1

Abstract—This paper reports the work performed on the MSc

dissertation “Dynamic Simulations in Realistic-Size Networks”.

This work is part of a continued effort in the development of a

student-grade program for transient stability analysis,

implemented in MATLAB environment and reported in previous

documents. The goal was to make the program capable of dealing

with networks of realistic sizes. Therefore, the whole structure of

the program and the numerical procedures for transient stability

are reviewed. The dynamic models that already existed in the

software were revisited and two new dynamic models were also

implemented.

The validation of the software is performed with a side by side

comparison with PSS/ETM

.

Index Terms— Power system analysis, Transient stability,

Dynamic models, Exciter system, Turbine-Governor systems.

I. INTRODUCTION

imulation and analysis of power systems is a crucial

activity for power systems engineers, which has become

increasingly complex given the size of large interconnected

networks, and also given the demands in terms of security and

quality of service.

Power system analysis techniques have been clearly

modified with the development of digital computation.

Combining the theoretical and empirical knowledge obtained

over the years with the new computing capabilities, it became

possible to simulate and analyze systems and their response to

occurred disturbances, in a more rigorous and precise way.

Thenceforward many commercial simulation software

packages emerged, and have been used by engineers for

analyzing and designing power systems. However, due to the

commercial nature of these programs, the access to the

dynamic models, as to its components, are hindered, making it

impossible for them to be consulted or personalized by the

user. From an academic point of view, this restrains the

learning processes since the construction of the dynamic

models and the program procedures are important features

when the intrinsic study of dynamic models and simulations is

required.

This work aimed to further expand a dynamic simulation

program which has been under development in previous works

performed by former I.S.T. master students. This simulation

package is intended for educational use, while accomplishing

an approximate or even similar level of precision when

compared to existing commercial packages. This work has a

particular interest for the simulation of existing AC systems of

realistic size, which requires a special focus on the generator

control systems – speed governing and excitation system – as

they are crucial for the stable operation of large networks.

Therefore, this paper reviews some of the generator control

models already present in the software and also presents two

newly added control systems representing common

components found in most network; notably:

Table 1 - Revisited dynamic models

Dynamic Model Nomenclature

IEEE Type 1 Exciter, Excitation control system IEEET1

Hydraulic Turbine and Governor HYGOV

Table 2 - Newly implemented models

Dynamic Model Nomenclature

Type DC1A Exciter, Excitation control system IEEEX1

Gas Turbine and Governor GAST

The nomenclature given to the dynamic models is the same

as the one used by PSS/ETM, since this is the simulation

software used as a reference. PSS/ETM is used to recognize the

developed software through a side by side comparison

between the results obtained by both programs.

The paper is organized as follows. Section II introduces the

developed simulation software. In Section III the differential

representation of the dynamic models is given. This Section

also describes some of the used numerical solutions for the

dynamic simulation. Section IV reports the simulation results

and discuses the obtained results. Section V gives the

conclusions.

II. POWER SYSTEM SIMULATION SOFTWARE

A. Simulation Software Algorithm

Figure 1 displays a basic scheme to represent the simulation

software algorithm.

Dynamic Simulations in Realistic-Size

Networks

Pedro Rafael Araújo

S

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Figure 1 - Simulation process flowchart

The program is divided in three main stages.

1) Data Acquisition

The first stage is the data acquisition. Basically this stage

reads the input files that contain the data regarding both the

network and the dynamic models.

2) Preliminary calculations

The second stage performs the necessary preliminary

calculations before entering the dynamic simulation.

It starts by computing the power flow solution, in which the

used method is the Newton-Raphson algorithm.

The admittance matrix used in the dynamic calculation is

also computed at this stage. This matrix has to include all the

generators and loads; each generator is modelled as an

equivalent impedance, the subtransient impedance. The loads

are converted adopting the constant admittance method. This

method considers that the loads can be converted into pure

equivalent impedances, by using

( 1 )

where i denotes the load bus.

In order to decrease the computational effort, the network is

reduced by using the Internal Node method [1].

One of the most important steps in the simulation procedure

is the computation of the initial values of the dynamic state

variables. This, together with the load flow results, acts as a

checkpoint before entering the dynamic simulation stage. The

initial conditions are retrieved from the differential equations

that represent the dynamic models.

