per unit representation, formula, per unit representation of system

 PER UNIT REPRESENTATION & TOPOLOGY

Per Unit (pu) System

In power system analysis, it is common practice to use per-unit quantities for analyzing and communicating voltage, current, power, and impedance values. These per-unit quantities are normalized or scaled on a selected base, as shown in the equation below, allowing engineers to simplify power system calculations with multiple voltage transformations

per unit quantity = actual quantity/ base quantity

Historically, per-unit values have made power calculations performed by hand much simpler. With many calculations now being done using computer software, this is no longer the primary advantage; however, some advantages still exist. For example, when analyzing voltage on a larger system scale with many different nominal voltages via step-up and step- down transformers, per-unit quantities provide an easy way to assess the condition of the entire system without verifying the specific nominal voltage of each subsystem. Another advantage is the fact that per-unit quantities tend to fall in a relatively narrow range, making it easy to identify incorrect data. In addition to these advantages, most power flow analysis software requires input and reports results per unit. For these reasons, it is important for engineers and technicians to understand the per-unit concept.

Understanding Per-Unit Quantities

In three-phase power systems, voltage and apparent power (VA) are typically chosen as bases; from these, current, impedance, and admittance bases can be determined using the following equations.

For equipment such as motors, generators, and transformers, the base power rating and voltage are typically used to calculate a per-unit impedance. In some instances it is necessary

 

to convert these per-unit values with different power and voltage bases to one common base. The power base will remain constant throughout the system, and the voltage base is typically the nominal voltage for each part of the system. The equation for converting to a new impedance base is as follows: