ERCOT equations/formulas (2x)
How to calculate relay scheme time of operation in seconds?
(# cycles to trip) ÷ 60 (cycles in second)
What is the phase difference between the two vectors in each of the following pairs? (1) 345 90° and 345 60° (2) 138 -90° and 138 +90°
(1) 30°, (2) 180° (draw sine wave & plot points to get answer)
A resistance of 5 ohms is connected to a resistance of 10 ohms in an electric circuit. What is the total resistance if the two resistances are connected (i) in series and (ii) in parallel?
(i) 15, (ii) 3.33 (resistors in series simply add; parallel make into fractions, add, then flip)
Given that the sending end voltage is 345 KV, the receiving end 354 KV, the path impedance 100 & power angle 10 . What is the MVAR transfer from the sending to the receiving bus? Use the reactive power transfer equation: Q = Vs(Vs - Vr) ÷ X
-31 MVAR
The power system is running at 61 HZ. At this frequency, what is the time, in seconds, to complete one cycle?
1 (sec) ÷ 61 (freq) = .0164 (Remember @ 60 Hz it's 1/60 or .017 secs. If running higher frequency then will be slower & vice versa for lower frequency.
How would you find the number of seconds for a power system running at exactly 60 HZ?
1 sec ÷ 60 = .017
If the frequency of the power system is exactly 60.0, the period is about __ thousandths of a second.
1 sec ÷ 60 = .017
How to determine current for circuit with known voltage & two parallel resistors?
1) Add resistance; 2) divide voltage by resistance (I = V ÷ R)
How would you calculate voltage in a circuit with two resistors in parallel & 3 amps current?
1) Add resistors 2) Multiply resistance by current (I × R = V)
How to determine voltage in a circuit with known amps & parallel resistors?
1) Add resistors; 2) multiply resistance by amps (V = I × R)
How to determine individual voltage drop across a series of resistors with a known current?
1) Calculate total resistor series current; 2) multiply current × individual resistors (V = I × R)
When problem involving Pythagoren theorem comes up, what are two key things to look for in answer?
1. When answering side length, square number & make sure it actually answers equation. 2. Also look for answer in cosine, should be there.
If the turns ratio of a transformer is 10:1 and low side voltage is 13.5 KV, what is the high side voltage?
13.5 x 10 = 135 KV (The high side is 10x the low side)
A transformer has a turns ratio of 250:100. The primary side voltage is 345 KV. What is the secondary side voltage?
138 Kv (250 = 2.5 × 100 therefore 138 × 2.5 = 345)
What is the peak value of the voltage amplitude for a 138 KV AC voltage?
138 ÷ .707 (RMS value) = 195.2 KV (Remember to DIVIDE by 707, they will try & trick you w/multiplication answer!)
If the nominal voltage is 138 KV and measured voltage is 1.02 per unit, what is the measured voltage in KV?
138 ÷ 1.02 = 140.8 KV
In a 3 phase power system the phase to phase voltage is 138 KV. What is the phase to ground voltage?
138 ÷ √3 = 79.7
What is the ratio of actual voltage to the nominal value of 138 KV, if SCADA shows the bus voltage to be 144 KV? If the operating criteria require voltage to be within 5% of the nominal value, is the bus voltage within limits?
144 ÷ 138 = 1.04, Yes. (Trick question, asking for RATIO initially, not percentage!)
If the complex power in a circuit is 250 MVA and the power factor is 0.95, what is the active power?
250 × .95 = 237.5 MW
What is the peak value of the voltage amplitude for a 345 KV AC voltage?
345 ÷ .707 = 487.9 KV (Remember to DIVIDE by .707, they will try & trick you w/multiplication answer!)
What would you read if you measured from one 345 KV phase to ground?
345 ÷ √3 = 199 KV
What is the per-unit value of a 345 KV bus voltage, if SCADA shows the actual bus voltage to be 358.8 KV? If operating criteria require voltage to be within 5% of the nominal value, is the bus voltage within limits?
358.8 ÷ 345 = 1.04, yes.
At a certain bus, current lags voltage by 36°. What fraction of a cycle does this 36° phase lag correspond to?
360° (1 cycle) ÷ 36° = 1/10th (Remember to equate to how many times 36° goes into 360°)
A transmission line conductor has a thermal limit of 500 amps, a CT in the conductor has a thermal limit of 600 amps, line voltage is 362 KV. What is the thermal capability of the transmission line in MVA?
362 × 500 × √3 = 313.5 MVA
If the nominal voltage is 345 KV & the measured voltage is 364 KV what is the per-unit value?
364 ÷ 345 = 1.055 p.u.
A resistance of 2 ohms is connected to a resistance of 4 ohms in an electric circuit. What is the total resistance if the two resistances are connected in parallel?