The last step of the preliminary calculations is the

construction of the algebraic state equations, which are used in

the digital numerical integration. These algebraic equations

are derived from the differential expressions that represent the

dynamics of each one of the systems included in the generator

group.

3) Dynamic Simulation

As it is known, this type of reckoning uses a discrete

method, due to the inherent digital nature of computers. The

simulation process is conducted in various time steps and, in

each interval the solution of the variables is computed.

The first step is the computation of the algebraic equations.

These correspond to the representative equations of all the

system components that are not differential and therefore, are

apart from the numerical integration.

In every time step, the dynamic simulation checks if there is

a network topology change (which corresponds to a fault). If

so, is changed and consequently reduced.

If the network topology is unaffected we jump to the

computation of the machine state equations parameters that

need to be computed in every time step (as shown in Section

III.C.).

Everything is now set to establish the computation of the

state variables using the numerical integration algorithm. An

integration algorithm proximate with the one used by PSS/ETM

– The Modified Euler-Chauchy – is presented in Section III.A.

Time is then incremented by one time-step, and a

comparison between the present and the maximum specified

times is made. If the maximum time is not reached, the

simulation continues. Otherwise the simulation is concluded,

and the results are plotted.

B. Simulation Software Improvements and Modifications

1) Reading of the Dynamic Data Files

In the previous version of the MATLAB program the

structure of the dynamic files was not compatible with

PSS/ETM. Because of this, a handmade conversion of the

dynamic files was necessary in order to compare the

developed software with PSS/ETM. For large power systems,

with a large number of generators, this was an arduous and

unnecessary task. Therefore, the function that read the *.dyr

files was changed in order to consider spaces, as the separation

of data, instead of commas as it did before.

The new function starts by predetermining the length of

eight arrays by allocating the number of characters from the

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beginning of the string (or row) to the last character of each

one of the seven columns presented in the file. Then, the size

of can be found through the difference between the

last element of and the last element of .

After the column allocation, each row of the file is read once

at a time, constituting an array of characters - or string. By

using the previously defined columns, we can separate each

data element given by a string and then address this element to

the respective data field variable.

2) Presentation of the Results

One of the main limitations on the preceding version of the

program was that it was designed to accommodate only three

specific cases. To plot the obtained results, each simulated

case needed a specific function. In addition, in each function,

the variables were printed one by one in a non cyclic manner

(a line code for each printed variable). Therefore, if any other

given case was to be simulated, the program could not

successfully complete the simulation, because the presentation

of the results was case dependent. So, a new function, which

no longer requires additional code each time a new case is

tested, was created.

3) Generator Reactive Power Limits

Another implemented feature was control of the generated

reactive power in the load flow computation.

The function that emulates this control is inserted in the

Newton-Raphson algorithm. After computing the injected

powers, angles and voltages in all buses, the program verifies

the reactive limits. Figure 2 shows a basic sketch of the

implemented function.

Figure 2 - Reactive Power limit verification function

III. DIFFERENTIAL-ALGEBRAIC MODEL

This section presents the dynamic models in their

representative differential forms. The description of the

models is not given due to the large number of dynamic

models presented in this paper. These models are described in

a vast amount of literature, so, this paper only concentrates on

the derivation of the differential and some of the algebraic

expressions that represent the dynamics of each of the models.

This Section also reviews some of the numerical procedures

used in the dynamic simulation.

A. Modified Euler-Cauchy integration algorithm

The Modified Euler-Cauchy integration method is an

integration method approximate with the one used by PSS/ETM

[2], and therefore was implemented in the simulation software.

This is an explicit algorithm, which belongs to the family of

the Second-Order Runge-Kutta method [3], and is given by:

( 2 )

where is the state variable, is the state function and

is the time step.

The modified Euler-Cauchy is composed of two steps.

Step 1: ( 3 )

Step 2: ( 4 )

Step 1 moves the state variable a half-step forward to time

( ) using the forward Euler method. Step 2 applies

once again the forward Euler method, but at this time using

the intermediate value found in ( 3 ).

