This case is based on Case 3, with the addition of
transmission lines in series with the parallel lines of Case 3. The lines are all modeled with the coupled pi model, using line lengths of one (1) metre. Coupled pi line sections require data for R, X and B selected as impedance per metre or pi per meter. By choosing a one-metre line section, the R, X and B values entered are for the entire line length. In this case, the one-metre line is equivalent to the 160 km (approximately 100 mile) line using the full frequency dependent model. FT3 FT2 3 Phase RMS F4 V3 F3 tap FT4 B4 -1.574 [MVAR]-6.447 [MW] F2 V2 3 Phase RMS F5 FT5 V1 Display off line tap
0.9 1.35 1.05 FT1 F1 B1 2.312 [MVAR]6.21 [MW] B2 1.684 [MVAR]6.099 [MW] 1.0 20.0 [MW] 5.0 [MVAR] B5 -1.336e-015 [MVAR]0.00012 [MW] B3 -0.1103 [MVAR]0.3487 [MW] SUBSTATION 1 Z1 = 52.9 [ohm] /_ 80.0 [°] V Ph 230.0 [kV], 60.0 [Hz]100.0 [MVA] Z1 = 52.9 [ohm] /_ 80.0 [°] V Ph 25.0 [kV], 60.0 [Hz]100.0 [MVA] #1 25 [MVA] 230.0 [kV]/10 [kV]/25 [kV] #3 #2 Plots B1 Plots B2 Plots B3 / 4
Note the breaker control for breaker 5 is located on the main page, and not in the Controls’ subpage.
FT1 V3 V4 FT2 B3 117.4 [MVAR]36.05 [MW] 3 Phase RMS V1 3 Phase RMS 3 Phase RMS FT5 FT3 FT7 FT6 FT8 Fault Fault Fault Fault Fault Fault V2 Fault SUBSTATION 2 FT4 B2 -65.69 [MVAR] -25.51 [MW] B1 117.4 [MVAR] 36.05 [MW] Fault Z1 = 17.95 [ohm] /_ 87.63 [°] V Ph 230.0 [kV], 60.0 [Hz]100.0 [MVA] 50 [%] 50 [%] Line 1 Line 2 Line 5 Line 4 Line 3 B5 82.54 [MVAR] 24.08 [MW] 3 Phase RMS 50 [%] 50 [%] B4 -65.69 [MVAR]-25.51 [MW] Z1 = 3.8 [ohm] /_ 87.69 [°] V Ph 230.0 [kV], 60.0 [Hz] 100.0 [MVA]
Chapter 4
PSCAD/Relay Components
TRANSMISSION LINE MODELING
The modeling of transmission lines for transient simulation is an important and complex topic. Transmission lines and cables in electric power systems are non-linear in nature due to frequency dependency in conductors (skin effect) and the ground or earth return path. PSCAD/Relay offers the most accurate time domain transmission line models offered today, but can also accommodate limited models based on the available system data.
There are two main methods for modeling transmission lines for PSCAD simulation in the time domain:
1. Use of coupled pi line sections. Although for frequency domain studies, transmission lines modeled with pi lines can be precise, in the time domain, particularly for long lines (where
propagation travel time spans many time steps), precision suffers. Pi line sections are most useful for very short transmission lines where the propagation travel time is less than a time step. At 50 µ sec time step, any line less then 15 km should be represented as a pi section.
2. Use of distributed or traveling wave modeling. The distributed transmission line models operate on the principle of traveling waves. A voltage disturbance will travel along a conductor at its propagation velocity (near the speed of light) until it is reflected at the end of the line. In a sense, a transmission line or cable is a delay function. Whatever is fed into one end will appear at the other end after some delay, perhaps slightly distorted. The calculation time step of the simulation should be less than the propagation time.
There is provision in PSCAD/Relay to model both pi line sections and distributed lines.
Distributed or Traveling Wave Transmission Line
There are three distributed transmission lines available in the Tlines and Cables’ pages of the Master Library. These are in order of increasing precision:
1. Bergeron model
2. Frequency Dependent (Mode) model 3. Frequency Dependent (Phase) model
The example cases implement a Frequency Dependent Phase Model. The user is required to provide the tower geometry and conductor information. A library of typical conductor types, radius and resistance per km information is provided based on Southwire’s ASCR data, found at
www.southwire.com/wc/catalog/sec11/11-04.pdf1. All
of the impedance calculations are performed automatically by the Line Constant program, which is part of PSCAD/Relay. If data regarding tower configuration is not available, it is suggested to convert the R, X and B from stability or load flow models into a Bergeron traveling wave model.
Displaying Line Data Calculated by Line Constants
In order to display data calculated by Line Constants, double click on the transmission line. Use the EDIT key to view the transmission line parameter page. There are three pieces of information on this page, the line model, line configuration and the sequence information. The following box is an example describing which modeling option was selected for this line.
