Basic Math for Relay Technicians Hands On Relay School 2015 Presented by Charlene Reyes
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
Please Excuse My Dear Aunt Sally Parentheses Exponents Multiplication Division Addition Subtraction 3
SI Units: Order of Magnitude 4
SI Units: Order of Magnitude 5
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
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
Conversions How many Snoqualmie Falls Hydroelectric Facilities does it take to match the capacity of the Hoover Dam? Snoqualmie 54000KW 1000KW 1MW 2080MW Hoover = 38.52 How many Hoover Dams does it take to match the capacity of the Grand Coulee Dam? Hoover 2080MW 6809MW Coulee = 3.27 8
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
Trigonometry SOH CAH TOA " θ = sin 1 $ # " θ = cos 1 $ # opposite hypotenuse adjacent hypotenuse % ' & % ' & θ hyp adj opp " θ = tan 1 $ # opposite adjacent % ' & 10
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
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
Polar Coordinates A vector with a magnitude and angle. A vector with a real component and an imaginary component. hyp opp θ adj 13
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
The Unit Circle 1 2 = 0.5 3 2 = 0.866 2 2 = 0.707 15
Mho Circle X Calculate the boundaries set by the mho circles. R 16
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
The Power Triangle p. f. = P S = cos(θ) 18
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
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
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
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 = 0.70. The synchronous motor operating at 8kVA, 480V, 60Hz is overexcited, produces a leading pf = 0.70. What is the system load power factor? 22
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