This way, the modified Euler-Cauchy uses a midway value

between and . Hence, this method is an explicit

integration algorithm that attempts to share some of the

advantages of implicit methods, by taking midway steps.

B. Models in Differential Form

In order to achieve a stable operation, the power system

requires the control systems to be coupled with the generators.

Excitation control systems regulate the voltages of the

power system by controlling the generator field voltage,

These systems also assure the stability of the voltage.

Speed control systems ensure that generators satisfy the

changes in demand so that the active power balance is

maintained and therefore making the frequency of the system

nearly constant.

1) Excitation Control System IEEE Type I, IEEET1

Detailed information about the system IEEE Type I can be

found in [4]-[6].

Figure 3 shows the block diagram of IEEET1. The

parameters of IEEET1 are given in Table 3.

Figure 3 – Block diagram of the IEEET1 dynamic model (Source: [7])

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Table 3 – Parameters of the IEEET1 model

Parameter Representation Units

Exciter control voltage (generator terminal voltage)

Sensed terminal voltage

Voltage regulator reference voltage

Voltage error

Feedback voltage

Maximum and minimum voltage regulator outputs

Exciter output voltage and generator field voltage

Exciter saturation factor

Exciter block constant

Water flow

Voltage regulator gain

Terminal voltage transducer time constant

Voltage regulator time constant

Excitation control system stabilizer time constant

Exciter block time constant

Special attention should be given to the feedback

voltage . In order to simplify the computation of the

differential equations, another model given by [8] may be

used. This model defines a new state variable (called rate-

feedback), which has the following form:

( 5 )

( 6 )

As a result, instead of using , from now on the used state

variable becomes .

Taking this into consideration, the representative

differential state equations for the IEEET1 model are:

( 7 )

( 8 )

( 9 )

( 10 )

with the limit constraint of the voltage regulator output

( 11 )

The regulator limits are of the non-windup type.

Each time exceeds the limit restriction, it is

instantaneously fixed with the limit values, or .

This implies an iterative computation of the other state

variables, as well as of the algebraic variables, so that they

take into account the voltage regulation limitation. It is evident

that this iterative step requires the integration of the state

variables once again. In this process, is no longer a state

variable becoming a fixed input.

2) Excitation Control System Type DC1A, IEEEX1

Detailed information about the system Type DC1A can be

found in [4]-[6].

Figure 4 shows the block diagram of IEEEX1.

Figure 4 - Block diagram of the IEEEX1 dynamic model (Source: [7])

After a close observation of the block diagrams displayed in

Figure 3 and Figure 4, we can see the resemblance between

IEEET1 and IEEEX1. In fact, the only difference between the

two diagrams is the introduction of a lead-lag block in the

voltage regulator of model IEEEX1. This block uses time

constants and , which are used to model equivalent time

constants inherent to the voltage regulators, that weren’t

accounted for in the IEEET1 model.

The considerations regarding the feedback voltage and the

regulator limits, made for IEEET1, should be repeated for this

model.

The representative differential state equations for the

IEEEX1 model are:

( 12 )

( 13 )

( 14 )

( 15 )

( 16 )

with the limit constraint of the voltage regulator output

( 17 )

3) Hydro-Turbine Governor, HYGOV

Detailed information about the Hydro-Turbine governor

system can be found in [9]-[11].

The block diagram and the parameters of the dynamic

model are respectively presented in Figure 5 and in Table 4.

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Figure 5 - Block diagram of the HYGOV dynamic model (adapted from [12])

Table 4 - Parameters of the HYGOV dynamic model

Parameter Representation Units

Speed reference

Speed deviation

Permanent droop

Temporary droop

Governor’s time constant

Filter time constant

Servo time constant

Hydraulic system’s time constant

Gate opening position

Desired gate opening position

Water flow

Water head

No load flow

Turbine gain

Turbine damping

The representative differential state equations for the

HYGOV model are:

( 18 )

( 19 )

( 20 )

( 21 )

From Figure 5, it is also possible to retrieve the algebraic

equations of the hydraulic turbine, given by:

( 22 )

( 23 )

There are two types of limit constraints in HYGOV; the

maximum and minimum limits of the gate opening values and

the gate velocity limit.

