In the power transmission

Power transmission

Power transmission is the movement of energy from its place of generation to a location where it is applied to performing useful work.Power is defined formally as units of energy per unit time...

 field of electrical engineering

Electrical engineering

Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

, a per-unit system is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per-unit are the same regardless of the voltage level. Similar types of apparatus will have impedances, voltage drops and losses that are the same when expressed as a per-unit fraction of the equipment rating, even if the unit size varies widely. Conversion of per-unit quantities to volts, ohms, or amperes requires a knowledge of the base that the per-unit quantities were referenced to.

A per-unit system provides units for power

Electric power

Electric power is the rate at which electric energy is transferred by an electric circuit. The SI unit of power is the watt.-Circuits:Electric power, like mechanical power, is represented by the letter P in electrical equations...

, voltage

Voltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

, current, impedance

Electrical impedance

Electrical impedance, or simply impedance, is the measure of the opposition that an electrical circuit presents to the passage of a current when a voltage is applied. In quantitative terms, it is the complex ratio of the voltage to the current in an alternating current circuit...

, and admittance

Admittance

In electrical engineering, the admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the inverse of the impedance . The SI unit of admittance is the siemens...

. Only two of these are independent, usually power and voltage. All quantities are specified as multiples of selected base values. For example, the base power might be the rated power of a transformer

Transformer

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core and thus a varying magnetic field...

, or perhaps an arbitrarily selected power which makes power quantities in the system more convenient. The base voltage might be the nominal voltage of a bus

Electrical bus

Electric bus is a bus powered by electric energy. "Electric bus" can also refer to:* Bus , used for connecting components of a computer or communication between computers* Busbars, thick conductors acting as nodes in electrical substations...

. Different types of quantities are labeled with the same symbol (pu); it should be clear from context whether the quantity is a voltage, current, etc.

Per-unit is used primarily in power flow studies

Power flow study

In power engineering, the power flow study is an important tool involving numerical analysis applied to a power system. A power flow study usually uses simplified notation such as a one-line diagram and per-unit system, and focuses on various forms of AC power...

; however, because parameters of transformers and machines (electric motor

Electric motor

An electric motor converts electrical energy into mechanical energy.Most electric motors operate through the interaction of magnetic fields and current-carrying conductors to generate force...

s and electrical generator

Electrical generator

In electricity generation, an electric generator is a device that converts mechanical energy to electrical energy. A generator forces electric charge to flow through an external electrical circuit. It is analogous to a water pump, which causes water to flow...

s) are often specified in terms of per-unit, it is important for all power engineers

Power engineering

Power engineering, also called power systems engineering, is a subfield of engineering that deals with the generation, transmission and distribution of electric power as well as the electrical devices connected to such systems including generators, motors and transformers...

 to be familiar with the concept.

Purpose

There are several reasons for using a per-unit system:

• Similar apparatus (generators, transformers, lines) will have similar per-unit impedances and losses expressed on their own rating, regardless of their absolute size.
• Use of the constant is reduced in three-phase calculations.
• Per-unit quantities are the same on either side of a transformer, independent of voltage level
• By normalizing quantities to a common base, both hand and automatic calculations are simplified.

The per unit system was developed to make manual analysis of power systems easier. Although power system analysis is now done by computer, results are often expressed as per-unit values on a convenient system-wide base.

Base quantities

Generally base values of power and voltage are chosen. The base power may be the rating of a single piece of apparatus such as a motor or generator. If a system is being studied, the base power is usually chosen as a convenient round number such as 10 MVA or 100 MVA. The base voltage is chosen as the nominal rated voltage of the system. All other base quantities are derived from these two base quantities. Once the base power and the base voltage are chosen, the base current and the base impedance are determined by the natural laws of electrical circuits.

Relationship between units

The relationship between units in a per-unit system depends on whether the system is single phase or three phase.

Single phase

Assuming that the independent base values are power and voltage, we have:

Alternatively, the base value for power may be given in terms of reactive or apparent power, in which case we have, respectively,

or

The rest of the units can be derived from power and voltage using the equations , , and (Ohm's law

Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

), being represented by . We have:

Three phase

Power and voltage are specified in the same way as single phase systems. However, due to differences in what these terms usually represent in three phase systems, the relationships for the derived units are different. Specifically, power is given as total (not per-phase) power, and voltage is line to line voltage.
In three phase systems the equations and also hold. The apparent power S now equals

Example of per-unit

As an example of how per-unit is used, consider a three phase power transmission system that deals with powers on the order of 500 MW and uses a nominal voltage of 138 kV for transmission. We arbitrarily select MVA, and use the nominal voltage 138 kV as the base voltage . We then have:

If, for example, the actual voltage at one of the buses is measured to be 136 kV, we have: