Snapshot-like power network studies

Power flow studies

Although in reality the power network is in a continuous dynamic state, it is useful to assume that at one point the transient produced by the last switching operation or topology change has died out and that the network has reached a state of equilibrium, i.e. steady state. This is the limiting case of long-term dynamics and the time frame of such steady state operation would be located at the far right-hand side of Figure 1.16. The analysis tool used to assess the steady state operation of the power 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 Kirchhoff'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).

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 function depends on the operating philosophy of each utility company. However, active power generation cost is a widely used objective function. Traditionally, the constraint 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).

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