# Power flow

Load Flow or Power Flow analysis is one of the fundamental types of study conducted on a power system. The system could be either a transmission system that supplies bulk power from the generators to the distribution substations at high voltages or a distribution system that delivers power from these substations to the consumers’ doorstep predominantly at various low voltages. The distribution network is sometimes also referred to as the low-voltage network.

Given the generation and load at various points in the system, the load flow reveals the flow of active (MW) and reactive (Mvar) power along the transmission lines and the voltage magnitudes and angles at various buses on the network when the system is operating under steady-state conditions. In essence a load flow study reveals the state of the system for evaluating the performance of the system under conditions known a priori. Each bus on the network is classified as a (i) P-Q or a load bus, (ii) P-V or a generator or voltage-controlled bus and (iii) a V-Q or a slack bus. Essentially, the parameters such as real (P) and reactive (Q) power injections and V at an angle θ are known or have to be determined based on the configuration of the bus. This results in a set of non-linear equations twice the number of the buses in the system. Therefore, only a numerical solution is possible unless the system is linearized through some assumptions.

Since the total number of variables is greater than the number of equations, we specify some of the variables depending on the type of bus in question. Once this is done, either an approximate solution is derived by making assumptions or we use rigorous methods such as Gauss-Seidel or Newton-Raphson to solve the set of non-linear algebraic equations in question. An improvement over these methods is the Fast Decoupled Load Flow (FDLF) which decouples the equations using the property of loose physical interaction between the MW and Mvar flows in the system. We also make use of the property of sparse connectivity between network buses to evaluate the bus admittance matrix in a faster and more efficient way for larger systems.

For the above load flow study we model each of the system components in detail, some of them being:

- Overhead and underground transmission lines.
- Various types of transformers such as three phase two-winding and three-winding transformers incorporating Y and ∆ connections and auto-transformers
- Various types of loads such as motors, lighting, and other wet appliances
- Power electronics components such as FACTS and STATCOM devices

— *Vijay Pakka 26/11/2010 12:28*