z-transform.

3.2 Implementation

The student began by drawing and analyzingthe equivalent circuit models that the HTBwould simulate. Once these models were com-pleted, the student would go about creating thesimulation programs in Simulink. If time hadpermitted, the student would have used thesesimulations to create C code that would havebeen used to simulate faults on the HTB.

3.2.1 Modeling

The circuit models used in this project, as men-tioned before, use the short transmission lineapproximation. This means that, in each branchof the circuit, there will only be a series resis-tance and inductance. While the line impedanceof a short transmission line is still a distributedparameter, this can easily be remedied. Thisis done by using the line length and the lo-cation of the fault. Any phases that the faultdoes not directly impact will have their dis-tributed impedance multiplied by the total linelength. Similarly, the phases that are directlyimpacted by the fault will have their sendingend impedance multiplied by the length of theline from the sending end to the fault. Likewise,their receiving end impedance multiplied bythe length of the line from the receiving endto the fault.

This causes what could be complicatedtransmission line models to become simplecircuits, which can be analyzed using simplecircuit analysis techniques. For example, thecircuit model of a typical Line-to-Ground faultis shown below in Figure 6.


Fig 6: Line-to-Ground circuit model

It should be noted that in this figure, thesending and receiving ends of the circuit areconnected to ground, as they are in the HTB.The receiving end voltage is also modeled as avoltage source, just as it is in the HTB.

Using this circuit model, equations for thepost-fault sending and receiving end currentscan be derived. The resultant equations for thiscase can be seen in Equations 2 and 3.

iA =V A ∗ (Za+ Zf)− V a ∗ ZfZA ∗ Zf + Za ∗ (ZA+ Zf)

(2)

ia =V A+ Zf − V a ∗ (Zf + ZA)

ZA ∗ Zf + Za ∗ (ZA+ Zf)(3)

Equation 4 can then be used to find the faultcurrent.

if = iA− ia (4)

In order to find the pre-fault current, onesimply takes the fault branch out of the circuitand analyzes that new circuit. The resulting linecurrent for this case can be seen in Equation 5.

iA =V A− V a

ZA+ Za(5)

This modeling process was done for each ofthe previously mentioned fault cases. Once thiswas done, it was appropriate to begin simulat-ing these models in Simulink.

3.2.2 SimulationIn order to create a complete model for theline and fault current that can be used for theHTB, it is necessary to include all of the pre-viously mentioned transition states of the cur-rent. These states are the pre-fault steady-state,transient state, and post-fault steady-state. Thestudent consequently decided to create differ-ent simulations until this result was achieved.

The student first attempted to use the statictransfer function blocks, as well as the typi-cal sinusoid and mathematical operator blocksavailable in Simulink. The idea behind thismethod is that one can initially run the sim-ulation using the pre-fault transfer function.Then a switching mechanism can be used toswitch from the pre-fault transfer function tothe post-fault transfer function at the time of thefault. Unfortunately, while this method can giveaccurate results for the pre-fault and post-faultcurrent, it does not give the transient effect. Thiscan be seen visually in Figures 7 and 8.

Fig 7: Result using static transfer function

Fig 8: Result using static transfer function

It can be see that, as previously mentioned,the transient effect is not seen as it is seen in


Figures 2 and 5. After several attempts with thismethod, it was determined that the use statictransfer function blocks would not work.

It was then decided that the use of a dy-namic transfer function, with variable coef-ficients, would be necessary. These kinds oftransfer functions are commonly used in adap-tive control systems, but can be used for thismodel as well. There are several methods forimplementing this kind of transfer function inSimulink, which can be found on various loca-tions on the Internet.

One such method is to use a Simulink blockcalled ”Time Fcn Direct Form II Time Vary-ing,” which allows the user to input the coef-ficients of the transfer function as a vector.[3]The block will use linear interpolation betweenthe indexes of the vectors to create varyingcoefficient values. By using large vectors withmany indexes, one can create approximate stepfunctions that can be used to switch the coef-ficients at the time that the fault occurs withminimal error. If successful, this method wouldproduce the desired result of a complete time-domain current waveform. However, it is worthnoting that this is a fairly high-level Simulinkblock, so translating it into C code for the HTBmight be difficult. Unfortunately, as the studentwas investigating this method and trying toimplement it, he ran out of time and had to dothe final documentation for the program.

4 CONCLUSION

While the project was not finished, many stepswere taken toward completing it. In future at-tempts at doing this project, it is recommendedthat dynamic transfer functions be looked into,for the reasons mentioned earlier. This was anoverall enjoyable experience for the student,which he would recommend to other studentsin the future.

ACKNOWLEDGMENTS

The author would like to thank the Depart-ment of Energy (DOE) and the National Sci-ence Foundation (NSF) for providing fundingto this summer research program. He would

also like to thank the University of Tennessee atKnoxville for hosting him during this program.Additionally, he would like to thank the fol-lowing people, who continuously helped himthroughout the summer with any questionshe had. These people are: Dr. Fred Wang, Dr.Kevin Tomsavic, Dr. Gerald Selvaggi, GeoffreyLaughon, Bo Liu, Yiwei Ma, Jessica Boles, andShouting Zhang.

REFERENCES

[1] C. Wagner and R. Evans, Symmetrical com-ponents as applied to the analysis of unbal-anced electrical circuits. New York: McGraw-Hill, 1933.[2] A. Sinha, ”Lecture -25 Short CircuitAnalysis”, YouTube, 2008. [Online]. Available:https://www.youtube.com/watch?v=HcMh7ahJxfoindex=7list=WL. [Accessed: 22- Jun- 2016].[3] ”How do I model a transferfunction with coefficients that vary withsimulation time in Simulink 7.5 (R2010a)?- MATLAB Answers - MATLAB Central”,Mathworks.com, 2011. [Online]. Available:http://www.mathworks.com/matlabcentral/answers/93681-how-do-i-model-a-transfer-function-with-coefficients-that-vary-with-simulation-time-in-simulink-7-5. [Accessed: 04-Jul- 2016].

fault simulation for hardware...

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