Index

# RELAYS 101

### General Notes on Protective Relays and Relay Testing

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#### Relays by Device Number

#### 21

21- Distance relay is a relay that functions when the circuit admittance, impedance, or reactance increases or decreases beyond a predetermined value. Connect test equipment to the relay per station drawing such that the test equipment can mimic the needed sequence. Monitor the output function for proper output as compared to engineering setting for distance setting. A distance relay operates its output for a specific value of voltage, current and phase angle. Zp-p = Ep-p/Ip-p (For a phase-phase fault) When a specific ratio of voltage and current is attained a fault, or other significant system event, is indicated and if this event is within the prescribed operating region of the protective relay then that relay must take action. Items on distance relays that need to be noted include: Type of characteristic Angle of Maximum Torque Operating quantities Tests include the following: Test angle of maximum torque Adjust as needed Re-test Test pick-up at angle of maximum torque Adjust as needed Re-test Test for pick-up point away from MTA (circle) 1 point at MTA plus 45 degrees 1 point at MTA minus 45 degrees Pick-up is predictable by the calculation ZPU@MTA +- 45 degrees = ZPU@MTA x 0.707 or ZPU@MTA +- (any new Test Angle) = ZPU@MTA x Cos(MTA - TA) If two or three plots show up to be correct on an electro-mechanical (E/M) relay then the remaining plots will most likely also be correct. There is more chance that your relay test equipment will fail to deliver the needed values than there is for the relay to not properly respond. Testing more than three points correctly on a circle is needlessly taxing your relay test equipment. A failure to reproduce a circle on an E/M relay would indicate a change in the physics of the relay such as a bearing failure or possibly the unit has been physically jarred and has fallen out of alignment. Since most relays simply sit on a shelf or in the panel then physical malformation is unlikely. Single-phase test connections. Note the jumper from IAN to IBN and that the current polarity at IB+ is 180 degrees out of phase with IA+. This brings out, during testing, the same phase relationship as occurs in the current during an A-B Fault. In this wired test Z = (Voltage Applied) / (Current Applied x 2) (The current is multiplied by two because, by virtue of the wiring, the current is used twice!) Three-phase test connections. The 3-phase test connections are the same connections as the relay would have when it is installed in the panel. To properly test the relay the simulated values must accurately reflect a system fault. An electro-mechanical Impedance or Mho relay will have a circle characteristic. A Reactance relay will have a straight line characteristic that is horizontal. Start with Z plot outside of pick-up point. Adjust voltage, current or phase angle to attain balance point pick-up. Find and adjust MTA Find and adjust reach at MTA Check characteristic A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 21 device and demonstrate the ability to identify a 21 device in a substation. 2. Explain how a 21 should be wired in a substation. 3. Explain the difference in the characteristics between a Mho Relay (21), an Impedance Relay (21), a Reactance Relay (21) and a Loss-of-Field Relay (IEEE Device 40). 4. Demonstrate the ability to hook up a 21 relay to a relay test set. 5. Demonstrate the ability to test and adjust the relay's Maximum Torque Angle (if applicable). 6. Demonstrate the ability to test and adjust the relay's Reach (if applicable). 7. Demonstrate the ability to test and adjust the relay's Characteristic (if applicable). 8. Demonstrate the ability to test and adjust the relay's Offset (if applicable). 9. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 21 relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 24

24- Volts per hertz relay is a relay that functions when the ratio of voltage to frequency exceeds a preset value. The relay may have an instantaneous or a time characteristic. This relay is tested just as the name implies. You will apply a voltage to the relay with a specific magnitude and frequency. This relay protects the generator or transformer from over-excitation. Over-excitation can occur with an increase in voltage or a decrease in frequency (V/Hz). For a relay with nominal values of 120 V and 60 Hz one can easily see that this produces a V/Hz ratio of 2. This would yield no operation. Over-excitation would occur at some ratio value greater than 2. If the voltage increases to 126 V and the frequency stays the same then this yields a ratio of 126/60 = 2.1 this value would typically yield a trip output (at least an alarm!). If the voltage stays at nominal then the same 2.1 ratio would also appear if the frequency dips to57.14 Hz. Or, obviously, the ratio can be attained at any number of variations of voltage and frequency. Testing the relay would be accomplished by wiring the relay to the test equipment in the same manner as the relay is connected to the station. The voltage signal would be varied in magnitude and frequency to achieve the alarm ratio setting and the trip ratio setting. Monitor the trip output function for proper operation when the value matches the ratio as specified in the engineer settings. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 24 device and demonstrate the ability to identify a 24 device in a substation. 2. Explain how a 24 should be wired in a substation. 3. Demonstrate the ability to hook up a 24 relay to a relay test set. 4. Demonstrate the ability to set and test the relay's voltage divided by frequency pick-up point. 5. Demonstrate the ability to set and test the relay's time-delay before trip point. To test this relay start with nominal values applied such as 120V/60Hz. The relay should not pick up. Raise voltage until over-excitation pick-up occurs Adjust as necessary for the trip value Re-apply nominal values The relay should not pick up Lower frequency until over-excitation pick-up occurs Adjust as necessary for the trip value Balance the relay for correct operation at high voltage or low frequency.

#### 25

25- Synchronizing or synchronism check device operates when two ac circuits are within the desired limits of frequency, phase angle, or voltage to permit or to cause the paralleling of these two circuits. When one sees that the restraint voltage is Bus V - Line V then this value is minimum (Vres = 0) when the two values are in phase and restraint is therefore at maximum when the two values are 180 degrees out of phase. Further inspection finds that the operate quantity is Bus V + Line V; this value is at maximum when the two values are in phase and the operate quantity is therefore at minimum (Vop = 0) when the two values are 180 degrees out of phase. Thus the disk will have maximum closing torque when the Bus V and Line V are in phase. The disk will have zero closing torque when the Bus V and the Line V are 180 degrees out of phase. The torque will increase from zero toward maximum as the angle between the two voltages decreases from 180 degrees. Closing Angle Test is much like a MTA test on a 21 relay: Start at Bus V = Nominal V at 0 degrees; Line V = Nominal V at 0 degrees. Ramp Line V Angle away from 0 degrees in a positive direction Find the angle at which the contacts dropout (+Sync Angle Setting) - adjust as needed Re-start at Bus V = Nominal V at 0 degrees; Line V = Nominal V at 0 degrees Ramp Line V Angle away from 0 degrees in a negative direction Find the angle at which the contacts dropout (-Sync Angle Setting) - adjust as needed Max Torque (Closing Angle) = (|+angle| + |-angle|) / 2 Perform timing test as appropriate for angle setting A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 25 device and demonstrate the ability to identify a 25 device in a substation. 2. Explain how a 25 should be wired in a substation. 3. Demonstrate the ability to hook up a 25 relay to a relay test set. 4. Demonstrate the ability to set and test the relay's phase angle set point. 5. Demonstrate the ability to set and test the relay's time-delay before enable point (if applicable and adjustable). 6. Explain "delta V" and demonstrate the ability to adjust the relay test set for various "delta V". 7. Demonstrate the ability to set and test the relay's delta-V pick-up point (if applicable and adjustable). 8. Demonstrate the ability to set and test the relay's under-voltage pick-up point (if applicable and adjustable). 9. Demonstrate the ability to set and test the relay's over-voltage pick-up point (if applicable and adjustable).

#### 27

27- Under voltage relay is a relay that operates when its input voltage is less than a predetermined value. Apply voltage for a normal un-faulted system Ramp voltage down until relay contacts pick A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 27 device and demonstrate the ability to identify a 27 device in a substation. 2. Explain how a 27 should be wired in a substation. 3. Demonstrate the ability to hook up a 27 relay to a relay test set. 4. Demonstrate the ability to set and test the relay's under-voltage pick-up point (if adjustable). 5. Demonstrate the ability to set and test the relay's time-delay before trip point (if applicable and adjustable).

