Technical Study GuideTechnical Study Guide How to pass the … · Follows the exam outline and...

Justin Kauwale, P.E.

Creates an understanding of the key exam concepts and skills

PE

Follows the exam outline and teaches the main topics.Simplifies and focuses your studying

ProEngineering Guides

Circuits, Electromagnetic Devices, Codes, PECs, Performance

PowerPower

How to pass the examHow to pass the exam

Transmission, Rotating Machines, Protection, Special Appl.

Technical Study GuideTechnical Study Guide

http://www.engproguides.com

SECTION 1

INTRODUCTION

Introduction-1 http://www.engproguides.com

Introduction Table of Contents 1.0 Introduction ............................................................................................................................. 2

1.1 Key Concepts and Skills ...................................................................................................... 2

1.2 Units .................................................................................................................................... 5

2.0 Disclaimer ............................................................................................................................... 5

3.0 How to use this Book .............................................................................................................. 5

4.0 Sample Exam Tips .................................................................................................................. 6

5.0 Recommended References ............................................................................................... 9

5.1 NFPA 70, NEC Handbook, 2014 Edition ........................................................................ 9

5.2 Engineering Unit Conversions Book ............................................................................... 9

5.3 Schaum's Outline of Basic Electricity ............................................................................. 9

5.4 Schaum's Outline of Electrical Power Systems ............................................................ 10

5.4 Electric Machines, Drives and Power Systems ............................................................ 10

5.5 Power System Analysis ................................................................................................ 10

5.6 Online Articles .............................................................................................................. 11

5.7 IEEE Color Books ......................................................................................................... 12


1.0 INTRODUCTION One of the most important steps in an engineer's career is obtaining the professional engineering (P.E.) license. It allows an individual to legally practice engineering in the state of licensure. This credential can also help to obtain higher compensation and develop a credible reputation. In order to obtain a P.E. license, the engineer must first meet the qualifications as required by the state of licensure, including minimum experience, references, and the passing of the National Council of Examiners for Engineering and Surveying (NCEES) exam. Engineering Pro Guides focuses on helping engineers pass the NCEES exam through the use of free content on the website, http://www.engproguides.com and through the creation of books like sample exams and guides that outline how to pass the PE exam.

The key to passing the PE exam is to learn the key concepts and skills that are tested on the exam. There are several issues that make this very difficult. First, the key concepts and skills are unknown to most engineers studying for the exam. Second, the key concepts and skills are not contained in a single document. This technical guide teaches you the key concepts and skills required to pass the Electrical Power PE Exam.

1.1 KEY CONCEPTS AND SKILLS How are the key concepts and skills determined?

The key concepts and skills tested in this sample exam were first developed through an analysis of the topics and information presented by NCEES. NCEES indicates on their website that the PE Exam will cover an AM exam (4 hours) followed by a PM exam (4 hours) and that the exam will be 80 questions long, 40 questions in the morning and 40 questions in the afternoon. The Power Electrical PE exam will focus on the following topics, as indicated by NCEES. (http://ncees.org/engineering/pe/):

I. General Power Engineering (24 questions)

A) Measurement and Instrumentation (6 questions) 1 Instrument transformers 2 Wattmeters 3 VOM metering 4 Insulation testing 5 Ground resistance testing

B) Special Applications (8 questions) 1 Lightning and surge protection 2 Reliability 3 Illumination engineering 4 Demand and energy management calculations 5 Engineering economics

C) Codes and Standards (10 questions) 1 National Electrical Code (NEC) 2 National Electrical Safety Code (NESC)

http://www.engproguides.com/

http://ncees.org/engineering/pe/


5.6 ONLINE ARTICLES 1. Instrument Transformer Basic Technical Information and Application http://www.gegridsolutions.com/products/manuals/ITITechInfo.pdf

This article covers everything you need to know to answer instrument transformers type questions.

Topics Covered: 9.0 Measurement and Instrumentation – Instrument Transformers

2. 3 Phase 2 Wattmeter Power Measurements http://www.newtons4th.com/wp-content/uploads/2010/03/APP014-3-Phase-2-Wattmeter-Explained.pdf This article provides a great explanation on the phasors and how a 3 phase power system can be measured with 2 watt meters. The other scenarios are provided in this book.

Topics Covered: 9.0 Measurement and Instrumentation – Wattmeters

3. VOM Metering aka Digital Multi Meters (DMM) http://support.fluke.com/find-sales/Download/Asset/1260898_6116_ENG_M_W.PDF VOM metering is basically an older name for the current digital multi meters that are used heavily in the electrical industry. Topics Covered: 9.0 Measurement and Instrumentation – VOM Metering

4. Insulation Testing https://www.instrumart.com/assets/Megger-insulationtester.pdf A megger is the common name for the equipment used to test insulation. This article provides background information on the equipment and also the process to test insulation under various scenarios. Topics Covered: 9.0 Measurement and Instrumentation – Insulation Testing

5. Ground Resistance Testing http://www.fluke.com/fluke/inen/solutions/earthground/ This website has a lot of information on the equipment used to conduct ground resistance testing and also information on the methods necessary for the exam. Topics Covered: 9.0 Measurement and Instrumentation – Ground Resistance Testing

http://www.gegridsolutions.com/products/manuals/ITITechInfo.pdf

http://www.newtons4th.com/wp-content/uploads/2010/03/APP014-3-Phase-2-Wattmeter-Explained.pdf

http://www.newtons4th.com/wp-content/uploads/2010/03/APP014-3-Phase-2-Wattmeter-Explained.pdf

http://support.fluke.com/find-sales/Download/Asset/1260898_6116_ENG_M_W.PDF

https://www.instrumart.com/assets/Megger-insulationtester.pdf

http://www.fluke.com/fluke/inen/solutions/earthground/


6. Bus Arrangements http://testguy.net/content/256-6-Common-Substation-Bus-Schemes-Every-Test-Tech-Should-Know This website has information on the common bus arrangements that are used to enhance reliability of an electrical power distribution system. Topics Covered: 10.0 Special Applications – Reliability

5.7 IEEE COLOR BOOKS By IEEE

The IEEE Color Books contain a lot of information that is used in nearly all of the recommended references. There are 13 volumes and each book is given a color as shown in the list below. For the purposes of the exam you should only get the items in bold.

Red Book™— IEEE STD 141™-1993 (R1999), Recommended Practice for the Electric Power Distribution for Industrial Plants

Green Book™— IEEE STD 142™-2007, Recommended Practice for Grounding of Industrial and Commercial Power Systems

This book will help you understand the purpose of grounding and the different approaches to grounding. There is also information on lightning protection in this book.

Topics Covered: 10.0 Special Applications – Lighting/Surge Protection

Gray Book™— IEEE STD 241™-1990 (R1997), Recommended Practice for Electrical Power Systems in Commercial Buildings

Buff Book™— IEEE STD 242™-2001, Recommended Practice for Protection and Coordination of Industrial and Commercial Power Systems

This book will help you to understand short circuit calculations, time current coordination graphs and different approaches to the protection of various types of equipment like motors, generators, transformers, buses and conductors.

http://testguy.net/content/256-6-Common-Substation-Bus-Schemes-Every-Test-Tech-Should-Know

http://testguy.net/content/256-6-Common-Substation-Bus-Schemes-Every-Test-Tech-Should-Know


SECTION 2

CIRCUITS

Circuits-1 http://www.engproguides.com

Section 2.0 – Circuits Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Direct Current ..................................................................................................................... 4

2.1 Ohm’s Law ...................................................................................................................... 5

2.2 Electrical Power .............................................................................................................. 5

2.3 Kirchhoff’s Laws ............................................................................................................. 6

2.3.1 Kirchhoff’s Voltage Law (KVL) ................................................................................. 6

2.3.2 Kirchhoff’s Current Law (KCL) ................................................................................. 7

2.4 Circuit Arrangements ...................................................................................................... 8

2.4.1 Series Circuits ......................................................................................................... 8

2.4.2 Parallel Circuits ....................................................................................................... 9

2.4.3 Open Circuit .......................................................................................................... 11

2.4.4 Short Circuit ........................................................................................................... 11

3.0 Alternating current ............................................................................................................ 12

3.1 Frequency ..................................................................................................................... 13

3.2 RMS and MAX .............................................................................................................. 13

3.3 Complex Numbers ........................................................................................................ 16

3.3.1 Rectangular Form .................................................................................................. 16

3.3.2 Polar Form ............................................................................................................. 17

3.3.3 Converting Polar and Rectangular Forms - Calculator .......................................... 18

3.4 Resistance, Inductance, Capacitance and Impedance ................................................ 19

3.4.1 Resistance (Resistors) .......................................................................................... 20

3.4.2 Inductance or Inductive Reactance (Inductors) ..................................................... 20

3.4.3 Capacitance or Capacitive Reactance (Capacitors) .............................................. 20

3.4.4 Impedance ............................................................................................................. 21

3.5 Single-Phase vs. Three-Phase ..................................................................................... 21

3.5.1 Single-Phase ......................................................................................................... 21

3.5.2 Three-Phase .......................................................................................................... 22

3.6 Delta versus Wye Arrangements .................................................................................. 23

3.6.1 Delta Arrangement ................................................................................................ 23

3.6.2 Wye Arrangement ................................................................................................. 24

3.6.3 Convert between Delta and Wye ........................................................................... 25

3.7 Power Factor ................................................................................................................ 27



3.7.1 Waveform – Current & Voltage ............................................................................. 27

3.7.2 Phasor – Current & Voltage .................................................................................. 30

3.7.3 Apparent Power, Real Power and Reactive Power ............................................... 32

4.0 Symmetrical Components ................................................................................................ 34

