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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