#### 40

40- Field relay functions on a given or abnormally low value or failure of machine field current, or on an excessive value of the reactive component of armature current in an ac machine indicating abnormally low field excitation. This relay comes in a variety of forms. One form is of a single-phase impedance relay. The action is similar to a Mho relay except that the circular characteristic will have its diameter (MTA) at 270 degrees for protection for Loss of Field where the MTA for a Mho relay is perhaps 60 degrees - 80 degrees (Quadrant I) Another form of the Loss of Field relay will be of a type that measures WATTS & VARS. If the VARS begin tracking down into the fourth quadrant then this indicates a field that needs to be increased; or the generator is using VARS from the system instead of producing VARS for the system; in such a situation the generator and system can become unstable.) (Recall that to increase WATTS - then the prime mover is increased. To increase VARS - then the field is increased.) The 40 relay needs to be tested as the form of the relay dictates. If the relay is of the style like a 21 relay then test the relay MTA, reach and characteristic at an angle of 270 degrees. If the relay is VAR measurement then find the plot of Watts and VARS for the relay pick-up. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 40 device and demonstrate the ability to identify a 40 device in a station. 2. Explain how a 40 should be wired in a station. 3. Demonstrate the ability to hook up a 40 relay to a relay test set. 4. Demonstrate the ability to test and adjust the relay's Maximum Torque Angle (if applicable). 5. Demonstrate the ability to test and adjust the relay's Reach (if applicable). 6. Demonstrate the ability to test and adjust the relay's Characteristic (if applicable). 7. Demonstrate the ability to test and adjust the relay's Offset (if applicable). 8. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 40 relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 46

46- Reverse-phase or phase-balance current relay is a relay that functions when the poly-phase currents are of reverse phase sequence or when the poly-phase currents are unbalanced or contain negative phase-sequence components above a given amount. A single phase hook-up simulates a phase-ground fault. Calculate I2 for a phase-ground fault and verify pick-up point. For example - applying 10 Amps on Phase - A current will produce 3.33 Amps of I2. Ramp the applied current as needed to produce the I2 required for pickup. If a single-phase hook-up is used then be sure to re-test on each of the three phases; this ensures that the entire network is functioning. A three phase hook-up simulates reverse phase sequence if the original phase sequence is changed to the reverse phase sequence by rolling B & C phases. I2 for reverse phase sequence equals 100% negative sequence. If all three phases are equal and 120 degrees apart and any 2 phases are rolled then verify pick-up point with displayed 3-phase test current. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 46 device and demonstrate the ability to identify a 46 device in a substation. 2. Explain how a 46 should be wired in a substation. 3. Explain pickup and demonstrate the ability to determine what negative sequence current (primary and secondary) should cause the relay to pickup. 4. Demonstrate the ability to hook up a 46 relay to a relay test set. 5. Demonstrate the ability to find and adjust as necessary the relay's pick-up point (if applicable). 6. Demonstrate the ability to find and adjust as necessary the relay's time delay point (if applicable). 7. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 46 relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 47

47- Phase-sequence or phase-balance voltage relay functions upon a predetermined value of poly-phase voltage in the desired phase sequence, or when the poly-phase voltages are unbalanced, or when the negative phase-sequence voltage exceeds a given amount. There are two basic types of reverse phase sequence relays, the Go/No-go and the Incremental types. For the Go/No-go type of 47 relay - This relay is used as a supervision relay to enable circuit operation if the relay detects the intended phase sequence. To test this type of relay: Hook up three phase voltages with the proper (intended) phase sequence, apply nominal system voltage and verify supervision circuit is enabled (supervision relay picks up). Next roll any two phases, apply nominal voltages and verify that supervision circuit is no longer enabling (possibly alarm contacts pick up). For the incremental type of 47 relay - A three phase hook-up simulates normal phase sequence. But if you were to unbalance the phases then V1, V2 & V0 all appear. This hook-up would simulate the system. Start at nominal volts for all three phases and have them all 120 degrees apart. This should produce V2=0 volts. Simulate an A-G Fault by dropping the A-Phase voltage slightly. V2 will equal 1/3 of the voltage drop. For example if you dropped A-Phase voltage by 3 volts then V2=1 volt; if you dropped A-Phase voltage by 30 volts then V2=10 volts. Ramp faulted voltage down until V2 pick-up is reached. Adjust pick-up point as needed. Another three phase hook-up simulates reverse phase sequence by rolling any two phase leads. V2 for reverse phase sequence, under such a circumstance, equals 100% negative sequence. This hook-up creates nothing but negative sequence voltage because two of the phases are rolled. Start at zero volts and ramp up to find pick-up point. This connection and procedure are generally not as accurate as the previous procedure. Because this method uses very small values placed on the measuring units, it is generally better to measure in the upper ranges of of a device as opposed to expecting it to work well "down in the mud". If all three phases are equal and 120 degrees apart and any 2 phases are rolled then verify pick-up point with displayed voltage. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 47 device and demonstrate the ability to identify a 47 device in a substation. 2. Explain how a 47 should be wired in a substation. 3. Explain pickup and demonstrate the ability to determine what negative sequence voltage (primary and secondary) should cause the relay to pickup. 4. Demonstrate the ability to hook up a 47 relay to a relay test set. 5. Demonstrate the ability to find and adjust as necessary the relay's pick-up point (if applicable). 6. Demonstrate the ability to find and adjust as necessary the relay's time delay point (if applicable). 7. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 47 relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 50

50- Instantaneous over current relay is a relay that functions instantaneously on an excessive value of current. Pulse vs Ramp - Some test equipment will distort the current on an instantaneously applied value; if so then ramp; if not then pulse can be applied if desired. Using a distorted value during calibration may result in the final pickup point being set at an incorrect value. Start with current low (or at zero) Ramp up (or pulse if undistorted waveform) until pick-up point is reached. Relay operates on (applied) phase value.

#### 51

51- Ac time over current relay is a relay with either a definite or inverse time characteristic that functions when the ac input current exceeds a predetermined value, and in which the input current and operating time are independently related or inversely related through a substantial portion of the performance range. Find pickup point - adjust as needed Apply fault current values at multiples of tap Plot pickup times on curve - adjust timing as needed Note that two plot points make a line; Three plot points make a curve; Industry accepted practice is to utilize (2 x tap), (4 x tap), (and any other point) Or test to a single accurate test point (check-point) While three points are indeed needed to plot out a curve, it should be noted that undamaged electro-mechanical induction disk relays will not change their characteristics - only their calibration point. An inverse relay will not change itself to a definite time relay or an extremely-inverse relay. Thus 2 points accurately plotted can reveal an induction disk relay timing curve. However, a solid-state relay can develop timing characteristics that can only be revealed through a test process that uses three or more test points on the curve. Note that "2 times and 4 times tap" practice dates to original motor-protection curves that were published with 2 times full-load current and 4 times full-load current values with trip-times. Excessive testing can damage relays and relay test equipment. The amount of test points selected to demonstrate the timing curve should be selected as a compromise between detailed testing and damage to the equipment. (In other words - TESTING SHOULD BE LIMITED TO ONLY NECESSARY AMOUNTS!) A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 50 device and demonstrate the ability to identify a 50 device in a substation. 2. Explain the purpose of a 51 device and demonstrate the ability to identify a 51 device in a substation. 3. Explain how a 50/51 should be wired in a substation. 4. Explain pickup and demonstrate the ability to determine what current (primary and secondary) should cause the relay to pickup. 5. Demonstrate the ability to hook up a 50/51 relay to a relay test set and find and adjust as necessary the relay's pick-up point. 6. Explain time delay setting and demonstrate the ability to determine what time delay before trip should occur for two times pick-up and 4 times pickup current value. 7. Demonstrate the ability to hook up a 50/51 relay to a relay test set and find and adjust as necessary the relay's time delay point. 8. Explain instantaneous pickup and demonstrate the ability to determine what current (primary and secondary) should cause the instantaneous function of the relay to pickup. 9. Demonstrate the ability to hook up a 50/51 relay to a relay test set and find and adjust as necessary the relay's Instantaneous current pickup value. 10. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 50/51 relay to a relay test set and find the dc current needed to cause the target to activate.

#### 59

59- Over voltage relay is a relay that operates when its input voltage is higher than a predetermined value. A 59 relay is measuring voltage. Typically it can measure either a phase-neutral voltage value, a phase-phase voltage value or even a residual voltage value. To test this relay start at nominal voltage and ramp up until the contacts pickup. Nominal value will differ depending upon whether this relay is phase-neutral, phase-phase or residual voltage. Inspection of the actual wiring of the potentials to the relay will determine the nominal value. Residual voltage nominal is typically zero volts. So, to test a 59N relay start at zero and ramp up until the contacts close. A 59N relay will usually be wired across the output of a "Broken Delta" PT configuration. The 59 (or 59N) should never pickup at nominal voltage value. This would result in a nuisance alarm or trip condition. A 59 relay deployed as over-excitation relay on a transformer might typically be set to trip at 110% of nominal. A phase-phase nominal voltage of 115 Volts should result in no pickup at 115V and a trip output with 126.5 Volts. Many 59 relays have timing functions too that should be tested like the 51 relay timing functions; that is pick a point on the curve and adjust the time to be correct. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 59 device and demonstrate the ability to identify a 59 device in a substation. 2. Explain how a 59 should be wired in a substation. 3. Explain pickup and demonstrate the ability to determine what voltage (primary and secondary) should cause the relay to pickup. 4. Demonstrate the ability to hook up a 59 relay to a relay test set and find and adjust as necessary the relay's pick-up point. 5. Explain time delay setting and demonstrate the ability to determine what time delay before trip should occur for two times pick-up and 4 times pickup voltage value. 6. Demonstrate the ability to hook up a 59 relay to a relay test set and find and adjust as necessary the relay's time delay point. 7. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 59 relay to a relay test set and find the dc current needed to cause the target to activate.

