Per Unit Systems Explained Simply

Welcome to understanding per unit systems in electrical engineering!Per unit systems provide a way to normalize electrical quantities by expressing them as decimal fractions of a base value.Let's look at a simple example. If we have a base voltage of 1000 volts, and an actual voltage of 900 volts...The per unit value would be 0.9, as 900 divided by 1000 equals zero point nine.Similarly, if we have a voltage of 1200 volts with the same base...The per unit value would be 1.2, indicating the voltage is 20 percent above the base value.This standardization offers several benefits. It makes it easier to compare relative magnitudes and quickly identify whether values are normal or abnormal.In a real system, per unit values make it easy to spot normal and abnormal conditions. Values close to 1.0 are normal, while values significantly higher or lower indicate potential issues.Now that we understand what per unit values are, let's move on to how we choose our base values.To establish a per unit system, we begin by selecting two primary base values.Typically, we choose base power in Mega Volt-Amperes and base voltage in kiloVolts. Here we've selected 100 MVA and 230 kV as our base values.From these primary base values, we can derive other important base quantities using power system relationships.Base current is calculated by dividing base power by base voltage. For our example, this gives us 434.8 amperes.Base impedance equals base voltage squared divided by base power, which calculates to 529 ohms.These relationships form an interconnected system. Let's visualize how these base values relate to each other.Base power and voltage are our primary values, from which we derive base current and impedance through mathematical relationships.Let's look at a practical example of using these base values.If we have an actual voltage of 220 kiloVolts and our base voltage is 230 kiloVolts, we can calculate the per unit value by dividing actual by base value.This gives us 0.957 per unit, meaning our actual voltage is about 95.7 percent of the base value.In power systems with multiple voltage levels, per unit calculations become invaluable.Consider these transformers with different impedances at various voltage levels. Without per unit, direct comparison is challenging.However, when converted to per unit, we can see these transformers actually have the same relative impedance.The per unit system offers several key advantages in power system analysis.Per unit systems are essential for various power system studies, including fault calculations, load flow analysis, stability studies, and protection coordination.These advantages make the per unit system an indispensable tool in power system analysis.