* Author: BSEE Hugo Reyes Hernández*

*1. INTRODUCTION*

Negative-Sequence Directional Elements (** 32Q**) determine the direction of the

**, they are used to supervise overcurrent elements (**

*PHASE-TO-PHASE CURRENTS, PHASE-TO-PHASE-TO-GROUND CURRENTS AND PHASE-TO-GROUND CURRENTS***) and distance elements (**

*50P/51P and 50N/51N***21**).

With electro-mechanical relays, negative-sequence directional elements were more complicated and costly to implement. In contrast, numerical or digital relays are easy to implement and economically viable, they allow the use of multiple directional elements in a single relay such as: ** positive-sequence directional elements (32P), negative-sequence directional elements (32Q) and zero-sequence directional elements (32N)**. In this article we have been focused in understand how the negative-sequence directional element works.

2. *BASIS OF THE NEGATIVE-SEQUENCE DIRECTIONAL ELEMENT (32Q)*

Negative-sequence and zero-sequence quantities are presents during unbalanced faulted conditions on an electrical power system, they are used to determine the direction of a current fault. Negative Sequence can be used to determine the direction of phase-to-phase currents, phase-to-phase-to-ground currents and phase-to-ground currents.

In ** Table 1** we can see the available sequence quantities for different types of short-circuits.

Where:

** V1 and I1**:

*they are the Positive-sequence of Voltage and Current at the point of fault.*** V2 and I2**:

*they are the Negative-sequence of Voltage and Current at the point of fault.*** V0 and I0**:

*they are the Zero-sequence of Voltage and Current at the point of fault.*In Table 1 we can find out that for three-phase faults just are presents the Positive-sequence of Voltage (** V1**) and Current (

**). For phase-to-phase faults we can see that only zero-sequence quantities (**

*I1***and**

*V0***) are not presents. Finally, for phase-to-phase-to-ground faults and phase-to-ground faults all sequence quantities are available (positive, negative y zero sequence values).**

*I0*In numerical or digital relays, ** PHASE DIRECTIONAL ELEMENTS (32P)** can use positive-sequence quantities for three-phase faults (balanced faults) while

**can be used for**

*NEGATIVE-SEQUENCE DIRECTIONAL ELEMENTS (32Q)*

*unbalanced faults: phase-to-phase faults, phase-to-phase-to-ground faults and phase-to-ground faults.*For most power transmission lines the negative-sequence polarization is preferred than zero-sequence polarization due to the negative-sequence source provides a larger signal. Negative-sequence voltage (** V2**) magnitude at the relay location is smaller with a stronger source (

*smaller***) and larger with a weaker source (higher**

*Z2***). Also, the negative sequence elements are immune to zero-sequence mutual coupling problems in parallel lines and less affected to Voltage Transformers (**

*Z2***) shift.**

*VTs*3. *COMPUTING THE NEGATIVE-SEQUENCE OPERATING QUANTITY*

The input for computing Negative-Sequence Current magnitude at the relay location is the fundamental phasor value:

Where:

Negative-sequence Overcurrent Relays (** 67Q**) commonly apply a positive-sequence current restrain for better performance, a small fraction “

**” (for example: 12.5%) of the positive-sequence current (**

*K***) magnitude is subtracted from the negative-sequence current magnitude forming the operating quantity:**

*I1** I2' = I2 – K . I1 ( EQ.1)*

Where:

*The positive-sequence current restraint allows more sensitive setting to the negative-sequence current element in cases of:*

*- System unbalances under heavy load conditions.*

*- Current transformers (CTs) errors during three-phase faults.*

*- Fault inception and switch-off transients.*

4. *UNDERSTANDING A NEGATIVE-SEQUENCE DIRECTIONAL ELEMENT (32Q)*

Figure 1 shows a ** One-Line-Diagram (OLD) and Sequence Network Connection** of a Power Systems with a Phase-A-to-Ground Fault at

**.**

*BUS "A"**I1 = I2 = I0*

*And,*

*V1 = E1 - Z1.I1 ( EQ. 2)*

*V2 = - Z2 . I2 (EQ. 3)*

*V0 = - Z0 . I0 (EQ. 4)*

Figure 2 shows the phase and negative sequence quantities presented to the directional relay (that is shown in Figure 1) for a forward phase-to-ground fault, considering a positive phase rotation of ** A-B-C**.

