Page 34 - Power Electronic Control in Electrical Systems

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24 Electrical power systems ± an overview

system is known as Load Flow or Power Flow (Arrillaga and Watson, 2001), and in
its most basic form has the following objectives:
. to determine the nodal voltage magnitudes and angles throughout the network;
. to determine the active and reactive power flows in all branches of the network;
. to determine the active and reactive power contributed by each generator;
. to determine active and reactive power losses in each component of the network.
In steady state operation, the plant components of the network are described by their
impedances and loads are normally recorded in MW and MVAr. Ohm's law and Kirch-
hoff's laws are used to model the power network as a single entity where the nodal voltage
magnitude and angle are the state variables. The power flow is a non-linear problem
because, at a given node, the power injection is related to the load impedance by the
square of the nodal voltage, which itself is not known at the beginning of the study. Thus,
the solution has to be reached by iteration. The solution of the non-linear set of algebraic
equations representing the power flow problem is achieved efficiently using the Newton±
Raphson method. The generators are represented as nodal power injections because in
the steady state the prime mover is assumed to drive the generator at a constant speed and
the AVR is assumed to keep the nodal voltage magnitude at a specified value.
Flexible alternating current transmission systems equipment provides adaptive
regulation of one or more network parameters at key locations. In general, these
controllers are able to regulate either nodal voltage magnitude or active power within
their design limits. The most advanced controller, i.e. the UPFC, is able to exert
simultaneous control of nodal voltage magnitude, active power and reactive power.
Comprehensive models of FACTS controllers suitable for efficient, large-scale power
flow solutions have been developed recently (Fuerte-Esquivel, 1997).

1.5.2 Optimal power flow studies
An optimal power flow is an advanced form of power flow algorithm. Optimal
power flow studies are also used to determine the steady state operating conditions
of power networks but they incorporate an objective function which is optimized
without violating system operational constraints. The choice of the objective func-
tion depends on the operating philosophy of each utility company. However, active
power generation cost is a widely used objective function. Traditionally, the con-
straint equations include the network equations, active and reactive power consumed
at the load points, limits on active and reactive power generation, stability and
thermal limits on transmission lines and transformers. Optimal power flow studies
provide an effective tool for reactive power management and for assessing the
effectiveness of FACTS equipment from the point of view of steady state operation.
Comprehensive models of FACTS controllers suitable for efficient, large-scale
optimal power flow solutions have been developed recently (Ambriz-Perez, 1998).

1.5.3 Fault studies
If it is assumed that the power network is operating in steady state and that a sudden
change takes place due to a faulty condition, then the network will enter a dynamic
state. Faults have a variable impact over time, with the highest values of current