I've had a few operators ask me about negative sequence relays and their purpose for substation and distribution purposes. I haven't personally set them but they do present some cool use cases such as open-phase detection and more sensitive ground fault detection through delta windings.

Fundamentally the 120 degree separation of negative sequence phase vectors gives us more information to analyze during faults than the uni-directional zero sequence vectors.

## Foundations of Symmetrical Components

To understand why we use negative sequence relays, you have to first understand symmetrical components and sequence networks. Symmetrical components are a way to break down three-phase sine waves (A-phase, B-phase, and C-phase) into components (Positive, Negative, and Zero Sequence) that allow us to understand and analyze unbalanced conditions.

Are sequence quantities real or only mathematical constructs? Positive sequence is generated, sold and consumed. Zero sequence flows in the neutral, ground, and deltas. Negative sequence can cause serious damage to rotating machines. But negative sequence cannot be measured directly by an ammeter or voltmeter. (~ Source Unknown, Potentially Blackburn/Domin)

Unbalanced conditions could be fault conditions, open phase conditions, or just regular imbalance due to load.

Many of these examples are taken from [Calero], with more focus on applications specific to the Distribution side.

### Unbalance During Faults

Here is a diagram of how the phase vectors shift during a fault. The faulted phase(s) voltage goes to 0 and the current increases to its fault current. Depending on the fault and system configuration, the other phase currents and voltages will shift to balance out.

The symmetrical component equations are given as (using A-phase as reference so $$V_0=V_{0,A}$$:

\begin{aligned} V_a&=V_0+V_1+V_2 \\ V_b&=V_0+\alpha^2 V_1+\alpha V_2 \\ V_c&= V_0+\alpha V_1 + \alpha^2 V_2 \end{aligned}

$V_{0}=\frac{1}{3}(V_a+V_b+V_c) \\ V_{1}=\frac{1}{3}(V_a+\textbf{a}V_b+\textbf{a}^2 V_c) \\ V_{2}=\frac{1}{3}(V_a + \textbf{a}^2 V_b + \textbf{a}V_c)$

An example of unbalanced conditions due to loading gives the vector below. The positive sequence dominates, but the negative and zero sequence quantities still exist due to the unbalance.

## Negative Sequence Relay Use Cases

### Generator Protection

The classical use case for negative sequence relays is as an unbalance current protection for generators, used as backups for phase to phase and ground faults (negative sequence is not created in balanced three-phase faults). When negative sequence currents flow in the stator, they induce an emf with a magnetic field rotating opposite of the normal rotation and at the same speed. Since this field is rotating opposite, the frequency of this emf will be 2x the synchronous frequency. The resulting currents usually have a high resistance path leading to heating thus expansion and finally irreparable damage — contact with the stator body. The $$K=I_2^2 t$$ curve gives the heating curve we want to clear faults for.

For induction motors the stator rotates at a frequency just below the synchronous frequency, thus the slip frequency $$s=f_s-f_r$$ is very small. The negative sequence currents create a "virtual" slip at frequency $$s=f_s-(-f_s) = 2f_s$$.

### More Secure Secondary Circuits

If there is a broken neutral lead in our CT secondary circuit we will measure no zero sequence current since the return path is interrupted. Negative sequence quantities are useful since they use the same path as load flow currents and do not need the broken ground return conductor.

Similarly, an unintentional ground in the PT secondary can create a voltage rise over some resistance, which leads to an extra term in $$3V_0=V_{a0}+V_{b0}+V_{c0}+V_{new}$$. For negative sequence the added term is multiplied by $$1+\alpha+\alpha^2 = 0$$ and thus disappears.

### Single Line to Ground Fault Through a Transformer (Radial)

For a radially fed distribution step-down transformer that is Delta-Wye, the protection on the source (Delta) side cannot see zero sequence current for a ground fault on the low (Wye) side. Sensitivity is lost if the high side can only operate on phase overcurrent for low side faults (bottom-limited by loading). There may or may not be low side protection depending on the circuit design since many 4kV circuits that are fed by stepdowns are older circuits. A solution to allow for more sensitive fault detection is to use negative sequence overcurrent (51Q). Note that since the negative sequence can be set more sensitive than load currents, coordination with downstream ground protection should be verified.

### Phase to Phase Fault

During phase-to-phase faults no zero sequence is created. Similarly for the ground fault beyond a delta, negative sequence relays can be used for more sensitive operation than phase currents. Note that we should still coordinate with downstream ground relays.

### Open Phase - Sensing a High Side Open Fuse

There are cases for small substation transformers (generally < 15MVA) where the only protection for the transformer is high side fusing. (Delta high side, Wye low side). With one blown fuse, partial voltages will be transferred across the transformer.

For a blown high side C-phase with the connections given, we will only have terminal voltage at H1 and H2. KVL and dot notation give $$V_{CA}=V_{BC}=-1/2*V_{AB}$$. This means that two of the winding voltages are shifted and reduced for high side. Transferring this across to the secondary gives us full line-to-neutral voltage on one phase and reduced on the other two. For line-to-line secondary voltages, two of the phases will be 86.6% of expected and the third will be 0V. (Since we are inducing Line-to-Neutral voltages on the low side with Line-to-Line voltages on the high side).

\begin{aligned} |V_{ab}|&= \sqrt{3} |V_{an}| =\sqrt{3}|V_{AB}|\\ |V'_{ab}|&=|V'_{an}-V'_{bn}| \\&=1.5 |V_{AB}| \\&=0.866|V_{ab}|\end{aligned}

This partial phasing is problematic for both three-phase and single phase loads. The negative sequence values provide a way to sense this on the low side. A phase unbalance (60Q) relay can be used to sense the sequence vector shift and the $$I_2$$ and $$I_1$$ vectors can be used to identify the open phsae.

The sequence vectors for this specific case (C-phase open, with a-phase reference) are:

$V_0=0\\V_1=V_2=\frac{1}{2}\angle 0^\circ$

It helps to look at all of the sequence vectors (instead of just the reference) which is shown below.

Although no LN voltages on the secondary will be 0, we can compare the negative sequence voltage to the positive sequence vector and determine which phase is open. In this example we can see that $$I_2/I_1$$ is $$1 \angle 0^\circ$$ (using a-phase as the sequence reference). The table below summarizes the different scenarios and the negative sequence comparison confirms this case that that C-phase is open.

### Polarizing for Directional Relays

Since in the negative sequence network the angles of impedance, $$V_2/I_2$$ are predictable, they can be used for polarization. When traditional polarizing quantities like $$3V_0$$ fail us, as in a solidly grounded Wye, the negative sequence impedance can be used for polarization.

Note: usually a hard tapped neutral current is used, but can misrepresent the fault direction due to zero-sequence mutual impedances between parallel lines. Although mutual impedances can be canceled out in the positive and negative sequence networks via transposing of the transmission lines, since the zero sequence flux of each phase has the same angle it cannot be canceled.

## Footnotes & References

[Calero] Rebirth of Negative Sequence Relays: https://cms-cdn.selinc.com/assets/Literature/Publications/Technical Papers/6155_RebirthofNegSeq_FC_20081105_Web.pdf?v=20150812-155337

Sequence Vector Demonstration: https://demonstrations.wolfram.com/FortescuesTheoremForAThreePhaseUnbalancedSystem/

Negative Sequence Impedance Element: https://cms-cdn.selinc.com/assets/Literature/Publications/Technical Papers/6072_NegSeq_Web.pdf?v=20180724-151349