4.1 Balanced vs. Unbalanced Loads .................................................................................. 34

4.2 Positive, Negative and Zero Components .................................................................... 35

5.0 Per Unit Analysis .............................................................................................................. 38

5.1 Change Per-Unit Base .................................................................................................. 38

5.2 Application of Per-Unit .................................................................................................. 39

6.0 Practice Problems ................................................................................................................. 40

6.1 Problem 1 – Per Unit .................................................................................................... 40

6.2 Problem 2 – Per Unit .................................................................................................... 40

6.3 Problem 3 – Power Factor ............................................................................................ 41

6.4 Problem 4 – Three-Phase Circuits ............................................................................... 41

6.5 Problem 5 – Three-Phase Circuits ............................................................................... 42

7.0 Solutions .......................................................................................................................... 43

7.1 Solution 1 – Per Unit ..................................................................................................... 43

7.2 Solution 2 – Per Unit ..................................................................................................... 44

7.3 Solution 3 – Power Factor ............................................................................................ 45

7.4 Solution 4 - Three-Phase Circuits ................................................................................. 46

7.5 Solution 5 - Three-Phase Circuits ................................................................................. 47



1.0 INTRODUCTION Circuits accounts for approximately 9 questions on the Electrical & Computer, Power PE exam.

This section provides a refresher on the basic electrical engineering concepts, beginning with direct current. Following the direct current section, exam type material will be covered with alternating current, per-unit analysis and symmetrical components.

The circuit analysis section of this book will serve as the basis for many of the other application sections. Therefore, the terms explained here will be used in sections such as 4.0 Rotating Machines, 5.0 Electromagnetic Devices, and 6.0 Transmission. In the latter sections, it will be expected that that you have a strong understanding of the material presented in this section, 2.0 Circuits. Specifically, this section will introduce three methods of understanding circuits, (1) one line diagrams, (2) phasor diagrams and (3) waveforms. These three methods are the basic tools that will be used in the other sections previously mentioned. The symmetrical components and the three methods will also be used in 8.0 Protection.

2.0 Circuits 9 questions

Direct Current Alternating Current Per Unit Analysis Symmetrical Components

• Ohm’s Law • Series Circuit • Parallel Circuit • Kirchhoff’s

Laws

• Frequency • RMS • Complex Numbers • Reactance • Impedance • Single-Phase • Three-Phase • Delta & Wye • Power Factor • Phasor Diagrams

• One-line Diagrams

• Changing Bases

• Unbalanced Loads

• Balanced Loads

• Positive, Negative and Zero Components



2.0 DIRECT CURRENT The PE exam will most likely not have any easy direct current problems, so you may skip this section if you are already familiar with the basics of electricity. This section is only provided as a basis for the terms that are used in the other sections throughout this book.

Direct current (DC) is the supply of current in one direction. In a circuit, current flows from the positive voltage terminal to the negative terminal. Current is deemed positive when it flows in this direction. Current is considered negative when it flows from a negative terminal to a positive terminal. DC current is a constant source and does not switch between negative and positive. Alternating current (AC) is able to supply current in both directions, positive to negative and negative to positive. This is shown in the graph below, where the current can be positive (above the 0-axis) or negative (below the 0-axis).

Figure 1: In an AC circuit, current can alternate its flow from positive to negative. In a DC circuit, current is constant.

There are three main elements to a basic circuit, (1) current, (2) voltage and (3) resistance. The flow of electrons in a circuit is called current (I) and current is given in units of amperes. The energy that drives the flow of electrons is called the voltage (V) and is given in units of volts. The voltage is measured between two points because it is the difference in energy (also known as the potential) that drives the current from one point to the next. The third term is resistance, which is measured in units of ohms (Ω). Resistance (R) is the opposition to the flow of current. One ohm is described as the level of resistance that will allow 1 ampere to flow when 1 volt is applied to a circuit.

In the following sections you will read about voltage in terms of “voltage between phases” or “voltage across two phases” or “voltage between phase and neutral”.



line with each other and can be simply added. Once the calculation is complete you can then convert your answer from wye back to delta.

Delta to Wye

These first sets of equations can be used for balanced and unbalanced circuits.

𝑍𝐴,𝑤𝑦𝑒 =𝑍𝐴𝐵 ∗ 𝑍𝐴𝐶

𝑍𝐴𝐵 + 𝑍𝐴𝐶 + 𝑍𝐵𝐶; 𝑍𝐵,𝑤𝑦𝑒 =

𝑍𝐴𝐵 ∗ 𝑍𝐵𝐶𝑍𝐴𝐵 + 𝑍𝐴𝐶 + 𝑍𝐵𝐶

;𝑍𝐶,𝑤𝑦𝑒 =𝑍𝐵𝐶 ∗ 𝑍𝐴𝐶

𝑍𝐴𝐵 + 𝑍𝐴𝐶 + 𝑍𝐵𝐶

If you assume that the impedances are balanced, then the above equations reduce to the following.

𝑍𝑑𝑒𝑙𝑡𝑎 = 3𝑍𝑤𝑦𝑒;

Figure 26: Conversion of delta to wye in a balanced circuit.

Wye to Delta

These first sets of equations can be used for balanced and unbalanced circuits.



Figure 38: Power factor triangle

The second diagram shows the power factor triangle with leading and lagging power factors. It also includes the inductor and capacitor effect.

Figure 39: Power factor



4.0 SYMMETRICAL COMPONENTS The technique, symmetrical components, is used to analyze unbalanced 3-phase loads (does not apply to 1-phase loads). This technique takes unbalanced loads and deconstructs the loads into three sets of symmetrical components, called the positive, negative and zero components. First, you should understand the difference between balanced and unbalanced loads.

4.1 BALANCED VS. UNBALANCED LOADS In balanced loads, each phase carries an equal amount of current that are each 120 degrees out of phase with one another. In addition, each of the phases has the same impedance and same voltage drop.

𝐼𝐴 = 𝐼∠0°; 𝐼𝐵 = 𝐼∠120°; 𝐼𝐶 = 𝐼∠240°

When each of the three phases reaches the load, the three phases “cancel” each other out, such that there is no return current.

𝐼𝐴 + 𝐼𝐵 + 𝐼𝐶 = 𝐼∠0° + 𝐼∠120° + 𝐼∠240°

Converting the polar form to rectangular form, you can see that the currents will sum to zero.

= (1 + 0𝑗)𝐼 + (−0.5 + 0.87𝑗)𝐼 + (−0.5 − 0.87𝑗)𝐼

𝐼𝐴 + 𝐼𝐵 + 𝐼𝐶 = 0

In a delta, 3-phase circuit, the phases must be balanced, due to KCL. However, if there is a wye, 4-phase circuit, then the KCL equation shall be as follows. The sum of the 3 phases and the neutral current shall be equal to zero.

𝐼𝐴 + 𝐼𝐵 + 𝐼𝐶 + 𝐼𝑁 = 0

In balanced loads, you know that the three phases add to 0, thus in a balanced load, the neutral will have 0 current and in an unbalanced load, the neutral will have a non-zero current.

𝐵𝑎𝑙𝑎𝑛𝑐𝑒𝑑 𝐿𝑜𝑎𝑑𝑠 → 𝐼𝑁 = 0

𝑈𝑛𝑏𝑎𝑙𝑎𝑛𝑐𝑒𝑑 𝐿𝑜𝑎𝑑𝑠 → 𝐼𝑁 ≠ 0

The difficulty with unbalanced loads and the neutral wire is that you lose the symmetry which allows for easy calculations. On the PE exam, most questions will indicate balanced loads, which means that you do not need to use the symmetrical components technique and can use the equations presented elsewhere in this book.

However, you will need to use the symmetrical components technique if one of the following situations is presented in a question.

(1) The load is unbalanced. (2) There is a reference to positive, negative, zero components. (3) There is an unsymmetrical fault, which is presented in Section 6.0 Transmission under fault analysis.



4.2 POSITIVE, NEGATIVE AND ZERO COMPONENTS The premise of the symmetrical components technique is that any unbalanced load can be expressed as a set of three balanced components called, (1) Positive-sequence, (2) Negative-sequence and (3) Zero-sequence. The following figure shows an unbalanced load that has different magnitude phasors and phasors that are not 120 degrees apart.

Figure 40: An unbalanced load can be broken down into three sets of symmetrical components. The right figure is the unbalanced load. The left are the symmetrical components that can

create the unbalanced load.

The figure above reconstructs the unbalanced load with three sets of symmetrical components. The individual sets of components can be seen below for clarity.

Figure 41: These phasors show the positive, negative and zero components, from left to right, that were used to construct the unbalanced loads.

The positive-sequence components are symmetrical and have the same magnitudes and are 120 degrees apart from one another. The sequence of the components is also in the same order as the original unbalanced load (clockwise: A-B-C). The negative sequence components are the same magnitude as the positive sequence. However, the negative sequence is arranged in an opposite sequence from the positive sequence (counterclockwise: A-B-C). In



7.5 SOLUTION 5 - THREE-PHASE CIRCUITS Based on the diagram below, what is the current through phase B? Assume a balanced load.

First find the phase voltage.

𝑉𝑝ℎ =𝑉𝐿𝐿√3

→ 𝑉𝑝ℎ =480√3

= 277𝑉

Next use the following equation to solve for current.

𝑉𝑝ℎ = 𝐼𝑍

277𝑉 = 𝐼(150 + 𝑗80)

Convert to polar and divide.

𝐼 =277∠0°

177∠28.1°

𝐼 = 1.57∠ − 28.1°

The correct answer is most nearly, (a) 1.6 A.



