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Evaluation of Fault Protection Methods

using ATP and MathCAD

Louis V. Dusang, Jr., Brian K. Johnson, Senior Member, IEEE

AbstractThis paper discusses combining the Alternative

Transients Program (ATP) and MathCAD to teach protective

relaying and to develop relay algorithms. A power system model

is created in ATP with appropriate current and voltage

measurements. The simulation output is converted to a

COMTRADE format and imported into a detailed relay model

implemented in MathCAD. The MathCAD model performs

digital filtering calculations, symmetrical components

calculations and models relay algorithms based on relay

manufacturers published information. Focus here is on

differential and ground fault protection for the common two bus,

parallel line case. Emphasis is placed on fault detection and

localization methods for ungrounded or high impedance

grounded systems.

Index TermsDigital simulation, power systems protection,

ungrounded power systems

I.INTRODUCTION

With fast responding modern protective relaying schemes it

is increasingly important to test them using transient

waveforms rather than using steady-state solutions from fault

programs [1]-[6]. One option is to use COMTRADE files

captured from field data, but this is limited only to events that

have actually occurred. Another option is to use transient

simulation to generate a more comprehensive set of test cases

and then play these waveforms to relays as COMTRADE files[1], [7].

The same approach should also be used when training

engineers and engineering students to set and test protective

relays. Understanding the operation and performance of

microprocessor based relays requires new engineering tools.

The challenge educators face when preparing the next

generation of protection engineers and relay designers is to

teach both the analysis tools and the fundamental concepts of

very complex relay systems and devices [8], [9]. This can

also be used in developing new protection algorithms. One

does not necessarily need to use commercial relays in an

educational environment, and the development of new

algorithms precludes use of commercial relays. One option is

to implement a model of the relay algorithm directly in the

transient simulation tool [2]-[10]. This has the advantage of

allowing

_____________________________

Louis Dusang is with Northrop Grumman Shipbuilding, Pascagoula, MS

39567 USA (phone: 228-935-2451; email: louis.dusang@ngc.com)

B. K. Johnson is with the Dept. of Electrical and Computer Engineering atthe University of Idaho, Moscow, ID 83844 USA (phone: 208-885-6902;

email: b.k.johnson@ieee.org).

closed loop testing. However, developing a complete model,

including anti-aliasing filters, cosine filters, and symmetrical

components calculations can be challenging. Some transient

simulation tools have built-in relay models that can help for

this purpose, but are not comprehensive.

In cases where closed loop testing of relays is not required

another option to implement a relay model in a general

purpose mathematical tool such as MATLAB or MathCAD

[11], [12]. These programs are more suited to implementing

complex digital filtering algorithms and relay algorithms.

However, they have limited ability to close the loop and open

simulated breakers in the transient simulation. Theseprograms are able to import data produced by other programs.

This paper will utilize relay models implemented in

MathCAD that import COMTRADE files generated from the

output of an ATP [13] simulation using ATP Analyzer. The

relay models implemented are based on protective algorithm

information published by relay manufacturers. The

approaches used in this paper have been used in several

university level courses to allow distance education students

to perform protective relaying labs that on campus students

are able to conduct using hardware.

COMTRADE (Common Format for Transient Data) is an

IEEE standard (C37.111) developed for the power industry to

allow easier exchange of event data between devices fromdifferent manufacturers both for post event analysis and for

equipment testing.

The ATP plotting function processes PL4 output files.

Each COMTRADE file consists of three text files

(assuming that you created the COMTRADE files in one of

the standard text formats):

1. DAT - contains the numerical data

2. CFG - configuration information cross-referencing

variables stored in DAT file

3. HDR - information about how the file was

created.

We are interested in reading both the *.CFG and *.DAT

files into MathCAD. The *.CFG file will be read into a

MathCAD array called config and the *.DAT file into an

array called data.

ATP Analyzer was developed by BPA to make it easier for

protection engineers to use ATP simulations (the development

of ATPDraw was also supported by BPA for the same reason).

