Whether you are new to the industry or are well seasoned and want to review some of the basic information that you learned in the past, these courses and lessons will clearly outline what you are looking for. “Power Systems Electric” is On-Line training that bridges the gaps between textbook theories and practical power systems experience. As a retired electrical engineer who has gone through the experience of developing a career in electrical power systems, I know how frustrating it can be to try and find the answers, so I put together these courses that I feel would have been a major help to me in my development. I have also taken suggestions from students of what they would like to see in addition to these courses which I have given live in person.

Basic Electrical Learning

For those new to the industry, there is a beginner’s group of courses that cover the “Fundamentals of Electricity ” including DC and AC Circuit Analysis. These lessons examine such basics as Ohm’s Law, Series, and Parallel Circuits. The first, and perhaps most important, relationship between current, voltage, and impedance, “Ohm’s Law”, and its relevance to Series and Parallel Circuits. Subsequently, this will lead to the development of Kirchhoff’s Laws as they help to further analyze Network Analysis & Metering Circuits.

Conductors and Insulators are investigated along with their connected components, Capacitors, Inductors, and how they are influenced by Electromagnetism.

Alternating Current (AC – an electric current that periodically reverses direction) is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans, and electric lamps into a wall socket.

The abbreviations AC and DC are often used to mean simply alternating and direct, as they are applied to current or voltage.

These AC courses deal specifically with sinusoidal waveforms and will provide the student with the basic understanding of working with circuits involving Alternating Current, which includes sinusoidal waveforms, vectors & phasors, reactance & impedance of R,L,C circuits, as they relate to the basic laws and theorems of electricity. This includes working with AC Power, Power Factor, Resonance, Complex Numbers, Reactance, and Impedance

Advanced Electrical Learning

These Courses involve subjects such as “Short Circuit Analysis for HV Three-Phase Systems ” which introduces the student to the basic concepts of fault studies on a high voltage three-phase system. System modeling is then used in order to aid in this process, with the ability to move between asymmetrical and symmetrical systems. With hey Searle and extensive study of “Per Phase” & “Per Unit” methodologies system faults are analyzed with the use of symmetrical components.

“A Per-Unit System ” is the expression of system quantities as fractions of a defined base unit quantity. Calculations are simplified because quantities expressed as per unit do not change when they are referred from one side of a transformer to the other.

In these courses, you will learn exactly what Per Unit Analysis is, the main advantages of using it, how manufacturers of equipment use and rate their products, and the technique of converting to and from the Per Unit system.

Several examples of working with Per Unit are demonstrated in this crisp clear presentation. When you finish you will have a though understanding of this subject.

It is important for all power engineers and technicians to be familiar with the concept of Per Unit as it is being used and referred to every day in power flow, short circuit evaluation, and motor starting studies.

The method of “Symmetrical Components ” is used to simplify asymmetrical three-phase voltages and current analysis by converting the unbalanced system into two sets of balanced phasors and a set of single-phase phasors, or symmetrical components. These sets of phasors are called the positive, negative, and zero sequence components.

An understanding of this method is essential for the understanding of fault analysis and modern-day protection schemes. These courses will provide you with the knowledge to comprehend the concept and how it is applied.

Supplemental Electrical Lessons

In all power electrical analyses, the student will encounter special Trigonometric and Mathematical identities and equations. This site contains special supplemental lessons that zero in on those identities and equations. For example, there are lessons that take you from the “Fundamentals of Trigonometry ” to the more sophisticated requirements in electrical engineering. As you work and study in electrical engineering you are going to run into proofs and equations that are based on trigonometry. A good example of this is when studying AC current, voltage, and impedance calculations, phasors or vectors are used and combined mathematically. Further adventures into complex power will also require a knowledge of trig functions and identities. As a student of this course, you will be introduced to these or at least re-introduced to these that may have been long since forgotten.
In mathematics, “The Derivative of a Function ” of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object’s velocity: this measures how quickly the position of the object changes when time advances.

Specialized Electrical Lessons

Specialized lessons include the “Protection & Control(P & C)” principles of high voltage stations. HV Bus Differential Protection is studied along with restrictions due to CT saturation & mismatch and its solution, “Restraint Differential Protection”.

High Voltage Circuit Breakers are examined as to the various Types (Oil, Vacuum, Air Blast, SF6), their Controls as well as the introduction of potential transformers & current transformers, and their use in conjunction with the relevant instruments such as ammeters, voltmeters, watt meters, and energy meters.

