Basic Math for Relay Technicians. Hands On Relay School 2015 Presented by Charlene Reyes
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1 Basic Math for Relay Technicians Hands On Relay School 2015 Presented by Charlene Reyes
2 Overview Order of Operations and Order of Magnitude Unit Analysis and Conversions Trigonometry Rectangular and Polar Coordinate Math The Unit Circle Common Electrical Calculations The Power Triangle Applications: o o o o o o Mho Circle Metering Transformers Per Unit Calculations Power System Analysis So much more 2
3 Please Excuse My Dear Aunt Sally Parentheses Exponents Multiplication Division Addition Subtraction 3
4 SI Units: Order of Magnitude 4
5 SI Units: Order of Magnitude 5
6 Unit Analysis Also known as Dimensional Analysis Used in everyday applications o At Work o At Grocery Store o At Home SI Units consists of base units and derived units o Seven Base Units Length = meter (m) Mass = kilogram (kg) Time = seconds (s) Electric Current = ampere (A) Temperature = kelvin (K) Amount of Substance = mole (mol) Luminous Intensity = candela (cd) 6
7 Unit Analysis SI Units consists of base units and derived units (cont.) o All others units are derived from base units Area = m 2 Volume = m 3 Force = m*kg*s -2 = newton (N) Energy = m 2 *kg*s -2 = N*m = joule (J) Power = m 2 *kg*s -3 = J/s = watt (W) Potential = m 2 *kg*s -3 *A -1 = W/A = volt (V) Useful when doing algebraic computations where you have a known quantities and an equation you just have to fill in the blank. o y = (slope*x) + b o F = mass * acceleration o V = I*R 7
8 Conversions How many Snoqualmie Falls Hydroelectric Facilities does it take to match the capacity of the Hoover Dam? Snoqualmie 54000KW 1000KW 1MW 2080MW Hoover = How many Hoover Dams does it take to match the capacity of the Grand Coulee Dam? Hoover 2080MW 6809MW Coulee =
9 Trigonometry SOH CAH TOA sin(θ) = cos(θ) = opposite hypotenuse adjacent hypotenuse θ hyp adj opp tan(θ) = opposite adjacent = opp / hyp adj / hyp = sin(θ) cos(θ) 9
10 Trigonometry SOH CAH TOA " θ = sin 1 $ # " θ = cos 1 $ # opposite hypotenuse adjacent hypotenuse % ' & % ' & θ hyp adj opp " θ = tan 1 $ # opposite adjacent % ' & 10
11 Rectangular Coordinates A vector with an x-coordinate and a y-coordinate. A vector with a real component and an imaginary component. hyp opp θ adj 11
12 Rectangular Coordinates A vector with an x-coordinate and a y-coordinate. A vector with a real component and an imaginary component. Im (X,Y ) Y = opp θ X = adj Re 12
13 Polar Coordinates A vector with a magnitude and angle. A vector with a real component and an imaginary component. hyp opp θ adj 13
14 Polar Coordinates A vector with a magnitude and angle. A vector with a real component and an imaginary component. Im (Z θ) Z = hyp θ Re 14
15 The Unit Circle 1 2 = = =
16 Mho Circle X Calculate the boundaries set by the mho circles. R 16
17 Ohm s Law: Joule s Law: Turns ratio: Efficiency: Per Unit: Common Electrical Equations V = I R P = I 2 R t = V I a = N 1 = V 1 = I 2 = Z 1 N 2 V 2 I 1 η = P out P in p.u. = actual base Z 2 17
18 The Power Triangle p. f. = P S = cos(θ) 18
19 Metering A SCADA system configuration requires maximum values (i.e. the actual value of the current when the transducer is full scale). The transducer has a full-scale ac current of 5A. Using a CT with turns ratio of 400:5, what is the maximum current value? What is the the secondary current when the transducer reads half the maximum current value? 19
20 Transformer Efficiency Test results for a 10kVA, 2300/230-V, single-phase transformer has the following test results: Open-circuit power consumption = 69W Short-circuit resistance = 10.9Ω What is the efficiency of the transformer when operated at full-load and unity power factor? 20
21 Per Unit Analysis A three-phase transmission line is rated for 55kV and 25MVA. The line impedance is 49Ω per phase. Assuming the line-rated values are the base values, what is the per-unit impedance of the line? 21
22 System Analysis A three-phase induction motor and a three-phase synchronous motor are connected to a 480V system. The induction motor draws a current of 14.43A and has lagging pf = The synchronous motor operating at 8kVA, 480V, 60Hz is overexcited, produces a leading pf = What is the system load power factor? 22
23 Summary You all do math everyday and don t even know it! Please Excuse My Dear Aunt Sally SOH CAH TOA Unit Circle Resources: o Hands-On Relay School Clipboard o Ugly s Electrical Reference o Scientific Calculator o Google 23
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