#### 67

67- Ac directional over current relay is a relay that functions on a desired value of ac over current flowing in a predetermined direction. Not all 67 relays are dual polarized. Some are voltage polarized, some are current polarized and some are both. A voltage polarized relay has a steady value of voltage applied to it and the faulted value of current is applied at various angles to be sure that the relay responds to the proper direction. A relay can be polarized from the same phase as the fault current protection, but note that during a maximum close-in fault then the polarizing value might go to zero; with no polarizing value then the relay may have no closing torque on its trip output. Thus cross-polarization frequently occurs on directional-phase over-current relays For example: B-C voltage might be used on A-Phase over-current C-A voltage might be used on B-Phase over-current A-B voltage might be used on C-Phase over-current Many other combinations of voltages can be used depending upon the MTA desired. For a 67N relay there is no need to test the Vpol and the Ipol at the same time (if the relay even has both polarizing values). Connecting the currents as shown will provide torque for a forward fault action (trip). Reversing the connections (only) on the Ipol+ and IpolN terminals will reverse the action on the relay and provide (opening) torque for a reverse fault action (no trip). For testing the Voltage Polarizing connections then wire the current only through the Iop+ (to IA) and IopN (to IN) terminals of the relay. Completing the calculations for 3I0 and 3V0 finds that a fault is forward when 3I0 is lagging -3V0. Correct angle manipulation is required to ascertain correct operation of the relay. The MTA will vary with the relay. The pickup of the relay at angles other than the MTA may be "wattmetric" "Wattmetric" means that the relay pickup at other than MTA will require more current for the relay to close its contacts. The amount of current can be predicted - Pickup at MTA = PICKUP Pickup away from MTA = PICKUP / Cos(MTA-new angle) Thus a 60 degree relay with PICKUP = 1A, that is being tested at 45 degrees will require: 1 Amp / Cos(60-45) = 1/Cos(15) = 1/0.9659 = 1.0353 Amps A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of a 67 device and demonstrate the ability to identify a 67 device in a substation. 2. Explain the difference between voltage polarization and current polarization. 3. Explain how a 67 should be wired in a substation. 4. Explain pickup and demonstrate the ability to determine what current (primary and secondary) should cause the relay to pickup. 5. Demonstrate the ability to hook up a 67 relay to a relay test set and find and adjust as necessary the relay's pick-up point. 6. Explain time delay setting and demonstrate the ability to determine what time delay before trip should occur for two times pick-up and 4 times pickup current value. 7. Demonstrate the ability to hook up a 67 relay to a relay test set and find and adjust as necessary the relay's time delay point. 8. Explain instantaneous pickup and demonstrate the ability to determine what current (primary and secondary) should cause the instantaneous function of the relay to pickup (if applicable). 9. Demonstrate the ability to hook up a 67 relay to a relay test set and find and adjust as necessary the relay's Instantaneous current pickup value (if applicable). 10. Demonstrate the ability to verify the correct operation of the directional element. 11. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up a 67 relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 81

81- Frequency relay is a relay that responds to the frequency of an electrical quantity, operating when the frequency or rate of change of frequency exceeds or is less than a predetermined value. Start at nominal voltage Start at nominal frequency Ramp frequency until pickup - adjust as needed Check timing function - adjust as needed Re-start at nominal frequency and voltage Lower frequency to well within trip values Lower voltage until under-voltage inhibit engages - adjust as needed. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of an 81 device and demonstrate the ability to identify an 81 device in a substation. 2. Explain how an 81 should be wired in a substation. 3. Demonstrate the ability to hook up an 81 relay to a relay test set. 4. Demonstrate the ability to set and test the relay's frequency pick-up point. 5. Demonstrate the ability to set and test the relay's time-delay before trip point. 6. Demonstrate the ability to set and test the relay's under-voltage inhibit function pick-up point.

#### 87T

87T Transformer Differential (Not microprocessor relays) Minimum pick-up test winding number 1. Start with Iapplied = 0; Ramp up until pickup Minimum pick-up test winding number 2. Start with Iapplied = 0; Ramp up until pickup (Repeat for all individual windings beyond #2 if applicable.) Harmonic Restraint test should be applied to the winding that will generally be involved with the energization of the transformer. Apply 60 HZ and 120 Hz current to the same winding under test. If applied 120 HZ is above the restraint setting then the relay should not trip. The object of this test is to verify that the relay can detect "Magnetizing Inrush" current. Magnetizing Inrush is current that has a lot of distortion to the waveforms. There are high quantities of 2nd and 5th harmonics that show up when a transformer is being energized. The current that is involved shows up on one winding of the transformer only. Thus the current balance function of the relay is defeated. The relay will try to trip for magnetizing inrush unless the tripping action can be stopped. The Harmonic Restraint section of the relay detects 2nd harmonics. When the amount of 2nd harmonics reaches a threshold (generally 15-20%) then tripping is restrained. To test this function apply 2nd harmonics current and fundamental current to the same winding. If the amount of 2nd harmonics is low enough and the total current is above minimum pickup the the relay will trip. Increasing the amount of 2nd harmonics can find the point of restraint. 120Hz can be applied or DC waveforms can be applied, but not pure DC (zero Hz). Note that the amount of current will vary depending upon whether half-wave or full-wave DC is applied. Note that the Harmonics Restraint calculation may be different depending upon the waveform applied. Slope test: 2-phase hook-up. Second current must be equal and opposite of first current. As the two currents are adjusted such the values are no longer equal then the relay will trip if the difference current is above minimum pickup. Slope setting greater than zero will de-sensitize the relay such that many system inequities can be accounted for. For example CT ratio errors could lead to an 87T trip unless the Slope Setting has been set to desensitize the relay. Errors are magnified as currents go up so a through fault represents the greatest challenge for the relay to respond correctly and NOT operate for a through fault. Slope Settings of 15%, 25% or 40% are typical for legacy relays where 40% might be a setting used for a transformer with a Load-Tap-Changer. Solid-state and Microprocessor relays might have variable slopes that actually de-sensitize the relay differently depending upon the amount of Through-Current is applied. A small amount of Through-Current might lead to a small amount of Slope so that a small detected fault within the transformer could be operated upon. A large amount of Through-Current would necessarily require a higher amount of de-sensitizing to prevent tripping action (from system inequities) on high load or a Through-Fault. The main significance of this fact to testing is that different values of Slope Percentage can be determined depending upon the amount of current applied during the testing. To ensure like test results (for comparison purposes) to prior years' tests then like values of current need to be applied. The Percentage Slope Characteristic will vary between manufacturers. Instruction manual should be consulted to verify the Percentage Slope calculation. The basic Percentage Slope calculation is: 100 x (Difference Current)/(Through Current) although some variations exist. Through-current test: 1-phase hook-up. Second current is equal and opposite of first current. This connection and applied current should never produce a trip as long as the tap settings are identical. If the tap settings are not identical then this connection and applied current will produce a trip output if the difference current is above the minimum pickup and the Percentage Slope calculates to be greater than the Slope Setting. A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of an 87T device and demonstrate the ability to identify an 87T device in a substation. 2. Explain how an 87T should be wired in a substation. 3. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary Winding One minimum pickup (if applicable). 4. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary Winding Two minimum pickup (if applicable). 5. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary Winding Three minimum pickup (if applicable). 6. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary Winding Four minimum pickup (if applicable). 7. Explain the need for Harmonic Restraint and Slope settings. 8. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary the Harmonic Restraint setting (if applicable). 9. Demonstrate the ability to hook up an 87T relay to a relay test set and find and adjust as necessary the Slope setting (if applicable). 10. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up an 87T relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### 87B

87B Bus Differential 87- Differential protective relay is a protective relay that functions on a percentage, or phase angle, or other quantitative difference between two currents or some other electrical quantities. (Some High Impedance relays are impossible to test with I) Start at Iapplied = 0; Ramp up until pickup (beware of distorted current waveforms) (If Voltage Setting is applicable then) Start at Vapplied = 0; Ramp up until pickup A journey level technician needs to be capable of the following tasks: 1. Explain the purpose of an 87B device and demonstrate the ability to identify an 87B device in a substation. 2. Explain how an 87B should be wired in a substation. 3. Explain pickup and demonstrate the ability to determine what current (primary and secondary) should cause the relay to pickup. 4. Demonstrate the ability to hook up an 87B relay to a relay test set. 5. Demonstrate the ability to find and adjust as necessary the relay's current value pick-up point (if applicable). 6. Demonstrate the ability to find and adjust as necessary the relay's voltage value pick-up point (if applicable). 7. Demonstrate the ability to change Target (and Seal-In) Pickup value and demonstrate the ability to hook up an 87B relay to a relay test set and find the dc current needed to cause the target to activate (if applicable).

