3.6 In situ high temperature ECR measurements
4.1.2 Results and Discussion of ECR measurements
GENERAL USAGE:
First of all it is important to realize that, in contrast with the previous branches (type 0), the capacitance values specified on the input cards of type 1,2,3 are for shunt connected capacitances, not for series connected ones. A further observation worth reminding is that the capacitance value that is entered, is internally allocated half at the beginning and half at the end of the model.
R
R
R
L
L
L C
C
C C C
C
C
C
C C C
C
86
This class of branches thus provides for the representation of lumped-element resistance, inductance and capacitance matrices. The lumped-elements of the matrices [R], [L] and [C] have the following meaning (steady state):
- diagonal Rii + jωLii : self impedance of branch i (impedance of loop
"branch i - ground return");
- off-diagonal Rik + jωLik : mutual impedance between branches i and k (Rik ≠ 0 with nonzero ground resistivity);
- diagonal Cii : sum of all capacitances connected to the nodes at both ends of branch i;
- off-diagonal Cik : negative value of capacitance from branch i to branch k.
[
Note that all matrices are assumed to be symmetric and that the matrix of the capacitance is split in two, with half of the total on each end of the branch.
This model, better known as a multi-phase nominal PI-equivalent, can be used to simulate transient phenomena on short lines or cables. By connecting many short sections in series, keeping track of any actual transposition (if any), even a transient model for a long line can be obtained. Yet because of increased running time and memory requirements, this modelling should generally be used only as a last resort, where more sophisticated models (e.g. distributed-parameter models) are believed to be inadequate. Note that this is not the CASCADED PI option referred to in section IV.F; cascaded PI uses the long-line equivalent, which is valid only for steady state, at one specific frequency.
The supporting routine LINE CONSTANTS (section XXI-E) or CABLE CONSTANTS (section XXIII-B) can be used as data generator for type 1,2,3 branch cards.
Indeed the parameters [R], [L] and [C] cannot easily be calculated by hand.
But also transformers can be modelled using PI-equivalents. Because most transformers have a small P.U. excitation current, the admittance matrix is nearly singular. The leakage impedance is rather low and can be obtained by substracting the mutual impedance from the self-impedance. Because off the fact that the admittance matrix is ill-conditioned, the leakage impedance can get lost in the magnetizing impedance. Therefor, it is necessary to have sufficient accuracy for the inductance. Hence, the normal card format (E6.0) is not sufficient. For transformers, either the alternative high-precision format should be used (see section IV.B.2 and related data generator BCTRAN, section XIX-C), or a more appropriate branch card format (type 51-52-53, see section IV-C) should be used (see data generator XFORMER, section XIX-A). In the ideal case of non-existing (or very low) P.U. excitation currents, the inductance matrix does not even exist. For this special situation, a special option (AR notation) is used.
Here, A stand for L-1 (the inverse of the inductance), which does exist (be it almost singular). This is later explained in more detail (see section IV.B.2). In both cases (AR and RL notation), the positions for the capacitance can be used succesfully to derive frequency dependent transformer models, where one needs to take into account the interwinding capacitances, as well as the capacitances to
k m km
ground. At this moment (November 1990), no related automatic data generator is available within EMTP.
SPECIAL USAGE:
A first special situation is when [C] = [0] (there are no capacitances).
This case represents only mutually-coupled RL branches, for which even a separate input format (type 51,52,53, see section IV.C.) has been provided. This is the normal situation for transformer modelling.
R L R L R L
C o u pling
88
If the user wants a multiphase capacitance matrix to ground (e.g. a capacitor bank), be it in star or in delta, then he can input near-infinite-impedance series branches and ground all conductors at the far end.
R
R
R C
C
C C C
C
89
Note hereby that the series impedances must be chosen large enough to represent an open-circuit. Recall that there is a limitation on the used values (see section IV.A.3). The C-matrix, specified in the input file must be twice the desired final matrix values, as mentioned before. Recall that the specified value is internally allocated half to the beginning and half to the far end of the model.
One can also obtain a single phase (i.e. uncoupled) PI-equivalent. The difference with the representation by uncoupled, lumped series RLC branches is that you can enter the shunt capacitance to ground directly instead of having to introduce two separate branches for this purpose. The only thing you have to do, is using branch type number 1.
