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.

September 12, 2022

Blog #7 - Residential Electrical Power Chapter Two

September 12, 2022/ Graham VanBrunt

Residential Electrical Power Chapter Two

This blog is designed to give the reader 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 situations. 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 student should check with the local authorities first, prior to changing any wires wiring in their homes. At the very least this blog will provide a starting point.

This first chapter will cover some of the essential rules that we will follow when justifying some of the circuitry to be found later. The first thing that is to be known, is that all functioning elements form electric circuits and current will flow from positive to negative in a circular fashion around a loop regardless if we are using AC or DC power sources. All electric circuits have Voltage, Current and Resistance that 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 120 Volts.

Of course, batteries don't operate household systems. It is AC current that is changing polarities 60 times a second (in North America). 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 current 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.

Let’s have a closer look at this changing polarity of 60 times a second. If we look at the voltage in the system 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 1/60th of a second. It does this in what is called a “sinusoidal” shape, as you see here in blue.For simplicity we will assume that most loads are resistive in nature (lightbulbs, baseboard electric heaters, electric stoves and ovens, etc.) Therefore, the instantaneous current in the circuit will follow the voltage and it too will be “sinusoidal”. We say that it is “in-phase” with the voltage, as you see here in red.The question now becomes…How do we describe the magnitude of this sinusoidal voltage and current, if it is continuously changing?…There are several ways.

We can measure and compare the amplitude or peak…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 placing all of the curves above zero. 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 and it is exactly the square root of 2 or 0.707 times the peak value.

This averaging is the equivalent of shaving off the areas of the peaks of the curve above the RMS line, (the mauve dotted 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 consumed by a customer. And as a matter of fact, all AC current and voltages are measured in RMS values and all voltmeters, ammeters, and multi-meters, unless otherwise stated are registered in RMS values. If you have a closer look at the average quality of the voltage overtime here 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.

The RMS values of current and voltages are used in calculating the average power and energy consumed. The power draw that a load such as a lightbulb takes from the circuit is expressed in watts. The load in power rating is usually marked on the device such as a lightbulb and in this case, it is 100 Watt bulb. The power in watts consumed by a load is given by the current times the voltage (using RMS values) or W = I x V.

Because the current in a circuit is equal to the voltage divided by the resistance, then we can rewrite the equation for watts in either of the following two ways… as depicted in the graphic above.

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.

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. For example, if the load were a 100 Watt incandescent light bulb. and we know that the connected voltage is 120 V. Then the connected current is 100/120 or 0.83 Amps.

Now if the load were not a 100 Watt incandescent light bulb but a 1 kilowatt heater and the connected voltage is still 120 V. Then the connected current is 1000/120 or 8.33 Amps.

Keeping the load of a 1 kilowatt heater and change the connected voltage to 240 V. Then the connected current is 1000/240 or dropping the current to 4.17 Amps. This time the 1 kW heater is rated at 240 V not 120 V.

Looking at the power panel and the incoming connections from the utility.

Measuring the voltages over time…Remember, voltage is a measurement of the potential difference between two points. Let’s measure that voltage over time starting with the potential difference between the hot terminal “A” with respect to the neutral. As you see it rises to a maximum of 120 V positive then returns to zero and goes to -120 V and back to zero and repeats itself. It will do this 60 times a second. Repeating the measurement this time of the hot terminal "B" with respect to the neutral. As you see it rises to a maximum of -120 V and then returns to zero and goes to +120 V and back to zero and repeats itself. It will do this 60 times a second. As is evident from this time measurement, the voltages are, at all times, 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. The potential difference between the two hot terminals “A” & “B” with respect to each other, rises to a maximum of 240 Volts positive then returns to zero and goes to -240 V and back to zero and repeats itself 60 times a second. In this way, the utility can supply both 120 V and 240 V to this customer.