When creating the file for use in MathCAD, the analog and

digital signals need to be in the order you establish in your

MathCAD file as you read the data into the file. Progressing

through the conversion process there is text box showing the

present sampling rate (in this case the ATP simulation time

2008 IEEE Electrical Power & Energy Conference

978-1-4244-2895-3/08/$25.00 2008 IEEE

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step), replace this with 960 (this is 16 samples per 60 Hz

cycle). This is a fairly common sampling rate for commercial

protective relays and the MathCAD file is set up for this.

Selecting Low Pass Filter removes the need to add the filter in

MathCAD.

The data in a COMTRADE file has both scaling and offset

factors defined for them. This scales the measured data before

its operation in the relay model. The MathCAD file can pull

these numbers from the COMTRADE configuration file. Bynot changing the scaling and offset factors, the generated

waveforms incur errors.

II.GROUNDING METHODS TO LIMIT GROUND FAULT

CURRENTS

The main goals of system grounding are to give assistance

in rapid detection and elimination of ground faults, minimize

voltage and thermal stresses on equipment, provide personnel

safety and reduce communication system interference [14]. In

some cases, an exception is made for systems supplying

critical processes or impacting personnel safety if the power

system shuts down. In these cases an ungrounded or high

resistance grounding scheme can be used. A phase-to-ground

fault does not result in large fault currents and, if loads are

connected phase-to-phase, can be tolerated until a clean

shutdown or reconfiguration can be performed.

Ground fault current magnitudes depend on the system

grounding methods. Because a single phase to ground fault in

ungrounded, high-impedance grounded and compensated

systems does not affect the phase to phase voltages, it is

possible to continue operating systems grounded in this

fashion with a single line to ground fault present. However

the system must have a phase-to-phase insulation level and all

loads must be connected phase-to-phase.

A. Ungrounded or Isolated Neutral System

In an ungrounded system the neutral has no intentional

connection to ground. However, because of the parasitic

distributed phase-to-ground capacitance, the neutral of an

ungrounded system may be considered to be grounded

through a capacitor connected between neutral and ground as

depicted in Fig. 1. The value of this capacitor will be equal to

sum of the phase-to-ground capacitances.

Fig. 1. Simplified Representation of an Ungrounded System

In this system, the two major factors limiting ground fault

current magnitude are the zero sequence line-to-ground

capacitance and fault resistance. A line-to-ground fault shifts

the system neutral voltage, but leaves the phase-to-phase

voltages intact as shown in Fig. 2.

Fig 2. Voltage phasor diagram for an ungrounded system

(a) Unfaulted system, (b) Solid phase A to ground fault

For a solid phase A to ground fault in an ideal lossless

system, the faulted phase and ground potentials are equal, as

shown in Fig 2. The phase-to-ground voltage of the two

remaining unfaulted phases equals the phase-to-phase voltage

(VBG = VBA, VCG = VCA) and the neutral-to-ground voltage

equals the negative of the source phase to neutral voltage

corresponding to the faulted phase (VNG= VAN). The phase-

to-phase voltages are not impacted, only the line-to-ground

and neutral-to-ground voltages. Thus continuity of service

can be achieved in the presence of a single line-to-ground fault

on this system if loads are connected phase-to-phase.

One important characteristic to be considered for an

ungrounded system is that this type of system is subject to

excessive overvoltages. Ungrounded neutral ac systems are

most commonly subject to overvoltages originating from

resonant effect of series LC circuits by a transient change in

voltage. Similarly, substantial overvoltages can be developed

in ungrounded ac systems by sputtering or intermittent ground

faults. In such faults the fault clears when the current througharc passes through a natural current zero. Since the ground

current is capacitive, it is 90 degrees out of phase with the

voltage. This results in trapped charge on the neutral to

ground parasitic capacitance. At the next half cycle it can arc

again, adding additional voltage to the capacitance at the next

current zero. This will cause the neutral-to-ground, and thus

the phase-to-ground, voltages to build up over time.

Intermittent ground fault conditions on low voltage

ungrounded neutral systems have quite often been observed to

create overvoltages of five or six times normal. These

overvoltages will deteriorate the insulation of the unfaulted

phases and might lead to a second ground fault or a phase-to-

phase fault. The second ground fault will involve large faultcurrents and will require instantaneous tripping of breakers.