Other lessons include the study of “Transformers ” including core construction along with losses, cooling, and mitigation techniques. Three-phase transformer configurations are studied along with harmonic distortion, CT saturation, and on-load tap-changer problems and how these problems are dealt with. Over-current and restraint differential transformer protection is developed along with a look at some examples of ” Old School relays” as well as modern IDE (intelligent Electrical Devices) relays.

Transformer Connections: (Y – Y; Delta – Delta; Y – Delta; Delta – Y & Y – Zag Zig) are examined along with Transformer Clock System Vector Nomenclature.

Lastly, there is a special section dedicated to “Single and Three-Phase Metering “, including old analog and new digital kilowatt-hour meters.

Conclusion

Regardless of whether or not you are new to the industrial power system, you’ll find what you’re looking for on this site in the way of training. In order to review or select any of these courses, left-click on any of the blue highlighted hyperlinked words of this posting or on “14 Courses Available” from the top menu of the landing page. All of the courses have a free introduction

As a bonus and in the way of a thank you, for your interest in PSPT’s WEB (and Blog) page, I’m making available my 50-page “Electrical Power” crib sheets. These were prepared for use with my courses that are available on this site. There is one section associated with each course and is extremely valuable while viewing the course, as well as a recall of the pertinent formulas and information after the fact. The contained information is also useful during any technical career as a quick reference from time to time. Simply click here or on the picture to the right to be taken to where you can download this item.

October 16, 2022

Blog #11 - Basic Rules & Formulas

October 16, 2022/ Graham VanBrunt

This blog is designed to give, the “do-it-yourselfer”, an introduction to the low-voltage electrical wiring found in residential homes. Most of it applies to any installation that uses a 120/240 AC volt supply. Of course, there are numerous permutations and combinations involved, but this blog will explain the most used, and generally familiar to the public. It is designed around the National Electric Code, (NEC) but codes vary, depending on where you are in North America, and indeed, the world. As a disclaimer, I am going to say that some of the wiring and some of the statements may not apply to local electrical codes. In order to be sure, the reader should check with the local authorities first, prior to changing any wiring in their homes. At the very least, this blog will provide a starting point for the aspiring student.

Reviewing the Basic Rules of Electricity, I am going to start with direct current circuits, and then very quickly move to AC circuits which are the type that is found in residential homes. All direct current electrical elements form electric circuits, and current will flow from positive to negative in a circular fashion around a loop. All electric circuits have Voltage, Current and Resistance (For the present time we are going to consider only resistive loads for simplicity). These three quantities are related by Ohm's law. which states that the current in a circuit will very, directly as the voltage and inversely as the resistance in the circuit.

In this illustration, current will flow in a circuit formed by the wires connecting the battery through the lightbulb back to the battery. The voltage of the source equals the voltage drop across the lightbulb in this case and let's say, it was 120 Volts.

Of course, batteries don't operate household systems. It is AC current, which is changing polarities, 60 times a second. This illustration is showing what a lightbulb might look like if the polarities were changing at 1.6 times a second. As you can see, the oscillations are very visible. A fact which is not at all acceptable.

Now, if we speed up the AC source to 60 cycles a second, the filament in the lightbulb does not get a chance to cool in between the cycle changes, hence the light looks like it's on steady. which indeed it is. The use of AC is mainly because it allows for voltage transformation. That is, to be stepped up, and transferred over long distances, and then, stepped down, to lower levels, to make it useful, and safe within homes.

The book is one of a kind in that it teaches the concepts of basic electricity in a way that is clear, concise, and very easy to understand. It forms an excellent foundation for those who wish to proceed from the basics to more advanced topics.

Numerous illustrations are included to simplify learning both theories and their applications. Direct-current and alternating-current devices and circuits are explained in detail. Magnetism, as well as motors and generators are

Let’s have a closer look at this changing polarity of 60 times a second. If we plot the voltage over time. one and a half seconds, you can see that it starts at “0”. rises to a maximum, then reduces back to “0”, and proceeds to a negative maximum. then goes back to “0” again. It repeats itself every one-sixtieth of a second. It does this in what is called a “sinusoidal” shape…as you see here.

For simplicity, we will assume that most loads are resistive in homes. (lightbulbs, baseboards, electric heaters, electric stoves, ovens, etc.). Therefore, the instantaneous current, in the circuit (shown here in red) will follow the voltage, and it too will be “sinusoidal” in shape. We say that the current is “in-phase “ with the voltage.

The question now becomes. How do we describe this sinusoidal voltage and current, if it is continuously changing? There are several ways.

We can measure and compare the amplitude or peak, as you see here. Another way is to measure and compare the peak to peak…. still, another way is to average the curve, but that would just be “0”. not too useful, unless we squared the value first, then found the square root. This would essentially change the shape of the curve, to look like all positive going curves above the zero line.

