Power System Analysis - Renewable Energy in Power Systems - page 168

variables and trigonometric functions. The load fl ow solution to such nonlinear simultaneous
equations requires iterative techniques and is beyond the terms of reference of this topic. In
general, therefore, the solution of most practical networks requires a very structured approach
to the mathematics and is carried out by computers. Indeed, it was one of the fi rst useful
applications of computers during the 1950s. There are many mathematical techniques for
performing load fl ow analysis. They are all iterative, and most begin by representing the
network as a matrix. They often use Newton-Raphson or Gauss-Seidel iterative methods or
embellished versions of these. They should all converge to very similar answers and the
choice between the methods is mostly a matter of speed and reliability of convergence. The
different methods can perform better or worse with different types of networks. For more
information consult power system simulation packages PSS/E and DIgSILENT. A recent
trend is that load fl ow software is being integrated into geographical information systems
(GIS) and this integrates with the asset management side of the electricity utility business.
The assumption of constant voltage at the PQ buses inherent in the formulation of the load
fl ow described above is not valid at the distribution level. The distribution transformers (11 kV
to 400V) shown in Figure 5.11 are not controlled and representing them as constant P and
Q will lead to some inaccuracy. Load fl ow software that is intended for modelling the lower
voltage levels of distribution networks often includes the facility to defi ne loads that do vary
with respect to voltage. However, obtaining load data that includes this characteristic may
be less straightforward.
5.6.6 Results
The basic results provided by a load fl ow analysis are the power fl ows (both active and reac-
tive) and the voltages and currents (both magnitude and phase) for all the lines and nodes
throughout the system. (Strictly speaking, some of this information is redundant.) From these
basic results, an engineer can readily identify or calculate:
• any overloaded lines or transformers;
• any voltages that are under or over acceptable limits;
• power losses, both active and reactive, for individual lines or for the whole system.
This information infl uences the design and operation of the network. Load fl ow studies are
routinely performed to check the state of the network as the demand varies through the day
or whenever changes to the network or to generation are being considered.
5.6.7 Unbalanced Load Flow
Ideally, the voltages and currents in three-phase power systems are perfectly balanced, which
leads to effi cient operation and greatly simplifi es any analysis. However, in low voltage net-
works particularly, the phases are not always balanced in practice and full analysis requires
unbalanced load fl ow techniques. Unbalanced load fl ow usually employs the method of
symmetrical components , which involves the description of the unbalanced network as the
sum of three simpler networks. Many software packages can perform unbalanced load fl ow