B. High Resistance Grounded System

The high resistance grounded neutral system is one in

which a large resistance has been inserted in the neutral

connection to ground to limit the neutral current under ground

fault conditions to a value not less than the system charging

current. The grounding resistor may be connected in the

neutral of a power or grounding transformer, generator or

generator grounding bus, or across a broken delta connection

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of distribution transformer secondary. Similar to the

ungrounded system, ground faults on these systems shift the

system neutral voltage without modifying the phase to phase

voltages. Hence the system need not be disconnected at the

occurrence of the first phase to ground fault.

An advantage of the high resistance grounded system is

that the potential line-to-ground overvoltage hazard associated

with the ungrounded system is greatly reduced. This is

because the distributed line-to-ground capacitance is bypassedby the neutral to ground high resistance connection so the

neutral current is closer to being in phase with the voltage and

providing a path to bleed off the trapped charge. The

resistance also creates an overdamped response to transient

variations.

III.RELAY PROTECTION OVERVIEW

A single digital relay may consist of many protection

elements, see Table I.

TABLE I

ELEMENT LEGEND

Elements Description

27 Phase Undervoltage: A-, B-, or C-Phase

59 Phase Overvoltage: A-, B-, or C-Phase

81 Under- and Overfrequency

25 Synchronism Check

59N Zero-Sequence Overvoltage

67P Directional Phase Overcurrent

50P Nondirectional Phase Overcurrent

32R Reverse Underpower

32F Forward Overpower

87 Phase Current Differential

67N Directional Ground Overcurrent

50N Nondirectional Ground Overcurrent

The power element (32), undervoltage (27) and

overvoltage (59) element, and underfrequency element (81)

are all based on a time delay scheme with no fault location

tripping selectivity (Table I). These elements are intended for

generator protection. Reverse power protection uses a time

delayed function to prevent a generator from acting as a motor

on the system.

The synchronism element (25) provides added protection

by preventing the closing of any breaker and connecting twosystems that are out of phase. To allow breaker closing when

power is only on one side of the breaker, a relay includes a

dead-bus feature that bypasses the synchronism check

element. Unlike with the previously described elements, a

line-to-line voltage helps prevent a ground fault from affecting

proper synchronism check element operation in an

ungrounded system.

A. Differential and Directional Protection

The primary protection used for protection of very short

transmission lines is line current differential (87). Line

current differential protection is ideal because the current

differential element zone of protection is the connection

between the two relays associated with a line and a high speed

communications link.

Fig. 3 shows a typical line current differential scheme

applied to a line.

Relay 2

87LA 87LB87LC

87LG87L2

Relay 1

Ia, Ib, Ic87LC87LB 87LA

87LG 87L2

Fig. 3. Typical Line Current Differential Scheme

Each relay exchanges time-synchronized Ia, Ib, and Ic

current samples with the other. Current differential elements

compare Ia, Ib, Ic, 3I2, and 3I0 (IG) currents from each line

terminal. If a fault condition exists between the two relays,

the line is isolated.Line current differential elements require an extensive

communications channel between the two relays protecting

the line since the sampled current waveforms need to be

transferred. If the communications channel fails, the line

current differential protection is disabled. The

communications channel signal integrity checking is an

automatic function within each relay.

Directional overcurrent elements (67) determine if a fault

exists on a line. The 67P element only detects multiphase

faults, while the 67N element detects phase-ground faults.

Both elements are necessary to detect all fault types because

of the difference in pickup and sensitivity levels. The 67P

elements operate from phase currents and the 67N elements

operate from the current delivered by the core-flux summing

current transformers or a CT in the neutral path. Depending

on the power system, directional overcurrent elements are

only enabled to trip when the current differential

communications channel fails.

B. Zero Sequence Detection

The positive, negative and zero sequence networks are

connected in series while evaluating single line-to-ground

faults as shown to Fig. 4. The zero sequence impedance of an

ungrounded and a high resistance grounded system has a very

high magnitude compared to the positive and negative

sequence impedance. Considering this high value one can

ignore the positive and negative sequence impedance without

significant loss of accuracy while evaluating single line-to-

ground faults.