#### Multi-Function Relays

Multi-Function Micro-Processor Relay A protective relay computer with three basic sections: 1. Input - receives the operating quantities and converts them to numerical quantities. 2. Processor - acts upon the input quantities and makes operating decisions. 3. Output - receives the operating decision and provides a means to communicate the action. Each section poses its own unique problems of detecting anomalies. While conventional relay tests are not always required to detect malfunctioning components, sometimes a simulated fault can be an efficient method of verifying correct operation. Other times, queries of the processor and interpretation of logged event reports can verify correct operation of the device. One way to view testing of these devices: every fault is essentially a relay test if you analyze the event report. A micro-processor relay should be tested at commissioning with a simulated fault to prove all three sections of the device. It is important to note that the simulated fault be an accurate representation of a fault. Electro-mechanical and vintage solid-state relays could be "tricked" into recognizing applied values as a fault and operating accordingly. Micro-processor (MPC) relays, on the other hand, cannot be tricked as easily. A simulated fault should simply be accurate and the relay can be tested for accuracy. Another aspect of testing micro-processor based relays is that there may very well be multiple quantities used as a concurrent check that the fault needs to be cleared by this particular device; in other words the relay settings may have numerous supervision elements in the trip output. Obviously, these elements will have to be met or temporarily removed in order to prove the relay functions. One such supervision element has its roots in solid-state technology - fuse failure detection logic. If the relay detects a fuse failure or loss of potential circumstance then the decision matrix of the relay will be different. Achieving a non-operation is not a successful test of the relay, it does prove that the relay is complex. Disabling this particular element could help with a conventional test, or one could,instead, always provide a simulated fault that is accurate. If the relay settings are changed then be sure that the settings are returned to the engineered setting before the relay is returned to service. However, if you find it necessary to change relay settings in order to prove a conventional test output, then perhaps it is better to simply utilize non-conventional testing methods. These non-conventional testing methods are non-conventional only in the electro-mechanical (or solid-state) sense. The non-conventional MPC relay test method is routine and even advisable to test the three sections of the MPC device. Function testing need not be routinely accomplished. It is understandable if the industry does not move to this type of testing right away. However, the manufacturers of microprocessor protective relays recommend different commissioning and routine tests than have generally been accomplished by utilities over the past few generations. One must try to remember that efficiencies can be achieved through testing these complex devices with new, more efficient methods as opposed to legacy methods employed on archaic devices. Testing the input section can be accomplished by querying the relay for the input values that are detected by the relay. A simple verification activity can show the numerical conversion took place properly. The micro-processor section can be queried for its status, presuming that there are on-board diagnostics available. The output section can be tested by creating any set of circumstances that force the processor to act and initiate output action. One failure mode of any device is "fried" open or welded-closed contacts; if an output action includes the operation of contacts then any proof that the contacts operated should be sufficient. A testing process that masks the trip output to a spare set of output contacts does not prove the integrity of the trip contacts used in the actual trip scheme. Therefore additional testing needs to be done to prove the integrity of the "in-service" output contacts. CB Maintenance note: If a contact set is found to be melted open or welded closed then chances are good that the circuit breaker operating mechanism needs additional maintenance. The CB trip time is slow and the CB needs lubrication! A journey level technician needs to be capable of the following tasks: 1. Explain some of the advantages of a microprocessor relay over a solid-state or electro-mechanical relay. 2. Explain how a microprocessor relay should be wired in a substation. 3. Demonstrate the ability to change the relay settings. 4. Demonstrate the ability to hook up a microprocessor relay to a relay test set. 5. Demonstrate the ability to force analog values into the microprocessor relay and determine if the relay responded as expected. 6. Demonstrate the ability to test the microprocessor relay utilizing its on-board diagnostics capability. 7. Demonstrate the ability to verify that the microprocessor relay is operating on the analog and digital input values correctly. 8. Demonstrate the ability to verify that the microprocessor relay is operating its output contacts correctly.

#### General Notes On Relaying

#### K0

Zero Sequence Compensation Distance relaying can be very accurate if you can control all of the variables. During a phase to phase fault the distance down one phase to the fault is the same as the distance down the other phase to the fault. And since the two phases are of identical construction, then the impedance of the two phases is identical. By measuring volts and amps on a continuous basis, we can determine impedance at any time, (Z = E / I). Relays are set to trip for a particular ratio of volts and amps (Z). The Z that we refer to here is the impedance of the circuit to the fault point in the line. However, determining the distance to the fault point in a line that is faulted to ground is another matter. Since the line has a different impedance than the ground paths, then getting a relay to accurately determine distance to a ground fault is slightly different than for a phase fault. For accurate distance (Z) measurements of a phase to ground fault the relaying circuitry must contain a method to compensate for the unequal impedances of the phase and ground paths. Depending on the design of the relay, there might be numerous ways of accomplishing this compensation. "K0" ("Kay-zero") is the term used for the "Zero sequence compensation factor". K0 is used in the impedance calculation to mimic (mathematically) the compensation that takes place in the distance relay. The relay is compensating for the two different impedances and so is your impedance calculation. K0 Calculation As we know, K0 ("Kay-zero") is the zero sequence compensation constant. Its purpose is to allow for accurate calculations of the impedance to a phase to ground fault. We also know that zero sequence compensation depends on the design and action of the relay. Regardless of the method of calculating Ko, the outcome will be the same. In relay testing, the relay instruction manual will show the method of finding K0. That instruction manual will also show the calculation used to find the impedance of a test fault. In G.E. solid-state relays SLS and SLYG we are told that K0 is a simple ratio of Z0 to Z1. K0 = Z0 / Z1 This will always yield a number greater than 1 because zero sequence impedance (Z0) is always greater than positive sequence impedance (Z1). G.E. then tells us to use the following calculation to calculate test fault impedance : Zfault = (3 x Vfault) / (Ifault x (2 + K0)) That appears to be quite different than the K0 calculation and impedance calculation that we see in the instruction books from RAZOA, Westinghouse and Schweitzer. But, if you take the time to calculate you will find that G.E.'s method ends up with the same impedance to the fault despite the difference in calculating K0. The non-G.E. calculation for K0 is: K0 = (Z0-Z1) / (3 x Z1) This will usually yield a number that is less than 1. And the calculation to determine the test fault impedance, during relay testing, is : Zfault = Vfault / Ifault x (1 + K0) When you calculate K0, for relay testing, it is generally OK to treat Z0 and Z1 as simple values, (magnitude only). However, it is important to note that Z0 and Z1 are vectors which means that they have both magnitude and direction. So, when performing the calculation for K0, for absolute accuracy, you should remember the rules for subtracting one vector from another and dividing one vector by another. When subtracting one vector from another you must convert from polar coordinates to rectangular, perform the subtraction, then convert back to polar. When dividing one vector by another, divide the top number by the bottom number. Then subtract the bottom angle from the top angle. If the zero sequence impedance angle is substantially different than the positive sequence impedance angle then a noticable difference in K0 is evident right away. Otherwise, the accuracy of the impedance calculation alone will show the importance of the method of calculating K0.

