Page 102 - Mathematical Models and Algorithms for Power System Optimization

92 Chapter 4

accepted movements and the number of rejected movements exceeds N max , the
temperature drops. At this point, the numbers of accepted and rejected movement are
reset to 0, and N max only affects the rate of temperature drop. For a normal situation,
the typical iteration counter in the power flow calculation is several to a few dozen. To
avoid affecting the calculation speed, N max is generally above the upper limit of the
iteration number. Therefore, N max ¼10–100 is recommended.

4.5 Implementation of SA based N-R Method

4.5.1 Initial Conditions of 197-Bus System

The actual operation mode of a 1990 winter peak load in a Chinese provincial network has been
selected in this section as a numerical example of an ill-conditioned power flow calculation. For
this operation mode, the N-R algorithm, PQ decoupled algorithm, and optimal multiplier
algorithm all failed to find a convergent solution. Therefore, it can be deemed as an ill-
conditioned system. This system consists of 197 buses, 28 equivalent generating units, 87 loads,
91 AC branches, and 136 transformer branches (including three-winding transformers). The
static voltage characteristic coefficients of the load buses are shown in Table 4.2. To test the
robustness of the proposed methods, the following ill-conditions were studied:

• R/X ratio ill-conditions
The power system data were manipulated to generate a system of high R/X ratios. The ratio
varied from 50 to 2000. The data were tested for single line as well as multiple lines. The high
R/X ratio was simulated at different lines taken individually, as well as five or six lines at a
time. The ratio was increased gradually when the test for multiple lines was performed, and
the results from the proposed method proved much better than that from the N-R method.
• Heavy loading conditions
In this case study, the loads at a group of buses were treated as voltage dependent loads. The
data were once again manipulated to create a heavy loading condition. The heavy load was
imposed on the system at various points considering a single bus system as well as a
multiple bus system. A very high degree of load severity could be imposed on the system for
all buses. Based on the static voltage characteristic coefficients, six different levels of load
severity could be created. The results indicated that the proposed method surpassed the
performance of the N-R method and gave a convergent solution. However, it was also
noticed that the proposed method could not always guarantee a convergent solution.
• Long-to-short line reactances
One of the other conditions that could create an ill-conditioned system is a high ratio of
long-to-short line reactance terminating at the same bus. The situation was simulated by
choosing buses where long-to-short lines terminate. Here, it was found that both N-R and
SA performed well and, as mentioned earlier, the computational time was quite long for SA.