The gate position limit imposes that the gate cannot open

more than , and that it cannot close more than , i.e.

( 24 )

At each time step, the desired position is checked. If this

variable is not within the limit range, its value must be fixed,

and afterwards, the remaining state variables must be

computed.

The other limit to be considered in HYGOV is the gate

velocity limit. In order to calculate the dynamic effects of this

type of limit, the input variable VELM is given. This variable

represents the reciprocal of the time taken for the gates to

move from fully open to fully close. Therefore VELM can be

seen as the growth rate of the gate position. Recalling that the

derivate of a position is in fact a velocity, we can use the

relations ( 25 ) and ( 27 ) to determine the maximum and

minimum desired gate position, due to velocity limits.

Gate

opening:

( 25 )

( 26 )

Gate

closing:

( 27 )

( 28 )

Here, is the numerical integration solution, is the

present value and is the simulation program time step. When

computing the integration solution, is compared with

and . If is higher than it

means that the gate is opening too fast. Otherwise, if is

smaller than , the gate is closing too fast. In both

cases, must be limited with the respective restriction

value.

4) Gas-Turbine Governor, GAST

Detailed information about the Gas-Turbine system can be

found in [13], [14] and [10].

Figure 6 shows the block diagram of GAST whereas Table

5 gives the parameters of the dynamic model.

Figure 6- Block diagram of the GAST dynamic model (Adapted from [12])

Table 5 - Parameters of the GAST model

Parameter Representation Units

Speed droop Fuel Flow to the combustion chamber Fuel valve opening Maximum valve position Minimum valve position Turbine’s Mechanical Power

Exhaust temperature load Ambient temperature load limit Governor time constant

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Combustion chamber time constant Exhaust gas measuring system time constant Temperature control loop gain

The representative differential state equations for the GAST

model are:

( 29 )

( 30 )

( 31 )

with the limit constraint of the valve opening

( 32 )

The fuel flow is controlled by the low value gate, which

selects the lowest value between the outputs of the load-

frequency control and the temperature control.

( 33 )

( 34 )

C. Models in Algebraic Form

The differential expressions presented in the last Section

need to be converted into an algebraic state equation so that

the integration algorithm represented by ( 2 ) can be applied in

the simulation software. The state function has the form of the

following algebraic expression.

( 35 )

This outline takes into account that the time constants and

the parameters associated with the dynamic models remain

constant throughout the simulation process and, therefore, do

not need to be computed in every time step.

Matrix includes the dependent associated time constants

and model parameters, constant in all the computation. Matrix

retrieves the non-constant terms, thus requiring to be

calculated in every time step. Matrix includes the

independent terms, related with the matrix , which contains

the fixed inputs. These matrices are also constant throughout

the simulation. Taking this into consideration, only matrix

needs to be consistently computed.

As an example, the algebraic state equation that represents

the IEEEX1 dynamic model is presented.

The IEEEX1 dynamic model represented by the differential

equations ( 12 ) – ( 16 ), in its algebraic form, is given by

( 36 )

The matrices , , and are specified by

( 37 )

( 38 )

( 39 )

( 40 )

IV. SIMULATION, RESULTS AND DISCUSSION

A set of five simulations are made in order to validate the

dynamic models and the capability of the software in dealing

with large networks.

A. Dynamic Simulations Procedures and Considerations

At the simulation starts;

At a three phase short circuit is applied to a specific bus;

At the fault is cleared by removing a branch connected to the faulted bus, enacting the

opening of the circuit breaker;

At the simulation ends.

In all the simulations, the system base is , the

nominal frequency is , and, with the exception in the

HYGOV validation, the used time-step is .

B. Validation of the Dynamic Models

Four validations are performed, one for each presented

model. The combination “synchronous generator + excitation

system + governor system” of the models that compose the

generator group is given in the following list GENROU + IEEET1 + GAST

GENROE + IEEEX1 + TGOV1

GENROE + IEEET1 + TGOV1

GENSAL + IEEET1 + HYGOV

The 2-Bus network presented in Figure 7 is used in these

simulations. Table 6 gives the results obtained by the load

flow computation. The symmetric three-phase short circuit is

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applied to Bus 1, and Branch 2 is tripped in order to replicate

the opening of the protection system.