#### Impedance Notes and Rambles

Line Constants The impedance of a line is a required bit of information for some relay testing calculations. While a relay tech may never calculate the impedance of a line, it does help the general understanding of relays if you know some of the variables that make up the impedance of a line. It is the line construction that determines the impedance. Remember that R + jX = Z so any variation of resistance or reactance will change the impedance. The length of the line, the size of the conductor, the type of the conductor, the distance of the phases from one another and from ground, the configuration of the phases and static lines can all vary Z. Generally, as a line moves up in voltage class and construction the line becomes more reactive. It would not be surprising to see a 46KV line that is equal parts resistance and reactance, (this would be a 45 degrees angle of Z). A 345KV line is much more reactive and would be closer to 85 degrees. The distance relay's Angle of Maximum Torque (MTA) would be set close to the angle of the line's impedance. It is also good to know that the zero sequence impedance will probably be different than the positive sequence impedance. (Zero sequence impedance is a concern in ground fault relaying.) Zero sequence impedance values might be 2-4 times larger than positive sequence impedance values. It seems logical that impedance through the ground paths will be different then impedance through the conductor. And frequency! The very same electrical components will have one value of impedance in a 60 Hertz system and a different value of impedance in a 50 Hertz system and a still different value in a 25 Hertz system. This is because Inductive Reactance and Capacitive Reactance will change with different frequencies; resistance does not change with frequency. Impedance is the combination of resistance and reactance thus any change in reactance from a change in frequency will result in a change in impedance. Impedance Calculations Impedance calculations are perhaps the main reason for our need to learn expanded techniques. Most every window that you have progressed through has given you a technique or concept that is needed now. Although the actual calculation is rooted in high school math, and the concept of distance being equal to impedance (Z) is rooted in AC Theory, putting the whole thing together seems to be a tough thing to do. It is basically very simple. Knowledge of conductive materials tells us that if a conductor has Resistance equal to .001 Ohms/foot then it would have 1 Ohm resistance if that conductor was 1000 feet long. We therefore, can translate distance into resistance. In an AC system, since we also have reactance, we can translate distance into impedance. AC Theory taught us that: Z = E / I So now we can translate impedance into a ratio of volts and amps. Algebraic substitution allows us to say that: Distance = E / I And since we constantly monitor volts and amps through instrument transformers, then we can easily determine the apparent impedance (distance) to any fault. All that is now required is to have a device that will look at the proper quantities and act during a fault. That device is a distance relay, and the action that it will perform would be to trip some other protective device. Our job in the whole system is to install and prove the settings in this relay. The settings that are installed are a result of the engineering calculations as to the impedance of the line, (remember the ohms per feet ?). The engineer must determine what settings should go into the relay based on which quantities the particular relay uses, the electrical constants of the line and the method of action that the relay should perform. Sounds complex, but it still is just Z = E / I . As for the actual calculation of impedance, the values that we use in place of the variables depend on the type of relay. If the relay type is a phase-to-phase distance type then we must use phase-to-phase values. If the relay type is a phase-to-ground distance type then we must use phase-to-ground values. Sounds complex, but it still is just Z = E / I . In our calculations we will simply use the values present in the relay measurement device. A close examination of a Three-Line diagram in a relay instruction manual for a phase-to-phase relay shows a curious thing. The second current brought in to the relay is wired subtractive. But, having learned that phase-phase (pronounced "Phase To Phase") means second phase subtracted from the first ("Phase 1 minus Phase 2"), then we should not be surprised ! Therefore the value that we use for the variable "E" will simply be phase-phase volts. And the value that we use for the variable "I" will be phase-phase current. To calculate the impedance in a phase-phase fault : Find the phase-phase voltage Find the phase-phase current Divide the voltage by the current Do not forget that to subtract one phasor (or vector) from another you need to convert to rectangular form, perform subtraction, then convert to polar form. Do not forget that to divide one phasor (or vector) by another you perform the division on the magnitude only. The angle of the divisor (the bottom number) is subtracted from the angle of the dividend (the top number) to get the angle of the quotient (the angle of the impedance). In relay testing, when you simulate perfect phase-phase faults (per instruction manual) the mathematics involved work out to: Z = (Volts #1 X SQR3) / (2 X I) Take the time to calculate, completely, various fault combinations, including a relay-testing simulated fault. Sounds complex, but it still is just Z = E / I . For an accurate distance measurement of a ground fault there must be a way to compensate for the difference between the impedance of the line and the impedance of the ground paths. If the two impedances were equal then we would not need to compensate. That is why we must use K0 ("KAY ZERO"). So to find the impedance of a ground fault we will use phase-ground measurements and our Zero-Sequence-Compensation-Factor (K0). Do not be frightened by what you are about to learn, just keep saying to yourself " It's only impedance...It's only impedance... " To calculate impedance to a ground fault: Find the phase-ground voltage Find the compensated ground current and the total current Divide the voltage by the total current The compensated ground current is: K0 X IR (where IR is residual current or 3I0). So the total current acted on by our relay would be the current flowing in the faulted phase and the compensated ground current. total current = (phase current) + (K0 X IR) Z = E / (total I) Now the only thing that makes this remotely tough are those pesky rules concerning vector math: You must convert to rectangular form to add or subtract. Multiplication or division is performed on the magnitude of the vectors. (The angles are then added in multiplication and subtracted in division) As you can see there are three separate problems in finding our total current. The first is that you must find the value of IR (3I0). The second is that (K0 X IR) will have an angular shift, (because of multiplication of vector quantities). The third is that there is now two phasors to be added together, which of course means converting to rectangular form, adding, then converting back to polar. Once you have performed the operations required to find the total current then you can move on to the final step of dividing the voltage by the current to get the impedance. Whew ! For relay testing there is an easier way. If you follow the manufacturer's relay connections diagram for testing and put in the recommended fault type, then it turns out that you are taking a shortcut. By connecting the simulated fault current in the recommended manner, you simply create Residual Current that is equal to the phase current. Thus, for relay testing with a perfect phase-ground fault: Z = E / (I x (1+K0)) (Where E and I are phase-ground measurements) This is not only easy, but it is recommended for relay testing, because otherwise you would need to get through all the required calculations to perform this relay test. Remember that Z = E / (I x (1+K0)) only works for the perfect values available during relay testing. Sounds complex, but it still is just Z = E / I . Impedance Plots Impedance plots are a method for us to examine the impedance of any given system. You can think of an impedance plot diagram as a modified quadrant diagram. The modification being that we put values along the two axes and plot points. The zero reference point is along the horizontal (R) axis to the right of the origin. The angles increase counterclockwise. A fault plot of some value (say 4 ohms) at some angle (say 75 degrees) would simply be plotted within the bounds of the diagram. In this case the plot falls within the first quadrant. (Remember from the quadrant discussion that the first quadrant means watts and vars leaving the system. That seems reasonable for a fault. Both real and reactive power leaving the system.) If you would calculate the impedance of the system during static load conditions, then you could plot the load point on the impedance diagram. This not only lets you see graphically in which quadrant your load exists, but also it would be possible to see if your relay might pick up on load alone. When you think about how a simple "A" phase to ground fault may be plotted, you would calculate the Z and plot that length at the fault angle, within your impedance diagram. Now if you label Va as your reference point and your current angle lags Va by (say) 75 degrees, then your current angle would be written as -75 degrees. Do not be tempted to rotate in a clockwise direction to plot your impedance. (Remember that counterclockwise increases from zero.) Do not forget that part of your calculation is dividing "E" by "I". And when you divide one phasor (or vector) by another you must also subtract the angle of the divisor from the angle of the dividend. Thus, if Va angle = 0 degrees and if Ia angle = -75 degrees then after your division to get Z you find its angle. In this case 0 degrees - ( -75 degrees ) = +75 degrees Therefore, you will not rotate your protractor clockwise, but rather counterclockwise. And once again we see that a forward fault plots in the first quadrant. Watts and Vars leaving the system. If you stop and think about the horizontal axis to the left of the origin, you will find that this part of the line is labeled as -R . What is negative resistance ? Do not think of this area of the diagram as negative resistance. Think of it instead as reversed perspective. If you consider the origin as the place in the world where your relay is located and if your relay has a max torque angle of 60 degrees then it should respond to faults that enter its zone of protection. Its zone is primarily within the first quadrant. But for every line leaving the system, you probably have a line coming into the system. You probably have relays protecting this line and they probably have similar MTA's. But, in effect their perspective of the system is reversed from the original relay discussed in our little system. Their zone of protection falls mainly within the third quadrant, when looked at from the perspective of our original relay. Their zone of protection when looked at from their own perspective is, of course, the first quadrant. So, it is not negative resistance. It is reversed perspective. It is opposite direction.