SECTION 3

DEVICES

Devices-1 http://www.engproguides.com

Section 3.0 – Devices Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Batteries ............................................................................................................................. 4

2.1 Equivalent Circuit ............................................................................................................ 4

2.2 Types .............................................................................................................................. 5

2.1.1 Lead Acid Battery .................................................................................................... 5

2.1.2 Valve Regulated Lead Acid Battery (VRLA) ............................................................ 6

2.1.3 Lithium Battery ........................................................................................................ 6

2.2 Ratings ........................................................................................................................... 6

2.2.1 C-Rating .................................................................................................................. 6

2.2.2 E-Rating .................................................................................................................. 8

2.2.3 Cycle Life ................................................................................................................. 8

2.2.4 Temperature Effect .................................................................................................. 9

2.2.5 State of Charge ..................................................................................................... 10

2.2.6 Cold Cranking Amps ............................................................................................. 10

3.0 Power Supplies ................................................................................................................ 11

3.1 AC to DC Inverters ....................................................................................................... 11

3.2 DC to AC Inverters ....................................................................................................... 11

4.0 Variable Speed Drives ..................................................................................................... 12

4.1 Thyristors, Diodes and IGBTs ...................................................................................... 12

4.2 Rectifiers ....................................................................................................................... 13

4.2.1 Half-Wave Rectifiers .............................................................................................. 13

4.2.2 Full-Wave Rectifiers .............................................................................................. 15

4.2.3 DC Bus Ripple ....................................................................................................... 17

4.2.4 Full-Wave Rectifier with Capacitor ........................................................................ 18

4.3 Inverters ........................................................................................................................ 19

4.4 Variable Speed Drives .................................................................................................. 19

4.4.1 Construction .......................................................................................................... 19

5.0 Controls ............................................................................................................................ 21

5.1 Relays and Switches .................................................................................................... 21

5.2 Programmable Logic Controllers .................................................................................. 21


6.1 Problem 1 - Battery ....................................................................................................... 22



6.2 Problem 2 – Half-Wave Rectifier .................................................................................. 22

6.3 Problem 3 – Full -Wave Rectifier .................................................................................. 23

7.0 Solutions ............................................................................................................................... 24

7.1 Solution 1 - Battery ....................................................................................................... 24

7.2 Solution 2 – Half-Wave Rectifier ................................................................................... 24

7.3 Solution 3 – Full-Wave Rectifier ................................................................................... 26



1.0 INTRODUCTION The section, Devices, accounts for approximately 7 questions on the Power Engineering, Electrical PE exam.

This section discusses the Devices and Power Electronic Circuits section. At first this section may seem very different from Power Engineering. However, upon closer inspection you will see how this section is important to practicing Power Engineering. Batteries are beginning to play an increasingly important role in the power field as intermittent renewable energy requires a form of energy storage. Power supplies, drives and controls are used heavily in the motor control section to reduce electricity costs and this effect is large, since motors account for more than 50% of all industrial electricity usage. Some estimates indicate that motors account for more than 2/3 of industrial electricity usage. But with these electricity savings comes unwanted effects to power quality, which Power Engineers must be equipped to resolve. As you can see this section is closely related to the 4.0 Machines section and the 7.0 Power System Performance section, so please be sure to read through this section before reading those sections.

Devices 7 questions

Batteries Power Supplies Drives Controls

• Diodes & Thyristors

• Rectifiers • Inverters • Variable Speed

Drives

• Relays • Switches • PLCs

• AC to DC Inverter

• DC to AC Inverter

• Types • Ratings • Safety



2.0 BATTERIES Batteries are used to store electrical energy as chemical energy. A battery consists of an electrolyte medium and two electrodes, one positive and the other negative. Current flows from the positively charged end of the battery, through the circuit, then to the negatively charged portion of the battery. Chemically, electrons are negatively charged and are attracted to the positively charged end of the battery.

Figure 1: A battery provides direct current to a circuit. Current flows from the positive terminal to the negative terminal.

This transfer of electrons creates this voltage potential, which drives the current during discharge as shown in the figure above. The same principal is used when the battery is being charged but in reverse.

2.1 EQUIVALENT CIRCUIT A battery is made up of internal resistance and capacitance. When a battery is placed in-line with a circuit, it is important to account for the internal losses in addition to the charge it provides. The figure below describes the equivalent circuit in a battery. The capacitance is where the charge is stored in the battery. The internal resistance (or losses) is comprised of the resistance through the terminals, electrodes, connections, electrolytes, and other components that the current travels through within the battery. In parallel with the capacitance is the resistance between the plates. This resistance is very small and most likely can be neglected.



7.3 SOLUTION 3 – FULL-WAVE RECTIFIER A single-phase, full-wave rectifier consists of a thyristor that is activated based on the gate current shown in the graph below. What is the average value of the output current?

The peak occurs at the maximum of the sine wave, which is at 90 degrees. This is also the same time that the gate current is activated. Also the rectifier is full-wave, so the negative portions of the waveform will also pass through the output as a positive. Thus, the amount of current that is output is shown in the shaded region.

Now you need to quantify the shaded region by taking the integral of the sine wave from 90 degrees to 180 degrees but 2X.

𝑆𝑢𝑚 = 2 ∗ � 𝑖𝑚𝑎𝑥 ∗ 𝑠𝑖𝑛 (𝜃)180

90

𝑆𝑢𝑚 = 2 ∗ 𝑖𝑚𝑎𝑥(−𝑐𝑜𝑠(180) + 𝑐𝑜𝑠(90)) → 𝑖𝑚𝑎𝑥(1 + 0)



SECTION 4

ROTATING MACHINES

Rotating Machines-1 http://www.engproguides.com

Section 4.0 – Rotating Machines Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Synchronous Machines ...................................................................................................... 4

2.1 Construction ................................................................................................................... 4

2.2 Synchronous Speed ....................................................................................................... 5

2.3 Synchronous Generator ................................................................................................. 6

2.3.2 Synchronous Generator – Leading Power Factor ................................................... 8

2.3.3 Synchronous Generator – Lagging Power Factor ................................................... 9

2.3.4 Generator Control .................................................................................................. 10

2.3.5 Voltage Regulation ................................................................................................ 15

2.3.5 Efficiency ............................................................................................................... 15

2.3.6 Generator Voltage Dip ........................................................................................... 15

2.3.7 Characteristics Under Various Loading Conditions ............................................... 16

2.4 Synchronous Motor ...................................................................................................... 17

2.4.1 Synchronous Motor - Leading Power Factor ......................................................... 17

2.4.2 Synchronous Motor - Lagging Power Factor ......................................................... 18

3.0 Induction Machines .......................................................................................................... 20

3.1 Construction ................................................................................................................. 20

3.2 Slip ................................................................................................................................ 21

3.3 Equivalent Circuits ........................................................................................................ 23

3.4 Voltage Regulation ....................................................................................................... 24

3.5 Voltage Unbalance ....................................................................................................... 24

3.6 Characteristics under Various Loading Conditions ....................................................... 25

4.0 Speed-Torque .................................................................................................................. 25

5.0 Starting Methods .............................................................................................................. 26

5.1 Across the Line Starters ............................................................................................... 27

5.2 Reduced Voltage Starters ............................................................................................ 27

5.3 Variable Speed Drive as a Starter ................................................................................ 28

6.0 Power Flow Between Voltage Sources ............................................................................ 28

7.0 Practice problems ............................................................................................................ 30

7.1 Problem 1 – Poles ........................................................................................................ 30

7.2 Problem 2 – Breakdown Torque ................................................................................... 30

7.3 Problem 3 – Speed Regulation ..................................................................................... 31



7.4 Problem 4 – Equivalent Circuits ................................................................................... 31

7.5 Problem 5 – Equivalent Circuits ................................................................................... 32

7.6 Problem 6 – Slip ........................................................................................................... 32

8.0 Solutions .......................................................................................................................... 33

8.1 Solution 1 – Poles ......................................................................................................... 33

8.2 Solution 2 – Breakdown Torque ................................................................................... 34

8.3 Solution 3 – Speed Regulation ..................................................................................... 35

8.4 Solution 4 – Equivalent Circuits .................................................................................... 36

8.5 Solution 5 – Equivalent Circuits .................................................................................... 37

8.6 Solution 6 – Slip ............................................................................................................ 38



The active power that is used by the motor can be found by summing up the power losses through each resistive component.

𝑃𝑎𝑐𝑡𝑖𝑣𝑒 𝑖𝑛 = 𝑃𝑐𝑜𝑟𝑒 𝑙𝑜𝑠𝑠𝑒𝑠 + 𝑃𝑠𝑡𝑎𝑡𝑜𝑟 𝑐𝑜𝑝𝑝𝑜𝑒𝑟 𝑙𝑜𝑠𝑠𝑒𝑠 + 𝑃𝑟𝑜𝑡𝑜𝑟

𝑃𝑎𝑐𝑡𝑖𝑣𝑒(𝑘𝑊) =(𝑉𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙)2

𝑅𝑀+ 𝐼02 ∗ 𝑅𝑠𝑡𝑎𝑡𝑜𝑟 + 𝐼32 ∗ 𝑅𝑟𝑜𝑡𝑜𝑟

However, we can find a relationship between the current through the stator, Io, and the current through the rotor, I2, with the slip across the air gap.