Figure 7 - 2-Bus network

Table 6 - Power flow results for the 2-Bus simulation

Power Flow Results

BUS Voltage

1 Swing 1.0400 0.0000 0.2508 0.0613 - -

2 P-Q 1.025 -0.5877 - - 0.2500 0.5000

In all figures the results of the developed program are

represented by a black continuous line, while the PSS/ETM

results are represented by a yellow filled area.

1) GAST Validation

Figure 8, Figure 9 and Figure 10 show the response of the

active ( ) and mechanical ( ) powers and the speed

deviation ( ) of the generator group.

Figure 8 – GAST validation, Generator Active Power

Figure 9 – GAST validation, Generator Mechanical Power

Figure 10 – GAST validation, Speed deviation

During the fault, decreases immensely and, the load

demand cannot be supplied. Because of this, a mismatch

between the mechanical and the electrical torques occurs,

which results in an increase of the speed of the machine.

Becoming aware of this speed increase the gas-turbine

governor acts on the turbine valve, by closing it. This

consequently results in a decrease of in an attempt to

approximate it to . However, when the fault is cleared,

rises, which combined with the decreased makes to

increase. As reaches its stationary value, so do the other

two variables (with a small delay due to the time lags of the

governor system).

2) IEEEX1 Validation

Figure 11 and Figure 12 show the response of the terminal

voltage in bus 1 ( ) and the exciter output voltage ( ).

Figure 11 – IEEEX1 validation, Voltage magnitude, Bus 1

Figure 12 - IEEEX1 validation, Exciter Field Voltage (generator terminal

voltage)

When the disturbance occurs, instantaneously dips to zero

because of the extremely low impedance cause by the short

circuit. raises its value, in order to compensate the

weakening of the air gap flux.

After clearance of the fault starts to rise in a damped

manner. This is due to the arrangement of the time constants

of the voltage regulator. In this simulation it was considered

an extreme case, as is big whereas is very small. A

Root-Locus analysis would show that the arrangement of these

time constants is in fact responsible for the slow and damped

response of the system.

3) IEEET1 Validation

This simulation intends to recognize the implementation of

the limit restrictions of the voltage regulator. To do this the

voltage regulator maximum limit ( ) is set with a small

value. Hence, as a result of this value, the infringement

endures from almost the instant the fault is applied until the

end of the simulation, that is, is equal to for most of

the simulation.

Figure 13 and Figure 14 show the response of the terminal

voltage in bus 1 ( ) and the exciter output voltage ( ).

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Figure 13 – IEEET1 validation, Voltage Magnitude, Bus 1

Figure 14 - IEEET1 validation, Exciter Field Voltage

When the disturbance occurs and the bus voltage

magnitudes decrease instantaneously, the exciter system

responds by increasing the signal to the voltage regulator,

whose output is eventually bigger than allowed. When the

limit is reached the voltage regulator output is instantaneously

set with the limit value in the form of a step function. Since

for most of the simulation, is a filtered

response of .

4) HYGOV Validation

This simulation intends to validate the implementation of

the limit restrictions of both the gate position and the gate

velocity limits. To do this the maximum limit of the gate

position ( ) and the limit of gate velocity ( ) are set

with small values in order for them to be violated. Figure 15

shows the response of the desired gate position, which is the

controlled variable in either limit constraint.

Figure 15 - Desired gate position state variable response

When the short circuit occurs, , as already seen in

previous cases, dips instantaneously to zero, increasing the

difference between electrical and mechanical torques. This,

due to the swing equation, raises the speed of the machine.

The governor detects the rapid speed increase and orders the

turbine to close its gates in order to decrease . However,

the velocity limits of the hydro-turbine gates are very small,

and as soon the governor enters in action, these limits are

broken, restricting the gate position. Figure 15(b) shows this

behaviour, where the desired gate position has a linear closing

response, denoting a constant velocity - . After the

clearance of the fault increases and, after the intrinsic

delays of the control system, the governor forces to

increase. Once again, is broken and the gate opening is

restricted.