#### Facts On Ohms

Primary Ohms to Secondary Ohms Calculation To convert primary ohms to secondary ohms first multiply the primary ohms by the current transformer ratio. Then, divide the product by the potential transformer ratio. (Ohms Secondary) = (Ohms Primary) x CTR / PTR To convert secondary ohms to primary ohms first multiply the secondary ohms by the potential transformer ratio. Then, divide the product by the current transformer ratio. (Ohms Primary) = (Ohms Secondary) x PTR / CTR Inductive Reactance Calculation XL in Ohms = 2 x Pi x F x L where F = system frequency L = Inductance in Henries Pi a constant (approx. 3.14159) Capacitive Reactance Calculation XC in Ohms = 1/(2 x Pi x F x C) where F = system frequency C = Capacitance in Farads Pi a constant (approx. 3.14159) Total Reactance is the Inductive Reactance minus the Capacitive Reactance. X = XL - XC Impedance Calculation Resistance (R) combines with Reactance (X) to yield Impedance (Z) Z = R + jX The "R+jX" demonstrates that Resistance "R" is the horizontal component of "Z" and the "jX" means that the "X" is the vertical component of "Z". To find the value of Z utilize the R and X components as the two sides in a right triangle and solve for the hypotenuse (which would be the magnitude of the Z). And of course Ohms Law states that the Impedance of a circuit equals the AC Voltage applied to that circuit divided by the AC Current through that circuit. Z = E/I Z, stated in Ohms, is a static vector quantity and has magnitude and direction E, stated in Volts, is a rotating vector (phasor) and has magnitude and direction I, stated in Amps, is a rotating vector (phasor) and has magnitude and direction Thus one volt divided by one amp equals one ohm.

#### FF & LOP

Fuse Failure Detection A practical application of Symmetrical Components. Electro-mechanical distance relays operate when the impedance detected is equal to or less than the impedance relay setting. Impedance is the ratio of voltage to current. With normal load current on an impedance relay it can operate with a simple blown fuse. This ratio produces an impedance of zero as seen by the relay. Zero is less than the relay setting. The relay will trip. There are circuits designed to detect system abnormalities to protect against tripping for a blown fuse. These circuits are collectively known as Fuse Failure (FF) Detectors or Loss of Potential (LOP) Protection. LOP (or FF) can be detected by calculating the symmetrical components existing. A simple blown fuse would yield zero sequence voltage and negative sequence voltage. These two sequence components would only exist during a faulted system but during a real system fault there would be BOTH zero sequence voltage AND zero sequence current; or there would be BOTH negative sequence voltage and negative sequence current. Therefore a situation wherein only zero sequence voltage exists would be a non-fault situation so trip-blocking might be desired. Or a situation wherein only negative sequence voltage exists would be a non-fault situation so trip-blocking might be desired. Thus, the detection circuits would be looking for V0 with I0 and for V2 with I2. If the sequence voltage shows up without the accompanying sequence current then this indicates a blown fuse or a loss of potential. This circuit is very handy in that it will help avoid tripping for merely pulling the paddles on the relay, or opening the test switches on the relay. However, understanding these circuits will also help in testing the protective relays. A relay with LOP (or FF) protection will not trip if these sequence components show up during a situation when those components should equal zero. For example if you are testing a phase-phase fault action on a relay and simply drop the voltage values on the two faulted voltages then you may have problems. Dropping the simulated voltage magnitude on the two faulted phases only would yield Positive, Negative and Zero Sequence voltages. But a Phase-Phase fault simulation would yield only Positive and Negative Sequence current. Thus you would have V0 with no I0 and the protective relay may detect a LOP (or FF). LOP (or FF) detection would disallow a trip. Your trip characteristic may well have some strange shapes if you tried to plot the trip actions considering that many trip characteristic plots would be masked by the LOP (or FF) detection circuit. When selecting your values to simulate system events you must ensure that you are simulating values that are real. Many times the relays are so smart that you may find yourself turning off many detection circuits in order to produce a trip output. On the LOP/FF simulation page note that the proper simulation will drop the faulted phase magnitudes and the two affected phases will collapse in towards one another. The phase angle collapse coincides with the phase magnitude colapse such that the two faulted phases will still pull against the unfaulted phase. The three voltages and the new phase angles combine to yield a balanced circuit. The balance is that the three phases, added together, result in V0 = 0. There can be no V0 unless there is I0. I0 is not a product of a phase to phase fault. Final result is that if a relay test has been set up that requires that the relay have a function bypassed (such as "LOPE") then the relay test is not an accurate simulation of the system during a fault. Only proper simulated faults should be expected to produce a true output. Some relays will use the existance of "V0" to make decisions of the type of fault. Since V0 only exists during a ground fault then some relays will utilize the Phase-Ground Distance calculations (or circuitry) to determine if the trip contacts should close. Thus if an improper simulation is set up then it is reasonable to expect that incorrect action could result. Incorrect action could produce values that make the report show that the relay is bad. Only proper simulated faults should be expected to produce a true output.

#### Rectangular to Polar Conversions

Rectangular to Polar Conversions Rectangular coordinates to polar coordinates conversion is needed whenever the line impedance data is presented in rectangular form, but, for relay testing, you need polar coordinates, (magnitude and angle). Polar-to-rectangular conversions (and back again) are necessary whenever you must perform addition or subtraction to phasor or vector quantities. (Vectors have magnitude and direction, phasors have magnitude, direction and rotation.) Many calculators can readily convert one coordinate form to another. But, converting is easy even if you forget how to operate your calculator. Calculating Impedance from Resistance and Reactance (Z = R + jX): In the rectangular coordinate method you will be given 2 numbers. The first number (designated as "R" for resistance) would represent a point on the horizontal ("R Axis") axis of a two axis diagram. The second number (designated as "X" for reactance) would represent a point on the vertical ("X Axis"). Now if you draw a vertical line through "R" and a horizontal line through "X" you will find the point of intersection. It is the distance from the origin to this point of intersection that we need. Draw a line from the origin to the R-X intersection. As you can see, by drawing the various horizontal, vertical, and diagonal lines, we have a right triangle. Since we know the length of the two sides, (side 1 = R ; side 2 = X), then we can find the length of the hypotenuse (Z) by using Pythagoras' theorem. Z = SQR((R * R) + (X * X)) Now we know the impedance of the line, next we must calculate the angle. Once again, using basic Trig. we can determine the angle between the horizontal axis and the diagonal by simply getting the ArcTangent of the ratio of the two original given sides, (R and X). Z(Angle) = ArcTan(X / R) Calculating R and X from Z: Converting from polar coordinates to rectangular coordinates is also a practical application of Trigonometry. R = Z x Cos(ZAngle) X = Z x Sin(ZAngle) Other Conversions: The power triangle is also a right triangle. Watts would be shown as the horizontal value of the right triangle. VARs would be shown as the vertical value of the right triangle. Volt-Amps would be shown as the hypotenuse of the right tright triangle. Load Angle would be the angle of the hypotenuse above the horizontal. (Thus the load angle is formed between the Watts and Volt-Amps.) Power Factor (efficiency of circuit) is found by multiplying the cosine of the Load Angle by 100 (yields percent). If you are given the Watts and VARs then you can calculate the Volt-Amps by utilizing Pythagorean Theorem. Volt-Amps equals the square root of the quantity of ((Watts times Watts) plus (VARs times VARs)). The Load Angle can then be found using either the sine, cosine or tangent functins of Trigonometry using the given or calculated sides of the triangle. If you are given the Volt-Amps and the Load Angle then the Watts would be found by multiplying the Volt-Amps by the cosine of the Load Angle and VARs would be found by multiplying the Volt-Amps by the sine of the Load Angle. Of course knowing Trigonometry and any two of the following: Watts, VARs, Volt-Amps, Load Angle then the remaining two values can also be found. You will also use the Polar/Rectangular conversions as steps towards calculating other power system values. Symmetrical components and voltage and current calculations require conversion from polar to rectangular and back.