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3ZF

Relay R

Z1S Z1R m Z1L (1-m) Z1L

Relay S

I1S I1R

Relay R

Z2S Z2R m Z2L (1-m) Z2L

Relay S

I2S I2R

Relay R

Z0R m Z0L (1-m) Z0L

Relay S

I0S I0R

Z0S

XC0S

2

XC0S

2

_

+

V2F

Fig. 4. Connection of Sequence Networks for a Single Line-to-Ground fault

A solid single phase A to ground fault in the forward

direction can be represented the circuit in Fig. 1 by closing

switch SF. The zero sequence representation for this forward

ground fault is shown in Fig. 5a. The primary current I0 is

flowing in at the CT polarity mark. A ground fault in the

reverse direction can be implemented by closing switch SRof

Fig. 1, with its zero sequence representation in Fig. 5b. The

primary current I0is not flowing in at the CT polarity mark.

Z0L

XC0S XC0LV0 I0

Relay

(a) Forward fault direction

(b) Reverse fault direction

Fig. 5. Zero Sequence Representation

IV.POWER SYSTEM OVERVIEW

Providing a reliable system is an important objective for

many commercial, industrial, and even residential

environments. One way to increase reliability is utilizing anungrounded system or a high resistance grounded system.

Since the majority of faults are single line-to-ground faults,

especially on overhead systems. Ungrounded system can

continue to supply the end user power under ground fault

conditions; hence, for the purpose of this paper an ungrounded

or high resistance ground power system is utilized.

Fig. 6 is a common multi-source power system typically

used to explain various components of a power system i.e.

relay protection. With the below figure one can explain power

system stability, distance protection, forward and reverse

direction of current as seen by each relay, differential

protection, etc. However, this paper will limit the protection

discussion to current differential and directional ground fault

protection.

Fig. 6. Power System Configuration

Differential protection is more or less the same regardless

of power system design. However, ground fault protection

including zero-sequence components depends on the

grounding scheme used. In this case, directional schemes for

ungrounded and high resistance grounded power systems are

explained.

V.ATPMODELING

ATP is a useful tool for evaluating power systems.

MathCAD is a helpful tool for analyzing relays. By combing

the two software programs, relay functionality can be taught

and better understood in universities in a practical sense.

A power system is developed using ATP. ATP Analyzer

produces a COMTRADE file from the ATP simulation output,

which is input as a data file into MathCAD. Relay algorithms

are developed in MathCAD. MathCAD takes data read from a

COMTRADE file and postprocesses it. The COMTRADE

configuration file format is such that the first row states how

the file was created and the version of the standard, the second

row gives the total number of inputs i.e. 18 - number of analog

inputs (12) and number of digital inputs (6). Rows 3 - 21 areinput in an order of choice. Data is sampled 16 times per

cycle or 960 hertz. Columns 0 and 1 of the COMTRADE file

do not store data, so Column 2 is the first one of interest.

This system is modeled as an ungrounded power system

utilizing ideal sources and employs high resistance to ground,

Fig. 7a. The system in Fig. 7b is similar to system in Fig. 7a.

However, to better represent the power system being analyzed

a transformer is added. The transformer adds source

impedance to the system. In this case the transformer is

modeled as a delta-delta. To improve numerical performance

of the simulation it is necessary to add either a very small

capacitance to ground (a few picofarads) or a very large

resistance (tens of Mohms) to ground. These values should be

chosen such that the current they carry does not impact the

circuit, while at the same time providing a suitable ground

reference.

EMTP-like programs such as ATP use nodal admittance

matrix methods that work best if circuits have a reference to

ground. The floating voltage sources in Fig. 7a and Fig. 7b

use an internal, ideal transformer to create a floating source.

The transformer used has some potential to create numerical

stability programs. To improve this, grounded sources are

connected behind the transformer, which is connected

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grounded wye to ungrounded wye (it could also be delta

connected on the side facing the power system of test. This

creates an appropriate ungrounded source. The parasitic

capacitances represented in cable models provide the ground

path that fault current would flow through. Fig. 7c shows a

system with a grounding transformer added to create a high

resistance ground. This is a common way to create a high

resistance to ground point in an ungrounded system.