Therefore, the active power equation becomes:

𝑃𝑎𝑐𝑡𝑖𝑣𝑒(𝑘𝑊) =(𝑉𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙)2

𝑅𝑀+ 𝐼02 ∗ 𝑅𝑠𝑡𝑎𝑡𝑜𝑟 + 𝐼02 ∗

𝑅𝑟𝑜𝑡𝑜𝑟𝑠

For a three phase motor, the active power equation becomes:

𝑃𝑎𝑐𝑡𝑖𝑣𝑒(𝑘𝑊) =3(𝑉𝑡𝑒𝑟𝑚𝑖𝑛𝑎𝑙)2

𝑅𝑀+ 3𝐼02 ∗ 𝑅𝑠𝑡𝑎𝑡𝑜𝑟 + 3𝐼02 ∗

𝑅𝑟𝑜𝑡𝑜𝑟𝑠

For mechanical power, you can ignore the Xm and Rm parallel circuit, because this circuit path will have a minimal effect on power. Basically you will have the same equivalent circuit as the synchronous motor.

3.4 VOLTAGE REGULATION The voltage regulation of a rotating machine at a given load, power factor, and at rated speed is defined as a function of the no load voltage and full load voltage.

𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 (𝑉𝑅)% =𝐸𝑛𝑜 𝑙𝑜𝑎𝑑 − 𝑉𝑓𝑢𝑙𝑙 𝑙𝑜𝑎𝑑

𝑉𝑓𝑢𝑙𝑙 𝑙𝑜𝑎𝑑∗ 100

This term describes the machine’s ability to keep voltage at the same level as the machine is loaded from “no load” to full load.

3.5 VOLTAGE UNBALANCE Voltage supply to a three-phase motor should be balanced upon each phase. However, this may not always be the case and voltages could be unbalanced between the three phases. When this happens, there will be unbalanced currents which will cause an increase in temperature at the motor due to the efficiency losses. Motors should be able to operate with increased temperatures and should also be able to operate with some voltage unbalance. The typical maximum recommended voltage unbalance is 5%. Voltage unbalance above this amount is not recommended.


8.0 SOLUTIONS

8.1 SOLUTION 1 – POLES A 3-phase motor, 60 Hz, induction motor has the following values on its nameplate:

Efficiency (50% , 75%, 100% load) 94%, 95%, 96% Efficiency (50% , 75%, 100% load) 0.78 pu, 0.85 pu, 0.88 pu Full Load Speed 1,784 RPM Full Load Torque 1,473 lb-ft Locked Rotor Torque 90% full load Breakdown Torque 220% full load Voltage 4,160 V

This question asks for the number of poles, which can be found with the following equation. The difficulty is that you don’t have the synchronous speed, but you can make a guess based on the full load speed of the induction motor, which should only be slightly less than the synchronous speed.

𝑆𝑦𝑛𝑐ℎ𝑟𝑜𝑛𝑜𝑢𝑠 𝑠𝑝𝑒𝑒𝑑 (𝑅𝑃𝑀) =120 ∗ 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 (𝐻𝑧)

𝑃 (# 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠)

# 𝑜𝑓 𝑝𝑜𝑙𝑒𝑠 𝑤𝑖𝑙𝑙 𝑎𝑙𝑤𝑎𝑦𝑠 𝑏𝑒 𝑒𝑣𝑒𝑛

Frequency 60 Hz

# of Poles Sync RPM

2 3,600.0 4 1,800.0 6 1,200.0

The closest greater synchronous speed that is greater than the full load speed of 1,784 RPM is 1,800 RPM, which corresponds to 4 poles. The correct answer is (d) 4.


SECTION 5

ELECTROMAGNETIC DEVICES

Electromagnetic Devices-1 http://www.engproguides.com

SECTION 5.0 – ELECTROMAGNETIC DEVICES

Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Transformers ...................................................................................................................... 4

2.1 Types .............................................................................................................................. 4

2.2 Construction ................................................................................................................... 5

2.1.1 Types ....................................................................................................................... 5

2.1.2 Tap Setting .............................................................................................................. 6

2.3 Ideal transformers ........................................................................................................... 6

2.4 Real transformers ........................................................................................................... 8

2.4.1 Equivalent Circuit .................................................................................................... 8

2.4.2 Coil Losses .............................................................................................................. 8

2.4.3 Core Losses ............................................................................................................ 9

2.5 Efficiency ........................................................................................................................ 9

2.6 Testing .......................................................................................................................... 10

2.6.1 Short Circuit Test ................................................................................................... 10

2.6.2 Open Circuit Test .................................................................................................. 11

2.7 Impedance .................................................................................................................... 11

2.8 Transformers in Parallel ............................................................................................... 12

3.0 Transformer Arrangements (3-Phase) ............................................................................. 12

3.1 Delta-Wye Transformer ................................................................................................ 12

3.2 Delta-Delta Transformer ............................................................................................... 13

3.3 Wye-Delta Transformer ................................................................................................ 15

3.4 Wye- Wye Transformer ................................................................................................ 16

4.0 Measurement Transformers ............................................................................................. 19

5.0 Autotransformers .............................................................................................................. 19

5.1 Step-Up Autotransformers ............................................................................................ 19

5.2 Step-Down Autotransformers ....................................................................................... 21

6.0 Reactors ........................................................................................................................... 22

6.1 Line/Load reactor .............................................................................................................. 22

7.0 Practice Problems ............................................................................................................ 23

7.1 Problem 1 – Transformer Losses ................................................................................. 23

7.2 Problem 2 – Transformer Losses ................................................................................. 23


Electromagnetic Devices-2 http://www.engproguides.com

7.3 Problem 3 - Autotransformer ........................................................................................ 24

7.4 Problem 4 - Autotransformer ........................................................................................ 24

7.5 Problem 5 – Transformer Arrangements ...................................................................... 25

7.6 Problem 6 - Transformer Arrangements ....................................................................... 25

8.0 Solutions .......................................................................................................................... 26

8.1 Solution 1 – Transformer Losses .................................................................................. 26

8.2 Solution 2 – Transformer Losses .................................................................................. 27

8.3 Solution 3 - Autotransformer ......................................................................................... 28

8.4 Solution 4 - Autotransformer ......................................................................................... 29

8.5 Solution 5 – Transformer Arrangements ...................................................................... 31

8.6 Solution 6 – Transformer Arrangements ...................................................................... 32


1 http://www.engproguides.com

SECTION 6

TRANSMISSION & DISTRIBUTION

Transmission & Distribution-1 http://www.engproguides.com

SECTION 6.0 – TRANSMISSION & DISTRIBUTION

Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Transmission Line Analysis ................................................................................................ 4

2.1 Equivalent Circuits .......................................................................................................... 4

2.1.1 Resistance ............................................................................................................... 4

2.1.2 Inductance ............................................................................................................... 7

2.1.3 Capacitance ............................................................................................................ 7

2.1.4 Impedance ............................................................................................................... 9

2.1.5 Short Transmission Line .......................................................................................... 9

2.1.6 Medium Transmission Line ................................................................................... 12

2.1.7 Long Transmission Line ........................................................................................ 16

2.2 Voltage Drop ................................................................................................................. 16

2.3 Voltage Regulation ....................................................................................................... 16

2.4 Power Factor Correction ............................................................................................... 18

2.4.1 Correcting a Lagging Power Factor ....................................................................... 18

2.4.2 Correcting a Leading Power Factor ....................................................................... 19

2.4.3 Power Factor Correction Tables ............................................................................ 20

2.5 Power Quality ............................................................................................................... 23

2.5.1 Harmonics ............................................................................................................. 23

2.6 Power Flow Between Voltage Sources ........................................................................ 25

3.0 Distribution Analysis ......................................................................................................... 26

3.1 Fault Current Analysis .................................................................................................. 26

3.1.1 Symmetrical Faults ................................................................................................ 27

3.1.2 Asymmetrical Faults .............................................................................................. 28

3.2 Grounding Design ......................................................................................................... 32

3.3 Transformer Connections ............................................................................................. 33


4.1 Problem 1 – Power Factor Correction .......................................................................... 34

4.2 Problem 2 – Geometric Mean Distance ........................................................................ 34

4.3 Problem 3 – Voltage Regulation ................................................................................... 35


5.1 Solution 1 – Power Factor Correction ........................................................................... 36



5.2 Solution 2 – Geometric Mean Distance ........................................................................ 37

5.3 Solution 3 – Voltage Regulation ................................................................................... 38



1.0 INTRODUCTION The section, Transmission & Distribution, accounts for approximately 10 questions on the Power Engineering, Electrical PE exam.

Transmission covers the extra-high (>230 kV) and high (115 kV to 230 kV) voltage lines that transport electricity from the electric power plants (generators) to the substations. These lines can travel miles and miles between substations and are typically under the jurisdiction of the electric utility. These transmission lines are also governed by the NES (under Section 11.0 Codes and Standards). The distribution system consists of the medium (69 kV to 2.4kV) and low voltage (600V and less) lines that transmit electricity between substations and also transmit electricity to consumers. These consumers can be residential, commercial voltages at 480V and below. But these consumers can also be industrial at medium voltages (69 kV to 2.4kV). Motors and generators are not included under this section, since they are covered under Rotating Machines. Transformers are also included in a separate section, but are technically covered under Transmission and Distribution. Protection devices are also technically part of Transmission and Distribution but are excluded from this section and are included in its own section.

Transmission Analysis Distribution Analysis

• Transformers • Grounding • Fault current

• Equivalent circuits • Voltage drop • Voltage regulation • Power factor

correction • Power quality



2.0 TRANSMISSION LINE ANALYSIS Transmission lines may seem very simple, since transmission lines are just very long conductors. However, the long length and high voltages on transmission lines make the analysis of transmission lines a little more difficult than a simple wire running from your residential panel to lights. On the PE exam, you should understand the following three parameters of transmission lines, (1) resistance, (2) inductance and (3) capacitance.

Transmission lines are typically constructed of either aluminum or copper. Aluminum conductors are lighter and cheaper, and copper conductors are more expensive and heavier. However, aluminum is less conductive than copper. This means that larger diameter aluminum conductors are needed to transmit the same amount of current than a smaller diameter copper conductor. Conductors are also provided with insulation and possibly strengthening steel to make the conductor more robust.

The purpose of transmission systems and distribution systems is to maintain power at all times and to ensure stable voltage and frequency.

2.1 EQUIVALENT CIRCUITS An equivalent circuit is typically used to understand the three parameters of transmission lines, however before the equivalent circuit is presented, you should first understand the details of the three parameters (1) Resistance, (2) Inductance and (3) Capacitance. Each different transmission line will have an equivalent circuit that consists of these three parameters, which are uniformly distributed the length of the transmission line.

2.1.1 Resistance The first voltage drop is the drop due to resistance in the transmission line. The resistance of the transmission line is directly related to the length and resistivity of the line. The voltage drop is inversely related to the cross sectional area of the line. In addition, the transmission line material will also affect the resistance of the line, which will affect the voltage drop.

𝑅 = 𝑝 ∗𝑙𝐴

Ω

𝑅 = 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (Ω); 𝑝 = 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 (𝑜ℎ𝑚 − 𝑐𝑚𝑖𝑙𝑠);

𝑙 = 𝑙𝑒𝑛𝑔𝑡ℎ (ft);𝐴 = 𝑎𝑟𝑒𝑎 (𝑐𝑚𝑖𝑙𝑠);

𝑋𝑅 = 𝑅∠0°

Make sure you use the correct units for these variables, because the exam may try to confuse you with varying units that require converting. A circular mil is the area of a circle with a diameter of 1 mil, where 1 mil is equal to .001 inches. Sometimes the exam will give you conductor sizes in terms of American Wire Gauge (AWG). AWG is a wire size rating system used in North America and common throughout the NEC. The increasing gauge number corresponds to decreasing conductor diameter. The AWG and corresponding diameters may



appear to be random, but the numbers follow the below formula. Each diameter is a function of the AWG number (N) and the reference point (N = 36), which corresponds to a diameter of 0.005 inches.

𝐷𝐴𝑊𝐺 = 0.005 𝑖𝑛 ∗ 9236−𝐴𝑊𝐺

39

The CMIL, KCMIL and area terms are found with the following equations.

𝐴𝑟𝑒𝑎 (𝑖𝑛2) = �14� ∗ 𝜋 ∗ 𝐷𝑎𝑤𝑔2

𝐴𝑟𝑒𝑎 (𝑐𝑚𝑖𝑙) = 𝐴𝑟𝑒𝑎 (𝑖𝑛2) ∗ �1

𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑐𝑖𝑟𝑐𝑙𝑒 𝑤𝑖𝑡ℎ 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 1 𝑚𝑖𝑙�

1 mil is equal to .001 inches.

𝐴𝑟𝑒𝑎 (𝐾𝐶𝑀𝐼𝐿 𝑜𝑟 𝑀𝐶𝑀) = 𝐴𝑟𝑒𝑎 (𝑐𝑚𝑖𝑙) ∗ (1

1000)

AWG CMIL KCMIL AREA DIAMETER

MM2 IN2 MM IN 36 25.00 0.03 0.0127 0.000019635 0.1270 0.0050 34 39.75 0.03 0.0201 0.000031221 0.1601 0.0063 32 63.21 0.06 0.0320 0.000049643 0.2019 0.0080 30 100.51 0.06 0.0509 0.000078935 0.2546 0.0100 28 159.81 0.16 0.0810 0.000125512 0.3211 0.0126 26 254.11 0.16 0.1288 0.000199572 0.4049 0.0159 24 404.05 0.40 0.2047 0.000317333 0.5106 0.0201 22 642.46 0.40 0.3255 0.000504579 0.6438 0.0253 20 1,021.55 1.02 0.5176 0.000802311 0.8118 0.0320 18 1,624.33 1.02 0.8230 0.001275725 1.0237 0.0403 16 2,582.78 2.58 1.3087 0.002028482 1.2908 0.0508 14 4,106.78 2.58 2.0809 0.003225413 1.6277 0.0641 12 6,530.04 6.53 3.3088 0.005128608 2.0525 0.0808 10 10,383.18 6.53 5.2612 0.008154806 2.5882 0.1019 8 16,509.90 16.51 8.3656 0.012966650 3.2636 0.1285 6 26,251.76 16.51 13.3018 0.020617781 4.1154 0.1620 4 41,741.94 41.74 21.1506 0.032783557 5.1894 0.2043 3 52,635.61 41.74 26.6705 0.041339302 5.8273 0.2294 2 66,372.28 66.37 33.6308 0.052127897 6.5437 0.2576 1 83,693.90 66.37 42.4077 0.065732064 7.3481 0.2893



5.3 SOLUTION 3 – VOLTAGE REGULATION A 3-phase transmission line is measured at no load and full load. It is found that the line to line voltage at full load is 13.8 KV and the line to line voltage is 14 KV at no load. What is the voltage regulation?

𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑅𝑒𝑔𝑢𝑙𝑎𝑡𝑖𝑜𝑛 % =14𝐾𝑉 − 13.8𝐾𝑉

13.8𝐾𝑉∗ 100 = 1.45%

The correct answer is most nearly, (a) 1.5%



SECTION 7

POWER SYSTEM PERFORMANCE

Power System Performance-1 http://www.engproguides.com

SECTION 7.0 – POWER SYSTEM PERFORMANCE Table of Contents

1.0 Introduction ........................................................................................................................ 2

2.0 Power Flow ........................................................................................................................ 3

2.1 Power Flow Basics ......................................................................................................... 3

3.0 Load Sharing ...................................................................................................................... 5

3.1 Parallel Generators ......................................................................................................... 5

3.1.1 Droop Compensation .............................................................................................. 6

3.1.2 Infinite Bus ............................................................................................................... 6

3.2 Parallel Transformers ................................................................................................... 10

3.2.1 Different KVA Transformers .................................................................................. 11

3.2.2 Different Impedance Transformers ........................................................................ 12

3.2.3 Different Impedance and Different KVA transformers ........................................... 13

3.2.4 Different X/R Ratios ............................................................................................... 14

3.2.5 Different Taps, Different Voltage Ratio, Different Turns Ratio............................... 14

4.0 Power System Stability .................................................................................................... 16


5.1 Problem 1 – Parallel Transformers ............................................................................... 17

5.2 Problem 2 – Parallel Transformers ............................................................................... 17

5.3 Problem 3 – Parallel Generators .................................................................................. 18

5.4 Problem 4 – Parallel Generators .................................................................................. 18


6.1 Solution 1 – Parallel Transformers ............................................................................... 19

6.2 Solution 2 – Parallel Transformers ............................................................................... 20

6.3 Solution 3 – Parallel Generators ................................................................................... 21

6.4 Solution 4 – Parallel Generators ................................................................................... 22



1.0 INTRODUCTION The section, Power System Performance, accounts for approximately 6 questions on the Power Engineering, Electrical PE exam.

Power system performance includes topics like power flow, load sharing and stability. These topics are vaguer than the other sections. These topics also involve computer software to complete many of the problems encountered in the actual practice in this field of power engineering. There are some basic concepts that govern these problems that might be tested on the exam, but this guide focuses on the concepts that have a higher probability of being tested.

Also notice that there are only 6 questions on this section, according to the NCEES exam outline. There is less opportunity for the test creator to ask detailed questions because they need to ensure that you have the minimal capability in this vast area of focus within only 6 questions and each question can only take 6 minutes to solve.

Power System Performance 6 questions

Power Flow Load Sharing Power System Stability

• Parallel generators • Parallel transformers

• Voltage drop • Unbalanced loads • Voltage instability



2.0 POWER FLOW In power engineering, power flow is the analysis of the power throughout a system. This analysis tracks voltage magnitude, voltage angle, reactive power and real power throughout the power system. If you can track these items through the equivalent circuits discussed in rotating machines and transformers, then you understand the basics of power flow analysis.

Power flow analysis also tracks the same items in the equivalent circuits for various scenarios like short circuit, fault analysis, harmonic analysis and motor starting. The analysis can get very long and even require iterations, since there will be multiple unknown variables in the system. Therefore, this analysis is always completed through the use of software like Paladin Design Based, which is linked below.

http://www.poweranalytics.com/paladin-software/paladin-designbase/

For the purposes of the exam, power flow analysis is too specific and difficult to test with a 6 minute problem. Thus you should only know the basics of power flow analysis. If you want real life context on power flow and a look at how power flow analysis is conducted in practice, then I suggest you read through these case studies and tutorials from the actual power flow analysis software.

Basic Power Flow Tutorials: http://www.poweranalytics.com/designbase-tutorials/

Power Flow Case Study: http://www.poweranalytics.com/company/pdf/M-12-DB-ADV-X-005-02%20DB%20Case%20Study%20%232%20Power%20Flow%20Analysis-v2r02e.pdf

Advanced Power Flow Guide: http://www.poweranalytics.com/designbase/pdf/Adv_Power_Flow.pdf

2.1 POWER FLOW BASICS When setting up a circuit for power flow analysis on a computer software program you must create buses. Power flow software has a limit on the amount of buses that can be created before the computations become too taxing even for a computer. There are three types of buses used in a power flow analysis: load bus, voltage-controlled bus, and a slack bus. A voltage-controlled bus is defined as a bus that maintains a constant voltage to the system, which is accomplished with a generator. A load bus is anything that isn’t a voltage-controlled bus. The slack bus has a varying voltage that is used to balance the difference between the voltage-controlled buses and the load buses.

In between the buses are the passive elements, like transformers, transmission lines, reactors and capacitors. These elements react to the circuit, but cannot manually affect the circuit. Transformers are modeled with their apparent power, voltage and their impedance. Transmission lines are modeled with their impedance, length and wire size. More detailed transmission lines can also be modeled as short, medium or long in accordance with the Transmission and Distribution section.


http://www.poweranalytics.com/paladin-software/paladin-designbase/

http://www.poweranalytics.com/designbase-tutorials/

http://www.poweranalytics.com/company/pdf/M-12-DB-ADV-X-005-02%20DB%20Case%20Study%20%232%20Power%20Flow%20Analysis-v2r02e.pdf

http://www.poweranalytics.com/company/pdf/M-12-DB-ADV-X-005-02%20DB%20Case%20Study%20%232%20Power%20Flow%20Analysis-v2r02e.pdf

http://www.poweranalytics.com/designbase/pdf/Adv_Power_Flow.pdf


6.0 PRACTICE PROBLEMS

6.1 SOLUTION 1 – PARALLEL TRANSFORMERS Two 1-phase, 480/120V, transformers are arranged in parallel. These transformers have the following ratings, Transformer A – 1,500 KVA, Z = 5% impedance and Transformer B – 1,000 KVA, 4% impedance. What is the total load provided by the transformers, assuming that you cannot exceed the ratings of each transformer?

𝑆𝐴 =1,500

5%1,500

5% + 1,0004%

𝑆𝑠𝑢𝑚; 𝑆𝐵 =1,000

4%1,500

5% + 1,0004%

𝑆𝑠𝑢𝑚

𝑆𝐴 =300550

𝑆𝑠𝑢𝑚; 𝑆𝐵 =250550

𝑆𝑠𝑢𝑚

Let’s try the scenario where Transformer A is maxed out, so SA = 1,500 KVA

1,500 =300550

𝑆𝑠𝑢𝑚 → 𝑆𝑠𝑢𝑚 = 2,750 𝐾𝑉𝐴 𝑎𝑛𝑑 𝑆𝐵 = 1,250 𝐾𝑉𝐴

This scenario does not work, because Transformer B’s capacity is exceeded.

Let’s try the scenario where Transformer B is maxed out, so S2 = 1,000 KVA

1,000 =250550

𝑆𝑠𝑢𝑚 → 𝑆𝑠𝑢𝑚 = 2,200 𝐾𝑉𝐴 𝑎𝑛𝑑 𝑆𝐴 = 1,200 𝐾𝑉𝐴

The total KVA is equal to 2,200 KVA. The correct answer is most nearly, (a) 2,200 KVA



SECTION 8

PROTECTION

Protection-1 http://www.engproguides.com

Section 8.0 – Protection Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Protective (Tripping) Devices ............................................................................................. 4

2.1 Fuses .............................................................................................................................. 4

2.2 Circuit Breakers .............................................................................................................. 4

2.3 Re-closers ...................................................................................................................... 5

3.0 Overcurrent Protection ....................................................................................................... 6

3.1 Short Circuit Current ....................................................................................................... 6

3.1.1 Transformer Fault .................................................................................................... 7

3.1.2 Generator/Motor Fault ............................................................................................. 7

3.1.3 Transmission Line Fault .......................................................................................... 7

3.2 MVA Method ................................................................................................................... 8

3.3 Per-Unit Method ........................................................................................................... 11

3.4 Ohmic Method .............................................................................................................. 12

4.0 Protective Relaying .......................................................................................................... 13

4.1 Relay Types .................................................................................................................. 13

4.1.1 Overcurrent/Undercurrent Relays ......................................................................... 17

4.1.2 Overvoltage/Undervoltage Relays ......................................................................... 17

4.1.3 Directional Relays ................................................................................................. 18

4.1.4 Differential Relays ................................................................................................. 18

4.1.5 Distance Relays .................................................................................................... 19

5.0 Coordination ..................................................................................................................... 21

5.1 Primary Relaying .......................................................................................................... 21

5.2 Backup relaying ............................................................................................................ 22

5.3 Time-Current Coordination Graph ................................................................................ 22


6.1 Problem 1 – Short Circuit Current ................................................................................ 25

6.2 Problem 2 – Differential Relay ...................................................................................... 25

6.3 Problem 3 – TCC .......................................................................................................... 26

6.4 Problem 4 – TCC .......................................................................................................... 27

7.0 Solutions ............................................................................................................................... 28

7.1 Solution 1 – Short Circuit Current ................................................................................. 28

7.2 Solution 2 – Differential Relay ...................................................................................... 29


7.3 Solution 3 – TCC .......................................................................................................... 30

7.4 Solution 4 – TCC .......................................................................................................... 31


4.1.3 Directional Relays A directional relay is used on distribution and transmission lines to distinguish the direction of the fault. There may be multiple overcurrent protection devices in a transmission distribution system. If a fault were to occur, then all of them could potentially trip. By determining the direction of the fault current, the protection devices will know which devices the fault falls in between and the appropriate overcurrent protection devices can be tripped to isolate the fault.

Figure 9: A directional relay is often used to protect a transmission line.

4.1.4 Differential Relays A differential relay consists of multiple circuit transformers (CTs) on either side of a bus or on either side of a transformer. The CTs measure the current going into the bus or transformer and they also measure the CTs leaving the bus or transformer. If the current values leaving and entering are not equal, then the relay will trip the circuit breakers.

Figure 10: A differential relay is often used to protect a busbar as shown in this figure.


7.4 SOLUTION 4 – TCC A TCC is provided below for a relay with multiple time dial settings (1-6). The pick-up current is set for 500 A. Short circuit calculations indicate that there will be a short circuit current of 1,500 A. The relay must operate in 5.5 seconds. Which time dial setting should be used?

The answer is most nearly, (b) TD-2.


SECTION 9

MEASUREMENT & INSTRUMENTATION

Measurement & Instrumenation-1 www.engproguides.com

Section 9.0 – Measurement & Instrumentation Table of Contents 1.0 Introduction ........................................................................................................................ 2

2.0 Instrument transformers ..................................................................................................... 3

2.1 Current Transformers ..................................................................................................... 3

2.2 Potential Transformers ................................................................................................... 4

3.0 Wattmeters ......................................................................................................................... 6

3.1 One-Wattmeter Method .................................................................................................. 6

3.2 Two-Wattmeter Method .................................................................................................. 6

3.3 Three-Wattmeter Method ............................................................................................... 7

4.0 VOM Metering .................................................................................................................. 10

4.1 Voltmeter ...................................................................................................................... 10

4.2 Ammeter ....................................................................................................................... 10

4.3 Ohmmeter ..................................................................................................................... 11

5.0 Insulation Testing ............................................................................................................. 11

5.1 Megger ......................................................................................................................... 11

6.0 Ground Resistance Testing .............................................................................................. 12

6.1 Soil Resistivity Testing .................................................................................................. 12

6.2 Fall of Potential Method ................................................................................................ 13

6.3 Additional Grounding Factors ....................................................................................... 14


7.1 Practice Problem 1 – Current Transformer ................................................................... 15

7.2 Practice Problem 2 – Potential Transformer ................................................................. 15

7.3 Practice Problem 3 – Wattmeters ................................................................................. 16

7.4 Practice Problem 4 - Wattmeters .................................................................................. 16

7.5 Practice Problem 5 – Ground Resistance Testing ........................................................ 17

8.0 Solutions .......................................................................................................................... 18

8.1 Solution 1 – Current Transformer ................................................................................. 18

8.2 Solution 2 – Potential Transformer ............................................................................... 18

8.3 Solution 3 – Wattmeters ............................................................................................... 19

8.4 Solution 4 – Wattmeters ............................................................................................... 20

8.5 Solution 5 – Ground Resistance Testing ...................................................................... 21


4.3 OHMMETER An ohmmeter measures the resistance of a circuit. An ohmmeter consists of a voltage supply that is applied to the circuit. In response to the voltage supply, a current will be produced, which is then measured by the ammeter. Since the voltage and current are known, the resistance can be calculated.

5.0 INSULATION TESTING The purpose of insulation on conductors, transformers, generators, motors, etc. is to ensure that current travels through the conductor and does not create a potential difference between the metal part of the conductor or equipment and anything else. For example, if a conductor is carrying 480 V and its insulation exposes the metal part of the conductor, then there will be a potential difference of 480 V and the air, with little impedance. If a person walks near a conductor then the potential difference between the exposed metal and the person will be 480 V. If the distance between the two is minimal then current will arc from the exposed metal conductor to the person. If the voltage is much larger, like 13.8 KV then the person could be a further distance away and current will still arc to the person.

Insulation in power systems will fail over time, and as it fails there will be unsafe conditions as previously discussed. Maintenance personnel use mega-ohmmeters to test insulation to ensure that the insulation meets safe code requirements. On the PE exam, you should be familiar with this device and the code requirements for insulation.

5.1 MEGGER A megaohmmeter is most often called a megger. The name of this device gives you a clue as to its purpose. A megger consists of two leads that are connected to a conductor and the insulation protecting the conductor. Next, the megger induces a large voltage, typically the rated voltage of the conductor being tested. The megger measures the current through the device and uses the known applied voltage to determine the resistance of the circuit. This resistance is typically on the order of 1-10 mega-ohms, hence the name megaohmmeter.


6.0 GROUND RESISTANCE TESTING One of the best sources for ground resistance testing and also grounding design is IEEE. It is recommended that you have IEEE 81 as a reference or to learn more about grounding.

6.1 SOIL RESISTIVITY TESTING The first thing that should be tested when designing a grounding system or when testing a grounding system is the soil resistivity. The various manufacturers of soil resistivity equipment testers like Fluke have whitepapers on the process of testing soil resistivity. This information is very good to get a practical idea of how soil resistivity is conducted, if you do not regularly conduct soil resistivity tests.

For the exam, you should be familiar with the following equation and the basic idea of soil resistivity resting. In a soil resistivity test, conductors are driven into the ground at certain distances and these conductors are connected to a voltage supply (soil resistivity tester). Then a known current is run through the test conductor and the voltage difference between two points will provide a quick calculation for the resistivity of the soil in between the driven conductors. The most common method of testing is the four-point method, which is shown in the figure below.

Figure 6: Ground resistance testing with four-point method

𝑝 = 2𝜋 ∗ 𝐷 ∗ 𝑅

𝑝 = 𝑠𝑜𝑖𝑙 𝑟𝑒𝑠𝑖𝑠𝑡𝑖𝑣𝑖𝑡𝑦 (𝑓𝑡 − 𝑜ℎ𝑚𝑠);𝐷 = 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑓𝑡)

𝑅 = 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑜ℎ𝑚𝑠) → 𝑅 =𝑉𝐼

You can only use the previous equation when D is sufficiently larger than B, on the order of 20 times B.

𝐷 > 20𝐵


SECTION 10

SPECIAL APPLICATIONS

Special Applications-1 http://www.engproguides.com

Section 10.0 – Special Applications Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 Lightning & Surge Protection ............................................................................................. 4

2.1 Design Standards ........................................................................................................... 4

2.2 Risk Assessment ............................................................................................................ 4

2.3 Lightning Protection Systems ......................................................................................... 5

2.3.1 Elevated Strike Device ............................................................................................ 6

2.3.2 Conductors Connecting Strike Device and Grounding System ............................... 6

2.3.3 Grounding System ................................................................................................... 6

2.4 Lightning Protection Design and Surge Protection ......................................................... 7

3.0 Reliability ............................................................................................................................ 8

4.0 Illumination engineering ................................................................................................... 10

4.1 Basics ........................................................................................................................... 10

4.2 Lumen Method or Zonal Cavity Method ....................................................................... 11

4.2.1 Determine Cavity Ratio ......................................................................................... 12

4.2.2 Determine Effective Cavity Reflectance ................................................................ 13

4.2.3 Select Coefficient of Utilization .............................................................................. 13

4.2.4 Compute Average Illuminance Level ..................................................................... 13

4.3 Point to Point Method ................................................................................................... 14

5.0 Demand and Energy Management/Calculations .............................................................. 16

5.1 Demand Factor ............................................................................................................. 16

5.1.1 Utility Company Demand Factor Perspective ........................................................ 16

5.1.2 Customer Demand Factor Perspective ................................................................. 18

6.0 Economic Analysis ........................................................................................................... 19

6.1 Interest Rate & Time Value of Money ........................................................................... 19

6.2 Annual Value/Annuities ................................................................................................ 20

6.3 Equipment Type Questions .......................................................................................... 22

6.4 Convert to Present Value ............................................................................................. 23

6.5 Convert to Future Value ............................................................................................... 24

6.6 Convert to Annualized Value ........................................................................................ 24

6.7 Convert to Rate of Return ............................................................................................. 25

6.8 Factor Tables ................................................................................................................ 26



7.1 Problem 1 - Lighting ..................................................................................................... 27

7.2 Problem 2 - Lighting ..................................................................................................... 27

7.3 Problem 3 - Economics ................................................................................................ 28

7.4 Problem 4 - Economics ................................................................................................ 28

8.0 Solutions .......................................................................................................................... 29

8.1 Solution 1 - Lighting ...................................................................................................... 29

8.2 Solution 2 - Lighting ...................................................................................................... 30

8.3 Solution 3 - Economics ................................................................................................. 31

8.4 Solution 4 - Economics ................................................................................................. 32


6.3 EQUIPMENT TYPE QUESTIONS In the Power Engineering field, often times the engineer must develop an economic analysis on purchasing one piece of equipment over another. In this event the engineer will use terms like present value, annualized cost, future value, initial cost and other terms like salvage value, equipment lifetime and rate of return.

Salvage value is the amount a piece of equipment will be worth at the end of its lifetime. Lifetime is typically given by a manufacturer as the average lifespan (years) of a piece of equipment. Looking at the figure below, initial cost is shown as a downward arrow at year 0. Annual gains are shown as the upward arrow and maintenance costs and other costs to run the piece of equipment are shown as downward arrows starting at year 1 and proceeding to the end of the lifetime. Finally, at the end of the lifetime there is an upward arrow indicating the salvage value.

As previously stated, the most important thing in engineering economic analysis is to convert all monetary gains and costs to like terms, whether it is present value, future value, annual value or rate of return. Each specific conversion will be discussed in the following sections.

Each of the sections will use the same example in order to illustrate the difference in converting between each of the different terms.


SECTION 11

CODES & STANDARDS

Codes & Standards-1 http://www.engproguides.com

Section 11.0 – Codes & Standards Table of Contents 1.0 Introduction ........................................................................................................................ 3

2.0 National Electric Code 2014 ............................................................................................... 4

2.1 Additional Resources .......................................................................................................... 4

2.1.1 Color Coded EZ Tabs for the 2014 National Electric Code .......................................... 4

2.1.2 Key Word Index ............................................................................................................ 5

2.2 Chapter 1: General ........................................................................................................ 6

2.3 Chapter 2: Wiring & Protection ...................................................................................... 6

2.3.1 Article 220 Load Calculations .................................................................................. 7

2.3.2 Article 240 Overcurrent Protection .......................................................................... 7

2.3.3 Article 250 Grounding .............................................................................................. 7

2.4 Chapter 3: Wiring Methods & Materials ......................................................................... 8

2.4.1 Tables 310.15 & 310.60 Set .................................................................................... 9

2.5 Chapter 4: Equipment for General Use ....................................................................... 10

2.5.1 Article 430 Motors, Motor Circuits and Controllers ................................................ 10

2.5.2 Article 450 Transformers ....................................................................................... 13

2.6 Chapter 5: Special occupancies .................................................................................. 14

2.6.1 Article 500 – Hazardous Locations ........................................................................ 14

2.7 Chapter 6: Special Equipment ..................................................................................... 16

2.8 Chapter 7: Special Conditions ..................................................................................... 17

2.9 Chapter 8: Communication Systems ........................................................................... 17

2.10 Chapter 9: Tables ........................................................................................................ 18

2.10.1 Table 8 & 9 Conductors ......................................................................................... 18

3.0 National Electric Safety Code .......................................................................................... 19

3.1 2017 National Electrical Safety Code© (NESC©) .......................................................... 19

3.2 Outline .......................................................................................................................... 19

3.3 Part 1: Electric supply stations and equipment ............................................................ 19

3.4 Part 2: Overhead electric supply and communication lines ......................................... 20

3.5 Part 3: Underground electric supply and communication lines .................................... 20

3.6 Part 4: Rules for the operation of electric supply and communication lines and equipment ................................................................................................................................ 21

3.7 Appendices ................................................................................................................... 21

4.0 Electrical safety ................................................................................................................ 22


4.1 NFPA 70E – Standard for Electrical Safety in the Workplace ...................................... 22


5.1 Problem 1: Conductor Size ........................................................................................... 23

5.2 Problem 2: Locked-Rotor Current ................................................................................. 23

5.3 Problem 3: Voltage Drop .............................................................................................. 24

5.4 Problem 4: Overload Device ......................................................................................... 24

5.5 Problem 5: Disconnect Switch ...................................................................................... 25

6.0 Solutions .......................................................................................................................... 26

6.1 Solution 1: Conductor Size .......................................................................................... 26

6.2 Solution 2: Locked Rotor Current ................................................................................ 27

6.3 Solution 3: Voltage Drop .............................................................................................. 28

6.4 Solution 4: Overload Device ......................................................................................... 29

6.5 Solution 5: Disconnect Switch ...................................................................................... 30


1.0 INTRODUCTION Codes & Standards accounts for approximately 10 questions on the Electrical & Computer Power PE exam.

The codes and standards section of the exam is the section where most people do well on the exam. Many of these questions simply test your familiarity with the NEC and NESC. You should be well prepared to go to any section in the book, although some sections of the codes are more used than others. The most common questions are highlighted in this section of the book. Also included in this section is a technique that you can use to quickly navigate to the correct part of the code to answer a question on the exam. This technique involves memorizing the format of the book, such that if you are given a certain type of code question, you will know exactly what section to look at in the book.

Codes & Standards 10 questions

National Electric Code (NEC)

• Resources • Outline • General • Wiring & protection • Wiring methods &

materials • Equipment for

general use • Special occupancies • Special equipment • Special conditions • Communication

systems • Tables

National Electrical Safety Codes (NESC)

• Resources • Outline • Electric supply

stations and equipment

• Overhead electric supply and communication lines

• Underground electric supply and communication lines

• Appendices

Electric Shock and Burns

• OSHA • Arc flash


2.6 CHAPTER 5: SPECIAL OCCUPANCIES This chapter covers the safety requirements for the installation of electrical requirement in various occupancies. These occupancies range from farming to aircraft hangars and from hospitals to gas stations. It would be unreasonable to test on the requirements of a mobile home park due to its limited and specific use, but it would not be unreasonable to test on the general hazardous locations requirements. Thus you should be familiar with the types of occupancies that are covered in the NEC, but you should not spend time reading into the verbiage of each type of occupancy, except for the general hazardous location requirements.

