A phasor represents a sinusoidal AC quantity with an arrow: its length is the value and its angle is the phase shift from a reference. The phasor diagram shows the voltages and currents of the three phases together, and with it you check phase sequence, current transformer polarity, power direction and wiring before energizing a protection.
Short answer
A phasor is an arrow that represents a sinusoidal AC voltage or current: its length gives the value and its angle gives the point of the wave relative to a reference. The phasor diagram draws the voltages and currents at one point of the system on the same plane. With it you can see at a glance the phase shift between voltage and current, the order of the three phases, and whether power flows toward or away from the load. It is the quickest way to check that a measurement makes sense, and you can practice with the phasor diagram tool.
From the wave to the phasor
A grid voltage is a sine wave that repeats its cycle at the system frequency. Two waves of the same frequency differ only in amplitude and in the instant they cross zero. Those two quantities are enough to describe them, and the phasor combines them: length equal to the amplitude (or the RMS value) and angle equal to the phase shift.
By convention, phasors are drawn rotating counterclockwise. Positive angles are measured in that direction, and a phasor that lags in time is drawn rotated clockwise. The transformer standard IEC 60076-1 uses this same convention to define the phase displacement between windings.
The three phases
In a balanced three-phase system there are three voltages of equal magnitude, separated by 120°. The order in which each reaches its maximum is the sequence: positive (A-B-C) when B lags A by 120° and C lags B by 120°; negative when the order is reversed. A reversed sequence makes a motor run backward, and a relay that assumes the wrong one miscalculates its sequence quantities.
In the diagram of a balanced system the three arrows form a symmetrical star and their sum is zero. If the sum is not zero, there is a zero-sequence component, which points to a ground fault or an imbalance. These components are explained in zero-sequence current and negative-sequence protection (46).
Voltage, current and power factor
The angle between the voltage phasor and the current phasor of the same phase is the load angle φ. Its cosine is the power factor.
| Load | Current angle | Example |
|---|---|---|
| Resistive | In phase with voltage | Heating |
| Inductive | Lagging | Motor, transformer |
| Capacitive | Leading | Capacitor bank |
The angle gives the power: the component of the current in phase with the voltage produces active power (P) and the component at 90° produces reactive power (Q). That is why the P-Q diagram and the voltage and current diagram are two ways of looking at the same thing. The sign of P tells whether energy flows into the measuring point or out of it, which is essential for directional functions such as 67.
The effect of that angle on the voltage reaching the load is calculated in the guide AC cable voltage drop.
What it is used for in protection and metering
- Checking current transformer polarity. A current transformer (CT) connected backward shows its current shifted 180° from what is expected. With a known load it can be detected without waiting for a fault.
- Verifying the sequence of voltages and currents. Two crossed phases give a symmetrical diagram but with the order reversed.
- Validating the connections of a differential protection. With the load as the source, the currents on the two sides must be opposite after compensating for the ratio and the vector group, as explained in transformer differential protection 87T and the connection symbol and clock number.
- Explaining a fault record. The phasors from an oscillogram show which phase faulted, whether the current reversed and how far the voltage shifted. See how to read an oscillography record.
- Reviewing metering. In meters and power quality analyzers, the diagram helps detect crossed phases or wrongly mounted CTs. See energy meter and multifunction meter.
The same phase shift is what forces vector group compensation in a transformer differential; the case is covered in Vector group compensation in the 87T differential. Fault phasors are read from a record, as explained in Fault analysis with oscillographic records.
How to interpret a diagram under load
An orderly reading has four steps:
- Confirm that the three voltages have similar magnitudes and are separated by about 120°.
- Confirm the sequence: the rotation order must be that of the system.
- Look at each current against its voltage: the angle must match the known type of load.
- Compare the power direction with the flow that dispatch or the utility expects.
When something does not match, the pattern in the diagram points to the most likely cause. A current 180° from what is expected in all three phases points to reversed CTs or a poorly defined direction reference. A single reversed phase points to the CT of that phase. Two swapped currents point to crossed wiring.
A reading example
Suppose a feeder with a motor load. The three voltages are separated by 120° and the three currents lag their voltage by about 30°, with the same magnitude. This is consistent: an inductive, balanced load with power flowing into the feeder. If one of the three currents appeared rotated 180°, the reading would no longer be consistent and the CT of that phase would have to be checked before enabling any directional function.
What should not be assumed
The diagram is a snapshot of one instant under one load. With very low load the angles are imprecise, because the current is small compared with the CT error. And a correct diagram does not by itself prove that the relay setting is right: it confirms the wiring, not the logic.
Calculate it here
To practice reading phasors you can use our free phasor diagram tool.
We can help with commissioning
At Tiza Group we verify protection wiring and settings with secondary injection and we also configure relays remotely. If you need to check an installation before energizing, we will quote the work.
Related guides
- Zero-sequence current
- Negative-sequence protection (46)
- AC cable voltage drop
- Vector group compensation in the 87T differential
- Fault analysis with oscillographic records
References
- IEC 60076-1, Power transformers - Part 1: General, clause 3.10 (counterclockwise phasors).
- IEC 60909-0, Short-circuit currents in three-phase a.c. systems, symmetrical components.
- IEEE Std C37.2, Standard for Electrical Power System Device Function Numbers.
Frequently asked questions
What does it mean for a current to lag the voltage?
Its wave reaches its maximum after the voltage wave does. On the diagram, the current phasor is rotated clockwise from the voltage phasor. This is what happens with inductive loads such as motors and transformers.
What is a phasor diagram used for when commissioning a protective relay?
To confirm, with real load, that the three voltages and three currents reach the relay with the correct sequence and polarity, and that the power direction matches what is expected. It is a check to make before trusting directional and differential functions.
What is the difference between a phasor and a vector?
A vector describes a quantity with a direction in space. A phasor represents a quantity that varies sinusoidally in time: its length is the RMS or peak value and its angle is the phase. They are drawn the same way, but the angle measures time, not space.