On
20 Maximum Order of Fitting for Prop. Func.:
20 Maximum Order of Fitting for ZSurge:
1.0E6 [Hz] Curve Fitting End Frequency:
Curve Fitting Starting Frequency: 0.5 [Hz]
Frequency Dependent (Mode) Model Options
Maximum Fitting Error for ZSurge: 2 [%]
2 [%] Maximum Fitting Error for Prop. Func.:
Travel Time Interpolation:
To change the type of line model simply delete this box and replace it with a different option from the master relay Library "Tlines."
Next is the line configuration and ground information. This set of data describes the tower configuration and contains the information on conductor and ground wire data. Again, if a different tower configuration is required, simply delete the current one and paste a new one from the T-line library.
The last item on the Tline edit page is the Sequence
Information display block. When Line Constants solves the line parameters, an output file is created in the “.emt” directory that corresponds to the current case, for example “case1.emt.” This output file, “linename.out” provides the data for the sequence display information, which can be viewed using any ASCII text viewer, such as Notepad. The display data takes into account the line length.
Tlines
Master Library T-Lines page icon 30 [m] 10 [m] C1 C2 C3 10 [m] Ground_Wires: 1/ 2"HighStrengthSteel Conductors: chukar Tower: 3H5 10 [m] 0 [m] 5 [m] G1 G2 100.0 [ohm*m] Relative Ground Permeability:
Ground Resistivity: 1.0 Earth Return Formula: Deri-Semlyen
3.62518 36.3595 1e-005 1e-005 1e-005 50.8645 132.732 0.000232266 POS ZERO NEG POS NEG ZERO 3.62518 R 50.8645 0.000327118 X Sequence Admittance 0.000327118 Sequence Impedance (mhos) (ohms) G B
Line Constants are solved either by running the case, or right click on the T-line Parameters’ page, and select “Solve Constants” option, as shown below.
Coupled Line Model Using Load Flow Parameters
PSCAD/Relay offers a coupled pi section line model. This coupled pi is located in the Main Library and not in the T-
Lines or Cables library pages. The coupled Pi line model uses data readily available from the Load Flow Parameters. This line model should be used when distances of less than 15 (at a 50 µ s time step) kilometres are to be simulated. In transient studies with pi sections, it is important to
consider whether one or several sections should represent a line. This is dependent upon:
1. The calculation time step DELT or ∆ t. 2. The length of the line.
3. The frequency of response required from the simulation model.
Typical transient studies for AC relay protection should represent frequencies up to 2000 Hz. A 50 µ sec calculation time step (∆ t) is adequate. At the speed of light, a wave may travel 15 km over 50 µ sec. If the length of the transmission line is less than 15 km when ∆ t = 50 µ sec, then one pi section is adequate to represent the line. If the line is longer than the 15 km, then two or more pi sections should be cascaded in series.
Converting Line Data
Often network data is only available in load flow program format. A transmission line is represented with positive sequence parameters in per unit (usually on 100 MVA base). The line is represented by the parameters R, X and B, where R = per unit Resistance,
X = per unit Reactance, and B = per unit Susceptance.
The load flow line model data can be transferred into the coupled pi section component. The steps to do this are as follows:
Decide how many coupled pi sections are to be cascaded for the line to be modeled. If the line length is not available, assume a length of 1.0 meter for each line section. To use the component, simply delete the full frequency dependent model and replace it with the coupled pi model, which can be found in the master library. There are two views available, single line diagram or three phase view. The single line diagram view is shown below.
50 [%]
50 [%]
A middle connection is optional, and is set within the
model’s main parameters. The parameters are available by double clicking on the component.
The middle connection location is determined by the
percentage entered in the Distance to middle connection parameter. The distance is taken from the left. For
example, if you had a 3-metre line and you entered a distance of 30%, the middle connection would be located 0.9 metres from the left hand side of the transmission line. The minimum distance to the middle connection is 5% and the maximum is 95%.
Data entry is in two formats, R, Xl, B (ohms) and R, Xl, B (per unit). B is susceptance, which is the reciprocal of reactance. Note that susceptance is entered in Mmhos*m, as shown below.
No other changes are necessary to use the coupled pi model in place of the full frequency dependent model.
The coupled pi model uses transformers to represent transmission lines of short length; therefore, the results will not be identical to the frequency dependent model.
However, these results will be more accurate for a sub 15 km line than the frequency dependent model’s results would be for such a short line.
The coupled pi section component is for a balanced 3-phase line, which is similar to being continually transposed, so that its positive sequence impedance is the same as its negative sequence impedance.
Manual Entry of Data for Bergeron Model
There is an option to insert data manually for the Bergeron Model Options, instead of using the tower and conductor geometry component described above.
The line data available is in positive sequence load flow format R+jX, (B) in per unit, without any details of the tower and conductor geometry. A “best fit” distributed line model is desirable over using coupled pi sections.
To enter data manually for the Bergeron Model, copy the “Manual Entry of Y, Z” component from the Tlines page in the Master Library to the TlineInfo subpage of the
transmission line being added to the simulation model under construction. Do not copy and transfer the tower and
conductor geometry component or the ground component to the TlineInfo subpage. If the ground component is already located there, then delete it.
Tower Component: 30 [m] 10 [m] C1 C2 C3 10 [m] Ground_Wires: 1/2"HighStrengthSteel Conductors: chukar Tower: 3H5 10 [m] 0 [m] 5 [m] G1 G2 Ground Component: 100.0 [ohm*m] Relative Ground Permeability:
Ground Resistivity: 1.0 Earth Return Formula: Deri-Semlyen
Consider the 500 kV, 222.07 km transmission line in its load flow/stability data format in per unit on 100 MVA base: R + jX (B) = 0.001525 + j0.034 (2.355)
If the line length is known, and it exceeds 100 km, the long line correction factor should be applied in converting the per unit line data for manual entry into a Bergeron line model. The line data with the long line correction removed enables parameters to be determined in terms of 1-metre sections for the Bergeron line model. The correction factors for long line effects can be enabled in the Bergeron line model or can be applied to the data conversion. In this example, the factors included are to compensate for effects of long, greater than 100 km lines.
Positive Sequence Resistance = R/(0.976*222070) [p.u./m] = 0.007036E-06 [p.u./m]
Positive Sequence Inductive Reactance = X/(0.987*22070)[p.u./m] = 0.1551E-06 [p.u./m]
Positive Sequence Capacitive Reactance*
= 1.006*222070/B [p.u.*m] = 0.09486E6 [p.u.*m]
Note: Charging capacitance is entered into the Bergeron manual data page in terms of per unit capacitive reactance (1/B), not the more familiar per unit admittance.
Although the Bergeron line model provides a good impedance match at steady state frequency, the lack of frequency dependency in the model will result in less damped transients at higher frequencies.
Additional information on Transmission Line modeling can be found in PSCAD/Relay Help by using the Help key, Table of Contents and select Tlines and Cables. This will bring up a topic about “Building a Transmission Line Model.” At the end of this chapter, there is a link to the PSCAD web site for more information on transmission line modeling theory, “Distributed Line and Cable Models.”
Conductor Database
When using a traveling wave transmission line model, the transmission tower geometry and conductor data is
required. Using different pre-configured tower geometries from the transmission line library can modify transmission tower geometry. Conductor radius in meters and DC
resistance in ohms per kilometre is required. This conductor data can be inserted into the t-line component directly or it can be read in from a conductor data file. A data file, “conductor.clb,” is supplied with PSCAD-Relay and contains many of the common ACSR conductor types. The user can add additional conductors to this conductor library file by editing the file using any ASCII text editor such as Notepad. By specifying the name of the conductor and the location of the data file, the user does not have to remember the precise numbers for a particular conductor type.
For example, to add and use a new conductor type named “polly” in any example case, the following steps are required:
1. Open up conductor.clb from the
examples/Relay_Cases directory, using an ASCII text editor, such as Microsoft’s Notepad.
2. Enter in your conductor type, as shown below. Data can be entered anywhere within the
“conductor.clb” file. Be sure to use spaces, not tabs to separate the data. PSCAD/Relay is case sensitive, so capital letters are different than lowercase.
3. Save conductor.clb.
4. Double click on the T-Line you which to change in your case. Click on the Edit button. This will bring up the Transmission Line page. On it, you will find
the T-Line component, as shown below. Note it is shown as using "chukar."
30 [m] 10 [m] C1 C2 C3 10 [m] Ground_Wires: 1/2"HighStrengthSteel Conductors: chukar Tower: 3H5 10 [m] 0 [m] 5 [m] G1 G2
5. Double click on the T-line component to bring up the properties, as shown below.
6. From the drop down menu, select Circuit 1
7. Under Data Entry Method for Conductors, click on From Library. This tells PSCAD to use the conductor.clb file to find the conductor geometry.
8. Enter in the correct name in Circuit 1 Cond. Name. For our example, it is “polly,” as shown below. Unless you wish to use a file in an alternate location, the pathname remains the same.
The path for the file can be absolute or relational. In the
\examples\Relay_Cases
examples provided with PSCAD_Relay, the conductor library file is entered as
“..\conductor.clb.”
This means the file is located in the same directory as the
9. Click OK.
10. To test and make sure that PSCAD/Relay is using the new geometry, right click on the T-Line page and select Solve Constants, or simply run the case. Notice the Sequence Impedance box. The values should change to reflect the new geometry. Note the conductor component also changes to reflect the new conductor type.