The orientation depicted in Fig. 8 reflects that shown inFig. 3. Note that I2 current flow can be in same direction as

I1. In this case the direction change needs to be

accommodated in the MathCAD file. This may seem

intuitively obvious, but you remember you are creating and

debugging two models.

FAULT

I1 I2

Fig. 8. ATP Current Flow

VI.MATHCADMODELING

Fig. 9 depicts an oversimplified rendition of differential

protection (analyzing each phase for a difference in current via

OR logic) in which the line currents (87A, 87B and 87C) are

calculated internal to the relay in a manner the manufacturer

utilizes. For current differential protection if B-phase and C-

phase have no differential current flow, but current flows

through the differential relay in A-phase the differential relay

will assert if the value exceeds the pickup setting.

Fig. 9. Simplified Differential Fault Protection Logic

Equation (1) represents Fig. 9 in MathCAD.

Tr_s1v

1 Is1_OPAv

s1_1 Is1_RTAv

>( ) Is1_OPAv Imin>( )if

1 Is1_OPBv

s1_1 Is1_RTBv

>( ) Is1_OPBv Imin>( )if1 Is1_OPC

v s1_1 Is1_RTC

v>( ) Is1_OPCv Imin>( )if

1 Tr_s1v 1

0.01>if

0 otherwise

:=

(1)

Fig. 10 is a differential relay Operate / Restraint curve

generated in MathCAD.

0 2 4 60

2

4

6

6

0

s_ 1 I.axis( )

60 I.axis

(a) Percentage Characteristic (b) MathCAD version

Fig. 10. Differential Relay Operate Curve

Ground fault algorithms while more complicated are

generated similar to the differential element. Ground fault

consists of overcurrent and directional elements. Fig. 11 is a

simple representation of ground fault sensing logic.

Fig. 11. Simplified Ground Fault Logic

Utilizing an SEL relay that incorporates a doubled-ended,zero-sequence impedance element that vectorially adds the

two zero-sequence current measurements, using the

communications link between two relays, to produce twice the

total zero-sequence line current.

To quantify this algorithm we construct Equation 2.

2

0

*

0000

3

)_13(3Re

I

AngZLIVZ T

= (2)

where:

3V0 = Summation of phase voltages (VA+ VB+

VC)

3I0 = Summation of phase currents (IA+ IB+ IC)

ZL0_Ang = Zero-sequence line-impedance angle

Re = Real operator

* = Complex conjugate

Equation (3) represents Equation (2) in MathCAD. To

avoid division by 0 add a 0.00001 constant to the

denominator.

Z0A_r1v

Re VA0_r1v

IA0_r1v

1 ej Z1ANG

( )

IA0_r1v( )

2.00001+

:=

(3)

Fig. 12 produces a forward/reverse fault impedance plane.

If the resulting impedance calculation is below the forward

threshold (and all of the supervisory conditionals are met), the

fault is declared forward. Conversely, if the impedance is

above the reverse threshold, the fault is declared reverse.

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Zero-Sequence

Impedance Plane X0

R0

Reverse Fault

Forward Fault

3V0

3I0 (Forward Fault)

3I0 (Reverse Fault)

(a) Zero-Seq. Phasors (b) Impedance-Plane DirectionalElement Characteristics

Fig. 12. Ground Directional Element Characteristics

Similarly, Fig. 13 is a MathCAD produced forward/reverse

fault impedance plane showing the relationship between 3V0

and 3I0for forward and reverse faults. Positive Z0Tindicates a

forward fault as indicated in Fig. 13a. Negative Z0Tindicates

a reverse fault as indicated in Fig. 13b.

0 5 10 15 20 25 303000

2000

1000

0

1000

VA0_r1v

IA0_r1 v

Z0A_r1 v

Z0A_r2 v

v

RS

(a) In-line section

0 5 10 15 20 25 30500

0

500

1000

1500

2000

VA0_r3v

IA0_r3v

Z0A_r3 v

Z0A_r4 v

v

RS

(b) Out-of-section

Fig. 13. Ground Directional Decision

As mentioned above relay manufacturers use their own

algorithms for relay protection elements. As such, our relay

model utilizes the 32 element in Equations (4)-(6), which

represents the ground directional protection of an SEL relay,

which utilizes the 32 element. The 50 element is essentially

the level equation enabled. Equation (4) consists of zero-

sequence algorithm resulting in Equation (6) equating to

Fig. 11.