At around a new event occurs; the violation of

the maximum boundary of the gate position. As

increases in order to “catch up” with , the gate reaches its

maximum opening, and therefore, cannot open any further.

This is observed in Figure 15(c) where the desired gate

position has a maximum value of , which is the

defined .

It should be noted that, when the position limits constraints

were broken, the program produced inaccurate results. The

problem resided on the used time-step of the simulation. In

order to obtain more accurate results, the time-step for this

simulation was reduced to .

C. 57-Bus Case

The topology of the network is represented in Figure 16,

whereas Table 7 gives the results of the load flow

computation.

(a) Desired gate position state variable response for the

entire simulation.

(b) Response after the fault – gate

velocity limits transgression

(c) Gate position limits

transgression

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Figure 16 - Single-line diagram of the 57-Bus network

Table 7 - Power flow results for the 57-Bus simulation.

Power Flow Results

BUS Voltage

1 Swing 1.0400 0.0000º 0.8807 1.9467 0.15 0.17

2 P-V 1.0100 1.3644º 0.8000 -0.2421 0.03 0.88

3 P-V 0.9850 0.5522º 1.0000 -0.2287 0.21 0.21

4 P-Q 0.9796 0.1897º - - - -

5 P-Q 0.9761 0.4927º - - 0.13 0.04

6 P-V 0.9800 1.0991º 1.0000 -0.3101 0.35 0.02

7 P-Q 0.9823 -0.9774º - - - -

8 P-V 1.0050 0.0327º 1.5000 0.9420 0.50 0.22

9 P-V 0.9800 -2.0483º 0.8000 -0.2939 0.70 0.26

10 P-Q 0.9834 -4.1283º - - 0.05 0.02

11 P-Q 0.9707 -3.5070º - - - -

12 P-V 1.0150 -2.8624º 1.5000 0.8869 1.0000 0.2400

13 P-Q 0.9781 -3.7933º - - 0.5800 0.0230

14 P-Q 0.9710 -3.7820º - - 0.1050 0.0530

15 P-Q 0.9852 -2.2859º - - 0.2200 0.0500

16 P-Q 1.0207 -2.4616º - - 0.1300 0.0300

17 P-Q 1.0212 -2.5692º - - 0.4200 0.0800

18 P-Q 0.9577 -7.9801º - - 0.2720 0.0980

19 P-Q 0.9250 -9.0583º - - 0.0330 0.0060

20 P-Q 0.9176 -8.9306º - - 0.0230 0.0100

21 P-Q 0.9154 -7.9254º - - - -

22 P-Q 0.9166 -7.7611º - - - -

23 P-Q 0.9150 -7.7937º - - 0.0630 0.0210

24 P-Q 0.9053 -7.4366º - - - -

25 P-Q 0.8334 -18.7511º - - 0.0630 0.0320

26 P-Q 0.9068 -7.0440º - - - -

27 P-Q 0.9370 -5.3290º - - 0.0930 0.0050

28 P-Q 0.9553 -4.1689º - - 0.0460 0.0230

29 P-Q 0.9710 -3.3830º - - 0.1700 0.0260

30 P-Q 0.8131 -19.2081º - - 0.0360 0.0180

31 P-Q 0.7889 -19.3464º - - 0.0580 0.0290

32 P-Q 0.8177 -16.9444º - - 0.0160 0.0080

33 P-Q 0.8150 -16.9980º - - 0.0380 0.0190

34 P-Q 0.8625 -9.6820º - - - -

35 P-Q 0.8722 -9.3056º - - 0.0600 0.0300

36 P-Q 0.8844 -8.9285º - - - -

37 P-Q 0.8936 -8.6356º - - - -

38 P-Q 0.9199 -7.6569º - - 0.1400 0.0700

39 P-Q 0.8921 -8.6797º - - - -

40 P-Q 0.8835 -8.9816º - - - -

41 P-Q 0.9298 -8.4914º - - 0.0630 0.0300

42 P-Q 0.8857 -10.1253º - - 0.0710 0.0440

43 P-Q 0.9578 -4.9534º - - 0.0200 0.0100

44 P-Q 0.9327 -6.9176º - - 0.1200 0.0180

45 P-Q 0.9713 -4.5545º - - - -

46 P-Q 0.9562 -5.6964º - - - -

47 P-Q 0.9332 -7.2639º - - 0.2970 0.1160

48 P-Q 0.9294 -7.3808º - - - -

49 P-Q 0.9363 -7.3509º - - 0.1800 0.0850

50 P-Q 0.9290 -7.4740º - - 0.2100 0.1050

51 P-Q 0.9731 -5.6697º - - 0.1800 0.0530

52 P-Q 0.9333 -4.9779º - - 0.0490 0.0220

53 P-Q 0.9200 -5.6526º - - 0.2000 0.1000

54 P-Q 0.9404 -4.7240º - - 0.0410 0.0140

55 P-Q 0.9707 -3.4209º - - 0.0680 0.0340

56 P-Q 0.8760 -10.6869º - - 0.0760 0.0220

57 P-Q 0.8667 -11.4109º - - 0.0670 0.0200

The three phase short circuit is applied to Bus 42 and, in

order to emulate the circuit breaker, the branch connecting