#### Symmetrical Components

Symmetrical Components Also known as Sequence Components. (For Positive Sequence, Negative Sequence and Zero Sequence) The theory of symmetrical components is general and valid for any "n" phase system. In our case "n" = 3. Any related group of 3 unbalanced phasors can be resolved into 3 sets of symmetrical phasors. Each set contains 3 vectors equal in magnitude and with phase displacement of either 0 degrees (zero sequence) or 120 degrees (positive and negative sequences). Each set contains symmetrical components of the original unsymmetrical set of vectors. This mathematical resolution can be applied to rotating phasors such as currents and voltages or to static vectors such as impedances. So, what we have said thus far is that symmetrical components are not some mysterious elements floating around in an extra-fancy relay. Symmetrical components are a resolution to a problem. The problem was finding a way to make sense of unequal voltages and currents during fault conditions. The mathematical solution to analyzing these unequal phasors was to replace 3 unequal current (or voltage) phasors with 3 sets of symmetrical phasors. These 3 sets of balanced phasors are: Positive sequence component - 3 phasors, equal magnitude, 120 degrees apart, original rotation, represented by a subscript 1. Negative sequence component - 3 phasors, equal magnitude, 120 degrees apart, opposite rotation from the original, represented by a subscript 2. Zero sequence component - 3 phasors, equal magnitude, 0 degrees apart, represented by subscript 0. Symmetrical Component Notes: A sequence component cannot exist in only one phase alone. If a sequence component is present in one phase then it simultaneously exists in all three phases. A phase voltage (or current) is equal to the sum of its components. Va = Va1 + Va2 + Va0 Vb = Vb1 + Vb2 + Vb0 Vc = Vc1 + Vc2 + Vc0 If the system voltages (or currents) are equal and 120 degrees apart then V2 = 0 and V0 = 0 therefore the positive sequence voltage equals the system voltage. A ("perfect") three-phase fault contains positive sequence components only. A phase-to-phase fault contains positive and negative sequence components. A phase-to-ground fault contains positive, negative and zero sequence components. When calculating sequence components, if no phase subscript is assigned then "A" phase is understood. Final Note: Consider symmetrical components as a mathematical method of solving problems. Then consider that certain protective relays are wired specifically to mimic this mathematical resolution. Together, this system allows for specialized protective relays that can protect equipment better than it would otherwise be accomplished. Zero Sequence Calculation Zero sequence is the component that only appears during ground faults, or unequal phase loading. It is labeled with a subscript of zero. I0 ("Eye-zero") is the term for the current. V0 ("Vee-zero") is the term for the voltage. Residual current (or voltage) or ground current (or voltage) are two other terms that refer to this component. To calculate the zero sequence component, (the process is the same for voltage, current or impedance), first convert all three phases to their rectangular coordinates. Second, add all three phases. Third, convert this sum to its polar form equivalent. Next, divide by 3. When converting to polar form equivalent make sure to use the rectangular components to calculate the angle of the sequence component. This value is understood to be any one of 3 phase's zero sequence. All three phases zero sequence components are in phase with one another and equal in magnitude. Note that the final step of dividing by 3 will yield I0 (or V0). If the quantity that you desire is 3I0 (or 3V0) then simply omit the last step. I0 = (Ia + Ib + Ic)/3 3I0 = (Ia + Ib + Ic) = IN = IR V0 = (Va + Vb + Vc)/3 3V0 = (Va + Vb + Vc) Positive Sequence Calculation (The following assumes phase sequence of A-B-C.) Positive sequence is the component that appears during all types of faults. If the system is balanced then it is 100% positive sequence. Positive sequence is labeled with a subscript of one. I1 ("Eye-one") is the term for the current. V1 ("Vee-one") is the term for the voltage. V1 = (Va + aVb + a2Vc) / 3 (Notice the use of "a" and "a2") I1 = (Ia + aIb + a2Ic) / 3 (Notice the use of "a" and "a2") To calculate positive (or negative) sequence components you must first be introduced to the "a" operator. The "a" operator is a function. Its sole purpose in life is to yield a new angle that is 120 degrees shifted from the orignal angle. Shift counterclockwise. The "a2" operator is a counterclockwise shift of 240 degrees. So, if "B" phase is lagging "A" phase by 120 degrees and you operate on it with "a" operator then the angle becomes 0 degrees. If "B" phase was 135 degrees (lag) then after "a" operation it becomes 15 degrees (lag). If "C" phase is lagging "A" by 240 degrees and you operate on it with the "a2" operator then the angle becomes 0 degrees. If "C" was lagging "A" by 270 degrees then after the "a2" operation it becomes 30 degrees (lag). To calculate the positive sequence component, (the process is the same for voltage, current or impedance), First operate on "B" phase with the "a" operator and on "C" phase with the "a2" operator. Second convert all three phases to their rectangular coordinates. Third, add all three phases. Fourth, convert this sum to its polar form equivalent. Calculate magnitude and angle. Last, divide by 3. This value is understood to be "A" phase positive sequence. To find the positive sequence component in "B" phase, shift the angle by 120 degrees in a clockwise direction. (The magnitudes are equal.) To find the positive sequence component in "C" phase, shift the angle by 240 degrees in a clockwise direction. (The magnitudes are equal.) Note that the final step of dividing by 3 will yield I1 (or V1). If the quantity that you desire is 3I1 (or 3V1) then simply omit the last step. Negative Sequence Calculation (The following assumes phase sequence of A-B-C.) Negative sequence is the component that appears during phase-to-phase and phase-to-ground faults. Negative sequence is labeled with a subscript of two. I2 ("Eye-two") is the term for the current. V2 ("Vee-two") is the term for the voltage. V2 = (Va + a2Vb + aVc) / 3 (Notice the use of "a" and "a2") I2 = (Ia + a2Ib + aIc) / 3 (Notice the use of "a" and "a2") To calculate negative (or positive) sequence components you must first be introduced to the "a" operator. The "a" operator is a function. Its sole purpose in life is to yield a new angle that is 120 degrees shifted from the orignal angle. Shift counterclockwise. The "a2" operator is a counterclockwise shift of 240 degrees. So, if "B" phase is lagging "A" phase by 120 degrees and you operate on it with "a2" operator then the angle becomes 240 degrees. If "B" phase was 135 degrees (lag) then after "a2" operation it becomes 255 degrees (lag). If "C" phase is lagging "A" by 240 degrees and you operate on it with the "a" operator then the angle becomes 120 degrees. If "C" was lagging "A" by 270 degrees then after the "a" operation it becomes 150 degrees (lag). To calculate the negative sequence component, (the process is the same for voltage, current or impedance), First operate on "B" phase with the "a2" operator and on "C" phase with the "a" operator. Second convert all three phases to their rectangular coordinates. Third, add all three phases. Fourth, convert this sum to its polar form equivalent. Calculate magnitude and angle. Last, divide by 3. This value is understood to be "A" phase negative sequence. To find the negative sequence component in "C" phase, shift the angle by 120 degrees in a clockwise direction. (The magnitudes are equal.) To find the negative sequence component in "B" phase, shift the angle by 240 degrees in a clockwise direction. (The magnitudes are equal.) Note that the final step of dividing by 3 will yield I2 (or V2). If the quantity that you desire is 3I2 (or 3V2) then simply omit the last step. Note that if the system is balanced and phase sequence of A-B-C then the negative sequence component will equal 0. If the system is balanced but any two phases are rolled (A-C-B) then it is 100% negative sequence. Forcing Neutral Current This is a technique used to prove the wiring in a relay circuit. It is based on the concept of a current imbalance showing up as current in the neutral of a circuit. Many times, in Transmission systems, there is not enough current imbalance between the three phases to measure a current on the neutral. If there are neutral relays in the circuit then you must be able to determine if the current path wiring is correct, even if the system has balanced three-phase currents. Before proceeding with this technique it is imperative that you familiarize yourself with all the relaying involved. This procedure can produce enough current on the neutral relays to cause a trip. And since the circuit breaker must be serving loads to have current available for a test, then a trip could mean system disturbances and customer outages. To produce neutral current you will short any current at the shorting strip prior to the point that the current enters the relaying circuits. Then the wire which leaves the shorting strip and goes to the relay circuits needs to be lifted. DANGER: Do not lift the wire leading away from the shorting strip back to the current transformer as this opens the secondary of the C.T. Now, since you have just created a current imbalance, (there is current on two phases and no current on the shorted phase) this imbalance flows through the neutral circuit before returning back to the current transformer. Neutral current is the vector-sum of all three phases. It is also known as IR, (residual current) or 3I0 ("three-eye-zero"). Since one of our phase currents has just been eliminated, the neutral current is the sum of the two un-shorted phases. Through vector addition of the two un-shorted phases you will calculate the 3I0 of the circuit. This quantity can then be compared to the measured current in the neutral relaying circuits. If there is significant differences between the 3I0 which was calculated and that which was measured then troubleshooting the circuitry may be advised. Some of the possible problems that can be detected are: There could be a mis-wire. There could be an extra inadvertant path to ground. There could be ct's incapable of providing secondary current through the circuit burden. Note that in calculating the Symmetrical Component calculation known as I0 ("eye-zero"), you will divide 3I0 by 3. So, to calculate IR (which equals 3I0) simply take I0 and multiply it by 3. IR = 3 x I0 or IR = 3I0 I0 = IR / 3 or I0 = 3I0 / 3

