Index

# RELAYS 101

### In-Depth Learn to Calculate Positive Sequence

Positive Sequence is one of three symmetrical components used in analysis of 3-phase electrical systems. Symmetrical Components were invented by a GE electrical engineer (named Charles Fortiscue) circa 1921. He originally put together the mathematical concept so he could try to understand the unbalanced behavior of the early GE 3-phase motors. There are 3 symmetrical components, (Positive Sequence, Negative Sequence and Zero Sequence). After considerable experience and analysis, it was found that the Positive Sequence component appears in all fault types of the 3-phase system phase-to-ground, phase-to-phase and three phase faults. Also if a fault is detected but only Positive Sequence components exist then the fault must be a three-phase fault. Note that Power Swings have Positive Sequence only with a shifting phase angle (power swings look like a "Moving 3-Phase Fault). Positive Sequence is calculated by applying a numerical angular shift to the second and third phases then summing the three phases and dividing by 3. Remember when adding vectors, first find the horizontal (cosine) components and the vertical (sine) components of the three phases. Then add together all of the horizontal components, then add together all of the vertical components, finally find the resultant vector from the two compoent sums. Mathematically it looks like this: PosSeq = (A + aB + a2C)/3; for Voltage: V1 = (VA + aVB + a2VC)/3; for Current: I1 = (IA + aIB +a2IC)/3; for Impedance: Z1 = (ZA + aZB + a2ZC)/3; Where "a" is the "A-Operator" and represents a shift of 120 degrees. Where "a2" is the "A squared-Operator" and represents a shift of 240 degrees. Any phase value is equal to the sum of its components. Mathematically: VA = VA0 + VA1 + VA2; VB = VB0 + VB1 + VB2; VC = VC0 + VC1 + VC2 IA = IA0 + IA1 + IA2; IB = IB0 + IB1 + IB2; IC = IC0 + IC1 + IC2 ZA = ZA0 + ZA1 + ZA2; ZB = ZB0 + ZB1 + ZB2; ZC = ZC0 + ZC1 + ZC2

Step 1: Enter the three phases of data (note that the vectors/phasors can be voltage, current or impedance).

Phase 1 Magnitude : Phase 1 Angle (deg) :

Phase 2 Magnitude : Phase 2 Angle (deg) :

Phase 3 Magnitude : Phase 3 Angle (deg) :

Step 2: Shift the Phase 2 Angle by the "A-Operator" which is done by adding 120 degrees to Phase 2 Angle

and shift the Phase 3 Angle by the "A squared-Operator" which is done by adding 240 degrees to Phase 3 Angle.

Angle 2 shifted : Angle 3 shifted :

Step 3: Find the horizontal and vertical components of each of the three vectors.

Phase 1 Horizontal Component is found by multiplying phase 1 magnitude by the cosine of phase 1 angle.

Phase 1 Vertical Component is found by multiplying phase 1 magnitude by the sine of phase 1 angle.

Phase 1 Horiz: Phase 1 Vert:

Phase 2 Horizontal Component is found by multiplying phase 2 magnitude by the cosine of (shifted) phase 2 angle.

Phase 2 Vertical Component is found by multiplying phase 2 magnitude by the sine of (shifted) phase 2 angle.

Phase 2 (shifted) Horiz: Phase 2 (shifted) Vert:

Phase 3 Horizontal Component is found by multiplying phase 3 magnitude by the cosine of (shifted) phase 3 angle.

Phase 3 Vertical Component is found by multiplying phase 3 magnitude by the sine of (shifted) phase 3 angle.

Phase 3 (shifted) Horiz: Phase 3 (shifted) Vert:

Step 4: Sum the three horizontal components and sum the three vertical components.

Horiz Comp Sum : Vert Comp Sum :

Step 5: Using Pythagorean Theorem on the horizontal and vertical component sums, find resultant vector magnitude.

Horiz Comp Sum (squared) : + Vert Comp Sum (squared) : =

Find square root of the sum of the two squares : = Resultant Vector

Step 6: Using Trigonometry on the final calculated triangle (arctan = vertical / horizontal), find resultant vector angle.

Vertical : / Horizontal : = Tangent of Positive Sequence Angle

Step 7: Divide Resultant Vector Magnitude By 3 and find the ArcTangent of calculated Tangent value.

Positive Sequence Magnitude : Positive Sequence Angle (deg) :

The following is a snapshot in time of the calculated symmetrical components during a 3-Phase Fault. In this example, Phase-A is colored black, Phase-B is colored green, Phase-C is colored red. One can visualize that "Positive" Sequence has the original phase sequence. (One can visualize a counter-clockwise rotation of the positive sequence set of vectors as having a "phase-sequence" of black-green-red (A-B-C). Note that since only Positive Sequence is present then this must be either "load" or a 3-Phase Fault. 3-Phase Faults do exist though they occur less often then phase-phase faults and phase-ground faults. Perhaps the most frequent 3-Phase Fault is a "bolted fault". Imagine a substation work crew has left their personal protective ground cables on the circuit breaker or on the bus and then the apparatus is energized. Or imagine a construction crew has left their grounds on the line and the line is energized into the grounds. Another incident can make the system feel a 3-Phase Fault. This is a power swing. A power swing occurs when a generation source is no longer in sync with a second generation source. (Note that there will be protective relays that prevent a second source from closing into a first generation source unless the two are close to syncronism.) During a power swing it is up to the automatic generation control to keep the two generators in sync. If a generator drifts out of sync then it reaches a point where it has the effect of "slipping a pole" (old-timer lingo). During this event that the generators drift apart the "load" begins to show an increasing phase angle as compared to the voltage. In fact high load at a high lagging phase angle looks like a fault. Thus a power swing event can look to the power system as a 3-Phase Fault. Power Systems can trip on these 3-Phase Faults. Other relaying may be in place to trip or block-trip on a power swing. The power system event that is shown in this picture is of a 3-Phase Fault but was a snapshot in time of a power swing between two generator sources.
Symmetrical Components during a sampled 3-Phase Fault
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