buses 42 and 56 is removed.

Table 8 presents the different combinations of the used

dynamic models in the seven generator groups, as well as their

location in the network.

Table 8 - Dynamic models used in the 57-Bus simulation

Bus Generator Group Combination

1 GENSAL + IEEET1 + HYGOV

2 GENROE + IEEET1 + GAST

3 GENROE + IEEEX1 + TGOV1

6 GENSAE + IEEET1 + HYGOV

8 GENROU + IEEET1 + TGOV1

9 GENROU + IEEET1 + GAST

12 GENSAL + IEEET1 + HYGOV

Due to the large dimensions of the case in study, the total

number of figures to display is enormous, therefore only a

selection of results is delivered. Regarding the network, the

voltages of buses 42 (faulted bus), 56 (adjacent bus) and 1

(distant bus) are displayed. In order to give an example of the

generator and control systems response, the generator group in

bus 2 is also displayed.

(a) Voltage Magnitude, Bus 42 (b) Voltage Magnitude, Bus 56

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Figure 17 - 57-Bus simulation results - Gen. group at bus 1, GENSAL +

IEEET1 + HYGOV

Through the observation of Figure 17, it is seen that the

computation of the first swing of all the represented variables

is correct and concordant with PSS/ETM.

However, a close examination of the speed deviation shows

that the behaviour of this variable is not in total agreement

with the result obtained by PSS/ETM. As already said the first

swing computation is correct but as the simulation advances in

time, suffers a shift, experiencing a delayed response when

compared with PSS/ETM. As a consequence, electrical and

mechanical powers also suffer some deviations, resulting in

small mismatches between the two simulation packages.

V. CONCLUSION

Through the observation of the validation results provided

in Section IV.B, it is possible to conclude that all the models

are correctly implemented, as their dynamic behaviour is

similar to the one obtained by PSS/ETM. However, it should be

noted that, when the HYGOV governor limits are broken,

there is a necessity to use smaller time-steps in order to

compute the dynamic solutions accurately. This denotes

numerical limitations when turbine-governors systems limits

are breached.

The results of the 57-Bus case also recognize the

similarities between the dynamic behaviours of MATLAB and

PSS/ETM results. This is especially noticeable in the first swing

and in the end of the simulation, when a new steady state has

been achieved. However, this simulation shows that the

differences between the results of the two software’s packages

increase due to both the restricting action of the governors and

the growth of the network. This is mainly visible in the speed

deviation, which, after a certain point, begins to exhibit delays

in comparison to PSS/ETM. Despite all of these differences, the

errors of the results, when compared with PSS/ETM outputs are

small, which complies with the objectives of the developed

work: the implementation of simulation software capable of

dealing with large networks, while accomplishing a level of

precision very close to other simulation packages with a

commercial nature.

ACKNOWLEDGMENT

The author would like to thank Instituto Superior Técnico

for having provided the resources necessary for the

development of the work.

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(d) Generator Active Power

(e) Generator Reactive Power (f) Exciter Field Voltage

(c) Voltage Magnitude, Bus 1

(g) Generator Mechanical Power (h) Speed Deviation