Now, we could average the value of this voltage, or current, and it would be a positive value, and greater than “0”. This value is known as the “Root-Mean-Square”, or RMS value of the voltage and current. It is exactly the square root of 2. or 0.707 times the peak value.

This averaging is the equivalent of shaving off the peaks of the curve above the RMS line, which would exactly fill the space between the curves below the RMS line.

This may seem like a bit of mathematical manipulation, however as it turns out, it is very useful in calculating the average power, and energy. And as a matter of fact, all AC current and voltages are measured in RMS values and all meters, voltmeters, ammeters, and multi-meters, unless otherwise stated, are registered in RMS values.

If you have a closer look at the RMS quality of the voltage over time, it is exactly what the DC voltage would look like, and in fact, RMS values are often referred to as the DC equivalent of AC voltage and current.

As I said, RMS values of current and voltages are used in calculating the average power, and energy. The power draw that a load, such as a lightbulb takes from the circuit, is expressed in watts. A load’s power rating is usually marked on the device, such as a lightbulb, and in this case, it is a 100 Watt bulb.

The power in watts consumed by a load is given by the current x voltage (using RMS values) or W = I x V where I is the current through the load, and voltage is the measured voltage drop across the load. Because the current in a circuit is equal to the voltage divided by the resistance we can rewrite the equation for watts, in either of the following two ways.

1) Watts = Current Squared times Voltage

2) Watts = Voltage Squared divided by the Load Resistance

As a final note, the standard symbol for an AC generator is not a two-ended battery, but a simple circle with a sinusoidal wave-shape in the middle.

Quite often, we have to calculate the current that a specific load will draw, given its rating in watts and we know the connected voltage. In that case, we will use the first equation re-written as…the current equals the rating in watts divided by the applied voltage. For example, if the load were a 100 watt incandescent light bulb and we know that the connected voltage is 120 Volts. Then the connected current is, 100 divided by 120 or 0.83 Amps.

Now if the load were not a 100 watt incandescent light bulb, but a 1 kilowatt heater. Then the connected current is 1000 divided by 120 or 8.33 Amps

Keeping the load of a 1 kilowatt heater changing its voltage rating and the connected voltage to 240 Volt. Then the connected current is, 1000 divided by 240. Which will drop the current to 4.17 Amps. At first glance, this might seem contradictive, in that we doubled the voltage, and you would think that we would double the current. however, the 1000 watt heater would have to be rated at 240 Volts. That is to say, that the load will consume 1000 Watts when connected to 240 Volts. Therefore, the connected current is given by, the rated power, 1000, divided by, the rated voltage 240.

Generally speaking, any AC circuit is made up of an AC Source. and load, usually a resistive load, which causes a current to flow. For example, let's say the voltage is 110 volts, and the load is 11 ohms. Ohm’s law tells us that the magnitude of the current is V divided by R or 110 divided by 11. Which equals 10 Amps. The power consumption can now be calculated 3 ways:

1) Voltage times the current…10 times 110 or 1100 Watts.

2) Current squared times the resistance or 100 times 11. Which is 1100 Watts.

3) Voltage square divided by the resistance. Which is 12,100 divided by 11 or 1100 Watts.

So far we have been dealing only with resistive loads. Which works the same for DC as well as AC power. However, there are 3 major types of linear loads, resistors, inductors, and capacitors. When dealing with capacitive and inductive loads, we have to be aware of the phase shift of the current that is introduced. Without going into details when dealing with these types of loads we have to look at the load as impedance, which will shift the current from the voltage, depending on the type of impedance, (capacitive or inductive). Also, we have to be certain that we are using RMS values for these loads, current, and voltage. In most cases we are not concerned about the phase shift when doing low-voltage wiring, however, we should be aware that some loads may cause the current to phase shift.

In order to understand some of the wiring techniques, we should first have a peek inside the main breaker panel. Power from the utility enters in the form of two hot wires, and one neutral, arriving into the breaker panel. The neutral is connected to a neutral busbar. This bus bar contains several screws that can receive outgoing neutral connections. One of the hot connections is connected to a hot bus bar, let's call it “A”. The voltage of this bus bar is 120 Volts RMS, with respect to the neutral. The outgoing current limiting devices, (breakers), are connected here.

The other hot connection is connected to a second hot bus bar, let's call it “B”. The voltage of this bus bar is also120 Volts RMS with respect to the neutral. The case of the main breaker panel is grounded, and these ground connections are connected to a ground bus bar. This bus bar contains several screws, that can receive outgoing ground connections.