4/3 ohms. (1/2 + 1/4 = 3/4, then reciprocal)
A certain relay scheme is designed to operate within 5 cycles of detecting a fault. What is the relay scheme's time of operation in seconds?
5 (cycles) ÷ 60 (cycles a second) = .083 seconds
An AC circuit has a capacitive reactance of 100 ohms and an inductive reactance of 500 ohms. What is the net reactance of the circuit?
500 - 100 = 400 ohms inductive
An AC circuit has a capacitive reactance of 100Ω and an inductive reactance of 500Ω. What is the net reactance of the circuit?
500 - 100 = 400Ω inductive
What is the total or complex power required by a load if the active power is 500 KW and the reactive power is 100 KVAR? What is the power factor of this load?
509.9 KVA, 0.98 KVA² = KW² + KVAR² PF = KW ÷ KVA²
How would you calculate the RPM of a 60 Hz generator?
60 Hz ÷ #poles x 120 = RPM
What is the speed of rotation (RPM) of a 24 pole-pair (24 north and 24 south poles) generator that is connected to a 60 HZ system?
60 Hz ÷ 48 poles x 120 = 150 RPM
What is the speed of rotation of a six-pole generator that is connected to a 60 HZ system?
60 Hz ÷ 6 poles x 120 = 1200 RPM
What is the scheduled system frequency in ERCOT? At this frequency, what is the time in seconds for the voltage to move from a peak value to a zero crossing?
60 Hz, .0042 seconds (1/60th = .017; .017 ÷ 2 = .0085; .0085 ÷ 2 = .0042)
Given that the sending end voltage is 345 KV, the receiving end voltage 354 KV, the path impedance 50Ω ,and the power angle 20°. What is the active power transfer? Use equation P = Vs × Vr ÷ X × δ
835.4 MW **REMEMBER TO MULTIPLY BY √3 (1.732)**
How to find the cosine θ in a right triangle?
CAH or Cos(θ) = Adjacent ÷ Hypotenuse
How to determine the peak value of a voltage amplitude?
Divide voltage by .707.
At 60 HZ, what is the time in seconds for the current to go from a zero crossing to its nearest peak value?
Four crossings in one .017 second sine wave cycle; .017 ÷ 4 = .0042.
How to determine current drop after individual parallel resistors in a circuit with known volts & amps?
I = V ÷ R
State the expression for power consumed by a resistance, R, when a current, I, flows through it.
Power = I² x R
How would you find the value of a third side in a right triangle?
Pythagorean theorem: O² + A² = H² 1) Square numbers in triangle, 2) add/subtract to get missing number, 3) get square root of missing number.
When using the power transfer equation P = Vs × Vr ÷ X × sin δ what is the most important final step?
REMEMBER TO MULTIPLY BY √3 (1.732)
Formula to find the sine θ in a right triangle?
SOH or Sin (θ) = Opposite ÷ Hypotenuse
What element of the reactive power transfer equation Q = Vs(Vs - Vr) ÷ X leads to the rule of thumb that reactive power flows downhill on voltage magnitude? a) The (Vs - Vr) portion b) The Vs(Vs - Vr) portion c) The whole equation d) None of the above
The (Vs - Vr) portion
What portion of the equation P = Vs × Vr ÷ X × sin δ is called Pmax? a) The quantity Vs × Vr ÷ X b) The quantity sin δ c) The entire equation d) The quanity sin δ ÷ X
The quantity Vs × Vr ÷ X
How to calculate the thermal capability of a line when voltage & limit given?
Thermal limit × voltage × √3
What's the value of I (current) for a 6V battery across a series resistor of 10 and 5 ohms?
Voltage (6) ÷ resistance (15 ohms) = .4 amps
How to determine circuit voltage when only current & resistance known?
Voltage = I × R
***SIMPLIFY*** Use the impedance triangle to calculate the resultant impedance for a circuit with the following components: 1)Resistance = 30 ohms 2)Capacitive Reactance = 20 ohms 3)Inductive Reactance = 60 ohms
Z² = R² + X² 60 - 20 = 40² = 1600 30² = 900 1600 + 900 = 2500² = 50 ohms
What is the impedance triangle formula?
Z² = R² + X² Z = Impedance R = Resistance X = Reactance
What is the side that is always next to the angle θ in a right triangle?
adjacent side (adjacent the angle θ)
The formula for ___ reactance is Xc = 1 / 2πfC
capacitive
The side opposite the right angle is called?
hypotenuse
What is the longest side of a right triangle called?
hypotenuse
The formula for ___ reactance is XL = 2πfL
inductive
What side of the right triangle is across from the angle θ?
opposite side (opposite the angle θ)
MVA²= MW²+ MVAR² is a graphical representation of what?
power triangle