F32G_r1v

Z0A_r1v

Z0Forward( ) IA0_r1v a0 IA1_r1v( ):= (4)

Level1G_r1_puv

1 IA0_r1v

Level_1_50G_r1if

1 Level1G_r1_puv 1

0.01if

0 otherwise

:=

(5)

TR67G_r1v

T32G_r1v

TR50G_r1v

:= (6)

VII.SIMULATION RESULTS

After modeling the power system in ATP, the generated a

COMTRADE file is incorporated into MathCAD to test the

relay algorithm. Fig. 14 shows differential element correctly

isolates fault by asserting both Relay 1 and Relay 2, only,

isolating two- and three-phase fault conditions on the faulted

line while leaving the unaffected line in tact. Additionally,

even though a ground phase may have been involved in boththe two- and three-phase faults i.e. double line-to-ground fault

the zero sequence algorithm remains low for all four relays

such that its associated element, 67N, did not pick-up.

0 10 20 300

0.5

1

1.5

2

Tr_R1v

Tr_R2v

v

RS

0 10 20 300

0.5

1

1.5

2

Tr_R3v

Tr_R4v

v

RS

(a) In-line section (b) Out-of section

Differential Element

0 10 20 300

0.5

1

1.5

2

Ind_R1v

Ind_R2v

v

RS

0 10 20 300

0.5

1

1.5

2

Ind_R3v

Ind_R4v

v

RS

(a) In-line section (b) Out-of sectionGround Directional Element

Fig. 14. Differential Protection Results

Likewise, Fig. 15 shows ground fault protection

appropriately indicates a single line-to-ground on the faulted

line. This is seen as a high signal on ground detection graph

and no state change for the unaffected line or an assert signal

by the differential protection graph.

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0 10 20 300

0.5

1

1.5

2

Tr_R1v

Tr_R2v

v

RS

0 10 20 300

0.5

1

1.5

2

Tr_R3v

Tr_R4v

v

RS

(a) In-line section (b) Out-of sectionDifferential Element

0 10 20 300

0.5

1

1.5

2

Ind_R1v

Ind_R2v

v

RS

0 10 20 300

0.5

1

1.5

2

Ind_R3v

Ind_R4v

v

RS

(a) In-line section (b) Out-of sectionGround Directional Element

Fig. 15. Ground Directional Protection Results

All three ATP models in Fig. 7 resulted in identical fault

isolation responses for both differential and ground fault

protection. The difference is a setting change in MathCAD.

VIII.CONCLUSIONS

Using two different software packages to develop models

requires a thorough knowledge of relay principles. The

current flow direction in ATP affects the MathCAD results.

While this may be seem obvious, it is easy to include anegative sign in MathCAD for direction as well.

A single line power system provides the concept of

differential and ground fault protection from a practical. In

doing so it teaches directional functionality. This becomes

more evident with the parallel line power system in that fault

isolation depends on relay settings. In other words, the

assertion of both relays in the single line system, does not

initially mean this occur for the parallel line system. Three

relays may assert, but this only means that the settings are

incorrect. The added benefit of the parallel is it use of explain

blocking schemes.

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Spokane, Washington, October 23-25, 2001. [Online]. Available:

http://www.selinc.com/techpprs/6123.pdf

X.BIBLIOGRAPHY

Louis Dusang received a Bachelor of Science in Electrical Engineeringdegree from Mississippi State University in 1988 and is pursuing his MSEE at

the University of Idaho. He is a Registered Engineer in South Carolina. He

has been an electrical engineer with Northrop Grumman Shipbuilding since

November 2001. He is the lead project engineer for LDA Power Systems.

Prior to joining NGSB, Mr. Dusang worked as both an electrical engineer and

controls engineer for Jacobs.

Brian K. Johnson (M92, SM2006) received the Ph.D. in Electrical

Engineering from the University of Wisconsin-Madison in August 1992. He is

currently an associate professor in the Department of Electrical Engineering at

the University of Idaho. His interests include HVdc transmission, power

system protection, and the application of power electronics to utility systems

and realtime simulation of traffic systems.