Electrical Power Notes & Formulas Copyright © 2022 by PSPT All rights reserved. This publication or any portion thereof may not be reproduced or used in any manner whatsoever without the express written permission of the publisher. |First Edition, 2022 | PSPT | 17 Island Bay Dr., Ontario Canada| | www.getpspt.com | graham@getpspt.com| Index 1) DC Circuit Analysis – 4 Pages 2) AC Circuit Analysis – 2 Pages 3) Power Analysis in AC Circuits – 3 Pages 4) Digital Electric Circuits – 4 Pages 5) Electrical Trigonometry – 6 Pages 6) Derivatives – 1 Page 7) Per Unit Analysis – 2 Pages 8) Symmetrical Components – 2 Pages 9) Short Circuit Analysis – 2 Pages 10) Protection and Control – 5 Pages 11) Three Phase Transformers – 2 Pages 12) Metering – 2 Pages 13) Rotating Machines – 5 Pages 14) Low Voltage Electrical Wiring – 7 Pages All 14 sections are numbered individually. 1) DC Circuit Analysis Ohm's Law Current, Voltage & Resistance Value 10−1 W Multiples Symbol Name daW decawatt 10−2 W cW centiwatt 102 W hW −3 10 W mW milliwatt 103 W kW kilowatt 10−6 W µW microwatt 106 W MW megawatt 10−9 W nW nanowatt 109 W GW gigawatt pW picowatt 1012 W TW terawatt 10−15 W fW femtowatt 1015 W PW petawatt −18 W aW attowatt 1018 W EW exawatt 10−21 W zW zeptowatt 1021 W ZW zettawatt 10−24 W yW yoctowatt YW 1024 W Common multiples are in bold face yottawatt Series & Parallel Circuits Kirchhoff's Voltage Law: The sum of the potential drops (voltage drops) around any closed loop is zero Electric Power 1 coulomb = 6.241 x 1018 electrons Work Done = Volts x Q(charge) Joules Work Done = Volts x I (amps) Joule Power = Work/time (sec) Watts hectowatt 10−12 W 10 Conductance SI multiples for watt (W) Submultiples Symbol Name Value dW deciwatt 101 W Kirchhoff's Current Law: All currents entering a note sum to zero Currents entering “+” Currents leaving “-” Circuit Theorems Homogeneity (scaling) property Additive property Page 2 Voltage and current sources Thevenin’s Theorem A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a voltage source VTH in series with a resistor RTH Source Transformation The transformation of a power source from a voltage source to a current source, or a current source to a voltage source. Norton’s Theorem A linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source INorton in parallel with a resistor RNorton Superposition Theorem In a linear circuit with several sources, the current though and voltage drop, for any element in the circuit, is the sum of the currents and voltages produced by each source acting independently. Mesh-Current (or Loop) Analysis Page 3 Ohm’s Law and a Capacitor Electric Fields and Capacitance Page 4 Energizing an Inductor Electromagnetic Induction 2) AC Circuit Analysis Sinusoidal Waves and RMS Values Page 2 Harmonic Frequency Reactance & Impedance 3) Power Analysis in AC Circuits Electric Energy Electric Power Value 10−1 W SI multiples for watt (W) Submultiples Symbol Name Value dW deciwatt 101 W Multiples Symbol Name daW decawatt 10−2 W cW centiwatt 102 W hW −3 10 W mW milliwatt 103 W kW kilowatt −6 10 W µW microwatt 6 10 W MW megawatt 10−9 W nW nanowatt 109 W GW gigawatt −12 12 hectowatt W pW picowatt 10 W TW terawatt 10−15 W fW femtowatt 1015 W PW petawatt 10−18 W aW attowatt 1018 W EW exawatt −21 W zW zeptowatt 21 ZW zettawatt 10−24 W yW YW 1024 W Common multiples are in bold face yottawatt 10 10 yoctowatt 10 W Page 2 AC Power Complex Power 4) Digital Electric Circuits Gates Page 2 Flip – Flops and Multi-Vibrators Page 3 Counters and Shift Registers Page 4 Adders 5) Electrical Trigonometry Angle