• Article 500 - Hazardous Locations, Classes I, II and III, Division 1 and 2

• Article 518 - Assembly Occupancies

• Article 501 - Class I Locations • Article 520 - Theaters, Audient Areas of Motion Picture and Television Studios, Performance Areas and Similar Locations

• Article 502 - Class II Locations • Article 522 - Control Systems for Permanent Amusement Attractions

• Article 503 - Class III Locations • Article 525 - Carnivals, Circuses, Fairs and Similar Events

• Article 504 - Intrinsically Safe Systems • Article 530 - Motion Picture and Television Studios and Similar Locations

• Article 505 - Zone 0, 1 and 2 Locations • Article 540 - Motion Picture Projection Rooms

• Article 506 - Zone 20, 21 and 22 Locations for Combustible Dusts or Ignitable Fibers/Flyings

• Article 545 - Manufactured Buildings

• Article 510 - Hazardous Locations - Specific

• Article 547 - Agricultural Buildings

• Article 511 - Commercial Garages, Repair and Storage

• Article 550 - Mobile Homes, Manufactured Homes and Mobile Home Parks

• Article 513 - Aircraft Hangars • Article 551 - Recreational vehicles and Recreational Vehicle Parks

• Article 514 - Motor Fuel Dispensing Facilities

• Article 552 - Park Trailers

• Article 515 - Bulk Storage Plants • Article 553 - Floating Buildings

• Article 516 - Spray Applications, Dipping, Coating and Printing Processes Using Flammable or Combustible Materials

• Article 555 - Marinas and Boatyards

• Article 517 - Health Care Facilities • Article 590 - Temporary Installations

2.6.1 Article 500 – Hazardous Locations • Class I – These locations are defined as locations where flammable gases or vapors

may be present in concentrations sufficient to facilitate explosions or to ignite. The designation of a location as Class I or non-hazardous is usually conducted by a Fire


6.5 SOLUTION 5: DISCONNECT SWITCH A 20-hp, three-phase, induction motor is operated at 230 V. The motor has a service factor of 1.15 and is a code letter B. What is the minimum size of a separate motor disconnect switch? Assume that there is already a circuit breaker and this is a separate motor disconnect switch.

Stationary Motors (<1/8 HP) Use branch circuit OCPD Stationary Motors (<2 HP) 2X FLC or FLC/0.8 or HP rating of motor Motors (<1,000 V) 115% of FLC rating of motor Horsepower Rating FLC Rating (430.248, 249 or 250) and LRC

Rating (430.251A & B) Ampere Rating 115% of FLC

Since the answers are looking for the ampere rating, you can use the equation 115% of the FLC.

The full load current can be found in Table 430.250.

𝐷𝑖𝑠𝑐𝑜𝑛𝑛𝑒𝑐𝑡 𝑆𝑤𝑖𝑡𝑐ℎ 𝐴𝑚𝑝𝑒𝑟𝑒 𝑅𝑎𝑡𝑖𝑛𝑔 = 115% ∗ 54𝐴 = 62.1 𝐴

You may be asked for the horsepower rating, which may differ for the various types of disconnect switches in practice. However, for the purposes of the exam, you should only be concerned about the specific rating asked for in the question.

The correct answer is most nearly, (c) 63A.


SECTION 12

CONCLUSION

Conclusion -1 http://www.engproguides.com

12.0 CONCLUSION If you have any questions on this book or any other Engineering Pro Guides product, then please contact me at my email below. Also if you are looking for more exam problems, then please visit the website and purchase the sample exam. In addition, the website has a bunch of free information that you can use to facilitate your studying.

Justin Kauwale at [email protected]

Hi. My name is Justin Kauwale, the creator of Engineering Pro Guides. I will be happy to answer any questions you may have about the PE exam. Good luck on your studying! I hope you pass the exam and I wish you the best in your career. Thank you for your purchase!

mailto:[email protected]


SECTION 13

CHEAT SHEETS

1http://www.engproguides.com

Section 1.0 - Basic/Common Equations

Term Equation Description Waveforms Max Voltage 𝑉𝑚𝑎𝑥

Root Mean Square Voltage

𝑉𝑟𝑚𝑠 =𝑉𝑚𝑎𝑥

√2

Average Voltage 𝑉𝑎𝑣𝑔 =2 ∗ 𝑉𝑚𝑎𝑥

𝜋

Square Wave RMS 𝑉𝑟𝑚𝑠 = 𝑉𝑚𝑎𝑥

Triangle/Sawtooth Wave RMS 𝑉𝑟𝑚𝑠 =𝑉𝑚𝑎𝑥

√3

Waveform RMS 𝑋𝑟𝑚𝑠 =1

𝑇2 − 𝑇1� 𝑓(𝑡)2

𝑇2

𝑇1

Power, Circuits

Apparent Power

𝑆 = 𝑃 + 𝑗𝑄

𝑆 =𝑉2

𝑍= 𝐼𝑉 =

𝐼2

𝑍


Section 8.0 – Protection Equations

Overcurrent Protection Protection Engineers that work for utility companies design protection systems as their full time job. There are many intricacies in this job, but for the PE exam you should only know the basics. Transmission lines end at circuit breakers. Transmission line impedances are about 1 ohm per mile. The impedance depends on many factors like conductor type, spacing, length and number of conductors. Underground transmission lines and overhead transmission lines. Short circuits can be caused by many things like lighting, wind, corrosion, fatigue, accidental contact, trees. The protection system must be able to isolate the faults, clear faults and then continue normal operation. Transformer faults.

Transformer: Phase to Ground Fault

Primary 𝐼𝐴 = 0

𝐼𝐵 = 0.577 ∗ 𝐼𝑃𝐻−𝐺𝑅 𝐼𝐶 = 0.577 ∗ 𝐼𝑃𝐻−𝐺𝑅

Secondary 𝐼𝑎 = 𝐼𝑃𝐻−𝐺𝑅

𝐼𝑏 = 0 𝐼𝑐 = 0

Transformer: Three-Phase Fault

Primary 𝐼𝐴 = 𝐼3𝑃𝐻 𝐼𝐵 = 𝐼3𝑃𝐻 𝐼𝐶 = 𝐼3𝑃𝐻

Secondary 𝐼𝑎 = 𝐼3𝑃𝐻 𝐼𝑏 = 𝐼3𝑃𝐻 𝐼𝑐 = 𝐼3𝑃𝐻

Transformer: Phase to Phase Fault

Primary 𝐼𝐴 = 0.5 ∗ 𝐼3𝑃𝐻

𝐼𝐵 = 𝐼3𝑃𝐻 𝐼𝐶 = 0.5 ∗ 𝐼3𝑃𝐻

Secondary 𝐼𝑎 = 0

𝐼𝑏 = 0.866 ∗ 𝐼3𝑃𝐻 𝐼𝑐 = 0.866 ∗ 𝐼3𝑃𝐻

Protective Devices

Re-closers

Re-closers can trip (interrupt) the flow of current and it can also close (recconnect) the flow of current. The tripping operation is powered by the fault current and closing operation Is powered by a transformer on the source side of the re-closer.

Circuit Breakers

Circuit breakers can automatically and manually interrupt the flow of current in a circuit. Circuit breakers trip based on a relay or signal. Circuit breakers are tripped from an external, independent power source. The circuit breaker can be closed by the same power source.

Fuses Fuses detect and trip circuits through an element that opens based on increased heat. Fuses can not be closed after it trips the circuit.


Section 11.0 - Codes and Standards

Term Equation Description National Electrical Code (NEC) Chapter 1 Definitions, general requirements and clearances. Chapter 2: Wiring & Protection: Identification, branch, feeders, service, OCP, grounding, surge arresters and protective devices

Article 215.2 Minimum Feeder Size (<600 Volts) shall be larger of:

a) 125% of continuous/non-continuous loads b) Max load served after adjustment/correction factors

Article 220 Branch, feeder and service load calculations

Article 240 Overcurrent Protection

• Part I-VII (≤1000 Volts) • Part VIII (>1000 Volts)

Article 250 Grounding and Bonding Article 250.53 Grounding Electrode Installation Article 250.122 Equipment Grounding Conductor Size TABLE Chapter 3: Wiring Methods & Materials: Wiring methods and materials, cables, conduits, raceways, wireways, cable trays, busways Article 310 Conductors

Table 310.15

Conductor ampacity rating, T, Size, Type (<2,000 Volts) Table 310.15(B)(16-21) – Ampacities allowed per conductor size

• 310.15(B)(2) – Temperature Correction Factor • 310.15(B)(3) – Additional Conductor Correction Factor

Table 310.60 Conductor ampacity rating, T, Size, Type (>2,000 Volts) Chapter 4: Equipment for General Use: Cords, cables, switches receptacles, panels, lighting, switchgear, appliances, electric heating, A/C, motors, generators, transformers, resistors, reactors, capacitors and batteries.

Article 430

Motors, Motor Circuits and Controllers • Motor Feeder - Short-Circuit and Ground Fault Protection: 430.61 - 430.63 • Motor Disconnect: 430.101 – 430.113 • Motor Branch - Short-Circuit and Ground Fault Protection: 430.52 • Motor Overload Protection: 430.31 through 430.44 • Motor Ampacity and Motor Rating Determination: 430.6

Article 430.6 Ampacity and motor rating determination Article 430.7 Locked rotor indicating code letters

Article 430.22 Conductors (Single Motor)

• 1.25*FLA, FLA from 430.6(A)(1) [Table 430.247-250] or 430.22(A)-(G)

Article 430.24 Multiple motors and loads

• Example on 430.28 Article 430.32 Continuous Duty Motor – Overload Protection, Thermal Protector Sizing

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