Inside this breaker panel, the ground bus bar is connected to the neutral busbar. This is called “bonding”. Bonding is the process of joining metal enclosures, equipment, raceways, metal water piping, gas piping, structural steel, and the like, together. Bonding items together, and connecting the bonded items to an equipment grounding conductor, places everything at the same potential, in this case, the neutral, and ensures an effective ground-fault current path, in the event of a ground fault occurring in an electrical system circuit. A Bonding Bar ensures that the neutral is at ground potential.

Lastly, there are two metal tracks that will hold one end of the breaker, the other end snaps and connects to the “hot” bus bar.

This is a more realistic picture of a power panel, using breakers. I've indicated where the hot leads and neutral are coming from, ultimately the utility. There is a couple of things to note with this power panel.

There is no main breaker, which probably means, this is a sub-panel being fed from the main breaker panel, and because the neutral lead from the utility is connected to only one neutral bus bar, in this example, on the right-hand side, there is a jumper, to connect it to the bus bar on the left hand side of the panel. This is usually a built-in connection of the power panel.

Looking at the incoming connections from the utility and measuring the voltages over time. Remember, voltage is a measurement of the potential difference between two points. Let’s measure that voltage, between the hot terminal “A” with respect to the neutral. As you see, it rises to a maximum of 120 Volts positive, then returns to zero and goes to -120 Volts and back to zero and repeats itself. It will do this 60 times a second.

Let’s repeat the measurement, this time, of the hot terminal “B", with respect to the neutral. As you see it goes to a maximum of -120 Volts and back to zero and repeats itself. It also will do this 60 times a second.

Quite evident, is the fact that the voltages are out of phase with each other. In fact, they are 180° out of phase with each other. That means, if we take the measure of the potential difference between the two hot terminals, “A” and “B”, the result would look like the red plotted sinusoidal curve.

This is the potential difference between the two hot terminals “A” and “B”, with respect to each other. As you see, it rises to a maximum of 240 Volts positive, then returns to zero and goes to -240 Volts and back to zero. and repeats itself and will do this 60 times a second.

Low voltage wiring will involve the requirement of different sizes or gauges of wire, depending on the load that it feeds, or more precisely, the amperage it will have to carry. Wire sizes are categorized by what is known in North America, as the American Wire Gauge, (AWG). This is a measure of wire thickness, (which also dictates the cross-sectional area, and for a given material, ampacity). For example. 14 AWG wire, has a nominal diameter of 0.0641in, or 1.62814 mm. Note here, that steel wire is measured by a different gauge. AWG only applies to wire used to conduct electricity.

These two charts describe the characteristics and capabilities, of the various wire gauges of copper wire. The chart on the left is the current caring capacity of the various copper conductors. for example, for a load that draws 15 amps, #14 AWG wire is required. The chart on the right, along with describing the diameter, indicates the resistance of the wire in ohms per foot. This is significant for long runs of cables.

When wiring a house, there are many types of wire to choose from, some copper, others aluminum, some rated for outdoors, and others indoors. In general, however, there are only a couple of varieties used for wiring a residential home.

Romex, (shown here in yellow), is the trade name for a type of electrical conductor with non-metallic sheathing, that is commonly used as residential branch wiring. In fact, Romex will be the most common cable you'll use in wiring a house.

NM, NMD, NMB and NMC conductors, are composed of two or more insulated conductors contained in a non-metallic sheath. The coating on NMC cable is non-conducting, flame-resistant and moisture-resistant. Unlike other cables commonly found in homes, they are permitted in damp environments, such as basements.

Underground feeder conductors appear similar to NM cables, except that UF cables, contain a solid plastic core and cannot be “rolled” between fingers.

Romex is used for most lighting and outlet circuits in your home. Romex will be labeled with, for example, “14-2" or "12-3". The first number indicates the gauge of the wire. Your choices are typically 10, 12, or 14 gauge. The second number indicates the number of conductors (excluding the ground wire excluding the ground wire). A 12-2 Romex will have a black, (hot) and a white (neutral) wire as well as an unsheathed copper wire for ground. A 12-3 Romex, will have a black (hot), a red, (hot), a white, (neutral), and bare copper.

Finally, a couple of comments in regard to wiring diagrams and house plans. Home electrical wiring diagrams should reflect code requirements, which help you enjoy lower energy bills when you implement energy efficiency into the electrical project design.

A typical set of house plans shows the electrical symbols that have been located on the floor plan but do not provide any wiring details. It is up to the electrician, to examine the total electrical requirements of the home, especially where specific devices are to be located in each area and then decide how to plan the circuits. The installation of the electrical wiring will depend on the type of structure, and construction methods being used. For example, a stick frame home, consisting of standard wood framing, will be wired differently then say, a log home, because of access restrictions.