#### Vector Math

Vector Math and its use in protective relays - A practical application of Trigonometry is the conversion of Polar Coordinates to Rectangular Coordinates. In power systems, values such as voltage, current (phasors) and impedance (vector) can be operated on using vector math. Vector Addition and Subtraction both begin by converting the vector quantities (in polar form) into their rectangular components. Polar form has a magnitude and a direction as its coordinates. Rectangular form has horizontal and vertical coordinates. To add vector quantities convert them to rectangular by: 1. multiply the magnitude of the first vector (or phasor) by the cosine of its angle to get the horizontal value. 2. multiply the magnitude of the first vector (or phasor) by the sine of its angle to get the vertical value. 3. multiply the magnitude of the second vector (or phasor) by the cosine of its angle to get the horizontal value. 4. multiply the magnitude of the second vector (or phasor) by the sine of its angle to get the vertical value. 5. add the two horizontal values together. 6. add the two vertical values together. 7. convert the resultant rectangular components back to polar - note that the resultant polar magnitude value is the hypotenuse in a right triangle with the other two sides formed by the resultant horizontal and vertical components 8. the final vector magnitude is the square root of the sum of the squares of the two rectangular components (Pythagorean Theorem). 9. the final vector angle is the angle formed by the hypotenuse and its adjacent horizontal side and can be found using the arctangent function of the value of vertical side divided by the horizontal side. To subtract vector quantities convert them to rectangular by: 1. multiply the magnitude of the first vector (or phasor) by the cosine of its angle to get the horizontal value. 2. multiply the magnitude of the first vector (or phasor) by the sine of its angle to get the vertical value. 3. multiply the magnitude of the second vector (or phasor) by the cosine of its angle to get the horizontal value. 4. multiply the magnitude of the second vector (or phasor) by the sine of its angle to get the vertical value. 5. subtract the second horizontal value from the first. 6. subtract the second vertical value from the first. 7. convert the resultant rectangular components back to polar - note that the resultant polar magnitude value is the hypotenuse in a right triangle with the other two sides formed by the resultant horizontal and vertical components 8. the final vector magnitude is the square root of the sum of the squares of the two rectangular components (Pythagorean Theorem). 9. the final vector angle is the angle formed by the hypotenuse and its adjacent horizontal side and can be found using the arctangent function of the value of vertical side divided by the horizontal side. To multiply vector quantities: 1. multiply the two magnitudes together to get the resultant magnitude. 2. add the two angles together to get the resultant angle. To divide vector quantities: 1. divide the dividend (top number or numerator) by the divisor (bottom number or denominator) to get the resultant magnitude. 2. subtract the angle of the divisor from the angle of the dividend (subtract the bottom angle from the top angle) to get the resultant angle. Vector addition is used to find Symetrical Components. Vector subtraction is used to find Phase-to-Phase Values. Phase-To-Phase Voltage Calculation - Note that everything learned to calculate phase-to-phase voltages also applies to calculating phase-to-phase current values. Too often we are tempted to declare that the voltage phase-to-phase is equal to the phase-to-neutral voltage times the square root of three. This is only true if both voltages are equal and if they are 120 degrees apart. This usually happens only during non-fault conditions. (Or relay testing.) There is no great secret to calculating the phase-to-phase voltage. VAB ("Vee-Ay-Bee") is Va minus Vb. VBC ("Vee-Bee-See") is Vb minus Vc. VCA ("Vee-See-Ay") is Vc minus Va. (This is also the case for currents, IAB is Ia minus Ib. Etc.) To subtract one phasor from another you must first convert them both to their rectangular components. Then you subtract the second set of rectangular coordinates from the first (such as Vb from Va). Then you convert the new resultant rectangular coordinates back to polar form. Open Delta Voltage Conversion Sometimes in relay testing, you might have to use two voltage channels to produce three voltages. This is done with an open delta configuration. The process to convert a 3-phase Wye configuration to an open delta configuration is only two phase-to-phase voltage conversions. The first would be Va minus Vb to yield VAB. The second would be Vc minus Vb to yield VCB. This works with fault voltages as well as normal system voltages. So, really the only trick to converting to open delta is that you use Vb BOTH times as the subtractor.

#### Watts and VARs

Watts Calculation To calculate watts in an AC circuit multiply the measured phase-to-neutral voltage by the current. Then multiply the product by the cosine of the measured angle between the voltage and current. W = V x I x Cos(Phase Angle) The power in a perfectly balanced 3-phase system would be 3 times greater. 3-phase power = 3 x (V x I x Cos(Phase Angle) Where V is a phase-neutral value. Or 3-Phase power = SQR3 x V x I x PF In this case "V" is a phase-phase value and PF = Power Factor which equals the Cos(phase Angle) Or In many cases, "Perfectly Balanced" does not apply. The total power, in such cases, is the sum of the power in each of the 3 phases. 3-phase power = (Va x Ia x Cos(Phase Angle "a") + (Vb x Ib x Cos(Phase Angle "b") + (Vc x Ic x Cos(Phase Angle "c") Where "a", "b" and "c" refer to the individual phases. Vars Calculation To calculate vars in an AC circuit multiply the measured phase-to-neutral voltage by the current. Then multiply the product by the sine of the measured angle between the voltage and current. Vars = V x I x Sin(Phase Angle) The reactive power in a perfectly balanced 3-phase system would be 3 times greater. 3-phase vars = 3 x (V x I x Sin(Phase Angle) In many cases, "Perfectly Balanced" does not apply. The total reactive power, in such cases, is the sum of the reactive power in each of the 3 phases. 3-phase vars = (Va x Ia x Sin(Phase Angle "a") + (Vb x Ib x Sin(Phase Angle "b") + (Vc x Ic x Sin(Phase Angle "c") Where "a", "b" and "c" refer to the individual phases. Load Angle The Load Angle of a circuit is the angle difference between the Apparent Power and the True Power of that circuit. Apparent Power is the total quantity of Volts times Amps in a circuit. Apparent Power (or Volt-Amps) = Volts x Amps True Power is the quantity of Volt-Amps in an AC circuit that is accomplishing work. This is found by multiplying the Apparent Power by the Power Factor. True Power (or Watts) = Volts x Amps x %PF Watts can be shown vectorially as the horizontal side of a right triangle and Volt-Amps can be shown as the hypotenuse, (Vars is the vertical side). Now, using basic Trigonometry concepts, the angle difference between the Watts and Volt-Amps can be found by dividing the total watts by the total Volt-Amps. Then find the arccosine of the quotient. Load Angle = ArcCos(Watts / Volt-Amps) Similarly, the Load Angle can be found by dividing the total Vars by the Apparent Power, then find the arcsine of the quotient. Load Angle = ArcSin(Vars / Volt-Amps) Since there is a multitude of ways to calculate the desired variable using Trigonometry, then it should not be surprising that the Load Angle can be found by dividing the total vars by the total watts. Then, find the arctangent of the quotient. Load Angle = ArcTan(Vars / Watts) Load Angle should be noted as being either leading or as lagging. Plots in the first and third quadrants are lagging. Plots in the second and fourth angles are leading. Power Factor The power factor of an AC circuit is simply the cosine of the angle measured between a phases's voltage and its current. The power factor is expressed as a percentage. It is sometimes referred to as the circuit efficiency rating. PF% = Cos(Phase Angle) x 100 The Power Factor is lagging when the sign of the Cosine of the load angle and the sign of the Sine of the load angle are the same. When the signs are different then the Power Factor is leading. That is, if the plot falls in either the first or third quadrant then the PF is lagging, if the plot falls in either the second or fourth quadrant then the PF is leading. This can be especially confusing if one recalls "ELI the ICE man" where Current Lags Voltage in an Inductive circuit and an RX plot has XL on the positive vertical axis and XC on the negative vertical axis. A plot in the third quadrant would suggest that it is capacitive because it falls within the XC axis, and this is true for the perspective of a CT at the origin of the quadrant diagram oriented to monitor positive values in the first quadrant. But for every CT oriented that way, there is a possible orientation in the opposite direction. For this one merely rolls the quadrant diagram around. Some, in both metering and relaying fields, find it easier to drop the reference to lag and lead altogether. WATTS in the first and fourth quadrants are true power leaving the system or power delivered. WATTS in the second and third quadrants are true power entering the system or power received. VARS in the first and second quadrants are reactive power leaving the system or VARS delivered. VARS in the third and fourth quadrants are reactive power entering the system or VARS received. The Power Factor of a 3-phase system can be found easily by taking the cosine of the circuit Load Angle and expressing it as a percentage. PF% = Cos(Load Angle) x 100
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