12.5169 45.2512 1e-005 1e-005 1e-005 37.3557 119.223 0.000290216 POS ZERO NEG POS NEG ZERO 12.5169 R 37.3557 0.000455103 X Sequence Admittance 0.000455103 Sequence Impedance (mhos) (ohms) G B
30 [m] 10 [m] C1 C2 C3 10 [m] Ground_Wires: 1/2"HighStrengthSteel Conductors: polly Tower: 3H5 10 [m] 0 [m] 5 [m] G1 G2
Values can also be added manually, without having to modify the conductor.clb file. In step seven (7), choose
Custom from the Conductor Data menu and enter in the
appropriate Conductor Radius and Conductor DC
Resistance.
For more information, search for “Transmission Line” in the Help files, or visit the PSCAD/Relay web site at
www.hvdc.ca.
Additional T-line References
An introduction to PSCAD V3 is provided free of charge from the Centre’s web site.
This web site requires a user name and password, which are free to users of PSCAD.
To obtain a username and password, follow these steps:
1. Log on to
http://www.hvdc.ca/main/downloads/pscad_v3/i ndex.html
2. Click on Register Online.
3. Fill out the form. The Name you enter will be your user name.
4. Click on Submit. The form will be submitted and a user name and password will be generated.
5. Write down your user name and password, for access to the site.
Either click on the go to downloads link at the bottom of the password page, or go to:
http://www.hvdc.ca/main/downloads/pscad_v3/pe_reg/pe/ind ex.html
Look for AN INTRODUCTION TO PSCAD/EMTDC V3 MANUAL: pscad-intro-v1-4.pdf (3.3 MB), and other useful information.
Chapter 5 deals specifically with Transmission Lines.
TRANSFORMERS
Simulation of transformers requires an understanding of some of their basic properties involving both core and winding configuration. This is complicated by the fact that the core of the transformer is prone to saturation leading to the phenomena of inrush current, remanence, geomagnetic current effects and ferroresonance.
In this section, the main emphasis is on the magnetic properties of transformers. The effects of winding
capacitance are generally minimal and need not be modeled providing the frequencies of interest are less than about 2000 Hz and switching transients are of interest. Winding capacitance is important when fast front studies are to be performed and magnetic effects can usually be neglected. The transformer models are in the Transformers Library Group in the Master Library of PSCAD.
#1 #3 #2
Three phase component of a transformer model.
TRANSFORMER MODELS
The models require that there is leakage reactance, and so the concept of an ideal transformer without leakage
reactance is not possible in PSCAD. If the leakage reactance is set to 0.0, the transformer model may actually run, but it may become numerically unstable. Fortunately, due to the double precision calculations of EMTDC, low values of leakage reactance (0.001 to 0.01 per unit) should solve satisfactorily if such a low value is needed.
Magnetizing current is a setting entered into each Winding Property Sheet of the transformer components. This is the unsaturated magnetizing current of the transformer at rated volts and at no load. Enter the same value for each winding in percent on the base of the winding rated voltage and transformer MVA rating. Usually, unsaturated magnetizing current at rated volts is less than 1% for most power (10 MVA or greater) transformers.
When saturation is included in the model (see below), the magnetizing current is merged into the saturation effects. Actual winding resistance must be added as an external resistance as PSCAD does not request it in the transformer components. For many studies, the effect of winding resistance is negligible.
Core Configuration
The positive and zero sequence leakage impedances of three-phase transformers are dependent upon both core configuration and winding configuration. If the core is three- limb, then the effect is to have zero sequence impedance similar in value to the positive sequence impedance. This is because if the transformer is subjected to zero sequence voltages, there is no core path for zero sequence flux to flow. Consequently, the zero sequence flux passes through air, yoke and tank causing zero sequence impedance to be quite low. In the general transformer model, adding a delta winding approximates this effect.
Some-three phase transformers have their zero sequence impedance larger than their positive sequence impedance. A compensating neutral reactance XN is mathematically
added at the star point to ground. If the positive sequence leakage reactance is XH-L, then the zero sequence reactance
XO of the transformer from its star winding is:
XO = XH-L + 3*XN
From which;
XN = [ XO – XH-L ]/3
The neutral reactance is patched into the network model as an inductance. Its value is:
LN = XN * MVA / (w * VH2)
Where:
XN = Neutral reactance in per unit on the
transformer base MVA and the star winding voltage rating.
MVA= Transformer base MVA rating.
VH = Rated line-to-line r.m.s. volts of the star
winding.
w = System frequency in radians per second. If a neutral reactor is incorporated in this way for modeling expediency, it should be noted that the transformer neutral point is removed from the actual ground to a node