**Figure 2 Negative Sequence Signals for a Phase-to-Ground Fault**

Negative-sequence directional elements perform phase comparison in order to calculate a torque-like digital quantity ** T32Q**. These elements compare

**with two thresholds. When**

*T32Q***is positive and above the positive thresholds, the negative-sequence directional element declares a**

*T32Q***. When**

*FORWARD FAULT***is negative and below the negative threshold, the element declares a**

*T32Q*

*REVERSE FAULT.*In typical numerical relay implementation, for negative-sequence polarization, the torque equation that is commonly used is:

Where:

** V2** =

*is the Negative-Sequence Voltage at the relay location.*** I2'** =

*is Negative-Sequence Current at the relay location (considering I1 restraint, see EQ. 1).*** ҨMT2** =

*is the Maximum Torque Angle Setting.*In numerical relays, the equation 4 provides a more efficient algorithm to calculate the Torque is comparison with using the traditional Torque equation that uses trigonometric functions. Numerical or digital relays allows the choice of independently applying a negative-sequence voltage, zero-sequence voltage, zero-sequence current, or dual zero-sequence, polarized directional element, all in one single relay.

*Numerical relays are equipped with the Negative-sequence Time Overcurrent function (67Q-TOC) and the Instantaneous Overcurrent function (67Q-IOC).The function protection 67Q-TOC and the 67Q-IOC may be used to determine both the direction of the current and its unbalance in order to clear unbalance in the protected circuit.*

*Time-current characteristics (IEEE OR IEC version) of Negative-sequence Time Overcurrent function (67Q-TOC) are:*

*- DEFINITE TIME*

*- MODERATELY INVERSE*

*- INVERSE*

*- VERY INVERSE*

*- EXTREMELY INVERSE *

*APPLICATION OF NEGATIVE SEQUENCE DIRECTIONAL ELEMENTS FOR GROUND PROTECTION*

*When there are not high-side VTs and no zero-sequence current source available for the relay polarization.*

*5.2. When there is not open-delta Bus VTs and/or No Ground Current source at the relay location.**5.3. When the Ground Current source is not suitable for polarization. Examples: Power Transformers groups a) Y-Y (grounded or not), b) Delta-Delta, c) Autotransformers.*

5.4. When there is zero-sequence mutual coupling in parallel transmission lines.

*SUMMARY*- *NEGATIVE-SEQUENCE DIRECTIONAL ELEMENTS (32Q) can be used for unbalanced faults: phase-to-phase faults, phase-to-phase-to-ground faults and phase-to-ground faults. - For most power transmission lines the negative-sequence polarization is preferred than zero-sequence polarization due to the negative-sequence source provides a larger signal.- The positive-sequence current restraints allows more sensitive setting to the negative-sequence current element in cases of:o System unbalances under heavy load conditions.o Current transformers (CTs) transformation errors during three-phase faults.o Fault inception and switch-off transients.- Negative-sequence directional elements perform phase comparison in order to calculate a torque-like digital quantity T32Q. These elements compare T32Q with two thresholds. When T32Q is positive and above the positive thresholds, the negative-sequence directional element declares a FORWARD FAULT. When T32Q is negative and below the negative threshold, the element declares a REVERSE FAULT.- Numerical relays are equipped with the Negative-sequence Time Overcurrent function (67Q-TOC) and the Instantaneous Overcurrent function (67Q-IOC).The function protection 67Q-TOC and the 67Q-IOC may be used to determine both the direction of the current and its unbalance in order to clear unbalance in the protected circuit.- Negative-sequence Directional Overcurrent elements are insensitive with parallel lines applications and can be used in systems with isolated zero-sequence sources.- They can be used at substation where only open-delta Voltage Transformers (VTs) are available- Negative-sequence Directional Overcurrent were not widely used with traditional relays.*

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