Measurement Page 2 Triangles Angle Sum Property of a Triangle The Pythagorean Theorem Page 3 Unique Triangles & Ratios Trigonometric Functions and Tangent Lines Page 4 The Unit Circle Unique Triangles Page 5 Unique Angles The Law of Sines The Law of Cosines Trig Identities Page 6 Product to Sum Formulas Sum to Product Formulas Cofunction Identities Double Angle Formulas 06) Derivatives Limit Properties Common Derivatives (Cont’d) The Slope of the Tangent to Any Point on f(x) = x2 The Squeeze Theorem Common Derivatives 7) Per Unit Analysis Phase Relationships Transformers & Per Unit Analysis Δ - Y Conversions Three Phase PU Analysis Normalization Page 2 Transformer Connections yy Star – Star (Y - Y) Change of Bases 8) Symmetrical Components Asymmetrical Phasors Symmetrical Components The “a” Operator Page 2 9) Short Circuit Analysis Asymmetrical Three Phase Faults Single Line to Ground Faults Phase to Phase Faults Phase to Phase to Ground or Faults Phase to Ground with Impedance 3 Phase Faults Page 2 Single-Line Diagrams for Network Components Modeling: Transformers (cont’d) The Generator Modeling: Synchronous Generators Zero Sequence through a Transformer Modeling: Transformers Modeling: Transmission Lines 10) Protection and Control Electrical Devices 1 – Master Element 2 – Time delay Starting or Closing Relay 3 – Checking or Interlocking Relay 4 – Master Contactor 5 – Stopping 6 – Starting Circuit Breaker 7 – Rate of Change Relay 8 – Control Power Disconnecting Device 9 – Reversing Device 10 – Unit Sequence Switch 11 – Multi-function Device 12 – Overspeed Device 13 – Synchronous-speed Device 14 – Underspeed Device 15 – Speed – or Frequency, Matching Device 16 – Data Communications Device 17 – Shunting or Discharge Switch 18 – Accelerating or Decelerating Device 19 – Starting to Running Transition Contractor 20 – Electrically Operated Valve 21 – Distance Relay 22 – Equalizer Circuit Breaker 23 – Temperature Control Device 24 – Volts Per Hertz Relay 25 – Synchronizing or Synchronize-Check Device 26 – Apparatus Thermal Device 27 – Undervoltage Relay 27s - DC under voltage Relay 28 – Flame detector 29 – Isolating Contactor or Switch 30 – Annunciator Relay 31 – Separate Excitation 32 – Directional Power Relay or Reverse Power Relay 33 – Position Switch 34 – Master Sequence Device 35 – Brush-Operating or Slip-Ring Short-Circuiting Device 36 – Polarity or Polarizing Voltage Devices 37 – Undercurrent or Underpower Relay 38 – Bearing Protective Device 39 – Mechanical Condition Monitor 40 – Field (over/under excitation) Relay 41 – Field Circuit Breaker 42 – Running Circuit Breaker 43 – Manual Transfer or Selector Device 44 – Unit Sequence Starting Relay 45 – DC over voltage Relay 46 – Reverse-phase or Phase-Balance Current Relay 47 – Phase-Sequence or Phase-Balance Voltage Relay 48 – Incomplete Sequence Relay 49 – Machine or Transformer, Thermal Relay-OLR 50 – Instantaneous Overcurrent Relay 50G - Instantaneous Earth Over Current Relay (Neutral CT Method) 50N - Instantaneous Earth Over Current Relay (Residual Method) 50BF - Breaker failure 51 – AC Inverse Time Overcurrent Relay 51G - AC Inverse Time Earth Overcurrent Relay (Neutral CT Method) 51N - AC Inverse Time Earth Overcurrent Relay (Residual Method) 52 – AC Circuit Breaker 52a - AC Circuit Breaker Position (Contact Open when Breaker Open) 52b - AC Circuit Breaker Position (Contact Closed when Breaker Open) 53 – Exciter or DC Generator Relay 54 – Turning Gear Engaging Device 55 – Power Factor Relay 56 – Field Application Relay 57 – Short-Circuiting or Grounding Device 58 – Rectification Failure Relay 59 – Overvoltage Relay 60 – Voltage or Current Balance Relay 61 – Density Switch or Sensor 62 – Time-Delay Stopping or Opening Relay ANSI numbers IEEE Standard Electric Power System Device Function Numbers acc. to IEEE C.37.2-1991 Page 2 Electrical Devices (Cont’d) 63 – Pressure Switch 64 – Ground Detector Relay 64R - Restricted earth fault 64S - Stator earth fault 65 – Governor 66 – Notching or Jogging Device 67 – AC Directional Overcurrent Relay 68 – Blocking Relay 69 – Permissive Control Device 70 – Rheostat 71 – Liquid Level Switch 72 – DC Circuit Breaker 73 – Load-Resistor Contactor 74 – Alarm Relay 75 – Position Changing Mechanism 76 – DC Overcurrent Relay 77 – Telemetering Device 78 – Phase-Angle Measuring Relay or "Out-of-Step" Relay 79 – AC Reclosing Relay (Auto Reclosing) 80 – Flow Switch 81 – Frequency Relay 82 – DC Reclosing Relay 83 – Automatic Selective Control or Transfer Relay 84 – Operating Mechanism 85 – Communications,Carrier or Pilot-Wire Relay 86 – Lockout Relay/Master Trip 87 – Differential Protective Relay 88 – Auxiliary Motor or Motor Generator 89 – Line Switch 90 – Regulating Device 91 – Voltage Directional Relay 92 – Voltage and Power Directional Relay 93 – Field Changing Contactor 94 – Tripping or Trip-Free Relay( trip circuit supervision Relay) 95 – For specific applications where other numbers are not suitable 96 – Busbar Trip Lockout relay 97 – For specific applications where other numbers are not suitable 98 – For specific applications where other numbers are not suitable 99 – For specific applications where other numbers are not suitable 150 – Earth Fault Indicator AFD – Arc Flash Detector CLK – Clock or Timing Source DDR – Dynamic Disturbance Recorder DFR – Digital Fault Recorder DME – Disturbance Monitor Equipment ENV – Environmental Data HIZ – High Impedance Fault Detector HMI – Human Machine Interface HST – Historian LGC – Scheme Logic MET – Substation Metering PDC – Phasor Data Concentrator PMU – Phasor Measurement Unit PQM – Power Quality Monitor RIO – Remote Input/Output Device RTU – Remote Terminal Unit/Data Concentrator SER – Sequence of Events Recorder TCM – Trip Circuit Monitor LRSS - LOCAL/REMOTE SELECTOR SWITCH SOTF - Switch On To Fault ANSI numbers IEEE Standard Electric Power System Device Function Numbers acc. to IEEE C.37.2-1991 Page 3 Protection Relay Schemes Types of Electrical Faults Page 4 Protection Relay Schemes Basic Electrical System Structure Instrument Transformers Elements of a Protective Relaying Scheme Polarity Zones of Protection Page 5 Polarity (Cont’d) HV Circuit Breaker Types Westinghouse (ABB) Type CO Overcurrent Relay Impedance Relaying Impedance Relaying Differential Protection Percent Differential Protection 11) Three Phase Transformers 3 Phase Power Transformer Connections Page 2 Transformer Connections (Cont’d) 12) Metering Power and Energy Electric Energy Page 2 Electric Power Industry Canada’s WEB Site Specifications for Electricity Meters Blondel’s Theorem Watt Hour Meters Cross Wattmeter Verification 13) Rotating Machines DC Machines The Induction Motor Page 2 Induction Motor Rotors Single Phase Induction Motors Page 3 Three Phase Induction Motors The Synchronous Generator Page 4 The Equivalent Circuit of a Synchronous Generator Page 5 14) Low Voltage Electrical Wiring Circuit Breakers Page 2 Page 3 Page 4 The following 4 slides schematically demonstrate how a four-way switch is connected and works. Page 5 Standard Home Wiring Diagram Symbols Bathroom Wiring Diagram Page 6 Page 7 Types of Outlets Around the World
