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Recun;"" ludder Method 71
4.1.2. Compkx Linear Update. Load current 1 0 in Figure 4.1 can be selected
arbitrarily, but for several reasons (to appear later in the chapter) it is
much more useful to specify load power P L and load impedance ZL, and thus
determine the load current:
10=~'
(4.1)
All other branch voltages and currents correspond to this condition; this
choice in no way precludes the later rescaling of all voltages and currents by
some meaningful factor. Again, this decision means that R L
must never be
zero, although R L = IE- 10 is perfectly satisfactory.
The recursive calculation of node voltages and series currents is shown in
Table 4.1. Load current 1 0 is found from (4.1) and multiplied by ZL to produce
the complex number V,. The current in the Y, branch is V,Y,. Admittance Y,
is calculated at this time, and the branch-I current is computed and added to
the load current. Kirchhoff's current law states that this sum is equal to
branch current I,. These operations are easily accomplished with Program
A2-1, for example.
Each line in Table 4.1 has the general form
& ='l\e+ 'D, (4.2)
where the variables are not the ABeD parameters. The variable e is either an
impedance Z or an admittance Y, as they appear in Table 4.1. There are two
good reasons for performing the operations in (4.2) in the rectangular format
shown in (4.3) rather than in a polar format such as Program Al-1.
~=brcr- bic j +dr.
aj= bic r + brei +d i .
(4.3)
•
Table 4.1.
Typical Ladder
Network Recursion
Scheme