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Steady State & Electromagnetic Transient Study of a

Power Grid During Consecutive Branches

ConnectionDiego Rodrguez

AbstractSwitching transients are an important factor on thestudy of connecting branches, loads, reactive banks, etc.

Switching transient is one of the primary causes of transient

overvoltage and over current in power systems. This report

focuses on a comparative study of the modeling and simulation of

a switching transient response using two simulation tools:

PSCAD/EMTDC and MATLAB (Chenxis code). The

comparative overvoltage transient results during the switching

study are also provided.

I.INTRODUCTIONThe opening or closing of breakers and switches in a powersystem produce switching transients. Those switching

operations are depicted mainly in two categories: i)

energization of a branch1 (main objective of this project) and

ii) de-energization of a branch.

The first category consists of energization of transformers,

reactors, capacitor banks, transmission lines or cables, loads,

and so on. The second category includes load rejections, faults

clearing, shunt reactor banks de-energization, etc.

As a result of the difficulty at the time of representing

mathematically all the elements involved, digital computer

simulations using Electromagnetic Transient Programs

(EMTP) plays an important factor in the analysis of switching

transient. The results from those studies are relevant in the

study of:

a. insulation co-ordination to determine overvoltagesstresses on equipment

b. determining the arrester characteristicsc. determining the transient recovery voltage across

circuit breakers.d. determining the effectiveness and security of a

connection during the re-energization of a system

(black start)

Those factors are currently analyzed by software as

PSCAD/EMTDC, ATP, EMTP-RV, etc. In this document, we

will use the theory developed by H. Dommel [1] during the

transient time to create a program in MATLAB which can

analyzed the voltage and current response to consecutive

1In this document a branch is a power system element as a

transformer, a resistor, an inductor, a capacitor, a line, etc.

connection of branches during the re-energization of a power

system.

To show the results this document it will be divided in threesections. Section I, will describe the models implemented in

MATLAB for the analysis. Section II, provides a model case

along with the comparison switching transient results for both

programs during the energization. Finally, Section III

concludes and exposes the future steps of the study.

II.MODELING REQUIREMENTSWith the use of EMTP representation of each element [1]during transient analysis, this section shows the standard

representation of each element during a switching transient

A.ResistanceFrom [1] the representation of a resistor takes the form of

Figure 1, this is the same as in steady state because there is not

exist any element which stores energy (capacitor or inductor)

R

)(ti

)(tek

)(tem

DATUMDATUM

Figure 1Resistance models

B.InductanceEquation 1, shows the relation between voltage and current in

the inductor

Equation 1In EMTP the model takes the form of

where

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)(, ttI mk

t

LR

2

)(,

timk

)(tek

)(tem

DATUMDATUM

Figure 2 Capacitance model for transient analysis

C.CapacitanceEquation 2, shows the relation between voltage and current in

a capacitor: () Equation 2In EMTP the model takes the form of

( ) Where

( ) The representation is homologous to inductor with a variation

in the current source () and the parallel resistor .D.LinesLines are represented using the Bergeron method [1], Figure

3.

Where H is

)(tek )(tem

DATUM

)(, ti mk

)( tIk

Z )( tIm Z

4'

'R

C

LZ

Surge Impedance or

Characteristic Impedance

)(, ti mk

Figure 3 Lines representation for long lines during transient

analysis

E.TransformersTransformers are represented by a combination of a series R-L

branch.

F.SourcesIn switching transient studies, the voltage source is modeled as

an ideal sine-wave source. Generators are modeled as a

voltage behind a (subtransient) Thevenin impedance.However, the simulations up to now used a dc voltage source

to reduce complexity.

III.STUDYCASEThe goal of this energization study case is to compare the

entire voltage wave during the connection of a new branch in

both programs. The comparison includes the settling time and

the maximum amplitude of the waves.

To achieve this objective a small system will be consecutive

energized and the result compared. The power system is

shown in Figure 4, is a 4 buses system 100 KVA and 230kV

with an open ended line at the bus 4. For the analysis thesystem is progressive connected in two steps.

Bus 2Bus 1 Bus 3

Line 1 Line 2TR

Load 1 Load 2VOLTAGE

SOURCE

Bus 4Swt 1 Swt 2

Figure 4 4 buses system example for progressive connections.

A.Step 1 -Voltage Magnitude & Settling time during the firstenergization

First, with transformer connected to the generator and in open

circuit2, the first loaded line at both ends is energized. The

voltage results are shown in Figure 5.

2Transformer saturation is not considered

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Figure 5 Result connecting loaded line to a transformer in

open circuit

To compare the error in maximum voltages and settling times

between Matlab code and PSCAD the next formula was used:

| || |

Bus

Name

Maximum voltage

magnitude (PE)

Settling time

(PE)

Bus 2 0.16 % 4.83 %

Bus 3 0.56 % 3.84 %

Table 1 Maximum voltage magnitude and settling time

comparison for the first energization

The second column ofTable 1 shows the result at the time of

comparing the maximum voltage at bus 2 and bus 3. The

results show a good approximation of the modeled system

with Matlab and the simulation in PSCAD. The same criteria

is applied for the settling time where the maximum error is

4.83 %

B.Step 2- Voltage Magnitude & Settling time during thesecond energization

When the steady state is reached the second open ended line is

switched on. The results from MATLAB code and PSCADare compared and the results summarize in Table 2.

Table 2 Maximum voltage magnitude and settling time

comparison for the second energization

Figure 6 Voltage magnitude at all buses when connecting an

open ended line to an already energized and loaded

Figure 6shows the voltage magnitudes in the system when the

second line is connected. The general forms of the waves are

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closed but the maximum magnitudes errors in Table 2 diverge

in comparison with the first energization.

.

IV.CONCLUSION AND FUTURE WORKA comparison of the performance of two simulation

environments (PSCAD/EMTDC and Matlab code) has been

demonstrated by modeling the switching overvoltage using a

small system. Both programs produced acceptable voltage

waves in magnitude and settling times during the connection

of new branches.

Future work includes the reduction in error percentage during

the connection of the second branch and the test in a bigger

power system to compare not only the transient response but

also the new steady state after each connection.

REFERENCES

[1] H. W. Dommel, Electromagnetic Transients

Program, 1987.

Bus Name Maximum voltage

magnitude (PE)

Settling time

(PE)

Bus 2 5.42 % 5.13 %

Bus 3 15 % 4.9 %

Bus 4 7.06% 6.19%