Card format
First, the three different card formats will be discussed:
. normal format ($VINTAGE, 0)
. high-precision format ($VINTAGE, 1)
. free format.
For this card-type, 2 different notations exist: the RL-notation and the AR-notation. The card formats first will be explained for the RL-notation (normal usage). Next, the AR-notation will be discussed.
RL notation
Normally the RL notation is used. You can stack the values for [R], [L] and [C] in the way explained in section IV.B.3 (remarks). If previously the AR notation was used, you can toggle to the RL notation by using the following card:
2345678901234567890123456789012345678901234567890123456789012345678901234567890
1 2 3 4 5 6 7 8
1
USERL
90
NORMAL CARD FORMAT ($VINTAGE, 0)
2345678901234567890123456789012345678901234567890123456789012345678901234567890
1 2 3 4 5 6 7 8
1
ITYPE
e l ements(k,m+2) e
lements(k,m+1) e
l ements(k,m) r
eferencebr. nodenames
I2
BUS1 BUS2 BUS3 BUS4
A6 A 6 A6 A6
R R R
E6.2 E6.2 E6.2 E6.2 E6.2 E6.2
L C L
E
6.2 E6.2 E6.2
C L C
91
If there is no special request card, the normal format is in use. The R, L and C fields only have a limited accuracy (E6.2 format). See section IV.B.3 (remarks) for further usage.
HIGH-PRECISION CARD FORMAT ($VINTAGE, 1)
2345678901234567890123456789012345678901234567890123456789012345678901234567890
Usage of an extended precision (E16.0) is possible for mutually coupled RLC branches. See section IV.B.3 (remarks) for further usage.
FREE FORMAT
Besides the regular format and the high-precision format, a third (but tricky) way can be used to input RLC branches. This input is called FREE FORMAT, but it is not totally "free". Some important rules apply here :
- separate each field by comma's (i.e. last sign of the variable CHRCOM in the STARTUP file);
- blanks are totally ignored, and node names are left adjusted;
- do not input node names after column 26;
- do not input values before column 27;
- Make sure there is always a total of five comma's before column 26 (delimiting one type field and four node name fields) and a total of eight comma's should follow column 27 (delimiting nine numeric fields for R, L, C).
- If the figures are to be continued on the next card because the number of columns per card exceeded, the continuation symbol (fifth character of CHRCOM of STARTUP, usually "$") must be used. On such card, no extra comma's are needed.
With these rules, only column 27 must be determined as position information.
On the other hand, a painstaking count of comma's is necessary. See section IV.B.3 (remarks) for further usage.
AR notation
In some cases, the [L]-1-matrix is ill-conditionned or singular, so [L] does not exist. Therefor the AR notation is used. "A" stands for the [L]-1-matrix and
"R" stands for the [R]-matrix.
Switching to the AR notation can be done by the following card:
2345678901234567890123456789012345678901234567890123456789012345678901234567890
Now we have to be carefull when punching the data in the input format. The [L]-1-matrix replaces R in the input format. In the same way, the [R]-matrix replaces L in the input format.
Remarks:
- This notation can not be used for single-phase situations; only for coupled phases (minimum two).
- Before using the AR notation, the program automatically sets XOPT as 0.1591549 (XOPT=1/2π). In this case ω = 1. COPT remains unchanged. The values of the corresponding term of the inverse of L are now to be specified in Henry-1. Before switching to the RL notation, the old value of XOPT can be restored using the command $UNITS,-1,-1.
- The AR notation can be combined with the use of the high extention format ($VINTAGE, 1) and the free format.
Parameters
Following is an explanation of the parameters used in the above card formats.
ITYPE: Numbers 1 up to 40 can be used to express each phase of the PI-equivalent. When there are continuation cards, ITYPE must be left blank for these (see remark 2).
BUS1, BUS2: Specify the terminal node names of each phase in these fields. Nodes may be grounded (indicated by blank field name), if desired.
BUS3, BUS4: Equally to uncoupled RLC branches, referencing can be used here. The same rules must be taken into account, except that only the first card (first phase) bears the reference nodes, specified as the nodes appearing on the first card used as reference set. The following cards (following phases) just specify the consecutive type numbers and the node names of the other input ports, not the nodes of the reference set nor the RLC values.